LMFDB - Embedded newform 1197.2.j.m.856.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1197,2,Mod(172,1197)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1197, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("1197.172");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1197 = 3^{2} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1197.j (of order $3$, degree $2$, 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:	$9.55809312195$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
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} + 13 x^{14} - 2 x^{13} + 118 x^{12} - 16 x^{11} + 534 x^{10} - 21 x^{9} + 1743 x^{8} - 101 x^{7} + \cdots + 256 $ x^16 + 13x^14 - 2x^13 + 118x^12 - 16x^11 + 534x^10 - 21x^9 + 1743x^8 - 101x^7 + 2902x^6 - 401x^5 + 3427x^4 - 294x^3 + 1076x^2 + 96x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 399)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			856.6
Root			$0.624863 - 1.08229i$ of defining polynomial
Character	$\chi$	$=$	1197.856
Dual form			1197.2.j.m.172.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.624863 - 1.08229i) q^{2} +(0.219092 + 0.379479i) q^{4} +(1.99797 - 3.46058i) q^{5} +(2.16069 - 1.52690i) q^{7} +3.04706 q^{8} +O(q^{10})$	\(q+(0.624863 - 1.08229i) q^{2} +(0.219092 + 0.379479i) q^{4} +(1.99797 - 3.46058i) q^{5} +(2.16069 - 1.52690i) q^{7} +3.04706 q^{8} +(-2.49691 - 4.32477i) q^{10} +(-1.18430 - 2.05127i) q^{11} -2.18914 q^{13} +(-0.302425 - 3.29260i) q^{14} +(1.46581 - 2.53886i) q^{16} +(-1.13610 - 1.96778i) q^{17} +(0.500000 - 0.866025i) q^{19} +1.75095 q^{20} -2.96011 q^{22} +(-4.29933 + 7.44667i) q^{23} +(-5.48373 - 9.49810i) q^{25} +(-1.36791 + 2.36929i) q^{26} +(1.05282 + 0.485402i) q^{28} +0.735824 q^{29} +(4.95449 + 8.58143i) q^{31} +(1.21520 + 2.10479i) q^{32} -2.83963 q^{34} +(-0.966988 - 10.5279i) q^{35} +(-4.09719 + 7.09654i) q^{37} +(-0.624863 - 1.08229i) q^{38} +(6.08793 - 10.5446i) q^{40} +8.35871 q^{41} -0.800311 q^{43} +(0.518943 - 0.898836i) q^{44} +(5.37299 + 9.30629i) q^{46} +(-2.46065 + 4.26197i) q^{47} +(2.33713 - 6.59832i) q^{49} -13.7063 q^{50} +(-0.479623 - 0.830732i) q^{52} +(-1.63914 - 2.83908i) q^{53} -9.46479 q^{55} +(6.58375 - 4.65257i) q^{56} +(0.459790 - 0.796379i) q^{58} +(-1.78048 - 3.08389i) q^{59} +(-1.37809 + 2.38693i) q^{61} +12.3835 q^{62} +8.90058 q^{64} +(-4.37382 + 7.57568i) q^{65} +(1.85054 + 3.20523i) q^{67} +(0.497821 - 0.862252i) q^{68} +(-11.9985 - 5.53194i) q^{70} -7.30367 q^{71} +(3.69123 + 6.39340i) q^{73} +(5.12036 + 8.86873i) q^{74} +0.438184 q^{76} +(-5.69100 - 2.62384i) q^{77} +(-0.458446 + 0.794052i) q^{79} +(-5.85729 - 10.1451i) q^{80} +(5.22305 - 9.04658i) q^{82} -4.91925 q^{83} -9.07955 q^{85} +(-0.500085 + 0.866173i) q^{86} +(-3.60865 - 6.25036i) q^{88} +(8.85073 - 15.3299i) q^{89} +(-4.73004 + 3.34260i) q^{91} -3.76780 q^{92} +(3.07514 + 5.32630i) q^{94} +(-1.99797 - 3.46058i) q^{95} +13.3590 q^{97} +(-5.68093 - 6.65251i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 10 q^{4} - 5 q^{5} + q^{7} + 6 q^{8}+O(q^{10}) $ 16 * q - 10 * q^4 - 5 * q^5 + q^7 + 6 * q^8	$ 16 q - 10 q^{4} - 5 q^{5} + q^{7} + 6 q^{8} + 3 q^{10} - 7 q^{11} - 12 q^{13} + 12 q^{14} - 10 q^{16} + 8 q^{19} + 32 q^{20} + 36 q^{22} - 9 q^{23} - 15 q^{25} - 12 q^{26} - 40 q^{28} - 8 q^{29} + 11 q^{31} - 26 q^{32} - 32 q^{34} + 7 q^{35} - 17 q^{37} + 3 q^{40} + 34 q^{41} + 16 q^{43} - 31 q^{44} - q^{46} - 29 q^{47} + q^{49} - 60 q^{50} + 25 q^{52} - 6 q^{53} - 42 q^{55} + 54 q^{56} + 37 q^{58} - 7 q^{59} + 2 q^{61} + 78 q^{62} + 58 q^{64} - 13 q^{65} - 13 q^{67} + 14 q^{68} - 81 q^{70} - 36 q^{71} + 20 q^{73} - 26 q^{74} - 20 q^{76} - 19 q^{77} + 3 q^{79} - 35 q^{80} + 5 q^{82} + 72 q^{83} + 10 q^{85} - 51 q^{86} - 53 q^{88} - q^{89} - 9 q^{91} - 30 q^{92} + 30 q^{94} + 5 q^{95} + 6 q^{97} + 75 q^{98}+O(q^{100}) $ 16 * q - 10 * q^4 - 5 * q^5 + q^7 + 6 * q^8 + 3 * q^10 - 7 * q^11 - 12 * q^13 + 12 * q^14 - 10 * q^16 + 8 * q^19 + 32 * q^20 + 36 * q^22 - 9 * q^23 - 15 * q^25 - 12 * q^26 - 40 * q^28 - 8 * q^29 + 11 * q^31 - 26 * q^32 - 32 * q^34 + 7 * q^35 - 17 * q^37 + 3 * q^40 + 34 * q^41 + 16 * q^43 - 31 * q^44 - q^46 - 29 * q^47 + q^49 - 60 * q^50 + 25 * q^52 - 6 * q^53 - 42 * q^55 + 54 * q^56 + 37 * q^58 - 7 * q^59 + 2 * q^61 + 78 * q^62 + 58 * q^64 - 13 * q^65 - 13 * q^67 + 14 * q^68 - 81 * q^70 - 36 * q^71 + 20 * q^73 - 26 * q^74 - 20 * q^76 - 19 * q^77 + 3 * q^79 - 35 * q^80 + 5 * q^82 + 72 * q^83 + 10 * q^85 - 51 * q^86 - 53 * q^88 - q^89 - 9 * q^91 - 30 * q^92 + 30 * q^94 + 5 * q^95 + 6 * q^97 + 75 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1197\mathbb{Z}\right)^\times$.

$n$	$514$	$533$	$1009$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$	0.624863	−	1.08229i	0.441845	−	0.765298i	−0.555982	−	0.831195i	$-0.687657\pi$
$2$	0.624863	−	1.08229i	0.441845	−	0.765298i	0.997826	+	0.0658968i	$0.0209908\pi$
$3$		0			0
$3$		0			0
$4$	0.219092	+	0.379479i	0.109546	+	0.189739i
$5$	1.99797	−	3.46058i	0.893517	−	1.54762i	0.0578880	−	0.998323i	$-0.481563\pi$
$5$	1.99797	−	3.46058i	0.893517	−	1.54762i	0.835629	−	0.549294i	$-0.185103\pi$
$6$		0			0
$7$	2.16069	−	1.52690i	0.816663	−	0.577115i
$7$	2.16069	−	1.52690i	0.816663	−	0.577115i
$8$	3.04706			1.07730
$9$		0			0
$10$	−2.49691	−	4.32477i	−0.789592	−	1.36761i
$11$	−1.18430	−	2.05127i	−0.357081	−	0.618482i	0.630391	−	0.776278i	$-0.282895\pi$
$11$	−1.18430	−	2.05127i	−0.357081	−	0.618482i	−0.987472	+	0.157796i	$0.949561\pi$
$12$		0			0
$13$	−2.18914			−0.607158			−0.303579	−	0.952806i	$-0.598182\pi$
$13$	−2.18914			−0.607158			−0.303579	+	0.952806i	$0.598182\pi$
$14$	−0.302425	−	3.29260i	−0.0808266	−	0.879986i
$15$		0			0
$16$	1.46581	−	2.53886i	0.366453	−	0.634716i
$17$	−1.13610	−	1.96778i	−0.275545	−	0.477257i	0.694728	−	0.719273i	$-0.255525\pi$
$17$	−1.13610	−	1.96778i	−0.275545	−	0.477257i	−0.970272	+	0.242016i	$0.922192\pi$
$18$		0			0
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i
$20$	1.75095			0.391525
$21$		0			0
$22$	−2.96011			−0.631098
$23$	−4.29933	+	7.44667i	−0.896473	+	1.55274i	−0.0645026	+	0.997918i	$0.520546\pi$
$23$	−4.29933	+	7.44667i	−0.896473	+	1.55274i	−0.831971	+	0.554820i	$0.812787\pi$
$24$		0			0
$25$	−5.48373	−	9.49810i	−1.09675	−	1.89962i
$26$	−1.36791	+	2.36929i	−0.268270	+	0.464657i
$27$		0			0
$28$	1.05282	+	0.485402i	0.198964	+	0.0917324i
$29$	0.735824			0.136639			0.0683196	−	0.997663i	$-0.478236\pi$
$29$	0.735824			0.136639			0.0683196	+	0.997663i	$0.478236\pi$
$30$		0			0
$31$	4.95449	+	8.58143i	0.889853	+	1.54127i	0.840048	+	0.542511i	$0.182526\pi$
$31$	4.95449	+	8.58143i	0.889853	+	1.54127i	0.0498045	+	0.998759i	$0.484140\pi$
$32$	1.21520	+	2.10479i	0.214819	+	0.372077i
$33$		0			0
$34$	−2.83963			−0.486992
$35$	−0.966988	−	10.5279i	−0.163451	−	1.77954i
$36$		0			0
$37$	−4.09719	+	7.09654i	−0.673574	+	1.16666i	0.303310	+	0.952892i	$0.401908\pi$
$37$	−4.09719	+	7.09654i	−0.673574	+	1.16666i	−0.976884	+	0.213772i	$0.931425\pi$
$38$	−0.624863	−	1.08229i	−0.101366	−	0.175571i
$39$		0			0
$40$	6.08793	−	10.5446i	0.962586	−	1.66725i
$41$	8.35871			1.30541			0.652705	−	0.757612i	$-0.273634\pi$
$41$	8.35871			1.30541			0.652705	+	0.757612i	$0.273634\pi$
$42$		0			0
$43$	−0.800311			−0.122046			−0.0610232	−	0.998136i	$-0.519436\pi$
$43$	−0.800311			−0.122046			−0.0610232	+	0.998136i	$0.519436\pi$
$44$	0.518943	−	0.898836i	0.0782337	−	0.135505i
$45$		0			0
$46$	5.37299	+	9.30629i	0.792204	+	1.37214i
$47$	−2.46065	+	4.26197i	−0.358923	+	0.621673i	−0.987781	−	0.155847i	$-0.950189\pi$
$47$	−2.46065	+	4.26197i	−0.358923	+	0.621673i	0.628858	+	0.777520i	$0.283523\pi$
$48$		0			0
$49$	2.33713	−	6.59832i	0.333876	−	0.942617i
$50$	−13.7063			−1.93837
$51$		0			0
$52$	−0.479623	−	0.830732i	−0.0665118	−	0.115202i
$53$	−1.63914	−	2.83908i	−0.225154	−	0.389978i	0.731212	−	0.682150i	$-0.238955\pi$
$53$	−1.63914	−	2.83908i	−0.225154	−	0.389978i	−0.956366	+	0.292173i	$0.905622\pi$
$54$		0			0
$55$	−9.46479			−1.27623
$56$	6.58375	−	4.65257i	0.879790	−	0.621726i
$57$		0			0
$58$	0.459790	−	0.796379i	0.0603733	−	0.104570i
$59$	−1.78048	−	3.08389i	−0.231799	−	0.401488i	0.726539	−	0.687126i	$-0.241128\pi$
$59$	−1.78048	−	3.08389i	−0.231799	−	0.401488i	−0.958338	+	0.285638i	$0.907795\pi$
$60$		0			0
$61$	−1.37809	+	2.38693i	−0.176447	+	0.305615i	−0.940661	−	0.339348i	$-0.889794\pi$
$61$	−1.37809	+	2.38693i	−0.176447	+	0.305615i	0.764214	+	0.644962i	$0.223127\pi$
$62$	12.3835			1.57271
$63$		0			0
$64$	8.90058			1.11257
$65$	−4.37382	+	7.57568i	−0.542506	+	0.939648i
$66$		0			0
$67$	1.85054	+	3.20523i	0.226080	+	0.391581i	0.956643	−	0.291264i	$-0.0940757\pi$
$67$	1.85054	+	3.20523i	0.226080	+	0.391581i	−0.730563	+	0.682845i	$0.760742\pi$
$68$	0.497821	−	0.862252i	0.0603697	−	0.104563i
$69$		0			0
$70$	−11.9985	−	5.53194i	−1.43410	−	0.661194i
$71$	−7.30367			−0.866786			−0.433393	−	0.901205i	$-0.642684\pi$
$71$	−7.30367			−0.866786			−0.433393	+	0.901205i	$0.642684\pi$
$72$		0			0
$73$	3.69123	+	6.39340i	0.432026	+	0.748291i	0.997048	−	0.0767854i	$-0.0244656\pi$
$73$	3.69123	+	6.39340i	0.432026	+	0.748291i	−0.565022	+	0.825076i	$0.691132\pi$
$74$	5.12036	+	8.86873i	0.595230	+	1.03097i
$75$		0			0
$76$	0.438184			0.0502632
$77$	−5.69100	−	2.62384i	−0.648550	−	0.299015i
$78$		0			0
$79$	−0.458446	+	0.794052i	−0.0515792	+	0.0893378i	−0.890662	−	0.454666i	$-0.849759\pi$
$79$	−0.458446	+	0.794052i	−0.0515792	+	0.0893378i	0.839083	+	0.544003i	$0.183092\pi$
$80$	−5.85729	−	10.1451i	−0.654864	−	1.13426i
$81$		0			0
$82$	5.22305	−	9.04658i	0.576789	−	0.999028i
$83$	−4.91925			−0.539957			−0.269979	−	0.962866i	$-0.587017\pi$
$83$	−4.91925			−0.539957			−0.269979	+	0.962866i	$0.587017\pi$
$84$		0			0
$85$	−9.07955			−0.984815
$86$	−0.500085	+	0.866173i	−0.0539256	+	0.0934018i
$87$		0			0
$88$	−3.60865	−	6.25036i	−0.384683	−	0.666291i
$89$	8.85073	−	15.3299i	0.938176	−	1.62497i	0.169306	−	0.985564i	$-0.445847\pi$
$89$	8.85073	−	15.3299i	0.938176	−	1.62497i	0.768870	−	0.639405i	$-0.220819\pi$
$90$		0			0
$91$	−4.73004	+	3.34260i	−0.495843	+	0.350400i
$92$	−3.76780			−0.392821
$93$		0			0
$94$	3.07514	+	5.32630i	0.317177	+	0.549366i
$95$	−1.99797	−	3.46058i	−0.204987	−	0.355048i
$96$		0			0
$97$	13.3590			1.35640			0.678201	−	0.734877i	$-0.262760\pi$
$97$	13.3590			1.35640			0.678201	+	0.734877i	$0.262760\pi$
$98$	−5.68093	−	6.65251i	−0.573861	−	0.672005i
$99$		0			0
$100$	2.40288	−	4.16192i	0.240288	−	0.416192i
$101$	−5.63762	−	9.76464i	−0.560964	−	0.971618i	−0.997413	−	0.0718890i	$-0.977097\pi$
$101$	−5.63762	−	9.76464i	−0.560964	−	0.971618i	0.436449	−	0.899729i	$-0.356236\pi$
$102$		0			0
$103$	4.93999	−	8.55632i	0.486752	−	0.843079i	−0.513132	−	0.858310i	$-0.671515\pi$
$103$	4.93999	−	8.55632i	0.486752	−	0.843079i	0.999884	+	0.0152305i	$0.00484820\pi$
$104$	−6.67044			−0.654091
$105$		0			0
$106$	−4.09696			−0.397932
$107$	3.46880	−	6.00814i	0.335342	−	0.580829i	−0.648209	−	0.761463i	$-0.724482\pi$
$107$	3.46880	−	6.00814i	0.335342	−	0.580829i	0.983550	+	0.180634i	$0.0578149\pi$
$108$		0			0
$109$	−1.84996	−	3.20423i	−0.177194	−	0.306909i	0.763724	−	0.645543i	$-0.223369\pi$
$109$	−1.84996	−	3.20423i	−0.177194	−	0.306909i	−0.940918	+	0.338633i	$0.890035\pi$
$110$	−5.91420	+	10.2437i	−0.563896	+	0.976697i
$111$		0			0
$112$	−0.709434	−	7.72384i	−0.0670352	−	0.729834i
$113$	2.09680			0.197250			0.0986252	−	0.995125i	$-0.468555\pi$
$113$	2.09680			0.197250			0.0986252	+	0.995125i	$0.468555\pi$
$114$		0			0
$115$	17.1798	+	29.7564i	1.60203	+	2.77479i
$116$	0.161213	+	0.279230i	0.0149683	+	0.0259258i
$117$		0			0
$118$	−4.45023			−0.409677
$119$	−5.45937	−	2.51705i	−0.500459	−	0.230737i
$120$		0			0
$121$	2.69485	−	4.66762i	0.244986	−	0.424329i
$122$	1.72224	+	2.98300i	0.155924	+	0.270069i
$123$		0			0
$124$	−2.17098	+	3.76025i	−0.194960	+	0.337680i
$125$	−23.8455			−2.13281
$126$		0			0
$127$	10.7759			0.956206			0.478103	−	0.878304i	$-0.341325\pi$
$127$	10.7759			0.956206			0.478103	+	0.878304i	$0.341325\pi$
$128$	3.13125	−	5.42348i	0.276766	−	0.479372i
$129$		0			0
$130$	5.46608	+	9.46753i	0.479407	+	0.830357i
$131$	−0.420271	+	0.727931i	−0.0367192	+	0.0635996i	−0.883801	−	0.467863i	$-0.845024\pi$
$131$	−0.420271	+	0.727931i	−0.0367192	+	0.0635996i	0.847082	+	0.531463i	$0.178357\pi$
$132$		0			0
$133$	−0.241993	−	2.63466i	−0.0209835	−	0.228454i
$134$	4.62534			0.399569
$135$		0			0
$136$	−3.46177	−	5.99596i	−0.296844	−	0.514149i
$137$	1.28098	+	2.21873i	0.109442	+	0.189559i	0.915544	−	0.402217i	$-0.131760\pi$
$137$	1.28098	+	2.21873i	0.109442	+	0.189559i	−0.806102	+	0.591776i	$0.798427\pi$
$138$		0			0
$139$	−10.8739			−0.922313			−0.461156	−	0.887319i	$-0.652565\pi$
$139$	−10.8739			−0.922313			−0.461156	+	0.887319i	$0.652565\pi$
$140$	3.78326	−	2.67354i	0.319744	−	0.225955i
$141$		0			0
$142$	−4.56379	+	7.90472i	−0.382985	+	0.663349i
$143$	2.59260	+	4.49052i	0.216804	+	0.375516i
$144$		0			0
$145$	1.47015	−	2.54638i	0.122089	−	0.211465i
$146$	9.22605			0.763554
$147$		0			0
$148$	−3.59065			−0.295149
$149$	−11.0309	+	19.1060i	−0.903684	+	1.56523i	−0.0810093	+	0.996713i	$0.525814\pi$
$149$	−11.0309	+	19.1060i	−0.903684	+	1.56523i	−0.822674	+	0.568513i	$0.807519\pi$
$150$		0			0
$151$	1.58958	+	2.75324i	0.129359	+	0.224056i	0.923428	−	0.383771i	$-0.125375\pi$
$151$	1.58958	+	2.75324i	0.129359	+	0.224056i	−0.794070	+	0.607827i	$0.792042\pi$
$152$	1.52353	−	2.63883i	0.123575	−	0.214038i
$153$		0			0
$154$	−6.39587	+	4.51980i	−0.515394	+	0.364216i
$155$	39.5956			3.18040
$156$		0			0
$157$	11.3194	+	19.6059i	0.903390	+	1.56472i	0.823064	+	0.567949i	$0.192263\pi$
$157$	11.3194	+	19.6059i	0.903390	+	1.56472i	0.0803267	+	0.996769i	$0.474404\pi$
$158$	0.572932	+	0.992348i	0.0455800	+	0.0789469i
$159$		0			0
$160$	9.71170			0.767777
$161$	2.08082	+	22.6546i	0.163992	+	1.78543i
$162$		0			0
$163$	7.31481	−	12.6696i	0.572940	−	0.992362i	−0.423322	−	0.905980i	$-0.639136\pi$
$163$	7.31481	−	12.6696i	0.572940	−	0.992362i	0.996262	−	0.0863825i	$-0.0275307\pi$
$164$	1.83133	+	3.17195i	0.143003	+	0.247688i
$165$		0			0
$166$	−3.07385	+	5.32407i	−0.238577	+	0.413228i
$167$	17.8027			1.37762			0.688808	−	0.724944i	$-0.258134\pi$
$167$	17.8027			1.37762			0.688808	+	0.724944i	$0.258134\pi$
$168$		0			0
$169$	−8.20767			−0.631359
$170$	−5.67347	+	9.82675i	−0.435136	+	0.753677i
$171$		0			0
$172$	−0.175342	−	0.303701i	−0.0133697	−	0.0231570i
$173$	−12.4672	+	21.5939i	−0.947866	+	1.64175i	−0.197957	+	0.980211i	$0.563431\pi$
$173$	−12.4672	+	21.5939i	−0.947866	+	1.64175i	−0.749909	+	0.661541i	$0.769903\pi$
$174$		0			0
$175$	−26.3513	−	12.1493i	−1.99197	−	0.918400i
$176$	−6.94387			−0.523414
$177$		0			0
$178$	−11.0610	−	19.1582i	−0.829057	−	1.43597i
$179$	6.81705	+	11.8075i	0.509530	+	0.882533i	0.999939	+	0.0110399i	$0.00351419\pi$
$179$	6.81705	+	11.8075i	0.509530	+	0.882533i	−0.490409	+	0.871493i	$0.663152\pi$
$180$		0			0
$181$	−3.79249			−0.281893			−0.140947	−	0.990017i	$-0.545015\pi$
$181$	−3.79249			−0.281893			−0.140947	+	0.990017i	$0.545015\pi$
$182$	0.662051	+	7.20797i	0.0490745	+	0.534290i
$183$		0			0
$184$	−13.1003	+	22.6905i	−0.965770	+	1.67276i
$185$	16.3721	+	28.3573i	1.20370	+	2.08487i
$186$		0			0
$187$	−2.69097	+	4.66090i	−0.196783	+	0.340839i
$188$	−2.15644			−0.157274
$189$		0			0
$190$	−4.99382			−0.362290
$191$	5.01829	−	8.69194i	0.363111	−	0.628926i	−0.625360	−	0.780336i	$-0.715048\pi$
$191$	5.01829	−	8.69194i	0.363111	−	0.628926i	0.988471	+	0.151410i	$0.0483813\pi$
$192$		0			0
$193$	−9.49470	−	16.4453i	−0.683444	−	1.18376i	−0.973923	−	0.226878i	$-0.927148\pi$
$193$	−9.49470	−	16.4453i	−0.683444	−	1.18376i	0.290480	−	0.956881i	$-0.406185\pi$
$194$	8.34755	−	14.4584i	0.599319	−	1.03805i
$195$		0			0
$196$	3.01597	−	0.558747i	0.215426	−	0.0399105i
$197$	−3.08525			−0.219815			−0.109908	−	0.993942i	$-0.535055\pi$
$197$	−3.08525			−0.219815			−0.109908	+	0.993942i	$0.535055\pi$
$198$		0			0
$199$	9.42704	+	16.3281i	0.668266	+	1.15747i	0.978389	+	0.206773i	$0.0662963\pi$
$199$	9.42704	+	16.3281i	0.668266	+	1.15747i	−0.310123	+	0.950696i	$0.600370\pi$
$200$	−16.7093	−	28.9413i	−1.18152	−	2.04646i
$201$		0			0
$202$	−14.0910			−0.991436
$203$	1.58989	−	1.12353i	0.111588	−	0.0788565i
$204$		0			0
$205$	16.7004	−	28.9260i	1.16641	−	2.02028i
$206$	−6.17364	−	10.6931i	−0.430138	−	0.745021i
$207$		0			0
$208$	−3.20887	+	5.55792i	−0.222495	+	0.385373i
$209$	−2.36861			−0.163840
$210$		0			0
$211$	−19.9172			−1.37115			−0.685577	−	0.728000i	$-0.740450\pi$
$211$	−19.9172			−1.37115			−0.685577	+	0.728000i	$0.740450\pi$
$212$	0.718247	−	1.24404i	0.0493294	−	0.0854411i
$213$		0			0
$214$	−4.33505	−	7.50853i	−0.296338	−	0.513272i
$215$	−1.59899	+	2.76954i	−0.109050	+	0.188881i
$216$		0			0
$217$	23.8081	+	10.9768i	1.61620	+	0.745151i
$218$	−4.62389			−0.313169
$219$		0			0
$220$	−2.07366	−	3.59169i	−0.139806	−	0.242151i
$221$	2.48708	+	4.30775i	0.167299	+	0.289771i
$222$		0			0
$223$	12.3503			0.827040			0.413520	−	0.910495i	$-0.364299\pi$
$223$	12.3503			0.827040			0.413520	+	0.910495i	$0.364299\pi$
$224$	5.83947	+	2.69229i	0.390166	+	0.179886i
$225$		0			0
$226$	1.31021	−	2.26936i	0.0871541	−	0.150955i
$227$	5.26897	+	9.12613i	0.349714	+	0.605722i	0.986199	−	0.165567i	$-0.0529455\pi$
$227$	5.26897	+	9.12613i	0.349714	+	0.605722i	−0.636485	+	0.771289i	$0.719612\pi$
$228$		0			0
$229$	−10.9731	+	19.0060i	−0.725126	+	1.25596i	0.233796	+	0.972286i	$0.424885\pi$
$229$	−10.9731	+	19.0060i	−0.725126	+	1.25596i	−0.958922	+	0.283669i	$0.908448\pi$
$230$	42.9402			2.83139
$231$		0			0
$232$	2.24210			0.147201
$233$	−3.30522	+	5.72481i	−0.216532	+	0.375045i	−0.953745	−	0.300615i	$-0.902808\pi$
$233$	−3.30522	+	5.72481i	−0.216532	+	0.375045i	0.737213	+	0.675660i	$0.236141\pi$
$234$		0			0
$235$	9.83259	+	17.0305i	0.641408	+	1.11095i
$236$	0.780180	−	1.35131i	0.0507854	−	0.0879629i
$237$		0			0
$238$	−6.13554	+	4.33583i	−0.397708	+	0.281050i
$239$	−16.2362			−1.05023			−0.525115	−	0.851031i	$-0.675978\pi$
$239$	−16.2362			−1.05023			−0.525115	+	0.851031i	$0.675978\pi$
$240$		0			0
$241$	−7.07793	−	12.2593i	−0.455929	−	0.789693i	0.542812	−	0.839854i	$-0.317360\pi$
$241$	−7.07793	−	12.2593i	−0.455929	−	0.789693i	−0.998741	+	0.0501617i	$0.984026\pi$
$242$	−3.36783	−	5.83325i	−0.216492	−	0.374975i
$243$		0			0
$244$	−1.20772			−0.0773162
$245$	−18.1645	−	21.2710i	−1.16049	−	1.35896i
$246$		0			0
$247$	−1.09457	+	1.89585i	−0.0696458	+	0.120630i
$248$	15.0966	+	26.1482i	0.958638	+	1.66041i
$249$		0			0
$250$	−14.9002	+	25.8079i	−0.942371	+	1.63224i
$251$	14.5157			0.916224			0.458112	−	0.888895i	$-0.348526\pi$
$251$	14.5157			0.916224			0.458112	+	0.888895i	$0.348526\pi$
$252$		0			0
$253$	20.3669			1.28045
$254$	6.73346	−	11.6627i	0.422495	−	0.731782i
$255$		0			0
$256$	4.98738	+	8.63839i	0.311711	+	0.539900i
$257$	1.66506	−	2.88397i	0.103864	−	0.179897i	−0.809410	−	0.587244i	$-0.800213\pi$
$257$	1.66506	−	2.88397i	0.103864	−	0.179897i	0.913273	+	0.407347i	$0.133546\pi$
$258$		0			0
$259$	1.98298	+	21.5894i	0.123217	+	1.34150i
$260$	−3.83308			−0.237718
$261$		0			0
$262$	0.525224	+	0.909714i	0.0324484	+	0.0562023i
$263$	11.9556	+	20.7076i	0.737211	+	1.27689i	0.953746	+	0.300612i	$0.0971911\pi$
$263$	11.9556	+	20.7076i	0.737211	+	1.27689i	−0.216535	+	0.976275i	$0.569476\pi$
$264$		0			0
$265$	−13.0998			−0.804715
$266$	−3.00269	−	1.38439i	−0.184107	−	0.0848827i
$267$		0			0
$268$	−0.810878	+	1.40448i	−0.0495323	+	0.0857924i
$269$	−9.12904	−	15.8120i	−0.556607	−	0.964072i	−0.997777	−	0.0666484i	$-0.978769\pi$
$269$	−9.12904	−	15.8120i	−0.556607	−	0.964072i	0.441169	−	0.897424i	$-0.354564\pi$
$270$		0			0
$271$	4.55023	−	7.88123i	0.276407	−	0.478751i	−0.694082	−	0.719896i	$-0.744190\pi$
$271$	4.55023	−	7.88123i	0.276407	−	0.478751i	0.970489	+	0.241145i	$0.0775230\pi$
$272$	−6.66124			−0.403897
$273$		0			0
$274$	3.20176			0.193425
$275$	−12.9888	+	22.4973i	−0.783254	+	1.35664i
$276$		0			0
$277$	−6.45503	−	11.1804i	−0.387845	−	0.671768i	0.604314	−	0.796746i	$-0.293447\pi$
$277$	−6.45503	−	11.1804i	−0.387845	−	0.671768i	−0.992159	+	0.124978i	$0.960114\pi$
$278$	−6.79470	+	11.7688i	−0.407519	+	0.705844i
$279$		0			0
$280$	−2.94647	−	32.0792i	−0.176086	−	1.91710i
$281$	−30.7965			−1.83716			−0.918582	−	0.395232i	$-0.870664\pi$
$281$	−30.7965			−1.83716			−0.918582	+	0.395232i	$0.870664\pi$
$282$		0			0
$283$	−11.6351	−	20.1526i	−0.691635	−	1.19795i	−0.971302	−	0.237850i	$-0.923557\pi$
$283$	−11.6351	−	20.1526i	−0.691635	−	1.19795i	0.279666	−	0.960097i	$-0.409776\pi$
$284$	−1.60018	−	2.77159i	−0.0949530	−	0.164463i
$285$		0			0
$286$	6.48009			0.383176
$287$	18.0605	−	12.7629i	1.06608	−	0.753372i
$288$		0			0
$289$	5.91856	−	10.2512i	0.348150	−	0.603014i
$290$	−1.83729	−	3.18227i	−0.107889	−	0.186870i
$291$		0			0
$292$	−1.61744	+	2.80149i	−0.0946535	+	0.163945i
$293$	−8.18298			−0.478055			−0.239027	−	0.971013i	$-0.576829\pi$
$293$	−8.18298			−0.478055			−0.239027	+	0.971013i	$0.576829\pi$
$294$		0			0
$295$	−14.2294			−0.828466
$296$	−12.4844	+	21.6236i	−0.725640	+	1.25685i
$297$		0			0
$298$	13.7856	+	23.8773i	0.798576	+	1.38317i
$299$	9.41184	−	16.3018i	0.544301	−	0.942757i
$300$		0			0
$301$	−1.72922	+	1.22200i	−0.0996707	+	0.0704348i
$302$	3.97309			0.228626
$303$		0			0
$304$	−1.46581	−	2.53886i	−0.0840701	−	0.145614i
$305$	5.50676	+	9.53799i	0.315316	+	0.546144i
$306$		0			0
$307$	19.1256			1.09156			0.545778	−	0.837930i	$-0.316234\pi$
$307$	19.1256			1.09156			0.545778	+	0.837930i	$0.316234\pi$
$308$	−0.251162	−	2.73448i	−0.0143113	−	0.155811i
$309$		0			0
$310$	24.7418	−	42.8541i	1.40524	−	2.43395i
$311$	17.1571	+	29.7170i	0.972890	+	1.68510i	0.686729	+	0.726914i	$0.259046\pi$
$311$	17.1571	+	29.7170i	0.972890	+	1.68510i	0.286161	+	0.958181i	$0.407621\pi$
$312$		0			0
$313$	1.47774	−	2.55952i	0.0835269	−	0.144673i	−0.821236	−	0.570589i	$-0.806715\pi$
$313$	1.47774	−	2.55952i	0.0835269	−	0.144673i	0.904763	+	0.425916i	$0.140048\pi$
$314$	28.2924			1.59663
$315$		0			0
$316$	−0.401768			−0.0226012
$317$	−6.26089	+	10.8442i	−0.351646	+	0.609069i	−0.986538	−	0.163532i	$-0.947711\pi$
$317$	−6.26089	+	10.8442i	−0.351646	+	0.609069i	0.634892	+	0.772601i	$0.281045\pi$
$318$		0			0
$319$	−0.871439	−	1.50938i	−0.0487912	−	0.0845089i
$320$	17.7831	−	30.8011i	0.994103	−	1.72184i
$321$		0			0
$322$	25.8192	+	11.9039i	1.43885	+	0.663381i
$323$	−2.27220			−0.126429
$324$		0			0
$325$	12.0046	+	20.7927i	0.665898	+	1.15337i
$326$	−9.14152	−	15.8336i	−0.506302	−	0.876940i
$327$		0			0
$328$	25.4695			1.40632
$329$	1.19092	+	12.9660i	0.0656577	+	0.714837i
$330$		0			0
$331$	−11.3692	+	19.6920i	−0.624906	+	1.08237i	0.363653	+	0.931535i	$0.381530\pi$
$331$	−11.3692	+	19.6920i	−0.624906	+	1.08237i	−0.988559	+	0.150835i	$0.951804\pi$
$332$	−1.07777	−	1.86675i	−0.0591502	−	0.102451i
$333$		0			0
$334$	11.1243	−	19.2678i	0.608693	−	1.05429i
$335$	14.7893			0.808024
$336$		0			0
$337$	4.05805			0.221056			0.110528	−	0.993873i	$-0.464746\pi$
$337$	4.05805			0.221056			0.110528	+	0.993873i	$0.464746\pi$
$338$	−5.12867	+	8.88312i	−0.278963	+	0.483178i
$339$		0			0
$340$	−1.98926	−	3.44550i	−0.107883	−	0.186858i
$341$	11.7352	−	20.3260i	0.635499	−	1.10072i
$342$		0			0
$343$	−5.02517	−	17.8255i	−0.271334	−	0.962485i
$344$	−2.43860			−0.131480
$345$		0			0
$346$	15.5806	+	26.9864i	0.837619	+	1.45080i
$347$	−11.5526	−	20.0097i	−0.620175	−	1.07417i	−0.989453	−	0.144855i	$-0.953728\pi$
$347$	−11.5526	−	20.0097i	−0.620175	−	1.07417i	0.369278	−	0.929319i	$-0.379605\pi$
$348$		0			0
$349$	17.9043			0.958394			0.479197	−	0.877707i	$-0.340928\pi$
$349$	17.9043			0.958394			0.479197	+	0.877707i	$0.340928\pi$
$350$	−29.6151	+	20.9282i	−1.58299	+	1.11866i
$351$		0			0
$352$	2.87833	−	4.98541i	0.153415	−	0.265723i
$353$	−4.45601	−	7.71803i	−0.237169	−	0.410790i	0.722732	−	0.691129i	$-0.242886\pi$
$353$	−4.45601	−	7.71803i	−0.237169	−	0.410790i	−0.959901	+	0.280339i	$0.909553\pi$
$354$		0			0
$355$	−14.5925	+	25.2749i	−0.774488	+	1.34145i
$356$	7.75651			0.411094
$357$		0			0
$358$	17.0389			0.900534
$359$	6.11826	−	10.5971i	0.322909	−	0.559295i	−0.658178	−	0.752863i	$-0.728672\pi$
$359$	6.11826	−	10.5971i	0.322909	−	0.559295i	0.981087	+	0.193567i	$0.0620058\pi$
$360$		0			0
$361$	−0.500000	−	0.866025i	−0.0263158	−	0.0455803i
$362$	−2.36978	+	4.10459i	−0.124553	+	0.215732i
$363$		0			0
$364$	−2.30476	−	1.06261i	−0.120802	−	0.0556961i
$365$	29.4998			1.54409
$366$		0			0
$367$	0.178424	+	0.309040i	0.00931366	+	0.0161317i	0.870645	−	0.491912i	$-0.163702\pi$
$367$	0.178424	+	0.309040i	0.00931366	+	0.0161317i	−0.861331	+	0.508044i	$0.830369\pi$
$368$	12.6040	+	21.8308i	0.657031	+	1.13801i
$369$		0			0
$370$	40.9212			2.12739
$371$	−7.87667	−	3.63155i	−0.408937	−	0.188541i
$372$		0			0
$373$	6.24199	−	10.8115i	0.323198	−	0.559796i	−0.657948	−	0.753063i	$-0.728575\pi$
$373$	6.24199	−	10.8115i	0.323198	−	0.559796i	0.981146	+	0.193268i	$0.0619086\pi$
$374$	3.36298	+	5.82485i	0.173896	+	0.301196i
$375$		0			0
$376$	−7.49776	+	12.9865i	−0.386667	+	0.669728i
$377$	−1.61082			−0.0829616
$378$		0			0
$379$	17.4065			0.894111			0.447056	−	0.894506i	$-0.352473\pi$
$379$	17.4065			0.894111			0.447056	+	0.894506i	$0.352473\pi$
$380$	0.875477	−	1.51637i	0.0449110	−	0.0777882i
$381$		0			0
$382$	−6.27149	−	10.8625i	−0.320877	−	0.555776i
$383$	−13.4769	+	23.3426i	−0.688636	+	1.19275i	0.283643	+	0.958930i	$0.408457\pi$
$383$	−13.4769	+	23.3426i	−0.688636	+	1.19275i	−0.972279	+	0.233823i	$0.924876\pi$
$384$		0			0
$385$	−20.4504	+	14.4518i	−1.04225	+	0.736532i
$386$	−23.7316			−1.20790
$387$		0			0
$388$	2.92685	+	5.06946i	0.148588	+	0.257363i
$389$	−17.3066	−	29.9760i	−0.877481	−	1.51984i	−0.854096	−	0.520116i	$-0.825889\pi$
$389$	−17.3066	−	29.9760i	−0.877481	−	1.51984i	−0.0233855	−	0.999727i	$-0.507445\pi$
$390$		0			0
$391$	19.5379			0.988073
$392$	7.12140	−	20.1055i	0.359685	−	1.01548i
$393$		0			0
$394$	−1.92786	+	3.33915i	−0.0971242	+	0.168224i
$395$	1.83192	+	3.17298i	0.0921738	+	0.159650i
$396$		0			0
$397$	8.83972	−	15.3108i	0.443653	−	0.768429i	−0.554304	−	0.832314i	$-0.687016\pi$
$397$	8.83972	−	15.3108i	0.443653	−	0.768429i	0.997957	+	0.0638847i	$0.0203490\pi$
$398$	23.5624			1.18108
$399$		0			0
$400$	−32.1525			−1.60762
$401$	−6.99922	+	12.1230i	−0.349524	+	0.605394i	−0.986165	−	0.165767i	$-0.946990\pi$
$401$	−6.99922	+	12.1230i	−0.349524	+	0.605394i	0.636641	+	0.771160i	$0.280323\pi$
$402$		0			0
$403$	−10.8461	−	18.7859i	−0.540281	−	0.935795i
$404$	2.47032	−	4.27871i	0.122903	−	0.212874i
$405$		0			0
$406$	−0.222532	−	2.42278i	−0.0110441	−	0.120241i
$407$	19.4093			0.962081
$408$		0			0
$409$	−15.2732	−	26.4540i	−0.755213	−	1.30807i	−0.945269	−	0.326294i	$-0.894200\pi$
$409$	−15.2732	−	26.4540i	−0.755213	−	1.30807i	0.190056	−	0.981773i	$-0.439133\pi$
$410$	−20.8709	−	36.1495i	−1.03074	−	1.78530i
$411$		0			0
$412$	4.32926			0.213287
$413$	−8.55586	−	3.94469i	−0.421006	−	0.194105i
$414$		0			0
$415$	−9.82848	+	17.0234i	−0.482461	+	0.835647i
$416$	−2.66024	−	4.60767i	−0.130429	−	0.225910i
$417$		0			0
$418$	−1.48005	+	2.56353i	−0.0723918	+	0.125386i
$419$	−17.2075			−0.840640			−0.420320	−	0.907376i	$-0.638082\pi$
$419$	−17.2075			−0.840640			−0.420320	+	0.907376i	$0.638082\pi$
$420$		0			0
$421$	−9.71684			−0.473570			−0.236785	−	0.971562i	$-0.576094\pi$
$421$	−9.71684			−0.473570			−0.236785	+	0.971562i	$0.576094\pi$
$422$	−12.4455	+	21.5562i	−0.605838	+	1.04934i
$423$		0			0
$424$	−4.99457	−	8.65085i	−0.242558	−	0.420123i
$425$	−12.4601	+	21.5816i	−0.604405	+	1.04686i
$426$		0			0
$427$	0.666978	+	7.26162i	0.0322774	+	0.351414i
$428$	3.03995			0.146941
$429$		0			0
$430$	1.99830	+	3.46117i	0.0963668	+	0.166912i
$431$	−9.28764	−	16.0867i	−0.447370	−	0.774868i	0.550844	−	0.834608i	$-0.314306\pi$
$431$	−9.28764	−	16.0867i	−0.447370	−	0.774868i	−0.998214	+	0.0597406i	$0.980973\pi$
$432$		0			0
$433$	−16.8441			−0.809474			−0.404737	−	0.914433i	$-0.632637\pi$
$433$	−16.8441			−0.809474			−0.404737	+	0.914433i	$0.632637\pi$
$434$	26.7569	−	18.9084i	1.28437	−	0.907633i
$435$		0			0
$436$	0.810624	−	1.40404i	0.0388219	−	0.0672414i
$437$	4.29933	+	7.44667i	0.205665	+	0.356222i
$438$		0			0
$439$	0.188178	−	0.325933i	0.00898123	−	0.0155559i	−0.861500	−	0.507758i	$-0.830474\pi$
$439$	0.188178	−	0.325933i	0.00898123	−	0.0155559i	0.870481	+	0.492202i	$0.163808\pi$
$440$	−28.8398			−1.37488
$441$		0			0
$442$	6.21634			0.295681
$443$	−16.2975	+	28.2280i	−0.774316	+	1.34115i	0.160863	+	0.986977i	$0.448572\pi$
$443$	−16.2975	+	28.2280i	−0.774316	+	1.34115i	−0.935178	+	0.354177i	$0.884761\pi$
$444$		0			0
$445$	−35.3669	−	61.2573i	−1.67655	−	2.90387i
$446$	7.71728	−	13.3667i	0.365424	−	0.632932i
$447$		0			0
$448$	19.2314	−	13.5903i	0.908597	−	0.642082i
$449$	−16.7178			−0.788964			−0.394482	−	0.918904i	$-0.629076\pi$
$449$	−16.7178			−0.788964			−0.394482	+	0.918904i	$0.629076\pi$
$450$		0			0
$451$	−9.89924	−	17.1460i	−0.466137	−	0.807373i
$452$	0.459393	+	0.795692i	0.0216080	+	0.0374262i
$453$		0			0
$454$	13.1695			0.618077
$455$	2.11687	+	23.0471i	0.0992405	+	1.08046i
$456$		0			0
$457$	−8.79534	+	15.2340i	−0.411428	+	0.712615i	−0.995046	−	0.0994135i	$-0.968303\pi$
$457$	−8.79534	+	15.2340i	−0.411428	+	0.712615i	0.583618	+	0.812029i	$0.301637\pi$
$458$	13.7134	+	23.7524i	0.640786	+	1.10987i
$459$		0			0
$460$	−7.52794	+	13.0388i	−0.350992	+	0.607936i
$461$	1.81881			0.0847103			0.0423552	−	0.999103i	$-0.486514\pi$
$461$	1.81881			0.0847103			0.0423552	+	0.999103i	$0.486514\pi$
$462$		0			0
$463$	−1.35124			−0.0627976			−0.0313988	−	0.999507i	$-0.509996\pi$
$463$	−1.35124			−0.0627976			−0.0313988	+	0.999507i	$0.509996\pi$
$464$	1.07858	−	1.86816i	0.0500719	−	0.0867270i
$465$		0			0
$466$	4.13062	+	7.15444i	0.191347	+	0.331423i
$467$	−7.99872	+	13.8542i	−0.370137	+	0.641095i	−0.989586	−	0.143941i	$-0.954022\pi$
$467$	−7.99872	+	13.8542i	−0.370137	+	0.641095i	0.619450	+	0.785036i	$0.287356\pi$
$468$		0			0
$469$	8.89252	+	4.09990i	0.410618	+	0.189316i
$470$	24.5761			1.13361
$471$		0			0
$472$	−5.42524	−	9.39679i	−0.249717	−	0.432523i
$473$	0.947811	+	1.64166i	0.0435804	+	0.0754835i
$474$		0			0
$475$	−10.9675			−0.503221
$476$	−0.240939	−	2.62318i	−0.0110434	−	0.120233i
$477$		0			0
$478$	−10.1454	+	17.5723i	−0.464039	+	0.803739i
$479$	−7.18238	−	12.4403i	−0.328171	−	0.568410i	0.653978	−	0.756514i	$-0.273099\pi$
$479$	−7.18238	−	12.4403i	−0.328171	−	0.568410i	−0.982149	+	0.188104i	$0.939766\pi$
$480$		0			0
$481$	8.96931	−	15.5353i	0.408966	−	0.708349i
$482$	−17.6909			−0.805800
$483$		0			0
$484$	2.36168			0.107349
$485$	26.6908	−	46.2299i	1.21197	−	2.09919i
$486$		0			0
$487$	7.84788	+	13.5929i	0.355621	+	0.615954i	0.987224	−	0.159338i	$-0.0509359\pi$
$487$	7.84788	+	13.5929i	0.355621	+	0.615954i	−0.631603	+	0.775292i	$0.717603\pi$
$488$	−4.19914	+	7.27312i	−0.190086	+	0.329238i
$489$		0			0
$490$	−34.3718	+	6.36782i	−1.55276	+	0.287669i
$491$	−38.8742			−1.75437			−0.877183	−	0.480156i	$-0.840580\pi$
$491$	−38.8742			−1.75437			−0.877183	+	0.480156i	$0.840580\pi$
$492$		0			0
$493$	−0.835970	−	1.44794i	−0.0376502	−	0.0652120i
$494$	1.36791	+	2.36929i	0.0615453	+	0.106600i
$495$		0			0
$496$	29.0494			1.30436
$497$	−15.7809	+	11.1520i	−0.707872	+	0.500235i
$498$		0			0
$499$	−21.9808	+	38.0719i	−0.983997	+	1.70433i	−0.337684	+	0.941260i	$0.609644\pi$
$499$	−21.9808	+	38.0719i	−0.983997	+	1.70433i	−0.646313	+	0.763073i	$0.723690\pi$
$500$	−5.22437	−	9.04888i	−0.233641	−	0.404678i
$501$		0			0
$502$	9.07033	−	15.7103i	0.404829	−	0.701184i
$503$	23.9459			1.06770			0.533848	−	0.845580i	$-0.320745\pi$
$503$	23.9459			1.06770			0.533848	+	0.845580i	$0.320745\pi$
$504$		0			0
$505$	−45.0551			−2.00492
$506$	12.7265	−	22.0429i	0.565762	−	0.979929i
$507$		0			0
$508$	2.36091	+	4.08922i	0.104749	+	0.181430i
$509$	−9.19234	+	15.9216i	−0.407444	+	0.705713i	−0.994602	−	0.103759i	$-0.966913\pi$
$509$	−9.19234	+	15.9216i	−0.407444	+	0.705713i	0.587159	+	0.809472i	$0.300246\pi$
$510$		0			0
$511$	17.7377	+	8.17798i	0.784669	+	0.361773i
$512$	24.9907			1.10444
$513$		0			0
$514$	−2.08087	−	3.60418i	−0.0917833	−	0.158973i
$515$	−19.7399	−	34.1905i	−0.869843	−	1.50661i
$516$		0			0
$517$	11.6566			0.512658
$518$	24.6052	+	11.3442i	1.08109	+	0.498438i
$519$		0			0
$520$	−13.3273	+	23.0836i	−0.584441	+	1.01228i
$521$	0.710069	+	1.22988i	0.0311087	+	0.0538819i	0.881161	−	0.472817i	$-0.156763\pi$
$521$	0.710069	+	1.22988i	0.0311087	+	0.0538819i	−0.850052	+	0.526699i	$0.823430\pi$
$522$		0			0
$523$	−11.6918	+	20.2507i	−0.511245	+	0.885503i	0.488670	+	0.872469i	$0.337482\pi$
$523$	−11.6918	+	20.2507i	−0.511245	+	0.885503i	−0.999915	+	0.0130338i	$0.995851\pi$
$524$	−0.368312			−0.0160898
$525$		0			0
$526$	29.8823			1.30293
$527$	11.2576	−	19.4987i	0.490388	−	0.849378i
$528$		0			0
$529$	−25.4686	−	44.1128i	−1.10733	−	1.91795i
$530$	−8.18558	+	14.1778i	−0.355559	+	0.615846i
$531$		0			0
$532$	0.946779	−	0.669065i	0.0410481	−	0.0290077i
$533$	−18.2984			−0.792591
$534$		0			0
$535$	−13.8611	−	24.0081i	−0.599267	−	1.03796i
$536$	5.63872	+	9.76654i	0.243555	+	0.421850i
$537$		0			0
$538$	−22.8176			−0.983737
$539$	−16.3028	+	3.02031i	−0.702213	+	0.130094i
$540$		0			0
$541$	−17.9064	+	31.0148i	−0.769856	+	1.33343i	0.167785	+	0.985824i	$0.446339\pi$
$541$	−17.9064	+	31.0148i	−0.769856	+	1.33343i	−0.937641	+	0.347606i	$0.886995\pi$
$542$	−5.68654	−	9.84938i	−0.244258	−	0.423067i
$543$		0			0
$544$	2.76117	−	4.78249i	0.118384	−	0.205048i
$545$	−14.7846			−0.633304
$546$		0			0
$547$	13.7734			0.588909			0.294455	−	0.955665i	$-0.404862\pi$
$547$	13.7734			0.588909			0.294455	+	0.955665i	$0.404862\pi$
$548$	−0.561308	+	0.972213i	−0.0239779	+	0.0415309i
$549$		0			0
$550$	16.2324	+	28.1154i	0.692154	+	1.19885i
$551$	0.367912	−	0.637243i	0.0156736	−	0.0271474i
$552$		0			0
$553$	0.221882	+	2.41570i	0.00943537	+	0.102726i
$554$	−16.1340			−0.685470
$555$		0			0
$556$	−2.38239	−	4.12642i	−0.101036	−	0.174999i
$557$	5.88752	+	10.1975i	0.249462	+	0.432081i	0.963377	−	0.268152i	$-0.0864128\pi$
$557$	5.88752	+	10.1975i	0.249462	+	0.432081i	−0.713914	+	0.700233i	$0.753079\pi$
$558$		0			0
$559$	1.75199			0.0741014
$560$	−28.1464	−	12.9769i	−1.18940	−	0.548375i
$561$		0			0
$562$	−19.2436	+	33.3308i	−0.811741	+	1.40598i
$563$	5.79905	+	10.0443i	0.244401	+	0.423315i	0.961963	−	0.273180i	$-0.0880754\pi$
$563$	5.79905	+	10.0443i	0.244401	+	0.423315i	−0.717562	+	0.696495i	$0.754742\pi$
$564$		0			0
$565$	4.18934	−	7.25614i	0.176247	−	0.305268i
$566$	−29.0814			−1.22238
$567$		0			0
$568$	−22.2547			−0.933788
$569$	8.10322	−	14.0352i	0.339705	−	0.588386i	−0.644673	−	0.764459i	$-0.723006\pi$
$569$	8.10322	−	14.0352i	0.339705	−	0.588386i	0.984377	+	0.176073i	$0.0563396\pi$
$570$		0			0
$571$	8.99591	+	15.5814i	0.376467	+	0.652060i	0.990545	−	0.137185i	$-0.0438054\pi$
$571$	8.99591	+	15.5814i	0.376467	+	0.652060i	−0.614078	+	0.789245i	$0.710472\pi$
$572$	−1.13604	+	1.96768i	−0.0475002	+	0.0822727i
$573$		0			0
$574$	−2.52789	−	27.5219i	−0.105512	−	1.14874i
$575$	94.3055			3.93281
$576$		0			0
$577$	11.9506	+	20.6990i	0.497509	+	0.861712i	0.999996	−	0.00287352i	$-0.000914671\pi$
$577$	11.9506	+	20.6990i	0.497509	+	0.861712i	−0.502486	+	0.864585i	$0.667581\pi$
$578$	−7.39657	−	12.8112i	−0.307657	−	0.532877i
$579$		0			0
$580$	1.28840			0.0534977
$581$	−10.6289	+	7.51121i	−0.440963	+	0.311618i
$582$		0			0
$583$	−3.88249	+	6.72466i	−0.160796	+	0.278507i
$584$	11.2474	+	19.4811i	0.465421	+	0.806133i
$585$		0			0
$586$	−5.11324	+	8.85640i	−0.211226	+	0.365854i
$587$	15.6293			0.645091			0.322545	−	0.946554i	$-0.395461\pi$
$587$	15.6293			0.645091			0.322545	+	0.946554i	$0.395461\pi$
$588$		0			0
$589$	9.90898			0.408293
$590$	−8.89141	+	15.4004i	−0.366053	+	0.634023i
$591$		0			0
$592$	12.0114	+	20.8044i	0.493666	+	0.855055i
$593$	4.12431	−	7.14351i	0.169365	−	0.293349i	−0.768832	−	0.639451i	$-0.779162\pi$
$593$	4.12431	−	7.14351i	0.169365	−	0.293349i	0.938197	+	0.346102i	$0.112495\pi$
$594$		0			0
$595$	−19.6181	+	13.8636i	−0.804262	+	0.568352i
$596$	−9.66711			−0.395980
$597$		0			0
$598$	−11.7622	−	20.3728i	−0.480993	−	0.833105i
$599$	−4.20849	−	7.28931i	−0.171954	−	0.297833i	0.767149	−	0.641469i	$-0.221675\pi$
$599$	−4.20849	−	7.28931i	−0.171954	−	0.297833i	−0.939103	+	0.343636i	$0.888341\pi$
$600$		0			0
$601$	−15.3330			−0.625446			−0.312723	−	0.949844i	$-0.601241\pi$
$601$	−15.3330			−0.625446			−0.312723	+	0.949844i	$0.601241\pi$
$602$	0.242034	+	2.63511i	0.00986459	+	0.107399i
$603$		0			0
$604$	−0.696531	+	1.20643i	−0.0283415	+	0.0490888i
$605$	−10.7684	−	18.6515i	−0.437799	−	0.758291i
$606$		0			0
$607$	1.88178	−	3.25934i	0.0763790	−	0.132292i	−0.825306	−	0.564686i	$-0.808997\pi$
$607$	1.88178	−	3.25934i	0.0763790	−	0.132292i	0.901685	+	0.432393i	$0.142331\pi$
$608$	2.43040			0.0985656
$609$		0			0
$610$	13.7639			0.557284
$611$	5.38671	−	9.33005i	0.217923	−	0.377454i
$612$		0			0
$613$	−8.76287	−	15.1777i	−0.353929	−	0.613023i	0.633005	−	0.774148i	$-0.281821\pi$
$613$	−8.76287	−	15.1777i	−0.353929	−	0.613023i	−0.986934	+	0.161125i	$0.948488\pi$
$614$	11.9509	−	20.6996i	0.482299	−	0.835366i
$615$		0			0
$616$	−17.3408	−	7.99502i	−0.698683	−	0.322128i
$617$	12.0057			0.483330			0.241665	−	0.970360i	$-0.422306\pi$
$617$	12.0057			0.483330			0.241665	+	0.970360i	$0.422306\pi$
$618$		0			0
$619$	−13.9364	−	24.1385i	−0.560150	−	0.970209i	−0.997483	−	0.0709089i	$-0.977410\pi$
$619$	−13.9364	−	24.1385i	−0.560150	−	0.970209i	0.437332	−	0.899300i	$-0.355923\pi$
$620$	8.67509	+	15.0257i	0.348400	+	0.603446i
$621$		0			0
$622$	42.8834			1.71947
$623$	−4.28364	−	46.6374i	−0.171620	−	1.86849i
$624$		0			0
$625$	−20.2239	+	35.0289i	−0.808957	+	1.40115i
$626$	−1.84677	−	3.19870i	−0.0738118	−	0.127846i
$627$		0			0
$628$	−4.96001	+	8.59098i	−0.197926	+	0.342818i
$629$	18.6193			0.742398
$630$		0			0
$631$	46.7972			1.86297			0.931483	−	0.363784i	$-0.118515\pi$
$631$	46.7972			1.86297			0.931483	+	0.363784i	$0.118515\pi$
$632$	−1.39691	+	2.41953i	−0.0555663	+	0.0962436i
$633$		0			0
$634$	7.82439	+	13.5522i	0.310746	+	0.538228i
$635$	21.5299	−	37.2908i	0.854386	−	1.47984i
$636$		0			0
$637$	−5.11631	+	14.4446i	−0.202716	+	0.572317i
$638$	−2.17812			−0.0862326
$639$		0			0
$640$	−12.5122	−	21.6718i	−0.494590	−	0.856655i
$641$	8.86536	+	15.3553i	0.350161	+	0.606496i	0.986277	−	0.165097i	$-0.0527936\pi$
$641$	8.86536	+	15.3553i	0.350161	+	0.606496i	−0.636117	+	0.771593i	$0.719460\pi$
$642$		0			0
$643$	−42.2257			−1.66522			−0.832609	−	0.553862i	$-0.813154\pi$
$643$	−42.2257			−1.66522			−0.832609	+	0.553862i	$0.813154\pi$
$644$	−8.14104	+	5.75307i	−0.320802	+	0.226703i
$645$		0			0
$646$	−1.41981	+	2.45919i	−0.0558618	+	0.0967555i
$647$	−20.2952	−	35.1523i	−0.797886	−	1.38198i	−0.920990	−	0.389586i	$-0.872618\pi$
$647$	−20.2952	−	35.1523i	−0.797886	−	1.38198i	0.123104	−	0.992394i	$-0.460715\pi$
$648$		0			0
$649$	−4.21726	+	7.30451i	−0.165542	+	0.286727i
$650$	30.0050			1.17689
$651$		0			0
$652$	6.41048			0.251054
$653$	4.32081	−	7.48386i	0.169086	−	0.292866i	−0.769013	−	0.639234i	$-0.779252\pi$
$653$	4.32081	−	7.48386i	0.169086	−	0.292866i	0.938099	+	0.346368i	$0.112585\pi$
$654$		0			0
$655$	1.67937	+	2.90876i	0.0656186	+	0.113655i
$656$	12.2523	−	21.2216i	0.478372	−	0.828564i
$657$		0			0
$658$	14.7772	+	6.81303i	0.576074	+	0.265599i
$659$	43.2307			1.68403			0.842015	−	0.539454i	$-0.181369\pi$
$659$	43.2307			1.68403			0.842015	+	0.539454i	$0.181369\pi$
$660$		0			0
$661$	−4.37679	−	7.58083i	−0.170237	−	0.294860i	0.768265	−	0.640132i	$-0.221120\pi$
$661$	−4.37679	−	7.58083i	−0.170237	−	0.294860i	−0.938503	+	0.345272i	$0.887787\pi$
$662$	14.2084	+	24.6096i	0.552223	+	0.956479i
$663$		0			0
$664$	−14.9893			−0.581696
$665$	−9.60094	−	4.42652i	−0.372309	−	0.171653i
$666$		0			0
$667$	−3.16356	+	5.47944i	−0.122493	+	0.212165i
$668$	3.90044	+	6.75576i	0.150912	+	0.261388i
$669$		0			0
$670$	9.24127	−	16.0063i	0.357021	−	0.618379i
$671$	6.52832			0.252023
$672$		0			0
$673$	0.331699			0.0127861			0.00639304	−	0.999980i	$-0.497965\pi$
$673$	0.331699			0.0127861			0.00639304	+	0.999980i	$0.497965\pi$
$674$	2.53573	−	4.39201i	0.0976726	−	0.169174i
$675$		0			0
$676$	−1.79824	−	3.11464i	−0.0691630	−	0.119794i
$677$	−13.9315	+	24.1301i	−0.535432	+	0.927395i	0.463711	+	0.885987i	$0.346518\pi$
$677$	−13.9315	+	24.1301i	−0.535432	+	0.927395i	−0.999142	+	0.0414081i	$0.986816\pi$
$678$		0			0
$679$	28.8646	−	20.3979i	1.10772	−	0.782799i
$680$	−27.6660			−1.06094
$681$		0			0
$682$	−14.6658	−	25.4020i	−0.561584	−	0.972692i
$683$	8.38990	+	14.5317i	0.321031	+	0.556042i	0.980701	−	0.195514i	$-0.0626374\pi$
$683$	8.38990	+	14.5317i	0.321031	+	0.556042i	−0.659670	+	0.751555i	$0.729304\pi$
$684$		0			0
$685$	10.2374			0.391153
$686$	−22.4325	−	5.69976i	−0.856475	−	0.217618i
$687$		0			0
$688$	−1.17311	+	2.03188i	−0.0447243	+	0.0774647i
$689$	3.58831	+	6.21514i	0.136704	+	0.236778i
$690$		0			0
$691$	12.9029	−	22.3485i	0.490850	−	0.850177i	−0.509095	−	0.860711i	$-0.670020\pi$
$691$	12.9029	−	22.3485i	0.490850	−	0.850177i	0.999945	+	0.0105336i	$0.00335300\pi$
$692$	−10.9259			−0.415340
$693$		0			0
$694$	−28.8751			−1.09608
$695$	−21.7257	+	37.6300i	−0.824102	+	1.42739i
$696$		0			0
$697$	−9.49632	−	16.4481i	−0.359699	−	0.623017i
$698$	11.1877	−	19.3777i	0.423461	−	0.733457i
$699$		0			0
$700$	−1.16296	−	12.6616i	−0.0439559	−	0.478563i
$701$	−14.8949			−0.562573			−0.281287	−	0.959624i	$-0.590761\pi$
$701$	−14.8949			−0.562573			−0.281287	+	0.959624i	$0.590761\pi$
$702$		0			0
$703$	4.09719	+	7.09654i	0.154528	+	0.267651i
$704$	−10.5410	−	18.2575i	−0.397278	−	0.688106i
$705$		0			0
$706$	−11.1376			−0.419168
$707$	−27.0908	−	12.4902i	−1.01885	−	0.469744i
$708$		0			0
$709$	−3.29447	+	5.70619i	−0.123726	+	0.214300i	−0.921234	−	0.389008i	$-0.872818\pi$
$709$	−3.29447	+	5.70619i	−0.123726	+	0.214300i	0.797508	+	0.603308i	$0.206151\pi$
$710$	18.2366	+	31.5867i	0.684407	+	1.18543i
$711$		0			0
$712$	26.9687	−	46.7112i	1.01070	−	1.75058i
$713$	−85.2041			−3.19092
$714$		0			0
$715$	20.7197			0.774874
$716$	−2.98713	+	5.17385i	−0.111634	+	0.193356i
$717$		0			0
$718$	−7.64615	−	13.2435i	−0.285352	−	0.494244i
$719$	−16.4386	+	28.4724i	−0.613055	+	1.06184i	0.377667	+	0.925942i	$0.376726\pi$
$719$	−16.4386	+	28.4724i	−0.613055	+	1.06184i	−0.990722	+	0.135902i	$0.956607\pi$
$720$		0			0
$721$	−2.39089	−	26.0304i	−0.0890414	−	0.969423i
$722$	−1.24973			−0.0465100
$723$		0			0
$724$	−0.830904	−	1.43917i	−0.0308803	−	0.0534863i
$725$	−4.03506	−	6.98893i	−0.149858	−	0.259562i
$726$		0			0
$727$	−15.7724			−0.584966			−0.292483	−	0.956271i	$-0.594481\pi$
$727$	−15.7724			−0.584966			−0.292483	+	0.956271i	$0.594481\pi$
$728$	−14.4127	+	10.1851i	−0.534172	+	0.377486i
$729$		0			0
$730$	18.4333	−	31.9275i	0.682248	−	1.18169i
$731$	0.909233	+	1.57484i	0.0336292	+	0.0582475i
$732$		0			0
$733$	−2.99896	+	5.19434i	−0.110769	+	0.191857i	−0.916081	−	0.400994i	$-0.868665\pi$
$733$	−2.99896	+	5.19434i	−0.110769	+	0.191857i	0.805312	+	0.592852i	$0.201998\pi$
$734$	0.445962			0.0164608
$735$		0			0
$736$	−20.8982			−0.770317
$737$	4.38320	−	7.59193i	0.161457	−	0.279652i
$738$		0			0
$739$	−5.50327	−	9.53195i	−0.202441	−	0.350638i	0.746873	−	0.664966i	$-0.231554\pi$
$739$	−5.50327	−	9.53195i	−0.202441	−	0.350638i	−0.949314	+	0.314328i	$0.898221\pi$
$740$	−7.17399	+	12.4257i	−0.263721	+	0.456778i
$741$		0			0
$742$	−8.85225	+	6.25566i	−0.324976	+	0.229653i
$743$	−23.7308			−0.870598			−0.435299	−	0.900286i	$-0.643357\pi$
$743$	−23.7308			−0.870598			−0.435299	+	0.900286i	$0.643357\pi$
$744$		0			0
$745$	44.0786	+	76.3463i	1.61491	+	2.79711i
$746$	−7.80078	−	13.5114i	−0.285607	−	0.494686i
$747$		0			0
$748$	−2.35829			−0.0862274
$749$	−1.67885	−	18.2782i	−0.0613439	−	0.667872i
$750$		0			0
$751$	16.2986	−	28.2300i	0.594745	−	1.03013i	−0.398838	−	0.917021i	$-0.630586\pi$
$751$	16.2986	−	28.2300i	0.594745	−	1.03013i	0.993583	−	0.113107i	$-0.0360803\pi$
$752$	7.21371	+	12.4945i	0.263057	+	0.455628i
$753$		0			0
$754$	−1.00654	+	1.74338i	−0.0366561	+	0.0634903i
$755$	12.7037			0.462336
$756$		0			0
$757$	−15.3780			−0.558923			−0.279461	−	0.960157i	$-0.590156\pi$
$757$	−15.3780			−0.558923			−0.279461	+	0.960157i	$0.590156\pi$
$758$	10.8767	−	18.8389i	0.395059	−	0.684261i
$759$		0			0
$760$	−6.08793	−	10.5446i	−0.220832	−	0.382493i
$761$	23.2625	−	40.2919i	0.843266	−	1.46058i	−0.0438521	−	0.999038i	$-0.513963\pi$
$761$	23.2625	−	40.2919i	0.843266	−	1.46058i	0.887118	−	0.461542i	$-0.152704\pi$
$762$		0			0
$763$	−8.88973	−	4.09862i	−0.321830	−	0.148380i
$764$	4.39788			0.159110
$765$		0			0
$766$	16.8424	+	29.1719i	0.608541	+	1.05402i
$767$	3.89772	+	6.75106i	0.140739	+	0.243766i
$768$		0			0
$769$	−41.6203			−1.50086			−0.750432	−	0.660947i	$-0.770155\pi$
$769$	−41.6203			−1.50086			−0.750432	+	0.660947i	$0.770155\pi$
$770$	2.86239	+	31.1638i	0.103153	+	1.12307i
$771$		0			0
$772$	4.16043	−	7.20608i	0.149737	−	0.259352i
$773$	6.51547	+	11.2851i	0.234345	+	0.405898i	0.959082	−	0.283128i	$-0.0913721\pi$
$773$	6.51547	+	11.2851i	0.234345	+	0.405898i	−0.724737	+	0.689026i	$0.758039\pi$
$774$		0			0
$775$	54.3382	−	94.1165i	1.95188	−	3.38076i
$776$	40.7057			1.46125
$777$		0			0
$778$	−43.2571			−1.55084
$779$	4.17935	−	7.23885i	0.149741	−	0.259359i
$780$		0			0
$781$	8.64976	+	14.9818i	0.309513	+	0.536092i
$782$	12.2085	−	21.1458i	0.436575	−	0.756171i
$783$		0			0
$784$	−13.3264	−	15.6056i	−0.475943	−	0.557341i
$785$	90.4634			3.22878
$786$		0			0
$787$	−5.41229	−	9.37436i	−0.192927	−	0.334160i	0.753292	−	0.657686i	$-0.228465\pi$
$787$	−5.41229	−	9.37436i	−0.192927	−	0.334160i	−0.946219	+	0.323527i	$0.895131\pi$
$788$	−0.675955	−	1.17079i	−0.0240799	−	0.0417076i
$789$		0			0
$790$	4.57879			0.162906
$791$	4.53053	−	3.20161i	0.161087	−	0.113836i
$792$		0			0
$793$	3.01684	−	5.22531i	0.107131	−	0.185556i
$794$	−11.0472	−	19.1344i	−0.392052	−	0.679053i
$795$		0			0
$796$	−4.13078	+	7.15473i	−0.146412	+	0.253593i
$797$	−1.01586			−0.0359836			−0.0179918	−	0.999838i	$-0.505727\pi$
$797$	−1.01586			−0.0359836			−0.0179918	+	0.999838i	$0.505727\pi$
$798$		0			0
$799$	11.1822			0.395597
$800$	13.3276	−	23.0841i	0.471203	−	0.816148i
$801$		0			0
$802$	8.74710	+	15.1504i	0.308871	+	0.534980i
$803$	8.74307	−	15.1434i	0.308536	−	0.534401i
$804$		0			0
$805$	82.5553	+	38.0622i	2.90969	+	1.34152i
$806$	−27.1092			−0.954882
$807$		0			0
$808$	−17.1782	−	29.7535i	−0.604326	−	1.04672i
$809$	−7.26173	−	12.5777i	−0.255309	−	0.442208i	0.709671	−	0.704534i	$-0.248844\pi$
$809$	−7.26173	−	12.5777i	−0.255309	−	0.442208i	−0.964979	+	0.262326i	$0.915510\pi$
$810$		0			0
$811$	−8.72354			−0.306325			−0.153162	−	0.988201i	$-0.548946\pi$
$811$	−8.72354			−0.306325			−0.153162	+	0.988201i	$0.548946\pi$
$812$	0.774689	+	0.357171i	0.0271862	+	0.0125342i
$813$		0			0
$814$	12.1281	−	21.0065i	0.425091	−	0.736278i
$815$	−29.2295	−	50.6270i	−1.02386	−	1.77339i
$816$		0			0
$817$	−0.400156	+	0.693090i	−0.0139997	+	0.0242481i
$818$	−38.1747			−1.33475
$819$		0			0
$820$	14.6357			0.511101
$821$	−11.9249	+	20.6545i	−0.416181	+	0.720846i	−0.995552	−	0.0942181i	$-0.969965\pi$
$821$	−11.9249	+	20.6545i	−0.416181	+	0.720846i	0.579371	+	0.815064i	$0.303298\pi$
$822$		0			0
$823$	12.2249	+	21.1742i	0.426134	+	0.738085i	0.996526	−	0.0832873i	$-0.0265419\pi$
$823$	12.2249	+	21.1742i	0.426134	+	0.738085i	−0.570392	+	0.821373i	$0.693209\pi$
$824$	15.0525	−	26.0716i	0.524378	−	0.908249i
$825$		0			0
$826$	−9.61556	+	6.79507i	−0.334568	+	0.236431i
$827$	17.8924			0.622179			0.311090	−	0.950381i	$-0.399306\pi$
$827$	17.8924			0.622179			0.311090	+	0.950381i	$0.399306\pi$
$828$		0			0
$829$	−7.77612	−	13.4686i	−0.270076	−	0.467785i	0.698805	−	0.715312i	$-0.253715\pi$
$829$	−7.77612	−	13.4686i	−0.270076	−	0.467785i	−0.968881	+	0.247527i	$0.920382\pi$
$830$	12.2829	+	21.2746i	0.426346	+	0.738453i
$831$		0			0
$832$	−19.4846			−0.675507
$833$	−15.6393	+	2.89737i	−0.541869	+	0.100388i
$834$		0			0
$835$	35.5692	−	61.6077i	1.23092	−	2.13202i
$836$	−0.518943	−	0.898836i	−0.0179480	−	0.0310869i
$837$		0			0
$838$	−10.7523	+	18.6236i	−0.371433	+	0.643340i
$839$	2.07381			0.0715959			0.0357979	−	0.999359i	$-0.488603\pi$
$839$	2.07381			0.0715959			0.0357979	+	0.999359i	$0.488603\pi$
$840$		0			0
$841$	−28.4586			−0.981330
$842$	−6.07169	+	10.5165i	−0.209244	+	0.362422i
$843$		0			0
$844$	−4.36370	−	7.55815i	−0.150205	−	0.260162i
$845$	−16.3986	+	28.4033i	−0.564130	+	0.977102i
$846$		0			0
$847$	−1.30427	−	14.2000i	−0.0448153	−	0.487919i
$848$	−9.61071			−0.330033
$849$		0			0
$850$	15.5717	+	26.9710i	0.534106	+	0.925099i
$851$	−35.2304	−	61.0208i	−1.20768	−	2.09177i
$852$		0			0
$853$	14.2407			0.487594			0.243797	−	0.969826i	$-0.421607\pi$
$853$	14.2407			0.487594			0.243797	+	0.969826i	$0.421607\pi$
$854$	8.27598	+	3.81565i	0.283198	+	0.130569i
$855$		0			0
$856$	10.5697	−	18.3072i	0.361263	−	0.625726i
$857$	12.6943	+	21.9872i	0.433630	+	0.751070i	0.997183	−	0.0750106i	$-0.0238990\pi$
$857$	12.6943	+	21.9872i	0.433630	+	0.751070i	−0.563552	+	0.826080i	$0.690566\pi$
$858$		0			0
$859$	19.5613	−	33.8811i	0.667421	−	1.15601i	−0.311201	−	0.950344i	$-0.600731\pi$
$859$	19.5613	−	33.8811i	0.667421	−	1.15601i	0.978623	−	0.205664i	$-0.0659353\pi$
$860$	−1.40131			−0.0477842
$861$		0			0
$862$	−23.2140			−0.790673
$863$	0.817785	−	1.41645i	0.0278377	−	0.0482164i	−0.851771	−	0.523914i	$-0.824471\pi$
$863$	0.817785	−	1.41645i	0.0278377	−	0.0482164i	0.879609	+	0.475698i	$0.157804\pi$
$864$		0			0
$865$	49.8182	+	86.2876i	1.69387	+	2.93387i
$866$	−10.5252	+	18.2302i	−0.357662	+	0.619489i
$867$		0			0
$868$	1.05073	+	11.4396i	0.0356640	+	0.388285i
$869$	2.17176			0.0736718
$870$		0			0
$871$	−4.05109	−	7.01670i	−0.137266	−	0.237752i
$872$	−5.63695	−	9.76348i	−0.190891	−	0.330633i
$873$		0			0
$874$	10.7460			0.363488
$875$	−51.5228	+	36.4098i	−1.74179	+	1.23088i
$876$		0			0
$877$	2.61968	−	4.53741i	0.0884602	−	0.153218i	−0.818400	−	0.574649i	$-0.805139\pi$
$877$	2.61968	−	4.53741i	0.0884602	−	0.153218i	0.906860	+	0.421431i	$0.138472\pi$
$878$	−0.235171	−	0.407327i	−0.00793662	−	0.0137466i
$879$		0			0
$880$	−13.8736	+	24.0298i	−0.467679	+	0.810044i
$881$	23.6123			0.795520			0.397760	−	0.917489i	$-0.369788\pi$
$881$	23.6123			0.795520			0.397760	+	0.917489i	$0.369788\pi$
$882$		0			0
$883$	−22.5324			−0.758277			−0.379138	−	0.925340i	$-0.623780\pi$
$883$	−22.5324			−0.758277			−0.379138	+	0.925340i	$0.623780\pi$
$884$	−1.08980	+	1.88759i	−0.0366539	+	0.0634865i
$885$		0			0
$886$	20.3674	+	35.2773i	0.684255	+	1.18516i
$887$	9.56395	−	16.5652i	0.321126	−	0.556206i	−0.659595	−	0.751621i	$-0.729272\pi$
$887$	9.56395	−	16.5652i	0.321126	−	0.556206i	0.980721	+	0.195415i	$0.0626054\pi$
$888$		0			0
$889$	23.2833	−	16.4537i	0.780898	−	0.551841i
$890$	−88.3979			−2.96311
$891$		0			0
$892$	2.70587	+	4.68670i	0.0905991	+	0.156922i
$893$	2.46065	+	4.26197i	0.0823426	+	0.142622i
$894$		0			0
$895$	54.4809			1.82110
$896$	−1.51548	−	16.4996i	−0.0506287	−	0.551211i
$897$		0			0
$898$	−10.4464	+	18.0936i	−0.348600	+	0.603792i
$899$	3.64564	+	6.31443i	0.121589	+	0.210598i
$900$		0			0
$901$	−3.72446	+	6.45095i	−0.124080	+	0.214912i
$902$	−24.7427			−0.823841
$903$		0			0
$904$	6.38909			0.212498
$905$	−7.57726	+	13.1242i	−0.251877	+	0.436263i
$906$		0			0
$907$	11.8397	+	20.5070i	0.393132	+	0.680924i	0.992861	−	0.119279i	$-0.0380583\pi$
$907$	11.8397	+	20.5070i	0.393132	+	0.680924i	−0.599729	+	0.800203i	$0.704725\pi$
$908$	−2.30878	+	3.99893i	−0.0766196	+	0.132709i
$909$		0			0
$910$	26.2665	+	12.1102i	0.870726	+	0.401449i
$911$	55.7299			1.84641			0.923207	−	0.384302i	$-0.125558\pi$
$911$	55.7299			1.84641			0.923207	+	0.384302i	$0.125558\pi$
$912$		0			0
$913$	5.82588	+	10.0907i	0.192808	+	0.333954i
$914$	10.9918	+	19.0383i	0.363575	+	0.629731i
$915$		0			0
$916$	−9.61653			−0.317739
$917$	0.203406	+	2.21454i	0.00671704	+	0.0731307i
$918$		0			0
$919$	9.01041	−	15.6065i	0.297226	−	0.514811i	−0.678274	−	0.734809i	$-0.737272\pi$
$919$	9.01041	−	15.6065i	0.297226	−	0.514811i	0.975500	+	0.219998i	$0.0706052\pi$
$920$	52.3481	+	90.6695i	1.72586	+	2.98928i
$921$		0			0
$922$	1.13651	−	1.96849i	0.0374288	−	0.0648286i
$923$	15.9887			0.526276
$924$		0			0
$925$	89.8715			2.95496
$926$	−0.844342	+	1.46244i	−0.0277468	+	0.0480589i
$927$		0			0
$928$	0.894173	+	1.54875i	0.0293527	+	0.0508403i
$929$	6.27043	−	10.8607i	0.205726	−	0.356328i	−0.744638	−	0.667469i	$-0.767378\pi$
$929$	6.27043	−	10.8607i	0.205726	−	0.356328i	0.950364	+	0.311141i	$0.100711\pi$
$930$		0			0
$931$	−4.54574	−	5.32318i	−0.148981	−	0.174460i
$932$	−2.89659			−0.0948810
$933$		0			0
$934$	9.99621	+	17.3139i	0.327086	+	0.566530i
$935$	10.7529	+	18.6246i	0.351659	+	0.609091i
$936$		0			0
$937$	−31.4153			−1.02629			−0.513147	−	0.858301i	$-0.671520\pi$
$937$	−31.4153			−1.02629			−0.513147	+	0.858301i	$0.671520\pi$
$938$	9.99391	−	7.06244i	0.326313	−	0.230597i
$939$		0			0
$940$	−4.30849	+	7.46252i	−0.140527	+	0.243401i
$941$	7.45006	+	12.9039i	0.242865	+	0.420654i	0.961529	−	0.274703i	$-0.0885795\pi$
$941$	7.45006	+	12.9039i	0.242865	+	0.420654i	−0.718664	+	0.695357i	$0.755246\pi$
$942$		0			0
$943$	−35.9369	+	62.2445i	−1.17027	+	2.02696i
$944$	−10.4394			−0.339774
$945$		0			0
$946$	2.36901			0.0770231
$947$	4.68806	−	8.11996i	0.152342	−	0.263863i	−0.779746	−	0.626096i	$-0.784652\pi$
$947$	4.68806	−	8.11996i	0.152342	−	0.263863i	0.932088	+	0.362232i	$0.117985\pi$
$948$		0			0
$949$	−8.08062	−	13.9960i	−0.262308	−	0.454331i
$950$	−6.85316	+	11.8700i	−0.222346	+	0.385114i
$951$		0			0
$952$	−16.6350	−	7.66960i	−0.539145	−	0.248573i
$953$	11.0785			0.358868			0.179434	−	0.983770i	$-0.442573\pi$
$953$	11.0785			0.358868			0.179434	+	0.983770i	$0.442573\pi$
$954$		0			0
$955$	−20.0527	−	34.7324i	−0.648892	−	1.12391i
$956$	−3.55722	−	6.16129i	−0.115049	−	0.199270i
$957$		0			0
$958$	−17.9520			−0.580004
$959$	6.15559	+	2.83804i	0.198774	+	0.0916452i
$960$		0			0
$961$	−33.5940	+	58.1865i	−1.08368	+	1.87698i
$962$	−11.2092	−	19.4149i	−0.361399	−	0.625961i
$963$		0			0
$964$	3.10144	−	5.37185i	0.0998906	−	0.173016i
$965$	−75.8803			−2.44267
$966$		0			0
$967$	51.5512			1.65778			0.828888	−	0.559415i	$-0.188974\pi$
$967$	51.5512			1.65778			0.828888	+	0.559415i	$0.188974\pi$
$968$	8.21138	−	14.2225i	0.263924	−	0.457129i
$969$		0			0
$970$	−33.3562	−	57.7747i	−1.07100	−	1.85503i
$971$	−6.76322	+	11.7142i	−0.217042	+	0.375928i	−0.953902	−	0.300117i	$-0.902974\pi$
$971$	−6.76322	+	11.7142i	−0.217042	+	0.375928i	0.736860	+	0.676045i	$0.236308\pi$
$972$		0			0
$973$	−23.4951	+	16.6034i	−0.753218	+	0.532280i
$974$	19.6154			0.628518
$975$		0			0
$976$	4.04005	+	6.99758i	0.129319	+	0.223987i
$977$	−22.2791	−	38.5885i	−0.712771	−	1.23455i	−0.963813	−	0.266579i	$-0.914107\pi$
$977$	−22.2791	−	38.5885i	−0.712771	−	1.23455i	0.251043	−	0.967976i	$-0.419227\pi$
$978$		0			0
$979$	−41.9278			−1.34002
$980$	4.09222	−	11.5534i	0.130721	−	0.369058i
$981$		0			0
$982$	−24.2910	+	42.0733i	−0.775158	+	1.34261i
$983$	−5.10725	−	8.84601i	−0.162896	−	0.282144i	0.773010	−	0.634394i	$-0.218750\pi$
$983$	−5.10725	−	8.84601i	−0.162896	−	0.282144i	−0.935906	+	0.352250i	$0.885417\pi$
$984$		0			0
$985$	−6.16423	+	10.6768i	−0.196409	+	0.340190i
$986$	−2.08947			−0.0665422
$987$		0			0
$988$	−0.959247			−0.0305177
$989$	3.44081	−	5.95965i	0.109411	−	0.189506i
$990$		0			0
$991$	9.45937	+	16.3841i	0.300487	+	0.520459i	0.976246	−	0.216664i	$-0.0695175\pi$
$991$	9.45937	+	16.3841i	0.300487	+	0.520459i	−0.675759	+	0.737122i	$0.736184\pi$
$992$	−12.0414	+	20.8563i	−0.382314	+	0.662188i
$993$		0			0
$994$	2.20881	+	24.0481i	0.0700593	+	0.762759i
$995$	75.3396			2.38843
$996$		0			0
$997$	−7.67167	−	13.2877i	−0.242964	−	0.420826i	0.718593	−	0.695431i	$-0.244786\pi$
$997$	−7.67167	−	13.2877i	−0.242964	−	0.420826i	−0.961557	+	0.274605i	$0.911453\pi$
$998$	27.4700	+	47.5794i	0.869548	+	1.50610i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1197.2.j.m.856.6		16
3.2	odd	2		399.2.j.g.58.3	✓	16
7.2	even	3		8379.2.a.cr.1.3		8
7.4	even	3	inner	1197.2.j.m.172.6		16
7.5	odd	6		8379.2.a.cq.1.3		8
21.2	odd	6		2793.2.a.bm.1.6		8
21.5	even	6		2793.2.a.bn.1.6		8
21.11	odd	6		399.2.j.g.172.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
399.2.j.g.58.3	✓	16	3.2	odd	2
399.2.j.g.172.3	yes	16	21.11	odd	6
1197.2.j.m.172.6		16	7.4	even	3	inner
1197.2.j.m.856.6		16	1.1	even	1	trivial
2793.2.a.bm.1.6		8	21.2	odd	6
2793.2.a.bn.1.6		8	21.5	even	6
8379.2.a.cq.1.3		8	7.5	odd	6
8379.2.a.cr.1.3		8	7.2	even	3

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:	\( N \)	\(=\)	\( 1197 = 3^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1197.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.624863 - 1.08229i) q^{2} +(0.219092 + 0.379479i) q^{4} +(1.99797 - 3.46058i) q^{5} +(2.16069 - 1.52690i) q^{7} +3.04706 q^{8} +O(q^{10})\)	\(q+(0.624863 - 1.08229i) q^{2} +(0.219092 + 0.379479i) q^{4} +(1.99797 - 3.46058i) q^{5} +(2.16069 - 1.52690i) q^{7} +3.04706 q^{8} +(-2.49691 - 4.32477i) q^{10} +(-1.18430 - 2.05127i) q^{11} -2.18914 q^{13} +(-0.302425 - 3.29260i) q^{14} +(1.46581 - 2.53886i) q^{16} +(-1.13610 - 1.96778i) q^{17} +(0.500000 - 0.866025i) q^{19} +1.75095 q^{20} -2.96011 q^{22} +(-4.29933 + 7.44667i) q^{23} +(-5.48373 - 9.49810i) q^{25} +(-1.36791 + 2.36929i) q^{26} +(1.05282 + 0.485402i) q^{28} +0.735824 q^{29} +(4.95449 + 8.58143i) q^{31} +(1.21520 + 2.10479i) q^{32} -2.83963 q^{34} +(-0.966988 - 10.5279i) q^{35} +(-4.09719 + 7.09654i) q^{37} +(-0.624863 - 1.08229i) q^{38} +(6.08793 - 10.5446i) q^{40} +8.35871 q^{41} -0.800311 q^{43} +(0.518943 - 0.898836i) q^{44} +(5.37299 + 9.30629i) q^{46} +(-2.46065 + 4.26197i) q^{47} +(2.33713 - 6.59832i) q^{49} -13.7063 q^{50} +(-0.479623 - 0.830732i) q^{52} +(-1.63914 - 2.83908i) q^{53} -9.46479 q^{55} +(6.58375 - 4.65257i) q^{56} +(0.459790 - 0.796379i) q^{58} +(-1.78048 - 3.08389i) q^{59} +(-1.37809 + 2.38693i) q^{61} +12.3835 q^{62} +8.90058 q^{64} +(-4.37382 + 7.57568i) q^{65} +(1.85054 + 3.20523i) q^{67} +(0.497821 - 0.862252i) q^{68} +(-11.9985 - 5.53194i) q^{70} -7.30367 q^{71} +(3.69123 + 6.39340i) q^{73} +(5.12036 + 8.86873i) q^{74} +0.438184 q^{76} +(-5.69100 - 2.62384i) q^{77} +(-0.458446 + 0.794052i) q^{79} +(-5.85729 - 10.1451i) q^{80} +(5.22305 - 9.04658i) q^{82} -4.91925 q^{83} -9.07955 q^{85} +(-0.500085 + 0.866173i) q^{86} +(-3.60865 - 6.25036i) q^{88} +(8.85073 - 15.3299i) q^{89} +(-4.73004 + 3.34260i) q^{91} -3.76780 q^{92} +(3.07514 + 5.32630i) q^{94} +(-1.99797 - 3.46058i) q^{95} +13.3590 q^{97} +(-5.68093 - 6.65251i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 10 q^{4} - 5 q^{5} + q^{7} + 6 q^{8}+O(q^{10}) \) 16 * q - 10 * q^4 - 5 * q^5 + q^7 + 6 * q^8	\( 16 q - 10 q^{4} - 5 q^{5} + q^{7} + 6 q^{8} + 3 q^{10} - 7 q^{11} - 12 q^{13} + 12 q^{14} - 10 q^{16} + 8 q^{19} + 32 q^{20} + 36 q^{22} - 9 q^{23} - 15 q^{25} - 12 q^{26} - 40 q^{28} - 8 q^{29} + 11 q^{31} - 26 q^{32} - 32 q^{34} + 7 q^{35} - 17 q^{37} + 3 q^{40} + 34 q^{41} + 16 q^{43} - 31 q^{44} - q^{46} - 29 q^{47} + q^{49} - 60 q^{50} + 25 q^{52} - 6 q^{53} - 42 q^{55} + 54 q^{56} + 37 q^{58} - 7 q^{59} + 2 q^{61} + 78 q^{62} + 58 q^{64} - 13 q^{65} - 13 q^{67} + 14 q^{68} - 81 q^{70} - 36 q^{71} + 20 q^{73} - 26 q^{74} - 20 q^{76} - 19 q^{77} + 3 q^{79} - 35 q^{80} + 5 q^{82} + 72 q^{83} + 10 q^{85} - 51 q^{86} - 53 q^{88} - q^{89} - 9 q^{91} - 30 q^{92} + 30 q^{94} + 5 q^{95} + 6 q^{97} + 75 q^{98}+O(q^{100}) \) 16 * q - 10 * q^4 - 5 * q^5 + q^7 + 6 * q^8 + 3 * q^10 - 7 * q^11 - 12 * q^13 + 12 * q^14 - 10 * q^16 + 8 * q^19 + 32 * q^20 + 36 * q^22 - 9 * q^23 - 15 * q^25 - 12 * q^26 - 40 * q^28 - 8 * q^29 + 11 * q^31 - 26 * q^32 - 32 * q^34 + 7 * q^35 - 17 * q^37 + 3 * q^40 + 34 * q^41 + 16 * q^43 - 31 * q^44 - q^46 - 29 * q^47 + q^49 - 60 * q^50 + 25 * q^52 - 6 * q^53 - 42 * q^55 + 54 * q^56 + 37 * q^58 - 7 * q^59 + 2 * q^61 + 78 * q^62 + 58 * q^64 - 13 * q^65 - 13 * q^67 + 14 * q^68 - 81 * q^70 - 36 * q^71 + 20 * q^73 - 26 * q^74 - 20 * q^76 - 19 * q^77 + 3 * q^79 - 35 * q^80 + 5 * q^82 + 72 * q^83 + 10 * q^85 - 51 * q^86 - 53 * q^88 - q^89 - 9 * q^91 - 30 * q^92 + 30 * q^94 + 5 * q^95 + 6 * q^97 + 75 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more