LMFDB - Embedded newform 605.2.j.j.124.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(9,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 6]))

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

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

chi := DirichletCharacter("605.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.j (of order $10$, degree $4$, not 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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	16.0.343361479062744140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 3 x^{14} - 8 x^{13} + 8 x^{12} + 7 x^{11} + 6 x^{10} + 56 x^{9} - 137 x^{8} + \cdots + 6561 $ x^16 - x^15 + 3x^14 - 8x^13 + 8x^12 + 7x^11 + 6x^10 + 56x^9 - 137x^8 + 168x^7 + 54x^6 + 189x^5 + 648x^4 - 1944x^3 + 2187x^2 - 2187x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			124.2
Root			$1.59696 + 0.670602i$ of defining polynomial
Character	$\chi$	$=$	605.124
Dual form			605.2.j.j.444.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.465695 - 0.640974i) q^{2} +(-2.40079 + 0.780063i) q^{3} +(0.424058 - 1.30512i) q^{4} +(2.04481 + 0.904839i) q^{5} +(1.61803 + 1.17557i) q^{6} +(3.29456 + 1.07047i) q^{7} +(-2.54105 + 0.825636i) q^{8} +(2.72823 - 1.98218i) q^{9} +(-0.372281 - 1.73205i) q^{10} +3.46410i q^{12} +(-0.848116 - 2.61023i) q^{14} +(-5.61500 - 0.577241i) q^{15} +(-0.507835 - 0.368964i) q^{16} +(-2.96754 + 4.08446i) q^{17} +(-2.54105 - 0.825636i) q^{18} +(1.23607 + 3.80423i) q^{19} +(2.04804 - 2.28502i) q^{20} -8.74456 q^{21} -2.52434i q^{23} +(5.45647 - 3.96435i) q^{24} +(3.36253 + 3.70046i) q^{25} +(-0.552379 + 0.760285i) q^{27} +(2.79417 - 3.84584i) q^{28} +(-0.848116 + 2.61023i) q^{29} +(2.24488 + 3.86788i) q^{30} +(1.91922 - 1.39439i) q^{31} +5.84096i q^{32} +4.00000 q^{34} +(5.76816 + 5.16995i) q^{35} +(-1.43004 - 4.40122i) q^{36} +(10.4969 + 3.41066i) q^{37} +(1.86278 - 2.56389i) q^{38} +(-5.94304 - 0.610965i) q^{40} +(0.848116 + 2.61023i) q^{41} +(4.07230 + 5.60503i) q^{42} -3.46410i q^{43} +(7.37228 - 1.58457i) q^{45} +(-1.61803 + 1.17557i) q^{46} +(6.30860 - 2.04979i) q^{47} +(1.50702 + 0.489660i) q^{48} +(4.04508 + 2.93893i) q^{49} +(0.805980 - 3.87858i) q^{50} +(3.93829 - 12.1208i) q^{51} +(1.86278 + 2.56389i) q^{53} +0.744563 q^{54} -9.25544 q^{56} +(-5.93507 - 8.16893i) q^{57} +(2.06805 - 0.671952i) q^{58} +(0.502993 - 1.54805i) q^{59} +(-3.13445 + 7.08345i) q^{60} +(8.69253 + 6.31550i) q^{61} +(-1.78754 - 0.580806i) q^{62} +(11.1102 - 3.60991i) q^{63} +(2.72823 - 1.98218i) q^{64} +0.644810i q^{67} +(4.07230 + 5.60503i) q^{68} +(1.96914 + 6.06040i) q^{69} +(0.627600 - 6.10485i) q^{70} +(-5.75765 - 4.18318i) q^{71} +(-5.29601 + 7.28933i) q^{72} +(6.58911 + 2.14093i) q^{73} +(-2.70222 - 8.31657i) q^{74} +(-10.9593 - 6.26102i) q^{75} +5.48913 q^{76} +(-10.3106 + 7.49107i) q^{79} +(-0.704576 - 1.21397i) q^{80} +(-2.39320 + 7.36552i) q^{81} +(1.27813 - 1.75919i) q^{82} +(3.89893 - 5.36641i) q^{83} +(-3.70820 + 11.4127i) q^{84} +(-9.76384 + 5.66683i) q^{85} +(-2.22040 + 1.61321i) q^{86} -6.92820i q^{87} +4.37228 q^{89} +(-4.44890 - 3.98751i) q^{90} +(-3.29456 - 1.07047i) q^{92} +(-3.51992 + 4.84475i) q^{93} +(-4.25174 - 3.08907i) q^{94} +(-0.914681 + 8.89738i) q^{95} +(-4.55632 - 14.0229i) q^{96} +(-2.41516 - 3.32418i) q^{97} -3.96143i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{4} + 3 q^{5} + 8 q^{6} + 2 q^{9} + 40 q^{10} - 12 q^{14} - q^{15} - 14 q^{16} - 16 q^{19} + 12 q^{20} - 48 q^{21} + 4 q^{24} - q^{25} - 12 q^{29} - 6 q^{30} - 2 q^{31} + 64 q^{34} + 18 q^{35}+ \cdots + 36 q^{96}+O(q^{100}) $ 16 * q + 6 * q^4 + 3 * q^5 + 8 * q^6 + 2 * q^9 + 40 * q^10 - 12 * q^14 - q^15 - 14 * q^16 - 16 * q^19 + 12 * q^20 - 48 * q^21 + 4 * q^24 - q^25 - 12 * q^29 - 6 * q^30 - 2 * q^31 + 64 * q^34 + 18 * q^35 + 30 * q^36 + 28 * q^40 + 12 * q^41 + 72 * q^45 - 8 * q^46 + 20 * q^49 - 18 * q^50 - 28 * q^51 - 80 * q^54 - 240 * q^56 - 18 * q^59 + 18 * q^60 + 20 * q^61 + 2 * q^64 - 14 * q^69 - 24 * q^70 + 6 * q^71 + 12 * q^74 - 15 * q^75 - 96 * q^76 - 28 * q^79 - 6 * q^80 + 8 * q^81 + 48 * q^84 + 2 * q^85 + 12 * q^86 + 24 * q^89 - 28 * q^90 - 44 * q^94 + 12 * q^95 + 36 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$-1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.465695	−	0.640974i	−0.329296	−	0.453237i	0.611981	−	0.790872i	$-0.290373\pi$
$2$	−0.465695	−	0.640974i	−0.329296	−	0.453237i	−0.941277	+	0.337636i	$0.890373\pi$
$3$	−2.40079	+	0.780063i	−1.38610	+	0.450370i	−0.904668	−	0.426116i	$-0.859881\pi$
$3$	−2.40079	+	0.780063i	−1.38610	+	0.450370i	−0.481427	+	0.876486i	$0.659881\pi$
$4$	0.424058	−	1.30512i	0.212029	−	0.652559i
$5$	2.04481	+	0.904839i	0.914469	+	0.404656i
$5$	2.04481	+	0.904839i	0.914469	+	0.404656i
$6$	1.61803	+	1.17557i	0.660560	+	0.479925i
$7$	3.29456	+	1.07047i	1.24523	+	0.404598i	0.856208	−	0.516632i	$-0.172814\pi$
$7$	3.29456	+	1.07047i	1.24523	+	0.404598i	0.389018	+	0.921230i	$0.372814\pi$
$8$	−2.54105	+	0.825636i	−0.898396	+	0.291906i
$9$	2.72823	−	1.98218i	0.909411	−	0.660726i
$10$	−0.372281	−	1.73205i	−0.117726	−	0.547723i
$11$		0			0
$11$		0			0
$12$			3.46410i			1.00000i
$13$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$13$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$14$	−0.848116	−	2.61023i	−0.226669	−	0.697614i
$15$	−5.61500	−	0.577241i	−1.44979	−	0.149043i
$16$	−0.507835	−	0.368964i	−0.126959	−	0.0922409i
$17$	−2.96754	+	4.08446i	−0.719733	+	0.990628i	0.279799	+	0.960059i	$0.409732\pi$
$17$	−2.96754	+	4.08446i	−0.719733	+	0.990628i	−0.999533	+	0.0305696i	$0.990268\pi$
$18$	−2.54105	−	0.825636i	−0.598930	−	0.194604i
$19$	1.23607	+	3.80423i	0.283573	+	0.872749i	0.986823	+	0.161806i	$0.0517318\pi$
$19$	1.23607	+	3.80423i	0.283573	+	0.872749i	−0.703249	+	0.710943i	$0.748268\pi$
$20$	2.04804	−	2.28502i	0.457956	−	0.510946i
$21$	−8.74456			−1.90822
$22$		0			0
$23$		−	2.52434i		−	0.526361i	−0.964747	−	0.263180i	$-0.915229\pi$
$23$		−	2.52434i		−	0.526361i	0.964747	−	0.263180i	$-0.0847714\pi$
$24$	5.45647	−	3.96435i	1.11380	−	0.809220i
$25$	3.36253	+	3.70046i	0.672507	+	0.740091i
$26$		0			0
$27$	−0.552379	+	0.760285i	−0.106305	+	0.146317i
$28$	2.79417	−	3.84584i	0.528048	−	0.726796i
$29$	−0.848116	+	2.61023i	−0.157491	+	0.484708i	−0.998405	−	0.0564612i	$-0.982018\pi$
$29$	−0.848116	+	2.61023i	−0.157491	+	0.484708i	0.840914	+	0.541170i	$0.182018\pi$
$30$	2.24488	+	3.86788i	0.409857	+	0.706176i
$31$	1.91922	−	1.39439i	0.344701	−	0.250440i	−0.401941	−	0.915665i	$-0.631664\pi$
$31$	1.91922	−	1.39439i	0.344701	−	0.250440i	0.746643	+	0.665225i	$0.231664\pi$
$32$			5.84096i			1.03255i
$33$		0			0
$34$	4.00000			0.685994
$35$	5.76816	+	5.16995i	0.974997	+	0.873881i
$36$	−1.43004	−	4.40122i	−0.238341	−	0.733537i
$37$	10.4969	+	3.41066i	1.72568	+	0.560708i	0.992815	−	0.119662i	$-0.0381811\pi$
$37$	10.4969	+	3.41066i	1.72568	+	0.560708i	0.732868	+	0.680370i	$0.238181\pi$
$38$	1.86278	−	2.56389i	0.302183	−	0.415919i
$39$		0			0
$40$	−5.94304	−	0.610965i	−0.939677	−	0.0966020i
$41$	0.848116	+	2.61023i	0.132454	+	0.407650i	0.995185	−	0.0980119i	$-0.0312483\pi$
$41$	0.848116	+	2.61023i	0.132454	+	0.407650i	−0.862732	+	0.505662i	$0.831248\pi$
$42$	4.07230	+	5.60503i	0.628369	+	0.864876i
$43$		−	3.46410i		−	0.528271i	−0.964486	−	0.264135i	$-0.914913\pi$
$43$		−	3.46410i		−	0.528271i	0.964486	−	0.264135i	$-0.0850865\pi$
$44$		0			0
$45$	7.37228	−	1.58457i	1.09899	−	0.236214i
$46$	−1.61803	+	1.17557i	−0.238566	+	0.173328i
$47$	6.30860	−	2.04979i	0.920203	−	0.298992i	0.189653	−	0.981851i	$-0.439264\pi$
$47$	6.30860	−	2.04979i	0.920203	−	0.298992i	0.730550	+	0.682859i	$0.239264\pi$
$48$	1.50702	+	0.489660i	0.217520	+	0.0706764i
$49$	4.04508	+	2.93893i	0.577869	+	0.419847i
$50$	0.805980	−	3.87858i	0.113983	−	0.548514i
$51$	3.93829	−	12.1208i	0.551470	−	1.69725i
$52$		0			0
$53$	1.86278	+	2.56389i	0.255872	+	0.352178i	0.917557	−	0.397604i	$-0.130158\pi$
$53$	1.86278	+	2.56389i	0.255872	+	0.352178i	−0.661685	+	0.749782i	$0.730158\pi$
$54$	0.744563			0.101322
$55$		0			0
$56$	−9.25544			−1.23681
$57$	−5.93507	−	8.16893i	−0.786120	−	1.08200i
$58$	2.06805	−	0.671952i	0.271549	−	0.0882316i
$59$	0.502993	−	1.54805i	0.0654841	−	0.201539i	−0.912961	−	0.408047i	$-0.866210\pi$
$59$	0.502993	−	1.54805i	0.0654841	−	0.201539i	0.978445	+	0.206508i	$0.0662099\pi$
$60$	−3.13445	+	7.08345i	−0.404656	+	0.914469i
$61$	8.69253	+	6.31550i	1.11296	+	0.808616i	0.983128	−	0.182919i	$-0.0585546\pi$
$61$	8.69253	+	6.31550i	1.11296	+	0.808616i	0.129837	+	0.991535i	$0.458555\pi$
$62$	−1.78754	−	0.580806i	−0.227017	−	0.0737624i
$63$	11.1102	−	3.60991i	1.39975	−	0.454806i
$64$	2.72823	−	1.98218i	0.341029	−	0.247772i
$65$		0			0
$66$		0			0
$67$			0.644810i			0.0787761i	0.999224	+	0.0393880i	$0.0125408\pi$
$67$			0.644810i			0.0787761i	−0.999224	+	0.0393880i	$0.987459\pi$
$68$	4.07230	+	5.60503i	0.493838	+	0.679710i
$69$	1.96914	+	6.06040i	0.237057	+	0.729586i
$70$	0.627600	−	6.10485i	0.0750126	−	0.729670i
$71$	−5.75765	−	4.18318i	−0.683307	−	0.496452i	0.191146	−	0.981562i	$-0.438780\pi$
$71$	−5.75765	−	4.18318i	−0.683307	−	0.496452i	−0.874453	+	0.485110i	$0.838780\pi$
$72$	−5.29601	+	7.28933i	−0.624141	+	0.859056i
$73$	6.58911	+	2.14093i	0.771197	+	0.250577i	0.668077	−	0.744092i	$-0.267117\pi$
$73$	6.58911	+	2.14093i	0.771197	+	0.250577i	0.103120	+	0.994669i	$0.467117\pi$
$74$	−2.70222	−	8.31657i	−0.314127	−	0.966782i
$75$	−10.9593	−	6.26102i	−1.26547	−	0.722960i
$76$	5.48913			0.629646
$77$		0			0
$78$		0			0
$79$	−10.3106	+	7.49107i	−1.16003	+	0.842811i	−0.989782	−	0.142591i	$-0.954457\pi$
$79$	−10.3106	+	7.49107i	−1.16003	+	0.842811i	−0.170248	+	0.985401i	$0.554457\pi$
$80$	−0.704576	−	1.21397i	−0.0787740	−	0.135726i
$81$	−2.39320	+	7.36552i	−0.265911	+	0.818391i
$82$	1.27813	−	1.75919i	0.141146	−	0.194270i
$83$	3.89893	−	5.36641i	0.427963	−	0.589040i	−0.539521	−	0.841972i	$-0.681395\pi$
$83$	3.89893	−	5.36641i	0.427963	−	0.589040i	0.967484	+	0.252932i	$0.0813948\pi$
$84$	−3.70820	+	11.4127i	−0.404598	+	1.24523i
$85$	−9.76384	+	5.66683i	−1.05904	+	0.614654i
$86$	−2.22040	+	1.61321i	−0.239432	+	0.173957i
$87$		−	6.92820i		−	0.742781i
$88$		0			0
$89$	4.37228			0.463461			0.231730	−	0.972780i	$-0.425561\pi$
$89$	4.37228			0.463461			0.231730	+	0.972780i	$0.425561\pi$
$90$	−4.44890	−	3.98751i	−0.468955	−	0.420321i
$91$		0			0
$92$	−3.29456	−	1.07047i	−0.343481	−	0.111604i
$93$	−3.51992	+	4.84475i	−0.364998	+	0.502377i
$94$	−4.25174	−	3.08907i	−0.438533	−	0.318613i
$95$	−0.914681	+	8.89738i	−0.0938443	+	0.912852i
$96$	−4.55632	−	14.0229i	−0.465028	−	1.43121i
$97$	−2.41516	−	3.32418i	−0.245222	−	0.337519i	0.668609	−	0.743614i	$-0.266890\pi$
$97$	−2.41516	−	3.32418i	−0.245222	−	0.337519i	−0.913831	+	0.406095i	$0.866890\pi$
$98$		−	3.96143i		−	0.400165i
$99$		0			0
$100$	6.25544	−	2.81929i	0.625544	−	0.281929i
$101$	4.85410	−	3.52671i	0.483001	−	0.350921i	−0.319485	−	0.947591i	$-0.603510\pi$
$101$	4.85410	−	3.52671i	0.483001	−	0.350921i	0.802486	+	0.596670i	$0.203510\pi$
$102$	−9.60315	+	3.12025i	−0.950854	+	0.308951i
$103$	−9.88367	−	3.21140i	−0.973867	−	0.316429i	−0.221491	−	0.975162i	$-0.571092\pi$
$103$	−9.88367	−	3.21140i	−0.973867	−	0.316429i	−0.752376	+	0.658734i	$0.771092\pi$
$104$		0			0
$105$	−17.8810	−	7.91242i	−1.74501	−	0.772173i
$106$	0.775903	−	2.38798i	0.0753624	−	0.231941i
$107$	−6.30860	+	2.04979i	−0.609875	+	0.198160i	−0.597640	−	0.801765i	$-0.703895\pi$
$107$	−6.30860	+	2.04979i	−0.609875	+	0.198160i	−0.0122352	+	0.999925i	$0.503895\pi$
$108$	0.758020	+	1.04332i	0.0729405	+	0.100394i
$109$	10.0000			0.957826			0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000			0.957826			0.478913	+	0.877862i	$0.341031\pi$
$110$		0			0
$111$	−27.8614			−2.64449
$112$	−1.27813	−	1.75919i	−0.120772	−	0.166228i
$113$	−15.2985	+	4.97078i	−1.43916	+	0.467612i	−0.921636	−	0.388056i	$-0.873147\pi$
$113$	−15.2985	+	4.97078i	−1.43916	+	0.467612i	−0.517526	+	0.855668i	$0.673147\pi$
$114$	−2.47214	+	7.60845i	−0.231537	+	0.712597i
$115$	2.28412	−	5.16180i	0.212995	−	0.481341i
$116$	3.04701	+	2.21378i	0.282908	+	0.205545i
$117$		0			0
$118$	−1.22650	+	0.398515i	−0.112909	+	0.0366862i
$119$	−14.1490	+	10.2798i	−1.29704	+	0.942352i
$120$	14.7446	−	3.16915i	1.34599	−	0.289302i
$121$		0			0
$122$		−	8.51278i		−	0.770711i
$123$	−4.07230	−	5.60503i	−0.367187	−	0.505389i
$124$	−1.00599	−	3.09610i	−0.0903402	−	0.278038i
$125$	3.52744	+	10.6093i	0.315504	+	0.948924i
$126$	−7.48781	−	5.44021i	−0.667067	−	0.484652i
$127$	6.86646	−	9.45088i	0.609300	−	0.838630i	−0.387220	−	0.921988i	$-0.626564\pi$
$127$	6.86646	−	9.45088i	0.609300	−	0.838630i	0.996520	+	0.0833579i	$0.0265645\pi$
$128$	8.56912	+	2.78428i	0.757411	+	0.246098i
$129$	2.70222	+	8.31657i	0.237917	+	0.732233i
$130$		0			0
$131$	−8.74456			−0.764016			−0.382008	−	0.924159i	$-0.624767\pi$
$131$	−8.74456			−0.764016			−0.382008	+	0.924159i	$0.624767\pi$
$132$		0			0
$133$			13.8564i			1.20150i
$134$	0.413306	−	0.300285i	0.0357042	−	0.0259406i
$135$	−1.81745	+	1.05483i	−0.156421	+	0.0907851i
$136$	4.16837	−	12.8289i	0.357435	−	1.10007i
$137$	1.31040	−	1.80361i	0.111955	−	0.154093i	−0.749362	−	0.662160i	$-0.769640\pi$
$137$	1.31040	−	1.80361i	0.111955	−	0.154093i	0.861317	+	0.508067i	$0.169640\pi$
$138$	2.96754	−	4.08446i	0.252614	−	0.347693i
$139$	5.63452	−	17.3413i	0.477914	−	1.47087i	−0.364074	−	0.931370i	$-0.618614\pi$
$139$	5.63452	−	17.3413i	0.477914	−	1.47087i	0.841988	−	0.539497i	$-0.181386\pi$
$140$	9.19342	−	5.33576i	0.776986	−	0.450954i
$141$	−13.5466	+	9.84221i	−1.14083	+	0.828863i
$142$			5.63858i			0.473179i
$143$		0			0
$144$	−2.11684			−0.176404
$145$	−4.09608	+	4.57004i	−0.340161	+	0.379521i
$146$	−1.69623	−	5.22047i	−0.140381	−	0.432049i
$147$	−12.0039	−	3.90032i	−0.990068	−	0.321693i
$148$	8.90261	−	12.2534i	0.731790	−	1.00722i
$149$	−9.29490	−	6.75314i	−0.761468	−	0.553239i	0.137892	−	0.990447i	$-0.455967\pi$
$149$	−9.29490	−	6.75314i	−0.761468	−	0.553239i	−0.899360	+	0.437209i	$0.855967\pi$
$150$	1.09055	+	9.94036i	0.0890428	+	0.811627i
$151$	−6.87059	−	21.1455i	−0.559120	−	1.72080i	−0.684806	−	0.728726i	$-0.740113\pi$
$151$	−6.87059	−	21.1455i	−0.559120	−	1.72080i	0.125685	−	0.992070i	$-0.459887\pi$
$152$	−6.28181	−	8.64617i	−0.509522	−	0.701297i
$153$			17.0256i			1.37643i
$154$		0			0
$155$	5.18614	−	1.11469i	0.416561	−	0.0895342i
$156$		0			0
$157$	5.13431	−	1.66824i	0.409762	−	0.133140i	−0.0968802	−	0.995296i	$-0.530886\pi$
$157$	5.13431	−	1.66824i	0.409762	−	0.133140i	0.506643	+	0.862156i	$0.330886\pi$
$158$	9.60315	+	3.12025i	0.763986	+	0.248234i
$159$	−6.47214	−	4.70228i	−0.513274	−	0.372915i
$160$	−5.28513	+	11.9437i	−0.417826	+	0.944231i
$161$	2.70222	−	8.31657i	0.212965	−	0.655438i
$162$	5.83560	−	1.89610i	0.458488	−	0.148972i
$163$	2.03615	+	2.80252i	0.159483	+	0.219510i	0.881279	−	0.472596i	$-0.156683\pi$
$163$	2.03615	+	2.80252i	0.159483	+	0.219510i	−0.721796	+	0.692106i	$0.756683\pi$
$164$	3.76631			0.294100
$165$		0			0
$166$	−5.25544			−0.407901
$167$	13.1483	+	18.0970i	1.01744	+	1.40039i	0.913980	+	0.405759i	$0.132993\pi$
$167$	13.1483	+	18.0970i	1.01744	+	1.40039i	0.103464	+	0.994633i	$0.467007\pi$
$168$	22.2203	−	7.21983i	1.71434	−	0.557022i
$169$	4.01722	−	12.3637i	0.309017	−	0.951057i
$170$	8.17926	+	3.61936i	0.627320	+	0.277592i
$171$	10.9129	+	7.92871i	0.834533	+	0.606324i
$172$	−4.52106	−	1.46898i	−0.344727	−	0.112009i
$173$	−1.78754	+	0.580806i	−0.135904	+	0.0441579i	−0.376179	−	0.926547i	$-0.622762\pi$
$173$	−1.78754	+	0.580806i	−0.135904	+	0.0441579i	0.240275	+	0.970705i	$0.422762\pi$
$174$	−4.44080	+	3.22643i	−0.336656	+	0.244595i
$175$	7.11684	+	15.7908i	0.537983	+	1.19368i
$176$		0			0
$177$			4.10891i			0.308845i
$178$	−2.03615	−	2.80252i	−0.152616	−	0.210058i
$179$	4.90144	+	15.0851i	0.366351	+	1.12751i	0.949131	+	0.314883i	$0.101965\pi$
$179$	4.90144	+	15.0851i	0.366351	+	1.12751i	−0.582780	+	0.812630i	$0.698035\pi$
$180$	1.05822	−	10.2936i	0.0788752	−	0.767243i
$181$	−5.56859	−	4.04582i	−0.413910	−	0.300723i	0.361273	−	0.932460i	$-0.382342\pi$
$181$	−5.56859	−	4.04582i	−0.413910	−	0.300723i	−0.775183	+	0.631737i	$0.782342\pi$
$182$		0			0
$183$	−25.7954	−	8.38144i	−1.90685	−	0.619574i
$184$	2.08418	+	6.41446i	0.153648	+	0.472880i
$185$	18.3782	+	16.4722i	1.35119	+	1.21106i
$186$	4.74456			0.347888
$187$		0			0
$188$		−	9.10268i		−	0.663881i
$189$	−2.63370	+	1.91350i	−0.191574	+	0.139187i
$190$	6.12895	−	3.55717i	0.444641	−	0.258065i
$191$	−4.21120	+	12.9607i	−0.304711	+	0.937806i	0.675073	+	0.737751i	$0.264112\pi$
$191$	−4.21120	+	12.9607i	−0.304711	+	0.937806i	−0.979785	+	0.200055i	$0.935888\pi$
$192$	−5.00368	+	6.88698i	−0.361110	+	0.497025i
$193$	−13.7329	+	18.9018i	−0.988518	+	1.36058i	−0.0564056	+	0.998408i	$0.517964\pi$
$193$	−13.7329	+	18.9018i	−0.988518	+	1.36058i	−0.932112	+	0.362170i	$0.882036\pi$
$194$	−1.00599	+	3.09610i	−0.0722255	+	0.222287i
$195$		0			0
$196$	5.55099	−	4.03303i	0.396500	−	0.288074i
$197$			1.87953i			0.133911i	0.997756	+	0.0669554i	$0.0213285\pi$
$197$			1.87953i			0.133911i	−0.997756	+	0.0669554i	$0.978671\pi$
$198$		0			0
$199$	8.00000			0.567105			0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000			0.567105			0.283552	+	0.958957i	$0.408487\pi$
$200$	−11.5996	−	6.62680i	−0.820214	−	0.468586i
$201$	−0.502993	−	1.54805i	−0.0354784	−	0.109191i
$202$	−4.52106	−	1.46898i	−0.318101	−	0.103357i
$203$	−5.58834	+	7.69168i	−0.392224	+	0.539850i
$204$	−14.1490	−	10.2798i	−0.990628	−	0.719733i
$205$	−0.627600	+	6.10485i	−0.0438335	+	0.426381i
$206$	2.54435	+	7.83070i	0.177273	+	0.545591i
$207$	−5.00368	−	6.88698i	−0.347780	−	0.478678i
$208$		0			0
$209$		0			0
$210$	3.25544	+	15.1460i	0.224647	+	1.04518i
$211$	−17.3851	+	12.6310i	−1.19684	+	0.869553i	−0.993970	−	0.109653i	$-0.965026\pi$
$211$	−17.3851	+	12.6310i	−1.19684	+	0.869553i	−0.202867	+	0.979206i	$0.565026\pi$
$212$	4.13611	−	1.34390i	0.284069	−	0.0922997i
$213$	17.0860	+	5.55159i	1.17072	+	0.380389i
$214$	4.25174	+	3.08907i	0.290643	+	0.211164i
$215$	3.13445	−	7.08345i	0.213768	−	0.483087i
$216$	0.775903	−	2.38798i	0.0527935	−	0.162482i
$217$	7.81561	−	2.53945i	0.530558	−	0.172389i
$218$	−4.65695	−	6.40974i	−0.315408	−	0.434122i
$219$	−17.4891			−1.18181
$220$		0			0
$221$		0			0
$222$	12.9749	+	17.8584i	0.870819	+	1.19858i
$223$	−7.20236	+	2.34019i	−0.482306	+	0.156711i	−0.540071	−	0.841620i	$-0.681603\pi$
$223$	−7.20236	+	2.34019i	−0.482306	+	0.156711i	0.0577650	+	0.998330i	$0.481603\pi$
$224$	−6.25255	+	19.2434i	−0.417766	+	1.28575i
$225$	16.5087	+	3.43057i	1.10058	+	0.228704i
$226$	10.3106	+	7.49107i	0.685849	+	0.498298i
$227$	−9.32263	−	3.02911i	−0.618765	−	0.201049i	−0.0171731	−	0.999853i	$-0.505467\pi$
$227$	−9.32263	−	3.02911i	−0.618765	−	0.201049i	−0.601592	+	0.798804i	$0.705467\pi$
$228$	−13.1782	+	4.28187i	−0.872749	+	0.283573i
$229$	16.4815	−	11.9745i	1.08913	−	0.791299i	0.109878	−	0.993945i	$-0.464954\pi$
$229$	16.4815	−	11.9745i	1.08913	−	0.791299i	0.979252	+	0.202646i	$0.0649541\pi$
$230$	−4.37228	+	0.939764i	−0.288300	+	0.0619662i
$231$		0			0
$232$		−	7.33296i		−	0.481433i
$233$	−10.0074	−	13.7740i	−0.655605	−	0.902362i	0.343721	−	0.939072i	$-0.388312\pi$
$233$	−10.0074	−	13.7740i	−0.655605	−	0.902362i	−0.999326	+	0.0367094i	$0.988312\pi$
$234$		0			0
$235$	14.7546	+	1.51683i	0.962486	+	0.0989469i
$236$	−1.80709	−	1.31293i	−0.117632	−	0.0854644i
$237$	18.9100	−	26.0274i	1.22834	−	1.69066i
$238$	13.1782	+	4.28187i	0.854217	+	0.277552i
$239$	−1.00599	−	3.09610i	−0.0650718	−	0.200270i	0.913234	−	0.407435i	$-0.133577\pi$
$239$	−1.00599	−	3.09610i	−0.0650718	−	0.200270i	−0.978306	+	0.207164i	$0.933577\pi$
$240$	2.63851	+	2.36487i	0.170315	+	0.152652i
$241$	−5.25544			−0.338532			−0.169266	−	0.985570i	$-0.554140\pi$
$241$	−5.25544			−0.338532			−0.169266	+	0.985570i	$0.554140\pi$
$242$		0			0
$243$		−	22.3692i		−	1.43498i
$244$	11.9286	−	8.66664i	0.763650	−	0.554825i
$245$	5.61219	+	9.66971i	0.358550	+	0.617775i
$246$	−1.69623	+	5.22047i	−0.108148	+	0.332845i
$247$		0			0
$248$	−3.72556	+	5.12779i	−0.236573	+	0.325615i
$249$	−5.17435	+	15.9250i	−0.327911	+	1.00921i
$250$	5.15757	−	7.20169i	0.326193	−	0.455475i
$251$	3.95056	−	2.87025i	0.249357	−	0.181168i	−0.456085	−	0.889936i	$-0.650749\pi$
$251$	3.95056	−	2.87025i	0.249357	−	0.181168i	0.705442	+	0.708768i	$0.250749\pi$
$252$		−	16.0309i		−	1.00985i
$253$		0			0
$254$	−9.25544			−0.580738
$255$	19.0204	−	21.2213i	1.19111	−	1.32893i
$256$	−4.29013	−	13.2037i	−0.268133	−	0.825229i
$257$	−22.7814	−	7.40212i	−1.42106	−	0.461731i	−0.505123	−	0.863047i	$-0.668553\pi$
$257$	−22.7814	−	7.40212i	−1.42106	−	0.461731i	−0.915940	+	0.401316i	$0.868553\pi$
$258$	4.07230	−	5.60503i	0.253530	−	0.348954i
$259$	30.9317	+	22.4732i	1.92200	+	1.39642i
$260$		0			0
$261$	2.86009	+	8.80244i	0.177035	+	0.544858i
$262$	4.07230	+	5.60503i	0.251587	+	0.346280i
$263$		−	14.1514i		−	0.872610i	−0.899799	−	0.436305i	$-0.856287\pi$
$263$		−	14.1514i		−	0.872610i	0.899799	−	0.436305i	$-0.143713\pi$
$264$		0			0
$265$	1.48913	+	6.92820i	0.0914762	+	0.425596i
$266$	8.88159	−	6.45285i	0.544565	−	0.395650i
$267$	−10.4969	+	3.41066i	−0.642401	+	0.208729i
$268$	0.841553	+	0.273437i	0.0514060	+	0.0167028i
$269$	9.29490	+	6.75314i	0.566720	+	0.411746i	0.833912	−	0.551897i	$-0.186096\pi$
$269$	9.29490	+	6.75314i	0.566720	+	0.411746i	−0.267192	+	0.963643i	$0.586096\pi$
$270$	1.52249	+	0.673709i	0.0926559	+	0.0410006i
$271$	2.93230	−	9.02469i	0.178125	−	0.548211i	−0.821638	−	0.570010i	$-0.806939\pi$
$271$	2.93230	−	9.02469i	0.178125	−	0.548211i	0.999762	+	0.0217988i	$0.00693933\pi$
$272$	3.01404	−	0.979321i	0.182753	−	0.0593800i
$273$		0			0
$274$	−1.76631			−0.106707
$275$		0			0
$276$	8.74456			0.526361
$277$	−4.83032	−	6.64836i	−0.290226	−	0.399461i	0.638862	−	0.769321i	$-0.279406\pi$
$277$	−4.83032	−	6.64836i	−0.290226	−	0.399461i	−0.929087	+	0.369860i	$0.879406\pi$
$278$	−13.7393	+	4.46416i	−0.824026	+	0.267742i
$279$	2.47214	−	7.60845i	0.148003	−	0.455506i
$280$	−18.9257	−	8.37468i	−1.13102	−	0.500483i
$281$	−19.0031	−	13.8066i	−1.13363	−	0.823630i	−0.147411	−	0.989075i	$-0.547094\pi$
$281$	−19.0031	−	13.8066i	−1.13363	−	0.823630i	−0.986219	+	0.165445i	$0.947094\pi$
$282$	12.6172	+	4.09957i	0.751343	+	0.244126i
$283$	−4.52106	+	1.46898i	−0.268749	+	0.0873218i	−0.440292	−	0.897855i	$-0.645125\pi$
$283$	−4.52106	+	1.46898i	−0.268749	+	0.0873218i	0.171543	+	0.985177i	$0.445125\pi$
$284$	−7.90111	+	5.74049i	−0.468845	+	0.340636i
$285$	−4.74456	−	22.0742i	−0.281044	−	1.30756i
$286$		0			0
$287$			9.50744i			0.561207i
$288$	11.5778	+	15.9355i	0.682230	+	0.939009i
$289$	−2.62328	−	8.07364i	−0.154311	−	0.474920i
$290$	4.83680	+	0.497239i	0.284026	+	0.0291989i
$291$	8.39135	+	6.09667i	0.491910	+	0.357393i
$292$	5.58834	−	7.69168i	0.327033	−	0.450122i
$293$	9.60315	+	3.12025i	0.561022	+	0.182287i	0.575781	−	0.817604i	$-0.304698\pi$
$293$	9.60315	+	3.12025i	0.561022	+	0.182287i	−0.0147589	+	0.999891i	$0.504698\pi$
$294$	3.09017	+	9.51057i	0.180222	+	0.554667i
$295$	2.42926	−	2.71035i	0.141437	−	0.157803i
$296$	−29.4891			−1.71402
$297$		0			0
$298$			9.10268i			0.527304i
$299$		0			0
$300$	−12.8188	+	11.6482i	−0.740091	+	0.672507i
$301$	3.70820	−	11.4127i	0.213737	−	0.657816i
$302$	−10.3541	+	14.2512i	−0.595812	+	0.820065i
$303$	−8.90261	+	12.2534i	−0.511442	+	0.703939i
$304$	0.775903	−	2.38798i	0.0445011	−	0.136960i
$305$	12.0601	+	20.7794i	0.690560	+	1.18982i
$306$	10.9129	−	7.92871i	0.623851	−	0.453254i
$307$		−	28.1176i		−	1.60475i	−0.596817	−	0.802377i	$-0.703568\pi$
$307$		−	28.1176i		−	1.60475i	0.596817	−	0.802377i	$-0.296432\pi$
$308$		0			0
$309$	26.2337			1.49238
$310$	−3.12965	−	2.80507i	−0.177752	−	0.159317i
$311$	−5.40444	−	16.6331i	−0.306458	−	0.943179i	−0.979129	−	0.203238i	$-0.934853\pi$
$311$	−5.40444	−	16.6331i	−0.306458	−	0.943179i	0.672672	−	0.739941i	$-0.265147\pi$
$312$		0			0
$313$	−18.7043	+	25.7443i	−1.05723	+	1.45515i	−0.174865	+	0.984592i	$0.555949\pi$
$313$	−18.7043	+	25.7443i	−1.05723	+	1.45515i	−0.882367	+	0.470562i	$0.844051\pi$
$314$	−3.46032	−	2.51407i	−0.195277	−	0.141877i
$315$	25.9846	+	2.67131i	1.46407	+	0.150511i
$316$	5.40444	+	16.6331i	0.304023	+	0.935688i
$317$	−2.06842	−	2.84693i	−0.116174	−	0.159900i	0.746970	−	0.664858i	$-0.231508\pi$
$317$	−2.06842	−	2.84693i	−0.116174	−	0.159900i	−0.863144	+	0.504958i	$0.831508\pi$
$318$			6.33830i			0.355434i
$319$		0			0
$320$	7.37228	−	1.58457i	0.412123	−	0.0885804i
$321$	13.5466	−	9.84221i	0.756099	−	0.549338i
$322$	−6.58911	+	2.14093i	−0.367197	+	0.119310i
$323$	−19.2063	−	6.24051i	−1.06867	−	0.347231i
$324$	8.59801	+	6.24682i	0.477667	+	0.347045i
$325$		0			0
$326$	0.848116	−	2.61023i	0.0469728	−	0.144568i
$327$	−24.0079	+	7.80063i	−1.32764	+	0.431376i
$328$	−4.31021	−	5.93249i	−0.237991	−	0.327567i
$329$	22.9783			1.26683
$330$		0			0
$331$	3.11684			0.171317			0.0856586	−	0.996325i	$-0.472701\pi$
$331$	3.11684			0.171317			0.0856586	+	0.996325i	$0.472701\pi$
$332$	−5.35042	−	7.36423i	−0.293643	−	0.404164i
$333$	35.3986	−	11.5017i	1.93983	−	0.630289i
$334$	5.47665	−	16.8554i	0.299669	−	0.922286i
$335$	−0.583449	+	1.31852i	−0.0318772	+	0.0720383i
$336$	4.44080	+	3.22643i	0.242265	+	0.176016i
$337$	−11.9517	−	3.88335i	−0.651052	−	0.211540i	−0.0351740	−	0.999381i	$-0.511199\pi$
$337$	−11.9517	−	3.88335i	−0.651052	−	0.211540i	−0.615878	+	0.787842i	$0.711199\pi$
$338$	−9.79563	+	3.18279i	−0.532812	+	0.173121i
$339$	32.8509	−	23.8676i	1.78422	−	1.29631i
$340$	3.25544	+	15.1460i	0.176551	+	0.821409i
$341$		0			0
$342$		−	10.6873i		−	0.577901i
$343$	−4.07230	−	5.60503i	−0.219883	−	0.302643i
$344$	2.86009	+	8.80244i	0.154206	+	0.474596i
$345$	−1.45715	+	14.1742i	−0.0784504	+	0.763111i
$346$	1.20473	+	0.875286i	0.0647666	+	0.0470557i
$347$	−17.2206	+	23.7021i	−0.924449	+	1.27239i	0.0375371	+	0.999295i	$0.488049\pi$
$347$	−17.2206	+	23.7021i	−0.924449	+	1.27239i	−0.961986	+	0.273099i	$0.911951\pi$
$348$	−9.04212	−	2.93796i	−0.484708	−	0.157491i
$349$	−2.31427	−	7.12258i	−0.123880	−	0.381263i	0.869815	−	0.493377i	$-0.164238\pi$
$349$	−2.31427	−	7.12258i	−0.123880	−	0.381263i	−0.993695	+	0.112114i	$0.964238\pi$
$350$	6.80723	−	11.9154i	0.363862	−	0.636906i
$351$		0			0
$352$		0			0
$353$			21.7244i			1.15627i	0.815941	+	0.578136i	$0.196220\pi$
$353$			21.7244i			1.15627i	−0.815941	+	0.578136i	$0.803780\pi$
$354$	2.63370	−	1.91350i	0.139980	−	0.101701i
$355$	−7.98822	−	13.7636i	−0.423971	−	0.730494i
$356$	1.85410	−	5.70634i	0.0982672	−	0.302435i
$357$	25.9498	−	35.7169i	1.37341	−	1.89034i
$358$	7.38657	−	10.1667i	0.390392	−	0.537329i
$359$	2.01197	−	6.19221i	0.106188	−	0.326812i	−0.883820	−	0.467828i	$-0.845037\pi$
$359$	2.01197	−	6.19221i	0.106188	−	0.326812i	0.990007	+	0.141015i	$0.0450367\pi$
$360$	−17.4250	+	10.1133i	−0.918380	+	0.533018i
$361$	2.42705	−	1.76336i	0.127740	−	0.0928082i
$362$			5.45343i			0.286626i
$363$		0			0
$364$		0			0
$365$	11.5363	+	10.3399i	0.603838	+	0.541215i
$366$	6.64050	+	20.4374i	0.347105	+	1.06828i
$367$	22.8336	+	7.41908i	1.19190	+	0.387273i	0.836776	−	0.547545i	$-0.184437\pi$
$367$	22.8336	+	7.41908i	1.19190	+	0.387273i	0.355128	+	0.934818i	$0.384437\pi$
$368$	−0.931389	+	1.28195i	−0.0485520	+	0.0668261i
$369$	7.48781	+	5.44021i	0.389800	+	0.283206i
$370$	1.99962	−	19.4509i	0.103955	−	1.01121i
$371$	3.39247	+	10.4409i	0.176128	+	0.542066i
$372$	4.83032	+	6.64836i	0.250440	+	0.344701i
$373$		−	8.21782i		−	0.425503i	−0.977106	−	0.212751i	$-0.931758\pi$
$373$		−	8.21782i		−	0.425503i	0.977106	−	0.212751i	$-0.0682424\pi$
$374$		0			0
$375$	−16.7446	−	22.7190i	−0.864685	−	1.17321i
$376$	−14.3381	+	10.4172i	−0.739429	+	0.537226i
$377$		0			0
$378$	2.45300	+	0.797029i	0.126169	+	0.0409948i
$379$	−5.15528	−	3.74553i	−0.264809	−	0.192395i	0.447455	−	0.894306i	$-0.352330\pi$
$379$	−5.15528	−	3.74553i	−0.264809	−	0.192395i	−0.712264	+	0.701911i	$0.752330\pi$
$380$	11.2242	+	4.96677i	0.575792	+	0.254790i
$381$	−9.11264	+	28.0458i	−0.466855	+	1.43683i
$382$	10.2686	−	3.33648i	0.525388	−	0.170709i
$383$	−3.34655	−	4.60613i	−0.171001	−	0.235362i	0.714912	−	0.699215i	$-0.246467\pi$
$383$	−3.34655	−	4.60613i	−0.171001	−	0.235362i	−0.885912	+	0.463852i	$0.846467\pi$
$384$	−22.7446			−1.16068
$385$		0			0
$386$	18.5109			0.942179
$387$	−6.86646	−	9.45088i	−0.349042	−	0.480415i
$388$	−5.36261	+	1.74242i	−0.272245	+	0.0884579i
$389$	3.04734	−	9.37876i	0.154506	−	0.475522i	−0.843604	−	0.536966i	$-0.819571\pi$
$389$	3.04734	−	9.37876i	0.154506	−	0.475522i	0.998111	+	0.0614438i	$0.0195705\pi$
$390$		0			0
$391$	10.3106	+	7.49107i	0.521428	+	0.378839i
$392$	−12.7052	−	4.12818i	−0.641711	−	0.208505i
$393$	20.9938	−	6.82131i	1.05900	−	0.344090i
$394$	1.20473	−	0.875286i	0.0606933	−	0.0440963i
$395$	−27.8614	+	5.98844i	−1.40186	+	0.301311i
$396$		0			0
$397$		−	23.3639i		−	1.17260i	−0.810095	−	0.586299i	$-0.800584\pi$
$397$		−	23.3639i		−	1.17260i	0.810095	−	0.586299i	$-0.199416\pi$
$398$	−3.72556	−	5.12779i	−0.186745	−	0.257033i
$399$	−10.8089	−	33.2663i	−0.541121	−	1.66540i
$400$	−0.342279	−	3.11987i	−0.0171139	−	0.155994i
$401$	−9.29490	−	6.75314i	−0.464165	−	0.337236i	0.330998	−	0.943631i	$-0.392615\pi$
$401$	−9.29490	−	6.75314i	−0.464165	−	0.337236i	−0.795163	+	0.606396i	$0.792615\pi$
$402$	−0.758020	+	1.04332i	−0.0378066	+	0.0520363i
$403$		0			0
$404$	−2.54435	−	7.83070i	−0.126586	−	0.389592i
$405$	−11.5583	+	12.8957i	−0.574334	+	0.640790i
$406$	7.53262			0.373838
$407$		0			0
$408$			34.0511i			1.68578i
$409$	−3.64937	+	2.65143i	−0.180450	+	0.131105i	−0.674343	−	0.738418i	$-0.735573\pi$
$409$	−3.64937	+	2.65143i	−0.180450	+	0.131105i	0.493894	+	0.869522i	$0.335573\pi$
$410$	4.20532	−	2.44072i	0.207686	−	0.120539i
$411$	−1.73906	+	5.35228i	−0.0857815	+	0.264008i
$412$	−8.38250	+	11.5375i	−0.412976	+	0.568413i
$413$	3.31428	−	4.56171i	0.163085	−	0.224467i
$414$	−2.08418	+	6.41446i	−0.102432	+	0.315254i
$415$	12.8283	−	7.44542i	0.629717	−	0.365481i
$416$		0			0
$417$			46.0280i			2.25400i
$418$		0			0
$419$	−22.9783			−1.12256			−0.561280	−	0.827626i	$-0.689691\pi$
$419$	−22.9783			−1.12256			−0.561280	+	0.827626i	$0.689691\pi$
$420$	−17.9092	+	19.9815i	−0.873881	+	0.974997i
$421$	9.73067	+	29.9479i	0.474244	+	1.45957i	0.846975	+	0.531634i	$0.178422\pi$
$421$	9.73067	+	29.9479i	0.474244	+	1.45957i	−0.372730	+	0.927940i	$0.621578\pi$
$422$	16.1923	+	5.26119i	0.788227	+	0.256111i
$423$	13.1483	−	18.0970i	0.639291	−	0.879909i
$424$	−6.85025	−	4.97700i	−0.332678	−	0.241704i
$425$	−25.0928	+	2.75291i	−1.21718	+	0.133536i
$426$	−4.39845	−	13.5370i	−0.213106	−	0.655872i
$427$	21.8775	+	30.1118i	1.05873	+	1.45721i
$428$			9.10268i			0.439995i
$429$		0			0
$430$	−6.00000	+	1.28962i	−0.289346	+	0.0621910i
$431$	25.6643	−	18.6462i	1.23621	−	0.898156i	0.238866	−	0.971053i	$-0.423224\pi$
$431$	25.6643	−	18.6462i	1.23621	−	0.898156i	0.997340	+	0.0728966i	$0.0232243\pi$
$432$	0.561035	−	0.182291i	0.0269928	−	0.00877050i
$433$	−19.5390	−	6.34862i	−0.938986	−	0.305095i	−0.200754	−	0.979642i	$-0.564339\pi$
$433$	−19.5390	−	6.34862i	−0.938986	−	0.305095i	−0.738232	+	0.674547i	$0.764339\pi$
$434$	−5.26741	−	3.82700i	−0.252844	−	0.183702i
$435$	6.26891	−	14.1669i	0.300571	−	0.679250i
$436$	4.24058	−	13.0512i	0.203087	−	0.625038i
$437$	9.60315	−	3.12025i	0.459381	−	0.149262i
$438$	8.14459	+	11.2101i	0.389164	+	0.535638i
$439$	−1.48913			−0.0710721			−0.0355360	−	0.999368i	$-0.511314\pi$
$439$	−1.48913			−0.0710721			−0.0355360	+	0.999368i	$0.511314\pi$
$440$		0			0
$441$	16.8614			0.802924
$442$		0			0
$443$	14.3525	−	4.66341i	0.681908	−	0.221565i	0.0524777	−	0.998622i	$-0.483288\pi$
$443$	14.3525	−	4.66341i	0.681908	−	0.221565i	0.629431	+	0.777057i	$0.283288\pi$
$444$	−11.8149	+	36.3624i	−0.560708	+	1.72568i
$445$	8.94050	+	3.95621i	0.423821	+	0.187542i
$446$	4.85410	+	3.52671i	0.229848	+	0.166995i
$447$	27.5830	+	8.96224i	1.30463	+	0.423900i
$448$	11.1102	−	3.60991i	0.524906	−	0.170552i
$449$	−17.6862	+	12.8498i	−0.834666	+	0.606420i	−0.920875	−	0.389857i	$-0.872524\pi$
$449$	−17.6862	+	12.8498i	−0.834666	+	0.606420i	0.0862097	+	0.996277i	$0.472524\pi$
$450$	−5.48913	−	12.1793i	−0.258760	−	0.574136i
$451$		0			0
$452$			22.0742i			1.03828i
$453$	32.9896	+	45.4064i	1.54999	+	2.13338i
$454$	2.39992	+	7.38620i	0.112634	+	0.346652i
$455$		0			0
$456$	21.8259	+	15.8574i	1.02209	+	0.742592i
$457$	−12.2169	+	16.8151i	−0.571482	+	0.786577i	−0.992729	−	0.120368i	$-0.961592\pi$
$457$	−12.2169	+	16.8151i	−0.571482	+	0.786577i	0.421247	+	0.906946i	$0.361592\pi$
$458$	−15.3507	−	4.98775i	−0.717292	−	0.233062i
$459$	−1.46615	−	4.51235i	−0.0684340	−	0.210618i
$460$	−5.76816	−	5.16995i	−0.268942	−	0.241050i
$461$	32.2337			1.50127			0.750636	−	0.660716i	$-0.229747\pi$
$461$	32.2337			1.50127			0.750636	+	0.660716i	$0.229747\pi$
$462$		0			0
$463$		−	20.1398i		−	0.935976i	−0.883735	−	0.467988i	$-0.844979\pi$
$463$		−	20.1398i		−	0.935976i	0.883735	−	0.467988i	$-0.155021\pi$
$464$	1.39379	−	1.01264i	0.0647049	−	0.0470108i
$465$	−11.5813	+	6.72166i	−0.537070	+	0.311709i
$466$	−4.16837	+	12.8289i	−0.193096	+	0.594288i
$467$	2.58853	−	3.56280i	0.119783	−	0.164867i	−0.744915	−	0.667159i	$-0.767510\pi$
$467$	2.58853	−	3.56280i	0.119783	−	0.164867i	0.864698	+	0.502293i	$0.167510\pi$
$468$		0			0
$469$	−0.690248	+	2.12436i	−0.0318727	+	0.0980940i
$470$	−5.89891	−	10.1637i	−0.272096	−	0.468817i
$471$	−11.0251	+	8.01017i	−0.508008	+	0.369089i
$472$			4.34896i			0.200177i
$473$		0			0
$474$	−25.4891			−1.17075
$475$	−9.92105	+	17.3659i	−0.455209	+	0.796800i
$476$	7.41641	+	22.8254i	0.339930	+	1.04620i
$477$	10.1642	+	3.30254i	0.465386	+	0.151213i
$478$	−1.51604	+	2.08665i	−0.0693420	+	0.0954411i
$479$	−14.1490	−	10.2798i	−0.646484	−	0.469698i	0.215587	−	0.976485i	$-0.430833\pi$
$479$	−14.1490	−	10.2798i	−0.646484	−	0.469698i	−0.862072	+	0.506786i	$0.830833\pi$
$480$	3.37164	−	32.7970i	0.153894	−	1.49697i
$481$		0			0
$482$	2.44743	+	3.36860i	0.111477	+	0.153435i
$483$			22.0742i			1.00441i
$484$		0			0
$485$	−1.93070	−	8.98266i	−0.0876687	−	0.407882i
$486$	−14.3381	+	10.4172i	−0.650387	+	0.472534i
$487$	21.6071	−	7.02057i	0.979111	−	0.318132i	0.224622	−	0.974446i	$-0.427885\pi$
$487$	21.6071	−	7.02057i	0.979111	−	0.318132i	0.754488	+	0.656313i	$0.227885\pi$
$488$	−27.3024	−	8.87110i	−1.23592	−	0.401576i
$489$	−7.07450	−	5.13992i	−0.319920	−	0.232435i
$490$	3.58446	−	8.10040i	0.161929	−	0.365939i
$491$	−9.11264	+	28.0458i	−0.411248	+	1.26569i	0.504317	+	0.863519i	$0.331744\pi$
$491$	−9.11264	+	28.0458i	−0.411248	+	1.26569i	−0.915564	+	0.402172i	$0.868256\pi$
$492$	−9.04212	+	2.93796i	−0.407650	+	0.132454i
$493$	−8.14459	−	11.2101i	−0.366814	−	0.504876i
$494$		0			0
$495$		0			0
$496$	−1.48913			−0.0668637
$497$	−14.4909	−	19.9451i	−0.650008	−	0.894659i
$498$	12.6172	−	4.09957i	0.565390	−	0.183706i
$499$	6.18034	−	19.0211i	0.276670	−	0.851503i	−0.712103	−	0.702075i	$-0.752257\pi$
$499$	6.18034	−	19.0211i	0.276670	−	0.851503i	0.988773	−	0.149427i	$-0.0477430\pi$
$500$	15.3422	−	0.104766i	0.686125	−	0.00468528i
$501$	−45.6831	−	33.1907i	−2.04097	−	1.48285i
$502$	−3.67951	−	1.19554i	−0.164224	−	0.0533597i
$503$	0.280518	−	0.0911457i	0.0125077	−	0.00406399i	−0.302756	−	0.953068i	$-0.597907\pi$
$503$	0.280518	−	0.0911457i	0.0125077	−	0.00406399i	0.315264	+	0.949004i	$0.397907\pi$
$504$	−25.2510	+	18.3459i	−1.12477	+	0.817192i
$505$	13.1168	−	2.81929i	0.583692	−	0.125457i
$506$		0			0
$507$			32.8164i			1.45743i
$508$	−9.42272	−	12.9693i	−0.418066	−	0.575418i
$509$	−8.76752	−	26.9836i	−0.388613	−	1.19603i	−0.933825	−	0.357730i	$-0.883551\pi$
$509$	−8.76752	−	26.9836i	−0.388613	−	1.19603i	0.545212	−	0.838299i	$-0.316449\pi$
$510$	−22.4600	−	2.30896i	−0.994545	−	0.102243i
$511$	19.4164	+	14.1068i	0.858931	+	0.624050i
$512$	4.12671	−	5.67993i	0.182377	−	0.251020i
$513$	−3.57507	−	1.16161i	−0.157843	−	0.0512864i
$514$	5.86460	+	18.0494i	0.258677	+	0.796124i
$515$	−17.3045	−	15.5098i	−0.762526	−	0.683445i
$516$	12.0000			0.528271
$517$		0			0
$518$		−	30.2921i		−	1.33096i
$519$	3.83843	−	2.78878i	0.168488	−	0.122414i
$520$		0			0
$521$	5.74956	−	17.6953i	0.251893	−	0.775246i	−0.742533	−	0.669809i	$-0.766376\pi$
$521$	5.74956	−	17.6953i	0.251893	−	0.775246i	0.994426	−	0.105437i	$-0.0336242\pi$
$522$	4.31021	−	5.93249i	0.188653	−	0.259658i
$523$	−5.35042	+	7.36423i	−0.233958	+	0.322015i	−0.909812	−	0.415020i	$-0.863775\pi$
$523$	−5.35042	+	7.36423i	−0.233958	+	0.322015i	0.675855	+	0.737035i	$0.263775\pi$
$524$	−3.70820	+	11.4127i	−0.161994	+	0.498565i
$525$	−29.4039	−	32.3589i	−1.28329	−	1.41226i
$526$	−9.07065	+	6.59021i	−0.395499	+	0.287347i
$527$			11.9769i			0.521721i
$528$		0			0
$529$	16.6277			0.722944
$530$	3.74732	−	4.18092i	0.162773	−	0.181607i
$531$	−1.69623	−	5.22047i	−0.0736102	−	0.226549i
$532$	18.0842	+	5.87592i	0.784051	+	0.254754i
$533$		0			0
$534$	7.07450	+	5.13992i	0.306144	+	0.222426i
$535$	−14.7546	−	1.51683i	−0.637898	−	0.0655782i
$536$	−0.532379	−	1.63849i	−0.0229953	−	0.0707721i
$537$	−23.5347	−	32.3927i	−1.01560	−	1.39785i
$538$		−	9.10268i		−	0.392445i
$539$		0			0
$540$	0.605969	+	2.81929i	0.0260768	+	0.121323i
$541$	−0.189058	+	0.137358i	−0.00812822	+	0.00590550i	−0.591842	−	0.806054i	$-0.701599\pi$
$541$	−0.189058	+	0.137358i	−0.00812822	+	0.00590550i	0.583714	+	0.811960i	$0.301599\pi$
$542$	−7.15015	+	2.32322i	−0.307125	+	0.0997910i
$543$	16.5250	+	5.36930i	0.709156	+	0.230419i
$544$	−23.8572	−	17.3333i	−1.02287	−	0.743158i
$545$	20.4481	+	9.04839i	0.875902	+	0.387590i
$546$		0			0
$547$	8.65717	−	2.81288i	0.370154	−	0.120270i	−0.118032	−	0.993010i	$-0.537659\pi$
$547$	8.65717	−	2.81288i	0.370154	−	0.120270i	0.488186	+	0.872739i	$0.337659\pi$
$548$	−1.79824	−	2.47506i	−0.0768168	−	0.105729i
$549$	36.2337			1.54642
$550$		0			0
$551$	−10.9783			−0.467689
$552$	−10.0074	−	13.7740i	−0.425942	−	0.586259i
$553$	−41.9877	+	13.6426i	−1.78550	+	0.580143i
$554$	−2.01197	+	6.19221i	−0.0854805	+	0.263082i
$555$	−56.9714	−	25.2101i	−2.41830	−	1.07011i
$556$	−20.2430	−	14.7074i	−0.858495	−	0.623733i
$557$	30.5970	+	9.94157i	1.29644	+	0.421238i	0.874340	−	0.485314i	$-0.161295\pi$
$557$	30.5970	+	9.94157i	1.29644	+	0.421238i	0.422096	+	0.906551i	$0.361295\pi$
$558$	−6.02808	+	1.95864i	−0.255189	+	0.0829159i
$559$		0			0
$560$	−1.02175	−	4.75372i	−0.0431768	−	0.200881i
$561$		0			0
$562$			18.6101i			0.785021i
$563$	−7.21320	−	9.92812i	−0.304000	−	0.418420i	0.629498	−	0.777002i	$-0.283261\pi$
$563$	−7.21320	−	9.92812i	−0.304000	−	0.418420i	−0.933498	+	0.358582i	$0.883261\pi$
$564$	7.10067	+	21.8536i	0.298992	+	0.920203i
$565$	−35.7803	−	3.67834i	−1.50529	−	0.154749i
$566$	3.04701	+	2.21378i	0.128075	+	0.0930522i
$567$	−15.7691	+	21.7043i	−0.662239	+	0.911494i
$568$	18.0842	+	5.87592i	0.758798	+	0.246548i
$569$	−11.9727	−	36.8483i	−0.501923	−	1.54476i	−0.805883	−	0.592075i	$-0.798309\pi$
$569$	−11.9727	−	36.8483i	−0.501923	−	1.54476i	0.303960	−	0.952685i	$-0.401691\pi$
$570$	−11.9395	+	13.3210i	−0.500090	+	0.557955i
$571$	21.4891			0.899292			0.449646	−	0.893207i	$-0.351550\pi$
$571$	21.4891			0.899292			0.449646	+	0.893207i	$0.351550\pi$
$572$		0			0
$573$		−	34.4010i		−	1.43712i
$574$	6.09402	−	4.42757i	0.254360	−	0.184803i
$575$	9.34120	−	8.48817i	0.389555	−	0.353981i
$576$	3.51423	−	10.8157i	0.146426	−	0.450653i
$577$	−18.7043	+	25.7443i	−0.778672	+	1.07175i	0.216755	+	0.976226i	$0.430453\pi$
$577$	−18.7043	+	25.7443i	−0.778672	+	1.07175i	−0.995427	+	0.0955239i	$0.969547\pi$
$578$	−3.95334	+	5.44131i	−0.164437	+	0.226328i
$579$	18.2253	−	56.0916i	0.757417	−	2.33109i
$580$	4.22746	+	7.28383i	0.175536	+	0.302445i
$581$	18.5898	−	13.5063i	0.771235	−	0.560335i
$582$		−	8.21782i		−	0.340640i
$583$		0			0
$584$	−18.5109			−0.765985
$585$		0			0
$586$	−2.47214	−	7.60845i	−0.102123	−	0.314302i
$587$	26.6370	+	8.65488i	1.09943	+	0.357225i	0.801881	−	0.597483i	$-0.203833\pi$
$587$	26.6370	+	8.65488i	1.09943	+	0.357225i	0.297544	+	0.954708i	$0.403833\pi$
$588$	−10.1807	+	14.0126i	−0.419847	+	0.577869i
$589$	7.67686	+	5.57757i	0.316320	+	0.229820i
$590$	−2.86856	−	0.294898i	−0.118097	−	0.0121408i
$591$	−1.46615	−	4.51235i	−0.0603094	−	0.185613i
$592$	−4.07230	−	5.60503i	−0.167370	−	0.230365i
$593$		−	43.5586i		−	1.78874i	−0.447333	−	0.894368i	$-0.647626\pi$
$593$		−	43.5586i		−	1.78874i	0.447333	−	0.894368i	$-0.352374\pi$
$594$		0			0
$595$	−38.2337	+	8.21782i	−1.56743	+	0.336898i
$596$	−12.7552	+	9.26721i	−0.522474	+	0.379600i
$597$	−19.2063	+	6.24051i	−0.786062	+	0.255407i
$598$		0			0
$599$	−28.2980	−	20.5597i	−1.15622	−	0.840047i	−0.166929	−	0.985969i	$-0.553385\pi$
$599$	−28.2980	−	20.5597i	−1.15622	−	0.840047i	−0.989296	+	0.145922i	$0.953385\pi$
$600$	33.0175	+	6.86113i	1.34793	+	0.280105i
$601$	−9.41494	+	28.9762i	−0.384043	+	1.18196i	0.553129	+	0.833096i	$0.313434\pi$
$601$	−9.41494	+	28.9762i	−0.384043	+	1.18196i	−0.937172	+	0.348868i	$0.886566\pi$
$602$	−9.04212	+	2.93796i	−0.368529	+	0.119742i
$603$	1.27813	+	1.75919i	0.0520494	+	0.0716398i
$604$	−30.5109			−1.24147
$605$		0			0
$606$	12.0000			0.487467
$607$	−2.03615	−	2.80252i	−0.0826447	−	0.113751i	0.765693	−	0.643206i	$-0.222396\pi$
$607$	−2.03615	−	2.80252i	−0.0826447	−	0.113751i	−0.848338	+	0.529456i	$0.822396\pi$
$608$	−22.2203	+	7.21983i	−0.901154	+	0.292803i
$609$	7.41641	−	22.8254i	0.300528	−	0.924930i
$610$	7.70269	−	17.4071i	0.311873	−	0.704791i
$611$		0			0
$612$	22.2203	+	7.21983i	0.898204	+	0.291844i
$613$	−41.9877	+	13.6426i	−1.69587	+	0.551020i	−0.987882	−	0.155208i	$-0.950395\pi$
$613$	−41.9877	+	13.6426i	−1.69587	+	0.551020i	−0.707985	+	0.706228i	$0.750395\pi$
$614$	−18.0226	+	13.0942i	−0.727334	+	0.528439i
$615$	−3.25544	−	15.1460i	−0.131272	−	0.610747i
$616$		0			0
$617$			3.75906i			0.151334i	0.997133	+	0.0756669i	$0.0241086\pi$
$617$			3.75906i			0.151334i	−0.997133	+	0.0756669i	$0.975891\pi$
$618$	−12.2169	−	16.8151i	−0.491435	−	0.676403i
$619$	0.963158	+	2.96429i	0.0387126	+	0.119145i	0.968545	−	0.248838i	$-0.0800486\pi$
$619$	0.963158	+	2.96429i	0.0387126	+	0.119145i	−0.929833	+	0.367983i	$0.880049\pi$
$620$	0.744422	−	7.24122i	0.0298967	−	0.290814i
$621$	1.91922	+	1.39439i	0.0770155	+	0.0559550i
$622$	−8.14459	+	11.2101i	−0.326568	+	0.449483i
$623$	14.4047	+	4.68038i	0.577113	+	0.187515i
$624$		0			0
$625$	−2.38674	+	24.8858i	−0.0954695	+	0.995432i
$626$	25.2119			1.00767
$627$		0			0
$628$		−	7.40830i		−	0.295624i
$629$	−45.0807	+	32.7530i	−1.79749	+	1.30595i
$630$	−10.3887	−	17.8995i	−0.413894	−	0.713132i
$631$	−5.13153	+	15.7932i	−0.204283	+	0.628718i	0.795459	+	0.606007i	$0.207230\pi$
$631$	−5.13153	+	15.7932i	−0.204283	+	0.628718i	−0.999742	+	0.0227109i	$0.992770\pi$
$632$	20.0147	−	27.5479i	0.796144	−	1.09580i
$633$	31.8849	−	43.8858i	1.26731	−	1.74430i
$634$	−0.861558	+	2.65160i	−0.0342169	+	0.105309i
$635$	22.5922	−	13.1122i	0.896543	−	0.520344i
$636$	−8.88159	+	6.45285i	−0.352178	+	0.255872i
$637$		0			0
$638$		0			0
$639$	−24.0000			−0.949425
$640$	15.0029	+	13.4470i	0.593044	+	0.531540i
$641$	−6.06530	−	18.6671i	−0.239565	−	0.737305i	−0.996483	−	0.0837952i	$-0.973296\pi$
$641$	−6.06530	−	18.6671i	−0.239565	−	0.737305i	0.756918	−	0.653510i	$-0.226704\pi$
$642$	−12.6172	−	4.09957i	−0.497961	−	0.161797i
$643$	23.0145	−	31.6768i	0.907605	−	1.24921i	−0.0603727	−	0.998176i	$-0.519229\pi$
$643$	23.0145	−	31.6768i	0.907605	−	1.24921i	0.967978	−	0.251035i	$-0.0807711\pi$
$644$	−9.70820	−	7.05342i	−0.382557	−	0.277944i
$645$	−1.99962	+	19.4509i	−0.0787351	+	0.765879i
$646$	4.94427	+	15.2169i	0.194530	+	0.598701i
$647$	24.1193	+	33.1974i	0.948228	+	1.30512i	0.952310	+	0.305132i	$0.0987006\pi$
$647$	24.1193	+	33.1974i	0.948228	+	1.30512i	−0.00408232	+	0.999992i	$0.501299\pi$
$648$		−	20.6920i		−	0.812860i
$649$		0			0
$650$		0			0
$651$	−16.7827	+	12.1933i	−0.657766	+	0.477895i
$652$	4.52106	−	1.46898i	0.177058	−	0.0575297i
$653$	24.3406	+	7.90874i	0.952522	+	0.309493i	0.743740	−	0.668469i	$-0.233050\pi$
$653$	24.3406	+	7.90874i	0.952522	+	0.309493i	0.208782	+	0.977962i	$0.433050\pi$
$654$	16.1803	+	11.7557i	0.632701	+	0.459684i
$655$	−17.8810	−	7.91242i	−0.698669	−	0.309164i
$656$	0.532379	−	1.63849i	0.0207859	−	0.0639724i
$657$	22.2203	−	7.21983i	0.866898	−	0.281672i
$658$	−10.7008	−	14.7285i	−0.417162	−	0.574175i
$659$	32.7446			1.27555			0.637774	−	0.770224i	$-0.279856\pi$
$659$	32.7446			1.27555			0.637774	+	0.770224i	$0.279856\pi$
$660$		0			0
$661$	35.3505			1.37498			0.687488	−	0.726196i	$-0.258713\pi$
$661$	35.3505			1.37498			0.687488	+	0.726196i	$0.258713\pi$
$662$	−1.45150	−	1.99781i	−0.0564140	−	0.0776473i
$663$		0			0
$664$	−5.47665	+	16.8554i	−0.212535	+	0.654116i
$665$	−12.5378	+	28.3338i	−0.486196	+	1.09874i
$666$	−23.8572	−	17.3333i	−0.924448	−	0.671651i
$667$	6.58911	+	2.14093i	0.255131	+	0.0828972i
$668$	29.1944	−	9.48584i	1.12957	−	0.367018i
$669$	15.4659	−	11.2366i	0.597944	−	0.434432i
$670$	1.11684	−	0.240051i	0.0431474	−	0.00927397i
$671$		0			0
$672$		−	51.0767i		−	1.97033i
$673$	−0.758020	−	1.04332i	−0.0292195	−	0.0402172i	0.794157	−	0.607712i	$-0.207913\pi$
$673$	−0.758020	−	1.04332i	−0.0292195	−	0.0402172i	−0.823377	+	0.567495i	$0.807913\pi$
$674$	3.07673	+	9.46920i	0.118511	+	0.364740i
$675$	−4.67079	+	0.512429i	−0.179779	+	0.0197234i
$676$	−14.4326	−	10.4859i	−0.555099	−	0.403303i
$677$	25.5385	−	35.1508i	0.981526	−	1.35095i	0.0455220	−	0.998963i	$-0.485505\pi$
$677$	25.5385	−	35.1508i	0.981526	−	1.35095i	0.936004	−	0.351991i	$-0.114495\pi$
$678$	−30.5970	−	9.94157i	−1.17507	−	0.381804i
$679$	−4.39845	−	13.5370i	−0.168797	−	0.519504i
$680$	20.1316	−	22.4611i	0.772013	−	0.861342i
$681$	24.7446			0.948214
$682$		0			0
$683$			44.4434i			1.70058i	0.526314	+	0.850290i	$0.323573\pi$
$683$			44.4434i			1.70058i	−0.526314	+	0.850290i	$0.676427\pi$
$684$	14.9756	−	10.8804i	0.572607	−	0.416023i
$685$	4.31150	−	2.50235i	0.164734	−	0.0956098i
$686$	−1.69623	+	5.22047i	−0.0647625	+	0.199318i
$687$	−30.2277	+	41.6049i	−1.15326	+	1.58733i
$688$	−1.27813	+	1.75919i	−0.0487282	+	0.0670686i
$689$		0			0
$690$	9.76384	−	5.66683i	0.371703	−	0.215733i
$691$	−13.0564	+	9.48603i	−0.496689	+	0.360865i	−0.807751	−	0.589524i	$-0.799315\pi$
$691$	−13.0564	+	9.48603i	−0.496689	+	0.360865i	0.311062	+	0.950390i	$0.399315\pi$
$692$			2.57924i			0.0980480i
$693$		0			0
$694$	23.2119			0.881113
$695$	27.2126	−	30.3613i	1.03223	−	1.15167i
$696$	5.72017	+	17.6049i	0.216823	+	0.667312i
$697$	−13.1782	−	4.28187i	−0.499161	−	0.162187i
$698$	−3.48765	+	4.80033i	−0.132009	+	0.181695i
$699$	34.7701	+	25.2620i	1.31513	+	0.955496i
$700$	23.6268	−	2.59208i	0.893011	−	0.0979714i
$701$	10.9667	+	33.7522i	0.414208	+	1.27480i	0.912957	+	0.408055i	$0.133793\pi$
$701$	10.9667	+	33.7522i	0.414208	+	1.27480i	−0.498749	+	0.866746i	$0.666207\pi$
$702$		0			0
$703$			44.1485i			1.66509i
$704$		0			0
$705$	−36.6060	+	7.86797i	−1.37866	+	0.296325i
$706$	13.9248	−	10.1169i	0.524065	−	0.380755i
$707$	19.7673	−	6.42280i	0.743427	−	0.241554i
$708$	5.36261	+	1.74242i	0.201539	+	0.0654841i
$709$	33.2642	+	24.1679i	1.24926	+	0.907644i	0.998179	−	0.0603214i	$-0.0192126\pi$
$709$	33.2642	+	24.1679i	1.24926	+	0.907644i	0.251085	+	0.967965i	$0.419213\pi$
$710$	−5.10201	+	11.5299i	−0.191475	+	0.432708i
$711$	−13.2810	+	40.8747i	−0.498077	+	1.53292i
$712$	−11.1102	+	3.60991i	−0.416371	+	0.135287i
$713$	−3.51992	−	4.84475i	−0.131822	−	0.181437i
$714$	−34.9783			−1.30903
$715$		0			0
$716$	21.7663			0.813445
$717$	4.83032	+	6.64836i	0.180391	+	0.248288i
$718$	−4.90601	+	1.59406i	−0.183091	+	0.0594897i
$719$	−6.59768	+	20.3056i	−0.246052	+	0.757270i	0.749410	+	0.662106i	$0.230337\pi$
$719$	−6.59768	+	20.3056i	−0.246052	+	0.757270i	−0.995462	+	0.0951633i	$0.969663\pi$
$720$	−4.32855	−	1.91540i	−0.161316	−	0.0713828i
$721$	−29.1246	−	21.1603i	−1.08466	−	0.788050i
$722$	−2.26053	−	0.734490i	−0.0841282	−	0.0273349i
$723$	12.6172	−	4.09957i	0.469238	−	0.152465i
$724$	−7.64167	+	5.55200i	−0.284001	+	0.206338i
$725$	−12.5109	+	5.63858i	−0.464642	+	0.209412i
$726$		0			0
$727$			15.7908i			0.585650i	0.956166	+	0.292825i	$0.0945953\pi$
$727$			15.7908i			0.585650i	−0.956166	+	0.292825i	$0.905405\pi$
$728$		0			0
$729$	10.2698	+	31.6071i	0.380362	+	1.17063i
$730$	1.25520	−	12.2097i	0.0464570	−	0.451902i
$731$	14.1490	+	10.2798i	0.523320	+	0.380214i
$732$	−21.8775	+	30.1118i	−0.808616	+	1.11296i
$733$	−28.8095	−	9.36076i	−1.06410	−	0.345748i	−0.275914	−	0.961182i	$-0.588980\pi$
$733$	−28.8095	−	9.36076i	−1.06410	−	0.345748i	−0.788188	+	0.615435i	$0.788980\pi$
$734$	−5.87804	−	18.0908i	−0.216963	−	0.667742i
$735$	−21.0167	−	18.8371i	−0.775212	−	0.694815i
$736$	14.7446			0.543492
$737$		0			0
$738$		−	7.33296i		−	0.269930i
$739$	−0.602364	+	0.437643i	−0.0221583	+	0.0160990i	−0.598809	−	0.800892i	$-0.704359\pi$
$739$	−0.602364	+	0.437643i	−0.0221583	+	0.0160990i	0.576651	+	0.816991i	$0.304359\pi$
$740$	29.2915	−	17.0005i	1.07678	−	0.624950i
$741$		0			0
$742$	5.11251	−	7.03677i	0.187686	−	0.258328i
$743$	12.8015	−	17.6198i	0.469643	−	0.646408i	−0.506831	−	0.862046i	$-0.669183\pi$
$743$	12.8015	−	17.6198i	0.469643	−	0.646408i	0.976473	+	0.215638i	$0.0691830\pi$
$744$	4.94427	−	15.2169i	0.181266	−	0.557879i
$745$	−12.8958	−	22.2193i	−0.472467	−	0.814052i
$746$	−5.26741	+	3.82700i	−0.192854	+	0.140116i
$747$		−	22.3692i		−	0.818446i
$748$		0			0
$749$	−22.9783			−0.839607
$750$	−6.76445	+	21.3130i	−0.247003	+	0.778239i
$751$	6.68333	+	20.5692i	0.243878	+	0.750580i	0.995819	+	0.0913493i	$0.0291180\pi$
$751$	6.68333	+	20.5692i	0.243878	+	0.750580i	−0.751941	+	0.659231i	$0.770882\pi$
$752$	−3.96002	−	1.28669i	−0.144407	−	0.0469207i
$753$	−7.24547	+	9.97254i	−0.264040	+	0.363420i
$754$		0			0
$755$	5.08419	−	49.4554i	0.185032	−	1.79987i
$756$	1.38050	+	4.24873i	0.0502081	+	0.154525i
$757$	−23.3936	−	32.1985i	−0.850253	−	1.17027i	−0.983807	−	0.179232i	$-0.942639\pi$
$757$	−23.3936	−	32.1985i	−0.850253	−	1.17027i	0.133554	−	0.991042i	$-0.457361\pi$
$758$			5.04868i			0.183376i
$759$		0			0
$760$	−5.02175	−	23.3639i	−0.182158	−	0.847496i
$761$	17.1960	−	12.4936i	0.623355	−	0.452894i	−0.230737	−	0.973016i	$-0.574114\pi$
$761$	17.1960	−	12.4936i	0.623355	−	0.452894i	0.854092	+	0.520122i	$0.174114\pi$
$762$	22.2203	−	7.21983i	0.804958	−	0.261547i
$763$	32.9456	+	10.7047i	1.19271	+	0.387535i
$764$	15.1295	+	10.9922i	0.547365	+	0.397684i
$765$	−15.4054	+	34.8141i	−0.556983	+	1.25871i
$766$	−1.39394	+	4.29010i	−0.0503650	+	0.155007i
$767$		0			0
$768$	20.5994	+	28.3526i	0.743316	+	1.02309i
$769$	−51.2119			−1.84675			−0.923375	−	0.383900i	$-0.874581\pi$
$769$	−51.2119			−1.84675			−0.923375	+	0.383900i	$0.874581\pi$
$770$		0			0
$771$	60.4674			2.17768
$772$	18.8454	+	25.9385i	0.678262	+	0.933548i
$773$	29.3705	−	9.54305i	1.05638	−	0.343240i	0.271213	−	0.962519i	$-0.412575\pi$
$773$	29.3705	−	9.54305i	1.05638	−	0.343240i	0.785170	+	0.619280i	$0.212575\pi$
$774$	−2.86009	+	8.80244i	−0.102804	+	0.316397i
$775$	11.6133	+	2.41328i	0.417163	+	0.0866877i
$776$	8.88159	+	6.45285i	0.318831	+	0.231644i
$777$	−91.7910	−	29.8247i	−3.29298	−	1.06996i
$778$	−7.43067	+	2.41437i	−0.266402	+	0.0865593i
$779$	−8.88159	+	6.45285i	−0.318216	+	0.231197i
$780$		0			0
$781$		0			0
$782$		−	10.0974i		−	0.361081i
$783$	−1.51604	−	2.08665i	−0.0541788	−	0.0745708i
$784$	−0.969879	−	2.98498i	−0.0346385	−	0.106606i
$785$	12.0082	+	1.23448i	0.428591	+	0.0440606i
$786$	−14.1490	−	10.2798i	−0.504678	−	0.366670i
$787$	2.79417	−	3.84584i	0.0996013	−	0.137089i	−0.756307	−	0.654216i	$-0.772999\pi$
$787$	2.79417	−	3.84584i	0.0996013	−	0.137089i	0.855909	+	0.517127i	$0.172999\pi$
$788$	2.45300	+	0.797029i	0.0873846	+	0.0283930i
$789$	11.0390	+	33.9744i	0.392997	+	1.20952i
$790$	16.8133	+	15.0696i	0.598192	+	0.536154i
$791$	−55.7228			−1.98128
$792$		0			0
$793$		0			0
$794$	−14.9756	+	10.8804i	−0.531465	+	0.386132i
$795$	−8.97951	−	15.4715i	−0.318470	−	0.548719i
$796$	3.39247	−	10.4409i	0.120243	−	0.370069i
$797$	18.3576	−	25.2671i	0.650260	−	0.895006i	−0.348851	−	0.937178i	$-0.613428\pi$
$797$	18.3576	−	25.2671i	0.650260	−	0.895006i	0.999110	+	0.0421727i	$0.0134280\pi$
$798$	−16.2892	+	22.4201i	−0.576631	+	0.793664i
$799$	−10.3487	+	31.8501i	−0.366111	+	1.12677i
$800$	−21.6142	+	19.6404i	−0.764178	+	0.694394i
$801$	11.9286	−	8.66664i	0.421476	−	0.306221i
$802$			9.10268i			0.321427i
$803$		0			0
$804$	−2.23369			−0.0787761
$805$	13.0507	−	14.5608i	0.459977	−	0.513200i
$806$		0			0
$807$	−27.5830	−	8.96224i	−0.970966	−	0.315486i
$808$	−9.42272	+	12.9693i	−0.331490	+	0.456257i
$809$	17.1960	+	12.4936i	0.604580	+	0.439253i	0.847501	−	0.530793i	$-0.178106\pi$
$809$	17.1960	+	12.4936i	0.604580	+	0.439253i	−0.242922	+	0.970046i	$0.578106\pi$
$810$	13.6484	+	1.40310i	0.479556	+	0.0493000i
$811$	−10.5788	−	32.5582i	−0.371472	−	1.14327i	−0.945828	−	0.324667i	$-0.894748\pi$
$811$	−10.5788	−	32.5582i	−0.371472	−	1.14327i	0.574357	−	0.818605i	$-0.305252\pi$
$812$	7.66877	+	10.5552i	0.269121	+	0.370413i
$813$			23.9538i			0.840095i
$814$		0			0
$815$	1.62772	+	7.57301i	0.0570165	+	0.265271i
$816$	−6.47214	+	4.70228i	−0.226570	+	0.164613i
$817$	13.1782	−	4.28187i	0.461048	−	0.149803i
$818$	3.39899	+	1.10440i	0.118843	+	0.0386144i
$819$		0			0
$820$	7.70141	+	3.40791i	0.268945	+	0.119009i
$821$	5.56231	−	17.1190i	0.194126	−	0.597458i	−0.805860	−	0.592106i	$-0.798297\pi$
$821$	5.56231	−	17.1190i	0.194126	−	0.597458i	0.999986	−	0.00535152i	$-0.00170345\pi$
$822$	4.24054	−	1.37784i	0.147906	−	0.0480575i
$823$	19.7003	+	27.1151i	0.686708	+	0.945173i	0.999990	−	0.00448737i	$-0.00142838\pi$
$823$	19.7003	+	27.1151i	0.686708	+	0.945173i	−0.313282	+	0.949660i	$0.601428\pi$
$824$	27.7663			0.967285
$825$		0			0
$826$	−4.46738			−0.155440
$827$	10.5920	+	14.5787i	0.368321	+	0.506950i	0.952443	−	0.304715i	$-0.0985614\pi$
$827$	10.5920	+	14.5787i	0.368321	+	0.506950i	−0.584123	+	0.811665i	$0.698561\pi$
$828$	−11.1102	+	3.60991i	−0.386105	+	0.125453i
$829$	−9.68785	+	29.8161i	−0.336473	+	1.03556i	0.629519	+	0.776985i	$0.283252\pi$
$829$	−9.68785	+	29.8161i	−0.336473	+	1.03556i	−0.965992	+	0.258572i	$0.916748\pi$
$830$	−10.7464	−	4.75532i	−0.373013	−	0.165060i
$831$	16.7827	+	12.1933i	0.582186	+	0.422983i
$832$		0			0
$833$	−24.0079	+	7.80063i	−0.831824	+	0.270276i
$834$	29.5027	−	21.4350i	1.02160	−	0.742233i
$835$	10.5109	+	48.9022i	0.363744	+	1.69233i
$836$		0			0
$837$			2.22938i			0.0770588i
$838$	10.7008	+	14.7285i	0.369655	+	0.508786i
$839$	−2.19923	−	6.76852i	−0.0759257	−	0.233675i	0.905890	−	0.423514i	$-0.139204\pi$
$839$	−2.19923	−	6.76852i	−0.0759257	−	0.233675i	−0.981815	+	0.189839i	$0.939204\pi$
$840$	51.9693	+	5.34262i	1.79311	+	0.184338i
$841$	17.3675	+	12.6182i	0.598878	+	0.435111i
$842$	14.6643	−	20.1837i	0.505366	−	0.695576i
$843$	56.3924	+	18.3230i	1.94226	+	0.631078i
$844$	9.11264	+	28.0458i	0.313670	+	0.965377i
$845$	19.4017	−	21.6466i	0.667437	−	0.744666i
$846$	−17.7228			−0.609323
$847$		0			0
$848$		−	1.98933i		−	0.0683140i
$849$	9.70820	−	7.05342i	0.333185	−	0.242073i
$850$	13.4501	+	14.8018i	0.461336	+	0.507698i
$851$	8.60965	−	26.4978i	0.295135	−	0.908332i
$852$	14.4909	−	19.9451i	0.496452	−	0.683307i
$853$	14.4909	−	19.9451i	0.496161	−	0.682906i	−0.485349	−	0.874321i	$-0.661307\pi$
$853$	14.4909	−	19.9451i	0.496161	−	0.682906i	0.981509	+	0.191414i	$0.0613074\pi$
$854$	9.11264	−	28.0458i	0.311828	−	0.959708i
$855$	15.1407	+	26.0872i	0.517802	+	0.892163i
$856$	14.3381	−	10.4172i	0.490065	−	0.356053i
$857$		−	10.6873i		−	0.365070i	−0.983199	−	0.182535i	$-0.941570\pi$
$857$		−	10.6873i		−	0.365070i	0.983199	−	0.182535i	$-0.0584303\pi$
$858$		0			0
$859$	−11.1168			−0.379302			−0.189651	−	0.981852i	$-0.560736\pi$
$859$	−11.1168			−0.379302			−0.189651	+	0.981852i	$0.560736\pi$
$860$	−7.91554	−	7.09462i	−0.269918	−	0.241925i
$861$	−7.41641	−	22.8254i	−0.252751	−	0.777886i
$862$	−23.9034	−	7.76670i	−0.814155	−	0.264535i
$863$	13.9063	−	19.1404i	0.473376	−	0.651546i	−0.503839	−	0.863797i	$-0.668080\pi$
$863$	13.9063	−	19.1404i	0.473376	−	0.651546i	0.977215	+	0.212252i	$0.0680796\pi$
$864$	−4.44080	−	3.22643i	−0.151079	−	0.109765i
$865$	−4.18072	−	0.429792i	−0.142149	−	0.0146134i
$866$	5.02993	+	15.4805i	0.170924	+	0.526050i
$867$	12.5959	+	17.3368i	0.427779	+	0.588787i
$868$		−	11.2772i		−	0.382772i
$869$		0			0
$870$	−12.0000	+	2.57924i	−0.406838	+	0.0874444i
$871$		0			0
$872$	−25.4105	+	8.25636i	−0.860507	+	0.279596i
$873$	−13.1782	−	4.28187i	−0.446015	−	0.144919i
$874$	−6.47214	−	4.70228i	−0.218923	−	0.159057i
$875$	0.264465	+	38.7289i	0.00894054	+	1.30928i
$876$	−7.41641	+	22.8254i	−0.250577	+	0.771197i
$877$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$877$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$878$	0.693478	+	0.954490i	0.0234037	+	0.0322125i
$879$	−25.4891			−0.859727
$880$		0			0
$881$	21.8614			0.736530			0.368265	−	0.929721i	$-0.379952\pi$
$881$	21.8614			0.736530			0.368265	+	0.929721i	$0.379952\pi$
$882$	−7.85227	−	10.8077i	−0.264400	−	0.363915i
$883$	−23.0619	+	7.49326i	−0.776095	+	0.252168i	−0.670172	−	0.742206i	$-0.733780\pi$
$883$	−23.0619	+	7.49326i	−0.776095	+	0.252168i	−0.105923	+	0.994374i	$0.533780\pi$
$884$		0			0
$885$	−3.71790	+	8.40196i	−0.124976	+	0.282429i
$886$	−9.67301	−	7.02786i	−0.324971	−	0.236105i
$887$	−13.4587	−	4.37301i	−0.451900	−	0.146831i	0.0742192	−	0.997242i	$-0.476354\pi$
$887$	−13.4587	−	4.37301i	−0.451900	−	0.146831i	−0.526120	+	0.850411i	$0.676354\pi$
$888$	70.7971	−	23.0034i	2.37580	−	0.771943i
$889$	32.7388	−	23.7861i	1.09802	−	0.797761i
$890$	−1.62772	−	7.57301i	−0.0545613	−	0.253848i
$891$		0			0
$892$			10.3923i			0.347960i
$893$	15.5957	+	21.4656i	0.521890	+	0.718320i
$894$	−7.10067	−	21.8536i	−0.237482	−	0.730894i
$895$	−3.62703	+	35.2812i	−0.121238	+	1.17932i
$896$	25.2510	+	18.3459i	0.843576	+	0.612894i
$897$		0			0
$898$	16.4728	+	5.35233i	0.549704	+	0.178610i
$899$	2.01197	+	6.19221i	0.0671030	+	0.206522i
$900$	11.4780	−	20.0911i	0.382598	−	0.669702i
$901$	−16.0000			−0.533037
$902$		0			0
$903$			30.2921i			1.00806i
$904$	34.7701	−	25.2620i	1.15644	−	0.840201i
$905$	−7.72592	−	13.3116i	−0.256818	−	0.442493i
$906$	13.7412	−	42.2910i	0.456520	−	1.40502i
$907$	−11.6968	+	16.0992i	−0.388385	+	0.534566i	−0.957782	−	0.287497i	$-0.907177\pi$
$907$	−11.6968	+	16.0992i	−0.388385	+	0.534566i	0.569396	+	0.822063i	$0.307177\pi$
$908$	−7.90668	+	10.8826i	−0.262392	+	0.361152i
$909$	6.25255	−	19.2434i	0.207384	−	0.638263i
$910$		0			0
$911$	24.6838	−	17.9338i	0.817811	−	0.594175i	−0.0982734	−	0.995159i	$-0.531332\pi$
$911$	24.6838	−	17.9338i	0.817811	−	0.594175i	0.916085	+	0.400985i	$0.131332\pi$
$912$			6.33830i			0.209882i
$913$		0			0
$914$	16.4674			0.544692
$915$	−45.1630	−	40.4792i	−1.49304	−	1.33820i
$916$	−8.63903	−	26.5882i	−0.285442	−	0.878499i
$917$	−28.8095	−	9.36076i	−0.951372	−	0.309120i
$918$	−2.20952	+	3.04114i	−0.0729249	+	0.100373i
$919$	−5.04316	−	3.66407i	−0.166358	−	0.120867i	0.501491	−	0.865163i	$-0.332785\pi$
$919$	−5.04316	−	3.66407i	−0.166358	−	0.120867i	−0.667850	+	0.744296i	$0.732785\pi$
$920$	−1.54228	+	15.0022i	−0.0508475	+	0.494609i
$921$	21.9335	+	67.5043i	0.722733	+	2.22434i
$922$	−15.0111	−	20.6609i	−0.494363	−	0.680432i
$923$		0			0
$924$		0			0
$925$	22.6753	+	50.3118i	0.745558	+	1.65424i
$926$	−12.9091	+	9.37900i	−0.424219	+	0.308213i
$927$	−33.3305	+	10.8297i	−1.09472	+	0.355695i
$928$	−15.2463	−	4.95382i	−0.500484	−	0.162617i
$929$	−42.8603	−	31.1398i	−1.40620	−	1.02166i	−0.993861	−	0.110635i	$-0.964712\pi$
$929$	−42.8603	−	31.1398i	−1.40620	−	1.02166i	−0.412340	−	0.911030i	$-0.635288\pi$
$930$	9.70175	+	4.29306i	0.318133	+	0.140775i
$931$	−6.18034	+	19.0211i	−0.202552	+	0.623392i
$932$	−22.2203	+	7.21983i	−0.727852	+	0.236493i
$933$	25.9498	+	35.7169i	0.849559	+	1.16932i
$934$	−3.48913			−0.114168
$935$		0			0
$936$		0			0
$937$	15.2490	+	20.9884i	0.498162	+	0.685661i	0.981867	−	0.189570i	$-0.0607093\pi$
$937$	15.2490	+	20.9884i	0.498162	+	0.685661i	−0.483705	+	0.875231i	$0.660709\pi$
$938$	1.68311	−	0.546874i	0.0549553	−	0.0178561i
$939$	24.8230	−	76.3972i	0.810067	−	2.49313i
$940$	8.23646	−	18.6133i	0.268644	−	0.607099i
$941$	8.46828	+	6.15257i	0.276058	+	0.200568i	0.717196	−	0.696871i	$-0.245425\pi$
$941$	8.46828	+	6.15257i	0.276058	+	0.200568i	−0.441138	+	0.897439i	$0.645425\pi$
$942$	10.2686	+	3.33648i	0.334570	+	0.108708i
$943$	6.58911	−	2.14093i	0.214571	−	0.0697184i
$944$	−0.826613	+	0.600569i	−0.0269039	+	0.0195469i
$945$	−7.11684	+	1.52967i	−0.231511	+	0.0497602i
$946$		0			0
$947$		−	56.1802i		−	1.82561i	−0.408393	−	0.912806i	$-0.633911\pi$
$947$		−	56.1802i		−	1.82561i	0.408393	−	0.912806i	$-0.366089\pi$
$948$	−25.9498	−	35.7169i	−0.842811	−	1.16003i
$949$		0			0
$950$	15.7512	−	1.72805i	0.511037	−	0.0560655i
$951$	7.18662	+	5.22139i	0.233042	+	0.169315i
$952$	27.4659	−	37.8035i	0.890173	−	1.22522i
$953$	39.6391	+	12.8795i	1.28404	+	0.417209i	0.870000	−	0.493051i	$-0.164119\pi$
$953$	39.6391	+	12.8795i	1.28404	+	0.417209i	0.414037	+	0.910260i	$0.364119\pi$
$954$	−2.61656	−	8.05295i	−0.0847144	−	0.260724i
$955$	−20.3385	+	22.6918i	−0.658138	+	0.734291i
$956$	−4.46738			−0.144485
$957$		0			0
$958$			13.8564i			0.447680i
$959$	6.24789	−	4.53936i	0.201755	−	0.146583i
$960$	−16.4632	+	9.55507i	−0.531348	+	0.308389i
$961$	−7.84047	+	24.1305i	−0.252918	+	0.778402i
$962$		0			0
$963$	−13.1483	+	18.0970i	−0.423697	+	0.583169i
$964$	−2.22861	+	6.85896i	−0.0717787	+	0.220912i
$965$	−45.1843	+	26.2245i	−1.45453	+	0.844196i
$966$	14.1490	−	10.2798i	0.455237	−	0.330749i
$967$		−	46.3229i		−	1.48965i	−0.667262	−	0.744823i	$-0.732534\pi$
$967$		−	46.3229i		−	1.48965i	0.667262	−	0.744823i	$-0.267466\pi$
$968$		0			0
$969$	50.9783			1.63766
$970$	−4.85853	+	5.42071i	−0.155998	+	0.174048i
$971$	16.7163	+	51.4475i	0.536452	+	1.65103i	0.740491	+	0.672066i	$0.234593\pi$
$971$	16.7163	+	51.4475i	0.536452	+	1.65103i	−0.204040	+	0.978963i	$0.565407\pi$
$972$	−29.1944	−	9.48584i	−0.936411	−	0.304258i
$973$	37.1265	−	51.1002i	1.19022	−	1.63820i
$974$	−14.5623	−	10.5801i	−0.466606	−	0.339009i
$975$		0			0
$976$	−2.08418	−	6.41446i	−0.0667131	−	0.205322i
$977$	−16.0835	−	22.1371i	−0.514558	−	0.708228i	0.470122	−	0.882602i	$-0.344210\pi$
$977$	−16.0835	−	22.1371i	−0.514558	−	0.708228i	−0.984680	+	0.174373i	$0.944210\pi$
$978$			6.92820i			0.221540i
$979$		0			0
$980$	15.0000	−	3.22405i	0.479157	−	0.102989i
$981$	27.2823	−	19.8218i	0.871058	−	0.632860i
$982$	22.2203	−	7.21983i	0.709080	−	0.230394i
$983$	−7.76340	−	2.52248i	−0.247614	−	0.0804547i	0.182580	−	0.983191i	$-0.441555\pi$
$983$	−7.76340	−	2.52248i	−0.247614	−	0.0804547i	−0.430194	+	0.902736i	$0.641555\pi$
$984$	14.9756	+	10.8804i	0.477405	+	0.346855i
$985$	−1.70067	+	3.84329i	−0.0541878	+	0.122457i
$986$	−3.39247	+	10.4409i	−0.108038	+	0.332507i
$987$	−55.1659	+	17.9245i	−1.75595	+	0.570543i
$988$		0			0
$989$	−8.74456			−0.278061
$990$		0			0
$991$	−26.9783			−0.856992			−0.428496	−	0.903544i	$-0.640956\pi$
$991$	−26.9783			−0.856992			−0.428496	+	0.903544i	$0.640956\pi$
$992$	8.14459	+	11.2101i	0.258591	+	0.355920i
$993$	−7.48288	+	2.43134i	−0.237462	+	0.0771561i
$994$	−6.03591	+	18.5766i	−0.191448	+	0.589215i
$995$	16.3585	+	7.23871i	0.518600	+	0.229483i
$996$	18.5898	+	13.5063i	0.589040	+	0.427963i
$997$	20.9938	+	6.82131i	0.664882	+	0.216033i	0.621964	−	0.783046i	$-0.286335\pi$
$997$	20.9938	+	6.82131i	0.664882	+	0.216033i	0.0429172	+	0.999079i	$0.486335\pi$
$998$	−15.0702	+	4.89660i	−0.477039	+	0.154999i
$999$	−8.39135	+	6.09667i	−0.265491	+	0.192890i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.j.j.124.2		16
5.4	even	2	inner	605.2.j.j.124.3		16
11.2	odd	10		55.2.b.a.34.2	✓	4
11.3	even	5	inner	605.2.j.j.269.2		16
11.4	even	5	inner	605.2.j.j.444.3		16
11.5	even	5	inner	605.2.j.j.9.3		16
11.6	odd	10		605.2.j.i.9.2		16
11.7	odd	10		605.2.j.i.444.2		16
11.8	odd	10		605.2.j.i.269.3		16
11.9	even	5		605.2.b.c.364.3		4
11.10	odd	2		605.2.j.i.124.3		16
33.2	even	10		495.2.c.a.199.3		4
44.35	even	10		880.2.b.h.529.1		4
55.2	even	20		275.2.a.h.1.3		4
55.4	even	10	inner	605.2.j.j.444.2		16
55.9	even	10		605.2.b.c.364.2		4
55.13	even	20		275.2.a.h.1.2		4
55.14	even	10	inner	605.2.j.j.269.3		16
55.19	odd	10		605.2.j.i.269.2		16
55.24	odd	10		55.2.b.a.34.3	yes	4
55.29	odd	10		605.2.j.i.444.3		16
55.39	odd	10		605.2.j.i.9.3		16
55.42	odd	20		3025.2.a.ba.1.2		4
55.49	even	10	inner	605.2.j.j.9.2		16
55.53	odd	20		3025.2.a.ba.1.3		4
55.54	odd	2		605.2.j.i.124.2		16
165.2	odd	20		2475.2.a.bi.1.2		4
165.68	odd	20		2475.2.a.bi.1.3		4
165.134	even	10		495.2.c.a.199.2		4
220.79	even	10		880.2.b.h.529.4		4
220.123	odd	20		4400.2.a.cc.1.4		4
220.167	odd	20		4400.2.a.cc.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.b.a.34.2	✓	4	11.2	odd	10
55.2.b.a.34.3	yes	4	55.24	odd	10
275.2.a.h.1.2		4	55.13	even	20
275.2.a.h.1.3		4	55.2	even	20
495.2.c.a.199.2		4	165.134	even	10
495.2.c.a.199.3		4	33.2	even	10
605.2.b.c.364.2		4	55.9	even	10
605.2.b.c.364.3		4	11.9	even	5
605.2.j.i.9.2		16	11.6	odd	10
605.2.j.i.9.3		16	55.39	odd	10
605.2.j.i.124.2		16	55.54	odd	2
605.2.j.i.124.3		16	11.10	odd	2
605.2.j.i.269.2		16	55.19	odd	10
605.2.j.i.269.3		16	11.8	odd	10
605.2.j.i.444.2		16	11.7	odd	10
605.2.j.i.444.3		16	55.29	odd	10
605.2.j.j.9.2		16	55.49	even	10	inner
605.2.j.j.9.3		16	11.5	even	5	inner
605.2.j.j.124.2		16	1.1	even	1	trivial
605.2.j.j.124.3		16	5.4	even	2	inner
605.2.j.j.269.2		16	11.3	even	5	inner
605.2.j.j.269.3		16	55.14	even	10	inner
605.2.j.j.444.2		16	55.4	even	10	inner
605.2.j.j.444.3		16	11.4	even	5	inner
880.2.b.h.529.1		4	44.35	even	10
880.2.b.h.529.4		4	220.79	even	10
2475.2.a.bi.1.2		4	165.2	odd	20
2475.2.a.bi.1.3		4	165.68	odd	20
3025.2.a.ba.1.2		4	55.42	odd	20
3025.2.a.ba.1.3		4	55.53	odd	20
4400.2.a.cc.1.1		4	220.167	odd	20
4400.2.a.cc.1.4		4	220.123	odd	20

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.j (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.465695 - 0.640974i) q^{2} +(-2.40079 + 0.780063i) q^{3} +(0.424058 - 1.30512i) q^{4} +(2.04481 + 0.904839i) q^{5} +(1.61803 + 1.17557i) q^{6} +(3.29456 + 1.07047i) q^{7} +(-2.54105 + 0.825636i) q^{8} +(2.72823 - 1.98218i) q^{9} +(-0.372281 - 1.73205i) q^{10} +3.46410i q^{12} +(-0.848116 - 2.61023i) q^{14} +(-5.61500 - 0.577241i) q^{15} +(-0.507835 - 0.368964i) q^{16} +(-2.96754 + 4.08446i) q^{17} +(-2.54105 - 0.825636i) q^{18} +(1.23607 + 3.80423i) q^{19} +(2.04804 - 2.28502i) q^{20} -8.74456 q^{21} -2.52434i q^{23} +(5.45647 - 3.96435i) q^{24} +(3.36253 + 3.70046i) q^{25} +(-0.552379 + 0.760285i) q^{27} +(2.79417 - 3.84584i) q^{28} +(-0.848116 + 2.61023i) q^{29} +(2.24488 + 3.86788i) q^{30} +(1.91922 - 1.39439i) q^{31} +5.84096i q^{32} +4.00000 q^{34} +(5.76816 + 5.16995i) q^{35} +(-1.43004 - 4.40122i) q^{36} +(10.4969 + 3.41066i) q^{37} +(1.86278 - 2.56389i) q^{38} +(-5.94304 - 0.610965i) q^{40} +(0.848116 + 2.61023i) q^{41} +(4.07230 + 5.60503i) q^{42} -3.46410i q^{43} +(7.37228 - 1.58457i) q^{45} +(-1.61803 + 1.17557i) q^{46} +(6.30860 - 2.04979i) q^{47} +(1.50702 + 0.489660i) q^{48} +(4.04508 + 2.93893i) q^{49} +(0.805980 - 3.87858i) q^{50} +(3.93829 - 12.1208i) q^{51} +(1.86278 + 2.56389i) q^{53} +0.744563 q^{54} -9.25544 q^{56} +(-5.93507 - 8.16893i) q^{57} +(2.06805 - 0.671952i) q^{58} +(0.502993 - 1.54805i) q^{59} +(-3.13445 + 7.08345i) q^{60} +(8.69253 + 6.31550i) q^{61} +(-1.78754 - 0.580806i) q^{62} +(11.1102 - 3.60991i) q^{63} +(2.72823 - 1.98218i) q^{64} +0.644810i q^{67} +(4.07230 + 5.60503i) q^{68} +(1.96914 + 6.06040i) q^{69} +(0.627600 - 6.10485i) q^{70} +(-5.75765 - 4.18318i) q^{71} +(-5.29601 + 7.28933i) q^{72} +(6.58911 + 2.14093i) q^{73} +(-2.70222 - 8.31657i) q^{74} +(-10.9593 - 6.26102i) q^{75} +5.48913 q^{76} +(-10.3106 + 7.49107i) q^{79} +(-0.704576 - 1.21397i) q^{80} +(-2.39320 + 7.36552i) q^{81} +(1.27813 - 1.75919i) q^{82} +(3.89893 - 5.36641i) q^{83} +(-3.70820 + 11.4127i) q^{84} +(-9.76384 + 5.66683i) q^{85} +(-2.22040 + 1.61321i) q^{86} -6.92820i q^{87} +4.37228 q^{89} +(-4.44890 - 3.98751i) q^{90} +(-3.29456 - 1.07047i) q^{92} +(-3.51992 + 4.84475i) q^{93} +(-4.25174 - 3.08907i) q^{94} +(-0.914681 + 8.89738i) q^{95} +(-4.55632 - 14.0229i) q^{96} +(-2.41516 - 3.32418i) q^{97} -3.96143i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{4} + 3 q^{5} + 8 q^{6} + 2 q^{9} + 40 q^{10} - 12 q^{14} - q^{15} - 14 q^{16} - 16 q^{19} + 12 q^{20} - 48 q^{21} + 4 q^{24} - q^{25} - 12 q^{29} - 6 q^{30} - 2 q^{31} + 64 q^{34} + 18 q^{35}+ \cdots + 36 q^{96}+O(q^{100}) \) 16 * q + 6 * q^4 + 3 * q^5 + 8 * q^6 + 2 * q^9 + 40 * q^10 - 12 * q^14 - q^15 - 14 * q^16 - 16 * q^19 + 12 * q^20 - 48 * q^21 + 4 * q^24 - q^25 - 12 * q^29 - 6 * q^30 - 2 * q^31 + 64 * q^34 + 18 * q^35 + 30 * q^36 + 28 * q^40 + 12 * q^41 + 72 * q^45 - 8 * q^46 + 20 * q^49 - 18 * q^50 - 28 * q^51 - 80 * q^54 - 240 * q^56 - 18 * q^59 + 18 * q^60 + 20 * q^61 + 2 * q^64 - 14 * q^69 - 24 * q^70 + 6 * q^71 + 12 * q^74 - 15 * q^75 - 96 * q^76 - 28 * q^79 - 6 * q^80 + 8 * q^81 + 48 * q^84 + 2 * q^85 + 12 * q^86 + 24 * q^89 - 28 * q^90 - 44 * q^94 + 12 * q^95 + 36 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more