LMFDB - Embedded newform 144.2.l.a.107.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,2,Mod(35,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 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("144.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	144.l (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:	$1.14984578911$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4x^{14} + 6x^{12} - 12x^{10} + 33x^{8} - 48x^{6} + 96x^{4} - 256x^{2} + 256 $ x^16 - 4x^14 + 6x^12 - 12x^10 + 33x^8 - 48x^6 + 96x^4 - 256*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			107.8
Root			$-0.944649 - 1.05244i$ of defining polynomial
Character	$\chi$	$=$	144.107
Dual form			144.2.l.a.35.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.32068 + 0.505776i) q^{2} +(1.48838 + 1.33594i) q^{4} +(2.10489 - 2.10489i) q^{5} -4.40731 q^{7} +(1.28999 + 2.51713i) q^{8} +O(q^{10})$	\(q+(1.32068 + 0.505776i) q^{2} +(1.48838 + 1.33594i) q^{4} +(2.10489 - 2.10489i) q^{5} -4.40731 q^{7} +(1.28999 + 2.51713i) q^{8} +(3.84448 - 1.71528i) q^{10} +(-0.215589 - 0.215589i) q^{11} +(-2.73544 + 2.73544i) q^{13} +(-5.82064 - 2.22912i) q^{14} +(0.430552 + 3.97676i) q^{16} -2.36438i q^{17} +(0.758681 + 0.758681i) q^{19} +(5.94487 - 0.320879i) q^{20} +(-0.175684 - 0.393764i) q^{22} +1.75549i q^{23} -3.86110i q^{25} +(-4.99616 + 2.22912i) q^{26} +(-6.55976 - 5.88789i) q^{28} +(-5.54221 - 5.54221i) q^{29} -9.01709i q^{31} +(-1.44273 + 5.46978i) q^{32} +(1.19585 - 3.12259i) q^{34} +(-9.27690 + 9.27690i) q^{35} +(3.10242 + 3.10242i) q^{37} +(0.618250 + 1.38570i) q^{38} +(8.01355 + 2.58300i) q^{40} +10.1014 q^{41} +(-3.54621 + 3.54621i) q^{43} +(-0.0328654 - 0.608892i) q^{44} +(-0.887886 + 2.31844i) q^{46} +3.90136 q^{47} +12.4244 q^{49} +(1.95286 - 5.09927i) q^{50} +(-7.72575 + 0.417003i) q^{52} +(-2.71378 + 2.71378i) q^{53} -0.907583 q^{55} +(-5.68537 - 11.0938i) q^{56} +(-4.51635 - 10.1226i) q^{58} +(3.40445 + 3.40445i) q^{59} +(-1.75868 + 1.75868i) q^{61} +(4.56063 - 11.9087i) q^{62} +(-4.67187 + 6.49412i) q^{64} +11.5156i q^{65} +(9.11951 + 9.11951i) q^{67} +(3.15866 - 3.51910i) q^{68} +(-16.9438 + 7.55976i) q^{70} -11.8897i q^{71} +0.482639i q^{73} +(2.52817 + 5.66643i) q^{74} +(0.115657 + 2.14275i) q^{76} +(0.950169 + 0.950169i) q^{77} +6.88995i q^{79} +(9.27690 + 7.46437i) q^{80} +(13.3407 + 5.10904i) q^{82} +(4.79951 - 4.79951i) q^{83} +(-4.97676 - 4.97676i) q^{85} +(-6.47699 + 2.88981i) q^{86} +(0.264559 - 0.820773i) q^{88} -7.00534 q^{89} +(12.0559 - 12.0559i) q^{91} +(-2.34522 + 2.61284i) q^{92} +(5.15244 + 1.97322i) q^{94} +3.19387 q^{95} -3.34374 q^{97} +(16.4086 + 6.28397i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 8 q^{10} - 16 q^{16} + 16 q^{19} - 40 q^{22} - 24 q^{28} + 24 q^{34} + 72 q^{40} - 32 q^{43} + 40 q^{46} + 16 q^{49} + 24 q^{52} - 64 q^{55} + 24 q^{58} - 32 q^{61} - 48 q^{64} - 16 q^{67} - 72 q^{70} + 80 q^{82} - 32 q^{85} + 48 q^{88} + 48 q^{91} + 72 q^{94}+O(q^{100}) $ 16 * q - 8 * q^10 - 16 * q^16 + 16 * q^19 - 40 * q^22 - 24 * q^28 + 24 * q^34 + 72 * q^40 - 32 * q^43 + 40 * q^46 + 16 * q^49 + 24 * q^52 - 64 * q^55 + 24 * q^58 - 32 * q^61 - 48 * q^64 - 16 * q^67 - 72 * q^70 + 80 * q^82 - 32 * q^85 + 48 * q^88 + 48 * q^91 + 72 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	1.32068	+	0.505776i	0.933860	+	0.357638i
$2$	1.32068	+	0.505776i	0.933860	+	0.357638i
$3$		0			0
$3$		0			0
$4$	1.48838	+	1.33594i	0.744190	+	0.667968i
$5$	2.10489	−	2.10489i	0.941334	−	0.941334i	−0.0570377	−	0.998372i	$-0.518166\pi$
$5$	2.10489	−	2.10489i	0.941334	−	0.941334i	0.998372	+	0.0570377i	$0.0181655\pi$
$6$		0			0
$7$	−4.40731			−1.66581			−0.832904	−	0.553418i	$-0.813323\pi$
$7$	−4.40731			−1.66581			−0.832904	+	0.553418i	$0.813323\pi$
$8$	1.28999	+	2.51713i	0.456079	+	0.889939i
$9$		0			0
$10$	3.84448	−	1.71528i	1.21573	−	0.542418i
$11$	−0.215589	−	0.215589i	−0.0650026	−	0.0650026i	0.673858	−	0.738861i	$-0.264636\pi$
$11$	−0.215589	−	0.215589i	−0.0650026	−	0.0650026i	−0.738861	+	0.673858i	$0.764636\pi$
$12$		0			0
$13$	−2.73544	+	2.73544i	−0.758675	+	0.758675i	−0.976081	−	0.217406i	$-0.930240\pi$
$13$	−2.73544	+	2.73544i	−0.758675	+	0.758675i	0.217406	+	0.976081i	$0.430240\pi$
$14$	−5.82064	−	2.22912i	−1.55563	−	0.595756i
$15$		0			0
$16$	0.430552	+	3.97676i	0.107638	+	0.994190i
$17$		−	2.36438i		−	0.573447i	−0.958013	−	0.286724i	$-0.907434\pi$
$17$		−	2.36438i		−	0.573447i	0.958013	−	0.286724i	$-0.0925661\pi$
$18$		0			0
$19$	0.758681	+	0.758681i	0.174053	+	0.174053i	0.788758	−	0.614704i	$-0.210725\pi$
$19$	0.758681	+	0.758681i	0.174053	+	0.174053i	−0.614704	+	0.788758i	$0.710725\pi$
$20$	5.94487	−	0.320879i	1.32931	−	0.0717507i
$21$		0			0
$22$	−0.175684	−	0.393764i	−0.0374560	−	0.0839508i
$23$			1.75549i			0.366045i	0.983109	+	0.183023i	$0.0585881\pi$
$23$			1.75549i			0.366045i	−0.983109	+	0.183023i	$0.941412\pi$
$24$		0			0
$25$		−	3.86110i		−	0.772221i
$26$	−4.99616	+	2.22912i	−0.979827	+	0.437165i
$27$		0			0
$28$	−6.55976	−	5.88789i	−1.23968	−	1.11271i
$29$	−5.54221	−	5.54221i	−1.02916	−	1.02916i	−0.999562	−	0.0296002i	$-0.990577\pi$
$29$	−5.54221	−	5.54221i	−1.02916	−	1.02916i	−0.0296002	−	0.999562i	$-0.509423\pi$
$30$		0			0
$31$		−	9.01709i		−	1.61952i	−0.586763	−	0.809759i	$-0.699598\pi$
$31$		−	9.01709i		−	1.61952i	0.586763	−	0.809759i	$-0.300402\pi$
$32$	−1.44273	+	5.46978i	−0.255041	+	0.966930i
$33$		0			0
$34$	1.19585	−	3.12259i	0.205086	−	0.535520i
$35$	−9.27690	+	9.27690i	−1.56808	+	1.56808i
$36$		0			0
$37$	3.10242	+	3.10242i	0.510035	+	0.510035i	0.914537	−	0.404502i	$-0.132555\pi$
$37$	3.10242	+	3.10242i	0.510035	+	0.510035i	−0.404502	+	0.914537i	$0.632555\pi$
$38$	0.618250	+	1.38570i	0.100293	+	0.224789i
$39$		0			0
$40$	8.01355	+	2.58300i	1.26705	+	0.408408i
$41$	10.1014			1.57757			0.788785	−	0.614669i	$-0.210710\pi$
$41$	10.1014			1.57757			0.788785	+	0.614669i	$0.210710\pi$
$42$		0			0
$43$	−3.54621	+	3.54621i	−0.540792	+	0.540792i	−0.923761	−	0.382969i	$-0.874901\pi$
$43$	−3.54621	+	3.54621i	−0.540792	+	0.540792i	0.382969	+	0.923761i	$0.374901\pi$
$44$	−0.0328654	−	0.608892i	−0.00495465	−	0.0917940i
$45$		0			0
$46$	−0.887886	+	2.31844i	−0.130912	+	0.341835i
$47$	3.90136			0.569072			0.284536	−	0.958665i	$-0.408160\pi$
$47$	3.90136			0.569072			0.284536	+	0.958665i	$0.408160\pi$
$48$		0			0
$49$	12.4244			1.77491
$50$	1.95286	−	5.09927i	0.276175	−	0.721146i
$51$		0			0
$52$	−7.72575	+	0.417003i	−1.07137	+	0.0578280i
$53$	−2.71378	+	2.71378i	−0.372766	+	0.372766i	−0.868484	−	0.495717i	$-0.834905\pi$
$53$	−2.71378	+	2.71378i	−0.372766	+	0.372766i	0.495717	+	0.868484i	$0.334905\pi$
$54$		0			0
$55$	−0.907583			−0.122378
$56$	−5.68537	−	11.0938i	−0.759740	−	1.48247i
$57$		0			0
$58$	−4.51635	−	10.1226i	−0.593026	−	1.32916i
$59$	3.40445	+	3.40445i	0.443222	+	0.443222i	0.893093	−	0.449871i	$-0.148530\pi$
$59$	3.40445	+	3.40445i	0.443222	+	0.443222i	−0.449871	+	0.893093i	$0.648530\pi$
$60$		0			0
$61$	−1.75868	+	1.75868i	−0.225176	+	0.225176i	−0.810674	−	0.585498i	$-0.800899\pi$
$61$	−1.75868	+	1.75868i	−0.225176	+	0.225176i	0.585498	+	0.810674i	$0.300899\pi$
$62$	4.56063	−	11.9087i	0.579201	−	1.51240i
$63$		0			0
$64$	−4.67187	+	6.49412i	−0.583984	+	0.811765i
$65$			11.5156i			1.42833i
$66$		0			0
$67$	9.11951	+	9.11951i	1.11413	+	1.11413i	0.992587	+	0.121539i	$0.0387831\pi$
$67$	9.11951	+	9.11951i	1.11413	+	1.11413i	0.121539	+	0.992587i	$0.461217\pi$
$68$	3.15866	−	3.51910i	0.383044	−	0.426754i
$69$		0			0
$70$	−16.9438	+	7.55976i	−2.02518	+	0.903564i
$71$		−	11.8897i		−	1.41105i	−0.708684	−	0.705526i	$-0.750711\pi$
$71$		−	11.8897i		−	1.41105i	0.708684	−	0.705526i	$-0.249289\pi$
$72$		0			0
$73$			0.482639i			0.0564886i	0.999601	+	0.0282443i	$0.00899163\pi$
$73$			0.482639i			0.0564886i	−0.999601	+	0.0282443i	$0.991008\pi$
$74$	2.52817	+	5.66643i	0.293894	+	0.658710i
$75$		0			0
$76$	0.115657	+	2.14275i	0.0132667	+	0.245791i
$77$	0.950169	+	0.950169i	0.108282	+	0.108282i
$78$		0			0
$79$			6.88995i			0.775180i	0.921832	+	0.387590i	$0.126692\pi$
$79$			6.88995i			0.775180i	−0.921832	+	0.387590i	$0.873308\pi$
$80$	9.27690	+	7.46437i	1.03719	+	0.834542i
$81$		0			0
$82$	13.3407	+	5.10904i	1.47323	+	0.564199i
$83$	4.79951	−	4.79951i	0.526814	−	0.526814i	−0.392807	−	0.919621i	$-0.628496\pi$
$83$	4.79951	−	4.79951i	0.526814	−	0.526814i	0.919621	+	0.392807i	$0.128496\pi$
$84$		0			0
$85$	−4.97676	−	4.97676i	−0.539805	−	0.539805i
$86$	−6.47699	+	2.88981i	−0.698432	+	0.311616i
$87$		0			0
$88$	0.264559	−	0.820773i	0.0282021	−	0.0874947i
$89$	−7.00534			−0.742564			−0.371282	−	0.928520i	$-0.621082\pi$
$89$	−7.00534			−0.742564			−0.371282	+	0.928520i	$0.621082\pi$
$90$		0			0
$91$	12.0559	−	12.0559i	1.26381	−	1.26381i
$92$	−2.34522	+	2.61284i	−0.244506	+	0.272407i
$93$		0			0
$94$	5.15244	+	1.97322i	0.531434	+	0.203522i
$95$	3.19387			0.327685
$96$		0			0
$97$	−3.34374			−0.339506			−0.169753	−	0.985487i	$-0.554297\pi$
$97$	−3.34374			−0.339506			−0.169753	+	0.985487i	$0.554297\pi$
$98$	16.4086	+	6.28397i	1.65752	+	0.634777i
$99$		0			0
$100$	5.15819	−	5.74679i	0.515819	−	0.574679i
$101$	1.76361	−	1.76361i	0.175486	−	0.175486i	−0.613899	−	0.789385i	$-0.710400\pi$
$101$	1.76361	−	1.76361i	0.175486	−	0.175486i	0.789385	+	0.613899i	$0.210400\pi$
$102$		0			0
$103$	−1.01709			−0.100217			−0.0501085	−	0.998744i	$-0.515957\pi$
$103$	−1.01709			−0.100217			−0.0501085	+	0.998744i	$0.515957\pi$
$104$	−10.4141	−	3.35678i	−1.02119	−	0.329159i
$105$		0			0
$106$	−4.95660	+	2.21146i	−0.481427	+	0.214796i
$107$	−2.33152	−	2.33152i	−0.225396	−	0.225396i	0.585370	−	0.810766i	$-0.300949\pi$
$107$	−2.33152	−	2.33152i	−0.225396	−	0.225396i	−0.810766	+	0.585370i	$0.800949\pi$
$108$		0			0
$109$	−8.07918	+	8.07918i	−0.773845	+	0.773845i	−0.978776	−	0.204931i	$-0.934303\pi$
$109$	−8.07918	+	8.07918i	−0.773845	+	0.773845i	0.204931	+	0.978776i	$0.434303\pi$
$110$	−1.19862	−	0.459034i	−0.114284	−	0.0437672i
$111$		0			0
$112$	−1.89758	−	17.5268i	−0.179304	−	1.65613i
$113$			2.09677i			0.197247i	0.995125	+	0.0986237i	$0.0314440\pi$
$113$			2.09677i			0.197247i	−0.995125	+	0.0986237i	$0.968556\pi$
$114$		0			0
$115$	3.69511	+	3.69511i	0.344571	+	0.344571i
$116$	−0.844880	−	15.6529i	−0.0784451	−	1.45334i
$117$		0			0
$118$	2.77429	+	6.21808i	0.255395	+	0.572421i
$119$			10.4206i			0.955253i
$120$		0			0
$121$		−	10.9070i		−	0.991549i
$122$	−3.21215	+	1.43315i	−0.290814	+	0.129751i
$123$		0			0
$124$	12.0463	−	13.4209i	1.08179	−	1.20523i
$125$	2.39725	+	2.39725i	0.214416	+	0.214416i
$126$		0			0
$127$		−	10.2802i		−	0.912218i	−0.889924	−	0.456109i	$-0.849243\pi$
$127$		−	10.2802i		−	0.912218i	0.889924	−	0.456109i	$-0.150757\pi$
$128$	−9.45461	+	6.21372i	−0.835677	+	0.549221i
$129$		0			0
$130$	−5.82432	+	15.2084i	−0.510826	+	1.33386i
$131$	6.80891	−	6.80891i	0.594897	−	0.594897i	−0.344053	−	0.938950i	$-0.611800\pi$
$131$	6.80891	−	6.80891i	0.594897	−	0.594897i	0.938950	+	0.344053i	$0.111800\pi$
$132$		0			0
$133$	−3.34374	−	3.34374i	−0.289939	−	0.289939i
$134$	7.43151	+	16.6564i	0.641984	+	1.43889i
$135$		0			0
$136$	5.95146	−	3.05002i	0.510333	−	0.261537i
$137$	−13.7922			−1.17834			−0.589172	−	0.808008i	$-0.700546\pi$
$137$	−13.7922			−1.17834			−0.589172	+	0.808008i	$0.700546\pi$
$138$		0			0
$139$	−13.1195	+	13.1195i	−1.11278	+	1.11278i	−0.120010	+	0.992773i	$0.538293\pi$
$139$	−13.1195	+	13.1195i	−1.11278	+	1.11278i	−0.992773	+	0.120010i	$0.961707\pi$
$140$	−26.2009	+	1.41421i	−2.21438	+	0.119523i
$141$		0			0
$142$	6.01355	−	15.7025i	0.504646	−	1.31773i
$143$	1.17946			0.0986317
$144$		0			0
$145$	−23.3314			−1.93757
$146$	−0.244107	+	0.637410i	−0.0202025	+	0.0527525i
$147$		0			0
$148$	0.472948	+	8.76222i	0.0388761	+	0.720250i
$149$	−7.76174	+	7.76174i	−0.635867	+	0.635867i	−0.949533	−	0.313667i	$-0.898443\pi$
$149$	−7.76174	+	7.76174i	−0.635867	+	0.635867i	0.313667	+	0.949533i	$0.398443\pi$
$150$		0			0
$151$	−0.202466			−0.0164765			−0.00823823	−	0.999966i	$-0.502622\pi$
$151$	−0.202466			−0.0164765			−0.00823823	+	0.999966i	$0.502622\pi$
$152$	−0.931009	+	2.88838i	−0.0755148	+	0.234279i
$153$		0			0
$154$	0.774294	+	1.73544i	0.0623944	+	0.139846i
$155$	−18.9800	−	18.9800i	−1.52451	−	1.52451i
$156$		0			0
$157$	3.75868	−	3.75868i	0.299975	−	0.299975i	−0.541029	−	0.841004i	$-0.681965\pi$
$157$	3.75868	−	3.75868i	0.299975	−	0.299975i	0.841004	+	0.541029i	$0.181965\pi$
$158$	−3.48478	+	9.09941i	−0.277234	+	0.723910i
$159$		0			0
$160$	8.47649	+	14.5501i	0.670125	+	1.15028i
$161$		−	7.73700i		−	0.609761i
$162$		0			0
$163$	−13.2684	−	13.2684i	−1.03926	−	1.03926i	−0.999197	−	0.0400655i	$-0.987243\pi$
$163$	−13.2684	−	13.2684i	−1.03926	−	1.03926i	−0.0400655	−	0.999197i	$-0.512757\pi$
$164$	15.0347	+	13.4948i	1.17401	+	1.05377i
$165$		0			0
$166$	8.76608	−	3.91113i	0.680380	−	0.303562i
$167$		−	20.1644i		−	1.56037i	−0.625548	−	0.780186i	$-0.715125\pi$
$167$		−	20.1644i		−	1.56037i	0.625548	−	0.780186i	$-0.284875\pi$
$168$		0			0
$169$		−	1.96528i		−	0.151175i
$170$	−4.05557	−	9.08983i	−0.311048	−	0.697158i
$171$		0			0
$172$	−10.0156	+	0.540601i	−0.763683	+	0.0412204i
$173$	3.98315	+	3.98315i	0.302833	+	0.302833i	0.842121	−	0.539288i	$-0.181307\pi$
$173$	3.98315	+	3.98315i	0.302833	+	0.302833i	−0.539288	+	0.842121i	$0.681307\pi$
$174$		0			0
$175$			17.0171i			1.28637i
$176$	0.764525	−	0.950169i	0.0576282	−	0.0716217i
$177$		0			0
$178$	−9.25179	−	3.54313i	−0.693451	−	0.265569i
$179$	14.7182	−	14.7182i	1.10009	−	1.10009i	0.105688	−	0.994399i	$-0.466296\pi$
$179$	14.7182	−	14.7182i	1.10009	−	1.10009i	0.994399	−	0.105688i	$-0.0337044\pi$
$180$		0			0
$181$	3.26456	+	3.26456i	0.242653	+	0.242653i	0.817947	−	0.575294i	$-0.195112\pi$
$181$	3.26456	+	3.26456i	0.242653	+	0.242653i	−0.575294	+	0.817947i	$0.695112\pi$
$182$	22.0196	−	9.82441i	1.63220	−	0.728233i
$183$		0			0
$184$	−4.41880	+	2.26456i	−0.325758	+	0.166945i
$185$	13.0605			0.960227
$186$		0			0
$187$	−0.509736	+	0.509736i	−0.0372756	+	0.0372756i
$188$	5.80671	+	5.21197i	0.423498	+	0.380122i
$189$		0			0
$190$	4.21808	+	1.61539i	0.306012	+	0.117192i
$191$	−7.69868			−0.557057			−0.278528	−	0.960428i	$-0.589847\pi$
$191$	−7.69868			−0.557057			−0.278528	+	0.960428i	$0.589847\pi$
$192$		0			0
$193$	−3.51736			−0.253185			−0.126593	−	0.991955i	$-0.540404\pi$
$193$	−3.51736			−0.253185			−0.126593	+	0.991955i	$0.540404\pi$
$194$	−4.41601	−	1.69119i	−0.317051	−	0.121420i
$195$		0			0
$196$	18.4922	+	16.5982i	1.32087	+	1.18559i
$197$	−6.40456	+	6.40456i	−0.456306	+	0.456306i	−0.897441	−	0.441135i	$-0.854576\pi$
$197$	−6.40456	+	6.40456i	−0.456306	+	0.456306i	0.441135	+	0.897441i	$0.354576\pi$
$198$		0			0
$199$	23.3491			1.65517			0.827586	−	0.561339i	$-0.189714\pi$
$199$	23.3491			1.65517			0.827586	+	0.561339i	$0.189714\pi$
$200$	9.71889	−	4.98077i	0.687230	−	0.352194i
$201$		0			0
$202$	3.22115	−	1.43717i	0.226640	−	0.101119i
$203$	24.4262	+	24.4262i	1.71439	+	1.71439i
$204$		0			0
$205$	21.2623	−	21.2623i	1.48502	−	1.48502i
$206$	−1.34325	−	0.514421i	−0.0935887	−	0.0358414i
$207$		0			0
$208$	−12.0559	−	9.70045i	−0.835929	−	0.672605i
$209$		−	0.327127i		−	0.0226278i
$210$		0			0
$211$	−6.63688	−	6.63688i	−0.456901	−	0.456901i	0.440736	−	0.897637i	$-0.354718\pi$
$211$	−6.63688	−	6.63688i	−0.456901	−	0.456901i	−0.897637	+	0.440736i	$0.854718\pi$
$212$	−7.66457	+	0.413701i	−0.526405	+	0.0284131i
$213$		0			0
$214$	−1.89996	−	4.25841i	−0.129878	−	0.291099i
$215$			14.9287i			1.01813i
$216$		0			0
$217$			39.7411i			2.69780i
$218$	−14.7563	+	6.58374i	−0.999420	+	0.445907i
$219$		0			0
$220$	−1.35083	−	1.21247i	−0.0910728	−	0.0817448i
$221$	6.46763	+	6.46763i	0.435060	+	0.435060i
$222$		0			0
$223$			13.2219i			0.885406i	0.896668	+	0.442703i	$0.145980\pi$
$223$			13.2219i			0.885406i	−0.896668	+	0.442703i	$0.854020\pi$
$224$	6.35857	−	24.1070i	0.424850	−	1.61072i
$225$		0			0
$226$	−1.06050	+	2.76916i	−0.0705431	+	0.184201i
$227$	−16.4029	+	16.4029i	−1.08870	+	1.08870i	−0.0930369	+	0.995663i	$0.529657\pi$
$227$	−16.4029	+	16.4029i	−1.08870	+	1.08870i	−0.995663	+	0.0930369i	$0.970343\pi$
$228$		0			0
$229$	−4.98677	−	4.98677i	−0.329535	−	0.329535i	0.522875	−	0.852410i	$-0.324860\pi$
$229$	−4.98677	−	4.98677i	−0.329535	−	0.329535i	−0.852410	+	0.522875i	$0.824860\pi$
$230$	3.01115	+	6.74895i	0.198549	+	0.445013i
$231$		0			0
$232$	6.80108	−	21.0998i	0.446513	−	1.38527i
$233$	1.05879			0.0693634			0.0346817	−	0.999398i	$-0.488958\pi$
$233$	1.05879			0.0693634			0.0346817	+	0.999398i	$0.488958\pi$
$234$		0			0
$235$	8.21193	−	8.21193i	0.535687	−	0.535687i
$236$	0.518991	+	9.61525i	0.0337834	+	0.625900i
$237$		0			0
$238$	−5.27048	+	13.7622i	−0.341635	+	0.892072i
$239$	0.317107			0.0205119			0.0102560	−	0.999947i	$-0.496735\pi$
$239$	0.317107			0.0205119			0.0102560	+	0.999947i	$0.496735\pi$
$240$		0			0
$241$	11.7334			0.755816			0.377908	−	0.925843i	$-0.376644\pi$
$241$	11.7334			0.755816			0.377908	+	0.925843i	$0.376644\pi$
$242$	5.51653	−	14.4047i	0.354616	−	0.925969i
$243$		0			0
$244$	−4.96707	+	0.268101i	−0.317984	+	0.0171634i
$245$	26.1520	−	26.1520i	1.67079	−	1.67079i
$246$		0			0
$247$	−4.15065			−0.264100
$248$	22.6972	−	11.6319i	1.44127	−	0.738628i
$249$		0			0
$250$	1.95352	+	4.37847i	0.123552	+	0.276918i
$251$	7.02450	+	7.02450i	0.443382	+	0.443382i	0.893147	−	0.449765i	$-0.148492\pi$
$251$	7.02450	+	7.02450i	0.443382	+	0.443382i	−0.449765	+	0.893147i	$0.648492\pi$
$252$		0			0
$253$	0.378465	−	0.378465i	0.0237939	−	0.0237939i
$254$	5.19947	−	13.5768i	0.326244	−	0.851884i
$255$		0			0
$256$	−15.6293	+	3.42440i	−0.976828	+	0.214025i
$257$		−	23.5830i		−	1.47107i	−0.677487	−	0.735535i	$-0.736931\pi$
$257$		−	23.5830i		−	1.47107i	0.677487	−	0.735535i	$-0.263069\pi$
$258$		0			0
$259$	−13.6733	−	13.6733i	−0.849621	−	0.849621i
$260$	−15.3841	+	17.1396i	−0.954081	+	1.06295i
$261$		0			0
$262$	12.4362	−	5.54859i	0.768309	−	0.342793i
$263$			20.1370i			1.24170i	0.783928	+	0.620851i	$0.213213\pi$
$263$			20.1370i			1.24170i	−0.783928	+	0.620851i	$0.786787\pi$
$264$		0			0
$265$			11.4244i			0.701796i
$266$	−2.72482	−	6.10719i	−0.167069	−	0.374456i
$267$		0			0
$268$	1.39022	+	25.7564i	0.0849213	+	1.57332i
$269$	−8.62201	−	8.62201i	−0.525693	−	0.525693i	0.393592	−	0.919285i	$-0.371232\pi$
$269$	−8.62201	−	8.62201i	−0.525693	−	0.525693i	−0.919285	+	0.393592i	$0.871232\pi$
$270$		0			0
$271$		−	2.18722i		−	0.132864i	−0.997791	−	0.0664319i	$-0.978838\pi$
$271$		−	2.18722i		−	0.132864i	0.997791	−	0.0664319i	$-0.0211615\pi$
$272$	9.40259	−	1.01799i	0.570115	−	0.0617247i
$273$		0			0
$274$	−18.2150	−	6.97575i	−1.10041	−	0.421421i
$275$	−0.832413	+	0.832413i	−0.0501964	+	0.0501964i
$276$		0			0
$277$	8.64248	+	8.64248i	0.519277	+	0.519277i	0.917352	−	0.398076i	$-0.130322\pi$
$277$	8.64248	+	8.64248i	0.519277	+	0.519277i	−0.398076	+	0.917352i	$0.630322\pi$
$278$	−23.9622	+	10.6911i	−1.43716	+	0.641210i
$279$		0			0
$280$	−35.3182	−	11.3841i	−2.11067	−	0.680328i
$281$	−14.8081			−0.883375			−0.441688	−	0.897169i	$-0.645620\pi$
$281$	−14.8081			−0.883375			−0.441688	+	0.897169i	$0.645620\pi$
$282$		0			0
$283$	6.12714	−	6.12714i	0.364221	−	0.364221i	−0.501144	−	0.865364i	$-0.667087\pi$
$283$	6.12714	−	6.12714i	0.364221	−	0.364221i	0.865364	+	0.501144i	$0.167087\pi$
$284$	15.8839	−	17.6964i	0.942537	−	1.05009i
$285$		0			0
$286$	1.55769	+	0.596545i	0.0921082	+	0.0352744i
$287$	−44.5199			−2.62793
$288$		0			0
$289$	11.4097			0.671158
$290$	−30.8133	−	11.8005i	−1.80942	−	0.692949i
$291$		0			0
$292$	−0.644774	+	0.718350i	−0.0377326	+	0.0420383i
$293$	−11.8979	+	11.8979i	−0.695080	+	0.695080i	−0.963345	−	0.268265i	$-0.913550\pi$
$293$	−11.8979	+	11.8979i	−0.695080	+	0.695080i	0.268265	+	0.963345i	$0.413550\pi$
$294$		0			0
$295$	14.3320			0.834441
$296$	−3.80711	+	11.8113i	−0.221284	+	0.686517i
$297$		0			0
$298$	−14.1765	+	6.32505i	−0.821221	+	0.366401i
$299$	−4.80204	−	4.80204i	−0.277709	−	0.277709i
$300$		0			0
$301$	15.6293	−	15.6293i	0.900855	−	0.900855i
$302$	−0.267393	−	0.102403i	−0.0153867	−	0.00589261i
$303$		0			0
$304$	−2.69044	+	3.34374i	−0.154307	+	0.191777i
$305$			7.40365i			0.423932i
$306$		0			0
$307$	4.91467	+	4.91467i	0.280495	+	0.280495i	0.833306	−	0.552811i	$-0.186445\pi$
$307$	4.91467	+	4.91467i	0.280495	+	0.280495i	−0.552811	+	0.833306i	$0.686445\pi$
$308$	0.144848	+	2.68358i	0.00825350	+	0.152911i
$309$		0			0
$310$	−15.4668	−	34.6660i	−0.878455	−	1.96890i
$311$			20.7712i			1.17783i	0.808195	+	0.588915i	$0.200445\pi$
$311$			20.7712i			1.17783i	−0.808195	+	0.588915i	$0.799555\pi$
$312$		0			0
$313$		−	16.3897i		−	0.926400i	−0.886254	−	0.463200i	$-0.846701\pi$
$313$		−	16.3897i		−	0.926400i	0.886254	−	0.463200i	$-0.153299\pi$
$314$	6.86506	−	3.06295i	0.387418	−	0.172853i
$315$		0			0
$316$	−9.20453	+	10.2549i	−0.517795	+	0.576881i
$317$	22.3592	+	22.3592i	1.25582	+	1.25582i	0.953070	+	0.302749i	$0.0979044\pi$
$317$	22.3592	+	22.3592i	1.25582	+	1.25582i	0.302749	+	0.953070i	$0.402096\pi$
$318$		0			0
$319$			2.38968i			0.133796i
$320$	3.83563	+	23.5032i	0.214418	+	1.31387i
$321$		0			0
$322$	3.91319	−	10.2181i	0.218074	−	0.569431i
$323$	1.79381	−	1.79381i	0.0998103	−	0.0998103i
$324$		0			0
$325$	10.5618	+	10.5618i	0.585865	+	0.585865i
$326$	−10.8125	−	24.2342i	−0.598846	−	1.34221i
$327$		0			0
$328$	13.0306	+	25.4265i	0.719497	+	1.40394i
$329$	−17.1945			−0.947965
$330$		0			0
$331$	−7.08533	+	7.08533i	−0.389445	+	0.389445i	−0.874490	−	0.485044i	$-0.838803\pi$
$331$	−7.08533	+	7.08533i	−0.389445	+	0.389445i	0.485044	+	0.874490i	$0.338803\pi$
$332$	13.5553	−	0.731659i	0.743945	−	0.0401550i
$333$		0			0
$334$	10.1987	−	26.6307i	0.558048	−	1.45717i
$335$	38.3911			2.09753
$336$		0			0
$337$	−23.3314			−1.27094			−0.635472	−	0.772124i	$-0.719195\pi$
$337$	−23.3314			−1.27094			−0.635472	+	0.772124i	$0.719195\pi$
$338$	0.993991	−	2.59550i	0.0540660	−	0.141177i
$339$		0			0
$340$	−0.758681	−	14.0559i	−0.0411452	−	0.762291i
$341$	−1.94399	+	1.94399i	−0.105273	+	0.105273i
$342$		0			0
$343$	−23.9070			−1.29086
$344$	−13.5008	−	4.35170i	−0.727916	−	0.234628i
$345$		0			0
$346$	3.24587	+	7.27503i	0.174499	+	0.391108i
$347$	−21.2074	−	21.2074i	−1.13847	−	1.13847i	−0.988724	−	0.149751i	$-0.952153\pi$
$347$	−21.2074	−	21.2074i	−1.13847	−	1.13847i	−0.149751	−	0.988724i	$-0.547847\pi$
$348$		0			0
$349$	5.38022	−	5.38022i	0.287996	−	0.287996i	−0.548291	−	0.836288i	$-0.684721\pi$
$349$	5.38022	−	5.38022i	0.287996	−	0.287996i	0.836288	+	0.548291i	$0.184721\pi$
$350$	−8.60684	+	22.4741i	−0.460055	+	1.20129i
$351$		0			0
$352$	1.49026	−	0.868189i	0.0794314	−	0.0462746i
$353$		−	10.5163i		−	0.559727i	−0.960040	−	0.279864i	$-0.909711\pi$
$353$		−	10.5163i		−	0.559727i	0.960040	−	0.279864i	$-0.0902892\pi$
$354$		0			0
$355$	−25.0266	−	25.0266i	−1.32827	−	1.32827i
$356$	−10.4266	−	9.35868i	−0.552609	−	0.496009i
$357$		0			0
$358$	26.8821	−	11.9939i	1.42076	−	0.633895i
$359$			11.7583i			0.620578i	0.950642	+	0.310289i	$0.100426\pi$
$359$			11.7583i			0.620578i	−0.950642	+	0.310289i	$0.899574\pi$
$360$		0			0
$361$		−	17.8488i		−	0.939411i
$362$	2.66029	+	5.96257i	0.139822	+	0.313386i
$363$		0			0
$364$	34.0498	−	1.83786i	1.78469	−	0.0963303i
$365$	1.01590	+	1.01590i	0.0531747	+	0.0531747i
$366$		0			0
$367$		−	3.49973i		−	0.182684i	−0.995820	−	0.0913422i	$-0.970884\pi$
$367$		−	3.49973i		−	0.182684i	0.995820	−	0.0913422i	$-0.0291157\pi$
$368$	−6.98117	+	0.755830i	−0.363918	+	0.0394004i
$369$		0			0
$370$	17.2487	+	6.60570i	0.896718	+	0.343414i
$371$	11.9605	−	11.9605i	0.620957	−	0.620957i
$372$		0			0
$373$	19.1831	+	19.1831i	0.993262	+	0.993262i	0.999977	−	0.00671500i	$-0.00213747\pi$
$373$	19.1831	+	19.1831i	0.993262	+	0.993262i	−0.00671500	+	0.999977i	$0.502137\pi$
$374$	−0.931009	+	0.415384i	−0.0481413	+	0.0214790i
$375$		0			0
$376$	5.03271	+	9.82023i	0.259542	+	0.506440i
$377$	30.3208			1.56160
$378$		0			0
$379$	−14.9977	+	14.9977i	−0.770381	+	0.770381i	−0.978173	−	0.207792i	$-0.933372\pi$
$379$	−14.9977	+	14.9977i	−0.770381	+	0.770381i	0.207792	+	0.978173i	$0.433372\pi$
$380$	4.75370	+	4.26681i	0.243860	+	0.218883i
$381$		0			0
$382$	−10.1675	−	3.89381i	−0.520213	−	0.199225i
$383$	−30.4027			−1.55351			−0.776754	−	0.629805i	$-0.783135\pi$
$383$	−30.4027			−1.55351			−0.776754	+	0.629805i	$0.783135\pi$
$384$		0			0
$385$	4.00000			0.203859
$386$	−4.64530	−	1.77900i	−0.236440	−	0.0905486i
$387$		0			0
$388$	−4.97676	−	4.46702i	−0.252657	−	0.226779i
$389$	19.4571	−	19.4571i	0.986516	−	0.986516i	−0.0133943	−	0.999910i	$-0.504264\pi$
$389$	19.4571	−	19.4571i	0.986516	−	0.986516i	0.999910	+	0.0133943i	$0.00426365\pi$
$390$		0			0
$391$	4.15065			0.209908
$392$	16.0273	+	31.2738i	0.809501	+	1.57957i
$393$		0			0
$394$	−11.6976	+	5.21909i	−0.589319	+	0.262934i
$395$	14.5026	+	14.5026i	0.729704	+	0.729704i
$396$		0			0
$397$	−20.4339	+	20.4339i	−1.02555	+	1.02555i	−0.0258815	+	0.999665i	$0.508239\pi$
$397$	−20.4339	+	20.4339i	−1.02555	+	1.02555i	−0.999665	+	0.0258815i	$0.991761\pi$
$398$	30.8366	+	11.8094i	1.54570	+	0.591952i
$399$		0			0
$400$	15.3547	−	1.66241i	0.767734	−	0.0831203i
$401$		−	22.5671i		−	1.12695i	−0.826133	−	0.563475i	$-0.809464\pi$
$401$		−	22.5671i		−	1.12695i	0.826133	−	0.563475i	$-0.190536\pi$
$402$		0			0
$403$	24.6657	+	24.6657i	1.22869	+	1.22869i
$404$	4.98099	−	0.268853i	0.247814	−	0.0133759i
$405$		0			0
$406$	19.9050	+	44.6134i	0.987867	+	2.21413i
$407$		−	1.33770i		−	0.0663073i
$408$		0			0
$409$			9.78286i			0.483731i	0.970310	+	0.241866i	$0.0777593\pi$
$409$			9.78286i			0.483731i	−0.970310	+	0.241866i	$0.922241\pi$
$410$	38.8346	−	17.3267i	1.91790	−	0.855702i
$411$		0			0
$412$	−1.51382	−	1.35877i	−0.0745805	−	0.0669417i
$413$	−15.0045	−	15.0045i	−0.738323	−	0.738323i
$414$		0			0
$415$		−	20.2048i		−	0.991817i
$416$	−11.0158	−	18.9088i	−0.540092	−	0.927079i
$417$		0			0
$418$	0.165453	−	0.432029i	0.00809257	−	0.0211312i
$419$	−9.09125	+	9.09125i	−0.444137	+	0.444137i	−0.893400	−	0.449263i	$-0.851687\pi$
$419$	−9.09125	+	9.09125i	−0.444137	+	0.444137i	0.449263	+	0.893400i	$0.351687\pi$
$420$		0			0
$421$	−17.9862	−	17.9862i	−0.876595	−	0.876595i	0.116586	−	0.993181i	$-0.462805\pi$
$421$	−17.9862	−	17.9862i	−0.876595	−	0.876595i	−0.993181	+	0.116586i	$0.962805\pi$
$422$	−5.40840	−	12.1220i	−0.263277	−	0.590087i
$423$		0			0
$424$	−10.3317	−	3.33019i	−0.501750	−	0.161729i
$425$	−9.12913			−0.442828
$426$		0			0
$427$	7.75106	−	7.75106i	0.375100	−	0.375100i
$428$	−0.355427	−	6.58494i	−0.0171802	−	0.318295i
$429$		0			0
$430$	−7.55061	+	19.7161i	−0.364123	+	0.950793i
$431$	30.7707			1.48217			0.741085	−	0.671411i	$-0.234311\pi$
$431$	30.7707			1.48217			0.741085	+	0.671411i	$0.234311\pi$
$432$		0			0
$433$	3.49735			0.168072			0.0840360	−	0.996463i	$-0.473219\pi$
$433$	3.49735			0.168072			0.0840360	+	0.996463i	$0.473219\pi$
$434$	−20.1001	+	52.4852i	−0.964837	+	2.51937i
$435$		0			0
$436$	−22.8182	+	1.23163i	−1.09279	+	0.0589843i
$437$	−1.33186	+	1.33186i	−0.0637113	+	0.0637113i
$438$		0			0
$439$	−21.1290			−1.00843			−0.504216	−	0.863578i	$-0.668218\pi$
$439$	−21.1290			−1.00843			−0.504216	+	0.863578i	$0.668218\pi$
$440$	−1.17077	−	2.28450i	−0.0558142	−	0.108909i
$441$		0			0
$442$	5.27048	+	11.8128i	0.250691	+	0.561879i
$443$	−12.6022	−	12.6022i	−0.598750	−	0.598750i	0.341230	−	0.939980i	$-0.389157\pi$
$443$	−12.6022	−	12.6022i	−0.598750	−	0.598750i	−0.939980	+	0.341230i	$0.889157\pi$
$444$		0			0
$445$	−14.7454	+	14.7454i	−0.699001	+	0.699001i
$446$	−6.68735	+	17.4619i	−0.316655	+	0.826846i
$447$		0			0
$448$	20.5904	−	28.6216i	0.972805	−	1.35224i
$449$			9.98731i			0.471330i	0.971834	+	0.235665i	$0.0757268\pi$
$449$			9.98731i			0.471330i	−0.971834	+	0.235665i	$0.924273\pi$
$450$		0			0
$451$	−2.17775	−	2.17775i	−0.102546	−	0.102546i
$452$	−2.80115	+	3.12079i	−0.131755	+	0.146790i
$453$		0			0
$454$	−29.9592	+	13.3668i	−1.40605	+	0.627333i
$455$		−	50.7528i		−	2.37933i
$456$		0			0
$457$			15.2508i			0.713402i	0.934219	+	0.356701i	$0.116098\pi$
$457$			15.2508i			0.713402i	−0.934219	+	0.356701i	$0.883902\pi$
$458$	−4.06372	−	9.10810i	−0.189885	−	0.425594i
$459$		0			0
$460$	0.563300	+	10.4362i	0.0262640	+	0.486588i
$461$	−14.3850	−	14.3850i	−0.669976	−	0.669976i	0.287734	−	0.957710i	$-0.407098\pi$
$461$	−14.3850	−	14.3850i	−0.669976	−	0.669976i	−0.957710	+	0.287734i	$0.907098\pi$
$462$		0			0
$463$			22.1295i			1.02845i	0.857657	+	0.514223i	$0.171920\pi$
$463$			22.1295i			1.02845i	−0.857657	+	0.514223i	$0.828080\pi$
$464$	19.6538	−	24.4262i	0.912406	−	1.13396i
$465$		0			0
$466$	1.39832	+	0.535509i	0.0647757	+	0.0248070i
$467$	4.79951	−	4.79951i	0.222095	−	0.222095i	−0.587285	−	0.809380i	$-0.699803\pi$
$467$	4.79951	−	4.79951i	0.222095	−	0.222095i	0.809380	+	0.587285i	$0.199803\pi$
$468$		0			0
$469$	−40.1926	−	40.1926i	−1.85592	−	1.85592i
$470$	14.9987	−	6.69192i	0.691839	−	0.308675i
$471$		0			0
$472$	−4.17775	+	12.9611i	−0.192297	+	0.596585i
$473$	1.52905			0.0703058
$474$		0			0
$475$	2.92934	−	2.92934i	0.134408	−	0.134408i
$476$	−13.9212	+	15.5098i	−0.638078	+	0.710890i
$477$		0			0
$478$	0.418796	+	0.160385i	0.0191553	+	0.00733584i
$479$	23.2801			1.06369			0.531847	−	0.846840i	$-0.321498\pi$
$479$	23.2801			1.06369			0.531847	+	0.846840i	$0.321498\pi$
$480$		0			0
$481$	−16.9730			−0.773902
$482$	15.4961	+	5.93449i	0.705827	+	0.270309i
$483$		0			0
$484$	14.5711	−	16.2338i	0.662323	−	0.737901i
$485$	−7.03820	+	7.03820i	−0.319588	+	0.319588i
$486$		0			0
$487$	21.0748			0.954990			0.477495	−	0.878635i	$-0.341545\pi$
$487$	21.0748			0.954990			0.477495	+	0.878635i	$0.341545\pi$
$488$	−6.69550	−	2.15815i	−0.303091	−	0.0976949i
$489$		0			0
$490$	47.7654	−	21.3113i	2.15782	−	0.962746i
$491$	26.1459	+	26.1459i	1.17995	+	1.17995i	0.979756	+	0.200194i	$0.0641571\pi$
$491$	26.1459	+	26.1459i	1.17995	+	1.17995i	0.200194	+	0.979756i	$0.435843\pi$
$492$		0			0
$493$	−13.1039	+	13.1039i	−0.590170	+	0.590170i
$494$	−5.48168	−	2.09930i	−0.246632	−	0.0944521i
$495$		0			0
$496$	35.8588	−	3.88233i	1.61011	−	0.174322i
$497$			52.4018i			2.35054i
$498$		0			0
$499$	21.0195	+	21.0195i	0.940961	+	0.940961i	0.998352	−	0.0573910i	$-0.0182782\pi$
$499$	21.0195	+	21.0195i	0.940961	+	0.940961i	−0.0573910	+	0.998352i	$0.518278\pi$
$500$	0.365448	+	6.77059i	0.0163433	+	0.302790i
$501$		0			0
$502$	5.72427	+	12.8299i	0.255487	+	0.572628i
$503$		−	44.4925i		−	1.98382i	−0.126929	−	0.991912i	$-0.540512\pi$
$503$		−	44.4925i		−	1.98382i	0.126929	−	0.991912i	$-0.459488\pi$
$504$		0			0
$505$		−	7.42440i		−	0.330382i
$506$	0.691249	−	0.308412i	0.0307298	−	0.0137106i
$507$		0			0
$508$	13.7336	−	15.3008i	0.609332	−	0.678864i
$509$	−11.7664	−	11.7664i	−0.521536	−	0.521536i	0.396499	−	0.918035i	$-0.370225\pi$
$509$	−11.7664	−	11.7664i	−0.521536	−	0.521536i	−0.918035	+	0.396499i	$0.870225\pi$
$510$		0			0
$511$		−	2.12714i		−	0.0940991i
$512$	−22.3732	−	3.38237i	−0.988765	−	0.149481i
$513$		0			0
$514$	11.9277	−	31.1456i	0.526110	−	1.37377i
$515$	−2.14086	+	2.14086i	−0.0943377	+	0.0943377i
$516$		0			0
$517$	−0.841092	−	0.841092i	−0.0369912	−	0.0369912i
$518$	−11.1424	−	24.9737i	−0.489570	−	1.09728i
$519$		0			0
$520$	−28.9862	+	14.8550i	−1.27113	+	0.651433i
$521$	29.6216			1.29775			0.648873	−	0.760897i	$-0.275241\pi$
$521$	29.6216			1.29775			0.648873	+	0.760897i	$0.275241\pi$
$522$		0			0
$523$	4.96353	−	4.96353i	0.217040	−	0.217040i	−0.590210	−	0.807250i	$-0.700955\pi$
$523$	4.96353	−	4.96353i	0.217040	−	0.217040i	0.807250	+	0.590210i	$0.200955\pi$
$524$	19.2305	−	1.03798i	0.840089	−	0.0453444i
$525$		0			0
$526$	−10.1848	+	26.5945i	−0.444080	+	1.15958i
$527$	−21.3199			−0.928708
$528$		0			0
$529$	19.9183			0.866011
$530$	−5.77819	+	15.0880i	−0.250989	+	0.655379i
$531$		0			0
$532$	−0.509736	−	9.44379i	−0.0220998	−	0.409440i
$533$	−27.6317	+	27.6317i	−1.19686	+	1.19686i
$534$		0			0
$535$	−9.81517			−0.424347
$536$	−11.1909	+	34.7190i	−0.483375	+	1.49963i
$537$		0			0
$538$	−7.02609	−	15.7477i	−0.302916	−	0.678932i
$539$	−2.67857	−	2.67857i	−0.115374	−	0.115374i
$540$		0			0
$541$	10.0792	−	10.0792i	0.433338	−	0.433338i	−0.456424	−	0.889762i	$-0.650870\pi$
$541$	10.0792	−	10.0792i	0.433338	−	0.433338i	0.889762	+	0.456424i	$0.150870\pi$
$542$	1.10624	−	2.88861i	0.0475172	−	0.124076i
$543$		0			0
$544$	12.9327	+	3.41117i	0.554483	+	0.146253i
$545$			34.0115i			1.45689i
$546$		0			0
$547$	2.48797	+	2.48797i	0.106378	+	0.106378i	0.758293	−	0.651914i	$-0.226034\pi$
$547$	2.48797	+	2.48797i	0.106378	+	0.106378i	−0.651914	+	0.758293i	$0.726034\pi$
$548$	−20.5280	−	18.4254i	−0.876912	−	0.787096i
$549$		0			0
$550$	−1.52036	+	0.678334i	−0.0648285	+	0.0289243i
$551$		−	8.40953i		−	0.358258i
$552$		0			0
$553$		−	30.3662i		−	1.29130i
$554$	7.04277	+	15.7851i	0.299219	+	0.670645i
$555$		0			0
$556$	−37.0537	+	2.00000i	−1.57142	+	0.0848189i
$557$	24.2575	+	24.2575i	1.02782	+	1.02782i	0.999602	+	0.0282205i	$0.00898407\pi$
$557$	24.2575	+	24.2575i	1.02782	+	1.02782i	0.0282205	+	0.999602i	$0.491016\pi$
$558$		0			0
$559$		−	19.4009i		−	0.820570i
$560$	−40.8862	−	32.8978i	−1.72776	−	1.39019i
$561$		0			0
$562$	−19.5567	−	7.48957i	−0.824949	−	0.315928i
$563$	−14.4061	+	14.4061i	−0.607143	+	0.607143i	−0.942198	−	0.335055i	$-0.891245\pi$
$563$	−14.4061	+	14.4061i	−0.607143	+	0.607143i	0.335055	+	0.942198i	$0.391245\pi$
$564$		0			0
$565$	4.41346	+	4.41346i	0.185676	+	0.185676i
$566$	11.1909	−	4.99302i	0.470390	−	0.209872i
$567$		0			0
$568$	29.9280	−	15.3376i	1.25575	−	0.643551i
$569$	−33.5254			−1.40546			−0.702729	−	0.711457i	$-0.748036\pi$
$569$	−33.5254			−1.40546			−0.702729	+	0.711457i	$0.748036\pi$
$570$		0			0
$571$	14.5368	−	14.5368i	0.608348	−	0.608348i	−0.334167	−	0.942514i	$-0.608455\pi$
$571$	14.5368	−	14.5368i	0.608348	−	0.608348i	0.942514	+	0.334167i	$0.108455\pi$
$572$	1.75549	+	1.57569i	0.0734008	+	0.0658828i
$573$		0			0
$574$	−58.7965	−	22.5171i	−2.45412	−	0.939847i
$575$	6.77813			0.282668
$576$		0			0
$577$	20.3662			0.847855			0.423927	−	0.905696i	$-0.360651\pi$
$577$	20.3662			0.847855			0.423927	+	0.905696i	$0.360651\pi$
$578$	15.0685	+	5.77075i	0.626768	+	0.240032i
$579$		0			0
$580$	−34.7261	−	31.1693i	−1.44192	−	1.29424i
$581$	−21.1529	+	21.1529i	−0.877571	+	0.877571i
$582$		0			0
$583$	1.17012			0.0484616
$584$	−1.21486	+	0.622597i	−0.0502714	+	0.0257633i
$585$		0			0
$586$	−21.7309	+	9.69558i	−0.897695	+	0.400521i
$587$	−17.4809	−	17.4809i	−0.721512	−	0.721512i	0.247401	−	0.968913i	$-0.420424\pi$
$587$	−17.4809	−	17.4809i	−0.721512	−	0.721512i	−0.968913	+	0.247401i	$0.920424\pi$
$588$		0			0
$589$	6.84109	−	6.84109i	0.281882	−	0.281882i
$590$	18.9279	+	7.24878i	0.779251	+	0.298428i
$591$		0			0
$592$	−11.0018	+	13.6733i	−0.452173	+	0.561971i
$593$		−	25.6632i		−	1.05386i	−0.849908	−	0.526930i	$-0.823343\pi$
$593$		−	25.6632i		−	1.05386i	0.849908	−	0.526930i	$-0.176657\pi$
$594$		0			0
$595$	21.9341	+	21.9341i	0.899212	+	0.899212i
$596$	−21.9216	+	1.18324i	−0.897944	+	0.0484672i
$597$		0			0
$598$	−3.91319	−	8.77071i	−0.160022	−	0.358661i
$599$			22.4652i			0.917902i	0.888461	+	0.458951i	$0.151775\pi$
$599$			22.4652i			0.917902i	−0.888461	+	0.458951i	$0.848225\pi$
$600$		0			0
$601$		−	31.8106i		−	1.29758i	−0.760967	−	0.648790i	$-0.775275\pi$
$601$		−	31.8106i		−	1.29758i	0.760967	−	0.648790i	$-0.224725\pi$
$602$	28.5461	−	12.7363i	1.16345	−	0.519093i
$603$		0			0
$604$	−0.301347	−	0.270482i	−0.0122616	−	0.0110057i
$605$	−22.9581	−	22.9581i	−0.933379	−	0.933379i
$606$		0			0
$607$		−	14.9829i		−	0.608138i	−0.952650	−	0.304069i	$-0.901655\pi$
$607$		−	14.9829i		−	0.608138i	0.952650	−	0.304069i	$-0.0983453\pi$
$608$	−5.24439	+	3.05525i	−0.212688	+	0.123907i
$609$		0			0
$610$	−3.74459	+	9.77784i	−0.151614	+	0.395893i
$611$	−10.6720	+	10.6720i	−0.431741	+	0.431741i
$612$		0			0
$613$	25.6734	+	25.6734i	1.03694	+	1.03694i	0.999291	+	0.0376494i	$0.0119870\pi$
$613$	25.6734	+	25.6734i	1.03694	+	1.03694i	0.0376494	+	0.999291i	$0.488013\pi$
$614$	4.00497	+	8.97642i	0.161627	+	0.362259i
$615$		0			0
$616$	−1.16599	+	3.61740i	−0.0469792	+	0.145749i
$617$	27.1598			1.09341			0.546705	−	0.837325i	$-0.315882\pi$
$617$	27.1598			1.09341			0.546705	+	0.837325i	$0.315882\pi$
$618$		0			0
$619$	−29.4244	+	29.4244i	−1.18267	+	1.18267i	−0.203616	+	0.979051i	$0.565269\pi$
$619$	−29.4244	+	29.4244i	−1.18267	+	1.18267i	−0.979051	+	0.203616i	$0.934731\pi$
$620$	−2.89339	−	53.6054i	−0.116202	−	2.15285i
$621$		0			0
$622$	−10.5056	+	27.4321i	−0.421236	+	1.09993i
$623$	30.8747			1.23697
$624$		0			0
$625$	29.3974			1.17590
$626$	8.28952	−	21.6455i	0.331316	−	0.865128i
$627$		0			0
$628$	10.6157	−	0.572991i	0.423613	−	0.0228648i
$629$	7.33532	−	7.33532i	0.292478	−	0.292478i
$630$		0			0
$631$	−7.84697			−0.312383			−0.156191	−	0.987727i	$-0.549922\pi$
$631$	−7.84697			−0.312383			−0.156191	+	0.987727i	$0.549922\pi$
$632$	−17.3429	+	8.88794i	−0.689863	+	0.353543i
$633$		0			0
$634$	18.2206	+	40.8381i	0.723631	+	1.62189i
$635$	−21.6386	−	21.6386i	−0.858702	−	0.858702i
$636$		0			0
$637$	−33.9862	+	33.9862i	−1.34658	+	1.34658i
$638$	−1.20864	+	3.15600i	−0.0478507	+	0.124947i
$639$		0			0
$640$	−6.82171	+	32.9801i	−0.269652	+	1.30365i
$641$			37.7956i			1.49284i	0.665477	+	0.746418i	$0.268228\pi$
$641$			37.7956i			1.49284i	−0.665477	+	0.746418i	$0.731772\pi$
$642$		0			0
$643$	27.3026	+	27.3026i	1.07671	+	1.07671i	0.996802	+	0.0799071i	$0.0254624\pi$
$643$	27.3026	+	27.3026i	1.07671	+	1.07671i	0.0799071	+	0.996802i	$0.474538\pi$
$644$	10.3361	−	11.5156i	0.407301	−	0.453778i
$645$		0			0
$646$	3.27632	−	1.46178i	0.128905	−	0.0575130i
$647$		−	0.100686i		−	0.00395836i	−0.999998	−	0.00197918i	$-0.999370\pi$
$647$		−	0.100686i		−	0.00395836i	0.999998	−	0.00197918i	$-0.000629993\pi$
$648$		0			0
$649$		−	1.46793i		−	0.0576212i
$650$	8.60684	+	19.2907i	0.337588	+	0.756643i
$651$		0			0
$652$	−2.02270	−	37.4742i	−0.0792150	−	1.46760i
$653$	−9.10477	−	9.10477i	−0.356297	−	0.356297i	0.506149	−	0.862446i	$-0.331069\pi$
$653$	−9.10477	−	9.10477i	−0.356297	−	0.356297i	−0.862446	+	0.506149i	$0.831069\pi$
$654$		0			0
$655$		−	28.6640i		−	1.11999i
$656$	4.34917	+	40.1708i	0.169806	+	1.56840i
$657$		0			0
$658$	−22.7084	−	8.69659i	−0.885267	−	0.339028i
$659$	14.6141	−	14.6141i	0.569285	−	0.569285i	−0.362643	−	0.931928i	$-0.618126\pi$
$659$	14.6141	−	14.6141i	0.569285	−	0.569285i	0.931928	+	0.362643i	$0.118126\pi$
$660$		0			0
$661$	5.87057	+	5.87057i	0.228339	+	0.228339i	0.811998	−	0.583660i	$-0.198380\pi$
$661$	5.87057	+	5.87057i	0.228339	+	0.228339i	−0.583660	+	0.811998i	$0.698380\pi$
$662$	−12.9410	+	5.77385i	−0.502968	+	0.224407i
$663$		0			0
$664$	18.2723	+	5.88968i	0.709102	+	0.228564i
$665$	−14.0764			−0.545860
$666$		0			0
$667$	9.72929	−	9.72929i	0.376720	−	0.376720i
$668$	26.9384	−	30.0124i	1.04228	−	1.16121i
$669$		0			0
$670$	50.7023	+	19.4173i	1.95880	+	0.750156i
$671$	0.758305			0.0292741
$672$		0			0
$673$	−27.3515			−1.05432			−0.527161	−	0.849766i	$-0.676743\pi$
$673$	−27.3515			−1.05432			−0.527161	+	0.849766i	$0.676743\pi$
$674$	−30.8133	−	11.8005i	−1.18688	−	0.454538i
$675$		0			0
$676$	2.62548	−	2.92508i	0.100980	−	0.112503i
$677$	31.2462	−	31.2462i	1.20089	−	1.20089i	0.226992	−	0.973897i	$-0.427111\pi$
$677$	31.2462	−	31.2462i	1.20089	−	1.20089i	0.973897	−	0.226992i	$-0.0728891\pi$
$678$		0			0
$679$	14.7369			0.565551
$680$	6.10719	−	18.9471i	0.234200	−	0.726588i
$681$		0			0
$682$	−3.55061	+	1.58416i	−0.135960	+	0.0606606i
$683$	15.0378	+	15.0378i	0.575406	+	0.575406i	0.933634	−	0.358228i	$-0.116619\pi$
$683$	15.0378	+	15.0378i	0.575406	+	0.575406i	−0.358228	+	0.933634i	$0.616619\pi$
$684$		0			0
$685$	−29.0310	+	29.0310i	−1.10922	+	1.10922i
$686$	−31.5735	−	12.0916i	−1.20548	−	0.461660i
$687$		0			0
$688$	−15.6293	−	12.5756i	−0.595860	−	0.479440i
$689$		−	14.8468i		−	0.565617i
$690$		0			0
$691$	4.24894	+	4.24894i	0.161637	+	0.161637i	0.783292	−	0.621654i	$-0.213539\pi$
$691$	4.24894	+	4.24894i	0.161637	+	0.161637i	−0.621654	+	0.783292i	$0.713539\pi$
$692$	0.607209	+	11.2497i	0.0230826	+	0.427648i
$693$		0			0
$694$	−17.2820	−	38.7344i	−0.656014	−	1.47034i
$695$			55.2302i			2.09500i
$696$		0			0
$697$		−	23.8835i		−	0.904653i
$698$	9.82672	−	4.38435i	0.371947	−	0.165950i
$699$		0			0
$700$	−22.7337	+	25.3279i	−0.859255	+	0.957305i
$701$	23.4629	+	23.4629i	0.886183	+	0.886183i	0.994154	−	0.107971i	$-0.0344354\pi$
$701$	23.4629	+	23.4629i	0.886183	+	0.886183i	−0.107971	+	0.994154i	$0.534435\pi$
$702$		0			0
$703$			4.70750i			0.177547i
$704$	2.40727	−	0.392858i	0.0907274	−	0.0148064i
$705$		0			0
$706$	5.31891	−	13.8887i	0.200180	−	0.522707i
$707$	−7.77278	+	7.77278i	−0.292326	+	0.292326i
$708$		0			0
$709$	2.79314	+	2.79314i	0.104898	+	0.104898i	0.757608	−	0.652710i	$-0.226368\pi$
$709$	2.79314	+	2.79314i	0.104898	+	0.104898i	−0.652710	+	0.757608i	$0.726368\pi$
$710$	−20.3942	−	45.7099i	−0.765380	−	1.71546i
$711$		0			0
$712$	−9.03679	−	17.6333i	−0.338668	−	0.660837i
$713$	15.8294			0.592816
$714$		0			0
$715$	2.48264	−	2.48264i	0.0928454	−	0.0928454i
$716$	41.5687	−	2.24371i	1.55350	−	0.0838512i
$717$		0			0
$718$	−5.94706	+	15.5289i	−0.221942	+	0.579533i
$719$	33.8130			1.26101			0.630507	−	0.776184i	$-0.282847\pi$
$719$	33.8130			1.26101			0.630507	+	0.776184i	$0.282847\pi$
$720$		0			0
$721$	4.48264			0.166942
$722$	9.02751	−	23.5725i	0.335969	−	0.877279i
$723$		0			0
$724$	0.497665	+	9.22015i	0.0184956	+	0.342664i
$725$	−21.3990	+	21.3990i	−0.794740	+	0.794740i
$726$		0			0
$727$	−2.42732			−0.0900245			−0.0450122	−	0.998986i	$-0.514333\pi$
$727$	−2.42732			−0.0900245			−0.0450122	+	0.998986i	$0.514333\pi$
$728$	45.8984	+	14.7944i	1.70111	+	0.548315i
$729$		0			0
$730$	0.827859	+	1.85550i	0.0306404	+	0.0686750i
$731$	8.38460	+	8.38460i	0.310115	+	0.310115i
$732$		0			0
$733$	16.8596	−	16.8596i	0.622725	−	0.622725i	−0.323503	−	0.946227i	$-0.604860\pi$
$733$	16.8596	−	16.8596i	0.622725	−	0.622725i	0.946227	+	0.323503i	$0.104860\pi$
$734$	1.77008	−	4.62202i	0.0653349	−	0.170602i
$735$		0			0
$736$	−9.60215	−	2.53270i	−0.353940	−	0.0933566i
$737$		−	3.93214i		−	0.144842i
$738$		0			0
$739$	25.2243	+	25.2243i	0.927892	+	0.927892i	0.997570	−	0.0696780i	$-0.0221972\pi$
$739$	25.2243	+	25.2243i	0.927892	+	0.927892i	−0.0696780	+	0.997570i	$0.522197\pi$
$740$	19.4390	+	17.4480i	0.714592	+	0.641401i
$741$		0			0
$742$	21.8453	−	9.74661i	0.801965	−	0.357809i
$743$		−	33.4926i		−	1.22872i	−0.789025	−	0.614361i	$-0.789414\pi$
$743$		−	33.4926i		−	1.22872i	0.789025	−	0.614361i	$-0.210586\pi$
$744$		0			0
$745$			32.6752i			1.19713i
$746$	15.6323	+	35.0370i	0.572340	+	1.28280i
$747$		0			0
$748$	−1.43965	+	0.0777065i	−0.0526390	+	0.00284123i
$749$	10.2757	+	10.2757i	0.375467	+	0.375467i
$750$		0			0
$751$			17.9247i			0.654081i	0.945010	+	0.327040i	$0.106051\pi$
$751$			17.9247i			0.654081i	−0.945010	+	0.327040i	$0.893949\pi$
$752$	1.67974	+	15.5148i	0.0612538	+	0.565766i
$753$		0			0
$754$	40.0440	+	15.3355i	1.45832	+	0.558487i
$755$	−0.426168	+	0.426168i	−0.0155099	+	0.0155099i
$756$		0			0
$757$	3.10619	+	3.10619i	0.112896	+	0.112896i	0.761298	−	0.648402i	$-0.224562\pi$
$757$	3.10619	+	3.10619i	0.112896	+	0.112896i	−0.648402	+	0.761298i	$0.724562\pi$
$758$	−27.3926	+	12.2217i	−0.994945	+	0.443910i
$759$		0			0
$760$	4.12005	+	8.03939i	0.149450	+	0.291619i
$761$	−1.10917			−0.0402073			−0.0201037	−	0.999798i	$-0.506400\pi$
$761$	−1.10917			−0.0402073			−0.0201037	+	0.999798i	$0.506400\pi$
$762$		0			0
$763$	35.6075	−	35.6075i	1.28908	−	1.28908i
$764$	−11.4586	−	10.2849i	−0.414556	−	0.372096i
$765$		0			0
$766$	−40.1522	−	15.3770i	−1.45076	−	0.555593i
$767$	−18.6254			−0.672523
$768$		0			0
$769$	22.4591			0.809897			0.404948	−	0.914340i	$-0.367289\pi$
$769$	22.4591			0.809897			0.404948	+	0.914340i	$0.367289\pi$
$770$	5.28271	+	2.02311i	0.190376	+	0.0729077i
$771$		0			0
$772$	−5.23517	−	4.69897i	−0.188418	−	0.169120i
$773$	22.6327	−	22.6327i	0.814041	−	0.814041i	−0.171196	−	0.985237i	$-0.554763\pi$
$773$	22.6327	−	22.6327i	0.814041	−	0.814041i	0.985237	+	0.171196i	$0.0547631\pi$
$774$		0			0
$775$	−34.8159			−1.25062
$776$	−4.31338	−	8.41663i	−0.154841	−	0.302139i
$777$		0			0
$778$	35.5376	−	15.8556i	1.27408	−	0.568453i
$779$	7.66372	+	7.66372i	0.274581	+	0.274581i
$780$		0			0
$781$	−2.56330	+	2.56330i	−0.0917221	+	0.0917221i
$782$	5.48168	+	2.09930i	0.196024	+	0.0750709i
$783$		0			0
$784$	5.34935	+	49.4089i	0.191048	+	1.76460i
$785$		−	15.8232i		−	0.564754i
$786$		0			0
$787$	−38.6505	−	38.6505i	−1.37774	−	1.37774i	−0.848425	−	0.529315i	$-0.822449\pi$
$787$	−38.6505	−	38.6505i	−1.37774	−	1.37774i	−0.529315	−	0.848425i	$-0.677551\pi$
$788$	−18.0885	+	0.976342i	−0.644377	+	0.0347807i
$789$		0			0
$790$	11.8182	+	26.4883i	0.420472	+	0.942411i
$791$		−	9.24111i		−	0.328576i
$792$		0			0
$793$		−	9.62153i		−	0.341671i
$794$	−37.3215	+	16.6516i	−1.32449	+	0.590943i
$795$		0			0
$796$	34.7523	+	31.1929i	1.23176	+	1.10560i
$797$	−37.8969	−	37.8969i	−1.34238	−	1.34238i	−0.893689	−	0.448686i	$-0.851892\pi$
$797$	−37.8969	−	37.8969i	−1.34238	−	1.34238i	−0.448686	−	0.893689i	$-0.648108\pi$
$798$		0			0
$799$		−	9.22432i		−	0.326333i
$800$	21.1194	+	5.57054i	0.746684	+	0.196948i
$801$		0			0
$802$	11.4139	−	29.8039i	0.403040	−	1.05241i
$803$	0.104052	−	0.104052i	0.00367191	−	0.00367191i
$804$		0			0
$805$	−16.2855	−	16.2855i	−0.573989	−	0.573989i
$806$	20.1001	+	45.0508i	0.707997	+	1.58685i
$807$		0			0
$808$	6.71427	+	2.16420i	0.236207	+	0.0761363i
$809$	−27.0719			−0.951799			−0.475899	−	0.879500i	$-0.657877\pi$
$809$	−27.0719			−0.951799			−0.475899	+	0.879500i	$0.657877\pi$
$810$		0			0
$811$	−19.0554	+	19.0554i	−0.669126	+	0.669126i	−0.957514	−	0.288388i	$-0.906881\pi$
$811$	−19.0554	+	19.0554i	−0.669126	+	0.669126i	0.288388	+	0.957514i	$0.406881\pi$
$812$	3.72365	+	68.9874i	0.130674	+	2.42098i
$813$		0			0
$814$	0.676576	−	1.76667i	0.0237140	−	0.0619217i
$815$	−55.8571			−1.95659
$816$		0			0
$817$	−5.38088			−0.188253
$818$	−4.94794	+	12.9200i	−0.173001	+	0.451737i
$819$		0			0
$820$	60.0514	−	3.24132i	2.09708	−	0.113192i
$821$	37.5393	−	37.5393i	1.31013	−	1.31013i	0.388817	−	0.921315i	$-0.372884\pi$
$821$	37.5393	−	37.5393i	1.31013	−	1.31013i	0.921315	−	0.388817i	$-0.127116\pi$
$822$		0			0
$823$	−27.9589			−0.974584			−0.487292	−	0.873239i	$-0.662015\pi$
$823$	−27.9589			−0.974584			−0.487292	+	0.873239i	$0.662015\pi$
$824$	−1.31203	−	2.56015i	−0.0457069	−	0.0891870i
$825$		0			0
$826$	−12.2272	−	27.4050i	−0.425438	−	0.953543i
$827$	2.04182	+	2.04182i	0.0710011	+	0.0710011i	0.741716	−	0.670715i	$-0.234012\pi$
$827$	2.04182	+	2.04182i	0.0710011	+	0.0710011i	−0.670715	+	0.741716i	$0.734012\pi$
$828$		0			0
$829$	34.5808	−	34.5808i	1.20104	−	1.20104i	0.227188	−	0.973851i	$-0.427047\pi$
$829$	34.5808	−	34.5808i	1.20104	−	1.20104i	0.973851	−	0.227188i	$-0.0729533\pi$
$830$	10.2191	−	26.6841i	0.354711	−	0.926218i
$831$		0			0
$832$	−4.98466	−	30.5439i	−0.172812	−	1.05892i
$833$		−	29.3760i		−	1.01782i
$834$		0			0
$835$	−42.4439	−	42.4439i	−1.46883	−	1.46883i
$836$	0.437020	−	0.486889i	0.0151147	−	0.0168394i
$837$		0			0
$838$	−16.6048	+	7.40847i	−0.573602	+	0.255922i
$839$		−	0.865723i		−	0.0298881i	−0.999888	−	0.0149440i	$-0.995243\pi$
$839$		−	0.865723i		−	0.0298881i	0.999888	−	0.0149440i	$-0.00475701\pi$
$840$		0			0
$841$			32.4321i			1.11835i
$842$	−14.6570	−	32.8510i	−0.505114	−	1.13212i
$843$		0			0
$844$	−1.01176	−	18.7446i	−0.0348261	−	0.645217i
$845$	−4.13669	−	4.13669i	−0.142306	−	0.142306i
$846$		0			0
$847$			48.0707i			1.65173i
$848$	−11.9605	−	9.62363i	−0.410724	−	0.330477i
$849$		0			0
$850$	−12.0566	−	4.61730i	−0.413539	−	0.158372i
$851$	−5.44628	+	5.44628i	−0.186696	+	0.186696i
$852$		0			0
$853$	−14.4262	−	14.4262i	−0.493942	−	0.493942i	0.415604	−	0.909546i	$-0.363570\pi$
$853$	−14.4262	−	14.4262i	−0.493942	−	0.493942i	−0.909546	+	0.415604i	$0.863570\pi$
$854$	14.1569	−	6.31635i	0.484441	−	0.216141i
$855$		0			0
$856$	2.86110	−	8.87635i	0.0977905	−	0.303388i
$857$	37.6532			1.28621			0.643105	−	0.765778i	$-0.277646\pi$
$857$	37.6532			1.28621			0.643105	+	0.765778i	$0.277646\pi$
$858$		0			0
$859$	−38.7470	+	38.7470i	−1.32203	+	1.32203i	−0.409901	+	0.912130i	$0.634437\pi$
$859$	−38.7470	+	38.7470i	−1.32203	+	1.32203i	−0.912130	+	0.409901i	$0.865563\pi$
$860$	−19.9438	+	22.2196i	−0.680079	+	0.757684i
$861$		0			0
$862$	40.6381	+	15.5631i	1.38414	+	0.530080i
$863$	−14.8672			−0.506085			−0.253043	−	0.967455i	$-0.581431\pi$
$863$	−14.8672			−0.506085			−0.253043	+	0.967455i	$0.581431\pi$
$864$		0			0
$865$	16.7681			0.570134
$866$	4.61887	+	1.76888i	0.156956	+	0.0601089i
$867$		0			0
$868$	−53.0916	+	59.1499i	−1.80205	+	2.00768i
$869$	1.48540	−	1.48540i	0.0503887	−	0.0503887i
$870$		0			0
$871$	−49.8918			−1.69052
$872$	−30.7584	−	9.91431i	−1.04161	−	0.335741i
$873$		0			0
$874$	−2.43258	+	1.08533i	−0.0822831	+	0.0367119i
$875$	−10.5654	−	10.5654i	−0.357176	−	0.357176i
$876$		0			0
$877$	−13.7699	+	13.7699i	−0.464976	+	0.464976i	−0.900283	−	0.435306i	$-0.856640\pi$
$877$	−13.7699	+	13.7699i	−0.464976	+	0.464976i	0.435306	+	0.900283i	$0.356640\pi$
$878$	−27.9046	−	10.6865i	−0.941734	−	0.360653i
$879$		0			0
$880$	−0.390761	−	3.60924i	−0.0131726	−	0.121667i
$881$		−	20.6232i		−	0.694812i	−0.937715	−	0.347406i	$-0.887063\pi$
$881$		−	20.6232i		−	0.694812i	0.937715	−	0.347406i	$-0.112937\pi$
$882$		0			0
$883$	−41.5416	−	41.5416i	−1.39799	−	1.39799i	−0.805802	−	0.592185i	$-0.798265\pi$
$883$	−41.5416	−	41.5416i	−1.39799	−	1.39799i	−0.592185	−	0.805802i	$-0.701735\pi$
$884$	0.985956	+	18.2666i	0.0331613	+	0.614373i
$885$		0			0
$886$	−10.2696	−	23.0174i	−0.345013	−	0.773285i
$887$			7.44312i			0.249916i	0.992162	+	0.124958i	$0.0398795\pi$
$887$			7.44312i			0.249916i	−0.992162	+	0.124958i	$0.960120\pi$
$888$		0			0
$889$			45.3079i			1.51958i
$890$	−26.9319	+	12.0161i	−0.902759	+	0.402780i
$891$		0			0
$892$	−17.6637	+	19.6793i	−0.591423	+	0.658911i
$893$	2.95989	+	2.95989i	0.0990489	+	0.0990489i
$894$		0			0
$895$		−	61.9602i		−	2.07110i
$896$	41.6694	−	27.3858i	1.39208	−	0.914896i
$897$		0			0
$898$	−5.05135	+	13.1900i	−0.168566	+	0.440157i
$899$	−49.9746	+	49.9746i	−1.66675	+	1.66675i
$900$		0			0
$901$	6.41642	+	6.41642i	0.213762	+	0.213762i
$902$	−1.77465	−	3.97756i	−0.0590894	−	0.132438i
$903$		0			0
$904$	−5.27783	+	2.70480i	−0.175538	+	0.0899604i
$905$	13.7431			0.456835
$906$		0			0
$907$	3.75106	−	3.75106i	0.124552	−	0.124552i	−0.642083	−	0.766635i	$-0.721930\pi$
$907$	3.75106	−	3.75106i	0.124552	−	0.124552i	0.766635	+	0.642083i	$0.221930\pi$
$908$	−46.3270	+	2.50054i	−1.53742	+	0.0829832i
$909$		0			0
$910$	25.6696	−	67.0281i	0.850938	−	2.22196i
$911$	−29.9816			−0.993334			−0.496667	−	0.867941i	$-0.665443\pi$
$911$	−29.9816			−0.993334			−0.496667	+	0.867941i	$0.665443\pi$
$912$		0			0
$913$	−2.06944			−0.0684886
$914$	−7.71349	+	20.1414i	−0.255140	+	0.666217i
$915$		0			0
$916$	−0.760206	−	14.0842i	−0.0251179	−	0.465355i
$917$	−30.0090	+	30.0090i	−0.990984	+	0.990984i
$918$		0			0
$919$	38.1402			1.25813			0.629064	−	0.777353i	$-0.283438\pi$
$919$	38.1402			1.25813			0.629064	+	0.777353i	$0.283438\pi$
$920$	−4.53443	+	14.0677i	−0.149496	+	0.463799i
$921$		0			0
$922$	−11.7224	−	26.2736i	−0.386055	−	0.865273i
$923$	32.5237	+	32.5237i	1.07053	+	1.07053i
$924$		0			0
$925$	11.9788	−	11.9788i	0.393860	−	0.393860i
$926$	−11.1926	+	29.2260i	−0.367811	+	0.960425i
$927$		0			0
$928$	38.3106	−	22.3188i	1.25761	−	0.732649i
$929$		−	13.8738i		−	0.455183i	−0.973757	−	0.227592i	$-0.926915\pi$
$929$		−	13.8738i		−	0.455183i	0.973757	−	0.227592i	$-0.0730851\pi$
$930$		0			0
$931$	9.42615	+	9.42615i	0.308930	+	0.308930i
$932$	1.57588	+	1.41447i	0.0516195	+	0.0463325i
$933$		0			0
$934$	8.76608	−	3.91113i	0.286835	−	0.127976i
$935$			2.14587i			0.0701775i
$936$		0			0
$937$		−	26.4097i		−	0.862767i	−0.902169	−	0.431384i	$-0.858026\pi$
$937$		−	26.4097i		−	0.862767i	0.902169	−	0.431384i	$-0.141974\pi$
$938$	−32.7530	−	73.4099i	−1.06942	−	2.39692i
$939$		0			0
$940$	23.1931	−	1.25187i	0.756475	−	0.0408313i
$941$	4.91123	+	4.91123i	0.160102	+	0.160102i	0.782612	−	0.622510i	$-0.213887\pi$
$941$	4.91123	+	4.91123i	0.160102	+	0.160102i	−0.622510	+	0.782612i	$0.713887\pi$
$942$		0			0
$943$			17.7329i			0.577462i
$944$	−12.0729	+	15.0045i	−0.392940	+	0.488355i
$945$		0			0
$946$	2.01938	+	0.773357i	0.0656558	+	0.0251440i
$947$	6.84386	−	6.84386i	0.222396	−	0.222396i	−0.587111	−	0.809507i	$-0.699735\pi$
$947$	6.84386	−	6.84386i	0.222396	−	0.222396i	0.809507	+	0.587111i	$0.199735\pi$
$948$		0			0
$949$	−1.32023	−	1.32023i	−0.0428565	−	0.0428565i
$950$	5.35031	−	2.38713i	0.173587	−	0.0774486i
$951$		0			0
$952$	−26.2299	+	13.4424i	−0.850117	+	0.435671i
$953$	−4.33045			−0.140277			−0.0701386	−	0.997537i	$-0.522344\pi$
$953$	−4.33045			−0.140277			−0.0701386	+	0.997537i	$0.522344\pi$
$954$		0			0
$955$	−16.2048	+	16.2048i	−0.524377	+	0.524377i
$956$	0.471975	+	0.423634i	0.0152648	+	0.0137013i
$957$		0			0
$958$	30.7455	+	11.7745i	0.993342	+	0.380417i
$959$	60.7864			1.96289
$960$		0			0
$961$	−50.3079			−1.62284
$962$	−22.4159	−	8.58454i	−0.722716	−	0.276777i
$963$		0			0
$964$	17.4638	+	15.6751i	0.562471	+	0.504861i
$965$	−7.40365	+	7.40365i	−0.238332	+	0.238332i
$966$		0			0
$967$	40.6664			1.30774			0.653871	−	0.756606i	$-0.273144\pi$
$967$	40.6664			1.30774			0.653871	+	0.756606i	$0.273144\pi$
$968$	27.4544	−	14.0699i	0.882419	−	0.452225i
$969$		0			0
$970$	−12.8550	+	5.73544i	−0.412748	+	0.184154i
$971$	−24.0742	−	24.0742i	−0.772577	−	0.772577i	0.205979	−	0.978556i	$-0.433962\pi$
$971$	−24.0742	−	24.0742i	−0.772577	−	0.772577i	−0.978556	+	0.205979i	$0.933962\pi$
$972$		0			0
$973$	57.8218	−	57.8218i	1.85368	−	1.85368i
$974$	27.8330	+	10.6591i	0.891827	+	0.341541i
$975$		0			0
$976$	−7.75106	−	6.23665i	−0.248105	−	0.199630i
$977$			21.0381i			0.673068i	0.941671	+	0.336534i	$0.109255\pi$
$977$			21.0381i			0.673068i	−0.941671	+	0.336534i	$0.890745\pi$
$978$		0			0
$979$	1.51028	+	1.51028i	0.0482686	+	0.0482686i
$980$	73.8614	−	3.98673i	2.35942	−	0.127351i
$981$		0			0
$982$	21.3064	+	47.7544i	0.679913	+	1.52390i
$983$			14.1206i			0.450376i	0.974315	+	0.225188i	$0.0722997\pi$
$983$			14.1206i			0.450376i	−0.974315	+	0.225188i	$0.927700\pi$
$984$		0			0
$985$			26.9618i			0.859074i
$986$	−23.9337	+	10.6784i	−0.762204	+	0.340069i
$987$		0			0
$988$	−6.17775	−	5.54500i	−0.196540	−	0.176410i
$989$	−6.22534	−	6.22534i	−0.197954	−	0.197954i
$990$		0			0
$991$			33.3338i			1.05888i	0.848346	+	0.529442i	$0.177599\pi$
$991$			33.3338i			1.05888i	−0.848346	+	0.529442i	$0.822401\pi$
$992$	49.3215	+	13.0092i	1.56596	+	0.413044i
$993$		0			0
$994$	−26.5036	+	69.2059i	−0.840643	+	2.19508i
$995$	49.1472	−	49.1472i	1.55807	−	1.55807i
$996$		0			0
$997$	24.8358	+	24.8358i	0.786559	+	0.786559i	0.980928	−	0.194369i	$-0.0622660\pi$
$997$	24.8358	+	24.8358i	0.786559	+	0.786559i	−0.194369	+	0.980928i	$0.562266\pi$
$998$	17.1288	+	38.3911i	0.542203	+	1.21525i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.2.l.a.107.8	yes	16
3.2	odd	2	inner	144.2.l.a.107.1	yes	16
4.3	odd	2		576.2.l.a.143.7		16
8.3	odd	2		1152.2.l.b.287.2		16
8.5	even	2		1152.2.l.a.287.2		16
12.11	even	2		576.2.l.a.143.2		16
16.3	odd	4	inner	144.2.l.a.35.1	✓	16
16.5	even	4		1152.2.l.b.863.7		16
16.11	odd	4		1152.2.l.a.863.7		16
16.13	even	4		576.2.l.a.431.2		16
24.5	odd	2		1152.2.l.a.287.7		16
24.11	even	2		1152.2.l.b.287.7		16
48.5	odd	4		1152.2.l.b.863.2		16
48.11	even	4		1152.2.l.a.863.2		16
48.29	odd	4		576.2.l.a.431.7		16
48.35	even	4	inner	144.2.l.a.35.8	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.l.a.35.1	✓	16	16.3	odd	4	inner
144.2.l.a.35.8	yes	16	48.35	even	4	inner
144.2.l.a.107.1	yes	16	3.2	odd	2	inner
144.2.l.a.107.8	yes	16	1.1	even	1	trivial
576.2.l.a.143.2		16	12.11	even	2
576.2.l.a.143.7		16	4.3	odd	2
576.2.l.a.431.2		16	16.13	even	4
576.2.l.a.431.7		16	48.29	odd	4
1152.2.l.a.287.2		16	8.5	even	2
1152.2.l.a.287.7		16	24.5	odd	2
1152.2.l.a.863.2		16	48.11	even	4
1152.2.l.a.863.7		16	16.11	odd	4
1152.2.l.b.287.2		16	8.3	odd	2
1152.2.l.b.287.7		16	24.11	even	2
1152.2.l.b.863.2		16	48.5	odd	4
1152.2.l.b.863.7		16	16.5	even	4

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	144.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.32068 + 0.505776i) q^{2} +(1.48838 + 1.33594i) q^{4} +(2.10489 - 2.10489i) q^{5} -4.40731 q^{7} +(1.28999 + 2.51713i) q^{8} +O(q^{10})\)	\(q+(1.32068 + 0.505776i) q^{2} +(1.48838 + 1.33594i) q^{4} +(2.10489 - 2.10489i) q^{5} -4.40731 q^{7} +(1.28999 + 2.51713i) q^{8} +(3.84448 - 1.71528i) q^{10} +(-0.215589 - 0.215589i) q^{11} +(-2.73544 + 2.73544i) q^{13} +(-5.82064 - 2.22912i) q^{14} +(0.430552 + 3.97676i) q^{16} -2.36438i q^{17} +(0.758681 + 0.758681i) q^{19} +(5.94487 - 0.320879i) q^{20} +(-0.175684 - 0.393764i) q^{22} +1.75549i q^{23} -3.86110i q^{25} +(-4.99616 + 2.22912i) q^{26} +(-6.55976 - 5.88789i) q^{28} +(-5.54221 - 5.54221i) q^{29} -9.01709i q^{31} +(-1.44273 + 5.46978i) q^{32} +(1.19585 - 3.12259i) q^{34} +(-9.27690 + 9.27690i) q^{35} +(3.10242 + 3.10242i) q^{37} +(0.618250 + 1.38570i) q^{38} +(8.01355 + 2.58300i) q^{40} +10.1014 q^{41} +(-3.54621 + 3.54621i) q^{43} +(-0.0328654 - 0.608892i) q^{44} +(-0.887886 + 2.31844i) q^{46} +3.90136 q^{47} +12.4244 q^{49} +(1.95286 - 5.09927i) q^{50} +(-7.72575 + 0.417003i) q^{52} +(-2.71378 + 2.71378i) q^{53} -0.907583 q^{55} +(-5.68537 - 11.0938i) q^{56} +(-4.51635 - 10.1226i) q^{58} +(3.40445 + 3.40445i) q^{59} +(-1.75868 + 1.75868i) q^{61} +(4.56063 - 11.9087i) q^{62} +(-4.67187 + 6.49412i) q^{64} +11.5156i q^{65} +(9.11951 + 9.11951i) q^{67} +(3.15866 - 3.51910i) q^{68} +(-16.9438 + 7.55976i) q^{70} -11.8897i q^{71} +0.482639i q^{73} +(2.52817 + 5.66643i) q^{74} +(0.115657 + 2.14275i) q^{76} +(0.950169 + 0.950169i) q^{77} +6.88995i q^{79} +(9.27690 + 7.46437i) q^{80} +(13.3407 + 5.10904i) q^{82} +(4.79951 - 4.79951i) q^{83} +(-4.97676 - 4.97676i) q^{85} +(-6.47699 + 2.88981i) q^{86} +(0.264559 - 0.820773i) q^{88} -7.00534 q^{89} +(12.0559 - 12.0559i) q^{91} +(-2.34522 + 2.61284i) q^{92} +(5.15244 + 1.97322i) q^{94} +3.19387 q^{95} -3.34374 q^{97} +(16.4086 + 6.28397i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 8 q^{10} - 16 q^{16} + 16 q^{19} - 40 q^{22} - 24 q^{28} + 24 q^{34} + 72 q^{40} - 32 q^{43} + 40 q^{46} + 16 q^{49} + 24 q^{52} - 64 q^{55} + 24 q^{58} - 32 q^{61} - 48 q^{64} - 16 q^{67} - 72 q^{70} + 80 q^{82} - 32 q^{85} + 48 q^{88} + 48 q^{91} + 72 q^{94}+O(q^{100}) \) 16 * q - 8 * q^10 - 16 * q^16 + 16 * q^19 - 40 * q^22 - 24 * q^28 + 24 * q^34 + 72 * q^40 - 32 * q^43 + 40 * q^46 + 16 * q^49 + 24 * q^52 - 64 * q^55 + 24 * q^58 - 32 * q^61 - 48 * q^64 - 16 * q^67 - 72 * q^70 + 80 * q^82 - 32 * q^85 + 48 * q^88 + 48 * q^91 + 72 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more