LMFDB - Embedded newform 945.2.p.b.433.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(433,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("945.433");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.p (of order $4$, 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:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			433.15
Character	$\chi$	$=$	945.433
Dual form			945.2.p.b.622.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.515806 - 0.515806i) q^{2} +1.46789i q^{4} +(-1.00702 + 1.99648i) q^{5} +(1.67258 + 2.04999i) q^{7} +(1.78876 + 1.78876i) q^{8} +O(q^{10})$	\(q+(0.515806 - 0.515806i) q^{2} +1.46789i q^{4} +(-1.00702 + 1.99648i) q^{5} +(1.67258 + 2.04999i) q^{7} +(1.78876 + 1.78876i) q^{8} +(0.510370 + 1.54922i) q^{10} +1.07449 q^{11} +(-3.17486 + 3.17486i) q^{13} +(1.92013 + 0.194673i) q^{14} -1.09047 q^{16} +(-3.65529 - 3.65529i) q^{17} -0.950808 q^{19} +(-2.93060 - 1.47819i) q^{20} +(0.554230 - 0.554230i) q^{22} +(-0.550594 - 0.550594i) q^{23} +(-2.97184 - 4.02097i) q^{25} +3.27523i q^{26} +(-3.00916 + 2.45516i) q^{28} -7.60321i q^{29} +7.14243i q^{31} +(-4.13999 + 4.13999i) q^{32} -3.77084 q^{34} +(-5.77708 + 1.27489i) q^{35} +(5.34833 - 5.34833i) q^{37} +(-0.490432 + 0.490432i) q^{38} +(-5.37252 + 1.76990i) q^{40} -1.45242i q^{41} +(5.98468 + 5.98468i) q^{43} +1.57723i q^{44} -0.568000 q^{46} +(1.26224 + 1.26224i) q^{47} +(-1.40496 + 6.85756i) q^{49} +(-3.60693 - 0.541149i) q^{50} +(-4.66034 - 4.66034i) q^{52} +(7.81473 + 7.81473i) q^{53} +(-1.08203 + 2.14520i) q^{55} +(-0.675105 + 6.65878i) q^{56} +(-3.92178 - 3.92178i) q^{58} -4.87683 q^{59} +9.22013i q^{61} +(3.68411 + 3.68411i) q^{62} +2.08992i q^{64} +(-3.14140 - 9.53568i) q^{65} +(-5.94390 + 5.94390i) q^{67} +(5.36556 - 5.36556i) q^{68} +(-2.32226 + 3.63745i) q^{70} +3.91987 q^{71} +(-3.60638 + 3.60638i) q^{73} -5.51740i q^{74} -1.39568i q^{76} +(1.79717 + 2.20270i) q^{77} -2.27730i q^{79} +(1.09812 - 2.17710i) q^{80} +(-0.749165 - 0.749165i) q^{82} +(2.44017 - 2.44017i) q^{83} +(10.9786 - 3.61676i) q^{85} +6.17387 q^{86} +(1.92201 + 1.92201i) q^{88} +8.49873 q^{89} +(-11.8187 - 1.19824i) q^{91} +(0.808211 - 0.808211i) q^{92} +1.30214 q^{94} +(0.957479 - 1.89827i) q^{95} +(9.19274 + 9.19274i) q^{97} +(2.81248 + 4.26186i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 8 q^{7}+O(q^{10}) $ 48 * q - 8 * q^7	$ 48 q - 8 q^{7} + 40 q^{16} + 8 q^{22} - 48 q^{25} - 20 q^{28} - 24 q^{37} - 40 q^{43} + 40 q^{46} - 80 q^{58} - 64 q^{67} - 4 q^{70} - 8 q^{85} - 48 q^{88} + 48 q^{91}+O(q^{100}) $ 48 * q - 8 * q^7 + 40 * q^16 + 8 * q^22 - 48 * q^25 - 20 * q^28 - 24 * q^37 - 40 * q^43 + 40 * q^46 - 80 * q^58 - 64 * q^67 - 4 * q^70 - 8 * q^85 - 48 * q^88 + 48 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.515806	−	0.515806i	0.364730	−	0.364730i	−0.500821	−	0.865551i	$-0.666968\pi$
$2$	0.515806	−	0.515806i	0.364730	−	0.364730i	0.865551	+	0.500821i	$0.166968\pi$
$3$		0			0
$3$		0			0
$4$			1.46789i			0.733944i
$5$	−1.00702	+	1.99648i	−0.450351	+	0.892851i
$5$	−1.00702	+	1.99648i	−0.450351	+	0.892851i
$6$		0			0
$7$	1.67258	+	2.04999i	0.632176	+	0.774825i
$7$	1.67258	+	2.04999i	0.632176	+	0.774825i
$8$	1.78876	+	1.78876i	0.632421	+	0.632421i
$9$		0			0
$10$	0.510370	+	1.54922i	0.161393	+	0.489906i
$11$	1.07449			0.323972			0.161986	−	0.986793i	$-0.448210\pi$
$11$	1.07449			0.323972			0.161986	+	0.986793i	$0.448210\pi$
$12$		0			0
$13$	−3.17486	+	3.17486i	−0.880548	+	0.880548i	−0.993590	−	0.113042i	$-0.963941\pi$
$13$	−3.17486	+	3.17486i	−0.880548	+	0.880548i	0.113042	+	0.993590i	$0.463941\pi$
$14$	1.92013	+	0.194673i	0.513175	+	0.0520286i
$15$		0			0
$16$	−1.09047			−0.272618
$17$	−3.65529	−	3.65529i	−0.886538	−	0.886538i	0.107651	−	0.994189i	$-0.465667\pi$
$17$	−3.65529	−	3.65529i	−0.886538	−	0.886538i	−0.994189	+	0.107651i	$0.965667\pi$
$18$		0			0
$19$	−0.950808			−0.218130			−0.109065	−	0.994035i	$-0.534786\pi$
$19$	−0.950808			−0.218130			−0.109065	+	0.994035i	$0.534786\pi$
$20$	−2.93060	−	1.47819i	−0.655303	−	0.330533i
$21$		0			0
$22$	0.554230	−	0.554230i	0.118162	−	0.118162i
$23$	−0.550594	−	0.550594i	−0.114807	−	0.114807i	0.647369	−	0.762176i	$-0.275869\pi$
$23$	−0.550594	−	0.550594i	−0.114807	−	0.114807i	−0.762176	+	0.647369i	$0.775869\pi$
$24$		0			0
$25$	−2.97184	−	4.02097i	−0.594367	−	0.804194i
$26$			3.27523i			0.642325i
$27$		0			0
$28$	−3.00916	+	2.45516i	−0.568678	+	0.463982i
$29$		−	7.60321i		−	1.41188i	−0.708271	−	0.705940i	$-0.750525\pi$
$29$		−	7.60321i		−	1.41188i	0.708271	−	0.705940i	$-0.249475\pi$
$30$		0			0
$31$			7.14243i			1.28282i	0.767199	+	0.641409i	$0.221650\pi$
$31$			7.14243i			1.28282i	−0.767199	+	0.641409i	$0.778350\pi$
$32$	−4.13999	+	4.13999i	−0.731853	+	0.731853i
$33$		0			0
$34$	−3.77084			−0.646694
$35$	−5.77708	+	1.27489i	−0.976505	+	0.215495i
$36$		0			0
$37$	5.34833	−	5.34833i	0.879260	−	0.879260i	−0.114198	−	0.993458i	$-0.536430\pi$
$37$	5.34833	−	5.34833i	0.879260	−	0.879260i	0.993458	+	0.114198i	$0.0364299\pi$
$38$	−0.490432	+	0.490432i	−0.0795586	+	0.0795586i
$39$		0			0
$40$	−5.37252	+	1.76990i	−0.849470	+	0.279846i
$41$		−	1.45242i		−	0.226829i	−0.993548	−	0.113415i	$-0.963821\pi$
$41$		−	1.45242i		−	0.226829i	0.993548	−	0.113415i	$-0.0361789\pi$
$42$		0			0
$43$	5.98468	+	5.98468i	0.912656	+	0.912656i	0.996480	−	0.0838249i	$-0.0267136\pi$
$43$	5.98468	+	5.98468i	0.912656	+	0.912656i	−0.0838249	+	0.996480i	$0.526714\pi$
$44$			1.57723i			0.237777i
$45$		0			0
$46$	−0.568000			−0.0837470
$47$	1.26224	+	1.26224i	0.184116	+	0.184116i	0.793147	−	0.609031i	$-0.208441\pi$
$47$	1.26224	+	1.26224i	0.184116	+	0.184116i	−0.609031	+	0.793147i	$0.708441\pi$
$48$		0			0
$49$	−1.40496	+	6.85756i	−0.200708	+	0.979651i
$50$	−3.60693	−	0.541149i	−0.510097	−	0.0765300i
$51$		0			0
$52$	−4.66034	−	4.66034i	−0.646273	−	0.646273i
$53$	7.81473	+	7.81473i	1.07344	+	1.07344i	0.997081	+	0.0763553i	$0.0243283\pi$
$53$	7.81473	+	7.81473i	1.07344	+	1.07344i	0.0763553	+	0.997081i	$0.475672\pi$
$54$		0			0
$55$	−1.08203	+	2.14520i	−0.145901	+	0.289259i
$56$	−0.675105	+	6.65878i	−0.0902147	+	0.889817i
$57$		0			0
$58$	−3.92178	−	3.92178i	−0.514955	−	0.514955i
$59$	−4.87683			−0.634909			−0.317455	−	0.948273i	$-0.602828\pi$
$59$	−4.87683			−0.634909			−0.317455	+	0.948273i	$0.602828\pi$
$60$		0			0
$61$			9.22013i			1.18052i	0.807215	+	0.590258i	$0.200974\pi$
$61$			9.22013i			1.18052i	−0.807215	+	0.590258i	$0.799026\pi$
$62$	3.68411	+	3.68411i	0.467882	+	0.467882i
$63$		0			0
$64$			2.08992i			0.261240i
$65$	−3.14140	−	9.53568i	−0.389643	−	1.18276i
$66$		0			0
$67$	−5.94390	+	5.94390i	−0.726163	+	0.726163i	−0.969853	−	0.243690i	$-0.921642\pi$
$67$	−5.94390	+	5.94390i	−0.726163	+	0.726163i	0.243690	+	0.969853i	$0.421642\pi$
$68$	5.36556	−	5.36556i	0.650669	−	0.650669i
$69$		0			0
$70$	−2.32226	+	3.63745i	−0.277563	+	0.434758i
$71$	3.91987			0.465203			0.232601	−	0.972572i	$-0.425276\pi$
$71$	3.91987			0.465203			0.232601	+	0.972572i	$0.425276\pi$
$72$		0			0
$73$	−3.60638	+	3.60638i	−0.422094	+	0.422094i	−0.885924	−	0.463830i	$-0.846475\pi$
$73$	−3.60638	+	3.60638i	−0.422094	+	0.422094i	0.463830	+	0.885924i	$0.346475\pi$
$74$		−	5.51740i		−	0.641385i
$75$		0			0
$76$		−	1.39568i		−	0.160095i
$77$	1.79717	+	2.20270i	0.204807	+	0.251021i
$78$		0			0
$79$		−	2.27730i		−	0.256217i	−0.991760	−	0.128108i	$-0.959109\pi$
$79$		−	2.27730i		−	0.256217i	0.991760	−	0.128108i	$-0.0408905\pi$
$80$	1.09812	−	2.17710i	0.122774	−	0.243407i
$81$		0			0
$82$	−0.749165	−	0.749165i	−0.0827315	−	0.0827315i
$83$	2.44017	−	2.44017i	0.267844	−	0.267844i	−0.560387	−	0.828231i	$-0.689348\pi$
$83$	2.44017	−	2.44017i	0.267844	−	0.267844i	0.828231	+	0.560387i	$0.189348\pi$
$84$		0			0
$85$	10.9786	−	3.61676i	1.19080	−	0.392293i
$86$	6.17387			0.665746
$87$		0			0
$88$	1.92201	+	1.92201i	0.204887	+	0.204887i
$89$	8.49873			0.900864			0.450432	−	0.892811i	$-0.351270\pi$
$89$	8.49873			0.900864			0.450432	+	0.892811i	$0.351270\pi$
$90$		0			0
$91$	−11.8187	−	1.19824i	−1.23893	−	0.125610i
$92$	0.808211	−	0.808211i	0.0842618	−	0.0842618i
$93$		0			0
$94$	1.30214			0.134305
$95$	0.957479	−	1.89827i	0.0982352	−	0.194758i
$96$		0			0
$97$	9.19274	+	9.19274i	0.933381	+	0.933381i	0.997915	−	0.0645346i	$-0.0205563\pi$
$97$	9.19274	+	9.19274i	0.933381	+	0.933381i	−0.0645346	+	0.997915i	$0.520556\pi$
$98$	2.81248	+	4.26186i	0.284104	+	0.430512i
$99$		0			0
$100$	5.90233	−	4.36232i	0.590233	−	0.436232i
$101$		−	15.5099i		−	1.54330i	−0.636050	−	0.771648i	$-0.719433\pi$
$101$		−	15.5099i		−	1.54330i	0.636050	−	0.771648i	$-0.280567\pi$
$102$		0			0
$103$	9.78671	−	9.78671i	0.964314	−	0.964314i	−0.0350712	−	0.999385i	$-0.511166\pi$
$103$	9.78671	−	9.78671i	0.964314	−	0.964314i	0.999385	+	0.0350712i	$0.0111658\pi$
$104$	−11.3581			−1.11376
$105$		0			0
$106$	8.06177			0.783028
$107$	−13.3297	+	13.3297i	−1.28863	+	1.28863i	−0.353013	+	0.935618i	$0.614843\pi$
$107$	−13.3297	+	13.3297i	−1.28863	+	1.28863i	−0.935618	+	0.353013i	$0.885157\pi$
$108$		0			0
$109$		−	5.09781i		−	0.488282i	−0.969740	−	0.244141i	$-0.921494\pi$
$109$		−	5.09781i		−	0.488282i	0.969740	−	0.244141i	$-0.0785060\pi$
$110$	0.548388	+	1.66462i	0.0522868	+	0.158716i
$111$		0			0
$112$	−1.82390	−	2.23546i	−0.172343	−	0.211231i
$113$	13.7013	+	13.7013i	1.28891	+	1.28891i	0.935450	+	0.353459i	$0.114995\pi$
$113$	13.7013	+	13.7013i	1.28891	+	1.28891i	0.353459	+	0.935450i	$0.385005\pi$
$114$		0			0
$115$	1.65371	−	0.544791i	0.154209	−	0.0508020i
$116$	11.1607			1.03624
$117$		0			0
$118$	−2.51550	+	2.51550i	−0.231570	+	0.231570i
$119$	1.37956	−	13.6071i	0.126464	−	1.24736i
$120$		0			0
$121$	−9.84547			−0.895042
$122$	4.75580	+	4.75580i	0.430570	+	0.430570i
$123$		0			0
$124$	−10.4843			−0.941516
$125$	11.0205	−	1.88402i	0.985700	−	0.168512i
$126$		0			0
$127$	7.28618	−	7.28618i	0.646544	−	0.646544i	−0.305612	−	0.952156i	$-0.598861\pi$
$127$	7.28618	−	7.28618i	0.646544	−	0.646544i	0.952156	+	0.305612i	$0.0988611\pi$
$128$	−7.20198	−	7.20198i	−0.636571	−	0.636571i
$129$		0			0
$130$	−6.53891	−	3.29821i	−0.573501	−	0.289272i
$131$		−	3.45300i		−	0.301690i	−0.988557	−	0.150845i	$-0.951801\pi$
$131$		−	3.45300i		−	0.301690i	0.988557	−	0.150845i	$-0.0481994\pi$
$132$		0			0
$133$	−1.59030	−	1.94915i	−0.137897	−	0.169013i
$134$			6.13180i			0.529707i
$135$		0			0
$136$		−	13.0769i		−	1.12133i
$137$	−1.82127	+	1.82127i	−0.155602	+	0.155602i	−0.780615	−	0.625013i	$-0.785094\pi$
$137$	−1.82127	+	1.82127i	−0.155602	+	0.155602i	0.625013	+	0.780615i	$0.285094\pi$
$138$		0			0
$139$	19.1239			1.62206			0.811032	−	0.585001i	$-0.198906\pi$
$139$	19.1239			1.62206			0.811032	+	0.585001i	$0.198906\pi$
$140$	−1.87139	−	8.48011i	−0.158161	−	0.716700i
$141$		0			0
$142$	2.02189	−	2.02189i	0.169673	−	0.169673i
$143$	−3.41137	+	3.41137i	−0.285273	+	0.285273i
$144$		0			0
$145$	15.1796	+	7.65655i	1.26060	+	0.635842i
$146$			3.72038i			0.307901i
$147$		0			0
$148$	7.85075	+	7.85075i	0.645328	+	0.645328i
$149$		−	3.10610i		−	0.254462i	−0.991873	−	0.127231i	$-0.959391\pi$
$149$		−	3.10610i		−	0.254462i	0.991873	−	0.127231i	$-0.0406089\pi$
$150$		0			0
$151$	−16.8410			−1.37050			−0.685251	−	0.728307i	$-0.740307\pi$
$151$	−16.8410			−1.37050			−0.685251	+	0.728307i	$0.740307\pi$
$152$	−1.70076	−	1.70076i	−0.137950	−	0.137950i
$153$		0			0
$154$	2.06316	+	0.209175i	0.166254	+	0.0168558i
$155$	−14.2597	−	7.19254i	−1.14537	−	0.577719i
$156$		0			0
$157$	1.59758	+	1.59758i	0.127501	+	0.127501i	0.767978	−	0.640477i	$-0.221263\pi$
$157$	1.59758	+	1.59758i	0.127501	+	0.127501i	−0.640477	+	0.767978i	$0.721263\pi$
$158$	−1.17465	−	1.17465i	−0.0934499	−	0.0934499i
$159$		0			0
$160$	−4.09635	−	12.4344i	−0.323845	−	0.983027i
$161$	0.207803	−	2.04963i	0.0163772	−	0.161533i
$162$		0			0
$163$	9.39211	+	9.39211i	0.735647	+	0.735647i	0.971732	−	0.236085i	$-0.0758645\pi$
$163$	9.39211	+	9.39211i	0.735647	+	0.735647i	−0.236085	+	0.971732i	$0.575864\pi$
$164$	2.13199			0.166480
$165$		0			0
$166$		−	2.51731i		−	0.195381i
$167$	−2.94097	−	2.94097i	−0.227579	−	0.227579i	0.584101	−	0.811681i	$-0.301447\pi$
$167$	−2.94097	−	2.94097i	−0.227579	−	0.227579i	−0.811681	+	0.584101i	$0.801447\pi$
$168$		0			0
$169$		−	7.15950i		−	0.550731i
$170$	3.79730	−	7.52840i	0.291240	−	0.577402i
$171$		0			0
$172$	−8.78485	+	8.78485i	−0.669838	+	0.669838i
$173$	−15.6294	+	15.6294i	−1.18828	+	1.18828i	−0.210742	+	0.977542i	$0.567588\pi$
$173$	−15.6294	+	15.6294i	−1.18828	+	1.18828i	−0.977542	+	0.210742i	$0.932412\pi$
$174$		0			0
$175$	3.27233	−	12.8176i	0.247365	−	0.968922i
$176$	−1.17170			−0.0883205
$177$		0			0
$178$	4.38370	−	4.38370i	0.328572	−	0.328572i
$179$			9.88722i			0.739005i	0.929230	+	0.369503i	$0.120472\pi$
$179$			9.88722i			0.739005i	−0.929230	+	0.369503i	$0.879528\pi$
$180$		0			0
$181$		−	16.6852i		−	1.24020i	−0.784523	−	0.620100i	$-0.787092\pi$
$181$		−	16.6852i		−	1.24020i	0.784523	−	0.620100i	$-0.212908\pi$
$182$	−6.71420	+	5.47808i	−0.497689	+	0.406062i
$183$		0			0
$184$		−	1.96976i		−	0.145213i
$185$	5.29196	+	16.0637i	0.389073	+	1.18102i
$186$		0			0
$187$	−3.92758	−	3.92758i	−0.287213	−	0.287213i
$188$	−1.85282	+	1.85282i	−0.135131	+	0.135131i
$189$		0			0
$190$	−0.485263	−	1.47301i	−0.0352047	−	0.106863i
$191$	0.0866992			0.00627333			0.00313667	−	0.999995i	$-0.499002\pi$
$191$	0.0866992			0.00627333			0.00313667	+	0.999995i	$0.499002\pi$
$192$		0			0
$193$	−6.28939	−	6.28939i	−0.452720	−	0.452720i	0.443536	−	0.896256i	$-0.353724\pi$
$193$	−6.28939	−	6.28939i	−0.452720	−	0.452720i	−0.896256	+	0.443536i	$0.853724\pi$
$194$	9.48334			0.680864
$195$		0			0
$196$	−10.0661	−	2.06232i	−0.719009	−	0.147309i
$197$	−14.9686	+	14.9686i	−1.06647	+	1.06647i	−0.0688392	+	0.997628i	$0.521930\pi$
$197$	−14.9686	+	14.9686i	−1.06647	+	1.06647i	−0.997628	+	0.0688392i	$0.978070\pi$
$198$		0			0
$199$	6.61257			0.468752			0.234376	−	0.972146i	$-0.424695\pi$
$199$	6.61257			0.468752			0.234376	+	0.972146i	$0.424695\pi$
$200$	1.87664	−	12.5084i	0.132699	−	0.884480i
$201$		0			0
$202$	−8.00012	−	8.00012i	−0.562886	−	0.562886i
$203$	15.5865	−	12.7170i	1.09396	−	0.892556i
$204$		0			0
$205$	2.89972	+	1.46261i	0.202525	+	0.102153i
$206$		−	10.0961i		−	0.703428i
$207$		0			0
$208$	3.46210	−	3.46210i	0.240053	−	0.240053i
$209$	−1.02164			−0.0706680
$210$		0			0
$211$	25.7438			1.77228			0.886138	−	0.463422i	$-0.153379\pi$
$211$	25.7438			1.77228			0.886138	+	0.463422i	$0.153379\pi$
$212$	−11.4712	+	11.4712i	−0.787842	+	0.787842i
$213$		0			0
$214$			13.7511i			0.940005i
$215$	−17.9750	+	5.92161i	−1.22588	+	0.403850i
$216$		0			0
$217$	−14.6419	+	11.9463i	−0.993959	+	0.810966i
$218$	−2.62948	−	2.62948i	−0.178091	−	0.178091i
$219$		0			0
$220$	−3.14891	−	1.58830i	−0.212300	−	0.107083i
$221$	23.2101			1.56128
$222$		0			0
$223$	14.8731	−	14.8731i	0.995973	−	0.995973i	−0.00401869	−	0.999992i	$-0.501279\pi$
$223$	14.8731	−	14.8731i	0.995973	−	0.995973i	0.999992	+	0.00401869i	$0.00127919\pi$
$224$	−15.4114	−	1.56250i	−1.02972	−	0.104399i
$225$		0			0
$226$	14.1344			0.940208
$227$	9.41496	+	9.41496i	0.624893	+	0.624893i	0.946778	−	0.321886i	$-0.104317\pi$
$227$	9.41496	+	9.41496i	0.624893	+	0.624893i	−0.321886	+	0.946778i	$0.604317\pi$
$228$		0			0
$229$	1.65239			0.109193			0.0545966	−	0.998508i	$-0.482613\pi$
$229$	1.65239			0.109193			0.0545966	+	0.998508i	$0.482613\pi$
$230$	0.571985	−	1.13400i	0.0377156	−	0.0747736i
$231$		0			0
$232$	13.6003	−	13.6003i	0.892903	−	0.892903i
$233$	4.78686	+	4.78686i	0.313597	+	0.313597i	0.846302	−	0.532704i	$-0.178824\pi$
$233$	4.78686	+	4.78686i	0.313597	+	0.313597i	−0.532704	+	0.846302i	$0.678824\pi$
$234$		0			0
$235$	−3.79112	+	1.24893i	−0.247305	+	0.0814714i
$236$		−	7.15864i		−	0.465988i
$237$		0			0
$238$	−6.30703	−	7.73021i	−0.408824	−	0.501075i
$239$		−	11.9087i		−	0.770313i	−0.922851	−	0.385156i	$-0.874147\pi$
$239$		−	11.9087i		−	0.770313i	0.922851	−	0.385156i	$-0.125853\pi$
$240$		0			0
$241$		−	0.171912i		−	0.0110738i	−0.999985	−	0.00553691i	$-0.998238\pi$
$241$		−	0.171912i		−	0.0110738i	0.999985	−	0.00553691i	$-0.00176246\pi$
$242$	−5.07835	+	5.07835i	−0.326449	+	0.326449i
$243$		0			0
$244$	−13.5341			−0.866433
$245$	−12.2761	−	9.71064i	−0.784294	−	0.620390i
$246$		0			0
$247$	3.01868	−	3.01868i	0.192074	−	0.192074i
$248$	−12.7761	+	12.7761i	−0.811281	+	0.811281i
$249$		0			0
$250$	4.71263	−	6.65621i	0.298053	−	0.420976i
$251$			1.51393i			0.0955582i	0.998858	+	0.0477791i	$0.0152144\pi$
$251$			1.51393i			0.0955582i	−0.998858	+	0.0477791i	$0.984786\pi$
$252$		0			0
$253$	−0.591609	−	0.591609i	−0.0371942	−	0.0371942i
$254$		−	7.51651i		−	0.471628i
$255$		0			0
$256$	−11.6095			−0.725593
$257$	−17.7332	−	17.7332i	−1.10616	−	1.10616i	−0.993650	−	0.112514i	$-0.964110\pi$
$257$	−17.7332	−	17.7332i	−1.10616	−	1.10616i	−0.112514	−	0.993650i	$-0.535890\pi$
$258$		0			0
$259$	19.9095	+	2.01854i	1.23712	+	0.125426i
$260$	13.9973	−	4.61122i	0.868076	−	0.285976i
$261$		0			0
$262$	−1.78108	−	1.78108i	−0.110035	−	0.110035i
$263$	5.50609	+	5.50609i	0.339520	+	0.339520i	0.856187	−	0.516666i	$-0.172827\pi$
$263$	5.50609	+	5.50609i	0.339520	+	0.339520i	−0.516666	+	0.856187i	$0.672827\pi$
$264$		0			0
$265$	−23.4715	+	7.73237i	−1.44184	+	0.474995i
$266$	−1.82567	−	0.185097i	−0.111939	−	0.0113490i
$267$		0			0
$268$	−8.72498	−	8.72498i	−0.532963	−	0.532963i
$269$	−1.66587			−0.101570			−0.0507848	−	0.998710i	$-0.516172\pi$
$269$	−1.66587			−0.101570			−0.0507848	+	0.998710i	$0.516172\pi$
$270$		0			0
$271$		−	22.3853i		−	1.35981i	−0.733301	−	0.679905i	$-0.762021\pi$
$271$		−	22.3853i		−	1.35981i	0.733301	−	0.679905i	$-0.237979\pi$
$272$	3.98599	+	3.98599i	0.241686	+	0.241686i
$273$		0			0
$274$			1.87885i			0.113505i
$275$	−3.19322	−	4.32050i	−0.192558	−	0.260536i
$276$		0			0
$277$	−4.20818	+	4.20818i	−0.252845	+	0.252845i	−0.822136	−	0.569291i	$-0.807218\pi$
$277$	−4.20818	+	4.20818i	−0.252845	+	0.252845i	0.569291	+	0.822136i	$0.307218\pi$
$278$	9.86420	−	9.86420i	0.591616	−	0.591616i
$279$		0			0
$280$	−12.6143	−	8.05333i	−0.753846	−	0.481279i
$281$	20.7722			1.23916			0.619582	−	0.784932i	$-0.287302\pi$
$281$	20.7722			1.23916			0.619582	+	0.784932i	$0.287302\pi$
$282$		0			0
$283$	12.3187	−	12.3187i	0.732269	−	0.732269i	−0.238800	−	0.971069i	$-0.576754\pi$
$283$	12.3187	−	12.3187i	0.732269	−	0.732269i	0.971069	+	0.238800i	$0.0767540\pi$
$284$			5.75393i			0.341433i
$285$		0			0
$286$			3.51921i			0.208095i
$287$	2.97745	−	2.42928i	0.175753	−	0.143396i
$288$		0			0
$289$			9.72229i			0.571900i
$290$	11.7790	−	3.88045i	0.691689	−	0.227868i
$291$		0			0
$292$	−5.29376	−	5.29376i	−0.309794	−	0.309794i
$293$	−0.185430	+	0.185430i	−0.0108329	+	0.0108329i	−0.712503	−	0.701670i	$-0.752438\pi$
$293$	−0.185430	+	0.185430i	−0.0108329	+	0.0108329i	0.701670	+	0.712503i	$0.252438\pi$
$294$		0			0
$295$	4.91105	−	9.73648i	0.285932	−	0.566880i
$296$	19.1337			1.11213
$297$		0			0
$298$	−1.60215	−	1.60215i	−0.0928098	−	0.0928098i
$299$	3.49612			0.202186
$300$		0			0
$301$	−2.25871	+	22.2784i	−0.130190	+	1.28411i
$302$	−8.68669	+	8.68669i	−0.499863	+	0.499863i
$303$		0			0
$304$	1.03683			0.0594663
$305$	−18.4078	−	9.28482i	−1.05403	−	0.531647i
$306$		0			0
$307$	10.9951	+	10.9951i	0.627524	+	0.627524i	0.947444	−	0.319921i	$-0.103656\pi$
$307$	10.9951	+	10.9951i	0.627524	+	0.627524i	−0.319921	+	0.947444i	$0.603656\pi$
$308$	−3.23332	+	2.63805i	−0.184236	+	0.150317i
$309$		0			0
$310$	−11.0652	+	3.64528i	−0.628460	+	0.207038i
$311$			25.4721i			1.44439i	0.691691	+	0.722194i	$0.256866\pi$
$311$			25.4721i			1.44439i	−0.691691	+	0.722194i	$0.743134\pi$
$312$		0			0
$313$	−2.70334	+	2.70334i	−0.152802	+	0.152802i	−0.779368	−	0.626566i	$-0.784460\pi$
$313$	−2.70334	+	2.70334i	−0.152802	+	0.152802i	0.626566	+	0.779368i	$0.284460\pi$
$314$	1.64808			0.0930067
$315$		0			0
$316$	3.34283			0.188049
$317$	−6.39377	+	6.39377i	−0.359110	+	0.359110i	−0.863485	−	0.504375i	$-0.831723\pi$
$317$	−6.39377	+	6.39377i	−0.359110	+	0.359110i	0.504375	+	0.863485i	$0.331723\pi$
$318$		0			0
$319$		−	8.16959i		−	0.457409i
$320$	−4.17247	−	2.10458i	−0.233248	−	0.117650i
$321$		0			0
$322$	−0.950025	−	1.16440i	−0.0529428	−	0.0648893i
$323$	3.47548	+	3.47548i	0.193381	+	0.193381i
$324$		0			0
$325$	22.2012	+	3.33085i	1.23150	+	0.184762i
$326$	9.68902			0.536625
$327$		0			0
$328$	2.59802	−	2.59802i	0.143452	−	0.143452i
$329$	−0.476388	+	4.69877i	−0.0262641	+	0.259051i
$330$		0			0
$331$	19.8595			1.09157			0.545787	−	0.837924i	$-0.316231\pi$
$331$	19.8595			1.09157			0.545787	+	0.837924i	$0.316231\pi$
$332$	3.58190	+	3.58190i	0.196582	+	0.196582i
$333$		0			0
$334$	−3.03394			−0.166010
$335$	−5.88125	−	17.8525i	−0.321327	−	0.975384i
$336$		0			0
$337$	20.0771	−	20.0771i	1.09367	−	1.09367i	0.0985342	−	0.995134i	$-0.468585\pi$
$337$	20.0771	−	20.0771i	1.09367	−	1.09367i	0.995134	−	0.0985342i	$-0.0314154\pi$
$338$	−3.69292	−	3.69292i	−0.200868	−	0.200868i
$339$		0			0
$340$	5.30901	+	16.1154i	0.287921	+	0.873981i
$341$			7.67448i			0.415596i
$342$		0			0
$343$	−16.4079	+	8.58965i	−0.885941	+	0.463798i
$344$			21.4103i			1.15437i
$345$		0			0
$346$			16.1235i			0.866805i
$347$	−3.29885	+	3.29885i	−0.177092	+	0.177092i	−0.790087	−	0.612995i	$-0.789965\pi$
$347$	−3.29885	+	3.29885i	−0.177092	+	0.177092i	0.612995	+	0.790087i	$0.289965\pi$
$348$		0			0
$349$	−4.24473			−0.227215			−0.113608	−	0.993526i	$-0.536241\pi$
$349$	−4.24473			−0.227215			−0.113608	+	0.993526i	$0.536241\pi$
$350$	−4.92353	−	8.29930i	−0.263174	−	0.443616i
$351$		0			0
$352$	−4.44838	+	4.44838i	−0.237100	+	0.237100i
$353$	9.31929	−	9.31929i	0.496016	−	0.496016i	−0.414179	−	0.910195i	$-0.635931\pi$
$353$	9.31929	−	9.31929i	0.496016	−	0.496016i	0.910195	+	0.414179i	$0.135931\pi$
$354$		0			0
$355$	−3.94737	+	7.82593i	−0.209505	+	0.415357i
$356$			12.4752i			0.661184i
$357$		0			0
$358$	5.09989	+	5.09989i	0.269537	+	0.269537i
$359$		−	13.7271i		−	0.724487i	−0.932084	−	0.362243i	$-0.882011\pi$
$359$		−	13.7271i		−	0.724487i	0.932084	−	0.362243i	$-0.117989\pi$
$360$		0			0
$361$	−18.0960			−0.952419
$362$	−8.60632	−	8.60632i	−0.452338	−	0.452338i
$363$		0			0
$364$	1.75889	−	17.3485i	0.0921907	−	0.909307i
$365$	−3.56837	−	10.8317i	−0.186777	−	0.566958i
$366$		0			0
$367$	−8.05073	−	8.05073i	−0.420244	−	0.420244i	0.465043	−	0.885288i	$-0.346039\pi$
$367$	−8.05073	−	8.05073i	−0.420244	−	0.420244i	−0.885288	+	0.465043i	$0.846039\pi$
$368$	0.600408	+	0.600408i	0.0312984	+	0.0312984i
$369$		0			0
$370$	11.0154	+	5.55611i	0.572661	+	0.288848i
$371$	−2.94940	+	29.0909i	−0.153125	+	1.51033i
$372$		0			0
$373$	22.8810	+	22.8810i	1.18473	+	1.18473i	0.978504	+	0.206228i	$0.0661187\pi$
$373$	22.8810	+	22.8810i	1.18473	+	1.18473i	0.206228	+	0.978504i	$0.433881\pi$
$374$	−4.05174			−0.209510
$375$		0			0
$376$			4.51567i			0.232878i
$377$	24.1391	+	24.1391i	1.24323	+	1.24323i
$378$		0			0
$379$		−	9.43826i		−	0.484811i	−0.970175	−	0.242405i	$-0.922064\pi$
$379$		−	9.43826i		−	0.484811i	0.970175	−	0.242405i	$-0.0779364\pi$
$380$	2.78644	+	1.40547i	0.142941	+	0.0720992i
$381$		0			0
$382$	0.0447200	−	0.0447200i	0.00228807	−	0.00228807i
$383$	19.4451	−	19.4451i	0.993597	−	0.993597i	−0.00638217	−	0.999980i	$-0.502032\pi$
$383$	19.4451	−	19.4451i	0.993597	−	0.993597i	0.999980	+	0.00638217i	$0.00203152\pi$
$384$		0			0
$385$	−6.20743	+	1.36986i	−0.316360	+	0.0698143i
$386$	−6.48821			−0.330241
$387$		0			0
$388$	−13.4939	+	13.4939i	−0.685049	+	0.685049i
$389$		−	13.0323i		−	0.660764i	−0.943847	−	0.330382i	$-0.892822\pi$
$389$		−	13.0323i		−	0.660764i	0.943847	−	0.330382i	$-0.107178\pi$
$390$		0			0
$391$			4.02516i			0.203561i
$392$	−14.7796	+	9.75338i	−0.746484	+	0.492620i
$393$		0			0
$394$			15.4418i			0.777945i
$395$	4.54658	+	2.29328i	0.228763	+	0.115388i
$396$		0			0
$397$	13.6492	+	13.6492i	0.685031	+	0.685031i	0.961129	−	0.276098i	$-0.0890415\pi$
$397$	13.6492	+	13.6492i	0.685031	+	0.685031i	−0.276098	+	0.961129i	$0.589041\pi$
$398$	3.41080	−	3.41080i	0.170968	−	0.170968i
$399$		0			0
$400$	3.24071	+	4.38476i	0.162035	+	0.219238i
$401$	−14.8083			−0.739493			−0.369746	−	0.929133i	$-0.620555\pi$
$401$	−14.8083			−0.739493			−0.369746	+	0.929133i	$0.620555\pi$
$402$		0			0
$403$	−22.6762	−	22.6762i	−1.12958	−	1.12958i
$404$	22.7669			1.13269
$405$		0			0
$406$	1.48014	−	14.5991i	0.0734582	−	0.724542i
$407$	5.74674	−	5.74674i	0.284855	−	0.284855i
$408$		0			0
$409$	−8.50808			−0.420698			−0.210349	−	0.977626i	$-0.567460\pi$
$409$	−8.50808			−0.420698			−0.210349	+	0.977626i	$0.567460\pi$
$410$	2.25011	−	0.741269i	0.111125	−	0.0366087i
$411$		0			0
$412$	14.3658	+	14.3658i	0.707752	+	0.707752i
$413$	−8.15689	−	9.99748i	−0.401374	−	0.491944i
$414$		0			0
$415$	2.41445	+	7.32904i	0.118521	+	0.359768i
$416$		−	26.2878i		−	1.28886i
$417$		0			0
$418$	−0.526966	+	0.526966i	−0.0257747	+	0.0257747i
$419$	−25.1222			−1.22730			−0.613649	−	0.789579i	$-0.710299\pi$
$419$	−25.1222			−1.22730			−0.613649	+	0.789579i	$0.710299\pi$
$420$		0			0
$421$	28.6936			1.39844			0.699221	−	0.714905i	$-0.253530\pi$
$421$	28.6936			1.39844			0.699221	+	0.714905i	$0.253530\pi$
$422$	13.2788	−	13.2788i	0.646402	−	0.646402i
$423$		0			0
$424$			27.9573i			1.35773i
$425$	−3.83488	+	25.5607i	−0.186019	+	1.23988i
$426$		0			0
$427$	−18.9012	+	15.4214i	−0.914694	+	0.746293i
$428$	−19.5665	−	19.5665i	−0.945784	−	0.945784i
$429$		0			0
$430$	−6.21719	+	12.3260i	−0.299819	+	0.594412i
$431$	−28.0055			−1.34898			−0.674489	−	0.738285i	$-0.735636\pi$
$431$	−28.0055			−1.34898			−0.674489	+	0.738285i	$0.735636\pi$
$432$		0			0
$433$	−21.9514	+	21.9514i	−1.05492	+	1.05492i	−0.0565169	+	0.998402i	$0.517999\pi$
$433$	−21.9514	+	21.9514i	−1.05492	+	1.05492i	−0.998402	+	0.0565169i	$0.982001\pi$
$434$	−1.39044	+	13.7144i	−0.0667432	+	0.658310i
$435$		0			0
$436$	7.48302			0.358372
$437$	0.523509	+	0.523509i	0.0250428	+	0.0250428i
$438$		0			0
$439$	−20.1967			−0.963934			−0.481967	−	0.876189i	$-0.660077\pi$
$439$	−20.1967			−0.963934			−0.481967	+	0.876189i	$0.660077\pi$
$440$	−5.77273	+	1.90175i	−0.275204	+	0.0906623i
$441$		0			0
$442$	11.9719	−	11.9719i	0.569445	−	0.569445i
$443$	26.4101	+	26.4101i	1.25478	+	1.25478i	0.953552	+	0.301227i	$0.0973962\pi$
$443$	26.4101	+	26.4101i	1.25478	+	1.25478i	0.301227	+	0.953552i	$0.402604\pi$
$444$		0			0
$445$	−8.55836	+	16.9675i	−0.405705	+	0.804337i
$446$		−	15.3432i		−	0.726523i
$447$		0			0
$448$	−4.28432	+	3.49555i	−0.202415	+	0.165149i
$449$		−	39.1278i		−	1.84655i	−0.384135	−	0.923277i	$-0.625500\pi$
$449$		−	39.1278i		−	1.84655i	0.384135	−	0.923277i	$-0.374500\pi$
$450$		0			0
$451$		−	1.56061i		−	0.0734863i
$452$	−20.1120	+	20.1120i	−0.945987	+	0.945987i
$453$		0			0
$454$	9.71258			0.455834
$455$	14.2938	−	22.3890i	0.670106	−	1.04961i
$456$		0			0
$457$	−20.2402	+	20.2402i	−0.946798	+	0.946798i	−0.998655	−	0.0518567i	$-0.983486\pi$
$457$	−20.2402	+	20.2402i	−0.946798	+	0.946798i	0.0518567	+	0.998655i	$0.483486\pi$
$458$	0.852314	−	0.852314i	0.0398260	−	0.0398260i
$459$		0			0
$460$	0.799693	+	2.42746i	0.0372859	+	0.113181i
$461$		−	10.2596i		−	0.477835i	−0.971040	−	0.238918i	$-0.923207\pi$
$461$		−	10.2596i		−	0.477835i	0.971040	−	0.238918i	$-0.0767926\pi$
$462$		0			0
$463$	−16.1778	−	16.1778i	−0.751845	−	0.751845i	0.222978	−	0.974823i	$-0.428422\pi$
$463$	−16.1778	−	16.1778i	−0.751845	−	0.751845i	−0.974823	+	0.222978i	$0.928422\pi$
$464$			8.29109i			0.384904i
$465$		0			0
$466$	4.93818			0.228757
$467$	−14.9066	−	14.9066i	−0.689793	−	0.689793i	0.272393	−	0.962186i	$-0.412185\pi$
$467$	−14.9066	−	14.9066i	−0.689793	−	0.689793i	−0.962186	+	0.272393i	$0.912185\pi$
$468$		0			0
$469$	−22.1266	−	2.24332i	−1.02171	−	0.103587i
$470$	−1.31127	+	2.59969i	−0.0604846	+	0.119915i
$471$		0			0
$472$	−8.72347	−	8.72347i	−0.401530	−	0.401530i
$473$	6.43050	+	6.43050i	0.295675	+	0.295675i
$474$		0			0
$475$	2.82564	+	3.82317i	0.129649	+	0.175419i
$476$	19.9737	+	2.02505i	0.915492	+	0.0928178i
$477$		0			0
$478$	−6.14260	−	6.14260i	−0.280956	−	0.280956i
$479$	20.4394			0.933898			0.466949	−	0.884284i	$-0.345353\pi$
$479$	20.4394			0.933898			0.466949	+	0.884284i	$0.345353\pi$
$480$		0			0
$481$			33.9604i			1.54846i
$482$	−0.0886732	−	0.0886732i	−0.00403895	−	0.00403895i
$483$		0			0
$484$		−	14.4520i		−	0.656911i
$485$	−27.6103	+	9.09585i	−1.25372	+	0.413021i
$486$		0			0
$487$	5.12783	−	5.12783i	0.232364	−	0.232364i	−0.581315	−	0.813679i	$-0.697461\pi$
$487$	5.12783	−	5.12783i	0.232364	−	0.232364i	0.813679	+	0.581315i	$0.197461\pi$
$488$	−16.4926	+	16.4926i	−0.746584	+	0.746584i
$489$		0			0
$490$	−11.3409	+	1.32330i	−0.512330	+	0.0597806i
$491$	21.3063			0.961539			0.480770	−	0.876847i	$-0.340357\pi$
$491$	21.3063			0.961539			0.480770	+	0.876847i	$0.340357\pi$
$492$		0			0
$493$	−27.7919	+	27.7919i	−1.25169	+	1.25169i
$494$		−	3.11411i		−	0.140110i
$495$		0			0
$496$		−	7.78862i		−	0.349719i
$497$	6.55629	+	8.03571i	0.294090	+	0.360451i
$498$		0			0
$499$		−	23.2516i		−	1.04089i	−0.853896	−	0.520443i	$-0.825767\pi$
$499$		−	23.2516i		−	1.04089i	0.853896	−	0.520443i	$-0.174233\pi$
$500$	2.76553	+	16.1768i	0.123678	+	0.723448i
$501$		0			0
$502$	0.780893	+	0.780893i	0.0348530	+	0.0348530i
$503$	7.88213	−	7.88213i	0.351447	−	0.351447i	−0.509201	−	0.860648i	$-0.670059\pi$
$503$	7.88213	−	7.88213i	0.351447	−	0.351447i	0.860648	+	0.509201i	$0.170059\pi$
$504$		0			0
$505$	30.9652	+	15.6188i	1.37793	+	0.695026i
$506$	−0.610311			−0.0271317
$507$		0			0
$508$	10.6953	+	10.6953i	0.474527	+	0.474527i
$509$	34.1089			1.51185			0.755924	−	0.654659i	$-0.227188\pi$
$509$	34.1089			1.51185			0.755924	+	0.654659i	$0.227188\pi$
$510$		0			0
$511$	−13.4250	−	1.36110i	−0.593887	−	0.0602116i
$512$	8.41573	−	8.41573i	0.371926	−	0.371926i
$513$		0			0
$514$	−18.2937			−0.806902
$515$	9.68356	+	29.3943i	0.426709	+	1.29527i
$516$		0			0
$517$	1.35626	+	1.35626i	0.0596484	+	0.0596484i
$518$	11.3106	−	9.22829i	0.496961	−	0.405468i
$519$		0			0
$520$	11.4378	−	22.6762i	0.501581	−	0.994418i
$521$		−	22.5674i		−	0.988696i	−0.869264	−	0.494348i	$-0.835407\pi$
$521$		−	22.5674i		−	0.988696i	0.869264	−	0.494348i	$-0.164593\pi$
$522$		0			0
$523$	−2.57446	+	2.57446i	−0.112573	+	0.112573i	−0.761150	−	0.648576i	$-0.775365\pi$
$523$	−2.57446	+	2.57446i	−0.112573	+	0.112573i	0.648576	+	0.761150i	$0.275365\pi$
$524$	5.06862			0.221424
$525$		0			0
$526$	5.68015			0.247666
$527$	26.1076	−	26.1076i	1.13727	−	1.13727i
$528$		0			0
$529$		−	22.3937i		−	0.973639i
$530$	−8.11833	+	16.0951i	−0.352638	+	0.699128i
$531$		0			0
$532$	2.86114	−	2.33438i	0.124046	−	0.101208i
$533$	4.61122	+	4.61122i	0.199734	+	0.199734i
$534$		0			0
$535$	−13.1892	−	40.0357i	−0.570220	−	1.73089i
$536$	−21.2644			−0.918482
$537$		0			0
$538$	−0.859263	+	0.859263i	−0.0370455	+	0.0370455i
$539$	−1.50962	+	7.36839i	−0.0650238	+	0.317379i
$540$		0			0
$541$	1.84893			0.0794915			0.0397458	−	0.999210i	$-0.487345\pi$
$541$	1.84893			0.0794915			0.0397458	+	0.999210i	$0.487345\pi$
$542$	−11.5465	−	11.5465i	−0.495963	−	0.495963i
$543$		0			0
$544$	30.2657			1.29763
$545$	10.1777	+	5.13358i	0.435963	+	0.219898i
$546$		0			0
$547$	−18.9146	+	18.9146i	−0.808729	+	0.808729i	−0.984442	−	0.175712i	$-0.943777\pi$
$547$	−18.9146	+	18.9146i	−0.808729	+	0.808729i	0.175712	+	0.984442i	$0.443777\pi$
$548$	−2.67342	−	2.67342i	−0.114203	−	0.114203i
$549$		0			0
$550$	−3.87562	−	0.581460i	−0.165257	−	0.0247935i
$551$			7.22919i			0.307974i
$552$		0			0
$553$	4.66846	−	3.80897i	0.198523	−	0.161974i
$554$			4.34121i			0.184441i
$555$		0			0
$556$			28.0717i			1.19050i
$557$	20.3600	−	20.3600i	0.862681	−	0.862681i	−0.128968	−	0.991649i	$-0.541166\pi$
$557$	20.3600	−	20.3600i	0.862681	−	0.862681i	0.991649	+	0.128968i	$0.0411665\pi$
$558$		0			0
$559$	−38.0011			−1.60727
$560$	6.29975	−	1.39023i	0.266213	−	0.0587479i
$561$		0			0
$562$	10.7144	−	10.7144i	0.451960	−	0.451960i
$563$	−30.5621	+	30.5621i	−1.28804	+	1.28804i	−0.352064	+	0.935976i	$0.614520\pi$
$563$	−30.5621	+	30.5621i	−1.28804	+	1.28804i	−0.935976	+	0.352064i	$0.885480\pi$
$564$		0			0
$565$	−41.1517	+	13.5569i	−1.73127	+	0.570342i
$566$		−	12.7081i		−	0.534161i
$567$		0			0
$568$	7.01170	+	7.01170i	0.294204	+	0.294204i
$569$			12.3043i			0.515825i	0.966168	+	0.257913i	$0.0830346\pi$
$569$			12.3043i			0.515825i	−0.966168	+	0.257913i	$0.916965\pi$
$570$		0			0
$571$	−6.55763			−0.274428			−0.137214	−	0.990541i	$-0.543815\pi$
$571$	−6.55763			−0.274428			−0.137214	+	0.990541i	$0.543815\pi$
$572$	−5.00750	−	5.00750i	−0.209374	−	0.209374i
$573$		0			0
$574$	0.282747	−	2.78882i	0.0118016	−	0.116403i
$575$	−0.577646	+	3.85020i	−0.0240895	+	0.160564i
$576$		0			0
$577$	3.42206	+	3.42206i	0.142462	+	0.142462i	0.774741	−	0.632279i	$-0.217880\pi$
$577$	3.42206	+	3.42206i	0.142462	+	0.142462i	−0.632279	+	0.774741i	$0.717880\pi$
$578$	5.01482	+	5.01482i	0.208589	+	0.208589i
$579$		0			0
$580$	−11.2390	+	22.2820i	−0.466673	+	0.925210i
$581$	9.08372	+	0.920959i	0.376856	+	0.0382078i
$582$		0			0
$583$	8.39687	+	8.39687i	0.347763	+	0.347763i
$584$	−12.9019			−0.533883
$585$		0			0
$586$			0.191292i			0.00790220i
$587$	5.94595	+	5.94595i	0.245416	+	0.245416i	0.819086	−	0.573670i	$-0.194481\pi$
$587$	5.94595	+	5.94595i	0.245416	+	0.245416i	−0.573670	+	0.819086i	$0.694481\pi$
$588$		0			0
$589$		−	6.79107i		−	0.279821i
$590$	−2.48899	−	7.55528i	−0.102470	−	0.311046i
$591$		0			0
$592$	−5.83221	+	5.83221i	−0.239702	+	0.239702i
$593$	−22.2121	+	22.2121i	−0.912140	+	0.912140i	−0.996440	−	0.0843004i	$-0.973134\pi$
$593$	−22.2121	+	22.2121i	−0.912140	+	0.912140i	0.0843004	+	0.996440i	$0.473134\pi$
$594$		0			0
$595$	25.7770	+	16.4568i	1.05675	+	0.674664i
$596$	4.55941			0.186761
$597$		0			0
$598$	1.80332	−	1.80332i	0.0737433	−	0.0737433i
$599$		−	32.8825i		−	1.34354i	−0.740759	−	0.671771i	$-0.765534\pi$
$599$		−	32.8825i		−	1.34354i	0.740759	−	0.671771i	$-0.234466\pi$
$600$		0			0
$601$			0.254300i			0.0103731i	0.999987	+	0.00518656i	$0.00165094\pi$
$601$			0.254300i			0.0103731i	−0.999987	+	0.00518656i	$0.998349\pi$
$602$	10.3263	+	12.6564i	0.420868	+	0.515837i
$603$		0			0
$604$		−	24.7207i		−	1.00587i
$605$	9.91454	−	19.6562i	0.403084	−	0.799140i
$606$		0			0
$607$	−2.73951	−	2.73951i	−0.111193	−	0.111193i	0.649321	−	0.760514i	$-0.275053\pi$
$607$	−2.73951	−	2.73951i	−0.111193	−	0.111193i	−0.760514	+	0.649321i	$0.775053\pi$
$608$	3.93633	−	3.93633i	0.159639	−	0.159639i
$609$		0			0
$610$	−14.2840	+	4.70567i	−0.578342	+	0.190527i
$611$	−8.01485			−0.324246
$612$		0			0
$613$	−9.19075	−	9.19075i	−0.371211	−	0.371211i	0.496707	−	0.867918i	$-0.334542\pi$
$613$	−9.19075	−	9.19075i	−0.371211	−	0.371211i	−0.867918	+	0.496707i	$0.834542\pi$
$614$	11.3427			0.457753
$615$		0			0
$616$	−0.725395	+	7.15481i	−0.0292270	+	0.288276i
$617$	−4.09441	+	4.09441i	−0.164835	+	0.164835i	−0.784705	−	0.619870i	$-0.787185\pi$
$617$	−4.09441	+	4.09441i	−0.164835	+	0.164835i	0.619870	+	0.784705i	$0.287185\pi$
$618$		0			0
$619$	30.9788			1.24514			0.622571	−	0.782563i	$-0.286088\pi$
$619$	30.9788			1.24514			0.622571	+	0.782563i	$0.286088\pi$
$620$	10.5578	−	20.9316i	0.424013	−	0.840634i
$621$		0			0
$622$	13.1386	+	13.1386i	0.526811	+	0.526811i
$623$	14.2148	+	17.4224i	0.569504	+	0.698012i
$624$		0			0
$625$	−7.33637	+	23.8993i	−0.293455	+	0.955973i
$626$			2.78879i			0.111463i
$627$		0			0
$628$	−2.34507	+	2.34507i	−0.0935784	+	0.0935784i
$629$	−39.0994			−1.55899
$630$		0			0
$631$	−10.4715			−0.416865			−0.208432	−	0.978037i	$-0.566836\pi$
$631$	−10.4715			−0.416865			−0.208432	+	0.978037i	$0.566836\pi$
$632$	4.07355	−	4.07355i	0.162037	−	0.162037i
$633$		0			0
$634$			6.59589i			0.261956i
$635$	7.20938	+	21.8840i	0.286096	+	0.868439i
$636$		0			0
$637$	−17.3113	−	26.2323i	−0.685897	−	1.03936i
$638$	−4.21392	−	4.21392i	−0.166831	−	0.166831i
$639$		0			0
$640$	21.6311	−	7.12608i	0.855045	−	0.281683i
$641$	−41.8992			−1.65492			−0.827459	−	0.561527i	$-0.810214\pi$
$641$	−41.8992			−1.65492			−0.827459	+	0.561527i	$0.810214\pi$
$642$		0			0
$643$	27.5315	−	27.5315i	1.08574	−	1.08574i	0.0897745	−	0.995962i	$-0.471385\pi$
$643$	27.5315	−	27.5315i	1.08574	−	1.08574i	0.995962	−	0.0897745i	$-0.0286146\pi$
$644$	3.00863	+	0.305032i	0.118556	+	0.0120199i
$645$		0			0
$646$	3.58534			0.141064
$647$	−9.26659	−	9.26659i	−0.364307	−	0.364307i	0.501089	−	0.865396i	$-0.332933\pi$
$647$	−9.26659	−	9.26659i	−0.364307	−	0.364307i	−0.865396	+	0.501089i	$0.832933\pi$
$648$		0			0
$649$	−5.24012			−0.205693
$650$	13.1696	−	9.73344i	0.516554	−	0.381777i
$651$		0			0
$652$	−13.7866	+	13.7866i	−0.539924	+	0.539924i
$653$	29.3099	+	29.3099i	1.14698	+	1.14698i	0.987143	+	0.159841i	$0.0510981\pi$
$653$	29.3099	+	29.3099i	1.14698	+	1.14698i	0.159841	+	0.987143i	$0.448902\pi$
$654$		0			0
$655$	6.89383	+	3.47723i	0.269364	+	0.135866i
$656$			1.58382i			0.0618378i
$657$		0			0
$658$	2.17793	+	2.66938i	0.0849045	+	0.104063i
$659$			46.3588i			1.80588i	0.429763	+	0.902942i	$0.358597\pi$
$659$			46.3588i			1.80588i	−0.429763	+	0.902942i	$0.641403\pi$
$660$		0			0
$661$			27.5493i			1.07155i	0.844362	+	0.535773i	$0.179980\pi$
$661$			27.5493i			1.07155i	−0.844362	+	0.535773i	$0.820020\pi$
$662$	10.2436	−	10.2436i	0.398130	−	0.398130i
$663$		0			0
$664$	8.72975			0.338780
$665$	5.49289	−	1.21217i	0.213005	−	0.0470060i
$666$		0			0
$667$	−4.18628	+	4.18628i	−0.162094	+	0.162094i
$668$	4.31702	−	4.31702i	0.167031	−	0.167031i
$669$		0			0
$670$	−12.2420	−	6.17482i	−0.472949	−	0.238554i
$671$			9.90695i			0.382454i
$672$		0			0
$673$	20.9275	+	20.9275i	0.806695	+	0.806695i	0.984132	−	0.177437i	$-0.0567806\pi$
$673$	20.9275	+	20.9275i	0.806695	+	0.806695i	−0.177437	+	0.984132i	$0.556781\pi$
$674$		−	20.7118i		−	0.797787i
$675$		0			0
$676$	10.5094			0.404206
$677$	12.5025	+	12.5025i	0.480508	+	0.480508i	0.905294	−	0.424786i	$-0.139651\pi$
$677$	12.5025	+	12.5025i	0.480508	+	0.480508i	−0.424786	+	0.905294i	$0.639651\pi$
$678$		0			0
$679$	−3.46948	+	34.2206i	−0.133147	+	1.31327i
$680$	26.1076	+	13.1686i	1.00118	+	0.504993i
$681$		0			0
$682$	3.95854	+	3.95854i	0.151580	+	0.151580i
$683$	−21.1425	−	21.1425i	−0.808995	−	0.808995i	0.175487	−	0.984482i	$-0.443850\pi$
$683$	−21.1425	−	21.1425i	−0.808995	−	0.808995i	−0.984482	+	0.175487i	$0.943850\pi$
$684$		0			0
$685$	−1.80208	−	5.47018i	−0.0688538	−	0.209005i
$686$	−4.03268	+	12.8939i	−0.153968	+	0.492290i
$687$		0			0
$688$	−6.52613	−	6.52613i	−0.248806	−	0.248806i
$689$	−49.6214			−1.89042
$690$		0			0
$691$		−	27.8769i		−	1.06049i	−0.847846	−	0.530243i	$-0.822101\pi$
$691$		−	27.8769i		−	1.06049i	0.847846	−	0.530243i	$-0.177899\pi$
$692$	−22.9423	−	22.9423i	−0.872134	−	0.872134i
$693$		0			0
$694$			3.40314i			0.129181i
$695$	−19.2580	+	38.1803i	−0.730499	+	1.44826i
$696$		0			0
$697$	−5.30901	+	5.30901i	−0.201093	+	0.201093i
$698$	−2.18946	+	2.18946i	−0.0828722	+	0.0828722i
$699$		0			0
$700$	18.8149	+	4.80342i	0.711135	+	0.181552i
$701$	−50.4143			−1.90412			−0.952061	−	0.305907i	$-0.901040\pi$
$701$	−50.4143			−1.90412			−0.952061	+	0.305907i	$0.901040\pi$
$702$		0			0
$703$	−5.08523	+	5.08523i	−0.191793	+	0.191793i
$704$			2.24560i			0.0846342i
$705$		0			0
$706$		−	9.61389i		−	0.361824i
$707$	31.7953	−	25.9416i	1.19578	−	0.975634i
$708$		0			0
$709$			7.54902i			0.283509i	0.989902	+	0.141755i	$0.0452744\pi$
$709$			7.54902i			0.283509i	−0.989902	+	0.141755i	$0.954726\pi$
$710$	2.00058	+	6.07274i	0.0750805	+	0.227906i
$711$		0			0
$712$	15.2022	+	15.2022i	0.569725	+	0.569725i
$713$	3.93258	−	3.93258i	0.147276	−	0.147276i
$714$		0			0
$715$	−3.37541	−	10.2460i	−0.126233	−	0.383179i
$716$	−14.5133			−0.542389
$717$		0			0
$718$	−7.08050	−	7.08050i	−0.264242	−	0.264242i
$719$	15.8665			0.591721			0.295861	−	0.955231i	$-0.404394\pi$
$719$	15.8665			0.591721			0.295861	+	0.955231i	$0.404394\pi$
$720$		0			0
$721$	36.4318	+	3.69366i	1.35679	+	0.137559i
$722$	−9.33401	+	9.33401i	−0.347376	+	0.347376i
$723$		0			0
$724$	24.4920			0.910237
$725$	−30.5723	+	22.5955i	−1.13543	+	0.839176i
$726$		0			0
$727$	−8.07498	−	8.07498i	−0.299484	−	0.299484i	0.541327	−	0.840812i	$-0.317922\pi$
$727$	−8.07498	−	8.07498i	−0.299484	−	0.299484i	−0.840812	+	0.541327i	$0.817922\pi$
$728$	−18.9974	−	23.2841i	−0.704089	−	0.862966i
$729$		0			0
$730$	−7.42765	−	3.74648i	−0.274910	−	0.138664i
$731$		−	43.7515i		−	1.61821i
$732$		0			0
$733$	0.0221320	−	0.0221320i	0.000817464	−	0.000817464i	−0.706698	−	0.707515i	$-0.749816\pi$
$733$	0.0221320	−	0.0221320i	0.000817464	−	0.000817464i	0.707515	+	0.706698i	$0.249816\pi$
$734$	−8.30523			−0.306551
$735$		0			0
$736$	4.55891			0.168044
$737$	−6.38667	+	6.38667i	−0.235256	+	0.235256i
$738$		0			0
$739$		−	23.3657i		−	0.859521i	−0.902943	−	0.429760i	$-0.858598\pi$
$739$		−	23.3657i		−	0.859521i	0.902943	−	0.429760i	$-0.141402\pi$
$740$	−23.5797	+	7.76800i	−0.866806	+	0.285557i
$741$		0			0
$742$	13.4840	+	16.5266i	0.495011	+	0.606710i
$743$	−9.83514	−	9.83514i	−0.360816	−	0.360816i	0.503297	−	0.864113i	$-0.332120\pi$
$743$	−9.83514	−	9.83514i	−0.360816	−	0.360816i	−0.864113	+	0.503297i	$0.832120\pi$
$744$		0			0
$745$	6.20126	+	3.12789i	0.227196	+	0.114597i
$746$	23.6043			0.864214
$747$		0			0
$748$	5.76525	−	5.76525i	0.210798	−	0.210798i
$749$	−49.6208	−	5.03084i	−1.81311	−	0.183823i
$750$		0			0
$751$	9.64570			0.351976			0.175988	−	0.984392i	$-0.443688\pi$
$751$	9.64570			0.351976			0.175988	+	0.984392i	$0.443688\pi$
$752$	−1.37643	−	1.37643i	−0.0501934	−	0.0501934i
$753$		0			0
$754$	24.9022			0.906886
$755$	16.9592	−	33.6227i	0.617207	−	1.22365i
$756$		0			0
$757$	17.0929	−	17.0929i	0.621253	−	0.621253i	−0.324599	−	0.945852i	$-0.605229\pi$
$757$	17.0929	−	17.0929i	0.621253	−	0.621253i	0.945852	+	0.324599i	$0.105229\pi$
$758$	−4.86831	−	4.86831i	−0.176825	−	0.176825i
$759$		0			0
$760$	5.10823	−	1.68284i	0.185295	−	0.0610430i
$761$		−	50.8870i		−	1.84465i	−0.386412	−	0.922326i	$-0.626286\pi$
$761$		−	50.8870i		−	1.84465i	0.386412	−	0.922326i	$-0.373714\pi$
$762$		0			0
$763$	10.4505	−	8.52650i	0.378333	−	0.308680i
$764$			0.127265i			0.00460428i
$765$		0			0
$766$		−	20.0598i		−	0.724789i
$767$	15.4833	−	15.4833i	0.559068	−	0.559068i
$768$		0			0
$769$	−29.2213			−1.05375			−0.526873	−	0.849944i	$-0.676636\pi$
$769$	−29.2213			−1.05375			−0.526873	+	0.849944i	$0.676636\pi$
$770$	−2.49525	+	3.90841i	−0.0899225	+	0.140849i
$771$		0			0
$772$	9.23212	−	9.23212i	0.332271	−	0.332271i
$773$	2.88171	−	2.88171i	0.103648	−	0.103648i	−0.653381	−	0.757029i	$-0.726650\pi$
$773$	2.88171	−	2.88171i	0.103648	−	0.103648i	0.757029	+	0.653381i	$0.226650\pi$
$774$		0			0
$775$	28.7195	−	21.2261i	1.03163	−	0.762465i
$776$			32.8872i			1.18058i
$777$		0			0
$778$	−6.72214	−	6.72214i	−0.241000	−	0.241000i
$779$			1.38097i			0.0494784i
$780$		0			0
$781$	4.21187			0.150713
$782$	2.07620	+	2.07620i	0.0742449	+	0.0742449i
$783$		0			0
$784$	1.53207	−	7.47798i	0.0547167	−	0.267071i
$785$	−4.79832	+	1.58074i	−0.171259	+	0.0564191i
$786$		0			0
$787$	−17.5018	−	17.5018i	−0.623873	−	0.623873i	0.322647	−	0.946519i	$-0.395427\pi$
$787$	−17.5018	−	17.5018i	−0.623873	−	0.623873i	−0.946519	+	0.322647i	$0.895427\pi$
$788$	−21.9722	−	21.9722i	−0.782727	−	0.782727i
$789$		0			0
$790$	3.52804	−	1.16227i	0.125522	−	0.0413516i
$791$	−5.17108	+	51.0041i	−0.183863	+	1.81350i
$792$		0			0
$793$	−29.2726	−	29.2726i	−1.03950	−	1.03950i
$794$	14.0806			0.499703
$795$		0			0
$796$			9.70651i			0.344038i
$797$	26.0052	+	26.0052i	0.921151	+	0.921151i	0.997111	−	0.0759597i	$-0.0242020\pi$
$797$	26.0052	+	26.0052i	0.921151	+	0.921151i	−0.0759597	+	0.997111i	$0.524202\pi$
$798$		0			0
$799$		−	9.22768i		−	0.326452i
$800$	28.9501	+	4.34339i	1.02354	+	0.153562i
$801$		0			0
$802$	−7.63822	+	7.63822i	−0.269715	+	0.269715i
$803$	−3.87502	+	3.87502i	−0.136747	+	0.136747i
$804$		0			0
$805$	3.88277	+	2.47888i	0.136850	+	0.0873691i
$806$	−23.3931			−0.823985
$807$		0			0
$808$	27.7435	−	27.7435i	0.976013	−	0.976013i
$809$			10.1068i			0.355337i	0.984090	+	0.177668i	$0.0568554\pi$
$809$			10.1068i			0.355337i	−0.984090	+	0.177668i	$0.943145\pi$
$810$		0			0
$811$		−	47.1825i		−	1.65680i	−0.560136	−	0.828401i	$-0.689251\pi$
$811$		−	47.1825i		−	1.65680i	0.560136	−	0.828401i	$-0.310749\pi$
$812$	18.6671	+	22.8793i	0.655086	+	0.802906i
$813$		0			0
$814$		−	5.92840i		−	0.207790i
$815$	−28.2091	+	9.29312i	−0.988123	+	0.325524i
$816$		0			0
$817$	−5.69028	−	5.69028i	−0.199078	−	0.199078i
$818$	−4.38852	+	4.38852i	−0.153441	+	0.153441i
$819$		0			0
$820$	−2.14694	+	4.25646i	−0.0749746	+	0.148642i
$821$	23.1645			0.808446			0.404223	−	0.914661i	$-0.367542\pi$
$821$	23.1645			0.808446			0.404223	+	0.914661i	$0.367542\pi$
$822$		0			0
$823$	2.84378	+	2.84378i	0.0991279	+	0.0991279i	0.754932	−	0.655804i	$-0.227670\pi$
$823$	2.84378	+	2.84378i	0.0991279	+	0.0991279i	−0.655804	+	0.754932i	$0.727670\pi$
$824$	35.0121			1.21971
$825$		0			0
$826$	−9.36413	−	0.949389i	−0.325820	−	0.0330335i
$827$	23.6696	−	23.6696i	0.823074	−	0.823074i	−0.163474	−	0.986548i	$-0.552270\pi$
$827$	23.6696	−	23.6696i	0.823074	−	0.823074i	0.986548	+	0.163474i	$0.0522699\pi$
$828$		0			0
$829$	−19.8787			−0.690415			−0.345207	−	0.938526i	$-0.612191\pi$
$829$	−19.8787			−0.690415			−0.345207	+	0.938526i	$0.612191\pi$
$830$	5.02575	+	2.53497i	0.174446	+	0.0879902i
$831$		0			0
$832$	−6.63520	−	6.63520i	−0.230034	−	0.230034i
$833$	30.2019	−	19.9308i	1.04643	−	0.690562i
$834$		0			0
$835$	8.83319	−	2.90998i	0.305685	−	0.100704i
$836$		−	1.49965i		−	0.0518664i
$837$		0			0
$838$	−12.9582	+	12.9582i	−0.447632	+	0.447632i
$839$	−33.0780			−1.14198			−0.570989	−	0.820958i	$-0.693440\pi$
$839$	−33.0780			−1.14198			−0.570989	+	0.820958i	$0.693440\pi$
$840$		0			0
$841$	−28.8088			−0.993406
$842$	14.8004	−	14.8004i	0.510054	−	0.510054i
$843$		0			0
$844$			37.7890i			1.30075i
$845$	14.2938	+	7.20974i	0.491721	+	0.248022i
$846$		0			0
$847$	−16.4673	−	20.1832i	−0.565824	−	0.693501i
$848$	−8.52175	−	8.52175i	−0.292638	−	0.292638i
$849$		0			0
$850$	11.2063	+	15.1624i	0.384374	+	0.520067i
$851$	−5.88952			−0.201890
$852$		0			0
$853$	16.6817	−	16.6817i	0.571171	−	0.571171i	−0.361285	−	0.932456i	$-0.617662\pi$
$853$	16.6817	−	16.6817i	0.571171	−	0.571171i	0.932456	+	0.361285i	$0.117662\pi$
$854$	−1.79491	+	17.7038i	−0.0614206	+	0.605812i
$855$		0			0
$856$	−47.6872			−1.62992
$857$	−24.8920	−	24.8920i	−0.850294	−	0.850294i	0.139875	−	0.990169i	$-0.455330\pi$
$857$	−24.8920	−	24.8920i	−0.850294	−	0.850294i	−0.990169	+	0.139875i	$0.955330\pi$
$858$		0			0
$859$	8.57133			0.292450			0.146225	−	0.989251i	$-0.453288\pi$
$859$	8.57133			0.292450			0.146225	+	0.989251i	$0.453288\pi$
$860$	−8.69226	−	26.3852i	−0.296403	−	0.899729i
$861$		0			0
$862$	−14.4454	+	14.4454i	−0.492012	+	0.492012i
$863$	−11.4706	−	11.4706i	−0.390464	−	0.390464i	0.484389	−	0.874853i	$-0.339042\pi$
$863$	−11.4706	−	11.4706i	−0.390464	−	0.390464i	−0.874853	+	0.484389i	$0.839042\pi$
$864$		0			0
$865$	−15.4647	−	46.9429i	−0.525816	−	1.59611i
$866$			22.6454i			0.769521i
$867$		0			0
$868$	−17.5358	−	21.4927i	−0.595204	−	0.729511i
$869$		−	2.44695i		−	0.0830069i
$870$		0			0
$871$		−	37.7421i		−	1.27884i
$872$	9.11875	−	9.11875i	0.308800	−	0.308800i
$873$		0			0
$874$	0.540059			0.0182678
$875$	22.2948	+	19.4407i	0.753702	+	0.657216i
$876$		0			0
$877$	14.1175	−	14.1175i	0.476713	−	0.476713i	−0.427366	−	0.904079i	$-0.640558\pi$
$877$	14.1175	−	14.1175i	0.476713	−	0.476713i	0.904079	+	0.427366i	$0.140558\pi$
$878$	−10.4176	+	10.4176i	−0.351575	+	0.351575i
$879$		0			0
$880$	1.17993	−	2.33928i	0.0397753	−	0.0788571i
$881$			35.8687i			1.20845i	0.796814	+	0.604224i	$0.206517\pi$
$881$			35.8687i			1.20845i	−0.796814	+	0.604224i	$0.793483\pi$
$882$		0			0
$883$	−1.76087	−	1.76087i	−0.0592578	−	0.0592578i	0.676857	−	0.736115i	$-0.263342\pi$
$883$	−1.76087	−	1.76087i	−0.0592578	−	0.0592578i	−0.736115	+	0.676857i	$0.763342\pi$
$884$			34.0698i			1.14589i
$885$		0			0
$886$	27.2449			0.915311
$887$	−21.3262	−	21.3262i	−0.716063	−	0.716063i	0.251733	−	0.967797i	$-0.418999\pi$
$887$	−21.3262	−	21.3262i	−0.716063	−	0.716063i	−0.967797	+	0.251733i	$0.918999\pi$
$888$		0			0
$889$	27.1233	+	2.74992i	0.909688	+	0.0922293i
$890$	4.33749	+	13.1664i	0.145393	+	0.441339i
$891$		0			0
$892$	21.8320	+	21.8320i	0.730989	+	0.730989i
$893$	−1.20014	−	1.20014i	−0.0401613	−	0.0401613i
$894$		0			0
$895$	−19.7396	−	9.95659i	−0.659822	−	0.332812i
$896$	2.71814	−	26.8099i	0.0908067	−	0.895657i
$897$		0			0
$898$	−20.1823	−	20.1823i	−0.673493	−	0.673493i
$899$	54.3053			1.81118
$900$		0			0
$901$		−	57.1302i		−	1.90328i
$902$	−0.804973	−	0.804973i	−0.0268027	−	0.0268027i
$903$		0			0
$904$			49.0166i			1.63027i
$905$	33.3116	+	16.8022i	1.10731	+	0.558526i
$906$		0			0
$907$	37.1345	−	37.1345i	1.23303	−	1.23303i	0.270239	−	0.962793i	$-0.412897\pi$
$907$	37.1345	−	37.1345i	1.23303	−	1.23303i	0.962793	−	0.270239i	$-0.0871027\pi$
$908$	−13.8201	+	13.8201i	−0.458636	+	0.458636i
$909$		0			0
$910$	−4.17554	−	18.9212i	−0.138418	−	0.627233i
$911$	−24.3602			−0.807089			−0.403545	−	0.914960i	$-0.632222\pi$
$911$	−24.3602			−0.807089			−0.403545	+	0.914960i	$0.632222\pi$
$912$		0			0
$913$	2.62195	−	2.62195i	0.0867738	−	0.0867738i
$914$			20.8801i			0.690651i
$915$		0			0
$916$			2.42553i			0.0801417i
$917$	7.07863	−	5.77541i	0.233757	−	0.190721i
$918$		0			0
$919$			28.4987i			0.940086i	0.882644	+	0.470043i	$0.155762\pi$
$919$			28.4987i			0.940086i	−0.882644	+	0.470043i	$0.844238\pi$
$920$	3.93258	+	1.98358i	0.129653	+	0.0653967i
$921$		0			0
$922$	−5.29194	−	5.29194i	−0.174281	−	0.174281i
$923$	−12.4450	+	12.4450i	−0.409634	+	0.409634i
$924$		0			0
$925$	−37.3998	−	5.61110i	−1.22970	−	0.184492i
$926$	−16.6892			−0.548441
$927$		0			0
$928$	31.4772	+	31.4772i	1.03329	+	1.03329i
$929$	44.8221			1.47057			0.735283	−	0.677760i	$-0.237049\pi$
$929$	44.8221			1.47057			0.735283	+	0.677760i	$0.237049\pi$
$930$		0			0
$931$	1.33584	−	6.52022i	0.0437805	−	0.213692i
$932$	−7.02657	+	7.02657i	−0.230163	+	0.230163i
$933$		0			0
$934$	−15.3778			−0.503177
$935$	11.7965	−	3.88619i	0.385786	−	0.127092i
$936$		0			0
$937$	7.08330	+	7.08330i	0.231401	+	0.231401i	0.813277	−	0.581876i	$-0.197681\pi$
$937$	7.08330	+	7.08330i	0.231401	+	0.231401i	−0.581876	+	0.813277i	$0.697681\pi$
$938$	−12.5702	+	10.2559i	−0.410430	+	0.334868i
$939$		0			0
$940$	−1.83329	−	5.56494i	−0.0597954	−	0.181508i
$941$			32.8916i			1.07223i	0.844144	+	0.536117i	$0.180109\pi$
$941$			32.8916i			1.07223i	−0.844144	+	0.536117i	$0.819891\pi$
$942$		0			0
$943$	−0.799693	+	0.799693i	−0.0260416	+	0.0260416i
$944$	5.31805			0.173088
$945$		0			0
$946$	6.63378			0.215683
$947$	26.6834	−	26.6834i	0.867095	−	0.867095i	−0.125055	−	0.992150i	$-0.539911\pi$
$947$	26.6834	−	26.6834i	0.867095	−	0.867095i	0.992150	+	0.125055i	$0.0399106\pi$
$948$		0			0
$949$		−	22.8995i		−	0.743349i
$950$	3.42950	+	0.514528i	0.111268	+	0.0166935i
$951$		0			0
$952$	26.8075	−	21.8721i	0.868836	−	0.708878i
$953$	12.9158	+	12.9158i	0.418384	+	0.418384i	0.884646	−	0.466263i	$-0.154400\pi$
$953$	12.9158	+	12.9158i	0.418384	+	0.418384i	−0.466263	+	0.884646i	$0.654400\pi$
$954$		0			0
$955$	−0.0873075	+	0.173093i	−0.00282520	+	0.00560116i
$956$	17.4807			0.565367
$957$		0			0
$958$	10.5427	−	10.5427i	0.340621	−	0.340621i
$959$	−6.77982	−	0.687376i	−0.218932	−	0.0221965i
$960$		0			0
$961$	−20.0142			−0.645621
$962$	17.5170	+	17.5170i	0.564770	+	0.564770i
$963$		0			0
$964$	0.252348			0.00812757
$965$	18.8901	−	6.22310i	0.608095	−	0.200329i
$966$		0			0
$967$	−35.5224	+	35.5224i	−1.14232	+	1.14232i	−0.154298	+	0.988024i	$0.549311\pi$
$967$	−35.5224	+	35.5224i	−1.14232	+	1.14232i	−0.988024	+	0.154298i	$0.950689\pi$
$968$	−17.6112	−	17.6112i	−0.566044	−	0.566044i
$969$		0			0
$970$	−9.54987	+	18.9333i	−0.306628	+	0.607910i
$971$		−	39.4945i		−	1.26744i	−0.773564	−	0.633719i	$-0.781528\pi$
$971$		−	39.4945i		−	1.26744i	0.773564	−	0.633719i	$-0.218472\pi$
$972$		0			0
$973$	31.9862	+	39.2038i	1.02543	+	1.25682i
$974$		−	5.28993i		−	0.169500i
$975$		0			0
$976$		−	10.0543i		−	0.321830i
$977$	7.50787	−	7.50787i	0.240198	−	0.240198i	−0.576734	−	0.816932i	$-0.695673\pi$
$977$	7.50787	−	7.50787i	0.240198	−	0.240198i	0.816932	+	0.576734i	$0.195673\pi$
$978$		0			0
$979$	9.13182			0.291854
$980$	14.2541	−	18.0200i	0.455331	−	0.575628i
$981$		0			0
$982$	10.9899	−	10.9899i	0.350702	−	0.350702i
$983$	36.4061	−	36.4061i	1.16117	−	1.16117i	0.176956	−	0.984219i	$-0.443375\pi$
$983$	36.4061	−	36.4061i	1.16117	−	1.16117i	0.984219	−	0.176956i	$-0.0566250\pi$
$984$		0			0
$985$	−14.8108	−	44.9580i	−0.471912	−	1.43248i
$986$			28.6705i			0.913055i
$987$		0			0
$988$	4.43109	+	4.43109i	0.140972	+	0.140972i
$989$		−	6.59027i		−	0.209558i
$990$		0			0
$991$	23.9788			0.761712			0.380856	−	0.924634i	$-0.375629\pi$
$991$	23.9788			0.761712			0.380856	+	0.924634i	$0.375629\pi$
$992$	−29.5696	−	29.5696i	−0.938834	−	0.938834i
$993$		0			0
$994$	7.52664	+	0.763094i	0.238731	+	0.0242039i
$995$	−6.65896	+	13.2018i	−0.211103	+	0.418526i
$996$		0			0
$997$	−18.4622	−	18.4622i	−0.584703	−	0.584703i	0.351489	−	0.936192i	$-0.385675\pi$
$997$	−18.4622	−	18.4622i	−0.584703	−	0.584703i	−0.936192	+	0.351489i	$0.885675\pi$
$998$	−11.9933	−	11.9933i	−0.379642	−	0.379642i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.p.b.433.15	yes	48
3.2	odd	2	inner	945.2.p.b.433.10	yes	48
5.2	odd	4	inner	945.2.p.b.622.16	yes	48
7.6	odd	2	inner	945.2.p.b.433.16	yes	48
15.2	even	4	inner	945.2.p.b.622.9	yes	48
21.20	even	2	inner	945.2.p.b.433.9	✓	48
35.27	even	4	inner	945.2.p.b.622.15	yes	48
105.62	odd	4	inner	945.2.p.b.622.10	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.p.b.433.9	✓	48	21.20	even	2	inner
945.2.p.b.433.10	yes	48	3.2	odd	2	inner
945.2.p.b.433.15	yes	48	1.1	even	1	trivial
945.2.p.b.433.16	yes	48	7.6	odd	2	inner
945.2.p.b.622.9	yes	48	15.2	even	4	inner
945.2.p.b.622.10	yes	48	105.62	odd	4	inner
945.2.p.b.622.15	yes	48	35.27	even	4	inner
945.2.p.b.622.16	yes	48	5.2	odd	4	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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.515806 - 0.515806i) q^{2} +1.46789i q^{4} +(-1.00702 + 1.99648i) q^{5} +(1.67258 + 2.04999i) q^{7} +(1.78876 + 1.78876i) q^{8} +O(q^{10})\)	\(q+(0.515806 - 0.515806i) q^{2} +1.46789i q^{4} +(-1.00702 + 1.99648i) q^{5} +(1.67258 + 2.04999i) q^{7} +(1.78876 + 1.78876i) q^{8} +(0.510370 + 1.54922i) q^{10} +1.07449 q^{11} +(-3.17486 + 3.17486i) q^{13} +(1.92013 + 0.194673i) q^{14} -1.09047 q^{16} +(-3.65529 - 3.65529i) q^{17} -0.950808 q^{19} +(-2.93060 - 1.47819i) q^{20} +(0.554230 - 0.554230i) q^{22} +(-0.550594 - 0.550594i) q^{23} +(-2.97184 - 4.02097i) q^{25} +3.27523i q^{26} +(-3.00916 + 2.45516i) q^{28} -7.60321i q^{29} +7.14243i q^{31} +(-4.13999 + 4.13999i) q^{32} -3.77084 q^{34} +(-5.77708 + 1.27489i) q^{35} +(5.34833 - 5.34833i) q^{37} +(-0.490432 + 0.490432i) q^{38} +(-5.37252 + 1.76990i) q^{40} -1.45242i q^{41} +(5.98468 + 5.98468i) q^{43} +1.57723i q^{44} -0.568000 q^{46} +(1.26224 + 1.26224i) q^{47} +(-1.40496 + 6.85756i) q^{49} +(-3.60693 - 0.541149i) q^{50} +(-4.66034 - 4.66034i) q^{52} +(7.81473 + 7.81473i) q^{53} +(-1.08203 + 2.14520i) q^{55} +(-0.675105 + 6.65878i) q^{56} +(-3.92178 - 3.92178i) q^{58} -4.87683 q^{59} +9.22013i q^{61} +(3.68411 + 3.68411i) q^{62} +2.08992i q^{64} +(-3.14140 - 9.53568i) q^{65} +(-5.94390 + 5.94390i) q^{67} +(5.36556 - 5.36556i) q^{68} +(-2.32226 + 3.63745i) q^{70} +3.91987 q^{71} +(-3.60638 + 3.60638i) q^{73} -5.51740i q^{74} -1.39568i q^{76} +(1.79717 + 2.20270i) q^{77} -2.27730i q^{79} +(1.09812 - 2.17710i) q^{80} +(-0.749165 - 0.749165i) q^{82} +(2.44017 - 2.44017i) q^{83} +(10.9786 - 3.61676i) q^{85} +6.17387 q^{86} +(1.92201 + 1.92201i) q^{88} +8.49873 q^{89} +(-11.8187 - 1.19824i) q^{91} +(0.808211 - 0.808211i) q^{92} +1.30214 q^{94} +(0.957479 - 1.89827i) q^{95} +(9.19274 + 9.19274i) q^{97} +(2.81248 + 4.26186i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 8 q^{7}+O(q^{10}) \) 48 * q - 8 * q^7	\( 48 q - 8 q^{7} + 40 q^{16} + 8 q^{22} - 48 q^{25} - 20 q^{28} - 24 q^{37} - 40 q^{43} + 40 q^{46} - 80 q^{58} - 64 q^{67} - 4 q^{70} - 8 q^{85} - 48 q^{88} + 48 q^{91}+O(q^{100}) \) 48 * q - 8 * q^7 + 40 * q^16 + 8 * q^22 - 48 * q^25 - 20 * q^28 - 24 * q^37 - 40 * q^43 + 40 * q^46 - 80 * q^58 - 64 * q^67 - 4 * q^70 - 8 * q^85 - 48 * q^88 + 48 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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