LMFDB - Embedded newform 961.2.c.h.521.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(439,961)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("961.439"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,12,0,12,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.207360000.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 6x^{6} + 32x^{4} + 24x^{2} + 16 $ x^8 + 6x^6 + 32x^4 + 24*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			521.3
Root			$0.437016 + 0.756934i$ of defining polynomial
Character	$\chi$	$=$	961.521
Dual form			961.2.c.h.439.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.61803 q^{2} +(-0.437016 - 0.756934i) q^{3} +4.85410 q^{4} +(-1.11803 + 1.93649i) q^{5} +(-1.14412 - 1.98168i) q^{6} +(0.500000 + 0.866025i) q^{7} +7.47214 q^{8} +(1.11803 - 1.93649i) q^{9} +(-2.92705 + 5.06980i) q^{10} +(2.12132 - 3.67423i) q^{11} +(-2.12132 - 3.67423i) q^{12} +(-1.31105 + 2.27080i) q^{13} +(1.30902 + 2.26728i) q^{14} +1.95440 q^{15} +9.85410 q^{16} +(1.85123 + 3.20642i) q^{17} +(2.92705 - 5.06980i) q^{18} +(-0.500000 - 0.866025i) q^{19} +(-5.42705 + 9.39993i) q^{20} +(0.437016 - 0.756934i) q^{21} +(5.55369 - 9.61927i) q^{22} +2.62210 q^{23} +(-3.26544 - 5.65591i) q^{24} +(-3.43237 + 5.94504i) q^{26} -4.57649 q^{27} +(2.42705 + 4.20378i) q^{28} +0.540182 q^{29} +5.11667 q^{30} +10.8541 q^{32} -3.70820 q^{33} +(4.84658 + 8.39453i) q^{34} -2.23607 q^{35} +(5.42705 - 9.39993i) q^{36} +(2.12132 + 3.67423i) q^{37} +(-1.30902 - 2.26728i) q^{38} +2.29180 q^{39} +(-8.35410 + 14.4697i) q^{40} +(0.736068 - 1.27491i) q^{41} +(1.14412 - 1.98168i) q^{42} +(-4.84658 - 8.39453i) q^{43} +(10.2971 - 17.8351i) q^{44} +(2.50000 + 4.33013i) q^{45} +6.86474 q^{46} -9.70820 q^{47} +(-4.30640 - 7.45890i) q^{48} +(3.00000 - 5.19615i) q^{49} +(1.61803 - 2.80252i) q^{51} +(-6.36396 + 11.0227i) q^{52} +(-6.86474 + 11.8901i) q^{53} -11.9814 q^{54} +(4.74342 + 8.21584i) q^{55} +(3.73607 + 6.47106i) q^{56} +(-0.437016 + 0.756934i) q^{57} +1.41421 q^{58} +(-5.97214 - 10.3440i) q^{59} +9.48683 q^{60} -13.9358 q^{61} +2.23607 q^{63} +8.70820 q^{64} +(-2.93159 - 5.07767i) q^{65} -9.70820 q^{66} +(-3.00000 + 5.19615i) q^{67} +(8.98606 + 15.5643i) q^{68} +(-1.14590 - 1.98475i) q^{69} -5.85410 q^{70} +(0.736068 - 1.27491i) q^{71} +(8.35410 - 14.4697i) q^{72} +(2.12132 - 3.67423i) q^{73} +(5.55369 + 9.61927i) q^{74} +(-2.42705 - 4.20378i) q^{76} +4.24264 q^{77} +6.00000 q^{78} +(-0.810272 - 1.40343i) q^{79} +(-11.0172 + 19.0824i) q^{80} +(-1.35410 - 2.34537i) q^{81} +(1.92705 - 3.33775i) q^{82} +(-1.58114 + 2.73861i) q^{83} +(2.12132 - 3.67423i) q^{84} -8.27895 q^{85} +(-12.6885 - 21.9772i) q^{86} +(-0.236068 - 0.408882i) q^{87} +(15.8508 - 27.4544i) q^{88} +15.3500 q^{89} +(6.54508 + 11.3364i) q^{90} -2.62210 q^{91} +12.7279 q^{92} -25.4164 q^{94} +2.23607 q^{95} +(-4.74342 - 8.21584i) q^{96} -7.00000 q^{97} +(7.85410 - 13.6037i) q^{98} +(-4.74342 - 8.21584i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 12 q^{2} + 12 q^{4} + 4 q^{7} + 24 q^{8} - 10 q^{10} + 6 q^{14} + 52 q^{16} + 10 q^{18} - 4 q^{19} - 30 q^{20} + 6 q^{28} + 60 q^{32} + 24 q^{33} + 30 q^{36} - 6 q^{38} + 72 q^{39} - 40 q^{40} - 12 q^{41}+ \cdots + 36 q^{98}+O(q^{100}) $ 8 * q + 12 * q^2 + 12 * q^4 + 4 * q^7 + 24 * q^8 - 10 * q^10 + 6 * q^14 + 52 * q^16 + 10 * q^18 - 4 * q^19 - 30 * q^20 + 6 * q^28 + 60 * q^32 + 24 * q^33 + 30 * q^36 - 6 * q^38 + 72 * q^39 - 40 * q^40 - 12 * q^41 + 20 * q^45 - 24 * q^47 + 24 * q^49 + 4 * q^51 + 12 * q^56 - 12 * q^59 + 16 * q^64 - 24 * q^66 - 24 * q^67 - 36 * q^69 - 20 * q^70 - 12 * q^71 + 40 * q^72 - 6 * q^76 + 48 * q^78 - 30 * q^80 + 16 * q^81 + 2 * q^82 + 16 * q^87 + 30 * q^90 - 96 * q^94 - 56 * q^97 + 36 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	2.61803			1.85123			0.925615	−	0.378467i	$-0.123549\pi$
$2$	2.61803			1.85123			0.925615	+	0.378467i	$0.123549\pi$
$3$	−0.437016	−	0.756934i	−0.252311	−	0.437016i	0.711850	−	0.702331i	$-0.247857\pi$
$3$	−0.437016	−	0.756934i	−0.252311	−	0.437016i	−0.964162	+	0.265315i	$0.914524\pi$
$4$	4.85410			2.42705
$5$	−1.11803	+	1.93649i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$5$	−1.11803	+	1.93649i	−0.500000	+	0.866025i	−1.00000			$\pi$
$6$	−1.14412	−	1.98168i	−0.467086	−	0.809017i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i	0.944911	−	0.327327i	$-0.106148\pi$
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i	−0.755929	+	0.654654i	$0.772814\pi$
$8$	7.47214			2.64180
$9$	1.11803	−	1.93649i	0.372678	−	0.645497i
$10$	−2.92705	+	5.06980i	−0.925615	+	1.60321i
$11$	2.12132	−	3.67423i	0.639602	−	1.10782i	−0.345918	−	0.938265i	$-0.612432\pi$
$11$	2.12132	−	3.67423i	0.639602	−	1.10782i	0.985520	−	0.169559i	$-0.0542342\pi$
$12$	−2.12132	−	3.67423i	−0.612372	−	1.06066i
$13$	−1.31105	+	2.27080i	−0.363619	+	0.629807i	−0.988554	−	0.150870i	$-0.951792\pi$
$13$	−1.31105	+	2.27080i	−0.363619	+	0.629807i	0.624934	+	0.780677i	$0.285126\pi$
$14$	1.30902	+	2.26728i	0.349850	+	0.605957i
$15$	1.95440			0.504623
$16$	9.85410			2.46353
$17$	1.85123	+	3.20642i	0.448989	+	0.777672i	0.998320	−	0.0579326i	$-0.0184509\pi$
$17$	1.85123	+	3.20642i	0.448989	+	0.777672i	−0.549331	+	0.835605i	$0.685118\pi$
$18$	2.92705	−	5.06980i	0.689913	−	1.19496i
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	0.802955	−	0.596040i	$-0.203260\pi$
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	−0.917663	+	0.397360i	$0.869927\pi$
$20$	−5.42705	+	9.39993i	−1.21353	+	2.10189i
$21$	0.437016	−	0.756934i	0.0953647	−	0.165177i
$22$	5.55369	−	9.61927i	1.18405	−	2.05084i
$23$	2.62210			0.546745			0.273372	−	0.961908i	$-0.411861\pi$
$23$	2.62210			0.546745			0.273372	+	0.961908i	$0.411861\pi$
$24$	−3.26544	−	5.65591i	−0.666556	−	1.15451i
$25$		0			0
$26$	−3.43237	+	5.94504i	−0.673143	+	1.16592i
$27$	−4.57649			−0.880746
$28$	2.42705	+	4.20378i	0.458670	+	0.794439i
$29$	0.540182			0.100309			0.0501546	−	0.998741i	$-0.484029\pi$
$29$	0.540182			0.100309			0.0501546	+	0.998741i	$0.484029\pi$
$30$	5.11667			0.934172
$31$		0			0
$31$		0			0
$32$	10.8541			1.91875
$33$	−3.70820			−0.645515
$34$	4.84658	+	8.39453i	0.831182	+	1.43965i
$35$	−2.23607			−0.377964
$36$	5.42705	−	9.39993i	0.904508	−	1.56665i
$37$	2.12132	+	3.67423i	0.348743	+	0.604040i	0.986026	−	0.166589i	$-0.0532753\pi$
$37$	2.12132	+	3.67423i	0.348743	+	0.604040i	−0.637284	+	0.770629i	$0.719942\pi$
$38$	−1.30902	−	2.26728i	−0.212351	−	0.367802i
$39$	2.29180			0.366981
$40$	−8.35410	+	14.4697i	−1.32090	+	2.28787i
$41$	0.736068	−	1.27491i	0.114955	−	0.199107i	−0.802807	−	0.596239i	$-0.796661\pi$
$41$	0.736068	−	1.27491i	0.114955	−	0.199107i	0.917762	+	0.397132i	$0.129994\pi$
$42$	1.14412	−	1.98168i	0.176542	−	0.305780i
$43$	−4.84658	−	8.39453i	−0.739097	−	1.28015i	−0.952902	−	0.303277i	$-0.901919\pi$
$43$	−4.84658	−	8.39453i	−0.739097	−	1.28015i	0.213806	−	0.976876i	$-0.431414\pi$
$44$	10.2971	−	17.8351i	1.55235	−	2.68874i
$45$	2.50000	+	4.33013i	0.372678	+	0.645497i
$46$	6.86474			1.01215
$47$	−9.70820			−1.41609			−0.708044	−	0.706169i	$-0.750422\pi$
$47$	−9.70820			−1.41609			−0.708044	+	0.706169i	$0.750422\pi$
$48$	−4.30640	−	7.45890i	−0.621575	−	1.07660i
$49$	3.00000	−	5.19615i	0.428571	−	0.742307i
$50$		0			0
$51$	1.61803	−	2.80252i	0.226570	−	0.392431i
$52$	−6.36396	+	11.0227i	−0.882523	+	1.52857i
$53$	−6.86474	+	11.8901i	−0.942944	+	1.63323i	−0.183128	+	0.983089i	$0.558622\pi$
$53$	−6.86474	+	11.8901i	−0.942944	+	1.63323i	−0.759816	+	0.650138i	$0.774711\pi$
$54$	−11.9814			−1.63046
$55$	4.74342	+	8.21584i	0.639602	+	1.10782i
$56$	3.73607	+	6.47106i	0.499253	+	0.864732i
$57$	−0.437016	+	0.756934i	−0.0578842	+	0.100258i
$58$	1.41421			0.185695
$59$	−5.97214	−	10.3440i	−0.777506	−	1.34668i	−0.933375	−	0.358902i	$-0.883151\pi$
$59$	−5.97214	−	10.3440i	−0.777506	−	1.34668i	0.155869	−	0.987778i	$-0.450182\pi$
$60$	9.48683			1.22474
$61$	−13.9358			−1.78430			−0.892148	−	0.451742i	$-0.850803\pi$
$61$	−13.9358			−1.78430			−0.892148	+	0.451742i	$0.850803\pi$
$62$		0			0
$63$	2.23607			0.281718
$64$	8.70820			1.08853
$65$	−2.93159	−	5.07767i	−0.363619	−	0.629807i
$66$	−9.70820			−1.19500
$67$	−3.00000	+	5.19615i	−0.366508	+	0.634811i	−0.989017	−	0.147802i	$-0.952780\pi$
$67$	−3.00000	+	5.19615i	−0.366508	+	0.634811i	0.622509	+	0.782613i	$0.286114\pi$
$68$	8.98606	+	15.5643i	1.08972	+	1.88745i
$69$	−1.14590	−	1.98475i	−0.137950	−	0.238936i
$70$	−5.85410			−0.699699
$71$	0.736068	−	1.27491i	0.0873552	−	0.151304i	−0.819037	−	0.573740i	$-0.805492\pi$
$71$	0.736068	−	1.27491i	0.0873552	−	0.151304i	0.906392	+	0.422437i	$0.138825\pi$
$72$	8.35410	−	14.4697i	0.984540	−	1.70527i
$73$	2.12132	−	3.67423i	0.248282	−	0.430037i	−0.714767	−	0.699362i	$-0.753467\pi$
$73$	2.12132	−	3.67423i	0.248282	−	0.430037i	0.963049	+	0.269326i	$0.0868008\pi$
$74$	5.55369	+	9.61927i	0.645603	+	1.11822i
$75$		0			0
$76$	−2.42705	−	4.20378i	−0.278402	−	0.482206i
$77$	4.24264			0.483494
$78$	6.00000			0.679366
$79$	−0.810272	−	1.40343i	−0.0911628	−	0.157899i	0.816838	−	0.576867i	$-0.195725\pi$
$79$	−0.810272	−	1.40343i	−0.0911628	−	0.157899i	−0.908001	+	0.418969i	$0.862392\pi$
$80$	−11.0172	+	19.0824i	−1.23176	+	2.13348i
$81$	−1.35410	−	2.34537i	−0.150456	−	0.260597i
$82$	1.92705	−	3.33775i	0.212807	−	0.368593i
$83$	−1.58114	+	2.73861i	−0.173553	+	0.300602i	−0.939659	−	0.342111i	$-0.888858\pi$
$83$	−1.58114	+	2.73861i	−0.173553	+	0.300602i	0.766107	+	0.642713i	$0.222191\pi$
$84$	2.12132	−	3.67423i	0.231455	−	0.400892i
$85$	−8.27895			−0.897978
$86$	−12.6885	−	21.9772i	−1.36824	−	2.36986i
$87$	−0.236068	−	0.408882i	−0.0253091	−	0.0438367i
$88$	15.8508	−	27.4544i	1.68970	−	2.92665i
$89$	15.3500			1.62710			0.813549	−	0.581496i	$-0.197532\pi$
$89$	15.3500			1.62710			0.813549	+	0.581496i	$0.197532\pi$
$90$	6.54508	+	11.3364i	0.689913	+	1.19496i
$91$	−2.62210			−0.274870
$92$	12.7279			1.32698
$93$		0			0
$94$	−25.4164			−2.62150
$95$	2.23607			0.229416
$96$	−4.74342	−	8.21584i	−0.484123	−	0.838525i
$97$	−7.00000			−0.710742			−0.355371	−	0.934725i	$-0.615646\pi$
$97$	−7.00000			−0.710742			−0.355371	+	0.934725i	$0.615646\pi$
$98$	7.85410	−	13.6037i	0.793384	−	1.37418i
$99$	−4.74342	−	8.21584i	−0.476731	−	0.825723i
$100$		0			0
$101$	2.23607			0.222497			0.111249	−	0.993793i	$-0.464515\pi$
$101$	2.23607			0.222497			0.111249	+	0.993793i	$0.464515\pi$
$102$	4.23607	−	7.33708i	0.419433	−	0.726480i
$103$	−5.35410	+	9.27358i	−0.527555	+	0.913753i	0.471929	+	0.881637i	$0.343558\pi$
$103$	−5.35410	+	9.27358i	−0.527555	+	0.913753i	−0.999484	+	0.0321160i	$0.989775\pi$
$104$	−9.79633	+	16.9677i	−0.960609	+	1.66382i
$105$	0.977198	+	1.69256i	0.0953647	+	0.165177i
$106$	−17.9721	+	31.1286i	−1.74561	+	3.02348i
$107$	−0.736068	−	1.27491i	−0.0711584	−	0.123250i	0.828251	−	0.560357i	$-0.189336\pi$
$107$	−0.736068	−	1.27491i	−0.0711584	−	0.123250i	−0.899409	+	0.437108i	$0.856003\pi$
$108$	−22.2148			−2.13762
$109$	−1.29180			−0.123732			−0.0618658	−	0.998084i	$-0.519705\pi$
$109$	−1.29180			−0.123732			−0.0618658	+	0.998084i	$0.519705\pi$
$110$	12.4184	+	21.5093i	1.18405	+	2.05084i
$111$	1.85410	−	3.21140i	0.175984	−	0.304812i
$112$	4.92705	+	8.53390i	0.465563	+	0.806378i
$113$	4.88197	−	8.45581i	0.459257	−	0.795456i	−0.539665	−	0.841880i	$-0.681449\pi$
$113$	4.88197	−	8.45581i	0.459257	−	0.795456i	0.998922	+	0.0464238i	$0.0147825\pi$
$114$	−1.14412	+	1.98168i	−0.107157	+	0.185601i
$115$	−2.93159	+	5.07767i	−0.273372	+	0.473495i
$116$	2.62210			0.243456
$117$	2.93159	+	5.07767i	0.271026	+	0.469431i
$118$	−15.6353	−	27.0811i	−1.43934	−	2.49301i
$119$	−1.85123	+	3.20642i	−0.169702	+	0.293932i
$120$	14.6035			1.33311
$121$	−3.50000	−	6.06218i	−0.318182	−	0.551107i
$122$	−36.4844			−3.30314
$123$	−1.28669			−0.116017
$124$		0			0
$125$	−11.1803			−1.00000
$126$	5.85410			0.521525
$127$	−4.74342	−	8.21584i	−0.420910	−	0.729038i	0.575119	−	0.818070i	$-0.304956\pi$
$127$	−4.74342	−	8.21584i	−0.420910	−	0.729038i	−0.996029	+	0.0890323i	$0.971623\pi$
$128$	1.09017			0.0963583
$129$	−4.23607	+	7.33708i	−0.372965	+	0.645994i
$130$	−7.67501	−	13.2935i	−0.673143	−	1.16592i
$131$	−3.70820	−	6.42280i	−0.323987	−	0.561162i	0.657320	−	0.753612i	$-0.271690\pi$
$131$	−3.70820	−	6.42280i	−0.323987	−	0.561162i	−0.981307	+	0.192450i	$0.938357\pi$
$132$	−18.0000			−1.56670
$133$	0.500000	−	0.866025i	0.0433555	−	0.0750939i
$134$	−7.85410	+	13.6037i	−0.678491	+	1.17518i
$135$	5.11667	−	8.86234i	0.440373	−	0.762749i
$136$	13.8326	+	23.9588i	1.18614	+	2.05445i
$137$	−1.31105	+	2.27080i	−0.112010	+	0.194008i	−0.916581	−	0.399850i	$-0.869062\pi$
$137$	−1.31105	+	2.27080i	−0.112010	+	0.194008i	0.804570	+	0.593857i	$0.202396\pi$
$138$	−3.00000	−	5.19615i	−0.255377	−	0.442326i
$139$	17.9721			1.52437			0.762187	−	0.647356i	$-0.224125\pi$
$139$	17.9721			1.52437			0.762187	+	0.647356i	$0.224125\pi$
$140$	−10.8541			−0.917339
$141$	4.24264	+	7.34847i	0.357295	+	0.618853i
$142$	1.92705	−	3.33775i	0.161715	−	0.280098i
$143$	5.56231	+	9.63420i	0.465143	+	0.805652i
$144$	11.0172	−	19.0824i	0.918102	−	1.59020i
$145$	−0.603941	+	1.04606i	−0.0501546	+	0.0868703i
$146$	5.55369	−	9.61927i	0.459627	−	0.796097i
$147$	−5.24419			−0.432534
$148$	10.2971	+	17.8351i	0.846417	+	1.46604i
$149$	6.70820	+	11.6190i	0.549557	+	0.951861i	0.998305	+	0.0582028i	$0.0185370\pi$
$149$	6.70820	+	11.6190i	0.549557	+	0.951861i	−0.448747	+	0.893659i	$0.648130\pi$
$150$		0			0
$151$	−12.5216			−1.01899			−0.509496	−	0.860473i	$-0.670168\pi$
$151$	−12.5216			−1.01899			−0.509496	+	0.860473i	$0.670168\pi$
$152$	−3.73607	−	6.47106i	−0.303035	−	0.524872i
$153$	8.27895			0.669313
$154$	11.1074			0.895058
$155$		0			0
$156$	11.1246			0.890682
$157$	8.70820			0.694990			0.347495	−	0.937682i	$-0.387032\pi$
$157$	8.70820			0.694990			0.347495	+	0.937682i	$0.387032\pi$
$158$	−2.12132	−	3.67423i	−0.168763	−	0.292306i
$159$	12.0000			0.951662
$160$	−12.1353	+	21.0189i	−0.959376	+	1.66169i
$161$	1.31105	+	2.27080i	0.103325	+	0.178964i
$162$	−3.54508	−	6.14027i	−0.278528	−	0.482425i
$163$	14.4164			1.12918			0.564590	−	0.825371i	$-0.309034\pi$
$163$	14.4164			1.12918			0.564590	+	0.825371i	$0.309034\pi$
$164$	3.57295	−	6.18853i	0.279000	−	0.483243i
$165$	4.14590	−	7.18091i	0.322758	−	0.559033i
$166$	−4.13948	+	7.16978i	−0.321286	+	0.556483i
$167$	−0.540182	−	0.935622i	−0.0418005	−	0.0724006i	0.844368	−	0.535763i	$-0.179976\pi$
$167$	−0.540182	−	0.935622i	−0.0418005	−	0.0724006i	−0.886169	+	0.463363i	$0.846643\pi$
$168$	3.26544	−	5.65591i	0.251934	−	0.436363i
$169$	3.06231	+	5.30407i	0.235562	+	0.408005i
$170$	−21.6746			−1.66236
$171$	−2.23607			−0.170996
$172$	−23.5258	−	40.7479i	−1.79383	−	3.10700i
$173$	−9.00000	+	15.5885i	−0.684257	+	1.18517i	0.289412	+	0.957205i	$0.406540\pi$
$173$	−9.00000	+	15.5885i	−0.684257	+	1.18517i	−0.973670	+	0.227964i	$0.926793\pi$
$174$	−0.618034	−	1.07047i	−0.0468530	−	0.0811518i
$175$		0			0
$176$	20.9037	−	36.2063i	1.57568	−	2.72915i
$177$	−5.21984	+	9.04103i	−0.392347	+	0.679565i
$178$	40.1869			3.01213
$179$	6.63405	+	11.4905i	0.495852	+	0.858841i	0.999989	−	0.00478274i	$-0.00152240\pi$
$179$	6.63405	+	11.4905i	0.495852	+	0.858841i	−0.504136	+	0.863624i	$0.668189\pi$
$180$	12.1353	+	21.0189i	0.904508	+	1.56665i
$181$	4.34581	−	7.52716i	0.323021	−	0.559489i	−0.658089	−	0.752940i	$-0.728635\pi$
$181$	4.34581	−	7.52716i	0.323021	−	0.559489i	0.981110	+	0.193451i	$0.0619681\pi$
$182$	−6.86474			−0.508848
$183$	6.09017	+	10.5485i	0.450198	+	0.779766i
$184$	19.5927			1.44439
$185$	−9.48683			−0.697486
$186$		0			0
$187$	15.7082			1.14870
$188$	−47.1246			−3.43692
$189$	−2.28825	−	3.96336i	−0.166445	−	0.288292i
$190$	5.85410			0.424701
$191$	−4.88197	+	8.45581i	−0.353247	+	0.611841i	−0.986816	−	0.161845i	$-0.948256\pi$
$191$	−4.88197	+	8.45581i	−0.353247	+	0.611841i	0.633570	+	0.773686i	$0.281589\pi$
$192$	−3.80562	−	6.59154i	−0.274647	−	0.475703i
$193$	10.3541	+	17.9338i	0.745305	+	1.29091i	0.950052	+	0.312091i	$0.101029\pi$
$193$	10.3541	+	17.9338i	0.745305	+	1.29091i	−0.204748	+	0.978815i	$0.565637\pi$
$194$	−18.3262			−1.31575
$195$	−2.56231	+	4.43804i	−0.183491	+	0.317815i
$196$	14.5623	−	25.2227i	1.04016	−	1.80162i
$197$	−0.540182	+	0.935622i	−0.0384863	+	0.0666603i	−0.884627	−	0.466299i	$-0.845587\pi$
$197$	−0.540182	+	0.935622i	−0.0384863	+	0.0666603i	0.846141	+	0.532960i	$0.178920\pi$
$198$	−12.4184	−	21.5093i	−0.882539	−	1.52860i
$199$	11.6082	−	20.1059i	0.822880	−	1.42527i	−0.0806485	−	0.996743i	$-0.525699\pi$
$199$	11.6082	−	20.1059i	0.822880	−	1.42527i	0.903529	−	0.428528i	$-0.140968\pi$
$200$		0			0
$201$	5.24419			0.369897
$202$	5.85410			0.411893
$203$	0.270091	+	0.467811i	0.0189567	+	0.0328339i
$204$	7.85410	−	13.6037i	0.549897	−	0.952450i
$205$	1.64590	+	2.85078i	0.114955	+	0.199107i
$206$	−14.0172	+	24.2785i	−0.976626	+	1.69157i
$207$	2.93159	−	5.07767i	0.203760	−	0.352922i
$208$	−12.9192	+	22.3767i	−0.895785	+	1.55155i
$209$	−4.24264			−0.293470
$210$	2.55834	+	4.43117i	0.176542	+	0.305780i
$211$	2.50000	+	4.33013i	0.172107	+	0.298098i	0.939156	−	0.343490i	$-0.111609\pi$
$211$	2.50000	+	4.33013i	0.172107	+	0.298098i	−0.767049	+	0.641588i	$0.778276\pi$
$212$	−33.3221	+	57.7156i	−2.28857	+	3.96393i
$213$	−1.28669			−0.0881628
$214$	−1.92705	−	3.33775i	−0.131730	−	0.228164i
$215$	21.6746			1.47819
$216$	−34.1962			−2.32675
$217$		0			0
$218$	−3.38197			−0.229056
$219$	−3.70820			−0.250577
$220$	23.0250	+	39.8805i	1.55235	+	2.68874i
$221$	−9.70820			−0.653044
$222$	4.85410	−	8.40755i	0.325786	−	0.564278i
$223$	8.07262	+	13.9822i	0.540583	+	0.936316i	0.998871	+	0.0475128i	$0.0151295\pi$
$223$	8.07262	+	13.9822i	0.540583	+	0.936316i	−0.458288	+	0.888804i	$0.651537\pi$
$224$	5.42705	+	9.39993i	0.362610	+	0.628059i
$225$		0			0
$226$	12.7812	−	22.1376i	0.850190	−	1.47257i
$227$	−1.14590	+	1.98475i	−0.0760559	+	0.131733i	−0.901545	−	0.432685i	$-0.857566\pi$
$227$	−1.14590	+	1.98475i	−0.0760559	+	0.131733i	0.825489	+	0.564418i	$0.190899\pi$
$228$	−2.12132	+	3.67423i	−0.140488	+	0.243332i
$229$	2.12132	+	3.67423i	0.140181	+	0.242800i	0.927565	−	0.373663i	$-0.121898\pi$
$229$	2.12132	+	3.67423i	0.140181	+	0.242800i	−0.787384	+	0.616463i	$0.788565\pi$
$230$	−7.67501	+	13.2935i	−0.506075	+	0.876548i
$231$	−1.85410	−	3.21140i	−0.121991	−	0.211295i
$232$	4.03631			0.264997
$233$	−13.4721			−0.882589			−0.441294	−	0.897362i	$-0.645481\pi$
$233$	−13.4721			−0.882589			−0.441294	+	0.897362i	$0.645481\pi$
$234$	7.67501	+	13.2935i	0.501731	+	0.869024i
$235$	10.8541	−	18.7999i	0.708044	−	1.22637i
$236$	−28.9894	−	50.2110i	−1.88705	−	3.26846i
$237$	−0.708204	+	1.22665i	−0.0460028	+	0.0796792i
$238$	−4.84658	+	8.39453i	−0.314157	+	0.544136i
$239$	6.05446	−	10.4866i	0.391631	−	0.678324i	−0.601034	−	0.799223i	$-0.705244\pi$
$239$	6.05446	−	10.4866i	0.391631	−	0.678324i	0.992665	+	0.120899i	$0.0385777\pi$
$240$	19.2588			1.24315
$241$	−11.6082	−	20.1059i	−0.747747	−	1.29514i	−0.948900	−	0.315576i	$-0.897802\pi$
$241$	−11.6082	−	20.1059i	−0.747747	−	1.29514i	0.201153	−	0.979560i	$-0.435531\pi$
$242$	−9.16312	−	15.8710i	−0.589028	−	1.02023i
$243$	−8.04827	+	13.9400i	−0.516296	+	0.894252i
$244$	−67.6458			−4.33058
$245$	6.70820	+	11.6190i	0.428571	+	0.742307i
$246$	−3.36861			−0.214775
$247$	2.62210			0.166840
$248$		0			0
$249$	2.76393			0.175157
$250$	−29.2705			−1.85123
$251$	5.51428	+	9.55102i	0.348058	+	0.602855i	0.985905	−	0.167309i	$-0.0535077\pi$
$251$	5.51428	+	9.55102i	0.348058	+	0.602855i	−0.637846	+	0.770164i	$0.720174\pi$
$252$	10.8541			0.683744
$253$	5.56231	−	9.63420i	0.349699	−	0.605697i
$254$	−12.4184	−	21.5093i	−0.779201	−	1.34962i
$255$	3.61803	+	6.26662i	0.226570	+	0.392431i
$256$	−14.5623			−0.910144
$257$	−3.02786	+	5.24441i	−0.188873	+	0.327138i	−0.944875	−	0.327432i	$-0.893817\pi$
$257$	−3.02786	+	5.24441i	−0.188873	+	0.327138i	0.756002	+	0.654570i	$0.227150\pi$
$258$	−11.0902	+	19.2087i	−0.690444	+	1.19588i
$259$	−2.12132	+	3.67423i	−0.131812	+	0.228306i
$260$	−14.2302	−	24.6475i	−0.882523	−	1.52857i
$261$	0.603941	−	1.04606i	0.0373830	−	0.0647493i
$262$	−9.70820	−	16.8151i	−0.599775	−	1.03884i
$263$	−18.5123			−1.14152			−0.570759	−	0.821118i	$-0.693351\pi$
$263$	−18.5123			−1.14152			−0.570759	+	0.821118i	$0.693351\pi$
$264$	−27.7082			−1.70532
$265$	−15.3500	−	26.5870i	−0.942944	−	1.63323i
$266$	1.30902	−	2.26728i	0.0802610	−	0.139016i
$267$	−6.70820	−	11.6190i	−0.410535	−	0.711068i
$268$	−14.5623	+	25.2227i	−0.889534	+	1.54072i
$269$	1.08036	−	1.87124i	0.0658709	−	0.114092i	−0.831209	−	0.555960i	$-0.812351\pi$
$269$	1.08036	−	1.87124i	0.0658709	−	0.114092i	0.897080	+	0.441868i	$0.145684\pi$
$270$	13.3956	−	23.2019i	0.815232	−	1.41202i
$271$	18.5911			1.12933			0.564665	−	0.825320i	$-0.309006\pi$
$271$	18.5911			1.12933			0.564665	+	0.825320i	$0.309006\pi$
$272$	18.2422	+	31.5964i	1.10610	+	1.91581i
$273$	1.14590	+	1.98475i	0.0693529	+	0.120123i
$274$	−3.43237	+	5.94504i	−0.207357	+	0.359153i
$275$		0			0
$276$	−5.56231	−	9.63420i	−0.334811	−	0.579910i
$277$	−10.1058			−0.607200			−0.303600	−	0.952800i	$-0.598189\pi$
$277$	−10.1058			−0.607200			−0.303600	+	0.952800i	$0.598189\pi$
$278$	47.0516			2.82197
$279$		0			0
$280$	−16.7082			−0.998506
$281$	13.3607			0.797031			0.398516	−	0.917162i	$-0.369525\pi$
$281$	13.3607			0.797031			0.398516	+	0.917162i	$0.369525\pi$
$282$	11.1074	+	19.2385i	0.661435	+	1.14564i
$283$	24.0000			1.42665			0.713326	−	0.700832i	$-0.247188\pi$
$283$	24.0000			1.42665			0.713326	+	0.700832i	$0.247188\pi$
$284$	3.57295	−	6.18853i	0.212016	−	0.367222i
$285$	−0.977198	−	1.69256i	−0.0578842	−	0.100258i
$286$	14.5623	+	25.2227i	0.861087	+	1.49145i
$287$	1.47214			0.0868974
$288$	12.1353	−	21.0189i	0.715077	−	1.23855i
$289$	1.64590	−	2.85078i	0.0968175	−	0.167693i
$290$	−1.58114	+	2.73861i	−0.0928477	+	0.160817i
$291$	3.05911	+	5.29854i	0.179328	+	0.310606i
$292$	10.2971	−	17.8351i	0.602593	−	1.04372i
$293$	1.14590	+	1.98475i	0.0669441	+	0.115951i	0.897555	−	0.440903i	$-0.145342\pi$
$293$	1.14590	+	1.98475i	0.0669441	+	0.115951i	−0.830611	+	0.556854i	$0.812008\pi$
$294$	−13.7295			−0.800719
$295$	26.7082			1.55501
$296$	15.8508	+	27.4544i	0.921309	+	1.59575i
$297$	−9.70820	+	16.8151i	−0.563327	+	0.975711i
$298$	17.5623	+	30.4188i	1.01736	+	1.76211i
$299$	−3.43769	+	5.95426i	−0.198807	+	0.344344i
$300$		0			0
$301$	4.84658	−	8.39453i	0.279352	−	0.483852i
$302$	−32.7820			−1.88639
$303$	−0.977198	−	1.69256i	−0.0561385	−	0.0972348i
$304$	−4.92705	−	8.53390i	−0.282586	−	0.489453i
$305$	15.5807	−	26.9866i	0.892148	−	1.54525i
$306$	21.6746			1.23905
$307$	−12.0623	−	20.8925i	−0.688432	−	1.19240i	−0.972345	−	0.233549i	$-0.924966\pi$
$307$	−12.0623	−	20.8925i	−0.688432	−	1.19240i	0.283913	−	0.958850i	$-0.408367\pi$
$308$	20.5942			1.17346
$309$	9.35931			0.532433
$310$		0			0
$311$	25.4721			1.44439			0.722196	−	0.691688i	$-0.243133\pi$
$311$	25.4721			1.44439			0.722196	+	0.691688i	$0.243133\pi$
$312$	17.1246			0.969490
$313$	−5.76002	−	9.97665i	−0.325576	−	0.563913i	0.656053	−	0.754715i	$-0.272225\pi$
$313$	−5.76002	−	9.97665i	−0.325576	−	0.563913i	−0.981629	+	0.190801i	$0.938891\pi$
$314$	22.7984			1.28659
$315$	−2.50000	+	4.33013i	−0.140859	+	0.243975i
$316$	−3.93314	−	6.81241i	−0.221257	−	0.383228i
$317$	−13.1180	−	22.7211i	−0.736782	−	1.27614i	−0.953937	−	0.300007i	$-0.903011\pi$
$317$	−13.1180	−	22.7211i	−0.736782	−	1.27614i	0.217155	−	0.976137i	$-0.430322\pi$
$318$	31.4164			1.76174
$319$	1.14590	−	1.98475i	0.0641580	−	0.111125i
$320$	−9.73607	+	16.8634i	−0.544263	+	0.942691i
$321$	−0.643347	+	1.11431i	−0.0359081	+	0.0621947i
$322$	3.43237	+	5.94504i	0.191278	+	0.331304i
$323$	1.85123	−	3.20642i	0.103005	−	0.178410i
$324$	−6.57295	−	11.3847i	−0.365164	−	0.632482i
$325$		0			0
$326$	37.7426			2.09037
$327$	0.564536	+	0.977804i	0.0312189	+	0.0540727i
$328$	5.50000	−	9.52628i	0.303687	−	0.526001i
$329$	−4.85410	−	8.40755i	−0.267615	−	0.463523i
$330$	10.8541	−	18.7999i	0.597499	−	1.03490i
$331$	15.6445	−	27.0970i	0.859897	−	1.48939i	−0.0121285	−	0.999926i	$-0.503861\pi$
$331$	15.6445	−	27.0970i	0.859897	−	1.48939i	0.872026	−	0.489460i	$-0.162806\pi$
$332$	−7.67501	+	13.2935i	−0.421221	+	0.729576i
$333$	9.48683			0.519875
$334$	−1.41421	−	2.44949i	−0.0773823	−	0.134030i
$335$	−6.70820	−	11.6190i	−0.366508	−	0.634811i
$336$	4.30640	−	7.45890i	0.234933	−	0.406917i
$337$	15.3500			0.836169			0.418084	−	0.908408i	$-0.362702\pi$
$337$	15.3500			0.836169			0.418084	+	0.908408i	$0.362702\pi$
$338$	8.01722	+	13.8862i	0.436079	+	0.755312i
$339$	−8.53399			−0.463503
$340$	−40.1869			−2.17944
$341$		0			0
$342$	−5.85410			−0.316554
$343$	13.0000			0.701934
$344$	−36.2143	−	62.7250i	−1.95255	−	3.38191i
$345$	5.12461			0.275900
$346$	−23.5623	+	40.8111i	−1.26672	+	2.19402i
$347$	−10.7979	−	18.7025i	−0.579661	−	1.00400i	−0.995518	−	0.0945718i	$-0.969852\pi$
$347$	−10.7979	−	18.7025i	−0.579661	−	1.00400i	0.415857	−	0.909430i	$-0.363482\pi$
$348$	−1.14590	−	1.98475i	−0.0614266	−	0.106394i
$349$	6.00000			0.321173			0.160586	−	0.987022i	$-0.448662\pi$
$349$	6.00000			0.321173			0.160586	+	0.987022i	$0.448662\pi$
$350$		0			0
$351$	6.00000	−	10.3923i	0.320256	−	0.554700i
$352$	23.0250	−	39.8805i	1.22724	−	2.12564i
$353$	4.78282	+	8.28409i	0.254564	+	0.440918i	0.964777	−	0.263069i	$-0.0847347\pi$
$353$	4.78282	+	8.28409i	0.254564	+	0.440918i	−0.710213	+	0.703987i	$0.751401\pi$
$354$	−13.6657	+	23.6697i	−0.726324	+	1.25803i
$355$	1.64590	+	2.85078i	0.0873552	+	0.151304i
$356$	74.5106			3.94905
$357$	3.23607			0.171271
$358$	17.3682	+	30.0826i	0.917936	+	1.58991i
$359$	−7.11803	+	12.3288i	−0.375675	+	0.650689i	−0.990428	−	0.138031i	$-0.955923\pi$
$359$	−7.11803	+	12.3288i	−0.375675	+	0.650689i	0.614752	+	0.788720i	$0.289256\pi$
$360$	18.6803	+	32.3553i	0.984540	+	1.70527i
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$	11.3775	−	19.7064i	0.597986	−	1.03574i
$363$	−3.05911	+	5.29854i	−0.160562	+	0.278101i
$364$	−12.7279			−0.667124
$365$	4.74342	+	8.21584i	0.248282	+	0.430037i
$366$	15.9443	+	27.6163i	0.833420	+	1.44353i
$367$	3.32920	−	5.76635i	0.173783	−	0.301001i	−0.765956	−	0.642892i	$-0.777734\pi$
$367$	3.32920	−	5.76635i	0.173783	−	0.301001i	0.939739	+	0.341892i	$0.111068\pi$
$368$	25.8384			1.34692
$369$	−1.64590	−	2.85078i	−0.0856820	−	0.148406i
$370$	−24.8369			−1.29121
$371$	−13.7295			−0.712799
$372$		0			0
$373$	−9.29180			−0.481111			−0.240555	−	0.970635i	$-0.577330\pi$
$373$	−9.29180			−0.481111			−0.240555	+	0.970635i	$0.577330\pi$
$374$	41.1246			2.12650
$375$	4.88599	+	8.46278i	0.252311	+	0.437016i
$376$	−72.5410			−3.74102
$377$	−0.708204	+	1.22665i	−0.0364744	+	0.0631754i
$378$	−5.99070	−	10.3762i	−0.308129	−	0.533694i
$379$	−3.70820	−	6.42280i	−0.190478	−	0.329917i	0.754931	−	0.655804i	$-0.227670\pi$
$379$	−3.70820	−	6.42280i	−0.190478	−	0.329917i	−0.945409	+	0.325887i	$0.894337\pi$
$380$	10.8541			0.556804
$381$	−4.14590	+	7.18091i	−0.212401	+	0.367889i
$382$	−12.7812	+	22.1376i	−0.653941	+	1.13266i
$383$	−3.20168	+	5.54548i	−0.163598	+	0.283361i	−0.936157	−	0.351583i	$-0.885643\pi$
$383$	−3.20168	+	5.54548i	−0.163598	+	0.283361i	0.772558	+	0.634944i	$0.218977\pi$
$384$	−0.476422	−	0.825187i	−0.0243123	−	0.0421101i
$385$	−4.74342	+	8.21584i	−0.241747	+	0.418718i
$386$	27.1074	+	46.9514i	1.37973	+	2.38976i
$387$	−21.6746			−1.10178
$388$	−33.9787			−1.72501
$389$	−8.40647	−	14.5604i	−0.426225	−	0.738243i	0.570309	−	0.821430i	$-0.306823\pi$
$389$	−8.40647	−	14.5604i	−0.426225	−	0.738243i	−0.996534	+	0.0831870i	$0.973490\pi$
$390$	−6.70820	+	11.6190i	−0.339683	+	0.588348i
$391$	4.85410	+	8.40755i	0.245482	+	0.425188i
$392$	22.4164	−	38.8264i	1.13220	−	1.96103i
$393$	−3.24109	+	5.61373i	−0.163491	+	0.283175i
$394$	−1.41421	+	2.44949i	−0.0712470	+	0.123404i
$395$	3.62365			0.182326
$396$	−23.0250	−	39.8805i	−1.15705	−	2.00407i
$397$	−7.35410	−	12.7377i	−0.369092	−	0.639286i	0.620332	−	0.784339i	$-0.286998\pi$
$397$	−7.35410	−	12.7377i	−0.369092	−	0.639286i	−0.989424	+	0.145054i	$0.953665\pi$
$398$	30.3905	−	52.6380i	1.52334	−	2.63850i
$399$	−0.874032			−0.0437563
$400$		0			0
$401$	0.540182			0.0269754			0.0134877	−	0.999909i	$-0.495707\pi$
$401$	0.540182			0.0269754			0.0134877	+	0.999909i	$0.495707\pi$
$402$	13.7295			0.684764
$403$		0			0
$404$	10.8541			0.540012
$405$	6.05573			0.300912
$406$	0.707107	+	1.22474i	0.0350931	+	0.0607831i
$407$	18.0000			0.892227
$408$	12.0902	−	20.9408i	0.598553	−	1.03672i
$409$	15.0405	+	26.0509i	0.743706	+	1.28814i	0.950797	+	0.309815i	$0.100267\pi$
$409$	15.0405	+	26.0509i	0.743706	+	1.28814i	−0.207091	+	0.978322i	$0.566400\pi$
$410$	4.30902	+	7.46344i	0.212807	+	0.368593i
$411$	2.29180			0.113046
$412$	−25.9894	+	45.0149i	−1.28040	+	2.21772i
$413$	5.97214	−	10.3440i	0.293870	−	0.508997i
$414$	7.67501	−	13.2935i	0.377206	−	0.653340i
$415$	−3.53553	−	6.12372i	−0.173553	−	0.300602i
$416$	−14.2302	+	24.6475i	−0.697695	+	1.20844i
$417$	−7.85410	−	13.6037i	−0.384617	−	0.666176i
$418$	−11.1074			−0.543280
$419$	30.5967			1.49475			0.747374	−	0.664403i	$-0.231314\pi$
$419$	30.5967			1.49475			0.747374	+	0.664403i	$0.231314\pi$
$420$	4.74342	+	8.21584i	0.231455	+	0.400892i
$421$	−13.2082	+	22.8773i	−0.643728	+	1.11497i	0.340865	+	0.940112i	$0.389280\pi$
$421$	−13.2082	+	22.8773i	−0.643728	+	1.11497i	−0.984594	+	0.174858i	$0.944053\pi$
$422$	6.54508	+	11.3364i	0.318610	+	0.551848i
$423$	−10.8541	+	18.7999i	−0.527744	+	0.914080i
$424$	−51.2942	+	88.8442i	−2.49107	+	4.31466i
$425$		0			0
$426$	−3.36861			−0.163210
$427$	−6.96790	−	12.0688i	−0.337200	−	0.584048i
$428$	−3.57295	−	6.18853i	−0.172705	−	0.299134i
$429$	4.86163	−	8.42060i	0.234722	−	0.406550i
$430$	56.7448			2.73648
$431$	17.9443	+	31.0804i	0.864345	+	1.49709i	0.867696	+	0.497095i	$0.165600\pi$
$431$	17.9443	+	31.0804i	0.864345	+	1.49709i	−0.00335076	+	0.999994i	$0.501067\pi$
$432$	−45.0972			−2.16974
$433$	25.8384			1.24171			0.620857	−	0.783924i	$-0.286785\pi$
$433$	25.8384			1.24171			0.620857	+	0.783924i	$0.286785\pi$
$434$		0			0
$435$	1.05573			0.0506183
$436$	−6.27051			−0.300303
$437$	−1.31105	−	2.27080i	−0.0627159	−	0.108627i
$438$	−9.70820			−0.463876
$439$	12.5000	−	21.6506i	0.596592	−	1.03333i	−0.396728	−	0.917936i	$-0.629854\pi$
$439$	12.5000	−	21.6506i	0.596592	−	1.03333i	0.993320	−	0.115392i	$-0.0368124\pi$
$440$	35.4435	+	61.3899i	1.68970	+	2.92665i
$441$	−6.70820	−	11.6190i	−0.319438	−	0.553283i
$442$	−25.4164			−1.20894
$443$	−3.02786	+	5.24441i	−0.143858	+	0.249170i	−0.928946	−	0.370214i	$-0.879284\pi$
$443$	−3.02786	+	5.24441i	−0.143858	+	0.249170i	0.785088	+	0.619384i	$0.212618\pi$
$444$	9.00000	−	15.5885i	0.427121	−	0.739795i
$445$	−17.1618	+	29.7252i	−0.813549	+	1.40911i
$446$	21.1344	+	36.6058i	1.00074	+	1.73334i
$447$	5.86319	−	10.1553i	0.277319	−	0.480331i
$448$	4.35410	+	7.54153i	0.205712	+	0.356304i
$449$	−33.7047			−1.59062			−0.795311	−	0.606201i	$-0.792693\pi$
$449$	−33.7047			−1.59062			−0.795311	+	0.606201i	$0.792693\pi$
$450$		0			0
$451$	−3.12287	−	5.40897i	−0.147050	−	0.254699i
$452$	23.6976	−	41.0454i	1.11464	−	1.93061i
$453$	5.47214	+	9.47802i	0.257103	+	0.445316i
$454$	−3.00000	+	5.19615i	−0.140797	+	0.243868i
$455$	2.93159	−	5.07767i	0.137435	−	0.238045i
$456$	−3.26544	+	5.65591i	−0.152918	+	0.264862i
$457$	−11.3137			−0.529233			−0.264616	−	0.964354i	$-0.585245\pi$
$457$	−11.3137			−0.529233			−0.264616	+	0.964354i	$0.585245\pi$
$458$	5.55369	+	9.61927i	0.259507	+	0.449479i
$459$	−8.47214	−	14.6742i	−0.395445	−	0.684932i
$460$	−14.2302	+	24.6475i	−0.663489	+	1.14920i
$461$	−5.16538			−0.240576			−0.120288	−	0.992739i	$-0.538382\pi$
$461$	−5.16538			−0.240576			−0.120288	+	0.992739i	$0.538382\pi$
$462$	−4.85410	−	8.40755i	−0.225833	−	0.391155i
$463$	3.82998			0.177994			0.0889971	−	0.996032i	$-0.471634\pi$
$463$	3.82998			0.177994			0.0889971	+	0.996032i	$0.471634\pi$
$464$	5.32300			0.247114
$465$		0			0
$466$	−35.2705			−1.63387
$467$	−15.6525			−0.724310			−0.362155	−	0.932118i	$-0.617959\pi$
$467$	−15.6525			−0.724310			−0.362155	+	0.932118i	$0.617959\pi$
$468$	14.2302	+	24.6475i	0.657794	+	1.13933i
$469$	−6.00000			−0.277054
$470$	28.4164	−	49.2187i	1.31075	−	2.27029i
$471$	−3.80562	−	6.59154i	−0.175354	−	0.303722i
$472$	−44.6246	−	77.2921i	−2.05401	−	3.55766i
$473$	−41.1246			−1.89091
$474$	−1.85410	+	3.21140i	−0.0851617	+	0.147504i
$475$		0			0
$476$	−8.98606	+	15.5643i	−0.411875	+	0.713389i
$477$	15.3500	+	26.5870i	0.702829	+	1.21734i
$478$	15.8508	−	27.4544i	0.724998	−	1.25573i
$479$	−8.26393	−	14.3136i	−0.377589	−	0.654003i	0.613122	−	0.789988i	$-0.289913\pi$
$479$	−8.26393	−	14.3136i	−0.377589	−	0.654003i	−0.990711	+	0.135985i	$0.956580\pi$
$480$	21.2132			0.968246
$481$	−11.1246			−0.507239
$482$	−30.3905	−	52.6380i	−1.38425	−	2.39759i
$483$	1.14590	−	1.98475i	0.0521402	−	0.0903094i
$484$	−16.9894	−	29.4264i	−0.772243	−	1.33756i
$485$	7.82624	−	13.5554i	0.355371	−	0.615521i
$486$	−21.0706	+	36.4954i	−0.955783	+	1.65547i
$487$	14.0390	−	24.3162i	0.636166	−	1.10187i	−0.350100	−	0.936712i	$-0.613852\pi$
$487$	14.0390	−	24.3162i	0.636166	−	1.10187i	0.986267	−	0.165160i	$-0.0528142\pi$
$488$	−104.130			−4.71375
$489$	−6.30020	−	10.9123i	−0.284905	−	0.493470i
$490$	17.5623	+	30.4188i	0.793384	+	1.37418i
$491$	−7.94510	+	13.7613i	−0.358557	+	0.621040i	−0.987720	−	0.156234i	$-0.950065\pi$
$491$	−7.94510	+	13.7613i	−0.358557	+	0.621040i	0.629163	+	0.777274i	$0.283398\pi$
$492$	−6.24574			−0.281580
$493$	1.00000	+	1.73205i	0.0450377	+	0.0780076i
$494$	6.86474			0.308859
$495$	21.2132			0.953463
$496$		0			0
$497$	1.47214			0.0660343
$498$	7.23607			0.324256
$499$	9.19239	+	15.9217i	0.411508	+	0.712752i	0.995055	−	0.0993269i	$-0.0316690\pi$
$499$	9.19239	+	15.9217i	0.411508	+	0.712752i	−0.583547	+	0.812079i	$0.698336\pi$
$500$	−54.2705			−2.42705
$501$	−0.472136	+	0.817763i	−0.0210935	+	0.0365350i
$502$	14.4366	+	25.0049i	0.644336	+	1.11602i
$503$	16.4443	+	28.4823i	0.733214	+	1.26996i	0.955503	+	0.294983i	$0.0953139\pi$
$503$	16.4443	+	28.4823i	0.733214	+	1.26996i	−0.222289	+	0.974981i	$0.571353\pi$
$504$	16.7082			0.744243
$505$	−2.50000	+	4.33013i	−0.111249	+	0.192688i
$506$	14.5623	−	25.2227i	0.647373	−	1.12128i
$507$	2.67655	−	4.63593i	0.118870	−	0.205889i
$508$	−23.0250	−	39.8805i	−1.02157	−	1.76941i
$509$	−3.97255	+	6.88066i	−0.176080	+	0.304980i	−0.940535	−	0.339698i	$-0.889675\pi$
$509$	−3.97255	+	6.88066i	−0.176080	+	0.304980i	0.764454	+	0.644678i	$0.223008\pi$
$510$	9.47214	+	16.4062i	0.419433	+	0.726480i
$511$	4.24264			0.187683
$512$	−40.3050			−1.78124
$513$	2.28825	+	3.96336i	0.101029	+	0.174987i
$514$	−7.92705	+	13.7301i	−0.349647	+	0.605607i
$515$	−11.9721	−	20.7363i	−0.527555	−	0.913753i
$516$	−20.5623	+	35.6150i	−0.905205	+	1.56786i
$517$	−20.5942	+	35.6702i	−0.905732	+	1.56877i
$518$	−5.55369	+	9.61927i	−0.244015	+	0.422647i
$519$	15.7326			0.690583
$520$	−21.9053	−	37.9410i	−0.960609	−	1.66382i
$521$	6.70820	+	11.6190i	0.293892	+	0.509035i	0.974726	−	0.223402i	$-0.0717161\pi$
$521$	6.70820	+	11.6190i	0.293892	+	0.509035i	−0.680835	+	0.732437i	$0.738383\pi$
$522$	1.58114	−	2.73861i	0.0692046	−	0.119866i
$523$	−0.618993			−0.0270667			−0.0135333	−	0.999908i	$-0.504308\pi$
$523$	−0.618993			−0.0270667			−0.0135333	+	0.999908i	$0.504308\pi$
$524$	−18.0000	−	31.1769i	−0.786334	−	1.36197i
$525$		0			0
$526$	−48.4658			−2.11321
$527$		0			0
$528$	−36.5410			−1.59024
$529$	−16.1246			−0.701070
$530$	−40.1869	−	69.6057i	−1.74561	−	3.02348i
$531$	−26.7082			−1.15904
$532$	2.42705	−	4.20378i	0.105226	−	0.182257i
$533$	1.93004	+	3.34293i	0.0835994	+	0.144798i
$534$	−17.5623	−	30.4188i	−0.759995	−	1.31635i
$535$	3.29180			0.142317
$536$	−22.4164	+	38.8264i	−0.968241	+	1.67704i
$537$	5.79837	−	10.0431i	0.250218	−	0.433391i
$538$	2.82843	−	4.89898i	0.121942	−	0.211210i
$539$	−12.7279	−	22.0454i	−0.548230	−	0.949563i
$540$	24.8369	−	43.0187i	1.06881	−	1.85123i
$541$	−12.9164	−	22.3719i	−0.555320	−	0.961842i	−0.997879	−	0.0651025i	$-0.979263\pi$
$541$	−12.9164	−	22.3719i	−0.555320	−	0.961842i	0.442559	−	0.896739i	$-0.354071\pi$
$542$	48.6722			2.09065
$543$	−7.59675			−0.326008
$544$	20.0934	+	34.8028i	0.861499	+	1.49216i
$545$	1.44427	−	2.50155i	0.0618658	−	0.107155i
$546$	3.00000	+	5.19615i	0.128388	+	0.222375i
$547$	−1.20820	+	2.09267i	−0.0516591	+	0.0894761i	−0.890699	−	0.454594i	$-0.849784\pi$
$547$	−1.20820	+	2.09267i	−0.0516591	+	0.0894761i	0.839040	+	0.544070i	$0.183118\pi$
$548$	−6.36396	+	11.0227i	−0.271855	+	0.470867i
$549$	−15.5807	+	26.9866i	−0.664968	+	1.15176i
$550$		0			0
$551$	−0.270091	−	0.467811i	−0.0115063	−	0.0199294i
$552$	−8.56231	−	14.8303i	−0.364436	−	0.631222i
$553$	0.810272	−	1.40343i	0.0344563	−	0.0596800i
$554$	−26.4574			−1.12407
$555$	4.14590	+	7.18091i	0.175984	+	0.304812i
$556$	87.2385			3.69974
$557$	10.6460			0.451086			0.225543	−	0.974233i	$-0.427584\pi$
$557$	10.6460			0.451086			0.225543	+	0.974233i	$0.427584\pi$
$558$		0			0
$559$	25.4164			1.07500
$560$	−22.0344			−0.931125
$561$	−6.86474	−	11.8901i	−0.289829	−	0.501999i
$562$	34.9787			1.47549
$563$	−4.88197	+	8.45581i	−0.205750	+	0.356370i	−0.950372	−	0.311117i	$-0.899297\pi$
$563$	−4.88197	+	8.45581i	−0.205750	+	0.356370i	0.744621	+	0.667487i	$0.232630\pi$
$564$	20.5942	+	35.6702i	0.867173	+	1.50199i
$565$	10.9164	+	18.9078i	0.459257	+	0.795456i
$566$	62.8328			2.64106
$567$	1.35410	−	2.34537i	0.0568669	−	0.0984964i
$568$	5.50000	−	9.52628i	0.230775	−	0.399714i
$569$	−5.86319	+	10.1553i	−0.245798	+	0.425734i	−0.962356	−	0.271794i	$-0.912383\pi$
$569$	−5.86319	+	10.1553i	−0.245798	+	0.425734i	0.716558	+	0.697527i	$0.245716\pi$
$570$	−2.55834	−	4.43117i	−0.107157	−	0.185601i
$571$	−1.31105	+	2.27080i	−0.0548657	+	0.0950301i	−0.892154	−	0.451732i	$-0.850806\pi$
$571$	−1.31105	+	2.27080i	−0.0548657	+	0.0950301i	0.837288	+	0.546762i	$0.184140\pi$
$572$	27.0000	+	46.7654i	1.12893	+	1.95536i
$573$	8.53399			0.356513
$574$	3.85410			0.160867
$575$		0			0
$576$	9.73607	−	16.8634i	0.405669	−	0.702640i
$577$	15.0000	+	25.9808i	0.624458	+	1.08159i	0.988645	+	0.150268i	$0.0480135\pi$
$577$	15.0000	+	25.9808i	0.624458	+	1.08159i	−0.364187	+	0.931326i	$0.618653\pi$
$578$	4.30902	−	7.46344i	0.179231	−	0.310438i
$579$	9.04982	−	15.6747i	0.376098	−	0.651420i
$580$	−2.93159	+	5.07767i	−0.121728	+	0.210839i
$581$	−3.16228			−0.131193
$582$	8.00886	+	13.8718i	0.331978	+	0.575003i
$583$	29.1246	+	50.4453i	1.20622	+	2.08923i
$584$	15.8508	−	27.4544i	0.655911	−	1.13607i
$585$	−13.1105			−0.542052
$586$	3.00000	+	5.19615i	0.123929	+	0.214651i
$587$	15.7326			0.649353			0.324676	−	0.945825i	$-0.394745\pi$
$587$	15.7326			0.649353			0.324676	+	0.945825i	$0.394745\pi$
$588$	−25.4558			−1.04978
$589$		0			0
$590$	69.9230			2.87868
$591$	0.944272			0.0388422
$592$	20.9037	+	36.2063i	0.859137	+	1.48807i
$593$	5.18034			0.212731			0.106366	−	0.994327i	$-0.466079\pi$
$593$	5.18034			0.212731			0.106366	+	0.994327i	$0.466079\pi$
$594$	−25.4164	+	44.0225i	−1.04285	+	1.80627i
$595$	−4.13948	−	7.16978i	−0.169702	−	0.293932i
$596$	32.5623	+	56.3996i	1.33380	+	2.31022i
$597$	−20.2918			−0.830488
$598$	−9.00000	+	15.5885i	−0.368037	+	0.637459i
$599$	−3.02786	+	5.24441i	−0.123715	+	0.214281i	−0.921230	−	0.389018i	$-0.872814\pi$
$599$	−3.02786	+	5.24441i	−0.123715	+	0.214281i	0.797515	+	0.603299i	$0.206148\pi$
$600$		0			0
$601$	9.08922	+	15.7430i	0.370757	+	0.642170i	0.989682	−	0.143280i	$-0.0457649\pi$
$601$	9.08922	+	15.7430i	0.370757	+	0.642170i	−0.618925	+	0.785450i	$0.712432\pi$
$602$	12.6885	−	21.9772i	0.517145	−	0.895722i
$603$	6.70820	+	11.6190i	0.273179	+	0.473160i
$604$	−60.7811			−2.47315
$605$	15.6525			0.636364
$606$	−2.55834	−	4.43117i	−0.103925	−	0.180004i
$607$	−7.56231	+	13.0983i	−0.306945	+	0.531644i	−0.977692	−	0.210042i	$-0.932640\pi$
$607$	−7.56231	+	13.0983i	−0.306945	+	0.531644i	0.670748	+	0.741685i	$0.265973\pi$
$608$	−5.42705	−	9.39993i	−0.220096	−	0.381217i
$609$	0.236068	−	0.408882i	0.00956596	−	0.0165687i
$610$	40.7908	−	70.6518i	1.65157	−	2.86061i
$611$	12.7279	−	22.0454i	0.514917	−	0.891862i
$612$	40.1869			1.62446
$613$	0.294445	+	0.509993i	0.0118925	+	0.0205984i	0.871910	−	0.489665i	$-0.162881\pi$
$613$	0.294445	+	0.509993i	0.0118925	+	0.0205984i	−0.860018	+	0.510264i	$0.829548\pi$
$614$	−31.5795	−	54.6973i	−1.27445	−	2.20741i
$615$	1.43857	−	2.49167i	0.0580086	−	0.100474i
$616$	31.7016			1.27729
$617$	3.43769	+	5.95426i	0.138396	+	0.239710i	0.926890	−	0.375334i	$-0.122472\pi$
$617$	3.43769	+	5.95426i	0.138396	+	0.239710i	−0.788493	+	0.615043i	$0.789139\pi$
$618$	24.5030			0.985655
$619$	−25.8384			−1.03853			−0.519267	−	0.854612i	$-0.673795\pi$
$619$	−25.8384			−1.03853			−0.519267	+	0.854612i	$0.673795\pi$
$620$		0			0
$621$	−12.0000			−0.481543
$622$	66.6869			2.67390
$623$	7.67501	+	13.2935i	0.307493	+	0.532593i
$624$	22.5836			0.904067
$625$	12.5000	−	21.6506i	0.500000	−	0.866025i
$626$	−15.0799	−	26.1192i	−0.602715	−	1.04393i
$627$	1.85410	+	3.21140i	0.0740457	+	0.128251i
$628$	42.2705			1.68678
$629$	−7.85410	+	13.6037i	−0.313164	+	0.542415i
$630$	−6.54508	+	11.3364i	−0.260762	+	0.451654i
$631$	−11.8145	+	20.4633i	−0.470327	+	0.814631i	−0.999424	−	0.0339308i	$-0.989197\pi$
$631$	−11.8145	+	20.4633i	−0.470327	+	0.814631i	0.529097	+	0.848561i	$0.322531\pi$
$632$	−6.05446	−	10.4866i	−0.240834	−	0.417136i
$633$	2.18508	−	3.78467i	0.0868491	−	0.150427i
$634$	−34.3435	−	59.4846i	−1.36395	−	2.36244i
$635$	21.2132			0.841820
$636$	58.2492			2.30973
$637$	7.86629	+	13.6248i	0.311674	+	0.539835i
$638$	3.00000	−	5.19615i	0.118771	−	0.205718i
$639$	−1.64590	−	2.85078i	−0.0651107	−	0.112775i
$640$	−1.21885	+	2.11111i	−0.0481792	+	0.0834488i
$641$	−4.24264	+	7.34847i	−0.167574	+	0.290247i	−0.937566	−	0.347806i	$-0.886927\pi$
$641$	−4.24264	+	7.34847i	−0.167574	+	0.290247i	0.769992	+	0.638053i	$0.220260\pi$
$642$	−1.68430	+	2.91730i	−0.0664742	+	0.115137i
$643$	4.65530			0.183587			0.0917936	−	0.995778i	$-0.470740\pi$
$643$	4.65530			0.183587			0.0917936	+	0.995778i	$0.470740\pi$
$644$	6.36396	+	11.0227i	0.250775	+	0.434355i
$645$	−9.47214	−	16.4062i	−0.372965	−	0.645994i
$646$	4.84658	−	8.39453i	0.190686	−	0.330278i
$647$	−31.7804			−1.24942			−0.624708	−	0.780858i	$-0.714782\pi$
$647$	−31.7804			−1.24942			−0.624708	+	0.780858i	$0.714782\pi$
$648$	−10.1180	−	17.5249i	−0.397474	−	0.688445i
$649$	−50.6753			−1.98918
$650$		0			0
$651$		0			0
$652$	69.9787			2.74058
$653$	24.6525			0.964726			0.482363	−	0.875971i	$-0.339779\pi$
$653$	24.6525			0.964726			0.482363	+	0.875971i	$0.339779\pi$
$654$	1.47797	+	2.55992i	0.0577933	+	0.100101i
$655$	16.5836			0.647975
$656$	7.25329	−	12.5631i	0.283193	−	0.490505i
$657$	−4.74342	−	8.21584i	−0.185058	−	0.320530i
$658$	−12.7082	−	22.0113i	−0.495417	−	0.858088i
$659$	24.8197			0.966837			0.483418	−	0.875389i	$-0.339395\pi$
$659$	24.8197			0.966837			0.483418	+	0.875389i	$0.339395\pi$
$660$	20.1246	−	34.8569i	0.783349	−	1.35680i
$661$	−3.91641	+	6.78342i	−0.152331	+	0.263844i	−0.932084	−	0.362243i	$-0.882011\pi$
$661$	−3.91641	+	6.78342i	−0.152331	+	0.263844i	0.779753	+	0.626087i	$0.215345\pi$
$662$	40.9577	−	70.9409i	1.59187	−	2.75720i
$663$	4.24264	+	7.34847i	0.164771	+	0.285391i
$664$	−11.8145	+	20.4633i	−0.458491	+	0.794130i
$665$	1.11803	+	1.93649i	0.0433555	+	0.0750939i
$666$	24.8369			0.962408
$667$	1.41641			0.0548435
$668$	−2.62210	−	4.54160i	−0.101452	−	0.175720i
$669$	7.05573	−	12.2209i	0.272790	−	0.472487i
$670$	−17.5623	−	30.4188i	−0.678491	−	1.17518i
$671$	−29.5623	+	51.2034i	−1.14124	+	1.97669i
$672$	4.74342	−	8.21584i	0.182981	−	0.316933i
$673$	19.9903	−	34.6242i	0.770568	−	1.33466i	−0.166684	−	0.986010i	$-0.553306\pi$
$673$	19.9903	−	34.6242i	0.770568	−	1.33466i	0.937252	−	0.348653i	$-0.113361\pi$
$674$	40.1869			1.54794
$675$		0			0
$676$	14.8647	+	25.7465i	0.571721	+	0.990250i
$677$	−10.6066	+	18.3712i	−0.407645	+	0.706062i	−0.994625	−	0.103540i	$-0.966983\pi$
$677$	−10.6066	+	18.3712i	−0.407645	+	0.706062i	0.586981	+	0.809601i	$0.300317\pi$
$678$	−22.3423			−0.858050
$679$	−3.50000	−	6.06218i	−0.134318	−	0.232645i
$680$	−61.8614			−2.37228
$681$	2.00310			0.0767591
$682$		0			0
$683$	−41.1803			−1.57572			−0.787861	−	0.615853i	$-0.788811\pi$
$683$	−41.1803			−1.57572			−0.787861	+	0.615853i	$0.788811\pi$
$684$	−10.8541			−0.415017
$685$	−2.93159	−	5.07767i	−0.112010	−	0.194008i
$686$	34.0344			1.29944
$687$	1.85410	−	3.21140i	0.0707384	−	0.122523i
$688$	−47.7587	−	82.7205i	−1.82078	−	3.15369i
$689$	−18.0000	−	31.1769i	−0.685745	−	1.18775i
$690$	13.4164			0.510754
$691$	24.2082	−	41.9298i	0.920923	−	1.59509i	0.122934	−	0.992415i	$-0.460770\pi$
$691$	24.2082	−	41.9298i	0.920923	−	1.59509i	0.797989	−	0.602671i	$-0.205897\pi$
$692$	−43.6869	+	75.6680i	−1.66073	+	2.87646i
$693$	4.74342	−	8.21584i	0.180187	−	0.312094i
$694$	−28.2692	−	48.9637i	−1.07308	−	1.85864i
$695$	−20.0934	+	34.8028i	−0.762187	+	1.32015i
$696$	−1.76393	−	3.05522i	−0.0668617	−	0.115808i
$697$	5.45052			0.206453
$698$	15.7082			0.594564
$699$	5.88754	+	10.1975i	0.222687	+	0.385706i
$700$		0			0
$701$	1.82624	+	3.16314i	0.0689761	+	0.119470i	0.898451	−	0.439074i	$-0.144693\pi$
$701$	1.82624	+	3.16314i	0.0689761	+	0.119470i	−0.829475	+	0.558544i	$0.811360\pi$
$702$	15.7082	−	27.2074i	0.592868	−	1.02688i
$703$	2.12132	−	3.67423i	0.0800071	−	0.138576i
$704$	18.4729	−	31.9960i	0.696223	−	1.20589i
$705$	−18.9737			−0.714590
$706$	12.5216	+	21.6880i	0.471256	+	0.816240i
$707$	1.11803	+	1.93649i	0.0420480	+	0.0728293i
$708$	−25.3376	+	43.8861i	−0.952246	+	1.64934i
$709$	41.1884			1.54686			0.773432	−	0.633880i	$-0.218538\pi$
$709$	41.1884			1.54686			0.773432	+	0.633880i	$0.218538\pi$
$710$	4.30902	+	7.46344i	0.161715	+	0.280098i
$711$	−3.62365			−0.135897
$712$	114.697			4.29847
$713$		0			0
$714$	8.47214			0.317062
$715$	−24.8754			−0.930287
$716$	32.2024	+	55.7761i	1.20346	+	2.08445i
$717$	−10.5836			−0.395251
$718$	−18.6353	+	32.2772i	−0.695462	+	1.20457i
$719$	−18.7824	−	32.5320i	−0.700465	−	1.21324i	−0.968303	−	0.249777i	$-0.919643\pi$
$719$	−18.7824	−	32.5320i	−0.700465	−	1.21324i	0.267839	−	0.963464i	$-0.413691\pi$
$720$	24.6353	+	42.6695i	0.918102	+	1.59020i
$721$	−10.7082			−0.398794
$722$	23.5623	−	40.8111i	0.876898	−	1.51883i
$723$	−10.1459	+	17.5732i	−0.377330	+	0.653555i
$724$	21.0950	−	36.5376i	0.783989	−	1.35791i
$725$		0			0
$726$	−8.00886	+	13.8718i	−0.297237	+	0.514829i
$727$	15.2082	+	26.3414i	0.564041	+	0.976948i	0.997138	+	0.0756005i	$0.0240874\pi$
$727$	15.2082	+	26.3414i	0.564041	+	0.976948i	−0.433097	+	0.901347i	$0.642579\pi$
$728$	−19.5927			−0.726152
$729$	5.94427			0.220158
$730$	12.4184	+	21.5093i	0.459627	+	0.796097i
$731$	17.9443	−	31.0804i	0.663693	−	1.14955i
$732$	29.5623	+	51.2034i	1.09265	+	1.89253i
$733$	7.20820	−	12.4850i	0.266241	−	0.461143i	−0.701647	−	0.712525i	$-0.747552\pi$
$733$	7.20820	−	12.4850i	0.266241	−	0.461143i	0.967888	+	0.251382i	$0.0808849\pi$
$734$	8.71597	−	15.0965i	0.321712	−	0.557222i
$735$	5.86319	−	10.1553i	0.216267	−	0.374585i
$736$	28.4605			1.04907
$737$	12.7279	+	22.0454i	0.468839	+	0.812053i
$738$	−4.30902	−	7.46344i	−0.158617	−	0.274733i
$739$	−17.5745	+	30.4399i	−0.646489	+	1.11975i	0.337467	+	0.941337i	$0.390430\pi$
$739$	−17.5745	+	30.4399i	−0.646489	+	1.11975i	−0.983956	+	0.178414i	$0.942903\pi$
$740$	−46.0501			−1.69283
$741$	−1.14590	−	1.98475i	−0.0420956	−	0.0729117i
$742$	−35.9442			−1.31955
$743$	36.4844			1.33848			0.669242	−	0.743045i	$-0.266619\pi$
$743$	36.4844			1.33848			0.669242	+	0.743045i	$0.266619\pi$
$744$		0			0
$745$	−30.0000			−1.09911
$746$	−24.3262			−0.890647
$747$	3.53553	+	6.12372i	0.129358	+	0.224055i
$748$	76.2492			2.78795
$749$	0.736068	−	1.27491i	0.0268953	−	0.0465841i
$750$	12.7917	+	22.1558i	0.467086	+	0.809017i
$751$	18.7705	+	32.5115i	0.684946	+	1.18636i	0.973454	+	0.228883i	$0.0735074\pi$
$751$	18.7705	+	32.5115i	0.684946	+	1.18636i	−0.288508	+	0.957477i	$0.593159\pi$
$752$	−95.6656			−3.48857
$753$	4.81966	−	8.34790i	0.175638	−	0.304214i
$754$	−1.85410	+	3.21140i	−0.0675224	+	0.116952i
$755$	13.9996	−	24.2480i	0.509496	−	0.882474i
$756$	−11.1074	−	19.2385i	−0.403971	−	0.699699i
$757$	4.64025	−	8.03715i	0.168653	−	0.292115i	−0.769294	−	0.638895i	$-0.779392\pi$
$757$	4.64025	−	8.03715i	0.168653	−	0.292115i	0.937946	+	0.346780i	$0.112725\pi$
$758$	−9.70820	−	16.8151i	−0.352618	−	0.610752i
$759$	−9.72327			−0.352932
$760$	16.7082			0.606070
$761$	20.0934	+	34.8028i	0.728386	+	1.26160i	0.957565	+	0.288218i	$0.0930627\pi$
$761$	20.0934	+	34.8028i	0.728386	+	1.26160i	−0.229178	+	0.973384i	$0.573604\pi$
$762$	−10.8541	+	18.7999i	−0.393203	+	0.681047i
$763$	−0.645898	−	1.11873i	−0.0233831	−	0.0405007i
$764$	−23.6976	+	41.0454i	−0.857348	+	1.48497i
$765$	−9.25615	+	16.0321i	−0.334657	+	0.579642i
$766$	−8.38212	+	14.5183i	−0.302858	+	0.524566i
$767$	31.3190			1.13086
$768$	6.36396	+	11.0227i	0.229640	+	0.397748i
$769$	−27.0623	−	46.8733i	−0.975892	−	1.69029i	−0.676960	−	0.736019i	$-0.736703\pi$
$769$	−27.0623	−	46.8733i	−0.975892	−	1.69029i	−0.298931	−	0.954275i	$-0.596630\pi$
$770$	−12.4184	+	21.5093i	−0.447529	+	0.775143i
$771$	5.29290			0.190619
$772$	50.2599	+	87.0526i	1.80889	+	3.13309i
$773$	11.1862			0.402339			0.201170	−	0.979556i	$-0.435526\pi$
$773$	11.1862			0.402339			0.201170	+	0.979556i	$0.435526\pi$
$774$	−56.7448			−2.03965
$775$		0			0
$776$	−52.3050			−1.87764
$777$	3.70820			0.133031
$778$	−22.0084	−	38.1197i	−0.789040	−	1.36666i
$779$	−1.47214			−0.0527447
$780$	−12.4377	+	21.5427i	−0.445341	+	0.771353i
$781$	−3.12287	−	5.40897i	−0.111745	−	0.193548i
$782$	12.7082	+	22.0113i	0.454444	+	0.787121i
$783$	−2.47214			−0.0883469
$784$	29.5623	−	51.2034i	1.05580	−	1.82869i
$785$	−9.73607	+	16.8634i	−0.347495	+	0.601879i
$786$	−8.48528	+	14.6969i	−0.302660	+	0.524222i
$787$	−18.7824	−	32.5320i	−0.669520	−	1.15964i	−0.978039	−	0.208424i	$-0.933167\pi$
$787$	−18.7824	−	32.5320i	−0.669520	−	1.15964i	0.308519	−	0.951218i	$-0.400167\pi$
$788$	−2.62210	+	4.54160i	−0.0934083	+	0.161788i
$789$	8.09017	+	14.0126i	0.288018	+	0.498861i
$790$	9.48683			0.337526
$791$	9.76393			0.347165
$792$	−35.4435	−	61.3899i	−1.25943	−	2.18139i
$793$	18.2705	−	31.6455i	0.648805	−	1.12376i
$794$	−19.2533	−	33.3477i	−0.683274	−	1.18346i
$795$	−13.4164	+	23.2379i	−0.475831	+	0.824163i
$796$	56.3472	−	97.5961i	1.99717	−	3.45920i
$797$	−6.86474	+	11.8901i	−0.243161	+	0.421168i	−0.961613	−	0.274409i	$-0.911518\pi$
$797$	−6.86474	+	11.8901i	−0.243161	+	0.421168i	0.718452	+	0.695577i	$0.244851\pi$
$798$	−2.28825			−0.0810030
$799$	−17.9721	−	31.1286i	−0.635808	−	1.10125i
$800$		0			0
$801$	17.1618	−	29.7252i	0.606384	−	1.05029i
$802$	1.41421			0.0499376
$803$	−9.00000	−	15.5885i	−0.317603	−	0.550105i
$804$	25.4558			0.897758
$805$	−5.86319			−0.206650
$806$		0			0
$807$	−1.88854			−0.0664799
$808$	16.7082			0.587793
$809$	23.7565	+	41.1474i	0.835234	+	1.44667i	0.893840	+	0.448386i	$0.148001\pi$
$809$	23.7565	+	41.1474i	0.835234	+	1.44667i	−0.0586064	+	0.998281i	$0.518666\pi$
$810$	15.8541			0.557056
$811$	8.29180	−	14.3618i	0.291164	−	0.504311i	−0.682921	−	0.730492i	$-0.739291\pi$
$811$	8.29180	−	14.3618i	0.291164	−	0.504311i	0.974085	+	0.226181i	$0.0726240\pi$
$812$	1.31105	+	2.27080i	0.0460088	+	0.0796895i
$813$	−8.12461	−	14.0722i	−0.284943	−	0.493535i
$814$	47.1246			1.65172
$815$	−16.1180	+	27.9173i	−0.564590	+	0.977899i
$816$	15.9443	−	27.6163i	0.558161	−	0.966763i
$817$	−4.84658	+	8.39453i	−0.169560	+	0.293687i
$818$	39.3766	+	68.2023i	1.37677	+	2.38464i
$819$	−2.93159	+	5.07767i	−0.102438	+	0.177428i
$820$	7.98936	+	13.8380i	0.279000	+	0.483243i
$821$	−23.8353			−0.831858			−0.415929	−	0.909397i	$-0.636543\pi$
$821$	−23.8353			−0.831858			−0.415929	+	0.909397i	$0.636543\pi$
$822$	6.00000			0.209274
$823$	−6.76157	−	11.7114i	−0.235694	−	0.408233i	0.723780	−	0.690030i	$-0.242403\pi$
$823$	−6.76157	−	11.7114i	−0.235694	−	0.408233i	−0.959474	+	0.281797i	$0.909069\pi$
$824$	−40.0066	+	69.2934i	−1.39370	+	2.41395i
$825$		0			0
$826$	15.6353	−	27.0811i	0.544020	−	0.942270i
$827$	−9.17734	+	15.8956i	−0.319127	+	0.552745i	−0.980306	−	0.197484i	$-0.936723\pi$
$827$	−9.17734	+	15.8956i	−0.319127	+	0.552745i	0.661179	+	0.750228i	$0.270056\pi$
$828$	14.2302	−	24.6475i	0.494535	−	0.856560i
$829$	−51.0879			−1.77436			−0.887178	−	0.461427i	$-0.847338\pi$
$829$	−51.0879			−1.77436			−0.887178	+	0.461427i	$0.847338\pi$
$830$	−9.25615	−	16.0321i	−0.321286	−	0.556483i
$831$	4.41641	+	7.64944i	0.153203	+	0.265356i
$832$	−11.4169	+	19.7746i	−0.395809	+	0.685561i
$833$	22.2148			0.769696
$834$	−20.5623	−	35.6150i	−0.712014	−	1.23325i
$835$	2.41577			0.0836010
$836$	−20.5942			−0.712266
$837$		0			0
$838$	80.1033			2.76712
$839$	−19.4164			−0.670329			−0.335164	−	0.942160i	$-0.608792\pi$
$839$	−19.4164			−0.670329			−0.335164	+	0.942160i	$0.608792\pi$
$840$	7.30175	+	12.6470i	0.251934	+	0.436363i
$841$	−28.7082			−0.989938
$842$	−34.5795	+	59.8935i	−1.19169	+	2.06407i
$843$	−5.83883	−	10.1132i	−0.201100	−	0.348315i
$844$	12.1353	+	21.0189i	0.417713	+	0.723500i
$845$	−13.6950			−0.471124
$846$	−28.4164	+	49.2187i	−0.976976	+	1.69217i
$847$	3.50000	−	6.06218i	0.120261	−	0.208299i
$848$	−67.6458	+	117.166i	−2.32297	+	4.02350i
$849$	−10.4884	−	18.1664i	−0.359960	−	0.623470i
$850$		0			0
$851$	5.56231	+	9.63420i	0.190673	+	0.330256i
$852$	−6.24574			−0.213976
$853$	−32.2918			−1.10565			−0.552825	−	0.833297i	$-0.686450\pi$
$853$	−32.2918			−1.10565			−0.552825	+	0.833297i	$0.686450\pi$
$854$	−18.2422	−	31.5964i	−0.624235	−	1.08121i
$855$	2.50000	−	4.33013i	0.0854982	−	0.148087i
$856$	−5.50000	−	9.52628i	−0.187986	−	0.325602i
$857$	3.00000	−	5.19615i	0.102478	−	0.177497i	−0.810227	−	0.586116i	$-0.800656\pi$
$857$	3.00000	−	5.19615i	0.102478	−	0.177497i	0.912705	+	0.408619i	$0.133990\pi$
$858$	12.7279	−	22.0454i	0.434524	−	0.752618i
$859$	−20.8005	+	36.0276i	−0.709705	+	1.22925i	0.255261	+	0.966872i	$0.417839\pi$
$859$	−20.8005	+	36.0276i	−0.709705	+	1.22925i	−0.964966	+	0.262374i	$0.915495\pi$
$860$	105.211			3.58765
$861$	−0.643347	−	1.11431i	−0.0219252	−	0.0379756i
$862$	46.9787	+	81.3695i	1.60010	+	2.77146i
$863$	−15.5413	+	26.9183i	−0.529032	+	0.916310i	0.470395	+	0.882456i	$0.344111\pi$
$863$	−15.5413	+	26.9183i	−0.529032	+	0.916310i	−0.999427	+	0.0338541i	$0.989222\pi$
$864$	−49.6737			−1.68993
$865$	−20.1246	−	34.8569i	−0.684257	−	1.18517i
$866$	67.6458			2.29870
$867$	−2.87714			−0.0977126
$868$		0			0
$869$	−6.87539			−0.233232
$870$	2.76393			0.0937061
$871$	−7.86629	−	13.6248i	−0.266539	−	0.461659i
$872$	−9.65248			−0.326874
$873$	−7.82624	+	13.5554i	−0.264878	+	0.458782i
$874$	−3.43237	−	5.94504i	−0.116102	−	0.201094i
$875$	−5.59017	−	9.68246i	−0.188982	−	0.327327i
$876$	−18.0000			−0.608164
$877$	14.3541	−	24.8620i	0.484704	−	0.839531i	−0.515142	−	0.857105i	$-0.672261\pi$
$877$	14.3541	−	24.8620i	0.484704	−	0.839531i	0.999846	+	0.0175736i	$0.00559415\pi$
$878$	32.7254	−	56.6821i	1.10443	−	1.91293i
$879$	1.00155	−	1.73474i	0.0337815	−	0.0585113i
$880$	46.7421	+	80.9597i	1.57568	+	2.72915i
$881$	3.62365	−	6.27634i	0.122084	−	0.211455i	−0.798505	−	0.601988i	$-0.794376\pi$
$881$	3.62365	−	6.27634i	0.122084	−	0.211455i	0.920589	+	0.390532i	$0.127709\pi$
$882$	−17.5623	−	30.4188i	−0.591354	−	1.02425i
$883$	33.9411			1.14221			0.571105	−	0.820877i	$-0.306515\pi$
$883$	33.9411			1.14221			0.571105	+	0.820877i	$0.306515\pi$
$884$	−47.1246			−1.58497
$885$	−11.6719	−	20.2163i	−0.392347	−	0.679565i
$886$	−7.92705	+	13.7301i	−0.266314	+	0.461270i
$887$	−12.6803	−	21.9630i	−0.425764	−	0.737445i	0.570727	−	0.821140i	$-0.306661\pi$
$887$	−12.6803	−	21.9630i	−0.425764	−	0.737445i	−0.996491	+	0.0836945i	$0.973328\pi$
$888$	13.8541	−	23.9960i	0.464913	−	0.805253i
$889$	4.74342	−	8.21584i	0.159089	−	0.275550i
$890$	−44.9303	+	77.8215i	−1.50607	+	2.60858i
$891$	−11.4899			−0.384927
$892$	39.1853	+	67.8710i	1.31202	+	2.27249i
$893$	4.85410	+	8.40755i	0.162436	+	0.281348i
$894$	15.3500	−	26.5870i	0.513381	−	0.889203i
$895$	−29.6684			−0.991705
$896$	0.545085	+	0.944115i	0.0182100	+	0.0315407i
$897$	6.00931			0.200645
$898$	−88.2400			−2.94461
$899$		0			0
$900$		0			0
$901$	−50.8328			−1.69349
$902$	−8.17578	−	14.1609i	−0.272224	−	0.471506i
$903$	−8.47214			−0.281935
$904$	36.4787	−	63.1830i	1.21326	−	2.10143i
$905$	9.71752	+	16.8312i	0.323021	+	0.559489i
$906$	14.3262	+	24.8138i	0.475957	+	0.824382i
$907$	11.5410			0.383213			0.191607	−	0.981472i	$-0.438630\pi$
$907$	11.5410			0.383213			0.191607	+	0.981472i	$0.438630\pi$
$908$	−5.56231	+	9.63420i	−0.184592	+	0.319722i
$909$	2.50000	−	4.33013i	0.0829198	−	0.143621i
$910$	7.67501	−	13.2935i	0.254424	−	0.440675i
$911$	−13.4594	−	23.3123i	−0.445929	−	0.772372i	0.552187	−	0.833720i	$-0.313793\pi$
$911$	−13.4594	−	23.3123i	−0.445929	−	0.772372i	−0.998116	+	0.0613480i	$0.980460\pi$
$912$	−4.30640	+	7.45890i	−0.142599	+	0.246989i
$913$	6.70820	+	11.6190i	0.222009	+	0.384531i
$914$	−29.6197			−0.979732
$915$	−27.2361			−0.900397
$916$	10.2971	+	17.8351i	0.340226	+	0.589289i
$917$	3.70820	−	6.42280i	0.122456	−	0.212099i
$918$	−22.1803	−	38.4175i	−0.732060	−	1.26797i
$919$	21.2705	−	36.8416i	0.701649	−	1.21529i	−0.266238	−	0.963907i	$-0.585781\pi$
$919$	21.2705	−	36.8416i	0.701649	−	1.21529i	0.967887	−	0.251385i	$-0.0808860\pi$
$920$	−21.9053	+	37.9410i	−0.722195	+	1.25088i
$921$	−10.5428	+	18.2607i	−0.347398	+	0.601712i
$922$	−13.5231			−0.445361
$923$	1.93004	+	3.34293i	0.0635281	+	0.110034i
$924$	−9.00000	−	15.5885i	−0.296078	−	0.512823i
$925$		0			0
$926$	10.0270			0.329508
$927$	11.9721	+	20.7363i	0.393217	+	0.681071i
$928$	5.86319			0.192468
$929$	−10.6460			−0.349284			−0.174642	−	0.984632i	$-0.555877\pi$
$929$	−10.6460			−0.349284			−0.174642	+	0.984632i	$0.555877\pi$
$930$		0			0
$931$	−6.00000			−0.196642
$932$	−65.3951			−2.14209
$933$	−11.1317	−	19.2807i	−0.364437	−	0.631223i
$934$	−40.9787			−1.34086
$935$	−17.5623	+	30.4188i	−0.574349	+	0.994801i
$936$	21.9053	+	37.9410i	0.715996	+	1.24014i
$937$	−12.1246	−	21.0004i	−0.396094	−	0.686055i	0.597146	−	0.802132i	$-0.296301\pi$
$937$	−12.1246	−	21.0004i	−0.396094	−	0.686055i	−0.993240	+	0.116078i	$0.962968\pi$
$938$	−15.7082			−0.512891
$939$	−5.03444	+	8.71991i	−0.164293	+	0.284563i
$940$	52.6869	−	91.2564i	1.71846	−	2.97646i
$941$	12.7673	−	22.1137i	0.416203	−	0.720885i	−0.579351	−	0.815078i	$-0.696694\pi$
$941$	12.7673	−	22.1137i	0.416203	−	0.720885i	0.995554	+	0.0941935i	$0.0300272\pi$
$942$	−9.96325	−	17.2569i	−0.324620	−	0.562259i
$943$	1.93004	−	3.34293i	0.0628508	−	0.108861i
$944$	−58.8500	−	101.931i	−1.91541	−	3.31758i
$945$	10.2333			0.332891
$946$	−107.666			−3.50051
$947$	20.0934	+	34.8028i	0.652949	+	1.13094i	0.982404	+	0.186769i	$0.0598017\pi$
$947$	20.0934	+	34.8028i	0.652949	+	1.13094i	−0.329455	+	0.944171i	$0.606865\pi$
$948$	−3.43769	+	5.95426i	−0.111651	+	0.193385i
$949$	5.56231	+	9.63420i	0.180560	+	0.312739i
$950$		0			0
$951$	−11.4656	+	19.8590i	−0.371797	+	0.643971i
$952$	−13.8326	+	23.9588i	−0.448318	+	0.776510i
$953$	−18.6699			−0.604778			−0.302389	−	0.953185i	$-0.597784\pi$
$953$	−18.6699			−0.604778			−0.302389	+	0.953185i	$0.597784\pi$
$954$	40.1869	+	69.6057i	1.30110	+	2.25357i
$955$	−10.9164	−	18.9078i	−0.353247	−	0.611841i
$956$	29.3890	−	50.9032i	0.950508	−	1.64633i
$957$	−2.00310			−0.0647511
$958$	−21.6353	−	37.4734i	−0.699003	−	1.21071i
$959$	−2.62210			−0.0846719
$960$	17.0193			0.549295
$961$		0			0
$962$	−29.1246			−0.939015
$963$	−3.29180			−0.106077
$964$	−56.3472	−	97.5961i	−1.81482	−	3.14336i
$965$	−46.3050			−1.49061
$966$	3.00000	−	5.19615i	0.0965234	−	0.167183i
$967$	22.0084	+	38.1197i	0.707743	+	1.22585i	0.965692	+	0.259689i	$0.0836200\pi$
$967$	22.0084	+	38.1197i	0.707743	+	1.22585i	−0.257949	+	0.966158i	$0.583047\pi$
$968$	−26.1525	−	45.2974i	−0.840572	−	1.45591i
$969$	−3.23607			−0.103957
$970$	20.4894	−	35.4886i	0.657874	−	1.13947i
$971$	−26.9443	+	46.6688i	−0.864683	+	1.49767i	0.00267892	+	0.999996i	$0.499147\pi$
$971$	−26.9443	+	46.6688i	−0.864683	+	1.49767i	−0.867362	+	0.497678i	$0.834186\pi$
$972$	−39.0671	+	67.6662i	−1.25308	+	2.17039i
$973$	8.98606	+	15.5643i	0.288080	+	0.498969i
$974$	36.7545	−	63.6607i	1.17769	−	2.03982i
$975$		0			0
$976$	−137.325			−4.39566
$977$	−42.4853			−1.35922			−0.679612	−	0.733571i	$-0.737852\pi$
$977$	−42.4853			−1.35922			−0.679612	+	0.733571i	$0.737852\pi$
$978$	−16.4941	−	28.5687i	−0.527424	−	0.913526i
$979$	32.5623	−	56.3996i	1.04070	−	1.80254i
$980$	32.5623	+	56.3996i	1.04016	+	1.80162i
$981$	−1.44427	+	2.50155i	−0.0461121	+	0.0798684i
$982$	−20.8005	+	36.0276i	−0.663772	+	1.14969i
$983$	26.9582	−	46.6929i	0.859832	−	1.48927i	−0.0122564	−	0.999925i	$-0.503901\pi$
$983$	26.9582	−	46.6929i	0.859832	−	1.48927i	0.872089	−	0.489348i	$-0.162765\pi$
$984$	−9.61435			−0.306494
$985$	−1.20788	−	2.09211i	−0.0384863	−	0.0666603i
$986$	2.61803	+	4.53457i	0.0833752	+	0.144410i
$987$	−4.24264	+	7.34847i	−0.135045	+	0.233904i
$988$	12.7279			0.404929
$989$	−12.7082	−	22.0113i	−0.404097	−	0.699917i
$990$	55.5369			1.76508
$991$	13.9358			0.442685			0.221343	−	0.975196i	$-0.428956\pi$
$991$	13.9358			0.442685			0.221343	+	0.975196i	$0.428956\pi$
$992$		0			0
$993$	−27.3475			−0.867847
$994$	3.85410			0.122245
$995$	25.9566	+	44.9582i	0.822880	+	1.42527i
$996$	13.4164			0.425115
$997$	29.3328	−	50.8059i	0.928980	−	1.60904i	0.143947	−	0.989585i	$-0.454021\pi$
$997$	29.3328	−	50.8059i	0.928980	−	1.60904i	0.785033	−	0.619454i	$-0.212646\pi$
$998$	24.0660	+	41.6835i	0.761795	+	1.31947i
$999$	−9.70820	−	16.8151i	−0.307154	−	0.532006i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.c.h.521.3		8
31.2	even	5		961.2.g.p.844.1		16
31.3	odd	30		961.2.d.j.628.1		8
31.4	even	5		961.2.g.i.338.1		16
31.5	even	3	inner	961.2.c.h.439.3		8
31.6	odd	6		961.2.a.h.1.3	✓	4
31.7	even	15		961.2.d.h.388.1		8
31.8	even	5		961.2.g.i.732.2		16
31.9	even	15		961.2.g.i.816.1		16
31.10	even	15		961.2.g.p.547.2		16
31.11	odd	30		961.2.g.i.235.1		16
31.12	odd	30		961.2.d.j.531.1		8
31.13	odd	30		961.2.g.p.846.2		16
31.14	even	15		961.2.d.h.374.1		8
31.15	odd	10		961.2.g.p.448.1		16
31.16	even	5		961.2.g.p.448.2		16
31.17	odd	30		961.2.d.h.374.2		8
31.18	even	15		961.2.g.p.846.1		16
31.19	even	15		961.2.d.j.531.2		8
31.20	even	15		961.2.g.i.235.2		16
31.21	odd	30		961.2.g.p.547.1		16
31.22	odd	30		961.2.g.i.816.2		16
31.23	odd	10		961.2.g.i.732.1		16
31.24	odd	30		961.2.d.h.388.2		8
31.25	even	3		961.2.a.h.1.4	yes	4
31.26	odd	6	inner	961.2.c.h.439.4		8
31.27	odd	10		961.2.g.i.338.2		16
31.28	even	15		961.2.d.j.628.2		8
31.29	odd	10		961.2.g.p.844.2		16
31.30	odd	2	inner	961.2.c.h.521.4		8
93.56	odd	6		8649.2.a.r.1.2		4
93.68	even	6		8649.2.a.r.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
961.2.a.h.1.3	✓	4	31.6	odd	6
961.2.a.h.1.4	yes	4	31.25	even	3
961.2.c.h.439.3		8	31.5	even	3	inner
961.2.c.h.439.4		8	31.26	odd	6	inner
961.2.c.h.521.3		8	1.1	even	1	trivial
961.2.c.h.521.4		8	31.30	odd	2	inner
961.2.d.h.374.1		8	31.14	even	15
961.2.d.h.374.2		8	31.17	odd	30
961.2.d.h.388.1		8	31.7	even	15
961.2.d.h.388.2		8	31.24	odd	30
961.2.d.j.531.1		8	31.12	odd	30
961.2.d.j.531.2		8	31.19	even	15
961.2.d.j.628.1		8	31.3	odd	30
961.2.d.j.628.2		8	31.28	even	15
961.2.g.i.235.1		16	31.11	odd	30
961.2.g.i.235.2		16	31.20	even	15
961.2.g.i.338.1		16	31.4	even	5
961.2.g.i.338.2		16	31.27	odd	10
961.2.g.i.732.1		16	31.23	odd	10
961.2.g.i.732.2		16	31.8	even	5
961.2.g.i.816.1		16	31.9	even	15
961.2.g.i.816.2		16	31.22	odd	30
961.2.g.p.448.1		16	31.15	odd	10
961.2.g.p.448.2		16	31.16	even	5
961.2.g.p.547.1		16	31.21	odd	30
961.2.g.p.547.2		16	31.10	even	15
961.2.g.p.844.1		16	31.2	even	5
961.2.g.p.844.2		16	31.29	odd	10
961.2.g.p.846.1		16	31.18	even	15
961.2.g.p.846.2		16	31.13	odd	30
8649.2.a.r.1.1		4	93.68	even	6
8649.2.a.r.1.2		4	93.56	odd	6

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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.61803 q^{2} +(-0.437016 - 0.756934i) q^{3} +4.85410 q^{4} +(-1.11803 + 1.93649i) q^{5} +(-1.14412 - 1.98168i) q^{6} +(0.500000 + 0.866025i) q^{7} +7.47214 q^{8} +(1.11803 - 1.93649i) q^{9} +(-2.92705 + 5.06980i) q^{10} +(2.12132 - 3.67423i) q^{11} +(-2.12132 - 3.67423i) q^{12} +(-1.31105 + 2.27080i) q^{13} +(1.30902 + 2.26728i) q^{14} +1.95440 q^{15} +9.85410 q^{16} +(1.85123 + 3.20642i) q^{17} +(2.92705 - 5.06980i) q^{18} +(-0.500000 - 0.866025i) q^{19} +(-5.42705 + 9.39993i) q^{20} +(0.437016 - 0.756934i) q^{21} +(5.55369 - 9.61927i) q^{22} +2.62210 q^{23} +(-3.26544 - 5.65591i) q^{24} +(-3.43237 + 5.94504i) q^{26} -4.57649 q^{27} +(2.42705 + 4.20378i) q^{28} +0.540182 q^{29} +5.11667 q^{30} +10.8541 q^{32} -3.70820 q^{33} +(4.84658 + 8.39453i) q^{34} -2.23607 q^{35} +(5.42705 - 9.39993i) q^{36} +(2.12132 + 3.67423i) q^{37} +(-1.30902 - 2.26728i) q^{38} +2.29180 q^{39} +(-8.35410 + 14.4697i) q^{40} +(0.736068 - 1.27491i) q^{41} +(1.14412 - 1.98168i) q^{42} +(-4.84658 - 8.39453i) q^{43} +(10.2971 - 17.8351i) q^{44} +(2.50000 + 4.33013i) q^{45} +6.86474 q^{46} -9.70820 q^{47} +(-4.30640 - 7.45890i) q^{48} +(3.00000 - 5.19615i) q^{49} +(1.61803 - 2.80252i) q^{51} +(-6.36396 + 11.0227i) q^{52} +(-6.86474 + 11.8901i) q^{53} -11.9814 q^{54} +(4.74342 + 8.21584i) q^{55} +(3.73607 + 6.47106i) q^{56} +(-0.437016 + 0.756934i) q^{57} +1.41421 q^{58} +(-5.97214 - 10.3440i) q^{59} +9.48683 q^{60} -13.9358 q^{61} +2.23607 q^{63} +8.70820 q^{64} +(-2.93159 - 5.07767i) q^{65} -9.70820 q^{66} +(-3.00000 + 5.19615i) q^{67} +(8.98606 + 15.5643i) q^{68} +(-1.14590 - 1.98475i) q^{69} -5.85410 q^{70} +(0.736068 - 1.27491i) q^{71} +(8.35410 - 14.4697i) q^{72} +(2.12132 - 3.67423i) q^{73} +(5.55369 + 9.61927i) q^{74} +(-2.42705 - 4.20378i) q^{76} +4.24264 q^{77} +6.00000 q^{78} +(-0.810272 - 1.40343i) q^{79} +(-11.0172 + 19.0824i) q^{80} +(-1.35410 - 2.34537i) q^{81} +(1.92705 - 3.33775i) q^{82} +(-1.58114 + 2.73861i) q^{83} +(2.12132 - 3.67423i) q^{84} -8.27895 q^{85} +(-12.6885 - 21.9772i) q^{86} +(-0.236068 - 0.408882i) q^{87} +(15.8508 - 27.4544i) q^{88} +15.3500 q^{89} +(6.54508 + 11.3364i) q^{90} -2.62210 q^{91} +12.7279 q^{92} -25.4164 q^{94} +2.23607 q^{95} +(-4.74342 - 8.21584i) q^{96} -7.00000 q^{97} +(7.85410 - 13.6037i) q^{98} +(-4.74342 - 8.21584i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 12 q^{2} + 12 q^{4} + 4 q^{7} + 24 q^{8} - 10 q^{10} + 6 q^{14} + 52 q^{16} + 10 q^{18} - 4 q^{19} - 30 q^{20} + 6 q^{28} + 60 q^{32} + 24 q^{33} + 30 q^{36} - 6 q^{38} + 72 q^{39} - 40 q^{40} - 12 q^{41}+ \cdots + 36 q^{98}+O(q^{100}) \) 8 * q + 12 * q^2 + 12 * q^4 + 4 * q^7 + 24 * q^8 - 10 * q^10 + 6 * q^14 + 52 * q^16 + 10 * q^18 - 4 * q^19 - 30 * q^20 + 6 * q^28 + 60 * q^32 + 24 * q^33 + 30 * q^36 - 6 * q^38 + 72 * q^39 - 40 * q^40 - 12 * q^41 + 20 * q^45 - 24 * q^47 + 24 * q^49 + 4 * q^51 + 12 * q^56 - 12 * q^59 + 16 * q^64 - 24 * q^66 - 24 * q^67 - 36 * q^69 - 20 * q^70 - 12 * q^71 + 40 * q^72 - 6 * q^76 + 48 * q^78 - 30 * q^80 + 16 * q^81 + 2 * q^82 + 16 * q^87 + 30 * q^90 - 96 * q^94 - 56 * q^97 + 36 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more