LMFDB - Embedded newform 475.2.l.f.226.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(101,475)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("475.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.l (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			226.1
Character	$\chi$	$=$	475.226
Dual form			475.2.l.f.351.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.340658 + 1.93197i) q^{2} +(-0.143793 - 0.120656i) q^{3} +(-1.73706 - 0.632239i) q^{4} +(0.282088 - 0.236700i) q^{6} +(0.338534 + 0.586358i) q^{7} +(-0.148561 + 0.257316i) q^{8} +(-0.514826 - 2.91972i) q^{9} +O(q^{10})$	\(q+(-0.340658 + 1.93197i) q^{2} +(-0.143793 - 0.120656i) q^{3} +(-1.73706 - 0.632239i) q^{4} +(0.282088 - 0.236700i) q^{6} +(0.338534 + 0.586358i) q^{7} +(-0.148561 + 0.257316i) q^{8} +(-0.514826 - 2.91972i) q^{9} +(-1.42035 + 2.46011i) q^{11} +(0.173493 + 0.300499i) q^{12} +(-3.65145 + 3.06393i) q^{13} +(-1.24815 + 0.454289i) q^{14} +(-3.27865 - 2.75111i) q^{16} +(-0.900181 + 5.10518i) q^{17} +5.81619 q^{18} +(-3.00824 + 3.15444i) q^{19} +(0.0220691 - 0.125160i) q^{21} +(-4.26900 - 3.58212i) q^{22} +(0.987537 + 0.359434i) q^{23} +(0.0524089 - 0.0190753i) q^{24} +(-4.67552 - 8.09823i) q^{26} +(-0.559818 + 0.969633i) q^{27} +(-0.217336 - 1.23257i) q^{28} +(-0.247630 - 1.40438i) q^{29} +(-0.135532 - 0.234748i) q^{31} +(5.97674 - 5.01508i) q^{32} +(0.501064 - 0.182372i) q^{33} +(-9.55639 - 3.47824i) q^{34} +(-0.951679 + 5.39724i) q^{36} -0.603754 q^{37} +(-5.06949 - 6.88641i) q^{38} +0.894735 q^{39} +(5.15980 + 4.32958i) q^{41} +(0.234288 + 0.0852737i) q^{42} +(-5.28994 + 1.92538i) q^{43} +(4.02261 - 3.37537i) q^{44} +(-1.03083 + 1.78544i) q^{46} +(-1.37102 - 7.77543i) q^{47} +(0.139507 + 0.791181i) q^{48} +(3.27079 - 5.66517i) q^{49} +(0.745413 - 0.625476i) q^{51} +(8.27993 - 3.01365i) q^{52} +(6.47288 + 2.35594i) q^{53} +(-1.68259 - 1.41186i) q^{54} -0.201172 q^{56} +(0.813167 - 0.0906217i) q^{57} +2.79757 q^{58} +(-1.75779 + 9.96889i) q^{59} +(7.02134 + 2.55556i) q^{61} +(0.499695 - 0.181874i) q^{62} +(1.53772 - 1.29030i) q^{63} +(3.37297 + 5.84216i) q^{64} +(0.181646 + 1.03016i) q^{66} +(-0.714967 - 4.05478i) q^{67} +(4.79137 - 8.29889i) q^{68} +(-0.0986326 - 0.170837i) q^{69} +(7.14680 - 2.60122i) q^{71} +(0.827775 + 0.301285i) q^{72} +(-12.3543 - 10.3665i) q^{73} +(0.205674 - 1.16643i) q^{74} +(7.21986 - 3.57753i) q^{76} -1.92334 q^{77} +(-0.304799 + 1.72860i) q^{78} +(11.3733 + 9.54332i) q^{79} +(-8.16041 + 2.97015i) q^{81} +(-10.1223 + 8.49365i) q^{82} +(7.09076 + 12.2815i) q^{83} +(-0.117467 + 0.203458i) q^{84} +(-1.91771 - 10.8759i) q^{86} +(-0.133840 + 0.231818i) q^{87} +(-0.422017 - 0.730955i) q^{88} +(6.31059 - 5.29521i) q^{89} +(-3.03270 - 1.10381i) q^{91} +(-1.48817 - 1.24872i) q^{92} +(-0.00883537 + 0.0501079i) q^{93} +15.4889 q^{94} -1.46451 q^{96} +(0.994738 - 5.64144i) q^{97} +(9.83071 + 8.24894i) q^{98} +(7.91407 + 2.88049i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 18 q^{4} - 6 q^{6} + 12 q^{9}+O(q^{10}) $ 48 * q + 18 * q^4 - 6 * q^6 + 12 * q^9	$ 48 q + 18 q^{4} - 6 q^{6} + 12 q^{9} - 12 q^{11} - 6 q^{14} - 42 q^{16} - 12 q^{19} - 54 q^{21} - 24 q^{24} + 12 q^{26} - 42 q^{31} + 36 q^{34} + 18 q^{36} + 48 q^{39} + 6 q^{41} + 6 q^{44} - 6 q^{46} - 12 q^{49} + 108 q^{51} - 24 q^{54} + 36 q^{56} + 36 q^{59} + 48 q^{61} + 180 q^{66} - 66 q^{69} - 24 q^{71} - 84 q^{74} + 66 q^{76} - 48 q^{79} - 78 q^{81} + 54 q^{84} - 42 q^{86} + 12 q^{89} - 30 q^{91} + 72 q^{94} - 240 q^{96} + 36 q^{99}+O(q^{100}) $ 48 * q + 18 * q^4 - 6 * q^6 + 12 * q^9 - 12 * q^11 - 6 * q^14 - 42 * q^16 - 12 * q^19 - 54 * q^21 - 24 * q^24 + 12 * q^26 - 42 * q^31 + 36 * q^34 + 18 * q^36 + 48 * q^39 + 6 * q^41 + 6 * q^44 - 6 * q^46 - 12 * q^49 + 108 * q^51 - 24 * q^54 + 36 * q^56 + 36 * q^59 + 48 * q^61 + 180 * q^66 - 66 * q^69 - 24 * q^71 - 84 * q^74 + 66 * q^76 - 48 * q^79 - 78 * q^81 + 54 * q^84 - 42 * q^86 + 12 * q^89 - 30 * q^91 + 72 * q^94 - 240 * q^96 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{5}{9}\right)$

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 $

$2$	−0.340658	+	1.93197i	−0.240881	+	1.36611i	0.588985	+	0.808144i	$0.299528\pi$
$2$	−0.340658	+	1.93197i	−0.240881	+	1.36611i	−0.829866	+	0.557963i	$0.811583\pi$
$3$	−0.143793	−	0.120656i	−0.0830188	−	0.0696611i	0.600334	−	0.799750i	$-0.295034\pi$
$3$	−0.143793	−	0.120656i	−0.0830188	−	0.0696611i	−0.683353	+	0.730088i	$0.739479\pi$
$4$	−1.73706	−	0.632239i	−0.868531	−	0.316120i
$5$		0			0
$5$		0			0
$6$	0.282088	−	0.236700i	0.115162	−	0.0966325i
$7$	0.338534	+	0.586358i	0.127954	+	0.221622i	0.922884	−	0.385079i	$-0.125826\pi$
$7$	0.338534	+	0.586358i	0.127954	+	0.221622i	−0.794930	+	0.606701i	$0.792492\pi$
$8$	−0.148561	+	0.257316i	−0.0525244	+	0.0909749i
$9$	−0.514826	−	2.91972i	−0.171609	−	0.973241i
$10$		0			0
$11$	−1.42035	+	2.46011i	−0.428250	+	0.741751i	−0.996718	−	0.0809546i	$-0.974203\pi$
$11$	−1.42035	+	2.46011i	−0.428250	+	0.741751i	0.568468	+	0.822706i	$0.307536\pi$
$12$	0.173493	+	0.300499i	0.0500832	+	0.0867467i
$13$	−3.65145	+	3.06393i	−1.01273	+	0.849781i	−0.988697	−	0.149930i	$-0.952095\pi$
$13$	−3.65145	+	3.06393i	−1.01273	+	0.849781i	−0.0240334	+	0.999711i	$0.507651\pi$
$14$	−1.24815	+	0.454289i	−0.333581	+	0.121414i
$15$		0			0
$16$	−3.27865	−	2.75111i	−0.819663	−	0.687779i
$17$	−0.900181	+	5.10518i	−0.218326	+	1.23819i	0.656715	+	0.754139i	$0.271946\pi$
$17$	−0.900181	+	5.10518i	−0.218326	+	1.23819i	−0.875041	+	0.484049i	$0.839166\pi$
$18$	5.81619			1.37089
$19$	−3.00824	+	3.15444i	−0.690138	+	0.723678i
$19$	−3.00824	+	3.15444i	−0.690138	+	0.723678i
$20$		0			0
$21$	0.0220691	−	0.125160i	0.00481588	−	0.0273122i
$22$	−4.26900	−	3.58212i	−0.910154	−	0.763710i
$23$	0.987537	+	0.359434i	0.205916	+	0.0749472i	0.442919	−	0.896562i	$-0.353943\pi$
$23$	0.987537	+	0.359434i	0.205916	+	0.0749472i	−0.237003	+	0.971509i	$0.576165\pi$
$24$	0.0524089	−	0.0190753i	0.0106979	−	0.00389373i
$25$		0			0
$26$	−4.67552	−	8.09823i	−0.916944	−	1.58819i
$27$	−0.559818	+	0.969633i	−0.107737	+	0.186606i
$28$	−0.217336	−	1.23257i	−0.0410727	−	0.232935i
$29$	−0.247630	−	1.40438i	−0.0459838	−	0.260787i	0.953145	−	0.302513i	$-0.0978255\pi$
$29$	−0.247630	−	1.40438i	−0.0459838	−	0.260787i	−0.999129	+	0.0417259i	$0.986714\pi$
$30$		0			0
$31$	−0.135532	−	0.234748i	−0.0243422	−	0.0421620i	0.853598	−	0.520933i	$-0.174416\pi$
$31$	−0.135532	−	0.234748i	−0.0243422	−	0.0421620i	−0.877940	+	0.478771i	$0.841082\pi$
$32$	5.97674	−	5.01508i	1.05655	−	0.886549i
$33$	0.501064	−	0.182372i	0.0872240	−	0.0317469i
$34$	−9.55639	−	3.47824i	−1.63891	−	0.596513i
$35$		0			0
$36$	−0.951679	+	5.39724i	−0.158613	+	0.899540i
$37$	−0.603754			−0.0992566			−0.0496283	−	0.998768i	$-0.515804\pi$
$37$	−0.603754			−0.0992566			−0.0496283	+	0.998768i	$0.515804\pi$
$38$	−5.06949	−	6.88641i	−0.822380	−	1.11712i
$39$	0.894735			0.143272
$40$		0			0
$41$	5.15980	+	4.32958i	0.805825	+	0.676167i	0.949607	−	0.313442i	$-0.101482\pi$
$41$	5.15980	+	4.32958i	0.805825	+	0.676167i	−0.143783	+	0.989609i	$0.545927\pi$
$42$	0.234288	+	0.0852737i	0.0361513	+	0.0131580i
$43$	−5.28994	+	1.92538i	−0.806709	+	0.293618i	−0.712264	−	0.701912i	$-0.752330\pi$
$43$	−5.28994	+	1.92538i	−0.806709	+	0.293618i	−0.0944453	+	0.995530i	$0.530108\pi$
$44$	4.02261	−	3.37537i	0.606431	−	0.508856i
$45$		0			0
$46$	−1.03083	+	1.78544i	−0.151987	+	0.263249i
$47$	−1.37102	−	7.77543i	−0.199983	−	1.13416i	−0.905141	−	0.425112i	$-0.860235\pi$
$47$	−1.37102	−	7.77543i	−0.199983	−	1.13416i	0.705157	−	0.709051i	$-0.250876\pi$
$48$	0.139507	+	0.791181i	0.0201360	+	0.114197i
$49$	3.27079	−	5.66517i	0.467256	−	0.809311i
$50$		0			0
$51$	0.745413	−	0.625476i	0.104379	−	0.0875841i
$52$	8.27993	−	3.01365i	1.14822	−	0.417918i
$53$	6.47288	+	2.35594i	0.889118	+	0.323613i	0.745884	−	0.666076i	$-0.232027\pi$
$53$	6.47288	+	2.35594i	0.889118	+	0.323613i	0.143235	+	0.989689i	$0.454250\pi$
$54$	−1.68259	−	1.41186i	−0.228972	−	0.192130i
$55$		0			0
$56$	−0.201172			−0.0268828
$57$	0.813167	−	0.0906217i	0.107707	−	0.0120031i
$58$	2.79757			0.367339
$59$	−1.75779	+	9.96889i	−0.228844	+	1.29784i	0.626354	+	0.779539i	$0.284546\pi$
$59$	−1.75779	+	9.96889i	−0.228844	+	1.29784i	−0.855198	+	0.518301i	$0.826565\pi$
$60$		0			0
$61$	7.02134	+	2.55556i	0.898990	+	0.327206i	0.749848	−	0.661610i	$-0.230127\pi$
$61$	7.02134	+	2.55556i	0.898990	+	0.327206i	0.149142	+	0.988816i	$0.452349\pi$
$62$	0.499695	−	0.181874i	0.0634614	−	0.0230980i
$63$	1.53772	−	1.29030i	0.193734	−	0.162562i
$64$	3.37297	+	5.84216i	0.421622	+	0.730270i
$65$		0			0
$66$	0.181646	+	1.03016i	0.0223591	+	0.126805i
$67$	−0.714967	−	4.05478i	−0.0873472	−	0.495370i	−0.996825	−	0.0796188i	$-0.974630\pi$
$67$	−0.714967	−	4.05478i	−0.0873472	−	0.495370i	0.909478	−	0.415752i	$-0.136481\pi$
$68$	4.79137	−	8.29889i	0.581039	−	1.00639i
$69$	−0.0986326	−	0.170837i	−0.0118740	−	0.0205663i
$70$		0			0
$71$	7.14680	−	2.60122i	0.848169	−	0.308708i	0.118875	−	0.992909i	$-0.462071\pi$
$71$	7.14680	−	2.60122i	0.848169	−	0.308708i	0.729294	+	0.684201i	$0.239849\pi$
$72$	0.827775	+	0.301285i	0.0975542	+	0.0355068i
$73$	−12.3543	−	10.3665i	−1.44596	−	1.21330i	−0.935463	−	0.353425i	$-0.885017\pi$
$73$	−12.3543	−	10.3665i	−1.44596	−	1.21330i	−0.510497	−	0.859879i	$-0.670539\pi$
$74$	0.205674	−	1.16643i	0.0239091	−	0.135595i
$75$		0			0
$76$	7.21986	−	3.57753i	0.828175	−	0.410371i
$77$	−1.92334			−0.219185
$78$	−0.304799	+	1.72860i	−0.0345117	+	0.195725i
$79$	11.3733	+	9.54332i	1.27959	+	1.07371i	0.993300	+	0.115565i	$0.0368679\pi$
$79$	11.3733	+	9.54332i	1.27959	+	1.07371i	0.286294	+	0.958142i	$0.407577\pi$
$80$		0			0
$81$	−8.16041	+	2.97015i	−0.906713	+	0.330016i
$82$	−10.1223	+	8.49365i	−1.11782	+	0.937966i
$83$	7.09076	+	12.2815i	0.778312	+	1.34808i	0.932914	+	0.360098i	$0.117257\pi$
$83$	7.09076	+	12.2815i	0.778312	+	1.34808i	−0.154603	+	0.987977i	$0.549410\pi$
$84$	−0.117467	+	0.203458i	−0.0128167	+	0.0221991i
$85$		0			0
$86$	−1.91771	−	10.8759i	−0.206792	−	1.17278i
$87$	−0.133840	+	0.231818i	−0.0143492	+	0.0248535i
$88$	−0.422017	−	0.730955i	−0.0449872	−	0.0779201i
$89$	6.31059	−	5.29521i	0.668921	−	0.561291i	−0.243825	−	0.969819i	$-0.578402\pi$
$89$	6.31059	−	5.29521i	0.668921	−	0.561291i	0.912746	+	0.408528i	$0.133958\pi$
$90$		0			0
$91$	−3.03270	−	1.10381i	−0.317913	−	0.115711i
$92$	−1.48817	−	1.24872i	−0.155152	−	0.130188i
$93$	−0.00883537	+	0.0501079i	−0.000916185	+	0.00519594i
$94$	15.4889			1.59756
$95$		0			0
$96$	−1.46451			−0.149471
$97$	0.994738	−	5.64144i	0.101000	−	0.572801i	−0.891742	−	0.452543i	$-0.850517\pi$
$97$	0.994738	−	5.64144i	0.101000	−	0.572801i	0.992743	−	0.120258i	$-0.0383721\pi$
$98$	9.83071	+	8.24894i	0.993051	+	0.833269i
$99$	7.91407	+	2.88049i	0.795394	+	0.289500i
$100$		0			0
$101$	−1.54918	+	1.29992i	−0.154149	+	0.129347i	−0.716601	−	0.697484i	$-0.754303\pi$
$101$	−1.54918	+	1.29992i	−0.154149	+	0.129347i	0.562451	+	0.826831i	$0.309858\pi$
$102$	0.954467	+	1.65319i	0.0945064	+	0.163690i
$103$	−9.11792	+	15.7927i	−0.898415	+	1.55610i	−0.0688957	+	0.997624i	$0.521948\pi$
$103$	−9.11792	+	15.7927i	−0.898415	+	1.55610i	−0.829520	+	0.558477i	$0.811386\pi$
$104$	−0.245934	−	1.39476i	−0.0241158	−	0.136767i
$105$		0			0
$106$	−6.75663	+	11.7028i	−0.656262	+	1.13668i
$107$	3.10671	+	5.38097i	0.300337	+	0.520198i	0.976212	−	0.216817i	$-0.0695676\pi$
$107$	3.10671	+	5.38097i	0.300337	+	0.520198i	−0.675876	+	0.737016i	$0.736234\pi$
$108$	1.58548	−	1.33037i	0.152563	−	0.128015i
$109$	−15.0243	+	5.46840i	−1.43907	+	0.523777i	−0.939515	−	0.342507i	$-0.888724\pi$
$109$	−15.0243	+	5.46840i	−1.43907	+	0.523777i	−0.499551	+	0.866284i	$0.666502\pi$
$110$		0			0
$111$	0.0868155	+	0.0728469i	0.00824017	+	0.00691432i
$112$	0.503203	−	2.85381i	0.0475482	−	0.269659i
$113$	7.88392			0.741657			0.370828	−	0.928701i	$-0.379074\pi$
$113$	7.88392			0.741657			0.370828	+	0.928701i	$0.379074\pi$
$114$	−0.101934	+	1.60188i	−0.00954696	+	0.150030i
$115$		0			0
$116$	−0.457755	+	2.59606i	−0.0425015	+	0.241038i
$117$	10.8257	+	9.08384i	1.00084	+	0.839801i
$118$	−18.6608	−	6.79196i	−1.71786	−	0.625251i
$119$	−3.29820	+	1.20045i	−0.302346	+	0.110045i
$120$		0			0
$121$	1.46524	+	2.53787i	0.133204	+	0.230715i
$122$	−7.32913	+	12.6944i	−0.663548	+	1.14930i
$123$	−0.219549	−	1.24513i	−0.0197961	−	0.112269i
$124$	0.0870104	+	0.493461i	0.00781376	+	0.0443141i
$125$		0			0
$126$	1.96898	+	3.41037i	0.175410	+	0.303820i
$127$	−12.0838	+	10.1395i	−1.07226	+	0.899736i	−0.995256	−	0.0972942i	$-0.968981\pi$
$127$	−12.0838	+	10.1395i	−1.07226	+	0.899736i	−0.0770082	+	0.997030i	$0.524537\pi$
$128$	2.22723	−	0.810645i	0.196861	−	0.0716516i
$129$	0.992966	+	0.361410i	0.0874258	+	0.0318204i
$130$		0			0
$131$	−0.706095	+	4.00446i	−0.0616918	+	0.349872i	0.938300	+	0.345822i	$0.112400\pi$
$131$	−0.706095	+	4.00446i	−0.0616918	+	0.349872i	−0.999992	+	0.00404921i	$0.998711\pi$
$132$	−0.985682			−0.0857926
$133$	−2.86802	−	0.696022i	−0.248689	−	0.0603527i
$134$	8.07726			0.697769
$135$		0			0
$136$	−1.17991	−	0.990064i	−0.101177	−	0.0848973i
$137$	−2.45449	−	0.893360i	−0.209701	−	0.0763249i	0.235034	−	0.971987i	$-0.424480\pi$
$137$	−2.45449	−	0.893360i	−0.209701	−	0.0763249i	−0.444735	+	0.895662i	$0.646702\pi$
$138$	0.363651	−	0.132358i	0.0309560	−	0.0112671i
$139$	6.87238	−	5.76661i	0.582908	−	0.489118i	−0.302993	−	0.952993i	$-0.597986\pi$
$139$	6.87238	−	5.76661i	0.582908	−	0.489118i	0.885901	+	0.463875i	$0.153541\pi$
$140$		0			0
$141$	−0.741013	+	1.28347i	−0.0624046	+	0.108088i
$142$	2.59086	+	14.6935i	0.217420	+	1.23305i
$143$	−2.35129	−	13.3348i	−0.196624	−	1.11511i
$144$	−6.34456	+	10.9891i	−0.528713	+	0.915758i
$145$		0			0
$146$	24.2363	−	20.3367i	2.00581	−	1.68307i
$147$	−1.15386	+	0.419969i	−0.0951684	+	0.0346385i
$148$	1.04876	+	0.381717i	0.0862075	+	0.0313770i
$149$	−1.32378	−	1.11078i	−0.108448	−	0.0909989i	0.586951	−	0.809622i	$-0.300328\pi$
$149$	−1.32378	−	1.11078i	−0.108448	−	0.0909989i	−0.695399	+	0.718623i	$0.744773\pi$
$150$		0			0
$151$	11.0738			0.901177			0.450589	−	0.892732i	$-0.351214\pi$
$151$	11.0738			0.901177			0.450589	+	0.892732i	$0.351214\pi$
$152$	−0.364779	−	1.24270i	−0.0295875	−	0.100796i
$153$	15.3692			1.24252
$154$	0.655201	−	3.71583i	0.0527976	−	0.299430i
$155$		0			0
$156$	−1.55421	−	0.565687i	−0.124437	−	0.0452912i
$157$	−1.84614	+	0.671940i	−0.147338	+	0.0536267i	−0.414637	−	0.909987i	$-0.636091\pi$
$157$	−1.84614	+	0.671940i	−0.147338	+	0.0536267i	0.267298	+	0.963614i	$0.413869\pi$
$158$	−22.3118	+	18.7218i	−1.77503	+	1.48943i
$159$	−0.646495	−	1.11976i	−0.0512704	−	0.0888029i
$160$		0			0
$161$	0.123558	+	0.700730i	0.00973771	+	0.0552253i
$162$	−2.95832	−	16.7775i	−0.232427	−	1.31816i
$163$	10.0656	−	17.4341i	0.788395	−	1.36554i	−0.138555	−	0.990355i	$-0.544246\pi$
$163$	10.0656	−	17.4341i	0.788395	−	1.36554i	0.926950	−	0.375186i	$-0.122421\pi$
$164$	−6.22556	−	10.7830i	−0.486134	−	0.842009i
$165$		0			0
$166$	−26.1431	+	9.51530i	−2.02910	+	0.738530i
$167$	16.7798	+	6.10733i	1.29846	+	0.472600i	0.896494	−	0.443056i	$-0.146106\pi$
$167$	16.7798	+	6.10733i	1.29846	+	0.472600i	0.401963	+	0.915656i	$0.368328\pi$
$168$	0.0289271	+	0.0242727i	0.00223178	+	0.00187268i
$169$	1.68799	−	9.57308i	0.129846	−	0.736391i
$170$		0			0
$171$	10.7588	+	7.15925i	0.822747	+	0.547481i
$172$	10.4063			0.793470
$173$	0.472701	−	2.68082i	0.0359388	−	0.203819i	−0.961551	−	0.274625i	$-0.911446\pi$
$173$	0.472701	−	2.68082i	0.0359388	−	0.203819i	0.997490	+	0.0708064i	$0.0225572\pi$
$174$	−0.402271	−	0.337545i	−0.0304961	−	0.0255893i
$175$		0			0
$176$	11.4249	−	4.15831i	0.861181	−	0.313444i
$177$	1.45557	−	1.22137i	0.109407	−	0.0918036i
$178$	8.08042	+	13.9957i	0.605653	+	1.04902i
$179$	−3.85817	+	6.68254i	−0.288373	+	0.499477i	−0.973422	−	0.229021i	$-0.926448\pi$
$179$	−3.85817	+	6.68254i	−0.288373	+	0.499477i	0.685049	+	0.728497i	$0.259781\pi$
$180$		0			0
$181$	−0.185874	−	1.05414i	−0.0138159	−	0.0783537i	0.977120	−	0.212688i	$-0.0682217\pi$
$181$	−0.185874	−	1.05414i	−0.0138159	−	0.0783537i	−0.990936	+	0.134334i	$0.957111\pi$
$182$	3.16564	−	5.48305i	0.234653	−	0.406431i
$183$	−0.701273	−	1.21464i	−0.0518396	−	0.0897888i
$184$	−0.239198	+	0.200711i	−0.0176339	+	0.0147966i
$185$		0			0
$186$	−0.0937969	−	0.0341393i	−0.00687752	−	0.00250321i
$187$	−11.2807	−	9.46566i	−0.824929	−	0.692198i
$188$	−2.53439	+	14.3732i	−0.184839	+	1.04827i
$189$	−0.758069			−0.0551414
$190$		0			0
$191$	5.38296			0.389497			0.194749	−	0.980853i	$-0.437611\pi$
$191$	5.38296			0.389497			0.194749	+	0.980853i	$0.437611\pi$
$192$	0.219885	−	1.24703i	0.0158689	−	0.0899967i
$193$	−11.8506	−	9.94387i	−0.853028	−	0.715775i	0.107426	−	0.994213i	$-0.465739\pi$
$193$	−11.8506	−	9.94387i	−0.853028	−	0.715775i	−0.960454	+	0.278438i	$0.910183\pi$
$194$	10.5602	+	3.84360i	0.758179	+	0.275954i
$195$		0			0
$196$	−9.26331	+	7.77284i	−0.661665	+	0.555203i
$197$	−10.6164	−	18.3882i	−0.756388	−	1.31010i	−0.944682	−	0.327989i	$-0.893629\pi$
$197$	−10.6164	−	18.3882i	−0.756388	−	1.31010i	0.188294	−	0.982113i	$-0.439704\pi$
$198$	−8.26100	+	14.3085i	−0.587083	+	1.01686i
$199$	1.31646	+	7.46602i	0.0933214	+	0.529252i	0.995249	+	0.0973643i	$0.0310412\pi$
$199$	1.31646	+	7.46602i	0.0933214	+	0.529252i	−0.901927	+	0.431888i	$0.857848\pi$
$200$		0			0
$201$	−0.386429	+	0.669314i	−0.0272566	+	0.0472098i
$202$	−1.98366	−	3.43580i	−0.139570	−	0.241742i
$203$	0.739638	−	0.620630i	0.0519124	−	0.0435597i
$204$	−1.69028	+	0.615211i	−0.118343	+	0.0430734i
$205$		0			0
$206$	−27.4049	−	22.9954i	−1.90939	−	1.60217i
$207$	0.541038	−	3.06838i	0.0376048	−	0.213267i
$208$	20.4011			1.41456
$209$	−3.48752	−	11.8810i	−0.241237	−	0.821826i
$210$		0			0
$211$	−2.30936	+	13.0971i	−0.158983	+	0.901639i	0.796070	+	0.605204i	$0.206909\pi$
$211$	−2.30936	+	13.0971i	−0.158983	+	0.901639i	−0.955053	+	0.296434i	$0.904202\pi$
$212$	−9.75428	−	8.18481i	−0.669927	−	0.562135i
$213$	−1.34151	−	0.488271i	−0.0919189	−	0.0334558i
$214$	−11.4542	+	4.16898i	−0.782992	+	0.284986i
$215$		0			0
$216$	−0.166335	−	0.288100i	−0.0113176	−	0.0196027i
$217$	0.0917642	−	0.158940i	0.00622936	−	0.0107896i
$218$	−5.44661	−	30.8893i	−0.368891	−	2.09209i
$219$	0.525675	+	2.98125i	0.0355218	+	0.201454i
$220$		0			0
$221$	−12.3550	−	21.3994i	−0.831084	−	1.43948i
$222$	−0.170312	+	0.142909i	−0.0114306	+	0.00959142i
$223$	18.6805	−	6.79915i	1.25094	−	0.455304i	0.370220	−	0.928944i	$-0.379282\pi$
$223$	18.6805	−	6.79915i	1.25094	−	0.455304i	0.880719	+	0.473640i	$0.157060\pi$
$224$	4.96396	+	1.80673i	0.331668	+	0.120717i
$225$		0			0
$226$	−2.68572	+	15.2315i	−0.178651	+	1.01318i
$227$	27.3022			1.81211			0.906054	−	0.423163i	$-0.139080\pi$
$227$	27.3022			1.81211			0.906054	+	0.423163i	$0.139080\pi$
$228$	−1.46982	−	0.356700i	−0.0973410	−	0.0236231i
$229$	−14.6429			−0.967633			−0.483816	−	0.875170i	$-0.660750\pi$
$229$	−14.6429			−0.967633			−0.483816	+	0.875170i	$0.660750\pi$
$230$		0			0
$231$	0.276562	+	0.232063i	0.0181965	+	0.0152686i
$232$	0.398158	+	0.144918i	0.0261403	+	0.00951431i
$233$	6.22953	−	2.26737i	0.408110	−	0.148540i	−0.129804	−	0.991540i	$-0.541435\pi$
$233$	6.22953	−	2.26737i	0.408110	−	0.148540i	0.537914	+	0.843000i	$0.319212\pi$
$234$	−21.2375	+	17.8204i	−1.38834	+	1.16496i
$235$		0			0
$236$	9.35611	−	16.2053i	0.609031	−	1.05487i
$237$	−0.483933	−	2.74452i	−0.0314348	−	0.178276i
$238$	−1.19567	−	6.78096i	−0.0775036	−	0.439544i
$239$	6.33959	−	10.9805i	0.410074	−	0.710269i	−0.584823	−	0.811161i	$-0.698836\pi$
$239$	6.33959	−	10.9805i	0.410074	−	0.710269i	0.994897	+	0.100892i	$0.0321695\pi$
$240$		0			0
$241$	10.8118	−	9.07218i	0.696450	−	0.584391i	−0.224311	−	0.974518i	$-0.572013\pi$
$241$	10.8118	−	9.07218i	0.696450	−	0.584391i	0.920761	+	0.390127i	$0.127569\pi$
$242$	−5.40222	+	1.96625i	−0.347268	+	0.126395i
$243$	4.68812	+	1.70633i	0.300743	+	0.109461i
$244$	−10.5808	−	8.87833i	−0.677365	−	0.568377i
$245$		0			0
$246$	2.48033			0.158140
$247$	1.31946	−	20.7353i	0.0839555	−	1.31936i
$248$	0.0805392			0.00511425
$249$	0.462249	−	2.62154i	0.0292938	−	0.166134i
$250$		0			0
$251$	−6.55337	−	2.38523i	−0.413645	−	0.150554i	0.126811	−	0.991927i	$-0.459526\pi$
$251$	−6.55337	−	2.38523i	−0.413645	−	0.150554i	−0.540456	+	0.841372i	$0.681748\pi$
$252$	−3.48689	+	1.26912i	−0.219653	+	0.0799472i
$253$	−2.28689	+	1.91893i	−0.143776	+	0.120642i
$254$	−15.4728	−	26.7996i	−0.970847	−	1.68156i
$255$		0			0
$256$	3.15026	+	17.8660i	0.196891	+	1.11663i
$257$	2.74031	+	15.5410i	0.170936	+	0.969424i	0.942731	+	0.333553i	$0.108248\pi$
$257$	2.74031	+	15.5410i	0.170936	+	0.969424i	−0.771796	+	0.635871i	$0.780641\pi$
$258$	−1.03649	+	1.79526i	−0.0645293	+	0.111768i
$259$	−0.204391	−	0.354016i	−0.0127003	−	0.0219975i
$260$		0			0
$261$	−3.97292	+	1.44602i	−0.245917	+	0.0895066i
$262$	−7.49595	−	2.72830i	−0.463102	−	0.168555i
$263$	−15.2391	−	12.7872i	−0.939686	−	0.788490i	0.0378448	−	0.999284i	$-0.487951\pi$
$263$	−15.2391	−	12.7872i	−0.939686	−	0.788490i	−0.977531	+	0.210794i	$0.932395\pi$
$264$	−0.0275114	+	0.156025i	−0.00169321	+	0.00960268i
$265$		0			0
$266$	2.32170	−	5.30381i	0.142353	−	0.325198i
$267$	−1.54632			−0.0946331
$268$	−1.32165	+	7.49544i	−0.0807325	+	0.457857i
$269$	−8.70147	−	7.30140i	−0.530538	−	0.445174i	0.337749	−	0.941236i	$-0.390334\pi$
$269$	−8.70147	−	7.30140i	−0.530538	−	0.445174i	−0.868287	+	0.496062i	$0.834779\pi$
$270$		0			0
$271$	−22.4471	+	8.17007i	−1.36356	+	0.496296i	−0.917154	−	0.398533i	$-0.869519\pi$
$271$	−22.4471	+	8.17007i	−1.36356	+	0.496296i	−0.446409	+	0.894829i	$0.647297\pi$
$272$	16.9963	−	14.2616i	1.03055	−	0.864737i
$273$	0.302898	+	0.524635i	0.0183322	+	0.0317523i
$274$	2.56208	−	4.43766i	0.154781	−	0.268089i
$275$		0			0
$276$	0.0633214	+	0.359114i	0.00381150	+	0.0216161i
$277$	2.34652	−	4.06428i	0.140988	−	0.244199i	−0.786881	−	0.617105i	$-0.788305\pi$
$277$	2.34652	−	4.06428i	0.140988	−	0.244199i	0.927869	+	0.372906i	$0.121639\pi$
$278$	8.79978	+	15.2417i	0.527776	+	0.914134i
$279$	−0.615624	+	0.516570i	−0.0368564	+	0.0309262i
$280$		0			0
$281$	−21.1014	−	7.68028i	−1.25880	−	0.458167i	−0.375436	−	0.926848i	$-0.622507\pi$
$281$	−21.1014	−	7.68028i	−1.25880	−	0.458167i	−0.883367	+	0.468681i	$0.844729\pi$
$282$	−2.22719	−	1.86884i	−0.132628	−	0.111288i
$283$	−1.88981	+	10.7176i	−0.112337	+	0.637097i	0.875697	+	0.482862i	$0.160403\pi$
$283$	−1.88981	+	10.7176i	−0.112337	+	0.637097i	−0.988034	+	0.154236i	$0.950709\pi$
$284$	−14.0590			−0.834250
$285$		0			0
$286$	26.5634			1.57073
$287$	−0.791919	+	4.49119i	−0.0467455	+	0.265107i
$288$	−17.7196	−	14.8685i	−1.04414	−	0.876137i
$289$	−9.27778	−	3.37683i	−0.545752	−	0.198637i
$290$		0			0
$291$	−0.823712	+	0.691177i	−0.0482869	+	0.0405175i
$292$	14.9061	+	25.8181i	0.872312	+	1.51089i
$293$	−6.23561	+	10.8004i	−0.364288	+	0.630965i	−0.988662	−	0.150161i	$-0.952021\pi$
$293$	−6.23561	+	10.8004i	−0.364288	+	0.630965i	0.624374	+	0.781126i	$0.285354\pi$
$294$	−0.418297	−	2.37228i	−0.0243955	−	0.138354i
$295$		0			0
$296$	0.0896946	−	0.155356i	0.00521339	−	0.00902986i
$297$	−1.59027	−	2.75443i	−0.0922767	−	0.159828i
$298$	2.59695	−	2.17910i	0.150437	−	0.126232i
$299$	−4.70722	+	1.71329i	−0.272226	+	0.0990821i
$300$		0			0
$301$	−2.91979	−	2.44999i	−0.168294	−	0.141215i
$302$	−3.77239	+	21.3943i	−0.217077	+	1.23110i
$303$	0.379605			0.0218077
$304$	18.5412	−	2.06628i	1.06341	−	0.118510i
$305$		0			0
$306$	−5.23562	+	29.6927i	−0.299301	+	1.69742i
$307$	3.20098	+	2.68594i	0.182689	+	0.153295i	0.729546	−	0.683932i	$-0.239731\pi$
$307$	3.20098	+	2.68594i	0.182689	+	0.153295i	−0.546857	+	0.837226i	$0.684176\pi$
$308$	3.34096	+	1.21601i	0.190369	+	0.0692886i
$309$	3.21658	−	1.17074i	0.182985	−	0.0666011i
$310$		0			0
$311$	6.04544	+	10.4710i	0.342806	+	0.593757i	0.984953	−	0.172825i	$-0.0552894\pi$
$311$	6.04544	+	10.4710i	0.342806	+	0.593757i	−0.642147	+	0.766582i	$0.721956\pi$
$312$	−0.132923	+	0.230230i	−0.00752529	+	0.0130342i
$313$	1.66330	+	9.43307i	0.0940155	+	0.533188i	0.995045	+	0.0994297i	$0.0317018\pi$
$313$	1.66330	+	9.43307i	0.0940155	+	0.533188i	−0.901029	+	0.433759i	$0.857187\pi$
$314$	−0.669264	−	3.79558i	−0.0377688	−	0.214197i
$315$		0			0
$316$	−13.7224	−	23.7680i	−0.771948	−	1.33705i
$317$	−8.55609	+	7.17941i	−0.480558	+	0.403236i	−0.850628	−	0.525768i	$-0.823778\pi$
$317$	−8.55609	+	7.17941i	−0.480558	+	0.403236i	0.370070	+	0.929004i	$0.379334\pi$
$318$	2.38358	−	0.867550i	0.133664	−	0.0486498i
$319$	3.80665	+	1.38551i	0.213132	+	0.0775735i
$320$		0			0
$321$	0.202527	−	1.14859i	0.0113040	−	0.0641080i
$322$	−1.39588			−0.0777893
$323$	−13.3960	−	18.1972i	−0.745374	−	1.01252i
$324$	16.0530			0.891833
$325$		0			0
$326$	30.2531	+	25.3854i	1.67556	+	1.40597i
$327$	2.82018	+	1.02646i	0.155956	+	0.0567635i
$328$	−1.88062	+	0.684489i	−0.103840	+	0.0377946i
$329$	4.09505	−	3.43615i	0.225767	−	0.189441i
$330$		0			0
$331$	10.8439	−	18.7822i	0.596034	−	1.03236i	−0.397366	−	0.917660i	$-0.630076\pi$
$331$	10.8439	−	18.7822i	0.596034	−	1.03236i	0.993400	−	0.114701i	$-0.0365911\pi$
$332$	−4.55221	−	25.8169i	−0.249835	−	1.41688i
$333$	0.310829	+	1.76280i	0.0170333	+	0.0966006i
$334$	−17.5153	+	30.3374i	−0.958396	+	1.65999i
$335$		0			0
$336$	−0.416687	+	0.349642i	−0.0227322	+	0.0190745i
$337$	−0.0496626	+	0.0180757i	−0.00270530	+	0.000984647i	−0.343372	−	0.939199i	$-0.611569\pi$
$337$	−0.0496626	+	0.0180757i	−0.00270530	+	0.000984647i	0.340667	+	0.940184i	$0.389347\pi$
$338$	17.9198	+	6.52229i	0.974711	+	0.354766i
$339$	−1.13365	−	0.951246i	−0.0615715	−	0.0516646i
$340$		0			0
$341$	0.770008			0.0416983
$342$	−17.4965	+	18.3468i	−0.946103	+	0.992082i
$343$	9.16856			0.495056
$344$	0.290450	−	1.64722i	0.0156600	−	0.0888124i
$345$		0			0
$346$	5.01823	+	1.82649i	0.269782	+	0.0981925i
$347$	−23.8553	+	8.68262i	−1.28062	+	0.466107i	−0.890637	−	0.454715i	$-0.849741\pi$
$347$	−23.8553	+	8.68262i	−1.28062	+	0.466107i	−0.389982	+	0.920822i	$0.627519\pi$
$348$	0.379053	−	0.318063i	0.0203194	−	0.0170500i
$349$	7.80995	+	13.5272i	0.418057	+	0.724096i	0.995744	−	0.0921622i	$-0.0293778\pi$
$349$	7.80995	+	13.5272i	0.418057	+	0.724096i	−0.577687	+	0.816259i	$0.696044\pi$
$350$		0			0
$351$	−0.926741	−	5.25581i	−0.0494658	−	0.280534i
$352$	3.84862	+	21.8266i	0.205132	+	1.16336i
$353$	−6.23564	+	10.8004i	−0.331890	+	0.574850i	−0.982882	−	0.184234i	$-0.941019\pi$
$353$	−6.23564	+	10.8004i	−0.331890	+	0.574850i	0.650993	+	0.759084i	$0.274353\pi$
$354$	1.86379	+	3.22818i	0.0990593	+	0.171576i
$355$		0			0
$356$	−14.3097	+	5.20831i	−0.758414	+	0.276040i
$357$	0.619100	+	0.225334i	0.0327662	+	0.0119259i
$358$	−11.5961	−	9.73031i	−0.612875	−	0.514263i
$359$	−5.84204	+	33.1318i	−0.308331	+	1.74863i	0.299065	+	0.954233i	$0.403325\pi$
$359$	−5.84204	+	33.1318i	−0.308331	+	1.74863i	−0.607396	+	0.794399i	$0.707786\pi$
$360$		0			0
$361$	−0.900964	−	18.9786i	−0.0474191	−	0.998875i
$362$	2.09989			0.110368
$363$	0.0955195	−	0.541718i	0.00501347	−	0.0284328i
$364$	4.57011	+	3.83478i	0.239539	+	0.200997i
$365$		0			0
$366$	2.58554	−	0.941060i	0.135148	−	0.0491900i
$367$	−19.6184	+	16.4618i	−1.02407	+	0.859299i	−0.990134	−	0.140125i	$-0.955250\pi$
$367$	−19.6184	+	16.4618i	−1.02407	+	0.859299i	−0.0339392	+	0.999424i	$0.510805\pi$
$368$	−2.24894	−	3.89529i	−0.117234	−	0.203056i
$369$	9.98479	−	17.2942i	0.519787	−	0.900298i
$370$		0			0
$371$	0.809867	+	4.59299i	0.0420462	+	0.238456i
$372$	0.0470277	−	0.0814544i	0.00243827	−	0.00422322i
$373$	10.8805	+	18.8456i	0.563372	+	0.975788i	0.997199	+	0.0747923i	$0.0238294\pi$
$373$	10.8805	+	18.8456i	0.563372	+	0.975788i	−0.433828	+	0.900996i	$0.642837\pi$
$374$	22.1302	−	18.5695i	1.14433	−	0.960204i
$375$		0			0
$376$	2.20442	+	0.802344i	0.113684	+	0.0413777i
$377$	5.20713	+	4.36930i	0.268181	+	0.225031i
$378$	0.258242	−	1.46456i	0.0132825	−	0.0753290i
$379$	−6.63029			−0.340575			−0.170288	−	0.985394i	$-0.554470\pi$
$379$	−6.63029			−0.340575			−0.170288	+	0.985394i	$0.554470\pi$
$380$		0			0
$381$	2.96096			0.151695
$382$	−1.83375	+	10.3997i	−0.0938226	+	0.532095i
$383$	20.7000	+	17.3693i	1.05772	+	0.887532i	0.993884	−	0.110429i	$-0.0352224\pi$
$383$	20.7000	+	17.3693i	1.05772	+	0.887532i	0.0638349	+	0.997960i	$0.479667\pi$
$384$	−0.418069	−	0.152165i	−0.0213345	−	0.00776512i
$385$		0			0
$386$	23.2482	−	19.5076i	1.18330	−	0.992910i
$387$	8.34499	+	14.4539i	0.424200	+	0.734735i
$388$	−5.29466	+	9.17062i	−0.268796	+	0.465568i
$389$	4.51305	+	25.5948i	0.228821	+	1.29771i	0.855245	+	0.518224i	$0.173407\pi$
$389$	4.51305	+	25.5948i	0.228821	+	1.29771i	−0.626424	+	0.779483i	$0.715482\pi$
$390$		0			0
$391$	−2.72394	+	4.71800i	−0.137755	+	0.238599i
$392$	0.971827	+	1.68325i	0.0490847	+	0.0850171i
$393$	0.584696	−	0.490618i	0.0294940	−	0.0247484i
$394$	39.1419	−	14.2465i	1.97194	−	0.717727i
$395$		0			0
$396$	−11.9261	−	10.0072i	−0.599308	−	0.502879i
$397$	3.70695	−	21.0231i	0.186046	−	1.05512i	−0.738557	−	0.674191i	$-0.764493\pi$
$397$	3.70695	−	21.0231i	0.186046	−	1.05512i	0.924604	−	0.380930i	$-0.124396\pi$
$398$	−14.8726			−0.745494
$399$	0.328421	+	0.446128i	0.0164416	+	0.0223343i
$400$		0			0
$401$	4.52547	−	25.6652i	0.225991	−	1.28166i	−0.634790	−	0.772685i	$-0.718913\pi$
$401$	4.52547	−	25.6652i	0.225991	−	1.28166i	0.860781	−	0.508975i	$-0.169975\pi$
$402$	−1.16145	−	0.974574i	−0.0579280	−	0.0486073i
$403$	1.21414	+	0.441911i	0.0604806	+	0.0220131i
$404$	3.51289	−	1.27859i	0.174773	−	0.0636120i
$405$		0			0
$406$	0.947073	+	1.64038i	0.0470024	+	0.0814106i
$407$	0.857540	−	1.48530i	0.0425067	−	0.0736237i
$408$	0.0502053	+	0.284728i	0.00248553	+	0.0140961i
$409$	−4.05420	−	22.9925i	−0.200467	−	1.13691i	−0.904415	−	0.426654i	$-0.859692\pi$
$409$	−4.05420	−	22.9925i	−0.200467	−	1.13691i	0.703948	−	0.710252i	$-0.251419\pi$
$410$		0			0
$411$	0.245148	+	0.424608i	0.0120922	+	0.0209444i
$412$	25.8232	−	21.6682i	1.27222	−	1.06752i
$413$	−6.44041	+	2.34412i	−0.316912	+	0.115346i
$414$	5.74370	+	2.09054i	0.282288	+	0.102744i
$415$		0			0
$416$	−6.45791	+	36.6246i	−0.316625	+	1.79567i
$417$	−1.68398			−0.0824648
$418$	24.1417	−	2.69043i	1.18081	−	0.131593i
$419$	21.9951			1.07453			0.537265	−	0.843413i	$-0.319457\pi$
$419$	21.9951			1.07453			0.537265	+	0.843413i	$0.319457\pi$
$420$		0			0
$421$	2.85822	+	2.39833i	0.139301	+	0.116888i	0.709776	−	0.704428i	$-0.248796\pi$
$421$	2.85822	+	2.39833i	0.139301	+	0.116888i	−0.570475	+	0.821315i	$0.693241\pi$
$422$	−24.5164	−	8.92323i	−1.19344	−	0.434376i
$423$	−21.9963	+	8.00599i	−1.06950	+	0.389264i
$424$	−1.56784	+	1.31557i	−0.0761410	+	0.0638899i
$425$		0			0
$426$	1.40032	−	2.42542i	0.0678457	−	0.117512i
$427$	0.878489	+	4.98216i	0.0425131	+	0.241104i
$428$	−1.99448	−	11.3113i	−0.0964069	−	0.546751i
$429$	−1.27083	+	2.20115i	−0.0613564	+	0.106272i
$430$		0			0
$431$	−19.0853	+	16.0145i	−0.919307	+	0.771390i	−0.973867	−	0.227120i	$-0.927069\pi$
$431$	−19.0853	+	16.0145i	−0.919307	+	0.771390i	0.0545594	+	0.998511i	$0.482625\pi$
$432$	4.50302	−	1.63896i	0.216651	−	0.0788547i
$433$	10.3105	+	3.75273i	0.495492	+	0.180345i	0.577666	−	0.816274i	$-0.303964\pi$
$433$	10.3105	+	3.75273i	0.495492	+	0.180345i	−0.0821730	+	0.996618i	$0.526186\pi$
$434$	0.275807	+	0.231430i	0.0132392	+	0.0111090i
$435$		0			0
$436$	29.5555			1.41545
$437$	−4.10456	+	2.03386i	−0.196348	+	0.0972927i
$438$	−5.93875			−0.283765
$439$	−1.47943	+	8.39029i	−0.0706096	+	0.400447i	0.928934	+	0.370245i	$0.120726\pi$
$439$	−1.47943	+	8.39029i	−0.0706096	+	0.400447i	−0.999544	+	0.0302020i	$0.990385\pi$
$440$		0			0
$441$	−18.2246	−	6.63322i	−0.867840	−	0.315868i
$442$	45.5518	−	16.5795i	2.16668	−	0.788606i
$443$	−7.21394	+	6.05322i	−0.342745	+	0.287597i	−0.797869	−	0.602831i	$-0.794039\pi$
$443$	−7.21394	+	6.05322i	−0.342745	+	0.287597i	0.455124	+	0.890428i	$0.349595\pi$
$444$	−0.104747	−	0.181428i	−0.00497109	−	0.00861018i
$445$		0			0
$446$	6.77206	+	38.4063i	0.320667	+	1.81859i
$447$	0.0563268	+	0.319445i	0.00266417	+	0.0151092i
$448$	−2.28373	+	3.95554i	−0.107896	+	0.186881i
$449$	−4.86372	−	8.42421i	−0.229533	−	0.397563i	0.728137	−	0.685432i	$-0.240387\pi$
$449$	−4.86372	−	8.42421i	−0.229533	−	0.397563i	−0.957670	+	0.287869i	$0.907053\pi$
$450$		0			0
$451$	−17.9799	+	6.54416i	−0.846642	+	0.308153i
$452$	−13.6949	−	4.98452i	−0.644152	−	0.234452i
$453$	−1.59234	−	1.33613i	−0.0748146	−	0.0627769i
$454$	−9.30069	+	52.7468i	−0.436503	+	2.47553i
$455$		0			0
$456$	−0.0974869	+	0.222704i	−0.00456524	+	0.0104291i
$457$	−10.4686			−0.489700			−0.244850	−	0.969561i	$-0.578739\pi$
$457$	−10.4686			−0.489700			−0.244850	+	0.969561i	$0.578739\pi$
$458$	4.98823	−	28.2897i	0.233085	−	1.32189i
$459$	−4.44621	−	3.73082i	−0.207531	−	0.174140i
$460$		0			0
$461$	21.3065	−	7.75492i	0.992342	−	0.361183i	0.205715	−	0.978612i	$-0.434048\pi$
$461$	21.3065	−	7.75492i	0.992342	−	0.361183i	0.786626	+	0.617429i	$0.211826\pi$
$462$	−0.542552	+	0.455255i	−0.0252418	+	0.0211804i
$463$	−17.8188	−	30.8631i	−0.828110	−	1.43433i	−0.899519	−	0.436881i	$-0.856083\pi$
$463$	−17.8188	−	30.8631i	−0.828110	−	1.43433i	0.0714094	−	0.997447i	$-0.477250\pi$
$464$	−3.05172	+	5.28573i	−0.141672	+	0.245384i
$465$		0			0
$466$	2.25833	+	12.8076i	0.104615	+	0.593303i
$467$	1.45080	−	2.51286i	0.0671350	−	0.116281i	−0.830504	−	0.557013i	$-0.811948\pi$
$467$	1.45080	−	2.51286i	0.0671350	−	0.116281i	0.897639	+	0.440731i	$0.145281\pi$
$468$	−13.0618	−	22.6236i	−0.603780	−	1.04578i
$469$	2.13551	−	1.79191i	0.0986088	−	0.0827426i
$470$		0			0
$471$	0.346536	+	0.126129i	0.0159675	+	0.00581170i
$472$	−2.30402	−	1.93330i	−0.106051	−	0.0889873i
$473$	2.77689	−	15.7486i	0.127682	−	0.724119i
$474$	5.46718			0.251116
$475$		0			0
$476$	6.48816			0.297384
$477$	3.54627	−	20.1119i	0.162373	−	0.920862i
$478$	19.0543	+	15.9885i	0.871524	+	0.731296i
$479$	−27.5809	−	10.0386i	−1.26020	−	0.458676i	−0.376365	−	0.926471i	$-0.622826\pi$
$479$	−27.5809	−	10.0386i	−1.26020	−	0.458676i	−0.883837	+	0.467795i	$0.845048\pi$
$480$		0			0
$481$	2.20458	−	1.84986i	0.100520	−	0.0843464i
$482$	13.8440	+	23.9786i	0.630578	+	1.09219i
$483$	0.0667810	−	0.115668i	0.00303864	−	0.00526308i
$484$	−0.940673	−	5.33482i	−0.0427578	−	0.242492i
$485$		0			0
$486$	−4.89363	+	8.47601i	−0.221979	+	0.384480i
$487$	−1.70841	−	2.95906i	−0.0774157	−	0.134088i	0.824719	−	0.565543i	$-0.191334\pi$
$487$	−1.70841	−	2.95906i	−0.0774157	−	0.134088i	−0.902134	+	0.431456i	$0.858000\pi$
$488$	−1.70069	+	1.42705i	−0.0769865	+	0.0645993i
$489$	−3.55089	+	1.29242i	−0.160577	+	0.0584451i
$490$		0			0
$491$	−19.2938	−	16.1894i	−0.870717	−	0.730618i	0.0935323	−	0.995616i	$-0.470184\pi$
$491$	−19.2938	−	16.1894i	−0.870717	−	0.730618i	−0.964249	+	0.264998i	$0.914629\pi$
$492$	−0.405846	+	2.30167i	−0.0182970	+	0.103767i
$493$	7.39253			0.332943
$494$	39.6105	+	9.61281i	1.78216	+	0.432501i
$495$		0			0
$496$	−0.201457	+	1.14252i	−0.00904569	+	0.0513007i
$497$	3.94468	+	3.30998i	0.176943	+	0.148473i
$498$	4.90727	+	1.78610i	0.219900	+	0.0800370i
$499$	32.6388	−	11.8795i	1.46111	−	0.531801i	0.515441	−	0.856925i	$-0.327628\pi$
$499$	32.6388	−	11.8795i	1.46111	−	0.531801i	0.945671	+	0.325124i	$0.105406\pi$
$500$		0			0
$501$	−1.67592	−	2.90278i	−0.0748746	−	0.129687i
$502$	6.84064	−	11.8483i	0.305313	−	0.528817i
$503$	3.89983	+	22.1171i	0.173885	+	0.986151i	0.939423	+	0.342760i	$0.111362\pi$
$503$	3.89983	+	22.1171i	0.173885	+	0.986151i	−0.765538	+	0.643391i	$0.777527\pi$
$504$	0.103569	+	0.587367i	0.00461332	+	0.0261634i
$505$		0			0
$506$	−2.92826	−	5.07189i	−0.130177	−	0.225473i
$507$	−1.39778	+	1.17287i	−0.0620774	+	0.0520891i
$508$	27.4009	−	9.97312i	1.21572	−	0.442486i
$509$	−2.20641	−	0.803067i	−0.0977974	−	0.0355953i	0.292658	−	0.956217i	$-0.405460\pi$
$509$	−2.20641	−	0.803067i	−0.0977974	−	0.0355953i	−0.390455	+	0.920622i	$0.627682\pi$
$510$		0			0
$511$	1.89612	−	10.7534i	0.0838794	−	0.475704i
$512$	−30.8493			−1.36336
$513$	−1.37458	−	4.68280i	−0.0606892	−	0.206751i
$514$	−30.9583			−1.36551
$515$		0			0
$516$	−1.49635	−	1.25558i	−0.0658730	−	0.0552740i
$517$	21.0757	+	7.67094i	0.926909	+	0.337367i
$518$	0.753575	−	0.274279i	0.0331102	−	0.0120511i
$519$	−0.391429	+	0.328448i	−0.0171818	+	0.0144173i
$520$		0			0
$521$	−0.761964	+	1.31976i	−0.0333822	+	0.0578197i	−0.882234	−	0.470811i	$-0.843961\pi$
$521$	−0.761964	+	1.31976i	−0.0333822	+	0.0578197i	0.848852	+	0.528631i	$0.177295\pi$
$522$	−1.44026	−	8.16814i	−0.0630386	−	0.357510i
$523$	2.33156	+	13.2229i	0.101952	+	0.578198i	0.992394	+	0.123101i	$0.0392840\pi$
$523$	2.33156	+	13.2229i	0.101952	+	0.578198i	−0.890442	+	0.455096i	$0.849605\pi$
$524$	3.75831	−	6.50958i	0.164183	−	0.284372i
$525$		0			0
$526$	29.8957	−	25.0855i	1.30351	−	1.09378i
$527$	1.32043	−	0.480599i	0.0575190	−	0.0209352i
$528$	−2.14454	−	0.780548i	−0.0933291	−	0.0339690i
$529$	−16.7730	−	14.0742i	−0.729260	−	0.611922i
$530$		0			0
$531$	30.0114			1.30238
$532$	4.54188	+	3.02231i	0.196915	+	0.131034i
$533$	−32.1063			−1.39068
$534$	0.526765	−	2.98744i	0.0227954	−	0.129279i
$535$		0			0
$536$	1.14958	+	0.418412i	0.0496541	+	0.0180726i
$537$	1.36107	−	0.495389i	0.0587345	−	0.0213776i
$538$	17.0703	−	14.3237i	0.735952	−	0.617537i
$539$	9.29130	+	16.0930i	0.400205	+	0.693175i
$540$		0			0
$541$	2.81801	+	15.9817i	0.121156	+	0.687109i	0.983517	+	0.180815i	$0.0578737\pi$
$541$	2.81801	+	15.9817i	0.121156	+	0.687109i	−0.862361	+	0.506294i	$0.831015\pi$
$542$	−8.13752	−	46.1502i	−0.349537	−	1.98232i
$543$	−0.100462	+	0.174005i	−0.00431123	+	0.00746726i
$544$	20.2227	+	35.0268i	0.867043	+	1.50176i
$545$		0			0
$546$	−1.11676	+	0.406468i	−0.0477930	+	0.0173952i
$547$	−9.31688	−	3.39107i	−0.398361	−	0.144992i	0.135068	−	0.990836i	$-0.456875\pi$
$547$	−9.31688	−	3.39107i	−0.398361	−	0.144992i	−0.533429	+	0.845845i	$0.679097\pi$
$548$	3.69878	+	3.10364i	0.158004	+	0.132581i
$549$	3.84676	−	21.8160i	0.164176	−	0.931086i
$550$		0			0
$551$	5.17496	+	3.44358i	0.220461	+	0.146702i
$552$	0.0586120			0.00249469
$553$	−1.74556	+	9.89954i	−0.0742286	+	0.420971i
$554$	7.05270	+	5.91792i	0.299641	+	0.251428i
$555$		0			0
$556$	−15.5836	+	5.67198i	−0.660894	+	0.240546i
$557$	17.5295	−	14.7090i	0.742748	−	0.623240i	−0.190826	−	0.981624i	$-0.561117\pi$
$557$	17.5295	−	14.7090i	0.742748	−	0.623240i	0.933574	+	0.358384i	$0.116672\pi$
$558$	−0.788279	−	1.36534i	−0.0333705	−	0.0577994i
$559$	13.4167	−	23.2385i	0.567467	−	0.982882i
$560$		0			0
$561$	0.479995	+	2.72219i	0.0202654	+	0.114931i
$562$	22.0264	−	38.1508i	0.929128	−	1.60930i
$563$	−6.24004	−	10.8081i	−0.262986	−	0.455505i	0.704048	−	0.710153i	$-0.251374\pi$
$563$	−6.24004	−	10.8081i	−0.262986	−	0.455505i	−0.967034	+	0.254647i	$0.918041\pi$
$564$	2.09865	−	1.76097i	0.0883690	−	0.0741504i
$565$		0			0
$566$	−20.0623	−	7.30209i	−0.843283	−	0.306930i
$567$	−4.50414	−	3.77943i	−0.189156	−	0.158721i
$568$	−0.392403	+	2.22543i	−0.0164649	+	0.0933768i
$569$	1.90233			0.0797500			0.0398750	−	0.999205i	$-0.487304\pi$
$569$	1.90233			0.0797500			0.0398750	+	0.999205i	$0.487304\pi$
$570$		0			0
$571$	−12.2153			−0.511193			−0.255596	−	0.966784i	$-0.582272\pi$
$571$	−12.2153			−0.511193			−0.255596	+	0.966784i	$0.582272\pi$
$572$	−4.34646	+	24.6500i	−0.181734	+	1.03067i
$573$	−0.774030	−	0.649489i	−0.0323356	−	0.0271328i
$574$	−8.40707	−	3.05992i	−0.350904	−	0.127719i
$575$		0			0
$576$	15.3210	−	12.8558i	0.638375	−	0.535660i
$577$	−12.6452	−	21.9021i	−0.526425	−	0.911796i	−0.999526	−	0.0307872i	$-0.990199\pi$
$577$	−12.6452	−	21.9021i	−0.526425	−	0.911796i	0.473100	−	0.881008i	$-0.343135\pi$
$578$	9.68448	−	16.7740i	0.402821	−	0.697707i
$579$	0.504245	+	2.85971i	0.0209557	+	0.118846i
$580$		0			0
$581$	−4.80092	+	8.31544i	−0.199176	+	0.344982i
$582$	−1.05473	−	1.82684i	−0.0437198	−	0.0757249i
$583$	−14.9896	+	12.5778i	−0.620805	+	0.520917i
$584$	4.50283	−	1.63890i	0.186328	−	0.0678180i
$585$		0			0
$586$	−18.7418	−	15.7262i	−0.774216	−	0.649644i
$587$	1.09777	−	6.22574i	0.0453097	−	0.256964i	−0.953736	−	0.300646i	$-0.902798\pi$
$587$	1.09777	−	6.22574i	0.0453097	−	0.256964i	0.999045	+	0.0436821i	$0.0139089\pi$
$588$	2.26984			0.0936067
$589$	1.14821	+	0.278652i	0.0473112	+	0.0114817i
$590$		0			0
$591$	−0.692087	+	3.92502i	−0.0284687	+	0.161454i
$592$	1.97950	+	1.66100i	0.0813569	+	0.0682666i
$593$	0.548512	+	0.199642i	0.0225247	+	0.00819832i	0.353258	−	0.935526i	$-0.385074\pi$
$593$	0.548512	+	0.199642i	0.0225247	+	0.00819832i	−0.330733	+	0.943724i	$0.607296\pi$
$594$	5.86320	−	2.13403i	0.240570	−	0.0875603i
$595$		0			0
$596$	1.59721	+	2.76645i	0.0654242	+	0.113318i
$597$	0.711526	−	1.23240i	0.0291208	−	0.0504387i
$598$	−1.70646	−	9.67784i	−0.0697825	−	0.395756i
$599$	7.38388	+	41.8761i	0.301697	+	1.71101i	0.638658	+	0.769491i	$0.279490\pi$
$599$	7.38388	+	41.8761i	0.301697	+	1.71101i	−0.336961	+	0.941519i	$0.609399\pi$
$600$		0			0
$601$	−8.13809	−	14.0956i	−0.331960	−	0.574971i	0.650936	−	0.759132i	$-0.274377\pi$
$601$	−8.13809	−	14.0956i	−0.331960	−	0.574971i	−0.982896	+	0.184161i	$0.941043\pi$
$602$	5.72795	−	4.80632i	0.233454	−	0.195891i
$603$	−11.4708	+	4.17501i	−0.467125	+	0.170020i
$604$	−19.2360	−	7.00132i	−0.782701	−	0.284880i
$605$		0			0
$606$	−0.129315	+	0.733384i	−0.00525308	+	0.0297917i
$607$	6.86749			0.278743			0.139371	−	0.990240i	$-0.455492\pi$
$607$	6.86749			0.278743			0.139371	+	0.990240i	$0.455492\pi$
$608$	−2.15972	+	33.9398i	−0.0875881	+	1.37644i
$609$	−0.181238			−0.00734412
$610$		0			0
$611$	28.8296	+	24.1909i	1.16632	+	0.978658i
$612$	−26.6972	−	9.71698i	−1.07917	−	0.392786i
$613$	5.49059	−	1.99841i	0.221763	−	0.0807150i	−0.228749	−	0.973485i	$-0.573464\pi$
$613$	5.49059	−	1.99841i	0.221763	−	0.0807150i	0.450512	+	0.892770i	$0.351241\pi$
$614$	−6.27958	+	5.26920i	−0.253423	+	0.212647i
$615$		0			0
$616$	0.285734	−	0.494906i	0.0115126	−	0.0199403i
$617$	6.69631	+	37.9767i	0.269583	+	1.52888i	0.755658	+	0.654966i	$0.227317\pi$
$617$	6.69631	+	37.9767i	0.269583	+	1.52888i	−0.486075	+	0.873917i	$0.661572\pi$
$618$	1.16608	+	6.61315i	0.0469065	+	0.266020i
$619$	−5.46007	+	9.45712i	−0.219459	+	0.380114i	−0.954643	−	0.297754i	$-0.903762\pi$
$619$	−5.46007	+	9.45712i	−0.219459	+	0.380114i	0.735184	+	0.677868i	$0.237096\pi$
$620$		0			0
$621$	−0.901359	+	0.756330i	−0.0361703	+	0.0303505i
$622$	−22.2891	+	8.11256i	−0.893711	+	0.325284i
$623$	5.24123	+	1.90765i	0.209986	+	0.0764285i
$624$	−2.93352	−	2.46152i	−0.117435	−	0.0985396i
$625$		0			0
$626$	−18.7910			−0.751039
$627$	−0.932038	+	2.12919i	−0.0372220	+	0.0850318i
$628$	3.63169			0.144920
$629$	0.543488	−	3.08228i	0.0216703	−	0.122898i
$630$		0			0
$631$	−7.62467	−	2.77515i	−0.303533	−	0.110477i	0.185763	−	0.982595i	$-0.440524\pi$
$631$	−7.62467	−	2.77515i	−0.303533	−	0.110477i	−0.489297	+	0.872117i	$0.662746\pi$
$632$	−4.14528	+	1.50876i	−0.164890	+	0.0600152i
$633$	1.91231	−	1.60462i	0.0760077	−	0.0637780i
$634$	−10.9557	−	18.9758i	−0.435106	−	0.753626i
$635$		0			0
$636$	0.415045	+	2.35383i	0.0164576	+	0.0933356i
$637$	5.41457	+	30.7076i	0.214533	+	1.21668i
$638$	−3.97352	+	6.88234i	−0.157313	+	0.272474i
$639$	−11.2742	−	19.5275i	−0.446001	−	0.772496i
$640$		0			0
$641$	−13.0690	+	4.75673i	−0.516195	+	0.187880i	−0.586964	−	0.809613i	$-0.699677\pi$
$641$	−13.0690	+	4.75673i	−0.516195	+	0.187880i	0.0707688	+	0.997493i	$0.477455\pi$
$642$	2.15004	+	0.782552i	0.0848555	+	0.0308849i
$643$	29.1929	+	24.4957i	1.15125	+	0.966017i	0.999748	−	0.0224393i	$-0.00714324\pi$
$643$	29.1929	+	24.4957i	1.15125	+	0.966017i	0.151506	+	0.988456i	$0.451588\pi$
$644$	0.228402	−	1.29533i	0.00900029	−	0.0510432i
$645$		0			0
$646$	39.7198	−	19.6816i	1.56276	−	0.774364i
$647$	28.6072			1.12466			0.562332	−	0.826912i	$-0.309904\pi$
$647$	28.6072			1.12466			0.562332	+	0.826912i	$0.309904\pi$
$648$	0.448056	−	2.54105i	0.0176013	−	0.0998221i
$649$	−22.0279	−	18.4836i	−0.864671	−	0.725545i
$650$		0			0
$651$	−0.0323722	+	0.0117825i	−0.00126877	+	0.000461793i
$652$	−28.5070	+	23.9202i	−1.11642	+	0.936787i
$653$	−5.94304	−	10.2937i	−0.232569	−	0.402822i	0.725994	−	0.687701i	$-0.241380\pi$
$653$	−5.94304	−	10.2937i	−0.232569	−	0.402822i	−0.958563	+	0.284879i	$0.908047\pi$
$654$	−2.94381	+	5.09883i	−0.115112	+	0.199380i
$655$		0			0
$656$	−5.00599	−	28.3904i	−0.195451	−	1.10846i
$657$	−23.9069	+	41.4080i	−0.932699	+	1.61548i
$658$	5.24352	+	9.08204i	0.204414	+	0.354055i
$659$	−28.2769	+	23.7271i	−1.10151	+	0.924278i	−0.997526	−	0.0703009i	$-0.977604\pi$
$659$	−28.2769	+	23.7271i	−1.10151	+	0.924278i	−0.103986	+	0.994579i	$0.533160\pi$
$660$		0			0
$661$	8.49572	+	3.09219i	0.330445	+	0.120272i	0.501914	−	0.864917i	$-0.332629\pi$
$661$	8.49572	+	3.09219i	0.330445	+	0.120272i	−0.171469	+	0.985189i	$0.554851\pi$
$662$	32.5925	+	27.3483i	1.26674	+	1.06292i
$663$	−0.805424	+	4.56779i	−0.0312801	+	0.177398i
$664$	−4.21365			−0.163521
$665$		0			0
$666$	−3.51155			−0.136070
$667$	0.260238	−	1.47588i	0.0100765	−	0.0571465i
$668$	−25.2862	−	21.2176i	−0.978353	−	0.820935i
$669$	−3.50648	−	1.27626i	−0.135568	−	0.0493429i
$670$		0			0
$671$	−16.2597	+	13.6435i	−0.627698	+	0.526701i
$672$	−0.495787	−	0.858729i	−0.0191254	−	0.0331262i
$673$	19.9182	−	34.4994i	0.767791	−	1.32985i	−0.170967	−	0.985277i	$-0.554689\pi$
$673$	19.9182	−	34.4994i	0.767791	−	1.32985i	0.938758	−	0.344577i	$-0.111978\pi$
$674$	−0.0180037	−	0.102104i	−0.000693478	−	0.00393291i
$675$		0			0
$676$	−8.98462	+	15.5618i	−0.345562	+	0.598532i
$677$	−9.01941	−	15.6221i	−0.346644	−	0.600405i	0.639007	−	0.769201i	$-0.279345\pi$
$677$	−9.01941	−	15.6221i	−0.346644	−	0.600405i	−0.985651	+	0.168796i	$0.946012\pi$
$678$	2.22396	−	1.86613i	0.0854108	−	0.0716682i
$679$	3.64465	−	1.32655i	0.139869	−	0.0509081i
$680$		0			0
$681$	−3.92585	−	3.29418i	−0.150439	−	0.126233i
$682$	−0.262309	+	1.48763i	−0.0100443	+	0.0569643i
$683$	−15.4271			−0.590301			−0.295151	−	0.955451i	$-0.595370\pi$
$683$	−15.4271			−0.590301			−0.295151	+	0.955451i	$0.595370\pi$
$684$	−14.1624	−	19.2382i	−0.541512	−	0.735591i
$685$		0			0
$686$	−3.12334	+	17.7134i	−0.119250	+	0.676299i
$687$	2.10555	+	1.76677i	0.0803317	+	0.0674063i
$688$	22.6408	+	8.24059i	0.863173	+	0.314169i
$689$	−30.8538	+	11.2299i	−1.17544	+	0.427824i
$690$		0			0
$691$	−1.51912	−	2.63119i	−0.0577901	−	0.100095i	0.835683	−	0.549212i	$-0.185072\pi$
$691$	−1.51912	−	2.63119i	−0.0577901	−	0.100095i	−0.893473	+	0.449117i	$0.851739\pi$
$692$	−2.51603	+	4.35789i	−0.0956452	+	0.165662i
$693$	0.990185	+	5.61562i	0.0376140	+	0.213320i
$694$	−8.64803	−	49.0454i	−0.328275	−	1.86174i
$695$		0			0
$696$	−0.0397670	−	0.0688784i	−0.00150736	−	0.00261083i
$697$	−26.7481	+	22.4443i	−1.01315	+	0.850138i
$698$	−28.7947	+	10.4804i	−1.08990	+	0.396689i
$699$	−1.16933	−	0.425603i	−0.0442283	−	0.0160978i
$700$		0			0
$701$	−7.95179	+	45.0968i	−0.300335	+	1.70328i	0.344355	+	0.938840i	$0.388098\pi$
$701$	−7.95179	+	45.0968i	−0.300335	+	1.70328i	−0.644690	+	0.764444i	$0.723013\pi$
$702$	10.4697			0.395155
$703$	1.81624	−	1.90451i	0.0685008	−	0.0718298i
$704$	−19.1631			−0.722238
$705$		0			0
$706$	−18.7419	−	15.7263i	−0.705360	−	0.591867i
$707$	−1.28667	−	0.468309i	−0.0483901	−	0.0176126i
$708$	−3.30061	+	1.20132i	−0.124045	+	0.0451485i
$709$	16.8950	−	14.1766i	0.634506	−	0.532414i	−0.267819	−	0.963469i	$-0.586303\pi$
$709$	16.8950	−	14.1766i	0.634506	−	0.532414i	0.902326	+	0.431055i	$0.141859\pi$
$710$		0			0
$711$	22.0086	−	38.1200i	0.825386	−	1.42961i
$712$	0.425032	+	2.41048i	0.0159288	+	0.0903365i
$713$	−0.0494663	−	0.280537i	−0.00185253	−	0.0105062i
$714$	−0.646239	+	1.11932i	−0.0241849	+	0.0418894i
$715$		0			0
$716$	10.9268	−	9.16871i	0.408355	−	0.342651i
$717$	−2.23645	+	0.814003i	−0.0835219	+	0.0303995i
$718$	−62.0195	−	22.5732i	−2.31455	−	0.842426i
$719$	−5.43476	−	4.56031i	−0.202682	−	0.170071i	0.535797	−	0.844347i	$-0.320011\pi$
$719$	−5.43476	−	4.56031i	−0.202682	−	0.170071i	−0.738479	+	0.674276i	$0.764456\pi$
$720$		0			0
$721$	−12.3469			−0.459822
$722$	36.9730	+	4.72459i	1.37599	+	0.175831i
$723$	−2.64928			−0.0985277
$724$	−0.343596	+	1.94863i	−0.0127696	+	0.0724202i
$725$		0			0
$726$	1.01404	+	0.369081i	0.0376346	+	0.0136979i
$727$	−26.5113	+	9.64932i	−0.983249	+	0.357873i	−0.783103	−	0.621893i	$-0.786364\pi$
$727$	−26.5113	+	9.64932i	−0.983249	+	0.357873i	−0.200147	+	0.979766i	$0.564142\pi$
$728$	0.734570	−	0.616378i	0.0272250	−	0.0228445i
$729$	12.5580	+	21.7510i	0.465110	+	0.805594i
$730$		0			0
$731$	−5.06752	−	28.7393i	−0.187429	−	1.06296i
$732$	0.450212	+	2.55328i	0.0166403	+	0.0943719i
$733$	−0.517931	+	0.897082i	−0.0191302	+	0.0331345i	−0.875432	−	0.483341i	$-0.839423\pi$
$733$	−0.517931	+	0.897082i	−0.0191302	+	0.0331345i	0.856302	+	0.516476i	$0.172756\pi$
$734$	−25.1205	−	43.5100i	−0.927214	−	1.60598i
$735$		0			0
$736$	7.70484	−	2.80433i	0.284004	−	0.103369i
$737$	10.9907	+	4.00029i	0.404848	+	0.147353i
$738$	30.0103	+	25.1817i	1.10470	+	0.926950i
$739$	3.37137	−	19.1200i	0.124018	−	0.703340i	−0.857868	−	0.513869i	$-0.828212\pi$
$739$	3.37137	−	19.1200i	0.124018	−	0.703340i	0.981886	−	0.189471i	$-0.0606773\pi$
$740$		0			0
$741$	−2.69158	+	2.82239i	−0.0988777	+	0.103683i
$742$	−9.14938			−0.335884
$743$	−2.20582	+	12.5098i	−0.0809237	+	0.458941i	0.917238	+	0.398339i	$0.130413\pi$
$743$	−2.20582	+	12.5098i	−0.0809237	+	0.458941i	−0.998162	+	0.0606022i	$0.980698\pi$
$744$	−0.0115810	−	0.00971758i	−0.000424579	−	0.000356264i
$745$		0			0
$746$	−40.1156	+	14.6009i	−1.46874	+	0.534576i
$747$	32.2082	−	27.0259i	1.17844	−	0.988826i
$748$	13.6108	+	23.5746i	0.497660	+	0.861972i
$749$	−2.10345	+	3.64328i	−0.0768584	+	0.133123i
$750$		0			0
$751$	−0.801897	−	4.54778i	−0.0292616	−	0.165951i	0.966675	−	0.256006i	$-0.0824068\pi$
$751$	−0.801897	−	4.54778i	−0.0292616	−	0.165951i	−0.995937	+	0.0900552i	$0.971296\pi$
$752$	−16.8960	+	29.2647i	−0.616134	+	1.06717i
$753$	0.654534	+	1.13369i	0.0238525	+	0.0413138i
$754$	−10.2152	+	8.57157i	−0.372016	+	0.312158i
$755$		0			0
$756$	1.31681	+	0.479281i	0.0478920	+	0.0174313i
$757$	−5.21680	−	4.37741i	−0.189608	−	0.159100i	0.543042	−	0.839705i	$-0.317272\pi$
$757$	−5.21680	−	4.37741i	−0.189608	−	0.159100i	−0.732650	+	0.680606i	$0.761717\pi$
$758$	2.25866	−	12.8095i	0.0820382	−	0.465262i
$759$	0.560370			0.0203401
$760$		0			0
$761$	24.4864			0.887632			0.443816	−	0.896118i	$-0.353624\pi$
$761$	24.4864			0.887632			0.443816	+	0.896118i	$0.353624\pi$
$762$	−1.00867	+	5.72048i	−0.0365404	+	0.207231i
$763$	−8.29266	−	6.95837i	−0.300215	−	0.251910i
$764$	−9.35053	−	3.40332i	−0.338290	−	0.123128i
$765$		0			0
$766$	−40.6086	+	34.0746i	−1.46725	+	1.23117i
$767$	−24.1255	−	41.7867i	−0.871123	−	1.50883i
$768$	1.70266	−	2.94910i	0.0614396	−	0.106417i
$769$	0.519478	+	2.94611i	0.0187329	+	0.106239i	0.992741	−	0.120276i	$-0.0383779\pi$
$769$	0.519478	+	2.94611i	0.0187329	+	0.106239i	−0.974008	+	0.226515i	$0.927267\pi$
$770$		0			0
$771$	1.48109	−	2.56533i	0.0533402	−	0.0923880i
$772$	14.2984	+	24.7656i	0.514611	+	0.891332i
$773$	15.1403	−	12.7042i	0.544557	−	0.456938i	−0.328536	−	0.944491i	$-0.606555\pi$
$773$	15.1403	−	12.7042i	0.544557	−	0.456938i	0.873093	+	0.487554i	$0.162111\pi$
$774$	−30.7673	+	11.1984i	−1.10591	+	0.402518i
$775$		0			0
$776$	1.30385	+	1.09406i	0.0468056	+	0.0392745i
$777$	−0.0133243	+	0.0755661i	−0.000478008	+	0.00271092i
$778$	−50.9857			−1.82792
$779$	−29.1793	+	3.25183i	−1.04546	+	0.116509i
$780$		0			0
$781$	−3.75163	+	21.2765i	−0.134244	+	0.761335i
$782$	−8.18709	−	6.86978i	−0.292770	−	0.245663i
$783$	1.50036	+	0.546087i	0.0536185	+	0.0195155i
$784$	−26.3093	+	9.57581i	−0.939618	+	0.341993i
$785$		0			0
$786$	0.748677	+	1.29675i	0.0267044	+	0.0462534i
$787$	−11.7733	+	20.3920i	−0.419673	+	0.726895i	−0.995906	−	0.0903901i	$-0.971189\pi$
$787$	−11.7733	+	20.3920i	−0.419673	+	0.726895i	0.576233	+	0.817285i	$0.304522\pi$
$788$	6.81565	+	38.6535i	0.242798	+	1.37697i
$789$	0.648425	+	3.67740i	0.0230846	+	0.130919i
$790$		0			0
$791$	2.66897	+	4.62280i	0.0948977	+	0.164368i
$792$	−1.91692	+	1.60849i	−0.0681148	+	0.0571551i
$793$	−33.4681	+	12.1814i	−1.18849	+	0.432574i
$794$	39.3532	+	14.3234i	1.39659	+	0.508318i
$795$		0			0
$796$	2.43353	−	13.8013i	0.0862543	−	0.489173i
$797$	5.96976			0.211460			0.105730	−	0.994395i	$-0.466282\pi$
$797$	5.96976			0.211460			0.105730	+	0.994395i	$0.466282\pi$
$798$	−0.973784	+	0.482522i	−0.0344716	+	0.0170811i
$799$	40.9291			1.44797
$800$		0			0
$801$	−18.7094	−	15.6991i	−0.661064	−	0.554699i
$802$	48.0427	+	17.4861i	1.69645	+	0.617456i
$803$	43.0500	−	15.6689i	1.51920	−	0.552945i
$804$	1.09442	−	0.918325i	0.0385971	−	0.0323868i
$805$		0			0
$806$	−1.26736	+	2.19514i	−0.0446409	+	0.0773204i
$807$	0.370247	+	2.09978i	0.0130333	+	0.0739157i
$808$	−0.104341	−	0.591747i	−0.00367070	−	0.0208176i
$809$	12.9533	−	22.4358i	0.455414	−	0.788801i	−0.543297	−	0.839540i	$-0.682824\pi$
$809$	12.9533	−	22.4358i	0.455414	−	0.788801i	0.998712	+	0.0507393i	$0.0161577\pi$
$810$		0			0
$811$	21.1791	−	17.7713i	0.743698	−	0.624036i	−0.190130	−	0.981759i	$-0.560891\pi$
$811$	21.1791	−	17.7713i	0.743698	−	0.624036i	0.933828	+	0.357723i	$0.116447\pi$
$812$	−1.67718	+	0.610445i	−0.0588576	+	0.0214224i
$813$	4.21350	+	1.53359i	0.147774	+	0.0537853i
$814$	2.57743	+	2.16272i	0.0903388	+	0.0758032i
$815$		0			0
$816$	−4.16470			−0.145794
$817$	9.83993	−	22.4788i	0.344256	−	0.786434i
$818$	45.8018			1.60142
$819$	−1.66151	+	9.42291i	−0.0580580	+	0.329263i
$820$		0			0
$821$	9.72970	+	3.54132i	0.339569	+	0.123593i	0.506175	−	0.862431i	$-0.331059\pi$
$821$	9.72970	+	3.54132i	0.339569	+	0.123593i	−0.166607	+	0.986023i	$0.553281\pi$
$822$	−0.903841	+	0.328971i	−0.0315251	+	0.0114742i
$823$	32.4417	−	27.2218i	1.13085	−	0.948893i	0.131746	−	0.991284i	$-0.457942\pi$
$823$	32.4417	−	27.2218i	1.13085	−	0.948893i	0.999101	+	0.0423901i	$0.0134972\pi$
$824$	−2.70914	−	4.69237i	−0.0943775	−	0.163467i
$825$		0			0
$826$	−2.33478	−	13.2412i	−0.0812374	−	0.460720i
$827$	−3.92136	−	22.2391i	−0.136359	−	0.773330i	−0.973904	−	0.226962i	$-0.927121\pi$
$827$	−3.92136	−	22.2391i	−0.136359	−	0.773330i	0.837545	−	0.546369i	$-0.183990\pi$
$828$	−2.87977	+	4.98791i	−0.100079	+	0.173342i
$829$	6.32446	+	10.9543i	0.219657	+	0.380458i	0.954703	−	0.297560i	$-0.0961727\pi$
$829$	6.32446	+	10.9543i	0.219657	+	0.380458i	−0.735046	+	0.678017i	$0.762839\pi$
$830$		0			0
$831$	−0.827794	+	0.301292i	−0.0287159	+	0.0104517i
$832$	−30.2162	−	10.9978i	−1.04756	−	0.381280i
$833$	25.9774	+	21.7977i	0.900065	+	0.755244i
$834$	0.573661	−	3.25339i	0.0198642	−	0.112656i
$835$		0			0
$836$	−1.45358	+	22.8430i	−0.0502732	+	0.790041i
$837$	0.303492			0.0104902
$838$	−7.49280	+	42.4938i	−0.258834	+	1.46792i
$839$	35.3478	+	29.6603i	1.22034	+	1.02399i	0.998807	+	0.0488360i	$0.0155512\pi$
$839$	35.3478	+	29.6603i	1.22034	+	1.02399i	0.221535	+	0.975152i	$0.428893\pi$
$840$		0			0
$841$	25.3401	−	9.22305i	0.873797	−	0.318036i
$842$	−5.60717	+	4.70498i	−0.193236	+	0.162144i
$843$	2.10755	+	3.65039i	0.0725880	+	0.125726i
$844$	12.2920	−	21.2903i	0.423108	−	0.732844i
$845$		0			0
$846$	−7.97410	−	45.2234i	−0.274155	−	1.55481i
$847$	−0.992066	+	1.71831i	−0.0340878	+	0.0590418i
$848$	−14.7409	−	25.5319i	−0.506203	−	0.876770i
$849$	1.56489	−	1.31310i	0.0537070	−	0.0450655i
$850$		0			0
$851$	−0.596230	−	0.217010i	−0.0204385	−	0.00743900i
$852$	2.02159	+	1.69631i	0.0692585	+	0.0581147i
$853$	6.50543	−	36.8941i	0.222742	−	1.26323i	−0.644214	−	0.764846i	$-0.722815\pi$
$853$	6.50543	−	36.8941i	0.222742	−	1.26323i	0.866955	−	0.498386i	$-0.166074\pi$
$854$	−9.92463			−0.339614
$855$		0			0
$856$	−1.84615			−0.0631000
$857$	5.87524	−	33.3201i	0.200694	−	1.13819i	−0.703378	−	0.710816i	$-0.748326\pi$
$857$	5.87524	−	33.3201i	0.200694	−	1.13819i	0.904073	−	0.427379i	$-0.140563\pi$
$858$	−3.81962	−	3.20505i	−0.130400	−	0.109418i
$859$	19.9349	+	7.25572i	0.680171	+	0.247562i	0.658921	−	0.752212i	$-0.271013\pi$
$859$	19.9349	+	7.25572i	0.680171	+	0.247562i	0.0212498	+	0.999774i	$0.493235\pi$
$860$		0			0
$861$	0.655764	−	0.550251i	0.0223484	−	0.0187525i
$862$	−24.4379	−	42.3277i	−0.832358	−	1.44169i
$863$	14.5696	−	25.2353i	0.495955	−	0.859019i	−0.504034	−	0.863684i	$-0.668152\pi$
$863$	14.5696	−	25.2353i	0.495955	−	0.859019i	0.999989	+	0.00466481i	$0.00148486\pi$
$864$	1.51690	+	8.60277i	0.0516060	+	0.292672i
$865$		0			0
$866$	−10.7625	+	18.6412i	−0.365725	+	0.633454i
$867$	0.926641	+	1.60499i	0.0314704	+	0.0545083i
$868$	−0.259888	+	0.218072i	−0.00882119	+	0.00740185i
$869$	−39.6316	+	14.4247i	−1.34441	+	0.489325i
$870$		0			0
$871$	15.0342	+	12.6152i	0.509416	+	0.427450i
$872$	0.824925	−	4.67838i	0.0279355	−	0.158430i
$873$	−16.9836			−0.574806
$874$	−2.53110	−	8.62273i	−0.0856157	−	0.291668i
$875$		0			0
$876$	0.971733	−	5.51097i	0.0328318	−	0.186198i
$877$	4.93198	+	4.13842i	0.166541	+	0.139745i	0.722249	−	0.691633i	$-0.243108\pi$
$877$	4.93198	+	4.13842i	0.166541	+	0.139745i	−0.555708	+	0.831377i	$0.687553\pi$
$878$	−15.7058	−	5.71644i	−0.530045	−	0.192920i
$879$	2.19977	−	0.800652i	0.0741965	−	0.0270053i
$880$		0			0
$881$	−7.19996	−	12.4707i	−0.242573	−	0.420148i	0.718874	−	0.695141i	$-0.244658\pi$
$881$	−7.19996	−	12.4707i	−0.242573	−	0.420148i	−0.961446	+	0.274993i	$0.911325\pi$
$882$	19.0235	−	32.9497i	0.640556	−	1.10948i
$883$	−4.48039	−	25.4096i	−0.150777	−	0.855100i	−0.962545	−	0.271121i	$-0.912606\pi$
$883$	−4.48039	−	25.4096i	−0.150777	−	0.855100i	0.811768	−	0.583980i	$-0.198505\pi$
$884$	7.93179	+	44.9834i	0.266775	+	1.51296i
$885$		0			0
$886$	−9.23713	−	15.9992i	−0.310327	−	0.537503i
$887$	−19.8739	+	16.6762i	−0.667300	+	0.559931i	−0.912265	−	0.409601i	$-0.865668\pi$
$887$	−19.8739	+	16.6762i	−0.667300	+	0.559931i	0.244965	+	0.969532i	$0.421224\pi$
$888$	−0.0316421	+	0.0115168i	−0.00106184	+	0.000386478i
$889$	−10.0362	−	3.65286i	−0.336602	−	0.122513i
$890$		0			0
$891$	4.28371	−	24.2942i	0.143510	−	0.813885i
$892$	−36.7479			−1.23041
$893$	28.6515	+	19.0656i	0.958785	+	0.638005i
$894$	−0.636346			−0.0212826
$895$		0			0
$896$	1.22932	+	1.03152i	0.0410687	+	0.0344607i
$897$	0.883584	+	0.321598i	0.0295020	+	0.0107379i
$898$	17.9321	−	6.52677i	0.598404	−	0.217801i
$899$	−0.296114	+	0.248469i	−0.00987595	+	0.00828690i
$900$		0			0
$901$	−17.8542	+	30.9245i	−0.594811	+	1.03024i
$902$	−6.51810	−	36.9660i	−0.217029	−	1.23083i
$903$	0.124237	+	0.704583i	0.00413435	+	0.0234470i
$904$	−1.17125	+	2.02866i	−0.0389551	+	0.0674722i
$905$		0			0
$906$	3.12381	−	2.62118i	0.103781	−	0.0870830i
$907$	28.1209	−	10.2352i	0.933740	−	0.339853i	0.170049	−	0.985436i	$-0.445607\pi$
$907$	28.1209	−	10.2352i	0.933740	−	0.339853i	0.763691	+	0.645582i	$0.223385\pi$
$908$	−47.4255	−	17.2615i	−1.57387	−	0.572843i
$909$	4.59296	+	3.85395i	0.152339	+	0.127828i
$910$		0			0
$911$	3.36120			0.111362			0.0556808	−	0.998449i	$-0.482267\pi$
$911$	3.36120			0.111362			0.0556808	+	0.998449i	$0.482267\pi$
$912$	−2.91540	−	1.94000i	−0.0965386	−	0.0642398i
$913$	−40.2853			−1.33325
$914$	3.56621	−	20.2250i	0.117960	−	0.668982i
$915$		0			0
$916$	25.4357	+	9.25784i	0.840419	+	0.305888i
$917$	−2.58708	+	0.941622i	−0.0854330	+	0.0310951i
$918$	8.72245	−	7.31900i	0.287884	−	0.241563i
$919$	−3.46233	−	5.99694i	−0.114212	−	0.197821i	0.803253	−	0.595639i	$-0.203101\pi$
$919$	−3.46233	−	5.99694i	−0.114212	−	0.197821i	−0.917464	+	0.397818i	$0.869768\pi$
$920$		0			0
$921$	−0.136202	−	0.772437i	−0.00448799	−	0.0254527i
$922$	7.72404	+	43.8052i	0.254378	+	1.44265i
$923$	−18.1262	+	31.3955i	−0.596632	+	1.03340i
$924$	−0.333687	−	0.577962i	−0.0109775	−	0.0190136i
$925$		0			0
$926$	65.6965	−	23.9116i	2.15892	−	0.785783i
$927$	50.8045	+	18.4913i	1.66864	+	0.607335i
$928$	−8.52310	−	7.15173i	−0.279785	−	0.234767i
$929$	4.74769	−	26.9255i	0.155767	−	0.883396i	−0.802315	−	0.596901i	$-0.796399\pi$
$929$	4.74769	−	26.9255i	0.155767	−	0.883396i	0.958082	−	0.286495i	$-0.0924903\pi$
$930$		0			0
$931$	8.03112	+	27.3597i	0.263209	+	0.896679i
$932$	−12.2546			−0.401413
$933$	0.394105	−	2.23508i	0.0129024	−	0.0731732i
$934$	4.36053	+	3.65892i	0.142681	+	0.119724i
$935$		0			0
$936$	−3.94570	+	1.43612i	−0.128969	+	0.0469409i
$937$	28.4491	−	23.8716i	0.929390	−	0.779851i	−0.0463175	−	0.998927i	$-0.514749\pi$
$937$	28.4491	−	23.8716i	0.929390	−	0.779851i	0.975708	+	0.219076i	$0.0703041\pi$
$938$	2.73443	+	4.73616i	0.0892822	+	0.154641i
$939$	0.898989	−	1.55710i	0.0293374	−	0.0508139i
$940$		0			0
$941$	8.80177	+	49.9173i	0.286929	+	1.62726i	0.698311	+	0.715794i	$0.253935\pi$
$941$	8.80177	+	49.9173i	0.286929	+	1.62726i	−0.411382	+	0.911463i	$0.634954\pi$
$942$	−0.361727	+	0.626529i	−0.0117857	+	0.0204134i
$943$	3.53929	+	6.13023i	0.115255	+	0.199628i
$944$	33.1887	−	27.8487i	1.08020	−	0.906396i
$945$		0			0
$946$	29.4797	+	10.7297i	0.958468	+	0.348854i
$947$	−3.11527	−	2.61402i	−0.101233	−	0.0849442i	0.590767	−	0.806842i	$-0.298825\pi$
$947$	−3.11527	−	2.61402i	−0.101233	−	0.0849442i	−0.691999	+	0.721898i	$0.743270\pi$
$948$	−0.894571	+	5.07336i	−0.0290543	+	0.164775i
$949$	76.8732			2.49541
$950$		0			0
$951$	2.09655			0.0679852
$952$	0.181091	−	1.02702i	0.00586921	−	0.0332859i
$953$	11.3629	+	9.53460i	0.368080	+	0.308856i	0.808002	−	0.589180i	$-0.200549\pi$
$953$	11.3629	+	9.53460i	0.368080	+	0.308856i	−0.439921	+	0.898036i	$0.644994\pi$
$954$	37.6475	+	13.7026i	1.21888	+	0.443637i
$955$		0			0
$956$	−17.9546	+	15.0657i	−0.580692	+	0.487258i
$957$	−0.380198	−	0.658523i	−0.0122901	−	0.0212870i
$958$	28.7899	−	49.8656i	0.930160	−	1.61108i
$959$	−0.307098	−	1.74164i	−0.00991671	−	0.0562405i
$960$		0			0
$961$	15.4633	−	26.7832i	0.498815	−	0.863973i
$962$	2.82286	+	4.88934i	0.0910128	+	0.157639i
$963$	14.1115	−	11.8410i	0.454738	−	0.381571i
$964$	−24.5166	+	8.92330i	−0.789626	+	0.287400i
$965$		0			0
$966$	0.200717	+	0.168422i	0.00645797	+	0.00541888i
$967$	9.84935	−	55.8584i	0.316734	−	1.79629i	−0.245595	−	0.969372i	$-0.578983\pi$
$967$	9.84935	−	55.8584i	0.316734	−	1.79629i	0.562329	−	0.826914i	$-0.309905\pi$
$968$	−0.870712			−0.0279858
$969$	−0.269358	+	4.23294i	−0.00865301	+	0.135982i
$970$		0			0
$971$	−2.18689	+	12.4025i	−0.0701805	+	0.398014i	0.929401	+	0.369073i	$0.120325\pi$
$971$	−2.18689	+	12.4025i	−0.0701805	+	0.398014i	−0.999581	+	0.0289410i	$0.990786\pi$
$972$	−7.06474	−	5.92802i	−0.226602	−	0.190141i
$973$	5.70783	+	2.07748i	0.182985	+	0.0666010i
$974$	6.29879	−	2.29257i	0.201826	−	0.0734588i
$975$		0			0
$976$	−15.9899	−	27.6953i	−0.511824	−	0.886505i
$977$	18.4486	−	31.9540i	0.590224	−	1.02230i	−0.403978	−	0.914769i	$-0.632373\pi$
$977$	18.4486	−	31.9540i	0.590224	−	1.02230i	0.994202	−	0.107529i	$-0.0342940\pi$
$978$	−1.28727	−	7.30047i	−0.0411623	−	0.233443i
$979$	4.06359	+	23.0458i	0.129873	+	0.736546i
$980$		0			0
$981$	23.7011	+	41.0515i	0.756718	+	1.31067i
$982$	37.8500	−	31.7599i	1.20784	−	1.01350i
$983$	−8.98405	+	3.26993i	−0.286547	+	0.104295i	−0.481295	−	0.876559i	$-0.659833\pi$
$983$	−8.98405	+	3.26993i	−0.286547	+	0.104295i	0.194748	+	0.980853i	$0.437611\pi$
$984$	0.353007	+	0.128484i	0.0112535	+	0.00409592i
$985$		0			0
$986$	−2.51832	+	14.2821i	−0.0801997	+	0.454835i
$987$	−1.00343			−0.0319396
$988$	−15.4017	+	35.1843i	−0.489992	+	1.11936i
$989$	−5.91606			−0.188120
$990$		0			0
$991$	−12.4584	−	10.4538i	−0.395755	−	0.332077i	0.423095	−	0.906085i	$-0.360944\pi$
$991$	−12.4584	−	10.4538i	−0.395755	−	0.332077i	−0.818850	+	0.574008i	$0.805388\pi$
$992$	−1.98732	−	0.723325i	−0.0630974	−	0.0229656i
$993$	−3.82546	+	1.39236i	−0.121397	+	0.0441851i
$994$	−7.73855	+	6.49342i	−0.245452	+	0.205959i
$995$		0			0
$996$	−2.46040	+	4.26153i	−0.0779607	+	0.135032i
$997$	6.36254	+	36.0838i	0.201504	+	1.14278i	0.902848	+	0.429961i	$0.141473\pi$
$997$	6.36254	+	36.0838i	0.201504	+	1.14278i	−0.701344	+	0.712823i	$0.747416\pi$
$998$	11.8322	+	67.1039i	0.374543	+	2.12414i
$999$	0.337992	−	0.585420i	0.0106936	−	0.0185219i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.l.f.226.1		48
5.2	odd	4		95.2.p.a.74.1	yes	48
5.3	odd	4		95.2.p.a.74.8	yes	48
5.4	even	2	inner	475.2.l.f.226.8		48
15.2	even	4		855.2.da.b.739.8		48
15.8	even	4		855.2.da.b.739.1		48
19.3	odd	18		9025.2.a.ct.1.21		24
19.9	even	9	inner	475.2.l.f.351.1		48
19.16	even	9		9025.2.a.cu.1.4		24
95.3	even	36		1805.2.b.l.1084.4		24
95.9	even	18	inner	475.2.l.f.351.8		48
95.22	even	36		1805.2.b.l.1084.21		24
95.28	odd	36		95.2.p.a.9.1	✓	48
95.47	odd	36		95.2.p.a.9.8	yes	48
95.54	even	18		9025.2.a.cu.1.21		24
95.73	odd	36		1805.2.b.k.1084.21		24
95.79	odd	18		9025.2.a.ct.1.4		24
95.92	odd	36		1805.2.b.k.1084.4		24
285.47	even	36		855.2.da.b.199.1		48
285.218	even	36		855.2.da.b.199.8		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.9.1	✓	48	95.28	odd	36
95.2.p.a.9.8	yes	48	95.47	odd	36
95.2.p.a.74.1	yes	48	5.2	odd	4
95.2.p.a.74.8	yes	48	5.3	odd	4
475.2.l.f.226.1		48	1.1	even	1	trivial
475.2.l.f.226.8		48	5.4	even	2	inner
475.2.l.f.351.1		48	19.9	even	9	inner
475.2.l.f.351.8		48	95.9	even	18	inner
855.2.da.b.199.1		48	285.47	even	36
855.2.da.b.199.8		48	285.218	even	36
855.2.da.b.739.1		48	15.8	even	4
855.2.da.b.739.8		48	15.2	even	4
1805.2.b.k.1084.4		24	95.92	odd	36
1805.2.b.k.1084.21		24	95.73	odd	36
1805.2.b.l.1084.4		24	95.3	even	36
1805.2.b.l.1084.21		24	95.22	even	36
9025.2.a.ct.1.4		24	95.79	odd	18
9025.2.a.ct.1.21		24	19.3	odd	18
9025.2.a.cu.1.4		24	19.16	even	9
9025.2.a.cu.1.21		24	95.54	even	18

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.340658 + 1.93197i) q^{2} +(-0.143793 - 0.120656i) q^{3} +(-1.73706 - 0.632239i) q^{4} +(0.282088 - 0.236700i) q^{6} +(0.338534 + 0.586358i) q^{7} +(-0.148561 + 0.257316i) q^{8} +(-0.514826 - 2.91972i) q^{9} +O(q^{10})\)	\(q+(-0.340658 + 1.93197i) q^{2} +(-0.143793 - 0.120656i) q^{3} +(-1.73706 - 0.632239i) q^{4} +(0.282088 - 0.236700i) q^{6} +(0.338534 + 0.586358i) q^{7} +(-0.148561 + 0.257316i) q^{8} +(-0.514826 - 2.91972i) q^{9} +(-1.42035 + 2.46011i) q^{11} +(0.173493 + 0.300499i) q^{12} +(-3.65145 + 3.06393i) q^{13} +(-1.24815 + 0.454289i) q^{14} +(-3.27865 - 2.75111i) q^{16} +(-0.900181 + 5.10518i) q^{17} +5.81619 q^{18} +(-3.00824 + 3.15444i) q^{19} +(0.0220691 - 0.125160i) q^{21} +(-4.26900 - 3.58212i) q^{22} +(0.987537 + 0.359434i) q^{23} +(0.0524089 - 0.0190753i) q^{24} +(-4.67552 - 8.09823i) q^{26} +(-0.559818 + 0.969633i) q^{27} +(-0.217336 - 1.23257i) q^{28} +(-0.247630 - 1.40438i) q^{29} +(-0.135532 - 0.234748i) q^{31} +(5.97674 - 5.01508i) q^{32} +(0.501064 - 0.182372i) q^{33} +(-9.55639 - 3.47824i) q^{34} +(-0.951679 + 5.39724i) q^{36} -0.603754 q^{37} +(-5.06949 - 6.88641i) q^{38} +0.894735 q^{39} +(5.15980 + 4.32958i) q^{41} +(0.234288 + 0.0852737i) q^{42} +(-5.28994 + 1.92538i) q^{43} +(4.02261 - 3.37537i) q^{44} +(-1.03083 + 1.78544i) q^{46} +(-1.37102 - 7.77543i) q^{47} +(0.139507 + 0.791181i) q^{48} +(3.27079 - 5.66517i) q^{49} +(0.745413 - 0.625476i) q^{51} +(8.27993 - 3.01365i) q^{52} +(6.47288 + 2.35594i) q^{53} +(-1.68259 - 1.41186i) q^{54} -0.201172 q^{56} +(0.813167 - 0.0906217i) q^{57} +2.79757 q^{58} +(-1.75779 + 9.96889i) q^{59} +(7.02134 + 2.55556i) q^{61} +(0.499695 - 0.181874i) q^{62} +(1.53772 - 1.29030i) q^{63} +(3.37297 + 5.84216i) q^{64} +(0.181646 + 1.03016i) q^{66} +(-0.714967 - 4.05478i) q^{67} +(4.79137 - 8.29889i) q^{68} +(-0.0986326 - 0.170837i) q^{69} +(7.14680 - 2.60122i) q^{71} +(0.827775 + 0.301285i) q^{72} +(-12.3543 - 10.3665i) q^{73} +(0.205674 - 1.16643i) q^{74} +(7.21986 - 3.57753i) q^{76} -1.92334 q^{77} +(-0.304799 + 1.72860i) q^{78} +(11.3733 + 9.54332i) q^{79} +(-8.16041 + 2.97015i) q^{81} +(-10.1223 + 8.49365i) q^{82} +(7.09076 + 12.2815i) q^{83} +(-0.117467 + 0.203458i) q^{84} +(-1.91771 - 10.8759i) q^{86} +(-0.133840 + 0.231818i) q^{87} +(-0.422017 - 0.730955i) q^{88} +(6.31059 - 5.29521i) q^{89} +(-3.03270 - 1.10381i) q^{91} +(-1.48817 - 1.24872i) q^{92} +(-0.00883537 + 0.0501079i) q^{93} +15.4889 q^{94} -1.46451 q^{96} +(0.994738 - 5.64144i) q^{97} +(9.83071 + 8.24894i) q^{98} +(7.91407 + 2.88049i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 18 q^{4} - 6 q^{6} + 12 q^{9}+O(q^{10}) \) 48 * q + 18 * q^4 - 6 * q^6 + 12 * q^9	\( 48 q + 18 q^{4} - 6 q^{6} + 12 q^{9} - 12 q^{11} - 6 q^{14} - 42 q^{16} - 12 q^{19} - 54 q^{21} - 24 q^{24} + 12 q^{26} - 42 q^{31} + 36 q^{34} + 18 q^{36} + 48 q^{39} + 6 q^{41} + 6 q^{44} - 6 q^{46} - 12 q^{49} + 108 q^{51} - 24 q^{54} + 36 q^{56} + 36 q^{59} + 48 q^{61} + 180 q^{66} - 66 q^{69} - 24 q^{71} - 84 q^{74} + 66 q^{76} - 48 q^{79} - 78 q^{81} + 54 q^{84} - 42 q^{86} + 12 q^{89} - 30 q^{91} + 72 q^{94} - 240 q^{96} + 36 q^{99}+O(q^{100}) \) 48 * q + 18 * q^4 - 6 * q^6 + 12 * q^9 - 12 * q^11 - 6 * q^14 - 42 * q^16 - 12 * q^19 - 54 * q^21 - 24 * q^24 + 12 * q^26 - 42 * q^31 + 36 * q^34 + 18 * q^36 + 48 * q^39 + 6 * q^41 + 6 * q^44 - 6 * q^46 - 12 * q^49 + 108 * q^51 - 24 * q^54 + 36 * q^56 + 36 * q^59 + 48 * q^61 + 180 * q^66 - 66 * q^69 - 24 * q^71 - 84 * q^74 + 66 * q^76 - 48 * q^79 - 78 * q^81 + 54 * q^84 - 42 * q^86 + 12 * q^89 - 30 * q^91 + 72 * q^94 - 240 * q^96 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

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