LMFDB - Embedded newform 756.2.b.d.55.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(55,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("756.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.60771337450861625344.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{10} + 11x^{8} - 26x^{6} + 44x^{4} - 64x^{2} + 64 $ x^12 - 4x^10 + 11x^8 - 26x^6 + 44x^4 - 64*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			55.2
Root			$1.40141 - 0.189886i$ of defining polynomial
Character	$\chi$	$=$	756.55
Dual form			756.2.b.d.55.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40141 + 0.189886i) q^{2} +(1.92789 - 0.532217i) q^{4} +1.46432i q^{5} +(2.07772 + 1.63801i) q^{7} +(-2.60069 + 1.11193i) q^{8} +O(q^{10})$	\(q+(-1.40141 + 0.189886i) q^{2} +(1.92789 - 0.532217i) q^{4} +1.46432i q^{5} +(2.07772 + 1.63801i) q^{7} +(-2.60069 + 1.11193i) q^{8} +(-0.278054 - 2.05211i) q^{10} -4.88653i q^{11} -6.31581i q^{13} +(-3.22277 - 1.90099i) q^{14} +(3.43349 - 2.05211i) q^{16} -4.18176i q^{17} +0.299664 q^{19} +(0.779335 + 2.82304i) q^{20} +(0.927886 + 6.84802i) q^{22} +4.88653i q^{23} +2.85577 q^{25} +(1.19929 + 8.85102i) q^{26} +(4.87738 + 2.05211i) q^{28} +3.64272 q^{29} -5.56732 q^{31} +(-4.42205 + 3.52781i) q^{32} +(0.794060 + 5.86035i) q^{34} +(-2.39857 + 3.04244i) q^{35} +3.59933 q^{37} +(-0.419952 + 0.0569022i) q^{38} +(-1.62822 - 3.80824i) q^{40} -4.62056i q^{41} -5.16865i q^{43} +(-2.60069 - 9.42068i) q^{44} +(-0.927886 - 6.84802i) q^{46} +9.24835 q^{47} +(1.63383 + 6.80666i) q^{49} +(-4.00210 + 0.542273i) q^{50} +(-3.36138 - 12.1762i) q^{52} +10.4028 q^{53} +7.15544 q^{55} +(-7.22487 - 1.94969i) q^{56} +(-5.10493 + 0.691703i) q^{58} -12.3657 q^{59} -5.40489i q^{61} +(7.80208 - 1.05716i) q^{62} +(5.52721 - 5.78359i) q^{64} +9.24835 q^{65} +6.31581i q^{67} +(-2.22560 - 8.06196i) q^{68} +(2.78366 - 4.71916i) q^{70} +6.13965i q^{71} -1.89262i q^{73} +(-5.04413 + 0.683464i) q^{74} +(0.577718 - 0.159486i) q^{76} +(8.00420 - 10.1528i) q^{77} +14.5242i q^{79} +(3.00494 + 5.02772i) q^{80} +(0.877382 + 6.47529i) q^{82} +14.0455 q^{83} +6.12343 q^{85} +(0.981456 + 7.24338i) q^{86} +(5.43349 + 12.7084i) q^{88} -13.6341i q^{89} +(10.3454 - 13.1225i) q^{91} +(2.60069 + 9.42068i) q^{92} +(-12.9607 + 1.75614i) q^{94} +0.438804i q^{95} +5.40489i q^{97} +(-3.58215 - 9.22866i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 8 q^{4} + 2 q^{7}+O(q^{10}) $ 12 * q + 8 * q^4 + 2 * q^7	$ 12 q + 8 q^{4} + 2 q^{7} + 4 q^{10} - 12 q^{16} - 12 q^{19} - 4 q^{22} + 4 q^{25} + 20 q^{28} + 24 q^{31} + 32 q^{34} + 12 q^{37} - 20 q^{40} + 4 q^{46} - 18 q^{49} + 28 q^{52} + 40 q^{55} + 8 q^{58} + 20 q^{64} - 12 q^{70} - 16 q^{76} - 28 q^{82} - 32 q^{85} + 12 q^{88} + 26 q^{91} - 56 q^{94}+O(q^{100}) $ 12 * q + 8 * q^4 + 2 * q^7 + 4 * q^10 - 12 * q^16 - 12 * q^19 - 4 * q^22 + 4 * q^25 + 20 * q^28 + 24 * q^31 + 32 * q^34 + 12 * q^37 - 20 * q^40 + 4 * q^46 - 18 * q^49 + 28 * q^52 + 40 * q^55 + 8 * q^58 + 20 * q^64 - 12 * q^70 - 16 * q^76 - 28 * q^82 - 32 * q^85 + 12 * q^88 + 26 * q^91 - 56 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.40141	+	0.189886i	−0.990945	+	0.134270i
$2$	−1.40141	+	0.189886i	−0.990945	+	0.134270i
$3$		0			0
$3$		0			0
$4$	1.92789	−	0.532217i	0.963943	−	0.266108i
$5$			1.46432i			0.654863i	0.944875	+	0.327431i	$0.106183\pi$
$5$			1.46432i			0.654863i	−0.944875	+	0.327431i	$0.893817\pi$
$6$		0			0
$7$	2.07772	+	1.63801i	0.785304	+	0.619111i
$7$	2.07772	+	1.63801i	0.785304	+	0.619111i
$8$	−2.60069	+	1.11193i	−0.919484	+	0.393127i
$9$		0			0
$10$	−0.278054	−	2.05211i	−0.0879285	−	0.648933i
$11$		−	4.88653i		−	1.47334i	−0.676250	−	0.736672i	$-0.736396\pi$
$11$		−	4.88653i		−	1.47334i	0.676250	−	0.736672i	$-0.263604\pi$
$12$		0			0
$13$		−	6.31581i		−	1.75169i	−0.482593	−	0.875845i	$-0.660305\pi$
$13$		−	6.31581i		−	1.75169i	0.482593	−	0.875845i	$-0.339695\pi$
$14$	−3.22277	−	1.90099i	−0.861321	−	0.508062i
$15$		0			0
$16$	3.43349	−	2.05211i	0.858373	−	0.513027i
$17$		−	4.18176i		−	1.01423i	−0.861880	−	0.507113i	$-0.830713\pi$
$17$		−	4.18176i		−	1.01423i	0.861880	−	0.507113i	$-0.169287\pi$
$18$		0			0
$19$	0.299664			0.0687477			0.0343738	−	0.999409i	$-0.489056\pi$
$19$	0.299664			0.0687477			0.0343738	+	0.999409i	$0.489056\pi$
$20$	0.779335	+	2.82304i	0.174264	+	0.631251i
$21$		0			0
$22$	0.927886	+	6.84802i	0.197826	+	1.46000i
$23$			4.88653i			1.01891i	0.860497	+	0.509456i	$0.170153\pi$
$23$			4.88653i			1.01891i	−0.860497	+	0.509456i	$0.829847\pi$
$24$		0			0
$25$	2.85577			0.571155
$26$	1.19929	+	8.85102i	0.235199	+	1.73583i
$27$		0			0
$28$	4.87738	+	2.05211i	0.921739	+	0.387812i
$29$	3.64272			0.676436			0.338218	−	0.941068i	$-0.390176\pi$
$29$	3.64272			0.676436			0.338218	+	0.941068i	$0.390176\pi$
$30$		0			0
$31$	−5.56732			−0.999920			−0.499960	−	0.866049i	$-0.666652\pi$
$31$	−5.56732			−0.999920			−0.499960	+	0.866049i	$0.666652\pi$
$32$	−4.42205	+	3.52781i	−0.781716	+	0.623635i
$33$		0			0
$34$	0.794060	+	5.86035i	0.136180	+	1.00504i
$35$	−2.39857	+	3.04244i	−0.405433	+	0.514266i
$36$		0			0
$37$	3.59933			0.591726			0.295863	−	0.955230i	$-0.404393\pi$
$37$	3.59933			0.591726			0.295863	+	0.955230i	$0.404393\pi$
$38$	−0.419952	+	0.0569022i	−0.0681251	+	0.00923075i
$39$		0			0
$40$	−1.62822	−	3.80824i	−0.257445	−	0.602136i
$41$		−	4.62056i		−	0.721611i	−0.932641	−	0.360805i	$-0.882502\pi$
$41$		−	4.62056i		−	0.721611i	0.932641	−	0.360805i	$-0.117498\pi$
$42$		0			0
$43$		−	5.16865i		−	0.788211i	−0.919065	−	0.394106i	$-0.871054\pi$
$43$		−	5.16865i		−	0.788211i	0.919065	−	0.394106i	$-0.128946\pi$
$44$	−2.60069	−	9.42068i	−0.392069	−	1.42022i
$45$		0			0
$46$	−0.927886	−	6.84802i	−0.136809	−	1.00969i
$47$	9.24835			1.34901			0.674505	−	0.738270i	$-0.264357\pi$
$47$	9.24835			1.34901			0.674505	+	0.738270i	$0.264357\pi$
$48$		0			0
$49$	1.63383	+	6.80666i	0.233404	+	0.972380i
$50$	−4.00210	+	0.542273i	−0.565983	+	0.0766889i
$51$		0			0
$52$	−3.36138	−	12.1762i	−0.466139	−	1.68853i
$53$	10.4028			1.42893			0.714465	−	0.699671i	$-0.246670\pi$
$53$	10.4028			1.42893			0.714465	+	0.699671i	$0.246670\pi$
$54$		0			0
$55$	7.15544			0.964839
$56$	−7.22487	−	1.94969i	−0.965464	−	0.260538i
$57$		0			0
$58$	−5.10493	+	0.691703i	−0.670311	+	0.0908250i
$59$	−12.3657			−1.60988			−0.804938	−	0.593359i	$-0.797801\pi$
$59$	−12.3657			−1.60988			−0.804938	+	0.593359i	$0.797801\pi$
$60$		0			0
$61$		−	5.40489i		−	0.692026i	−0.938230	−	0.346013i	$-0.887535\pi$
$61$		−	5.40489i		−	0.692026i	0.938230	−	0.346013i	$-0.112465\pi$
$62$	7.80208	−	1.05716i	0.990865	−	0.134259i
$63$		0			0
$64$	5.52721	−	5.78359i	0.690902	−	0.722949i
$65$	9.24835			1.14712
$66$		0			0
$67$			6.31581i			0.771598i	0.922583	+	0.385799i	$0.126074\pi$
$67$			6.31581i			0.771598i	−0.922583	+	0.385799i	$0.873926\pi$
$68$	−2.22560	−	8.06196i	−0.269894	−	0.977656i
$69$		0			0
$70$	2.78366	−	4.71916i	0.332711	−	0.564047i
$71$			6.13965i			0.728643i	0.931273	+	0.364321i	$0.118699\pi$
$71$			6.13965i			0.728643i	−0.931273	+	0.364321i	$0.881301\pi$
$72$		0			0
$73$		−	1.89262i		−	0.221514i	−0.993847	−	0.110757i	$-0.964672\pi$
$73$		−	1.89262i		−	0.221514i	0.993847	−	0.110757i	$-0.0353276\pi$
$74$	−5.04413	+	0.683464i	−0.586368	+	0.0794510i
$75$		0			0
$76$	0.577718	−	0.159486i	0.0662688	−	0.0182943i
$77$	8.00420	−	10.1528i	0.912164	−	1.15702i
$78$		0			0
$79$			14.5242i			1.63410i	0.576564	+	0.817052i	$0.304393\pi$
$79$			14.5242i			1.63410i	−0.576564	+	0.817052i	$0.695607\pi$
$80$	3.00494	+	5.02772i	0.335962	+	0.562116i
$81$		0			0
$82$	0.877382	+	6.47529i	0.0968907	+	0.715076i
$83$	14.0455			1.54169			0.770847	−	0.637021i	$-0.219834\pi$
$83$	14.0455			1.54169			0.770847	+	0.637021i	$0.219834\pi$
$84$		0			0
$85$	6.12343			0.664179
$86$	0.981456	+	7.24338i	0.105833	+	0.781074i
$87$		0			0
$88$	5.43349	+	12.7084i	0.579212	+	1.35472i
$89$		−	13.6341i		−	1.44521i	−0.691261	−	0.722605i	$-0.742945\pi$
$89$		−	13.6341i		−	1.44521i	0.691261	−	0.722605i	$-0.257055\pi$
$90$		0			0
$91$	10.3454	−	13.1225i	1.08449	−	1.37561i
$92$	2.60069	+	9.42068i	0.271141	+	0.982173i
$93$		0			0
$94$	−12.9607	+	1.75614i	−1.33679	+	0.181132i
$95$			0.438804i			0.0450203i
$96$		0			0
$97$			5.40489i			0.548784i	0.961618	+	0.274392i	$0.0884765\pi$
$97$			5.40489i			0.548784i	−0.961618	+	0.274392i	$0.911523\pi$
$98$	−3.58215	−	9.22866i	−0.361852	−	0.932236i
$99$		0			0
$100$	5.50560	−	1.51989i	0.550560	−	0.151989i
$101$		−	9.38903i		−	0.934244i	−0.884193	−	0.467122i	$-0.845291\pi$
$101$		−	9.38903i		−	0.934244i	0.884193	−	0.467122i	$-0.154709\pi$
$102$		0			0
$103$	−14.0112			−1.38057			−0.690283	−	0.723540i	$-0.742514\pi$
$103$	−14.0112			−1.38057			−0.690283	+	0.723540i	$0.742514\pi$
$104$	7.02275	+	16.4255i	0.688637	+	1.61065i
$105$		0			0
$106$	−14.5785	+	1.97535i	−1.41599	+	0.191863i
$107$		−	3.19460i		−	0.308834i	−0.988006	−	0.154417i	$-0.950650\pi$
$107$		−	3.19460i		−	0.308834i	0.988006	−	0.154417i	$-0.0493499\pi$
$108$		0			0
$109$	−4.96799			−0.475847			−0.237924	−	0.971284i	$-0.576467\pi$
$109$	−4.96799			−0.475847			−0.237924	+	0.971284i	$0.576467\pi$
$110$	−10.0277	+	1.35872i	−0.956102	+	0.129549i
$111$		0			0
$112$	10.4952	+	1.36040i	0.991704	+	0.128546i
$113$	5.60563			0.527333			0.263667	−	0.964614i	$-0.415068\pi$
$113$	5.60563			0.527333			0.263667	+	0.964614i	$0.415068\pi$
$114$		0			0
$115$	−7.15544			−0.667248
$116$	7.02275	−	1.93872i	0.652046	−	0.180005i
$117$		0			0
$118$	17.3294	−	2.34808i	1.59530	−	0.216158i
$119$	6.84978	−	8.68852i	0.627918	−	0.796475i
$120$		0			0
$121$	−12.8782			−1.17074
$122$	1.02632	+	7.57446i	0.0929183	+	0.685759i
$123$		0			0
$124$	−10.7332	+	2.96302i	−0.963866	+	0.266087i
$125$			11.5033i			1.02889i
$126$		0			0
$127$		−	0.910913i		−	0.0808304i	−0.999183	−	0.0404152i	$-0.987132\pi$
$127$		−	0.910913i		−	0.0808304i	0.999183	−	0.0404152i	$-0.0128681\pi$
$128$	−6.64765	+	9.15471i	−0.587575	+	0.809170i
$129$		0			0
$130$	−12.9607	+	1.75614i	−1.13673	+	0.154023i
$131$	7.56854			0.661267			0.330633	−	0.943759i	$-0.392738\pi$
$131$	7.56854			0.661267			0.330633	+	0.943759i	$0.392738\pi$
$132$		0			0
$133$	0.622618	+	0.490854i	0.0539878	+	0.0425624i
$134$	−1.19929	−	8.85102i	−0.103603	−	0.764611i
$135$		0			0
$136$	4.64983	+	10.8755i	0.398720	+	0.932564i
$137$	−1.15443			−0.0986293			−0.0493146	−	0.998783i	$-0.515704\pi$
$137$	−1.15443			−0.0986293			−0.0493146	+	0.998783i	$0.515704\pi$
$138$		0			0
$139$	4.66833			0.395962			0.197981	−	0.980206i	$-0.436562\pi$
$139$	4.66833			0.395962			0.197981	+	0.980206i	$0.436562\pi$
$140$	−3.00494	+	7.14204i	−0.253963	+	0.603612i
$141$		0			0
$142$	−1.16584	−	8.60416i	−0.0978349	−	0.722045i
$143$	−30.8624			−2.58084
$144$		0			0
$145$			5.33410i			0.442973i
$146$	0.359383	+	2.65233i	0.0297427	+	0.219509i
$147$		0			0
$148$	6.93910	−	1.91562i	0.570390	−	0.157463i
$149$	−0.808486			−0.0662338			−0.0331169	−	0.999451i	$-0.510543\pi$
$149$	−0.808486			−0.0662338			−0.0331169	+	0.999451i	$0.510543\pi$
$150$		0			0
$151$		−	13.7788i		−	1.12130i	−0.828053	−	0.560650i	$-0.810551\pi$
$151$		−	13.7788i		−	1.12130i	0.828053	−	0.560650i	$-0.189449\pi$
$152$	−0.779335	+	0.333206i	−0.0632124	+	0.0270266i
$153$		0			0
$154$	−9.28926	+	15.7482i	−0.748550	+	1.26902i
$155$		−	8.15232i		−	0.654810i
$156$		0			0
$157$		−	3.51227i		−	0.280310i	−0.990130	−	0.140155i	$-0.955240\pi$
$157$		−	3.51227i		−	0.280310i	0.990130	−	0.140155i	$-0.0447601\pi$
$158$	−2.75796	−	20.3544i	−0.219411	−	1.61931i
$159$		0			0
$160$	−5.16584	−	6.47529i	−0.408395	−	0.511917i
$161$	−8.00420	+	10.1528i	−0.630820	+	0.800156i
$162$		0			0
$163$		−	10.7390i		−	0.841143i	−0.907259	−	0.420571i	$-0.861830\pi$
$163$		−	10.7390i		−	0.841143i	0.907259	−	0.420571i	$-0.138170\pi$
$164$	−2.45914	−	8.90792i	−0.192027	−	0.695592i
$165$		0			0
$166$	−19.6835	+	2.66705i	−1.52773	+	0.207003i
$167$	4.79714			0.371214			0.185607	−	0.982624i	$-0.440575\pi$
$167$	4.79714			0.371214			0.185607	+	0.982624i	$0.440575\pi$
$168$		0			0
$169$	−26.8894			−2.06842
$170$	−8.58142	+	1.16276i	−0.658165	+	0.0891793i
$171$		0			0
$172$	−2.75084	−	9.96456i	−0.209750	−	0.759791i
$173$			14.0096i			1.06513i	0.846389	+	0.532565i	$0.178772\pi$
$173$			14.0096i			1.06513i	−0.846389	+	0.532565i	$0.821228\pi$
$174$		0			0
$175$	5.93349	+	4.67779i	0.448530	+	0.353608i
$176$	−10.0277	−	16.7779i	−0.755865	−	1.26468i
$177$		0			0
$178$	2.58893	+	19.1069i	0.194048	+	1.43212i
$179$			26.0065i			1.94382i	0.235355	+	0.971909i	$0.424375\pi$
$179$			26.0065i			1.94382i	−0.235355	+	0.971909i	$0.575625\pi$
$180$		0			0
$181$			21.8217i			1.62200i	0.585048	+	0.810999i	$0.301076\pi$
$181$			21.8217i			1.62200i	−0.585048	+	0.810999i	$0.698924\pi$
$182$	−12.0063	+	20.3544i	−0.889966	+	1.50877i
$183$		0			0
$184$	−5.43349	−	12.7084i	−0.400562	−	0.936874i
$185$			5.27056i			0.387499i
$186$		0			0
$187$	−20.4343			−1.49430
$188$	17.8298	−	4.92213i	1.30037	−	0.358983i
$189$		0			0
$190$	−0.0833229	−	0.614943i	−0.00604488	−	0.0446126i
$191$		−	11.1990i		−	0.810333i	−0.914243	−	0.405166i	$-0.867214\pi$
$191$		−	11.1990i		−	0.810333i	0.914243	−	0.405166i	$-0.132786\pi$
$192$		0			0
$193$	−12.4663			−0.897345			−0.448672	−	0.893696i	$-0.648103\pi$
$193$	−12.4663			−0.897345			−0.448672	+	0.893696i	$0.648103\pi$
$194$	−1.02632	−	7.57446i	−0.0736852	−	0.543814i
$195$		0			0
$196$	6.77245	+	12.2529i	0.483746	+	0.875208i
$197$	−2.48829			−0.177283			−0.0886417	−	0.996064i	$-0.528253\pi$
$197$	−2.48829			−0.177283			−0.0886417	+	0.996064i	$0.528253\pi$
$198$		0			0
$199$	5.82376			0.412836			0.206418	−	0.978464i	$-0.433819\pi$
$199$	5.82376			0.412836			0.206418	+	0.978464i	$0.433819\pi$
$200$	−7.42699	+	3.17542i	−0.525167	+	0.224536i
$201$		0			0
$202$	1.78285	+	13.1579i	0.125441	+	0.925784i
$203$	7.56854	+	5.96682i	0.531208	+	0.418789i
$204$		0			0
$205$	6.76597			0.472556
$206$	19.6354	−	2.66054i	1.36806	−	0.185369i
$207$		0			0
$208$	−12.9607	−	21.6853i	−0.898663	−	1.50360i
$209$		−	1.46432i		−	0.101289i
$210$		0			0
$211$			11.4845i			0.790622i	0.918547	+	0.395311i	$0.129363\pi$
$211$			11.4845i			0.790622i	−0.918547	+	0.395311i	$0.870637\pi$
$212$	20.0554	−	5.53653i	1.37741	−	0.380250i
$213$		0			0
$214$	0.606612	+	4.47694i	0.0414672	+	0.306038i
$215$	7.56854			0.516170
$216$		0			0
$217$	−11.5673	−	9.11934i	−0.785241	−	0.619061i
$218$	6.96218	−	0.943354i	0.471538	−	0.0638920i
$219$		0			0
$220$	13.7949	−	3.80824i	0.930050	−	0.256752i
$221$	−26.4112			−1.77661
$222$		0			0
$223$	15.9792			1.07005			0.535023	−	0.844837i	$-0.320303\pi$
$223$	15.9792			1.07005			0.535023	+	0.844837i	$0.320303\pi$
$224$	−14.9664	+	0.0864175i	−0.999983	+	0.00577401i
$225$		0			0
$226$	−7.85577	+	1.06443i	−0.522558	+	0.0708051i
$227$	−12.0197			−0.797779			−0.398889	−	0.916999i	$-0.630604\pi$
$227$	−12.0197			−0.797779			−0.398889	+	0.916999i	$0.630604\pi$
$228$		0			0
$229$		−	6.38660i		−	0.422038i	−0.977482	−	0.211019i	$-0.932322\pi$
$229$		−	6.38660i		−	0.422038i	0.977482	−	0.211019i	$-0.0676783\pi$
$230$	10.0277	−	1.35872i	0.661206	−	0.0895914i
$231$		0			0
$232$	−9.47359	+	4.05045i	−0.621972	+	0.265925i
$233$	−17.6882			−1.15879			−0.579397	−	0.815046i	$-0.696712\pi$
$233$	−17.6882			−1.15879			−0.579397	+	0.815046i	$0.696712\pi$
$234$		0			0
$235$			13.5425i			0.883417i
$236$	−23.8396	+	6.58122i	−1.55183	+	0.428401i
$237$		0			0
$238$	−7.94950	+	13.4768i	−0.515289	+	0.873573i
$239$		−	0.915967i		−	0.0592490i	−0.999561	−	0.0296245i	$-0.990569\pi$
$239$		−	0.915967i		−	0.0592490i	0.999561	−	0.0296245i	$-0.00943115\pi$
$240$		0			0
$241$			6.31581i			0.406837i	0.979092	+	0.203418i	$0.0652052\pi$
$241$			6.31581i			0.406837i	−0.979092	+	0.203418i	$0.934795\pi$
$242$	18.0476	−	2.44539i	1.16014	−	0.157196i
$243$		0			0
$244$	−2.87657	−	10.4200i	−0.184154	−	0.667073i
$245$	−9.96711	+	2.39244i	−0.636776	+	0.152848i
$246$		0			0
$247$		−	1.89262i		−	0.120425i
$248$	14.4789	−	6.19048i	0.919410	−	0.393096i
$249$		0			0
$250$	−2.18433	−	16.1209i	−0.138149	−	1.01957i
$251$	−18.4967			−1.16750			−0.583751	−	0.811933i	$-0.698415\pi$
$251$	−18.4967			−1.16750			−0.583751	+	0.811933i	$0.698415\pi$
$252$		0			0
$253$	23.8782			1.50121
$254$	0.172970	+	1.27656i	0.0108531	+	0.0800985i
$255$		0			0
$256$	7.57772	−	14.0918i	0.473607	−	0.880736i
$257$			11.0810i			0.691211i	0.938380	+	0.345606i	$0.112327\pi$
$257$			11.0810i			0.691211i	−0.938380	+	0.345606i	$0.887673\pi$
$258$		0			0
$259$	7.47839	+	5.89575i	0.464685	+	0.366344i
$260$	17.8298	−	4.92213i	1.10576	−	0.305257i
$261$		0			0
$262$	−10.6066	+	1.43716i	−0.655279	+	0.0887883i
$263$		−	3.70460i		−	0.228435i	−0.993456	−	0.114218i	$-0.963564\pi$
$263$		−	3.70460i		−	0.228435i	0.993456	−	0.114218i	$-0.0364361\pi$
$264$		0			0
$265$			15.2330i			0.935754i
$266$	−0.965747	−	0.569659i	−0.0592138	−	0.0349281i
$267$		0			0
$268$	3.36138	+	12.1762i	0.205329	+	0.743777i
$269$		−	10.8534i		−	0.661741i	−0.943676	−	0.330870i	$-0.892658\pi$
$269$		−	10.8534i		−	0.661741i	0.943676	−	0.330870i	$-0.107342\pi$
$270$		0			0
$271$	−29.0016			−1.76172			−0.880861	−	0.473374i	$-0.843036\pi$
$271$	−29.0016			−1.76172			−0.880861	+	0.473374i	$0.843036\pi$
$272$	−8.58142	−	14.3580i	−0.520325	−	0.870584i
$273$		0			0
$274$	1.61782	−	0.219210i	0.0977362	−	0.0132430i
$275$		−	13.9548i		−	0.841507i
$276$		0			0
$277$	28.0016			1.68245			0.841227	−	0.540682i	$-0.181834\pi$
$277$	28.0016			1.68245			0.841227	+	0.540682i	$0.181834\pi$
$278$	−6.54223	+	0.886452i	−0.392377	+	0.0531658i
$279$		0			0
$280$	2.85496	−	10.5795i	0.170617	−	0.632246i
$281$	−25.2568			−1.50669			−0.753346	−	0.657625i	$-0.771561\pi$
$281$	−25.2568			−1.50669			−0.753346	+	0.657625i	$0.771561\pi$
$282$		0			0
$283$	4.62175			0.274734			0.137367	−	0.990520i	$-0.456136\pi$
$283$	4.62175			0.274734			0.137367	+	0.990520i	$0.456136\pi$
$284$	3.26763	+	11.8366i	0.193898	+	0.702370i
$285$		0			0
$286$	43.2508	−	5.86035i	2.55747	−	0.346530i
$287$	7.56854	−	9.60023i	0.446757	−	0.566684i
$288$		0			0
$289$	−0.487111			−0.0286536
$290$	−1.01287	−	7.47525i	−0.0594780	−	0.438962i
$291$		0			0
$292$	−1.00728	−	3.64876i	−0.0589468	−	0.213527i
$293$			13.4229i			0.784173i	0.919928	+	0.392087i	$0.128247\pi$
$293$			13.4229i			0.784173i	−0.919928	+	0.392087i	$0.871753\pi$
$294$		0			0
$295$		−	18.1073i		−	1.05425i
$296$	−9.36075	+	4.00221i	−0.544083	+	0.232624i
$297$		0			0
$298$	1.13302	−	0.153521i	0.0656340	−	0.00889321i
$299$	30.8624			1.78482
$300$		0			0
$301$	8.46631	−	10.7390i	0.487990	−	0.618985i
$302$	2.61640	+	19.3097i	0.150557	+	1.11115i
$303$		0			0
$304$	1.02889	−	0.614943i	0.0590111	−	0.0352694i
$305$	7.91448			0.453182
$306$		0			0
$307$	9.94221			0.567432			0.283716	−	0.958908i	$-0.408433\pi$
$307$	9.94221			0.567432			0.283716	+	0.958908i	$0.408433\pi$
$308$	10.0277	−	23.8335i	0.571380	−	1.35804i
$309$		0			0
$310$	1.54802	+	11.4247i	0.0879214	+	0.648881i
$311$	−21.2681			−1.20600			−0.603002	−	0.797740i	$-0.706029\pi$
$311$	−21.2681			−1.20600			−0.603002	+	0.797740i	$0.706029\pi$
$312$		0			0
$313$			2.53057i			0.143036i	0.997439	+	0.0715180i	$0.0227843\pi$
$313$			2.53057i			0.143036i	−0.997439	+	0.0715180i	$0.977216\pi$
$314$	0.666933	+	4.92213i	0.0376372	+	0.277772i
$315$		0			0
$316$	7.73004	+	28.0011i	0.434849	+	1.57518i
$317$	8.37703			0.470501			0.235250	−	0.971935i	$-0.424409\pi$
$317$	8.37703			0.470501			0.235250	+	0.971935i	$0.424409\pi$
$318$		0			0
$319$		−	17.8003i		−	0.996623i
$320$	8.46901	+	8.09360i	0.473432	+	0.452446i
$321$		0			0
$322$	9.28926	−	15.7482i	0.517670	−	0.877610i
$323$		−	1.25312i		−	0.0697256i
$324$		0			0
$325$		−	18.0365i		−	1.00049i
$326$	2.03919	+	15.0497i	0.112940	+	0.833526i
$327$		0			0
$328$	5.13775	+	12.0167i	0.283685	+	0.663510i
$329$	19.2155	+	15.1489i	1.05938	+	0.835187i
$330$		0			0
$331$		−	7.06127i		−	0.388122i	−0.980989	−	0.194061i	$-0.937834\pi$
$331$		−	7.06127i		−	0.388122i	0.980989	−	0.194061i	$-0.0621660\pi$
$332$	27.0781	−	7.47525i	1.48610	−	0.410257i
$333$		0			0
$334$	−6.72275	+	0.910913i	−0.367853	+	0.0498429i
$335$	−9.24835			−0.505291
$336$		0			0
$337$	10.1987			0.555556			0.277778	−	0.960645i	$-0.410402\pi$
$337$	10.1987			0.555556			0.277778	+	0.960645i	$0.410402\pi$
$338$	37.6830	−	5.10593i	2.04969	−	0.277726i
$339$		0			0
$340$	11.8053	−	3.25899i	0.640231	−	0.176744i
$341$			27.2049i			1.47323i
$342$		0			0
$343$	−7.75476	+	16.8185i	−0.418718	+	0.908116i
$344$	5.74718	+	13.4421i	0.309867	+	0.724748i
$345$		0			0
$346$	−2.66023	−	19.6332i	−0.143015	−	1.05548i
$347$		−	19.3733i		−	1.04001i	−0.854162	−	0.520006i	$-0.825930\pi$
$347$		−	19.3733i		−	1.04001i	0.854162	−	0.520006i	$-0.174070\pi$
$348$		0			0
$349$		−	22.4597i		−	1.20224i	−0.799159	−	0.601120i	$-0.794721\pi$
$349$		−	22.4597i		−	1.20224i	0.799159	−	0.601120i	$-0.205279\pi$
$350$	−9.20349	−	5.42880i	−0.491947	−	0.290182i
$351$		0			0
$352$	17.2388	+	21.6085i	0.918829	+	1.15174i
$353$			16.7903i			0.893659i	0.894619	+	0.446829i	$0.147447\pi$
$353$			16.7903i			0.893659i	−0.894619	+	0.446829i	$0.852553\pi$
$354$		0			0
$355$	−8.99041			−0.477161
$356$	−7.25628	−	26.2850i	−0.384582	−	1.39310i
$357$		0			0
$358$	−4.93829	−	36.4457i	−0.260997	−	1.92622i
$359$			31.9819i			1.68794i	0.536392	+	0.843969i	$0.319787\pi$
$359$			31.9819i			1.68794i	−0.536392	+	0.843969i	$0.680213\pi$
$360$		0			0
$361$	−18.9102			−0.995274
$362$	−4.14365	−	30.5812i	−0.217786	−	1.60731i
$363$		0			0
$364$	12.9607	−	30.8046i	0.679326	−	1.61460i
$365$	2.77140			0.145062
$366$		0			0
$367$	16.7980			0.876848			0.438424	−	0.898768i	$-0.355537\pi$
$367$	16.7980			0.876848			0.438424	+	0.898768i	$0.355537\pi$
$368$	10.0277	+	16.7779i	0.522729	+	0.874606i
$369$		0			0
$370$	−1.00081	−	7.38620i	−0.0520295	−	0.383990i
$371$	21.6140	+	17.0399i	1.12214	+	0.884666i
$372$		0			0
$373$	12.0112			0.621917			0.310958	−	0.950424i	$-0.399350\pi$
$373$	12.0112			0.621917			0.310958	+	0.950424i	$0.399350\pi$
$374$	28.6368	−	3.88020i	1.48077	−	0.200640i
$375$		0			0
$376$	−24.0521	+	10.2835i	−1.24039	+	0.530333i
$377$		−	23.0067i		−	1.18491i
$378$		0			0
$379$			6.15035i			0.315922i	0.987445	+	0.157961i	$0.0504921\pi$
$379$			6.15035i			0.315922i	−0.987445	+	0.157961i	$0.949508\pi$
$380$	0.233539	+	0.845963i	0.0119803	+	0.0433970i
$381$		0			0
$382$	2.12654	+	15.6944i	0.108803	+	0.802995i
$383$	21.6140			1.10443			0.552213	−	0.833703i	$-0.313784\pi$
$383$	21.6140			1.10443			0.552213	+	0.833703i	$0.313784\pi$
$384$		0			0
$385$	14.8670	+	11.7207i	0.757692	+	0.597342i
$386$	17.4704	−	2.36718i	0.889219	−	0.120486i
$387$		0			0
$388$	2.87657	+	10.4200i	0.146036	+	0.528996i
$389$	5.60563			0.284217			0.142108	−	0.989851i	$-0.454612\pi$
$389$	5.60563			0.284217			0.142108	+	0.989851i	$0.454612\pi$
$390$		0			0
$391$	20.4343			1.03341
$392$	−11.8176	−	15.8853i	−0.596880	−	0.802330i
$393$		0			0
$394$	3.48711	−	0.472493i	0.175678	−	0.0238039i
$395$	−21.2681			−1.07011
$396$		0			0
$397$		−	32.2878i		−	1.62048i	−0.586101	−	0.810238i	$-0.699338\pi$
$397$		−	32.2878i		−	1.62048i	0.586101	−	0.810238i	$-0.300662\pi$
$398$	−8.16146	+	1.10585i	−0.409097	+	0.0554314i
$399$		0			0
$400$	9.80527	−	5.86035i	0.490263	−	0.293017i
$401$	−26.8737			−1.34201			−0.671005	−	0.741453i	$-0.734137\pi$
$401$	−26.8737			−1.34201			−0.671005	+	0.741453i	$0.734137\pi$
$402$		0			0
$403$			35.1621i			1.75155i
$404$	−4.99700	−	18.1010i	−0.248610	−	0.900558i
$405$		0			0
$406$	−11.7396	−	6.92478i	−0.582628	−	0.343671i
$407$		−	17.5882i		−	0.871816i
$408$		0			0
$409$			29.7572i			1.47140i	0.677308	+	0.735699i	$0.263146\pi$
$409$			29.7572i			1.47140i	−0.677308	+	0.735699i	$0.736854\pi$
$410$	−9.48189	+	1.28477i	−0.468277	+	0.0634501i
$411$		0			0
$412$	−27.0120	+	7.45700i	−1.33079	+	0.367380i
$413$	−25.6924	−	20.2552i	−1.26424	−	0.996691i
$414$		0			0
$415$			20.5671i			1.00960i
$416$	22.2810	+	27.9288i	1.09241	+	1.36932i
$417$		0			0
$418$	0.278054	+	2.05211i	0.0136001	+	0.100372i
$419$	−26.4112			−1.29027			−0.645135	−	0.764068i	$-0.723199\pi$
$419$	−26.4112			−1.29027			−0.645135	+	0.764068i	$0.723199\pi$
$420$		0			0
$421$	−16.0482			−0.782141			−0.391071	−	0.920361i	$-0.627895\pi$
$421$	−16.0482			−0.782141			−0.391071	+	0.920361i	$0.627895\pi$
$422$	−2.18074	−	16.0944i	−0.106157	−	0.783463i
$423$		0			0
$424$	−27.0544	+	11.5672i	−1.31388	+	0.561752i
$425$		−	11.9422i		−	0.579280i
$426$		0			0
$427$	8.85328	−	11.2298i	0.428440	−	0.543450i
$428$	−1.70022	−	6.15883i	−0.0821833	−	0.297699i
$429$		0			0
$430$	−10.6066	+	1.43716i	−0.511496	+	0.0693062i
$431$		−	20.8625i		−	1.00491i	−0.864602	−	0.502457i	$-0.832430\pi$
$431$		−	20.8625i		−	1.00491i	0.864602	−	0.502457i	$-0.167570\pi$
$432$		0			0
$433$		−	5.33410i		−	0.256340i	−0.991752	−	0.128170i	$-0.959090\pi$
$433$		−	5.33410i		−	0.256340i	0.991752	−	0.128170i	$-0.0409104\pi$
$434$	17.9422	+	10.5834i	0.861251	+	0.508021i
$435$		0			0
$436$	−9.57772	+	2.64405i	−0.458690	+	0.126627i
$437$			1.46432i			0.0700478i
$438$		0			0
$439$	−3.08980			−0.147468			−0.0737340	−	0.997278i	$-0.523492\pi$
$439$	−3.08980			−0.147468			−0.0737340	+	0.997278i	$0.523492\pi$
$440$	−18.6091	+	7.95636i	−0.887154	+	0.379305i
$441$		0			0
$442$	37.0128	−	5.01513i	1.76052	−	0.238545i
$443$			9.67142i			0.459503i	0.973249	+	0.229751i	$0.0737913\pi$
$443$			9.67142i			0.459503i	−0.973249	+	0.229751i	$0.926209\pi$
$444$		0			0
$445$	19.9646			0.946414
$446$	−22.3934	+	3.03423i	−1.06036	+	0.143675i
$447$		0			0
$448$	20.9576	−	2.96302i	0.990153	−	0.139990i
$449$	12.0826			0.570212			0.285106	−	0.958496i	$-0.407971\pi$
$449$	12.0826			0.570212			0.285106	+	0.958496i	$0.407971\pi$
$450$		0			0
$451$	−22.5785			−1.06318
$452$	10.8070	−	2.98341i	0.508319	−	0.140328i
$453$		0			0
$454$	16.8446	−	2.28239i	0.790555	−	0.107118i
$455$	19.2155	+	15.1489i	0.900835	+	0.710192i
$456$		0			0
$457$	−8.95342			−0.418823			−0.209412	−	0.977828i	$-0.567155\pi$
$457$	−8.95342			−0.418823			−0.209412	+	0.977828i	$0.567155\pi$
$458$	1.21273	+	8.95023i	0.0566671	+	0.418217i
$459$		0			0
$460$	−13.7949	+	3.80824i	−0.643189	+	0.177560i
$461$			15.5372i			0.723640i	0.932248	+	0.361820i	$0.117844\pi$
$461$			15.5372i			0.723640i	−0.932248	+	0.361820i	$0.882156\pi$
$462$		0			0
$463$			0.981707i			0.0456238i	0.999740	+	0.0228119i	$0.00726189\pi$
$463$			0.981707i			0.0456238i	−0.999740	+	0.0228119i	$0.992738\pi$
$464$	12.5072	−	7.47525i	0.580634	−	0.347030i
$465$		0			0
$466$	24.7884	−	3.35875i	1.14830	−	0.155591i
$467$	2.77140			0.128245			0.0641225	−	0.997942i	$-0.479575\pi$
$467$	2.77140			0.128245			0.0641225	+	0.997942i	$0.479575\pi$
$468$		0			0
$469$	−10.3454	+	13.1225i	−0.477705	+	0.605939i
$470$	−2.57154	−	18.9786i	−0.118616	−	0.875417i
$471$		0			0
$472$	32.1594	−	13.7498i	1.48025	−	0.632886i
$473$	−25.2568			−1.16131
$474$		0			0
$475$	0.855773			0.0392655
$476$	8.58142	−	20.3960i	0.393329	−	0.934851i
$477$		0			0
$478$	0.173930	+	1.28364i	0.00795536	+	0.0587125i
$479$	−15.1371			−0.691631			−0.345816	−	0.938303i	$-0.612398\pi$
$479$	−15.1371			−0.691631			−0.345816	+	0.938303i	$0.612398\pi$
$480$		0			0
$481$		−	22.7327i		−	1.03652i
$482$	−1.19929	−	8.85102i	−0.0546260	−	0.403153i
$483$		0			0
$484$	−24.8277	+	6.85399i	−1.12853	+	0.311545i
$485$	−7.91448			−0.359378
$486$		0			0
$487$		−	26.9904i		−	1.22305i	−0.791225	−	0.611526i	$-0.790556\pi$
$487$		−	26.9904i		−	1.22305i	0.791225	−	0.611526i	$-0.209444\pi$
$488$	6.00987	+	14.0565i	0.272054	+	0.636307i
$489$		0			0
$490$	13.5137	−	5.24541i	0.610487	−	0.236963i
$491$			19.1457i			0.864033i	0.901866	+	0.432016i	$0.142198\pi$
$491$			19.1457i			0.864033i	−0.901866	+	0.432016i	$0.857802\pi$
$492$		0			0
$493$		−	15.2330i		−	0.686059i
$494$	0.359383	+	2.65233i	0.0161694	+	0.119334i
$495$		0			0
$496$	−19.1153	+	11.4247i	−0.858304	+	0.512985i
$497$	−10.0568	+	12.7565i	−0.451111	+	0.572206i
$498$		0			0
$499$		−	28.3030i		−	1.26702i	−0.773736	−	0.633508i	$-0.781614\pi$
$499$		−	28.3030i		−	1.26702i	0.773736	−	0.633508i	$-0.218386\pi$
$500$	6.12227	+	22.1772i	0.273796	+	0.991792i
$501$		0			0
$502$	25.9214	−	3.51227i	1.15693	−	0.156760i
$503$	−12.3657			−0.551359			−0.275679	−	0.961250i	$-0.588903\pi$
$503$	−12.3657			−0.551359			−0.275679	+	0.961250i	$0.588903\pi$
$504$		0			0
$505$	13.7485			0.611802
$506$	−33.4631	+	4.53415i	−1.48762	+	0.201567i
$507$		0			0
$508$	−0.484803	−	1.75614i	−0.0215097	−	0.0779159i
$509$		−	34.3786i		−	1.52380i	−0.647693	−	0.761901i	$-0.724266\pi$
$509$		−	34.3786i		−	1.52380i	0.647693	−	0.761901i	$-0.275734\pi$
$510$		0			0
$511$	3.10014	−	3.93233i	0.137142	−	0.173956i
$512$	−7.94363	+	21.1872i	−0.351062	+	0.936352i
$513$		0			0
$514$	−2.10412	−	15.5289i	−0.0928090	−	0.684952i
$515$		−	20.5169i		−	0.904081i
$516$		0			0
$517$		−	45.1923i		−	1.98756i
$518$	−11.5998	−	6.84230i	−0.509666	−	0.300633i
$519$		0			0
$520$	−24.0521	+	10.2835i	−1.05476	+	0.450963i
$521$			41.4725i			1.81694i	0.417945	+	0.908472i	$0.362751\pi$
$521$			41.4725i			1.81694i	−0.417945	+	0.908472i	$0.637249\pi$
$522$		0			0
$523$	12.4231			0.543224			0.271612	−	0.962407i	$-0.412443\pi$
$523$	12.4231			0.543224			0.271612	+	0.962407i	$0.412443\pi$
$524$	14.5913	−	4.02810i	0.637423	−	0.175969i
$525$		0			0
$526$	0.703453	+	5.19165i	0.0306720	+	0.226367i
$527$			23.2812i			1.01414i
$528$		0			0
$529$	−0.878191			−0.0381822
$530$	−2.89254	−	21.3476i	−0.125644	−	0.927281i
$531$		0			0
$532$	1.46158	+	0.614943i	0.0633674	+	0.0266611i
$533$	−29.1826			−1.26404
$534$		0			0
$535$	4.67792			0.202244
$536$	−7.02275	−	16.4255i	−0.303336	−	0.709472i
$537$		0			0
$538$	2.06090	+	15.2100i	0.0888519	+	0.655748i
$539$	33.2610	−	7.98375i	1.43265	−	0.343884i
$540$		0			0
$541$	25.5577			1.09881			0.549406	−	0.835555i	$-0.314854\pi$
$541$	25.5577			1.09881			0.549406	+	0.835555i	$0.314854\pi$
$542$	40.6431	−	5.50701i	1.74577	−	0.236547i
$543$		0			0
$544$	14.7525	+	18.4920i	0.632506	+	0.792836i
$545$		−	7.27472i		−	0.311615i
$546$		0			0
$547$			36.9131i			1.57829i	0.614206	+	0.789146i	$0.289476\pi$
$547$			36.9131i			1.57829i	−0.614206	+	0.789146i	$0.710524\pi$
$548$	−2.22560	+	0.614405i	−0.0950730	+	0.0262461i
$549$		0			0
$550$	2.64983	+	19.5564i	0.112989	+	0.833887i
$551$	1.09159			0.0465034
$552$		0			0
$553$	−23.7909	+	30.1773i	−1.01169	+	1.28327i
$554$	−39.2417	+	5.31713i	−1.66722	+	0.225903i
$555$		0			0
$556$	9.00000	−	2.48456i	0.381685	−	0.105369i
$557$	16.0084			0.678298			0.339149	−	0.940733i	$-0.389861\pi$
$557$	16.0084			0.678298			0.339149	+	0.940733i	$0.389861\pi$
$558$		0			0
$559$	−32.6442			−1.38070
$560$	−1.99206	+	15.3683i	−0.0841800	+	0.649430i
$561$		0			0
$562$	35.3950	−	4.79592i	1.49305	−	0.202303i
$563$	−22.9479			−0.967139			−0.483569	−	0.875306i	$-0.660660\pi$
$563$	−22.9479			−0.967139			−0.483569	+	0.875306i	$0.660660\pi$
$564$		0			0
$565$			8.20843i			0.345331i
$566$	−6.47695	+	0.877607i	−0.272247	+	0.0368886i
$567$		0			0
$568$	−6.82688	−	15.9674i	−0.286449	−	0.669976i
$569$	45.7164			1.91653			0.958265	−	0.285882i	$-0.0922866\pi$
$569$	45.7164			1.91653			0.958265	+	0.285882i	$0.0922866\pi$
$570$		0			0
$571$		−	5.40489i		−	0.226188i	−0.993584	−	0.113094i	$-0.963924\pi$
$571$		−	5.40489i		−	0.226188i	0.993584	−	0.113094i	$-0.0360761\pi$
$572$	−59.4992	+	16.4255i	−2.48779	+	0.686784i
$573$		0			0
$574$	−8.78366	+	14.8910i	−0.366623	+	0.621538i
$575$			13.9548i			0.581956i
$576$		0			0
$577$			9.82808i			0.409148i	0.978851	+	0.204574i	$0.0655809\pi$
$577$			9.82808i			0.409148i	−0.978851	+	0.204574i	$0.934419\pi$
$578$	0.682642	−	0.0924959i	0.0283941	−	0.00384732i
$579$		0			0
$580$	2.83890	+	10.2835i	0.117879	+	0.427001i
$581$	29.1826	+	23.0067i	1.21070	+	0.954479i
$582$		0			0
$583$		−	50.8335i		−	2.10531i
$584$	2.10446	+	4.92213i	0.0870834	+	0.203679i
$585$		0			0
$586$	−2.54882	−	18.8109i	−0.105291	−	0.777072i
$587$	−26.4112			−1.09011			−0.545053	−	0.838402i	$-0.683490\pi$
$587$	−26.4112			−1.09011			−0.545053	+	0.838402i	$0.683490\pi$
$588$		0			0
$589$	−1.66833			−0.0687421
$590$	3.43833	+	25.3757i	0.141554	+	1.04470i
$591$		0			0
$592$	12.3583	−	7.38620i	0.507921	−	0.303571i
$593$			29.1080i			1.19532i	0.801749	+	0.597661i	$0.203903\pi$
$593$			29.1080i			1.19532i	−0.801749	+	0.597661i	$0.796097\pi$
$594$		0			0
$595$	12.7228	+	10.0303i	0.521582	+	0.411200i
$596$	−1.55867	+	0.430290i	−0.0638456	+	0.0176254i
$597$		0			0
$598$	−43.2508	+	5.86035i	−1.76866	+	0.239647i
$599$			2.49835i			0.102080i	0.998697	+	0.0510398i	$0.0162535\pi$
$599$			2.49835i			0.102080i	−0.998697	+	0.0510398i	$0.983746\pi$
$600$		0			0
$601$			20.5671i			0.838948i	0.907767	+	0.419474i	$0.137786\pi$
$601$			20.5671i			0.838948i	−0.907767	+	0.419474i	$0.862214\pi$
$602$	−9.82556	+	16.6573i	−0.400460	+	0.678903i
$603$		0			0
$604$	−7.33329	−	26.5639i	−0.298387	−	1.08087i
$605$		−	18.8578i		−	0.766677i
$606$		0			0
$607$	25.3125			1.02740			0.513701	−	0.857969i	$-0.328274\pi$
$607$	25.3125			1.02740			0.513701	+	0.857969i	$0.328274\pi$
$608$	−1.32513	+	1.05716i	−0.0537411	+	0.0428734i
$609$		0			0
$610$	−11.0914	+	1.50285i	−0.449078	+	0.0608487i
$611$		−	58.4108i		−	2.36305i
$612$		0			0
$613$	−16.8990			−0.682544			−0.341272	−	0.939965i	$-0.610858\pi$
$613$	−16.8990			−0.682544			−0.341272	+	0.939965i	$0.610858\pi$
$614$	−13.9331	+	1.88789i	−0.562294	+	0.0761891i
$615$		0			0
$616$	−9.52721	+	35.3045i	−0.383862	+	1.42246i
$617$	31.6709			1.27502			0.637511	−	0.770442i	$-0.279964\pi$
$617$	31.6709			1.27502			0.637511	+	0.770442i	$0.279964\pi$
$618$		0			0
$619$	−32.8204			−1.31916			−0.659582	−	0.751633i	$-0.729267\pi$
$619$	−32.8204			−1.31916			−0.659582	+	0.751633i	$0.729267\pi$
$620$	−4.33880	−	15.7168i	−0.174251	−	0.631200i
$621$		0			0
$622$	29.8053	−	4.03852i	1.19508	−	0.161930i
$623$	22.3328	−	28.3278i	0.894745	−	1.13493i
$624$		0			0
$625$	−2.56570			−0.102628
$626$	−0.480520	−	3.54635i	−0.0192054	−	0.141741i
$627$		0			0
$628$	−1.86929	−	6.77126i	−0.0745928	−	0.270203i
$629$		−	15.0515i		−	0.600144i
$630$		0			0
$631$			44.3522i			1.76563i	0.469717	+	0.882817i	$0.344356\pi$
$631$			44.3522i			1.76563i	−0.469717	+	0.882817i	$0.655644\pi$
$632$	−16.1500	−	37.7731i	−0.642411	−	1.50253i
$633$		0			0
$634$	−11.7396	+	1.59068i	−0.466240	+	0.0631741i
$635$	1.33387			0.0529329
$636$		0			0
$637$	42.9895	−	10.3189i	1.70331	−	0.408851i
$638$	3.38003	+	24.9454i	0.133817	+	0.987598i
$639$		0			0
$640$	−13.4054	−	9.73428i	−0.529895	−	0.384781i
$641$	10.4028			0.410885			0.205442	−	0.978669i	$-0.434137\pi$
$641$	10.4028			0.410885			0.205442	+	0.978669i	$0.434137\pi$
$642$		0			0
$643$	−1.03201			−0.0406985			−0.0203493	−	0.999793i	$-0.506478\pi$
$643$	−1.03201			−0.0406985			−0.0203493	+	0.999793i	$0.506478\pi$
$644$	−10.0277	+	23.8335i	−0.395146	+	0.939171i
$645$		0			0
$646$	0.237951	+	1.75614i	0.00936206	+	0.0690943i
$647$	20.5224			0.806820			0.403410	−	0.915019i	$-0.367825\pi$
$647$	20.5224			0.806820			0.403410	+	0.915019i	$0.367825\pi$
$648$		0			0
$649$			60.4253i			2.37190i
$650$	3.42489	+	25.2765i	0.134335	+	0.991426i
$651$		0			0
$652$	−5.71547	−	20.7036i	−0.223835	−	0.810814i
$653$	−29.9911			−1.17364			−0.586820	−	0.809717i	$-0.699621\pi$
$653$	−29.9911			−1.17364			−0.586820	+	0.809717i	$0.699621\pi$
$654$		0			0
$655$			11.0828i			0.433039i
$656$	−9.48189	−	15.8647i	−0.370205	−	0.619411i
$657$		0			0
$658$	−29.8053	−	17.5810i	−1.16193	−	0.685381i
$659$			17.2839i			0.673285i	0.941632	+	0.336643i	$0.109291\pi$
$659$			17.2839i			0.673285i	−0.941632	+	0.336643i	$0.890709\pi$
$660$		0			0
$661$			10.7390i			0.417698i	0.977948	+	0.208849i	$0.0669718\pi$
$661$			10.7390i			0.417698i	−0.977948	+	0.208849i	$0.933028\pi$
$662$	1.34084	+	9.89571i	0.0521132	+	0.384608i
$663$		0			0
$664$	−36.5280	+	15.6176i	−1.41756	+	0.606082i
$665$	−0.718766	+	0.911710i	−0.0278725	+	0.0353546i
$666$		0			0
$667$			17.8003i			0.689229i
$668$	9.24835	−	2.55312i	0.357829	−	0.0987832i
$669$		0			0
$670$	12.9607	−	1.75614i	0.500716	−	0.0678455i
$671$	−26.4112			−1.01959
$672$		0			0
$673$	−45.2901			−1.74580			−0.872902	−	0.487896i	$-0.837765\pi$
$673$	−45.2901			−1.74580			−0.872902	+	0.487896i	$0.837765\pi$
$674$	−14.2925	+	1.93659i	−0.550526	+	0.0745945i
$675$		0			0
$676$	−51.8397	+	14.3110i	−1.99383	+	0.550423i
$677$		−	16.5627i		−	0.636557i	−0.947997	−	0.318278i	$-0.896895\pi$
$677$		−	16.5627i		−	0.636557i	0.947997	−	0.318278i	$-0.103105\pi$
$678$		0			0
$679$	−8.85328	+	11.2298i	−0.339758	+	0.430962i
$680$	−15.9252	+	6.80883i	−0.610702	+	0.261107i
$681$		0			0
$682$	−5.16584	−	38.1251i	−0.197810	−	1.45989i
$683$			22.1540i			0.847700i	0.905732	+	0.423850i	$0.139322\pi$
$683$			22.1540i			0.847700i	−0.905732	+	0.423850i	$0.860678\pi$
$684$		0			0
$685$		−	1.69045i		−	0.0645887i
$686$	7.67397	−	25.0422i	0.292994	−	0.956114i
$687$		0			0
$688$	−10.6066	−	17.7465i	−0.404373	−	0.676579i
$689$		−	65.7019i		−	2.50304i
$690$		0			0
$691$	27.3367			1.03994			0.519968	−	0.854186i	$-0.325944\pi$
$691$	27.3367			1.03994			0.519968	+	0.854186i	$0.325944\pi$
$692$	7.45614	+	27.0089i	0.283440	+	1.02672i
$693$		0			0
$694$	3.67873	+	27.1499i	0.139643	+	1.03060i
$695$			6.83591i			0.259301i
$696$		0			0
$697$	−19.3221			−0.731876
$698$	4.26479	+	31.4752i	0.161425	+	1.19135i
$699$		0			0
$700$	13.9287	+	5.86035i	0.526455	+	0.221500i
$701$	−4.27176			−0.161342			−0.0806712	−	0.996741i	$-0.525706\pi$
$701$	−4.27176			−0.161342			−0.0806712	+	0.996741i	$0.525706\pi$
$702$		0			0
$703$	1.07859			0.0406798
$704$	−28.2617	−	27.0089i	−1.06515	−	1.01794i
$705$		0			0
$706$	−3.18826	−	23.5301i	−0.119992	−	0.885567i
$707$	15.3794	−	19.5078i	0.578400	−	0.733665i
$708$		0			0
$709$	−41.1683			−1.54611			−0.773053	−	0.634341i	$-0.781271\pi$
$709$	−41.1683			−1.54611			−0.773053	+	0.634341i	$0.781271\pi$
$710$	12.5992	−	1.70716i	0.472840	−	0.0640685i
$711$		0			0
$712$	15.1602	+	35.4581i	0.568151	+	1.32885i
$713$		−	27.2049i		−	1.01883i
$714$		0			0
$715$		−	45.1923i		−	1.69010i
$716$	13.8411	+	50.1376i	0.517266	+	1.87373i
$717$		0			0
$718$	−6.07292	−	44.8196i	−0.226639	−	1.67265i
$719$	22.9479			0.855812			0.427906	−	0.903823i	$-0.359251\pi$
$719$	22.9479			0.855812			0.427906	+	0.903823i	$0.359251\pi$
$720$		0			0
$721$	−29.1113	−	22.9505i	−1.08416	−	0.854723i
$722$	26.5009	−	3.59079i	0.986261	−	0.133635i
$723$		0			0
$724$	11.6139	+	42.0698i	0.431627	+	1.56351i
$725$	10.4028			0.386349
$726$		0			0
$727$	−4.53531			−0.168205			−0.0841026	−	0.996457i	$-0.526802\pi$
$727$	−4.53531			−0.168205			−0.0841026	+	0.996457i	$0.526802\pi$
$728$	−12.3139	+	45.6309i	−0.456382	+	1.69119i
$729$		0			0
$730$	−3.88386	+	0.526251i	−0.143748	+	0.0194774i
$731$	−21.6140			−0.799424
$732$		0			0
$733$			44.5544i			1.64565i	0.568292	+	0.822827i	$0.307605\pi$
$733$			44.5544i			1.64565i	−0.568292	+	0.822827i	$0.692395\pi$
$734$	−23.5408	+	3.18971i	−0.868908	+	0.117734i
$735$		0			0
$736$	−17.2388	−	21.6085i	−0.635429	−	0.796500i
$737$	30.8624			1.13683
$738$		0			0
$739$		−	51.3060i		−	1.88732i	−0.330915	−	0.943660i	$-0.607357\pi$
$739$		−	51.3060i		−	1.88732i	0.330915	−	0.943660i	$-0.392643\pi$
$740$	2.80508	+	10.1610i	0.103117	+	0.373527i
$741$		0			0
$742$	−33.5257	−	19.7756i	−1.23077	−	0.725985i
$743$		−	24.3615i		−	0.893736i	−0.894600	−	0.446868i	$-0.852539\pi$
$743$		−	24.3615i		−	0.893736i	0.894600	−	0.446868i	$-0.147461\pi$
$744$		0			0
$745$		−	1.18388i		−	0.0433740i
$746$	−16.8326	+	2.28077i	−0.616285	+	0.0835048i
$747$		0			0
$748$	−39.3950	+	10.8755i	−1.44042	+	0.397647i
$749$	5.23280	−	6.63749i	0.191203	−	0.242529i
$750$		0			0
$751$			37.4931i			1.36814i	0.729415	+	0.684072i	$0.239793\pi$
$751$			37.4931i			1.36814i	−0.729415	+	0.684072i	$0.760207\pi$
$752$	31.7541	−	18.9786i	1.15795	−	0.692078i
$753$		0			0
$754$	4.36866	+	32.2418i	0.159097	+	1.17418i
$755$	20.1765			0.734298
$756$		0			0
$757$	26.1779			0.951450			0.475725	−	0.879594i	$-0.342186\pi$
$757$	26.1779			0.951450			0.475725	+	0.879594i	$0.342186\pi$
$758$	−1.16787	−	8.61915i	−0.0424189	−	0.313062i
$759$		0			0
$760$	−0.487920	−	1.14119i	−0.0176987	−	0.0413954i
$761$			3.30415i			0.119775i	0.998205	+	0.0598877i	$0.0190743\pi$
$761$			3.30415i			0.119775i	−0.998205	+	0.0598877i	$0.980926\pi$
$762$		0			0
$763$	−10.3221	−	8.13763i	−0.373684	−	0.294602i
$764$	−5.96031	−	21.5904i	−0.215636	−	0.781115i
$765$		0			0
$766$	−30.2901	+	4.10421i	−1.09442	+	0.148291i
$767$			78.0993i			2.82000i
$768$		0			0
$769$			25.1924i			0.908462i	0.890884	+	0.454231i	$0.150086\pi$
$769$			25.1924i			0.908462i	−0.890884	+	0.454231i	$0.849914\pi$
$770$	−23.0603	−	13.6024i	−0.831036	−	0.490198i
$771$		0			0
$772$	−24.0336	+	6.63478i	−0.864989	+	0.238791i
$773$		−	38.9194i		−	1.39983i	−0.714224	−	0.699917i	$-0.753220\pi$
$773$		−	38.9194i		−	1.39983i	0.714224	−	0.699917i	$-0.246780\pi$
$774$		0			0
$775$	−15.8990			−0.571109
$776$	−6.00987	−	14.0565i	−0.215742	−	0.504598i
$777$		0			0
$778$	−7.85577	+	1.06443i	−0.281643	+	0.0381618i
$779$		−	1.38462i		−	0.0496090i
$780$		0			0
$781$	30.0016			1.07354
$782$	−28.6368	+	3.88020i	−1.02405	+	0.138756i
$783$		0			0
$784$	19.5777	+	20.0178i	0.699204	+	0.714922i
$785$	5.14308			0.183565
$786$		0			0
$787$	−23.2677			−0.829402			−0.414701	−	0.909958i	$-0.636114\pi$
$787$	−23.2677			−0.829402			−0.414701	+	0.909958i	$0.636114\pi$
$788$	−4.79714	+	1.32431i	−0.170891	+	0.0471766i
$789$		0			0
$790$	29.8053	−	4.03852i	1.06042	−	0.143684i
$791$	11.6469	+	9.18210i	0.414117	+	0.326478i
$792$		0			0
$793$	−34.1363			−1.21221
$794$	6.13101	+	45.2483i	0.217581	+	1.60580i
$795$		0			0
$796$	11.2276	−	3.09950i	0.397950	−	0.109859i
$797$		−	10.4778i		−	0.371144i	−0.982631	−	0.185572i	$-0.940586\pi$
$797$		−	10.4778i		−	0.371144i	0.982631	−	0.185572i	$-0.0594138\pi$
$798$		0			0
$799$		−	38.6744i		−	1.36820i
$800$	−12.6284	+	10.0746i	−0.446481	+	0.356192i
$801$		0			0
$802$	37.6610	−	5.10296i	1.32986	−	0.180192i
$803$	−9.24835			−0.326367
$804$		0			0
$805$	−14.8670	−	11.7207i	−0.523992	−	0.413100i
$806$	−6.67681	−	49.2764i	−0.235180	−	1.73569i
$807$		0			0
$808$	10.4400	+	24.4180i	0.367277	+	0.859022i
$809$	40.6361			1.42869			0.714345	−	0.699794i	$-0.246725\pi$
$809$	40.6361			1.42869			0.714345	+	0.699794i	$0.246725\pi$
$810$		0			0
$811$	3.97920			0.139729			0.0698643	−	0.997557i	$-0.477743\pi$
$811$	3.97920			0.139729			0.0698643	+	0.997557i	$0.477743\pi$
$812$	17.7669	+	7.47525i	0.623497	+	0.262330i
$813$		0			0
$814$	3.33977	+	24.6483i	0.117059	+	0.863922i
$815$	15.7253			0.550833
$816$		0			0
$817$		−	1.54886i		−	0.0541877i
$818$	−5.65049	−	41.7020i	−0.197565	−	1.45808i
$819$		0			0
$820$	13.0440	−	3.60096i	0.455517	−	0.125751i
$821$	48.3083			1.68597			0.842986	−	0.537936i	$-0.180796\pi$
$821$	48.3083			1.68597			0.842986	+	0.537936i	$0.180796\pi$
$822$		0			0
$823$			26.2449i			0.914841i	0.889251	+	0.457420i	$0.151227\pi$
$823$			26.2449i			0.914841i	−0.889251	+	0.457420i	$0.848773\pi$
$824$	36.4389	−	15.5795i	1.26941	−	0.542738i
$825$		0			0
$826$	39.8517	+	23.5071i	1.38662	+	0.817916i
$827$			3.40580i			0.118431i	0.998245	+	0.0592156i	$0.0188600\pi$
$827$			3.40580i			0.118431i	−0.998245	+	0.0592156i	$0.981140\pi$
$828$		0			0
$829$		−	15.1622i		−	0.526604i	−0.964713	−	0.263302i	$-0.915188\pi$
$829$		−	15.1622i		−	0.526604i	0.964713	−	0.263302i	$-0.0848116\pi$
$830$	−3.90541	−	28.8228i	−0.135559	−	1.00046i
$831$		0			0
$832$	−36.5280	−	34.9088i	−1.26638	−	1.21025i
$833$	28.4638	−	6.83227i	0.986213	−	0.236724i
$834$		0			0
$835$			7.02455i			0.243094i
$836$	−0.779335	−	2.82304i	−0.0269538	−	0.0976368i
$837$		0			0
$838$	37.0128	−	5.01513i	1.27859	−	0.173245i
$839$	−20.2802			−0.700149			−0.350075	−	0.936722i	$-0.613844\pi$
$839$	−20.2802			−0.700149			−0.350075	+	0.936722i	$0.613844\pi$
$840$		0			0
$841$	−15.7306			−0.542435
$842$	22.4901	−	3.04734i	0.775059	−	0.105018i
$843$		0			0
$844$	6.11222	+	22.1407i	0.210391	+	0.762115i
$845$		−	39.3746i		−	1.35453i
$846$		0			0
$847$	−26.7573	−	21.0946i	−0.919390	−	0.724821i
$848$	35.7178	−	21.3476i	1.22656	−	0.733080i
$849$		0			0
$850$	2.26765	+	16.7358i	0.0777799	+	0.574034i
$851$			17.5882i			0.602917i
$852$		0			0
$853$			30.6681i			1.05006i	0.851085	+	0.525028i	$0.175945\pi$
$853$			30.6681i			1.05006i	−0.851085	+	0.525028i	$0.824055\pi$
$854$	−10.2747	+	17.4187i	−0.351592	+	0.596056i
$855$		0			0
$856$	3.55218	+	8.30819i	0.121411	+	0.283968i
$857$			23.8210i			0.813711i	0.913493	+	0.406855i	$0.133375\pi$
$857$			23.8210i			0.813711i	−0.913493	+	0.406855i	$0.866625\pi$
$858$		0			0
$859$	33.9696			1.15903			0.579514	−	0.814962i	$-0.303242\pi$
$859$	33.9696			1.15903			0.579514	+	0.814962i	$0.303242\pi$
$860$	14.5913	−	4.02810i	0.497559	−	0.137357i
$861$		0			0
$862$	3.96151	+	29.2369i	0.134930	+	0.995813i
$863$		−	16.9163i		−	0.575837i	−0.957655	−	0.287919i	$-0.907037\pi$
$863$		−	16.9163i		−	0.575837i	0.957655	−	0.287919i	$-0.0929632\pi$
$864$		0			0
$865$	−20.5145			−0.697514
$866$	1.01287	+	7.47525i	0.0344188	+	0.254019i
$867$		0			0
$868$	−27.1539	−	11.4247i	−0.921665	−	0.387781i
$869$	70.9731			2.40760
$870$		0			0
$871$	39.8894			1.35160
$872$	12.9202	−	5.52407i	0.437534	−	0.187068i
$873$		0			0
$874$	−0.278054	−	2.05211i	−0.00940532	−	0.0694135i
$875$	−18.8426	+	23.9007i	−0.636997	+	0.807992i
$876$		0			0
$877$	52.7996			1.78292			0.891458	−	0.453103i	$-0.149683\pi$
$877$	52.7996			1.78292			0.891458	+	0.453103i	$0.149683\pi$
$878$	4.33007	−	0.586711i	0.146133	−	0.0198005i
$879$		0			0
$880$	24.5681	−	14.6837i	0.828191	−	0.494988i
$881$		−	13.1789i		−	0.444007i	−0.975046	−	0.222004i	$-0.928740\pi$
$881$		−	13.1789i		−	0.444007i	0.975046	−	0.222004i	$-0.0712597\pi$
$882$		0			0
$883$		−	32.9624i		−	1.10927i	−0.832092	−	0.554637i	$-0.812857\pi$
$883$		−	32.9624i		−	1.10927i	0.832092	−	0.554637i	$-0.187143\pi$
$884$	−50.9177	+	14.0565i	−1.71255	+	0.472770i
$885$		0			0
$886$	−1.83647	−	13.5536i	−0.0616975	−	0.455342i
$887$	4.45120			0.149457			0.0747284	−	0.997204i	$-0.476191\pi$
$887$	4.45120			0.149457			0.0747284	+	0.997204i	$0.476191\pi$
$888$		0			0
$889$	1.49209	−	1.89262i	0.0500430	−	0.0634764i
$890$	−27.9786	+	3.79101i	−0.937844	+	0.127075i
$891$		0			0
$892$	30.8061	−	8.50440i	1.03146	−	0.284748i
$893$	2.77140			0.0927413
$894$		0			0
$895$	−38.0818			−1.27293
$896$	−28.8075	+	8.13196i	−0.962391	+	0.271670i
$897$		0			0
$898$	−16.9326	+	2.29432i	−0.565049	+	0.0765624i
$899$	−20.2802			−0.676381
$900$		0			0
$901$		−	43.5019i		−	1.44926i
$902$	31.6417	−	4.28736i	1.05355	−	0.142753i
$903$		0			0
$904$	−14.5785	+	6.23308i	−0.484875	+	0.207309i
$905$	−31.9540			−1.06219
$906$		0			0
$907$			14.5583i			0.483401i	0.970351	+	0.241700i	$0.0777051\pi$
$907$			14.5583i			0.483401i	−0.970351	+	0.241700i	$0.922295\pi$
$908$	−23.1727	+	6.39711i	−0.769013	+	0.212296i
$909$		0			0
$910$	−29.8053	−	17.5810i	−0.988035	−	0.582806i
$911$			17.7696i			0.588732i	0.955693	+	0.294366i	$0.0951085\pi$
$911$			17.7696i			0.588732i	−0.955693	+	0.294366i	$0.904891\pi$
$912$		0			0
$913$		−	68.6337i		−	2.27145i
$914$	12.5474	−	1.70013i	0.415031	−	0.0562354i
$915$		0			0
$916$	−3.39906	−	12.3126i	−0.112308	−	0.406821i
$917$	15.7253	+	12.3974i	0.519295	+	0.409397i
$918$		0			0
$919$			4.09228i			0.134992i	0.997720	+	0.0674960i	$0.0215010\pi$
$919$			4.09228i			0.134992i	−0.997720	+	0.0674960i	$0.978499\pi$
$920$	18.6091	−	7.95636i	0.613524	−	0.262313i
$921$		0			0
$922$	−2.95030	−	21.7740i	−0.0971631	−	0.717087i
$923$	38.7769			1.27636
$924$		0			0
$925$	10.2789			0.337967
$926$	−0.186413	−	1.37577i	−0.00612591	−	0.0452107i
$927$		0			0
$928$	−16.1083	+	12.8508i	−0.528781	+	0.421849i
$929$		−	1.05834i		−	0.0347231i	−0.999849	−	0.0173615i	$-0.994473\pi$
$929$		−	1.05834i		−	0.0347231i	0.999849	−	0.0173615i	$-0.00552663\pi$
$930$		0			0
$931$	0.489599	+	2.03971i	0.0160460	+	0.0668488i
$932$	−34.1009	+	9.41396i	−1.11701	+	0.308365i
$933$		0			0
$934$	−3.88386	+	0.526251i	−0.127084	+	0.0172195i
$935$		−	29.9223i		−	0.978564i
$936$		0			0
$937$		−	14.7972i		−	0.483403i	−0.970351	−	0.241702i	$-0.922294\pi$
$937$		−	14.7972i		−	0.483403i	0.970351	−	0.241702i	$-0.0777055\pi$
$938$	12.0063	−	20.3544i	0.392020	−	0.664594i
$939$		0			0
$940$	7.20756	+	26.1084i	0.235085	+	0.851564i
$941$			48.8105i			1.59118i	0.605837	+	0.795589i	$0.292839\pi$
$941$			48.8105i			1.59118i	−0.605837	+	0.795589i	$0.707161\pi$
$942$		0			0
$943$	22.5785			0.735258
$944$	−42.4575	+	25.3757i	−1.38187	+	0.825909i
$945$		0			0
$946$	35.3950	−	4.79592i	1.15079	−	0.155929i
$947$			42.6404i			1.38563i	0.721116	+	0.692814i	$0.243629\pi$
$947$			42.6404i			1.38563i	−0.721116	+	0.692814i	$0.756371\pi$
$948$		0			0
$949$	−11.9534			−0.388024
$950$	−1.19929	+	0.162500i	−0.0389100	+	0.00527218i
$951$		0			0
$952$	−8.15313	+	30.2127i	−0.264244	+	0.979198i
$953$	−16.5338			−0.535582			−0.267791	−	0.963477i	$-0.586294\pi$
$953$	−16.5338			−0.535582			−0.267791	+	0.963477i	$0.586294\pi$
$954$		0			0
$955$	16.3989			0.530657
$956$	−0.487493	−	1.76588i	−0.0157666	−	0.0571127i
$957$		0			0
$958$	21.2132	−	2.87433i	0.685368	−	0.0928653i
$959$	−2.39857	−	1.89096i	−0.0774539	−	0.0610624i
$960$		0			0
$961$	−0.00497563			−0.000160504
$962$	4.31662	+	31.8577i	0.139174	+	1.02713i
$963$		0			0
$964$	3.36138	+	12.1762i	0.108263	+	0.392168i
$965$		−	18.2546i		−	0.587638i
$966$		0			0
$967$			18.6744i			0.600530i	0.953856	+	0.300265i	$0.0970751\pi$
$967$			18.6744i			0.600530i	−0.953856	+	0.300265i	$0.902925\pi$
$968$	33.4922	−	14.3197i	1.07648	−	0.460252i
$969$		0			0
$970$	11.0914	−	1.50285i	0.356124	−	0.0482537i
$971$	58.9534			1.89190			0.945952	−	0.324307i	$-0.105131\pi$
$971$	58.9534			1.89190			0.945952	+	0.324307i	$0.105131\pi$
$972$		0			0
$973$	9.69946	+	7.64678i	0.310951	+	0.245144i
$974$	5.12511	+	37.8245i	0.164219	+	1.21198i
$975$		0			0
$976$	−11.0914	−	18.5576i	−0.355028	−	0.594016i
$977$	−17.4459			−0.558145			−0.279072	−	0.960270i	$-0.590027\pi$
$977$	−17.4459			−0.558145			−0.279072	+	0.960270i	$0.590027\pi$
$978$		0			0
$979$	−66.6234			−2.12929
$980$	−17.9422	+	9.91702i	−0.573141	+	0.316788i
$981$		0			0
$982$	−3.63551	−	26.8309i	−0.116014	−	0.856209i
$983$	−58.9534			−1.88032			−0.940160	−	0.340733i	$-0.889325\pi$
$983$	−58.9534			−1.88032			−0.940160	+	0.340733i	$0.889325\pi$
$984$		0			0
$985$		−	3.64365i		−	0.116096i
$986$	2.89254	+	21.3476i	0.0921171	+	0.679846i
$987$		0			0
$988$	−1.00728	−	3.64876i	−0.0320460	−	0.116082i
$989$	25.2568			0.803118
$990$		0			0
$991$			57.3147i			1.82066i	0.413880	+	0.910331i	$0.364173\pi$
$991$			57.3147i			1.82066i	−0.413880	+	0.910331i	$0.635827\pi$
$992$	24.6190	−	19.6404i	0.781653	−	0.623585i
$993$		0			0
$994$	11.6714	−	19.7867i	0.370196	−	0.627595i
$995$			8.52784i			0.270351i
$996$		0			0
$997$			14.5950i			0.462229i	0.972927	+	0.231115i	$0.0742372\pi$
$997$			14.5950i			0.462229i	−0.972927	+	0.231115i	$0.925763\pi$
$998$	5.37436	+	39.6640i	0.170122	+	1.25554i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.b.d.55.2	yes	12
3.2	odd	2	inner	756.2.b.d.55.11	yes	12
4.3	odd	2		756.2.b.c.55.1	✓	12
7.6	odd	2		756.2.b.c.55.2	yes	12
12.11	even	2		756.2.b.c.55.12	yes	12
21.20	even	2		756.2.b.c.55.11	yes	12
28.27	even	2	inner	756.2.b.d.55.1	yes	12
84.83	odd	2	inner	756.2.b.d.55.12	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.b.c.55.1	✓	12	4.3	odd	2
756.2.b.c.55.2	yes	12	7.6	odd	2
756.2.b.c.55.11	yes	12	21.20	even	2
756.2.b.c.55.12	yes	12	12.11	even	2
756.2.b.d.55.1	yes	12	28.27	even	2	inner
756.2.b.d.55.2	yes	12	1.1	even	1	trivial
756.2.b.d.55.11	yes	12	3.2	odd	2	inner
756.2.b.d.55.12	yes	12	84.83	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40141 + 0.189886i) q^{2} +(1.92789 - 0.532217i) q^{4} +1.46432i q^{5} +(2.07772 + 1.63801i) q^{7} +(-2.60069 + 1.11193i) q^{8} +O(q^{10})\)	\(q+(-1.40141 + 0.189886i) q^{2} +(1.92789 - 0.532217i) q^{4} +1.46432i q^{5} +(2.07772 + 1.63801i) q^{7} +(-2.60069 + 1.11193i) q^{8} +(-0.278054 - 2.05211i) q^{10} -4.88653i q^{11} -6.31581i q^{13} +(-3.22277 - 1.90099i) q^{14} +(3.43349 - 2.05211i) q^{16} -4.18176i q^{17} +0.299664 q^{19} +(0.779335 + 2.82304i) q^{20} +(0.927886 + 6.84802i) q^{22} +4.88653i q^{23} +2.85577 q^{25} +(1.19929 + 8.85102i) q^{26} +(4.87738 + 2.05211i) q^{28} +3.64272 q^{29} -5.56732 q^{31} +(-4.42205 + 3.52781i) q^{32} +(0.794060 + 5.86035i) q^{34} +(-2.39857 + 3.04244i) q^{35} +3.59933 q^{37} +(-0.419952 + 0.0569022i) q^{38} +(-1.62822 - 3.80824i) q^{40} -4.62056i q^{41} -5.16865i q^{43} +(-2.60069 - 9.42068i) q^{44} +(-0.927886 - 6.84802i) q^{46} +9.24835 q^{47} +(1.63383 + 6.80666i) q^{49} +(-4.00210 + 0.542273i) q^{50} +(-3.36138 - 12.1762i) q^{52} +10.4028 q^{53} +7.15544 q^{55} +(-7.22487 - 1.94969i) q^{56} +(-5.10493 + 0.691703i) q^{58} -12.3657 q^{59} -5.40489i q^{61} +(7.80208 - 1.05716i) q^{62} +(5.52721 - 5.78359i) q^{64} +9.24835 q^{65} +6.31581i q^{67} +(-2.22560 - 8.06196i) q^{68} +(2.78366 - 4.71916i) q^{70} +6.13965i q^{71} -1.89262i q^{73} +(-5.04413 + 0.683464i) q^{74} +(0.577718 - 0.159486i) q^{76} +(8.00420 - 10.1528i) q^{77} +14.5242i q^{79} +(3.00494 + 5.02772i) q^{80} +(0.877382 + 6.47529i) q^{82} +14.0455 q^{83} +6.12343 q^{85} +(0.981456 + 7.24338i) q^{86} +(5.43349 + 12.7084i) q^{88} -13.6341i q^{89} +(10.3454 - 13.1225i) q^{91} +(2.60069 + 9.42068i) q^{92} +(-12.9607 + 1.75614i) q^{94} +0.438804i q^{95} +5.40489i q^{97} +(-3.58215 - 9.22866i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 8 q^{4} + 2 q^{7}+O(q^{10}) \) 12 * q + 8 * q^4 + 2 * q^7	\( 12 q + 8 q^{4} + 2 q^{7} + 4 q^{10} - 12 q^{16} - 12 q^{19} - 4 q^{22} + 4 q^{25} + 20 q^{28} + 24 q^{31} + 32 q^{34} + 12 q^{37} - 20 q^{40} + 4 q^{46} - 18 q^{49} + 28 q^{52} + 40 q^{55} + 8 q^{58} + 20 q^{64} - 12 q^{70} - 16 q^{76} - 28 q^{82} - 32 q^{85} + 12 q^{88} + 26 q^{91} - 56 q^{94}+O(q^{100}) \) 12 * q + 8 * q^4 + 2 * q^7 + 4 * q^10 - 12 * q^16 - 12 * q^19 - 4 * q^22 + 4 * q^25 + 20 * q^28 + 24 * q^31 + 32 * q^34 + 12 * q^37 - 20 * q^40 + 4 * q^46 - 18 * q^49 + 28 * q^52 + 40 * q^55 + 8 * q^58 + 20 * q^64 - 12 * q^70 - 16 * q^76 - 28 * q^82 - 32 * q^85 + 12 * q^88 + 26 * q^91 - 56 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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