LMFDB - Embedded newform 930.2.h.d.371.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(371,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("930.371");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.h (of order $2$, degree $1$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4x^{14} + 6x^{12} + 36x^{10} - 142x^{8} + 324x^{6} + 486x^{4} - 2916x^{2} + 6561 $ x^16 - 4x^14 + 6x^12 + 36x^10 - 142x^8 + 324x^6 + 486x^4 - 2916*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{31}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			371.1
Root			$0.206738 + 1.71967i$ of defining polynomial
Character	$\chi$	$=$	930.371
Dual form			930.2.h.d.371.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-1.71967 - 0.206738i) q^{3} -1.00000 q^{4} +1.00000i q^{5} +(-0.206738 + 1.71967i) q^{6} -1.18164 q^{7} +1.00000i q^{8} +(2.91452 + 0.711040i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-1.71967 - 0.206738i) q^{3} -1.00000 q^{4} +1.00000i q^{5} +(-0.206738 + 1.71967i) q^{6} -1.18164 q^{7} +1.00000i q^{8} +(2.91452 + 0.711040i) q^{9} +1.00000 q^{10} +1.57649 q^{11} +(1.71967 + 0.206738i) q^{12} -3.43934i q^{13} +1.18164i q^{14} +(0.206738 - 1.71967i) q^{15} +1.00000 q^{16} -4.55264 q^{17} +(0.711040 - 2.91452i) q^{18} +6.64740 q^{19} -1.00000i q^{20} +(2.03203 + 0.244290i) q^{21} -1.57649i q^{22} -1.16301 q^{23} +(0.206738 - 1.71967i) q^{24} -1.00000 q^{25} -3.43934 q^{26} +(-4.86501 - 1.82529i) q^{27} +1.18164 q^{28} -8.20323 q^{29} +(-1.71967 - 0.206738i) q^{30} +(-5.56676 - 0.105626i) q^{31} -1.00000i q^{32} +(-2.71104 - 0.325920i) q^{33} +4.55264i q^{34} -1.18164i q^{35} +(-2.91452 - 0.711040i) q^{36} -9.82943i q^{37} -6.64740i q^{38} +(-0.711040 + 5.91452i) q^{39} -1.00000 q^{40} -5.42208i q^{41} +(0.244290 - 2.03203i) q^{42} +6.82897i q^{43} -1.57649 q^{44} +(-0.711040 + 2.91452i) q^{45} +1.16301i q^{46} +1.46575i q^{47} +(-1.71967 - 0.206738i) q^{48} -5.60372 q^{49} +1.00000i q^{50} +(7.82904 + 0.941203i) q^{51} +3.43934i q^{52} -7.16734 q^{53} +(-1.82529 + 4.86501i) q^{54} +1.57649i q^{55} -1.18164i q^{56} +(-11.4313 - 1.37427i) q^{57} +8.20323i q^{58} +6.84416i q^{59} +(-0.206738 + 1.71967i) q^{60} -11.8448i q^{61} +(-0.105626 + 5.56676i) q^{62} +(-3.44392 - 0.840195i) q^{63} -1.00000 q^{64} +3.43934 q^{65} +(-0.325920 + 2.71104i) q^{66} -13.6144 q^{67} +4.55264 q^{68} +(2.00000 + 0.240439i) q^{69} -1.18164 q^{70} -6.52980i q^{71} +(-0.711040 + 2.91452i) q^{72} +4.67746i q^{73} -9.82943 q^{74} +(1.71967 + 0.206738i) q^{75} -6.64740 q^{76} -1.86285 q^{77} +(5.91452 + 0.711040i) q^{78} +6.13816i q^{79} +1.00000i q^{80} +(7.98884 + 4.14468i) q^{81} -5.42208 q^{82} -3.86184 q^{83} +(-2.03203 - 0.244290i) q^{84} -4.55264i q^{85} +6.82897 q^{86} +(14.1068 + 1.69592i) q^{87} +1.57649i q^{88} +10.2683 q^{89} +(2.91452 + 0.711040i) q^{90} +4.06406i q^{91} +1.16301 q^{92} +(9.55115 + 1.33250i) q^{93} +1.46575 q^{94} +6.64740i q^{95} +(-0.206738 + 1.71967i) q^{96} +3.46575 q^{97} +5.60372i q^{98} +(4.59471 + 1.12095i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} + 4 q^{7} - 8 q^{9}+O(q^{10}) $ 16 * q - 16 * q^4 + 4 * q^7 - 8 * q^9	$ 16 q - 16 q^{4} + 4 q^{7} - 8 q^{9} + 16 q^{10} + 16 q^{16} - 8 q^{18} + 20 q^{19} - 16 q^{25} - 4 q^{28} - 8 q^{31} - 24 q^{33} + 8 q^{36} + 8 q^{39} - 16 q^{40} + 8 q^{45} - 28 q^{49} + 16 q^{51} - 4 q^{63} - 16 q^{64} - 44 q^{66} - 24 q^{67} + 32 q^{69} + 4 q^{70} + 8 q^{72} - 20 q^{76} + 40 q^{78} + 8 q^{81} - 48 q^{82} + 16 q^{87} - 8 q^{90} + 12 q^{93} - 40 q^{94} - 8 q^{97}+O(q^{100}) $ 16 * q - 16 * q^4 + 4 * q^7 - 8 * q^9 + 16 * q^10 + 16 * q^16 - 8 * q^18 + 20 * q^19 - 16 * q^25 - 4 * q^28 - 8 * q^31 - 24 * q^33 + 8 * q^36 + 8 * q^39 - 16 * q^40 + 8 * q^45 - 28 * q^49 + 16 * q^51 - 4 * q^63 - 16 * q^64 - 44 * q^66 - 24 * q^67 + 32 * q^69 + 4 * q^70 + 8 * q^72 - 20 * q^76 + 40 * q^78 + 8 * q^81 - 48 * q^82 + 16 * q^87 - 8 * q^90 + 12 * q^93 - 40 * q^94 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−1.71967	−	0.206738i	−0.992851	−	0.119360i
$3$	−1.71967	−	0.206738i	−0.992851	−	0.119360i
$4$	−1.00000			−0.500000
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	−0.206738	+	1.71967i	−0.0844003	+	0.702052i
$7$	−1.18164			−0.446619			−0.223309	−	0.974748i	$-0.571686\pi$
$7$	−1.18164			−0.446619			−0.223309	+	0.974748i	$0.571686\pi$
$8$			1.00000i			0.353553i
$9$	2.91452	+	0.711040i	0.971506	+	0.237013i
$10$	1.00000			0.316228
$11$	1.57649			0.475330			0.237665	−	0.971347i	$-0.423618\pi$
$11$	1.57649			0.475330			0.237665	+	0.971347i	$0.423618\pi$
$12$	1.71967	+	0.206738i	0.496426	+	0.0596800i
$13$		−	3.43934i		−	0.953900i	−0.878930	−	0.476950i	$-0.841742\pi$
$13$		−	3.43934i		−	0.953900i	0.878930	−	0.476950i	$-0.158258\pi$
$14$			1.18164i			0.315807i
$15$	0.206738	−	1.71967i	0.0533794	−	0.444016i
$16$	1.00000			0.250000
$17$	−4.55264			−1.10418			−0.552089	−	0.833785i	$-0.686169\pi$
$17$	−4.55264			−1.10418			−0.552089	+	0.833785i	$0.686169\pi$
$18$	0.711040	−	2.91452i	0.167594	−	0.686959i
$19$	6.64740			1.52502			0.762509	−	0.646978i	$-0.223967\pi$
$19$	6.64740			1.52502			0.762509	+	0.646978i	$0.223967\pi$
$20$		−	1.00000i		−	0.223607i
$21$	2.03203	+	0.244290i	0.443426	+	0.0533084i
$22$		−	1.57649i		−	0.336109i
$23$	−1.16301			−0.242505			−0.121253	−	0.992622i	$-0.538691\pi$
$23$	−1.16301			−0.242505			−0.121253	+	0.992622i	$0.538691\pi$
$24$	0.206738	−	1.71967i	0.0422001	−	0.351026i
$25$	−1.00000			−0.200000
$26$	−3.43934			−0.674509
$27$	−4.86501	−	1.82529i	−0.936271	−	0.351278i
$28$	1.18164			0.223309
$29$	−8.20323			−1.52330			−0.761651	−	0.647987i	$-0.775611\pi$
$29$	−8.20323			−1.52330			−0.761651	+	0.647987i	$0.775611\pi$
$30$	−1.71967	−	0.206738i	−0.313967	−	0.0377450i
$31$	−5.56676	−	0.105626i	−0.999820	−	0.0189710i
$31$	−5.56676	−	0.105626i	−0.999820	−	0.0189710i
$32$		−	1.00000i		−	0.176777i
$33$	−2.71104	−	0.325920i	−0.471932	−	0.0567354i
$34$			4.55264i			0.780772i
$35$		−	1.18164i		−	0.199734i
$36$	−2.91452	−	0.711040i	−0.485753	−	0.118507i
$37$		−	9.82943i		−	1.61595i	−0.589218	−	0.807974i	$-0.700564\pi$
$37$		−	9.82943i		−	1.61595i	0.589218	−	0.807974i	$-0.299436\pi$
$38$		−	6.64740i		−	1.07835i
$39$	−0.711040	+	5.91452i	−0.113858	+	0.947081i
$40$	−1.00000			−0.158114
$41$		−	5.42208i		−	0.846787i	−0.905946	−	0.423393i	$-0.860839\pi$
$41$		−	5.42208i		−	0.846787i	0.905946	−	0.423393i	$-0.139161\pi$
$42$	0.244290	−	2.03203i	0.0376947	−	0.313549i
$43$			6.82897i			1.04141i	0.853737	+	0.520704i	$0.174330\pi$
$43$			6.82897i			1.04141i	−0.853737	+	0.520704i	$0.825670\pi$
$44$	−1.57649			−0.237665
$45$	−0.711040	+	2.91452i	−0.105996	+	0.434471i
$46$			1.16301i			0.171477i
$47$			1.46575i			0.213802i	0.994270	+	0.106901i	$0.0340928\pi$
$47$			1.46575i			0.213802i	−0.994270	+	0.106901i	$0.965907\pi$
$48$	−1.71967	−	0.206738i	−0.248213	−	0.0298400i
$49$	−5.60372			−0.800532
$50$			1.00000i			0.141421i
$51$	7.82904	+	0.941203i	1.09628	+	0.131795i
$52$			3.43934i			0.476950i
$53$	−7.16734			−0.984509			−0.492255	−	0.870451i	$-0.663827\pi$
$53$	−7.16734			−0.984509			−0.492255	+	0.870451i	$0.663827\pi$
$54$	−1.82529	+	4.86501i	−0.248391	+	0.662044i
$55$			1.57649i			0.212574i
$56$		−	1.18164i		−	0.157904i
$57$	−11.4313	−	1.37427i	−1.51412	−	0.182026i
$58$			8.20323i			1.07714i
$59$			6.84416i			0.891034i	0.895273	+	0.445517i	$0.146980\pi$
$59$			6.84416i			0.891034i	−0.895273	+	0.445517i	$0.853020\pi$
$60$	−0.206738	+	1.71967i	−0.0266897	+	0.222008i
$61$		−	11.8448i		−	1.51657i	−0.651923	−	0.758285i	$-0.726037\pi$
$61$		−	11.8448i		−	1.51657i	0.651923	−	0.758285i	$-0.273963\pi$
$62$	−0.105626	+	5.56676i	−0.0134145	+	0.706980i
$63$	−3.44392	−	0.840195i	−0.433893	−	0.105855i
$64$	−1.00000			−0.125000
$65$	3.43934			0.426597
$66$	−0.325920	+	2.71104i	−0.0401180	+	0.333706i
$67$	−13.6144			−1.66326			−0.831632	−	0.555327i	$-0.812593\pi$
$67$	−13.6144			−1.66326			−0.831632	+	0.555327i	$0.812593\pi$
$68$	4.55264			0.552089
$69$	2.00000	+	0.240439i	0.240772	+	0.0289454i
$70$	−1.18164			−0.141233
$71$		−	6.52980i		−	0.774945i	−0.921881	−	0.387472i	$-0.873348\pi$
$71$		−	6.52980i		−	0.774945i	0.921881	−	0.387472i	$-0.126652\pi$
$72$	−0.711040	+	2.91452i	−0.0837969	+	0.343479i
$73$			4.67746i			0.547455i	0.961807	+	0.273727i	$0.0882566\pi$
$73$			4.67746i			0.547455i	−0.961807	+	0.273727i	$0.911743\pi$
$74$	−9.82943			−1.14265
$75$	1.71967	+	0.206738i	0.198570	+	0.0238720i
$76$	−6.64740			−0.762509
$77$	−1.86285			−0.212291
$78$	5.91452	+	0.711040i	0.669687	+	0.0805095i
$79$			6.13816i			0.690597i	0.938493	+	0.345299i	$0.112222\pi$
$79$			6.13816i			0.690597i	−0.938493	+	0.345299i	$0.887778\pi$
$80$			1.00000i			0.111803i
$81$	7.98884	+	4.14468i	0.887649	+	0.460520i
$82$	−5.42208			−0.598769
$83$	−3.86184			−0.423892			−0.211946	−	0.977281i	$-0.567980\pi$
$83$	−3.86184			−0.423892			−0.211946	+	0.977281i	$0.567980\pi$
$84$	−2.03203	−	0.244290i	−0.221713	−	0.0266542i
$85$		−	4.55264i		−	0.493804i
$86$	6.82897			0.736386
$87$	14.1068	+	1.69592i	1.51241	+	0.181821i
$88$			1.57649i			0.168054i
$89$	10.2683			1.08844			0.544219	−	0.838943i	$-0.316826\pi$
$89$	10.2683			1.08844			0.544219	+	0.838943i	$0.316826\pi$
$90$	2.91452	+	0.711040i	0.307217	+	0.0749502i
$91$			4.06406i			0.426030i
$92$	1.16301			0.121253
$93$	9.55115	+	1.33250i	0.990408	+	0.138174i
$94$	1.46575			0.151181
$95$			6.64740i			0.682008i
$96$	−0.206738	+	1.71967i	−0.0211001	+	0.175513i
$97$	3.46575			0.351894			0.175947	−	0.984400i	$-0.443701\pi$
$97$	3.46575			0.351894			0.175947	+	0.984400i	$0.443701\pi$
$98$			5.60372i			0.566061i
$99$	4.59471	+	1.12095i	0.461786	+	0.112660i
$100$	1.00000			0.100000
$101$		−	13.3740i		−	1.33076i	−0.746505	−	0.665380i	$-0.768270\pi$
$101$		−	13.3740i		−	1.33076i	0.746505	−	0.665380i	$-0.231730\pi$
$102$	0.941203	−	7.82904i	0.0931930	−	0.775190i
$103$	−6.40696			−0.631296			−0.315648	−	0.948876i	$-0.602222\pi$
$103$	−6.40696			−0.631296			−0.315648	+	0.948876i	$0.602222\pi$
$104$	3.43934			0.337255
$105$	−0.244290	+	2.03203i	−0.0238402	+	0.198306i
$106$			7.16734i			0.696153i
$107$		−	9.49156i		−	0.917584i	−0.888544	−	0.458792i	$-0.848282\pi$
$107$		−	9.49156i		−	0.917584i	0.888544	−	0.458792i	$-0.151718\pi$
$108$	4.86501	+	1.82529i	0.468136	+	0.175639i
$109$	−14.8139			−1.41892			−0.709458	−	0.704748i	$-0.751060\pi$
$109$	−14.8139			−1.41892			−0.709458	+	0.704748i	$0.751060\pi$
$110$	1.57649			0.150312
$111$	−2.03211	+	16.9034i	−0.192880	+	1.60440i
$112$	−1.18164			−0.111655
$113$		−	17.6839i		−	1.66356i	−0.555106	−	0.831780i	$-0.687322\pi$
$113$		−	17.6839i		−	1.66356i	0.555106	−	0.831780i	$-0.312678\pi$
$114$	−1.37427	+	11.4313i	−0.128712	+	1.07064i
$115$		−	1.16301i		−	0.108452i
$116$	8.20323			0.761651
$117$	2.44551	−	10.0240i	0.226087	−	0.926720i
$118$	6.84416			0.630056
$119$	5.37959			0.493147
$120$	1.71967	+	0.206738i	0.156984	+	0.0188725i
$121$	−8.51468			−0.774062
$122$	−11.8448			−1.07238
$123$	−1.12095	+	9.32418i	−0.101072	+	0.840733i
$124$	5.56676	+	0.105626i	0.499910	+	0.00948550i
$125$		−	1.00000i		−	0.0894427i
$126$	−0.840195	+	3.44392i	−0.0748505	+	0.306809i
$127$		−	14.7956i		−	1.31289i	−0.754373	−	0.656446i	$-0.772059\pi$
$127$		−	14.7956i		−	1.31289i	0.754373	−	0.656446i	$-0.227941\pi$
$128$			1.00000i			0.0883883i
$129$	1.41180	−	11.7436i	0.124302	−	1.03396i
$130$		−	3.43934i		−	0.301650i
$131$			2.84416i			0.248496i	0.992251	+	0.124248i	$0.0396518\pi$
$131$			2.84416i			0.248496i	−0.992251	+	0.124248i	$0.960348\pi$
$132$	2.71104	+	0.325920i	0.235966	+	0.0283677i
$133$	−7.85484			−0.681101
$134$			13.6144i			1.17611i
$135$	1.82529	−	4.86501i	0.157096	−	0.418713i
$136$		−	4.55264i		−	0.390386i
$137$	−5.52980			−0.472443			−0.236221	−	0.971699i	$-0.575909\pi$
$137$	−5.52980			−0.472443			−0.236221	+	0.971699i	$0.575909\pi$
$138$	0.240439	−	2.00000i	0.0204675	−	0.170251i
$139$			21.6833i			1.83915i	0.392915	+	0.919575i	$0.371467\pi$
$139$			21.6833i			1.83915i	−0.392915	+	0.919575i	$0.628533\pi$
$140$			1.18164i			0.0998670i
$141$	0.303027	−	2.52061i	0.0255194	−	0.212274i
$142$	−6.52980			−0.547969
$143$		−	5.42208i		−	0.453417i
$144$	2.91452	+	0.711040i	0.242877	+	0.0592534i
$145$		−	8.20323i		−	0.681241i
$146$	4.67746			0.387109
$147$	9.63654	+	1.15850i	0.794809	+	0.0955515i
$148$			9.82943i			0.807974i
$149$			6.52980i			0.534942i	0.963566	+	0.267471i	$0.0861880\pi$
$149$			6.52980i			0.534942i	−0.963566	+	0.267471i	$0.913812\pi$
$150$	0.206738	−	1.71967i	0.0168801	−	0.140410i
$151$		−	9.72099i		−	0.791083i	−0.918448	−	0.395541i	$-0.870557\pi$
$151$		−	9.72099i		−	0.791083i	0.918448	−	0.395541i	$-0.129443\pi$
$152$			6.64740i			0.539175i
$153$	−13.2688	−	3.23711i	−1.07272	−	0.261705i
$154$			1.86285i			0.150112i
$155$	0.105626	−	5.56676i	0.00848409	−	0.447133i
$156$	0.711040	−	5.91452i	0.0569288	−	0.473541i
$157$	22.0161			1.75708			0.878538	−	0.477672i	$-0.158519\pi$
$157$	22.0161			1.75708			0.878538	+	0.477672i	$0.158519\pi$
$158$	6.13816			0.488326
$159$	12.3254	+	1.48176i	0.977471	+	0.117511i
$160$	1.00000			0.0790569
$161$	1.37427			0.108307
$162$	4.14468	−	7.98884i	0.325637	−	0.627663i
$163$	14.4283			1.13011			0.565057	−	0.825052i	$-0.308854\pi$
$163$	14.4283			1.13011			0.565057	+	0.825052i	$0.308854\pi$
$164$			5.42208i			0.423393i
$165$	0.325920	−	2.71104i	0.0253728	−	0.211054i
$166$			3.86184i			0.299737i
$167$	−1.16301			−0.0899968			−0.0449984	−	0.998987i	$-0.514328\pi$
$167$	−1.16301			−0.0899968			−0.0449984	+	0.998987i	$0.514328\pi$
$168$	−0.244290	+	2.03203i	−0.0188474	+	0.156775i
$169$	1.17096			0.0900740
$170$	−4.55264			−0.349172
$171$	19.3740	+	4.72657i	1.48156	+	0.361450i
$172$		−	6.82897i		−	0.520704i
$173$		−	3.88241i		−	0.295174i	−0.989049	−	0.147587i	$-0.952849\pi$
$173$		−	3.88241i		−	0.295174i	0.989049	−	0.147587i	$-0.0471506\pi$
$174$	1.69592	−	14.1068i	0.128567	−	1.06944i
$175$	1.18164			0.0893237
$176$	1.57649			0.118832
$177$	1.41495	−	11.7697i	0.106354	−	0.884664i
$178$		−	10.2683i		−	0.769642i
$179$	10.6411			0.795353			0.397677	−	0.917526i	$-0.369817\pi$
$179$	10.6411			0.795353			0.397677	+	0.917526i	$0.369817\pi$
$180$	0.711040	−	2.91452i	0.0529978	−	0.217235i
$181$			16.8606i			1.25324i	0.779325	+	0.626620i	$0.215562\pi$
$181$			16.8606i			1.25324i	−0.779325	+	0.626620i	$0.784438\pi$
$182$	4.06406			0.301248
$183$	−2.44876	+	20.3691i	−0.181018	+	1.50573i
$184$		−	1.16301i		−	0.0857386i
$185$	9.82943			0.722674
$186$	1.33250	−	9.55115i	0.0977037	−	0.700324i
$187$	−7.17720			−0.524849
$188$		−	1.46575i		−	0.106901i
$189$	5.74870	+	2.15684i	0.418156	+	0.156887i
$190$	6.64740			0.482253
$191$		−	26.2574i		−	1.89992i	−0.312378	−	0.949958i	$-0.601126\pi$
$191$		−	26.2574i		−	1.89992i	0.312378	−	0.949958i	$-0.398874\pi$
$192$	1.71967	+	0.206738i	0.124106	+	0.0149200i
$193$	−20.5459			−1.47893			−0.739464	−	0.673197i	$-0.764921\pi$
$193$	−20.5459			−1.47893			−0.739464	+	0.673197i	$0.764921\pi$
$194$		−	3.46575i		−	0.248827i
$195$	−5.91452	−	0.711040i	−0.423548	−	0.0509187i
$196$	5.60372			0.400266
$197$	5.40391			0.385012			0.192506	−	0.981296i	$-0.438338\pi$
$197$	5.40391			0.385012			0.192506	+	0.981296i	$0.438338\pi$
$198$	1.12095	−	4.59471i	0.0796623	−	0.326532i
$199$		−	6.28837i		−	0.445771i	−0.974845	−	0.222885i	$-0.928452\pi$
$199$		−	6.28837i		−	0.445771i	0.974845	−	0.222885i	$-0.0715476\pi$
$200$		−	1.00000i		−	0.0707107i
$201$	23.4123	+	2.81461i	1.65137	+	0.198527i
$202$	−13.3740			−0.940989
$203$	9.69328			0.680335
$204$	−7.82904	−	0.941203i	−0.548142	−	0.0658974i
$205$	5.42208			0.378695
$206$			6.40696i			0.446394i
$207$	−3.38963	−	0.826951i	−0.235596	−	0.0574770i
$208$		−	3.43934i		−	0.238475i
$209$	10.4796			0.724886
$210$	2.03203	+	0.244290i	0.140224	+	0.0168576i
$211$	−10.0792			−0.693879			−0.346939	−	0.937888i	$-0.612779\pi$
$211$	−10.0792			−0.693879			−0.346939	+	0.937888i	$0.612779\pi$
$212$	7.16734			0.492255
$213$	−1.34996	+	11.2291i	−0.0924975	+	0.769405i
$214$	−9.49156			−0.648830
$215$	−6.82897			−0.465732
$216$	1.82529	−	4.86501i	0.124196	−	0.331022i
$217$	6.57792	+	0.124812i	0.446538	+	0.00847280i
$218$			14.8139i			1.00332i
$219$	0.967006	−	8.04367i	0.0653442	−	0.543541i
$220$		−	1.57649i		−	0.106287i
$221$			15.6581i			1.05328i
$222$	16.9034	+	2.03211i	1.13448	+	0.136387i
$223$		−	12.7191i		−	0.851737i	−0.904785	−	0.425868i	$-0.859969\pi$
$223$		−	12.7191i		−	0.851737i	0.904785	−	0.425868i	$-0.140031\pi$
$224$			1.18164i			0.0789518i
$225$	−2.91452	−	0.711040i	−0.194301	−	0.0474027i
$226$	−17.6839			−1.17631
$227$			12.3357i			0.818750i	0.912366	+	0.409375i	$0.134253\pi$
$227$			12.3357i			0.818750i	−0.912366	+	0.409375i	$0.865747\pi$
$228$	11.4313	+	1.37427i	0.757058	+	0.0910131i
$229$			3.44164i			0.227430i	0.993513	+	0.113715i	$0.0362751\pi$
$229$			3.44164i			0.227430i	−0.993513	+	0.113715i	$0.963725\pi$
$230$	−1.16301			−0.0766869
$231$	3.20348	+	0.385121i	0.210773	+	0.0253391i
$232$		−	8.20323i		−	0.538569i
$233$			14.8397i			0.972182i	0.873908	+	0.486091i	$0.161578\pi$
$233$			14.8397i			0.972182i	−0.873908	+	0.486091i	$0.838422\pi$
$234$	−10.0240	−	2.44551i	−0.655290	−	0.159868i
$235$	−1.46575			−0.0956153
$236$		−	6.84416i		−	0.445517i
$237$	1.26899	−	10.5556i	0.0824297	−	0.685660i
$238$		−	5.37959i		−	0.348707i
$239$	−2.48085			−0.160473			−0.0802365	−	0.996776i	$-0.525568\pi$
$239$	−2.48085			−0.160473			−0.0802365	+	0.996776i	$0.525568\pi$
$240$	0.206738	−	1.71967i	0.0133449	−	0.111004i
$241$		−	12.9304i		−	0.832920i	−0.909154	−	0.416460i	$-0.863271\pi$
$241$		−	12.9304i		−	0.832920i	0.909154	−	0.416460i	$-0.136729\pi$
$242$			8.51468i			0.547344i
$243$	−12.8813	−	8.77907i	−0.826336	−	0.563178i
$244$			11.8448i			0.758285i
$245$		−	5.60372i		−	0.358009i
$246$	9.32418	+	1.12095i	0.594488	+	0.0714690i
$247$		−	22.8626i		−	1.45471i
$248$	0.105626	−	5.56676i	0.00670726	−	0.353490i
$249$	6.64109	+	0.798388i	0.420862	+	0.0505958i
$250$	−1.00000			−0.0632456
$251$	5.73203			0.361802			0.180901	−	0.983501i	$-0.442099\pi$
$251$	5.73203			0.361802			0.180901	+	0.983501i	$0.442099\pi$
$252$	3.44392	+	0.840195i	0.216946	+	0.0529273i
$253$	−1.83348			−0.115270
$254$	−14.7956			−0.928355
$255$	−0.941203	+	7.82904i	−0.0589404	+	0.490273i
$256$	1.00000			0.0625000
$257$		−	4.35803i		−	0.271847i	−0.990719	−	0.135923i	$-0.956600\pi$
$257$		−	4.35803i		−	0.271847i	0.990719	−	0.135923i	$-0.0434001\pi$
$258$	−11.7436	−	1.41180i	−0.731122	−	0.0878951i
$259$			11.6149i			0.721713i
$260$	−3.43934			−0.213299
$261$	−23.9085	−	5.83283i	−1.47990	−	0.361043i
$262$	2.84416			0.175713
$263$	17.8491			1.10062			0.550312	−	0.834959i	$-0.314509\pi$
$263$	17.8491			1.10062			0.550312	+	0.834959i	$0.314509\pi$
$264$	0.325920	−	2.71104i	0.0200590	−	0.166853i
$265$		−	7.16734i		−	0.440286i
$266$			7.85484i			0.481611i
$267$	−17.6581	−	2.12284i	−1.08066	−	0.129916i
$268$	13.6144			0.831632
$269$	5.38862			0.328550			0.164275	−	0.986415i	$-0.447472\pi$
$269$	5.38862			0.328550			0.164275	+	0.986415i	$0.447472\pi$
$270$	−4.86501	−	1.82529i	−0.296075	−	0.111084i
$271$			29.0008i			1.76167i	0.473421	+	0.880837i	$0.343019\pi$
$271$			29.0008i			1.76167i	−0.473421	+	0.880837i	$0.656981\pi$
$272$	−4.55264			−0.276045
$273$	0.840195	−	6.98884i	0.0508509	−	0.422984i
$274$			5.52980i			0.334068i
$275$	−1.57649			−0.0950659
$276$	−2.00000	−	0.240439i	−0.120386	−	0.0144727i
$277$		−	0.131535i		−	0.00790315i	−0.999992	−	0.00395158i	$-0.998742\pi$
$277$		−	0.131535i		−	0.00790315i	0.999992	−	0.00395158i	$-0.00125783\pi$
$278$	21.6833			1.30048
$279$	−16.1493	−	4.26604i	−0.966835	−	0.255401i
$280$	1.18164			0.0706166
$281$		−	0.682894i		−	0.0407380i	−0.999793	−	0.0203690i	$-0.993516\pi$
$281$		−	0.682894i		−	0.0407380i	0.999793	−	0.0203690i	$-0.00648410\pi$
$282$	−2.52061	−	0.303027i	−0.150100	−	0.0180450i
$283$	10.0953			0.600102			0.300051	−	0.953923i	$-0.402996\pi$
$283$	10.0953			0.600102			0.300051	+	0.953923i	$0.402996\pi$
$284$			6.52980i			0.387472i
$285$	1.37427	−	11.4313i	0.0814046	−	0.677133i
$286$	−5.42208			−0.320614
$287$			6.40696i			0.378191i
$288$	0.711040	−	2.91452i	0.0418985	−	0.171740i
$289$	3.72657			0.219210
$290$	−8.20323			−0.481710
$291$	−5.95995	−	0.716502i	−0.349378	−	0.0420021i
$292$		−	4.67746i		−	0.273727i
$293$			31.3464i			1.83128i	0.402004	+	0.915638i	$0.368314\pi$
$293$			31.3464i			1.83128i	−0.402004	+	0.915638i	$0.631686\pi$
$294$	1.15850	−	9.63654i	0.0675651	−	0.562015i
$295$	−6.84416			−0.398482
$296$	9.82943			0.571324
$297$	−7.66964	−	2.87756i	−0.445037	−	0.166973i
$298$	6.52980			0.378261
$299$			4.00000i			0.231326i
$300$	−1.71967	−	0.206738i	−0.0992851	−	0.0119360i
$301$		−	8.06939i		−	0.465112i
$302$	−9.72099			−0.559380
$303$	−2.76490	+	22.9988i	−0.158839	+	1.32125i
$304$	6.64740			0.381254
$305$	11.8448			0.678231
$306$	−3.23711	+	13.2688i	−0.185053	+	0.758525i
$307$	−11.4863			−0.655558			−0.327779	−	0.944754i	$-0.606300\pi$
$307$	−11.4863			−0.655558			−0.327779	+	0.944754i	$0.606300\pi$
$308$	1.86285			0.106146
$309$	11.0178	+	1.32456i	0.626783	+	0.0753515i
$310$	−5.56676	−	0.105626i	−0.316171	−	0.00599916i
$311$			1.22976i			0.0697332i	0.999392	+	0.0348666i	$0.0111006\pi$
$311$			1.22976i			0.0697332i	−0.999392	+	0.0348666i	$0.988899\pi$
$312$	−5.91452	−	0.711040i	−0.334844	−	0.0402547i
$313$		−	2.64912i		−	0.149737i	−0.997193	−	0.0748685i	$-0.976146\pi$
$313$		−	2.64912i		−	0.149737i	0.997193	−	0.0748685i	$-0.0238537\pi$
$314$		−	22.0161i		−	1.24244i
$315$	0.840195	−	3.44392i	0.0473396	−	0.194043i
$316$		−	6.13816i		−	0.345299i
$317$			17.6581i			0.991776i	0.868386	+	0.495888i	$0.165157\pi$
$317$			17.6581i			0.991776i	−0.868386	+	0.495888i	$0.834843\pi$
$318$	1.48176	−	12.3254i	0.0830929	−	0.691177i
$319$	−12.9323			−0.724071
$320$		−	1.00000i		−	0.0559017i
$321$	−1.96226	+	16.3223i	−0.109523	+	0.911024i
$322$		−	1.37427i		−	0.0765849i
$323$	−30.2632			−1.68389
$324$	−7.98884	−	4.14468i	−0.443825	−	0.230260i
$325$			3.43934i			0.190780i
$326$		−	14.4283i		−	0.799111i
$327$	25.4750	+	3.06259i	1.40877	+	0.169362i
$328$	5.42208			0.299384
$329$		−	1.73200i		−	0.0954881i
$330$	−2.71104	−	0.325920i	−0.149238	−	0.0179413i
$331$			36.3183i			1.99624i	0.0613165	+	0.998118i	$0.480470\pi$
$331$			36.3183i			1.99624i	−0.0613165	+	0.998118i	$0.519530\pi$
$332$	3.86184			0.211946
$333$	6.98912	−	28.6481i	0.383002	−	1.56990i
$334$			1.16301i			0.0636373i
$335$		−	13.6144i		−	0.743834i
$336$	2.03203	+	0.244290i	0.110856	+	0.0133271i
$337$		−	27.9926i		−	1.52485i	−0.647074	−	0.762427i	$-0.724008\pi$
$337$		−	27.9926i		−	1.52485i	0.647074	−	0.762427i	$-0.275992\pi$
$338$		−	1.17096i		−	0.0636919i
$339$	−3.65592	+	30.4104i	−0.198563	+	1.65167i
$340$			4.55264i			0.246902i
$341$	−8.77595	−	0.166518i	−0.475244	−	0.00901748i
$342$	4.72657	−	19.3740i	0.255583	−	1.04762i
$343$	14.8931			0.804151
$344$	−6.82897			−0.368193
$345$	−0.240439	+	2.00000i	−0.0129448	+	0.107676i
$346$	−3.88241			−0.208719
$347$	0.131535			0.00706115			0.00353058	−	0.999994i	$-0.498876\pi$
$347$	0.131535			0.00706115			0.00353058	+	0.999994i	$0.498876\pi$
$348$	−14.1068	−	1.69592i	−0.756206	−	0.0909107i
$349$	−13.2734			−0.710511			−0.355255	−	0.934769i	$-0.615606\pi$
$349$	−13.2734			−0.710511			−0.355255	+	0.934769i	$0.615606\pi$
$350$		−	1.18164i		−	0.0631614i
$351$	−6.27780	+	16.7324i	−0.335084	+	0.893109i
$352$		−	1.57649i		−	0.0840272i
$353$	−23.1169			−1.23039			−0.615193	−	0.788376i	$-0.710922\pi$
$353$	−23.1169			−1.23039			−0.615193	+	0.788376i	$0.710922\pi$
$354$	−11.7697	−	1.41495i	−0.625552	−	0.0752035i
$355$	6.52980			0.346566
$356$	−10.2683			−0.544219
$357$	−9.25112	−	1.11216i	−0.489621	−	0.0588620i
$358$		−	10.6411i		−	0.562400i
$359$		−	28.5201i		−	1.50523i	−0.658459	−	0.752617i	$-0.728791\pi$
$359$		−	28.5201i		−	1.50523i	0.658459	−	0.752617i	$-0.271209\pi$
$360$	−2.91452	−	0.711040i	−0.153609	−	0.0374751i
$361$	25.1879			1.32568
$362$	16.8606			0.886175
$363$	14.6424	+	1.76030i	0.768528	+	0.0923920i
$364$		−	4.06406i		−	0.213015i
$365$	−4.67746			−0.244829
$366$	20.3691	+	2.44876i	1.06471	+	0.127999i
$367$			17.5260i			0.914851i	0.889248	+	0.457426i	$0.151228\pi$
$367$			17.5260i			0.914851i	−0.889248	+	0.457426i	$0.848772\pi$
$368$	−1.16301			−0.0606263
$369$	3.85532	−	15.8028i	0.200700	−	0.822659i
$370$		−	9.82943i		−	0.511008i
$371$	8.46922			0.439700
$372$	−9.55115	−	1.33250i	−0.495204	−	0.0690870i
$373$	9.14170			0.473339			0.236670	−	0.971590i	$-0.423944\pi$
$373$	9.14170			0.473339			0.236670	+	0.971590i	$0.423944\pi$
$374$			7.17720i			0.371124i
$375$	−0.206738	+	1.71967i	−0.0106759	+	0.0888033i
$376$	−1.46575			−0.0755905
$377$			28.2137i			1.45308i
$378$	2.15684	−	5.74870i	0.110936	−	0.295681i
$379$	−2.25387			−0.115773			−0.0578867	−	0.998323i	$-0.518436\pi$
$379$	−2.25387			−0.115773			−0.0578867	+	0.998323i	$0.518436\pi$
$380$		−	6.64740i		−	0.341004i
$381$	−3.05880	+	25.4434i	−0.156707	+	1.30351i
$382$	−26.2574			−1.34344
$383$	−5.43602			−0.277768			−0.138884	−	0.990309i	$-0.544352\pi$
$383$	−5.43602			−0.277768			−0.138884	+	0.990309i	$0.544352\pi$
$384$	0.206738	−	1.71967i	0.0105500	−	0.0877565i
$385$		−	1.86285i		−	0.0949395i
$386$			20.5459i			1.04576i
$387$	−4.85567	+	19.9032i	−0.246828	+	1.01173i
$388$	−3.46575			−0.175947
$389$	37.6062			1.90671			0.953354	−	0.301854i	$-0.0976054\pi$
$389$	37.6062			1.90671			0.953354	+	0.301854i	$0.0976054\pi$
$390$	−0.711040	+	5.91452i	−0.0360049	+	0.299493i
$391$	5.29479			0.267769
$392$		−	5.60372i		−	0.283031i
$393$	0.587995	−	4.89101i	0.0296604	−	0.246719i
$394$		−	5.40391i		−	0.272245i
$395$	−6.13816			−0.308845
$396$	−4.59471	−	1.12095i	−0.230893	−	0.0563298i
$397$	18.1656			0.911704			0.455852	−	0.890056i	$-0.349335\pi$
$397$	18.1656			0.911704			0.455852	+	0.890056i	$0.349335\pi$
$398$	−6.28837			−0.315208
$399$	13.5077	+	1.62389i	0.676232	+	0.0812963i
$400$	−1.00000			−0.0500000
$401$	−27.8508			−1.39080			−0.695400	−	0.718623i	$-0.744773\pi$
$401$	−27.8508			−1.39080			−0.695400	+	0.718623i	$0.744773\pi$
$402$	2.81461	−	23.4123i	0.140380	−	1.16770i
$403$	−0.363284	+	19.1460i	−0.0180964	+	0.953729i
$404$			13.3740i			0.665380i
$405$	−4.14468	+	7.98884i	−0.205951	+	0.396969i
$406$		−	9.69328i		−	0.481070i
$407$		−	15.4960i		−	0.768108i
$408$	−0.941203	+	7.82904i	−0.0465965	+	0.387595i
$409$		−	2.73048i		−	0.135013i	−0.997719	−	0.0675067i	$-0.978496\pi$
$409$		−	2.73048i		−	0.135013i	0.997719	−	0.0675067i	$-0.0215044\pi$
$410$		−	5.42208i		−	0.267777i
$411$	9.50943	+	1.14322i	0.469066	+	0.0563908i
$412$	6.40696			0.315648
$413$		−	8.08735i		−	0.397952i
$414$	−0.826951	+	3.38963i	−0.0406424	+	0.166591i
$415$		−	3.86184i		−	0.189570i
$416$	−3.43934			−0.168627
$417$	4.48274	−	37.2880i	0.219521	−	1.82600i
$418$		−	10.4796i		−	0.512572i
$419$			3.91265i			0.191146i	0.995422	+	0.0955728i	$0.0304683\pi$
$419$			3.91265i			0.191146i	−0.995422	+	0.0955728i	$0.969532\pi$
$420$	0.244290	−	2.03203i	0.0119201	−	0.0991530i
$421$	−5.57073			−0.271501			−0.135750	−	0.990743i	$-0.543345\pi$
$421$	−5.57073			−0.271501			−0.135750	+	0.990743i	$0.543345\pi$
$422$			10.0792i			0.490646i
$423$	−1.04221	+	4.27197i	−0.0506740	+	0.207710i
$424$		−	7.16734i		−	0.348077i
$425$	4.55264			0.220836
$426$	11.2291	+	1.34996i	0.544051	+	0.0654056i
$427$			13.9963i			0.677329i
$428$			9.49156i			0.458792i
$429$	−1.12095	+	9.32418i	−0.0541199	+	0.450176i
$430$			6.82897i			0.329322i
$431$		−	18.9412i		−	0.912366i	−0.889886	−	0.456183i	$-0.849216\pi$
$431$		−	18.9412i		−	0.912366i	0.889886	−	0.456183i	$-0.150784\pi$
$432$	−4.86501	−	1.82529i	−0.234068	−	0.0878195i
$433$			33.6653i			1.61785i	0.587912	+	0.808925i	$0.299950\pi$
$433$			33.6653i			1.61785i	−0.587912	+	0.808925i	$0.700050\pi$
$434$	0.124812	−	6.57792i	0.00599118	−	0.315750i
$435$	−1.69592	+	14.1068i	−0.0813130	+	0.676371i
$436$	14.8139			0.709458
$437$	−7.73102			−0.369825
$438$	−8.04367	−	0.967006i	−0.384342	−	0.0462053i
$439$	25.8504			1.23377			0.616886	−	0.787052i	$-0.288394\pi$
$439$	25.8504			1.23377			0.616886	+	0.787052i	$0.288394\pi$
$440$	−1.57649			−0.0751562
$441$	−16.3322	−	3.98447i	−0.777722	−	0.189737i
$442$	15.6581			0.744779
$443$		−	3.89058i		−	0.184847i	−0.995720	−	0.0924236i	$-0.970539\pi$
$443$		−	3.89058i		−	0.184847i	0.995720	−	0.0924236i	$-0.0294614\pi$
$444$	2.03211	−	16.9034i	0.0964398	−	0.802198i
$445$			10.2683i			0.486764i
$446$	−12.7191			−0.602269
$447$	1.34996	−	11.2291i	0.0638507	−	0.531118i
$448$	1.18164			0.0558273
$449$	−16.8673			−0.796019			−0.398010	−	0.917381i	$-0.630299\pi$
$449$	−16.8673			−0.796019			−0.398010	+	0.917381i	$0.630299\pi$
$450$	−0.711040	+	2.91452i	−0.0335188	+	0.137392i
$451$		−	8.54786i		−	0.402503i
$452$			17.6839i			0.831780i
$453$	−2.00969	+	16.7169i	−0.0944237	+	0.785427i
$454$	12.3357			0.578944
$455$	−4.06406			−0.190526
$456$	1.37427	−	11.4313i	0.0643560	−	0.535321i
$457$		−	6.15575i		−	0.287954i	−0.989581	−	0.143977i	$-0.954011\pi$
$457$		−	6.15575i		−	0.287954i	0.989581	−	0.143977i	$-0.0459891\pi$
$458$	3.44164			0.160817
$459$	22.1486	+	8.30992i	1.03381	+	0.387874i
$460$			1.16301i			0.0542258i
$461$	6.44714			0.300273			0.150137	−	0.988665i	$-0.452029\pi$
$461$	6.44714			0.300273			0.150137	+	0.988665i	$0.452029\pi$
$462$	0.385121	−	3.20348i	0.0179174	−	0.149039i
$463$			29.6849i			1.37957i	0.724013	+	0.689787i	$0.242296\pi$
$463$			29.6849i			1.37957i	−0.724013	+	0.689787i	$0.757704\pi$
$464$	−8.20323			−0.380826
$465$	−1.33250	+	9.55115i	−0.0617933	+	0.442924i
$466$	14.8397			0.687437
$467$			17.1558i			0.793878i	0.917845	+	0.396939i	$0.129927\pi$
$467$			17.1558i			0.793878i	−0.917845	+	0.396939i	$0.870073\pi$
$468$	−2.44551	+	10.0240i	−0.113044	+	0.463360i
$469$	16.0873			0.742845
$470$			1.46575i			0.0676102i
$471$	−37.8604	−	4.55156i	−1.74452	−	0.209725i
$472$	−6.84416			−0.315028
$473$			10.7658i			0.495012i
$474$	−10.5556	−	1.26899i	−0.484835	−	0.0582866i
$475$	−6.64740			−0.305003
$476$	−5.37959			−0.246573
$477$	−20.8893	−	5.09627i	−0.956457	−	0.233342i
$478$			2.48085i			0.113472i
$479$		−	28.7338i		−	1.31288i	−0.754378	−	0.656440i	$-0.772061\pi$
$479$		−	28.7338i		−	1.31288i	0.754378	−	0.656440i	$-0.227939\pi$
$480$	−1.71967	−	0.206738i	−0.0784918	−	0.00943624i
$481$	−33.8067			−1.54145
$482$	−12.9304			−0.588963
$483$	−2.36328	−	0.284113i	−0.107533	−	0.0129276i
$484$	8.51468			0.387031
$485$			3.46575i			0.157372i
$486$	−8.77907	+	12.8813i	−0.398227	+	0.584308i
$487$			9.91982i			0.449510i	0.974415	+	0.224755i	$0.0721581\pi$
$487$			9.91982i			0.449510i	−0.974415	+	0.224755i	$0.927842\pi$
$488$	11.8448			0.536189
$489$	−24.8119	−	2.98288i	−1.12203	−	0.134890i
$490$	−5.60372			−0.253150
$491$	−26.2946			−1.18666			−0.593330	−	0.804959i	$-0.702187\pi$
$491$	−26.2946			−1.18666			−0.593330	+	0.804959i	$0.702187\pi$
$492$	1.12095	−	9.32418i	0.0505362	−	0.420367i
$493$	37.3464			1.68200
$494$	−22.8626			−1.02864
$495$	−1.12095	+	4.59471i	−0.0503829	+	0.206517i
$496$	−5.56676	−	0.105626i	−0.249955	−	0.00474275i
$497$			7.71589i			0.346105i
$498$	0.798388	−	6.64109i	0.0357766	−	0.297594i
$499$			9.24144i			0.413703i	0.978372	+	0.206852i	$0.0663218\pi$
$499$			9.24144i			0.413703i	−0.978372	+	0.206852i	$0.933678\pi$
$500$			1.00000i			0.0447214i
$501$	2.00000	+	0.240439i	0.0893534	+	0.0107420i
$502$		−	5.73203i		−	0.255833i
$503$			16.0953i			0.717653i	0.933404	+	0.358827i	$0.116823\pi$
$503$			16.0953i			0.717653i	−0.933404	+	0.358827i	$0.883177\pi$
$504$	0.840195	−	3.44392i	0.0374253	−	0.153404i
$505$	13.3740			0.595134
$506$			1.83348i			0.0815082i
$507$	−2.01367	−	0.242082i	−0.0894300	−	0.0107512i
$508$			14.7956i			0.656446i
$509$	−4.54361			−0.201392			−0.100696	−	0.994917i	$-0.532107\pi$
$509$	−4.54361			−0.201392			−0.100696	+	0.994917i	$0.532107\pi$
$510$	7.82904	+	0.941203i	0.346676	+	0.0416772i
$511$		−	5.52708i		−	0.244504i
$512$		−	1.00000i		−	0.0441942i
$513$	−32.3396	−	12.1335i	−1.42783	−	0.535705i
$514$	−4.35803			−0.192225
$515$		−	6.40696i		−	0.282324i
$516$	−1.41180	+	11.7436i	−0.0621512	+	0.516981i
$517$			2.31075i			0.101627i
$518$	11.6149			0.510328
$519$	−0.802639	+	6.67645i	−0.0352320	+	0.293064i
$520$			3.43934i			0.150825i
$521$		−	32.0864i		−	1.40573i	−0.711323	−	0.702865i	$-0.751904\pi$
$521$		−	32.0864i		−	1.40573i	0.711323	−	0.702865i	$-0.248096\pi$
$522$	−5.83283	+	23.9085i	−0.255296	+	1.04645i
$523$			34.3945i			1.50396i	0.659183	+	0.751982i	$0.270902\pi$
$523$			34.3945i			1.50396i	−0.659183	+	0.751982i	$0.729098\pi$
$524$		−	2.84416i		−	0.124248i
$525$	−2.03203	−	0.244290i	−0.0886852	−	0.0106617i
$526$		−	17.8491i		−	0.778258i
$527$	25.3435	+	0.480878i	1.10398	+	0.0209474i
$528$	−2.71104	−	0.325920i	−0.117983	−	0.0141838i
$529$	−21.6474			−0.941191
$530$	−7.16734			−0.311329
$531$	−4.86648	+	19.9474i	−0.211187	+	0.865645i
$532$	7.85484			0.340551
$533$	−18.6484			−0.807750
$534$	−2.12284	+	17.6581i	−0.0918645	+	0.764140i
$535$	9.49156			0.410356
$536$		−	13.6144i		−	0.588053i
$537$	−18.2992	−	2.19992i	−0.789667	−	0.0949334i
$538$		−	5.38862i		−	0.232320i
$539$	−8.83421			−0.380517
$540$	−1.82529	+	4.86501i	−0.0785482	+	0.209357i
$541$	6.24569			0.268523			0.134262	−	0.990946i	$-0.457134\pi$
$541$	6.24569			0.268523			0.134262	+	0.990946i	$0.457134\pi$
$542$	29.0008			1.24569
$543$	3.48572	−	28.9947i	0.149587	−	1.24428i
$544$			4.55264i			0.195193i
$545$		−	14.8139i		−	0.634558i
$546$	−6.98884	−	0.840195i	−0.299095	−	0.0359570i
$547$	8.65265			0.369960			0.184980	−	0.982742i	$-0.440778\pi$
$547$	8.65265			0.369960			0.184980	+	0.982742i	$0.440778\pi$
$548$	5.52980			0.236221
$549$	8.42213	−	34.5219i	0.359448	−	1.47336i
$550$			1.57649i			0.0672218i
$551$	−54.5301			−2.32306
$552$	−0.240439	+	2.00000i	−0.0102338	+	0.0851257i
$553$		−	7.25311i		−	0.308434i
$554$	−0.131535			−0.00558837
$555$	−16.9034	−	2.03211i	−0.717508	−	0.0862584i
$556$		−	21.6833i		−	0.919575i
$557$	−10.2362			−0.433721			−0.216861	−	0.976203i	$-0.569582\pi$
$557$	−10.2362			−0.433721			−0.216861	+	0.976203i	$0.569582\pi$
$558$	−4.26604	+	16.1493i	−0.180596	+	0.683656i
$559$	23.4871			0.993399
$560$		−	1.18164i		−	0.0499335i
$561$	12.3424	+	1.48380i	0.521097	+	0.0626460i
$562$	−0.682894			−0.0288061
$563$		−	25.3464i		−	1.06822i	−0.845414	−	0.534112i	$-0.820646\pi$
$563$		−	25.3464i		−	1.06822i	0.845414	−	0.534112i	$-0.179354\pi$
$564$	−0.303027	+	2.52061i	−0.0127597	+	0.106137i
$565$	17.6839			0.743966
$566$		−	10.0953i		−	0.424336i
$567$	−9.43995	−	4.89753i	−0.396441	−	0.205677i
$568$	6.52980			0.273984
$569$	18.0733			0.757674			0.378837	−	0.925463i	$-0.376324\pi$
$569$	18.0733			0.757674			0.378837	+	0.925463i	$0.376324\pi$
$570$	−11.4313	−	1.37427i	−0.478805	−	0.0575617i
$571$		−	0.635396i		−	0.0265905i	−0.999912	−	0.0132953i	$-0.995768\pi$
$571$		−	0.635396i		−	0.0265905i	0.999912	−	0.0132953i	$-0.00423214\pi$
$572$			5.42208i			0.226709i
$573$	−5.42838	+	45.1539i	−0.226774	+	1.88633i
$574$	6.40696			0.267421
$575$	1.16301			0.0485011
$576$	−2.91452	−	0.711040i	−0.121438	−	0.0296267i
$577$	31.0365			1.29207			0.646033	−	0.763310i	$-0.276427\pi$
$577$	31.0365			1.29207			0.646033	+	0.763310i	$0.276427\pi$
$578$		−	3.72657i		−	0.155005i
$579$	35.3322	+	4.24761i	1.46835	+	0.176525i
$580$			8.20323i			0.340621i
$581$	4.56331			0.189318
$582$	−0.716502	+	5.95995i	−0.0297000	+	0.247048i
$583$	−11.2992			−0.467967
$584$	−4.67746			−0.193555
$585$	10.0240	+	2.44551i	0.414442	+	0.101109i
$586$	31.3464			1.29491
$587$	−13.3315			−0.550248			−0.275124	−	0.961409i	$-0.588719\pi$
$587$	−13.3315			−0.550248			−0.275124	+	0.961409i	$0.588719\pi$
$588$	−9.63654	−	1.15850i	−0.397404	−	0.0477758i
$589$	−37.0045	−	0.702138i	−1.52474	−	0.0289311i
$590$			6.84416i			0.281770i
$591$	−9.29293	−	1.11719i	−0.382260	−	0.0459551i
$592$		−	9.82943i		−	0.403987i
$593$		−	0.630480i		−	0.0258907i	−0.999916	−	0.0129453i	$-0.995879\pi$
$593$		−	0.630480i		−	0.0258907i	0.999916	−	0.0129453i	$-0.00412075\pi$
$594$	−2.87756	+	7.66964i	−0.118068	+	0.314689i
$595$			5.37959i			0.220542i
$596$		−	6.52980i		−	0.267471i
$597$	−1.30004	+	10.8139i	−0.0532072	+	0.442584i
$598$	4.00000			0.163572
$599$			29.3340i			1.19856i	0.800541	+	0.599278i	$0.204546\pi$
$599$			29.3340i			1.19856i	−0.800541	+	0.599278i	$0.795454\pi$
$600$	−0.206738	+	1.71967i	−0.00844003	+	0.0702052i
$601$		−	28.6093i		−	1.16700i	−0.812114	−	0.583499i	$-0.801683\pi$
$601$		−	28.6093i		−	1.16700i	0.812114	−	0.583499i	$-0.198317\pi$
$602$	−8.06939			−0.328884
$603$	−39.6794	−	9.68039i	−1.61587	−	0.394216i
$604$			9.72099i			0.395541i
$605$		−	8.51468i		−	0.346171i
$606$	22.9988	+	2.76490i	0.934262	+	0.112316i
$607$	−20.7561			−0.842464			−0.421232	−	0.906953i	$-0.638402\pi$
$607$	−20.7561			−0.842464			−0.421232	+	0.906953i	$0.638402\pi$
$608$		−	6.64740i		−	0.269588i
$609$	−16.6692	−	2.00397i	−0.675471	−	0.0812048i
$610$		−	11.8448i		−	0.479582i
$611$	5.04122			0.203946
$612$	13.2688	+	3.23711i	0.536358	+	0.130853i
$613$		−	17.8581i		−	0.721284i	−0.932704	−	0.360642i	$-0.882558\pi$
$613$		−	17.8581i		−	0.721284i	0.932704	−	0.360642i	$-0.117442\pi$
$614$			11.4863i			0.463550i
$615$	−9.32418	−	1.12095i	−0.375987	−	0.0452010i
$616$		−	1.86285i		−	0.0750562i
$617$		−	12.4017i		−	0.499274i	−0.968340	−	0.249637i	$-0.919689\pi$
$617$		−	12.4017i		−	0.499274i	0.968340	−	0.249637i	$-0.0803113\pi$
$618$	1.32456	−	11.0178i	0.0532816	−	0.443203i
$619$		−	24.5533i		−	0.986879i	−0.869780	−	0.493440i	$-0.835739\pi$
$619$		−	24.5533i		−	0.986879i	0.869780	−	0.493440i	$-0.164261\pi$
$620$	−0.105626	+	5.56676i	−0.00424205	+	0.223567i
$621$	5.65808	+	2.12284i	0.227051	+	0.0851868i
$622$	1.22976			0.0493088
$623$	−12.1335			−0.486117
$624$	−0.711040	+	5.91452i	−0.0284644	+	0.236770i
$625$	1.00000			0.0400000
$626$	−2.64912			−0.105880
$627$	−18.0214	−	2.16652i	−0.719704	−	0.0865224i
$628$	−22.0161			−0.878538
$629$			44.7499i			1.78430i
$630$	−3.44392	−	0.840195i	−0.137209	−	0.0334742i
$631$		−	20.9901i		−	0.835604i	−0.908538	−	0.417802i	$-0.862801\pi$
$631$		−	20.9901i		−	0.835604i	0.908538	−	0.417802i	$-0.137199\pi$
$632$	−6.13816			−0.244163
$633$	17.3328	+	2.08374i	0.688918	+	0.0828214i
$634$	17.6581			0.701292
$635$	14.7956			0.587144
$636$	−12.3254	−	1.48176i	−0.488736	−	0.0587555i
$637$			19.2731i			0.763628i
$638$			12.9323i			0.511995i
$639$	4.64295	−	19.0312i	0.183672	−	0.752864i
$640$	−1.00000			−0.0395285
$641$	30.3243			1.19774			0.598868	−	0.800847i	$-0.295617\pi$
$641$	30.3243			1.19774			0.598868	+	0.800847i	$0.295617\pi$
$642$	16.3223	+	1.96226i	0.644191	+	0.0774443i
$643$		−	0.443485i		−	0.0174893i	−0.999962	−	0.00874467i	$-0.997216\pi$
$643$		−	0.443485i		−	0.0174893i	0.999962	−	0.00874467i	$-0.00278355\pi$
$644$	−1.37427			−0.0541537
$645$	11.7436	+	1.41180i	0.462402	+	0.0555897i
$646$			30.2632i			1.19069i
$647$	42.7074			1.67900			0.839500	−	0.543360i	$-0.182848\pi$
$647$	42.7074			1.67900			0.839500	+	0.543360i	$0.182848\pi$
$648$	−4.14468	+	7.98884i	−0.162818	+	0.313831i
$649$			10.7898i			0.423535i
$650$	3.43934			0.134902
$651$	−11.2860	−	1.57454i	−0.442335	−	0.0617111i
$652$	−14.4283			−0.565057
$653$		−	10.1390i		−	0.396768i	−0.980124	−	0.198384i	$-0.936431\pi$
$653$		−	10.1390i		−	0.396768i	0.980124	−	0.198384i	$-0.0635693\pi$
$654$	3.06259	−	25.4750i	0.119757	−	0.996152i
$655$	−2.84416			−0.111131
$656$		−	5.42208i		−	0.211697i
$657$	−3.32586	+	13.6325i	−0.129754	+	0.531856i
$658$	−1.73200			−0.0675203
$659$		−	8.63922i		−	0.336536i	−0.985741	−	0.168268i	$-0.946183\pi$
$659$		−	8.63922i		−	0.336536i	0.985741	−	0.168268i	$-0.0538174\pi$
$660$	−0.325920	+	2.71104i	−0.0126864	+	0.105527i
$661$	−36.6412			−1.42518			−0.712589	−	0.701582i	$-0.752477\pi$
$661$	−36.6412			−1.42518			−0.712589	+	0.701582i	$0.752477\pi$
$662$	36.3183			1.41155
$663$	3.23711	−	26.9267i	0.125719	−	1.04575i
$664$		−	3.86184i		−	0.149869i
$665$		−	7.85484i		−	0.304598i
$666$	−28.6481	−	6.98912i	−1.11009	−	0.270823i
$667$	9.54048			0.369409
$668$	1.16301			0.0449984
$669$	−2.62953	+	21.8727i	−0.101663	+	0.845648i
$670$	−13.6144			−0.525970
$671$		−	18.6732i		−	0.720871i
$672$	0.244290	−	2.03203i	0.00942369	−	0.0783873i
$673$		−	44.1754i		−	1.70284i	−0.524487	−	0.851418i	$-0.675743\pi$
$673$		−	44.1754i		−	1.70284i	0.524487	−	0.851418i	$-0.324257\pi$
$674$	−27.9926			−1.07823
$675$	4.86501	+	1.82529i	0.187254	+	0.0702556i
$676$	−1.17096			−0.0450370
$677$	−39.6526			−1.52397			−0.761986	−	0.647594i	$-0.775776\pi$
$677$	−39.6526			−1.52397			−0.761986	+	0.647594i	$0.775776\pi$
$678$	30.4104	+	3.65592i	1.16790	+	0.140405i
$679$	−4.09528			−0.157162
$680$	4.55264			0.174586
$681$	2.55026	−	21.2133i	0.0977261	−	0.812897i
$682$	−0.166518	+	8.77595i	−0.00637632	+	0.336048i
$683$		−	47.0748i		−	1.80127i	−0.434581	−	0.900633i	$-0.643103\pi$
$683$		−	47.0748i		−	1.80127i	0.434581	−	0.900633i	$-0.356897\pi$
$684$	−19.3740	−	4.72657i	−0.740782	−	0.180725i
$685$		−	5.52980i		−	0.211283i
$686$		−	14.8931i		−	0.568621i
$687$	0.711517	−	5.91849i	0.0271461	−	0.225804i
$688$			6.82897i			0.260352i
$689$			24.6509i			0.939124i
$690$	2.00000	+	0.240439i	0.0761387	+	0.00915335i
$691$	15.3740			0.584853			0.292427	−	0.956288i	$-0.405537\pi$
$691$	15.3740			0.584853			0.292427	+	0.956288i	$0.405537\pi$
$692$			3.88241i			0.147587i
$693$	−5.42930	−	1.32456i	−0.206242	−	0.0503158i
$694$		−	0.131535i		−	0.00499299i
$695$	−21.6833			−0.822493
$696$	−1.69592	+	14.1068i	−0.0642836	+	0.534718i
$697$			24.6848i			0.935004i
$698$			13.2734i			0.502407i
$699$	3.06793	−	25.5194i	0.116040	−	0.965232i
$700$	−1.18164			−0.0446619
$701$			3.33322i			0.125894i	0.998017	+	0.0629469i	$0.0200499\pi$
$701$			3.33322i			0.125894i	−0.998017	+	0.0629469i	$0.979950\pi$
$702$	16.7324	+	6.27780i	0.631524	+	0.236940i
$703$		−	65.3401i		−	2.46435i
$704$	−1.57649			−0.0594162
$705$	2.52061	+	0.303027i	0.0949317	+	0.0114126i
$706$			23.1169i			0.870015i
$707$			15.8032i			0.594342i
$708$	−1.41495	+	11.7697i	−0.0531769	+	0.442332i
$709$		−	9.73232i		−	0.365505i	−0.983159	−	0.182753i	$-0.941499\pi$
$709$		−	9.73232i		−	0.365505i	0.983159	−	0.182753i	$-0.0585007\pi$
$710$		−	6.52980i		−	0.245059i
$711$	−4.36448	+	17.8898i	−0.163681	+	0.670920i
$712$			10.2683i			0.384821i
$713$	6.47423	+	0.122845i	0.242462	+	0.00460057i
$714$	−1.11216	+	9.25112i	−0.0416217	+	0.346214i
$715$	5.42208			0.202774
$716$	−10.6411			−0.397677
$717$	4.26624	+	0.512885i	0.159326	+	0.0191541i
$718$	−28.5201			−1.06436
$719$	44.2748			1.65117			0.825586	−	0.564276i	$-0.190845\pi$
$719$	44.2748			1.65117			0.825586	+	0.564276i	$0.190845\pi$
$720$	−0.711040	+	2.91452i	−0.0264989	+	0.108618i
$721$	7.57073			0.281949
$722$		−	25.1879i		−	0.937396i
$723$	−2.67320	+	22.2360i	−0.0994174	+	0.826966i
$724$		−	16.8606i		−	0.626620i
$725$	8.20323			0.304660
$726$	1.76030	−	14.6424i	0.0653310	−	0.543431i
$727$	7.70700			0.285837			0.142918	−	0.989734i	$-0.454351\pi$
$727$	7.70700			0.285837			0.142918	+	0.989734i	$0.454351\pi$
$728$	−4.06406			−0.150624
$729$	20.3366	+	17.7601i	0.753207	+	0.657783i
$730$			4.67746i			0.173120i
$731$		−	31.0899i		−	1.14990i
$732$	2.44876	−	20.3691i	0.0905089	−	0.752864i
$733$	34.7400			1.28315			0.641575	−	0.767060i	$-0.278281\pi$
$733$	34.7400			1.28315			0.641575	+	0.767060i	$0.278281\pi$
$734$	17.5260			0.646897
$735$	−1.15850	+	9.63654i	−0.0427319	+	0.355449i
$736$			1.16301i			0.0428693i
$737$	−21.4630			−0.790599
$738$	−15.8028	−	3.85532i	−0.581708	−	0.141916i
$739$		−	30.2620i		−	1.11321i	−0.830779	−	0.556603i	$-0.812104\pi$
$739$		−	30.2620i		−	1.11321i	0.830779	−	0.556603i	$-0.187896\pi$
$740$	−9.82943			−0.361337
$741$	−4.72657	+	39.3162i	−0.173635	+	1.44431i
$742$		−	8.46922i		−	0.310915i
$743$	15.6965			0.575849			0.287925	−	0.957653i	$-0.407035\pi$
$743$	15.6965			0.575849			0.287925	+	0.957653i	$0.407035\pi$
$744$	−1.33250	+	9.55115i	−0.0488519	+	0.350162i
$745$	−6.52980			−0.239233
$746$		−	9.14170i		−	0.334701i
$747$	−11.2554	−	2.74593i	−0.411814	−	0.100468i
$748$	7.17720			0.262424
$749$			11.2156i			0.409810i
$750$	1.71967	+	0.206738i	0.0627934	+	0.00754899i
$751$	−8.88864			−0.324351			−0.162176	−	0.986762i	$-0.551851\pi$
$751$	−8.88864			−0.324351			−0.162176	+	0.986762i	$0.551851\pi$
$752$			1.46575i			0.0534506i
$753$	−9.85719	−	1.18503i	−0.359216	−	0.0431847i
$754$	28.2137			1.02748
$755$	9.72099			0.353783
$756$	−5.74870	−	2.15684i	−0.209078	−	0.0784437i
$757$		−	15.7490i		−	0.572407i	−0.958169	−	0.286204i	$-0.907607\pi$
$757$		−	15.7490i		−	0.572407i	0.958169	−	0.286204i	$-0.0923934\pi$
$758$			2.25387i			0.0818641i
$759$	3.15298	+	0.379050i	0.114446	+	0.0137586i
$760$	−6.64740			−0.241126
$761$	27.2961			0.989483			0.494742	−	0.869040i	$-0.335263\pi$
$761$	27.2961			0.989483			0.494742	+	0.869040i	$0.335263\pi$
$762$	25.4434	+	3.05880i	0.921719	+	0.110809i
$763$	17.5047			0.633714
$764$			26.2574i			0.949958i
$765$	3.23711	−	13.2688i	0.117038	−	0.479733i
$766$			5.43602i			0.196412i
$767$	23.5394			0.849958
$768$	−1.71967	−	0.206738i	−0.0620532	−	0.00746000i
$769$	−34.1753			−1.23239			−0.616196	−	0.787593i	$-0.711327\pi$
$769$	−34.1753			−1.23239			−0.616196	+	0.787593i	$0.711327\pi$
$770$	−1.86285			−0.0671323
$771$	−0.900969	+	7.49437i	−0.0324476	+	0.269903i
$772$	20.5459			0.739464
$773$	−3.28221			−0.118053			−0.0590264	−	0.998256i	$-0.518800\pi$
$773$	−3.28221			−0.118053			−0.0590264	+	0.998256i	$0.518800\pi$
$774$	19.9032	+	4.85567i	0.715404	+	0.174533i
$775$	5.56676	+	0.105626i	0.199964	+	0.00379420i
$776$			3.46575i			0.124413i
$777$	2.40123	−	19.9737i	0.0861437	−	0.716553i
$778$		−	37.6062i		−	1.34825i
$779$		−	36.0427i		−	1.29136i
$780$	5.91452	+	0.711040i	0.211774	+	0.0254593i
$781$		−	10.2942i		−	0.368354i
$782$		−	5.29479i		−	0.189341i
$783$	39.9088	+	14.9733i	1.42622	+	0.535103i
$784$	−5.60372			−0.200133
$785$			22.0161i			0.785789i
$786$	−4.89101	−	0.587995i	−0.174457	−	0.0209731i
$787$			32.1550i			1.14620i	0.819485	+	0.573101i	$0.194260\pi$
$787$			32.1550i			1.14620i	−0.819485	+	0.573101i	$0.805740\pi$
$788$	−5.40391			−0.192506
$789$	−30.6946	−	3.69008i	−1.09276	−	0.131370i
$790$			6.13816i			0.218386i
$791$			20.8960i			0.742977i
$792$	−1.12095	+	4.59471i	−0.0398312	+	0.163266i
$793$	−40.7382			−1.44666
$794$		−	18.1656i		−	0.644672i
$795$	−1.48176	+	12.3254i	−0.0525526	+	0.437138i
$796$			6.28837i			0.222885i
$797$	5.20507			0.184373			0.0921866	−	0.995742i	$-0.470614\pi$
$797$	5.20507			0.184373			0.0921866	+	0.995742i	$0.470614\pi$
$798$	1.62389	−	13.5077i	0.0574851	−	0.478168i
$799$		−	6.67306i		−	0.236076i
$800$			1.00000i			0.0353553i
$801$	29.9272	+	7.30118i	1.05742	+	0.257974i
$802$			27.8508i			0.983445i
$803$			7.37396i			0.260222i
$804$	−23.4123	−	2.81461i	−0.825687	−	0.0992636i
$805$			1.37427i			0.0484365i
$806$	19.1460	+	0.363284i	0.674388	+	0.0127961i
$807$	−9.26665	−	1.11403i	−0.326201	−	0.0392158i
$808$	13.3740			0.470494
$809$	−37.0068			−1.30109			−0.650546	−	0.759467i	$-0.725460\pi$
$809$	−37.0068			−1.30109			−0.650546	+	0.759467i	$0.725460\pi$
$810$	7.98884	+	4.14468i	0.280699	+	0.145629i
$811$	−26.6990			−0.937529			−0.468764	−	0.883323i	$-0.655301\pi$
$811$	−26.6990			−0.937529			−0.468764	+	0.883323i	$0.655301\pi$
$812$	−9.69328			−0.340168
$813$	5.99556	−	49.8718i	0.210273	−	1.74908i
$814$	−15.4960			−0.543135
$815$			14.4283i			0.505402i
$816$	7.82904	+	0.941203i	0.274071	+	0.0329487i
$817$			45.3948i			1.58816i
$818$	−2.73048			−0.0954689
$819$	−2.88971	+	11.8448i	−0.100975	+	0.413891i
$820$	−5.42208			−0.189347
$821$	13.8371			0.482917			0.241458	−	0.970411i	$-0.422374\pi$
$821$	13.8371			0.482917			0.241458	+	0.970411i	$0.422374\pi$
$822$	1.14322	−	9.50943i	0.0398743	−	0.331679i
$823$		−	16.8720i		−	0.588119i	−0.955787	−	0.294060i	$-0.904994\pi$
$823$		−	16.8720i		−	0.588119i	0.955787	−	0.294060i	$-0.0950065\pi$
$824$		−	6.40696i		−	0.223197i
$825$	2.71104	+	0.325920i	0.0943863	+	0.0113471i
$826$	−8.08735			−0.281395
$827$	52.8196			1.83672			0.918359	−	0.395748i	$-0.129515\pi$
$827$	52.8196			1.83672			0.918359	+	0.395748i	$0.129515\pi$
$828$	3.38963	+	0.826951i	0.117798	+	0.0287385i
$829$		−	25.2938i		−	0.878489i	−0.898367	−	0.439245i	$-0.855246\pi$
$829$		−	25.2938i		−	0.878489i	0.898367	−	0.439245i	$-0.144754\pi$
$830$	−3.86184			−0.134046
$831$	−0.0271932	+	0.226196i	−0.000943320	+	0.00784665i
$832$			3.43934i			0.119238i
$833$	25.5118			0.883930
$834$	−37.2880	−	4.48274i	−1.29118	−	0.155225i
$835$		−	1.16301i		−	0.0402478i
$836$	−10.4796			−0.362443
$837$	26.8895	+	10.6749i	0.929439	+	0.368977i
$838$	3.91265			0.135160
$839$			30.6893i			1.05951i	0.848150	+	0.529756i	$0.177717\pi$
$839$			30.6893i			1.05951i	−0.848150	+	0.529756i	$0.822283\pi$
$840$	−2.03203	−	0.244290i	−0.0701118	−	0.00842880i
$841$	38.2930			1.32045
$842$			5.57073i			0.191980i
$843$	−0.141180	+	1.17435i	−0.00486249	+	0.0404468i
$844$	10.0792			0.346939
$845$			1.17096i			0.0402823i
$846$	4.27197	+	1.04221i	0.146873	+	0.0358319i
$847$	10.0613			0.345710
$848$	−7.16734			−0.246127
$849$	−17.3605	−	2.08707i	−0.595812	−	0.0716282i
$850$		−	4.55264i		−	0.156154i
$851$			11.4318i			0.391876i
$852$	1.34996	−	11.2291i	0.0462487	−	0.384702i
$853$	22.9779			0.786747			0.393374	−	0.919379i	$-0.371308\pi$
$853$	22.9779			0.786747			0.393374	+	0.919379i	$0.371308\pi$
$854$	13.9963			0.478944
$855$	−4.72657	+	19.3740i	−0.161645	+	0.662576i
$856$	9.49156			0.324415
$857$		−	32.0982i		−	1.09645i	−0.836330	−	0.548227i	$-0.815303\pi$
$857$		−	32.0982i		−	1.09645i	0.836330	−	0.548227i	$-0.184697\pi$
$858$	9.32418	+	1.12095i	0.318322	+	0.0382685i
$859$		−	18.3241i		−	0.625209i	−0.949883	−	0.312604i	$-0.898799\pi$
$859$		−	18.3241i		−	0.625209i	0.949883	−	0.312604i	$-0.101201\pi$
$860$	6.82897			0.232866
$861$	1.32456	−	11.0178i	0.0451409	−	0.375487i
$862$	−18.9412			−0.645140
$863$	−36.1664			−1.23112			−0.615560	−	0.788090i	$-0.711070\pi$
$863$	−36.1664			−1.23112			−0.615560	+	0.788090i	$0.711070\pi$
$864$	−1.82529	+	4.86501i	−0.0620978	+	0.165511i
$865$	3.88241			0.132006
$866$	33.6653			1.14399
$867$	−6.40846	−	0.770422i	−0.217643	−	0.0261649i
$868$	−6.57792	−	0.124812i	−0.223269	−	0.00423640i
$869$			9.67675i			0.328261i
$870$	14.1068	+	1.69592i	0.478267	+	0.0574970i
$871$			46.8245i			1.58659i
$872$		−	14.8139i		−	0.501662i
$873$	10.1010	+	2.46429i	0.341867	+	0.0834036i
$874$			7.73102i			0.261506i
$875$			1.18164i			0.0399468i
$876$	−0.967006	+	8.04367i	−0.0326721	+	0.271771i
$877$	−5.02482			−0.169676			−0.0848380	−	0.996395i	$-0.527037\pi$
$877$	−5.02482			−0.169676			−0.0848380	+	0.996395i	$0.527037\pi$
$878$		−	25.8504i		−	0.872409i
$879$	6.48048	−	53.9054i	0.218581	−	1.81818i
$880$			1.57649i			0.0531435i
$881$	−24.6770			−0.831389			−0.415695	−	0.909504i	$-0.636461\pi$
$881$	−24.6770			−0.831389			−0.415695	+	0.909504i	$0.636461\pi$
$882$	−3.98447	+	16.3322i	−0.134164	+	0.549932i
$883$			27.6485i			0.930447i	0.885193	+	0.465224i	$0.154026\pi$
$883$			27.6485i			0.930447i	−0.885193	+	0.465224i	$0.845974\pi$
$884$		−	15.6581i		−	0.526638i
$885$	11.7697	+	1.41495i	0.395634	+	0.0475629i
$886$	−3.89058			−0.130707
$887$			30.8122i			1.03457i	0.855813	+	0.517285i	$0.173057\pi$
$887$			30.8122i			1.03457i	−0.855813	+	0.517285i	$0.826943\pi$
$888$	−16.9034	−	2.03211i	−0.567240	−	0.0681933i
$889$			17.4830i			0.586362i
$890$	10.2683			0.344194
$891$	12.5943	+	6.53405i	0.421926	+	0.218899i
$892$			12.7191i			0.425868i
$893$			9.74345i			0.326052i
$894$	−11.2291	−	1.34996i	−0.375557	−	0.0451493i
$895$			10.6411i			0.355693i
$896$		−	1.18164i		−	0.0394759i
$897$	0.826951	−	6.87867i	0.0276111	−	0.229672i
$898$			16.8673i			0.562871i
$899$	45.6654	+	0.866475i	1.52303	+	0.0288986i
$900$	2.91452	+	0.711040i	0.0971506	+	0.0237013i
$901$	32.6303			1.08707
$902$	−8.54786			−0.284613
$903$	−1.66825	+	13.8767i	−0.0555158	+	0.461787i
$904$	17.6839			0.588157
$905$	−16.8606			−0.560466
$906$	16.7169	+	2.00969i	0.555381	+	0.0667676i
$907$	−1.99207			−0.0661455			−0.0330727	−	0.999453i	$-0.510529\pi$
$907$	−1.99207			−0.0661455			−0.0330727	+	0.999453i	$0.510529\pi$
$908$		−	12.3357i		−	0.409375i
$909$	9.50943	−	38.9787i	0.315408	−	1.29284i
$910$			4.06406i			0.134722i
$911$	−28.2930			−0.937390			−0.468695	−	0.883360i	$-0.655276\pi$
$911$	−28.2930			−0.937390			−0.468695	+	0.883360i	$0.655276\pi$
$912$	−11.4313	−	1.37427i	−0.378529	−	0.0455065i
$913$	−6.08815			−0.201489
$914$	−6.15575			−0.203614
$915$	−20.3691	−	2.44876i	−0.673382	−	0.0809537i
$916$		−	3.44164i		−	0.113715i
$917$		−	3.36078i		−	0.110983i
$918$	8.30992	−	22.1486i	0.274268	−	0.731014i
$919$	23.2183			0.765901			0.382951	−	0.923769i	$-0.374908\pi$
$919$	23.2183			0.765901			0.382951	+	0.923769i	$0.374908\pi$
$920$	1.16301			0.0383435
$921$	19.7526	+	2.37465i	0.650872	+	0.0782474i
$922$		−	6.44714i		−	0.212325i
$923$	−22.4582			−0.739220
$924$	−3.20348	−	0.385121i	−0.105387	−	0.0126695i
$925$			9.82943i			0.323190i
$926$	29.6849			0.975506
$927$	−18.6732	−	4.55561i	−0.613308	−	0.149626i
$928$			8.20323i			0.269284i
$929$	15.4931			0.508311			0.254156	−	0.967163i	$-0.418202\pi$
$929$	15.4931			0.508311			0.254156	+	0.967163i	$0.418202\pi$
$930$	9.55115	+	1.33250i	0.313195	+	0.0436944i
$931$	−37.2502			−1.22082
$932$		−	14.8397i		−	0.486091i
$933$	0.254237	−	2.11478i	0.00832336	−	0.0692347i
$934$	17.1558			0.561356
$935$		−	7.17720i		−	0.234719i
$936$	10.0240	+	2.44551i	0.327645	+	0.0799339i
$937$	33.8512			1.10587			0.552935	−	0.833224i	$-0.313508\pi$
$937$	33.8512			1.10587			0.552935	+	0.833224i	$0.313508\pi$
$938$		−	16.0873i		−	0.525271i
$939$	−0.547673	+	4.55561i	−0.0178726	+	0.148667i
$940$	1.46575			0.0478076
$941$	32.4549			1.05800			0.528999	−	0.848622i	$-0.322567\pi$
$941$	32.4549			1.05800			0.528999	+	0.848622i	$0.322567\pi$
$942$	−4.55156	+	37.8604i	−0.148298	+	1.23356i
$943$			6.30596i			0.205350i
$944$			6.84416i			0.222758i
$945$	−2.15684	+	5.74870i	−0.0701622	+	0.187005i
$946$	10.7658			0.350026
$947$	−7.36847			−0.239443			−0.119722	−	0.992808i	$-0.538200\pi$
$947$	−7.36847			−0.239443			−0.119722	+	0.992808i	$0.538200\pi$
$948$	−1.26899	+	10.5556i	−0.0412149	+	0.342830i
$949$	16.0873			0.522217
$950$			6.64740i			0.215670i
$951$	3.65059	−	30.3660i	0.118378	−	0.984686i
$952$			5.37959i			0.174354i
$953$	46.3285			1.50073			0.750364	−	0.661024i	$-0.229878\pi$
$953$	46.3285			1.50073			0.750364	+	0.661024i	$0.229878\pi$
$954$	−5.09627	+	20.8893i	−0.164998	+	0.676317i
$955$	26.2574			0.849668
$956$	2.48085			0.0802365
$957$	22.2393	+	2.67360i	0.718894	+	0.0864251i
$958$	−28.7338			−0.928347
$959$	6.53425			0.211002
$960$	−0.206738	+	1.71967i	−0.00667243	+	0.0555021i
$961$	30.9777	+	1.17599i	0.999280	+	0.0379352i
$962$			33.8067i			1.08997i
$963$	6.74888	−	27.6633i	0.217480	−	0.891438i
$964$			12.9304i			0.416460i
$965$		−	20.5459i		−	0.661396i
$966$	−0.284113	+	2.36328i	−0.00914118	+	0.0760374i
$967$		−	46.2902i		−	1.48859i	−0.667850	−	0.744296i	$-0.732785\pi$
$967$		−	46.2902i		−	1.48859i	0.667850	−	0.744296i	$-0.267215\pi$
$968$		−	8.51468i		−	0.273672i
$969$	52.0427	+	6.25655i	1.67185	+	0.200989i
$970$	3.46575			0.111279
$971$		−	50.8264i		−	1.63110i	−0.578689	−	0.815548i	$-0.696436\pi$
$971$		−	50.8264i		−	1.63110i	0.578689	−	0.815548i	$-0.303564\pi$
$972$	12.8813	+	8.77907i	0.413168	+	0.281589i
$973$		−	25.6218i		−	0.821398i
$974$	9.91982			0.317851
$975$	0.711040	−	5.91452i	0.0227715	−	0.189416i
$976$		−	11.8448i		−	0.379143i
$977$			43.9331i			1.40554i	0.711416	+	0.702772i	$0.248054\pi$
$977$			43.9331i			1.40554i	−0.711416	+	0.702772i	$0.751946\pi$
$978$	−2.98288	+	24.8119i	−0.0953819	+	0.793398i
$979$	16.1879			0.517367
$980$			5.60372i			0.179004i
$981$	−43.1754	−	10.5333i	−1.37849	−	0.336302i
$982$			26.2946i			0.839095i
$983$	47.5531			1.51671			0.758354	−	0.651843i	$-0.226004\pi$
$983$	47.5531			1.51671			0.758354	+	0.651843i	$0.226004\pi$
$984$	−9.32418	−	1.12095i	−0.297244	−	0.0357345i
$985$			5.40391i			0.172183i
$986$		−	37.3464i		−	1.18935i
$987$	−0.358069	+	2.97846i	−0.0113975	+	0.0948054i
$988$			22.8626i			0.727357i
$989$		−	7.94219i		−	0.252547i
$990$	4.59471	+	1.12095i	0.146029	+	0.0356261i
$991$		−	50.6232i		−	1.60810i	−0.594562	−	0.804050i	$-0.702675\pi$
$991$		−	50.6232i		−	1.60810i	0.594562	−	0.804050i	$-0.297325\pi$
$992$	−0.105626	+	5.56676i	−0.00335363	+	0.176745i
$993$	7.50837	−	62.4555i	0.238271	−	1.98197i
$994$	7.71589			0.244733
$995$	6.28837			0.199355
$996$	−6.64109	−	0.798388i	−0.210431	−	0.0252979i
$997$	−38.6333			−1.22353			−0.611764	−	0.791040i	$-0.709540\pi$
$997$	−38.6333			−1.22353			−0.611764	+	0.791040i	$0.709540\pi$
$998$	9.24144			0.292533
$999$	−17.9416	+	47.8203i	−0.567647	+	1.51297i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.h.d.371.1	✓	16
3.2	odd	2	inner	930.2.h.d.371.16	yes	16
31.30	odd	2	inner	930.2.h.d.371.8	yes	16
93.92	even	2	inner	930.2.h.d.371.9	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.h.d.371.1	✓	16	1.1	even	1	trivial
930.2.h.d.371.8	yes	16	31.30	odd	2	inner
930.2.h.d.371.9	yes	16	93.92	even	2	inner
930.2.h.d.371.16	yes	16	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-1.71967 - 0.206738i) q^{3} -1.00000 q^{4} +1.00000i q^{5} +(-0.206738 + 1.71967i) q^{6} -1.18164 q^{7} +1.00000i q^{8} +(2.91452 + 0.711040i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-1.71967 - 0.206738i) q^{3} -1.00000 q^{4} +1.00000i q^{5} +(-0.206738 + 1.71967i) q^{6} -1.18164 q^{7} +1.00000i q^{8} +(2.91452 + 0.711040i) q^{9} +1.00000 q^{10} +1.57649 q^{11} +(1.71967 + 0.206738i) q^{12} -3.43934i q^{13} +1.18164i q^{14} +(0.206738 - 1.71967i) q^{15} +1.00000 q^{16} -4.55264 q^{17} +(0.711040 - 2.91452i) q^{18} +6.64740 q^{19} -1.00000i q^{20} +(2.03203 + 0.244290i) q^{21} -1.57649i q^{22} -1.16301 q^{23} +(0.206738 - 1.71967i) q^{24} -1.00000 q^{25} -3.43934 q^{26} +(-4.86501 - 1.82529i) q^{27} +1.18164 q^{28} -8.20323 q^{29} +(-1.71967 - 0.206738i) q^{30} +(-5.56676 - 0.105626i) q^{31} -1.00000i q^{32} +(-2.71104 - 0.325920i) q^{33} +4.55264i q^{34} -1.18164i q^{35} +(-2.91452 - 0.711040i) q^{36} -9.82943i q^{37} -6.64740i q^{38} +(-0.711040 + 5.91452i) q^{39} -1.00000 q^{40} -5.42208i q^{41} +(0.244290 - 2.03203i) q^{42} +6.82897i q^{43} -1.57649 q^{44} +(-0.711040 + 2.91452i) q^{45} +1.16301i q^{46} +1.46575i q^{47} +(-1.71967 - 0.206738i) q^{48} -5.60372 q^{49} +1.00000i q^{50} +(7.82904 + 0.941203i) q^{51} +3.43934i q^{52} -7.16734 q^{53} +(-1.82529 + 4.86501i) q^{54} +1.57649i q^{55} -1.18164i q^{56} +(-11.4313 - 1.37427i) q^{57} +8.20323i q^{58} +6.84416i q^{59} +(-0.206738 + 1.71967i) q^{60} -11.8448i q^{61} +(-0.105626 + 5.56676i) q^{62} +(-3.44392 - 0.840195i) q^{63} -1.00000 q^{64} +3.43934 q^{65} +(-0.325920 + 2.71104i) q^{66} -13.6144 q^{67} +4.55264 q^{68} +(2.00000 + 0.240439i) q^{69} -1.18164 q^{70} -6.52980i q^{71} +(-0.711040 + 2.91452i) q^{72} +4.67746i q^{73} -9.82943 q^{74} +(1.71967 + 0.206738i) q^{75} -6.64740 q^{76} -1.86285 q^{77} +(5.91452 + 0.711040i) q^{78} +6.13816i q^{79} +1.00000i q^{80} +(7.98884 + 4.14468i) q^{81} -5.42208 q^{82} -3.86184 q^{83} +(-2.03203 - 0.244290i) q^{84} -4.55264i q^{85} +6.82897 q^{86} +(14.1068 + 1.69592i) q^{87} +1.57649i q^{88} +10.2683 q^{89} +(2.91452 + 0.711040i) q^{90} +4.06406i q^{91} +1.16301 q^{92} +(9.55115 + 1.33250i) q^{93} +1.46575 q^{94} +6.64740i q^{95} +(-0.206738 + 1.71967i) q^{96} +3.46575 q^{97} +5.60372i q^{98} +(4.59471 + 1.12095i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} + 4 q^{7} - 8 q^{9}+O(q^{10}) \) 16 * q - 16 * q^4 + 4 * q^7 - 8 * q^9	\( 16 q - 16 q^{4} + 4 q^{7} - 8 q^{9} + 16 q^{10} + 16 q^{16} - 8 q^{18} + 20 q^{19} - 16 q^{25} - 4 q^{28} - 8 q^{31} - 24 q^{33} + 8 q^{36} + 8 q^{39} - 16 q^{40} + 8 q^{45} - 28 q^{49} + 16 q^{51} - 4 q^{63} - 16 q^{64} - 44 q^{66} - 24 q^{67} + 32 q^{69} + 4 q^{70} + 8 q^{72} - 20 q^{76} + 40 q^{78} + 8 q^{81} - 48 q^{82} + 16 q^{87} - 8 q^{90} + 12 q^{93} - 40 q^{94} - 8 q^{97}+O(q^{100}) \) 16 * q - 16 * q^4 + 4 * q^7 - 8 * q^9 + 16 * q^10 + 16 * q^16 - 8 * q^18 + 20 * q^19 - 16 * q^25 - 4 * q^28 - 8 * q^31 - 24 * q^33 + 8 * q^36 + 8 * q^39 - 16 * q^40 + 8 * q^45 - 28 * q^49 + 16 * q^51 - 4 * q^63 - 16 * q^64 - 44 * q^66 - 24 * q^67 + 32 * q^69 + 4 * q^70 + 8 * q^72 - 20 * q^76 + 40 * q^78 + 8 * q^81 - 48 * q^82 + 16 * q^87 - 8 * q^90 + 12 * q^93 - 40 * q^94 - 8 * q^97

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