LMFDB - Embedded newform 144.2.l.a.107.1

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			107.1
Root			$0.944649 + 1.05244i$ of defining polynomial
Character	$\chi$	$=$	144.107
Dual form			144.2.l.a.35.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32068 - 0.505776i) q^{2} +(1.48838 + 1.33594i) q^{4} +(-2.10489 + 2.10489i) q^{5} -4.40731 q^{7} +(-1.28999 - 2.51713i) q^{8} +O(q^{10})$	\(q+(-1.32068 - 0.505776i) q^{2} +(1.48838 + 1.33594i) q^{4} +(-2.10489 + 2.10489i) q^{5} -4.40731 q^{7} +(-1.28999 - 2.51713i) q^{8} +(3.84448 - 1.71528i) q^{10} +(0.215589 + 0.215589i) q^{11} +(-2.73544 + 2.73544i) q^{13} +(5.82064 + 2.22912i) q^{14} +(0.430552 + 3.97676i) q^{16} +2.36438i q^{17} +(0.758681 + 0.758681i) q^{19} +(-5.94487 + 0.320879i) q^{20} +(-0.175684 - 0.393764i) q^{22} -1.75549i q^{23} -3.86110i q^{25} +(4.99616 - 2.22912i) q^{26} +(-6.55976 - 5.88789i) q^{28} +(5.54221 + 5.54221i) q^{29} -9.01709i q^{31} +(1.44273 - 5.46978i) q^{32} +(1.19585 - 3.12259i) q^{34} +(9.27690 - 9.27690i) q^{35} +(3.10242 + 3.10242i) q^{37} +(-0.618250 - 1.38570i) q^{38} +(8.01355 + 2.58300i) q^{40} -10.1014 q^{41} +(-3.54621 + 3.54621i) q^{43} +(0.0328654 + 0.608892i) q^{44} +(-0.887886 + 2.31844i) q^{46} -3.90136 q^{47} +12.4244 q^{49} +(-1.95286 + 5.09927i) q^{50} +(-7.72575 + 0.417003i) q^{52} +(2.71378 - 2.71378i) q^{53} -0.907583 q^{55} +(5.68537 + 11.0938i) q^{56} +(-4.51635 - 10.1226i) q^{58} +(-3.40445 - 3.40445i) q^{59} +(-1.75868 + 1.75868i) q^{61} +(-4.56063 + 11.9087i) q^{62} +(-4.67187 + 6.49412i) q^{64} -11.5156i q^{65} +(9.11951 + 9.11951i) q^{67} +(-3.15866 + 3.51910i) q^{68} +(-16.9438 + 7.55976i) q^{70} +11.8897i q^{71} +0.482639i q^{73} +(-2.52817 - 5.66643i) q^{74} +(0.115657 + 2.14275i) q^{76} +(-0.950169 - 0.950169i) q^{77} +6.88995i q^{79} +(-9.27690 - 7.46437i) q^{80} +(13.3407 + 5.10904i) q^{82} +(-4.79951 + 4.79951i) q^{83} +(-4.97676 - 4.97676i) q^{85} +(6.47699 - 2.88981i) q^{86} +(0.264559 - 0.820773i) q^{88} +7.00534 q^{89} +(12.0559 - 12.0559i) q^{91} +(2.34522 - 2.61284i) q^{92} +(5.15244 + 1.97322i) q^{94} -3.19387 q^{95} -3.34374 q^{97} +(-16.4086 - 6.28397i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	−0.998372	−	0.0570377i	$-0.981834\pi$
$5$	−2.10489	+	2.10489i	−0.941334	+	0.941334i	0.0570377	+	0.998372i	$0.481834\pi$
$6$		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	0.738861	−	0.673858i	$-0.235364\pi$
$11$	0.215589	+	0.215589i	0.0650026	+	0.0650026i	−0.673858	+	0.738861i	$0.735364\pi$
$12$		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	$0.0925661\pi$
$17$			2.36438i			0.573447i	−0.958013	+	0.286724i	$0.907434\pi$
$18$		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	$-0.941412\pi$
$23$		−	1.75549i		−	0.366045i	0.983109	−	0.183023i	$-0.0585881\pi$
$24$		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	$0.00942341\pi$
$29$	5.54221	+	5.54221i	1.02916	+	1.02916i	0.0296002	+	0.999562i	$0.490577\pi$
$30$		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	$-0.789290\pi$
$41$	−10.1014			−1.57757			−0.788785	+	0.614669i	$0.789290\pi$
$42$		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	$-0.591840\pi$
$47$	−3.90136			−0.569072			−0.284536	+	0.958665i	$0.591840\pi$
$48$		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	−0.495717	−	0.868484i	$-0.665095\pi$
$53$	2.71378	−	2.71378i	0.372766	−	0.372766i	0.868484	+	0.495717i	$0.165095\pi$
$54$		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	0.449871	−	0.893093i	$-0.351470\pi$
$59$	−3.40445	−	3.40445i	−0.443222	−	0.443222i	−0.893093	+	0.449871i	$0.851470\pi$
$60$		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	$0.249289\pi$
$71$			11.8897i			1.41105i	−0.708684	+	0.705526i	$0.750711\pi$
$72$		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	−0.919621	−	0.392807i	$-0.871504\pi$
$83$	−4.79951	+	4.79951i	−0.526814	+	0.526814i	0.392807	+	0.919621i	$0.371504\pi$
$84$		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	$-0.378918\pi$
$89$	7.00534			0.742564			0.371282	+	0.928520i	$0.378918\pi$
$90$		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	−0.789385	−	0.613899i	$-0.789600\pi$
$101$	−1.76361	+	1.76361i	−0.175486	+	0.175486i	0.613899	+	0.789385i	$0.289600\pi$
$102$		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	0.810766	−	0.585370i	$-0.199051\pi$
$107$	2.33152	+	2.33152i	0.225396	+	0.225396i	−0.585370	+	0.810766i	$0.699051\pi$
$108$		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	$-0.968556\pi$
$113$		−	2.09677i		−	0.197247i	0.995125	−	0.0986237i	$-0.0314440\pi$
$114$		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	−0.938950	−	0.344053i	$-0.888200\pi$
$131$	−6.80891	+	6.80891i	−0.594897	+	0.594897i	0.344053	+	0.938950i	$0.388200\pi$
$132$		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	$-0.299454\pi$
$137$	13.7922			1.17834			0.589172	+	0.808008i	$0.299454\pi$
$138$		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	−0.313667	−	0.949533i	$-0.601557\pi$
$149$	7.76174	−	7.76174i	0.635867	−	0.635867i	0.949533	+	0.313667i	$0.101557\pi$
$150$		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	$0.284875\pi$
$167$			20.1644i			1.56037i	−0.625548	+	0.780186i	$0.715125\pi$
$168$		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	0.539288	−	0.842121i	$-0.318693\pi$
$173$	−3.98315	−	3.98315i	−0.302833	−	0.302833i	−0.842121	+	0.539288i	$0.818693\pi$
$174$		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	$0.533704\pi$
$179$	−14.7182	+	14.7182i	−1.10009	+	1.10009i	−0.994399	+	0.105688i	$0.966296\pi$
$180$		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	$-0.410153\pi$
$191$	7.69868			0.557057			0.278528	+	0.960428i	$0.410153\pi$
$192$		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	−0.441135	−	0.897441i	$-0.645424\pi$
$197$	6.40456	−	6.40456i	0.456306	−	0.456306i	0.897441	+	0.441135i	$0.145424\pi$
$198$		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	$-0.470343\pi$
$227$	16.4029	−	16.4029i	1.08870	−	1.08870i	0.995663	−	0.0930369i	$-0.0296574\pi$
$228$		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	$-0.511042\pi$
$233$	−1.05879			−0.0693634			−0.0346817	+	0.999398i	$0.511042\pi$
$234$		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	$-0.503265\pi$
$239$	−0.317107			−0.0205119			−0.0102560	+	0.999947i	$0.503265\pi$
$240$		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	0.449765	−	0.893147i	$-0.351508\pi$
$251$	−7.02450	−	7.02450i	−0.443382	−	0.443382i	−0.893147	+	0.449765i	$0.851508\pi$
$252$		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	$0.263069\pi$
$257$			23.5830i			1.47107i	−0.677487	+	0.735535i	$0.736931\pi$
$258$		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	$-0.786787\pi$
$263$		−	20.1370i		−	1.24170i	0.783928	−	0.620851i	$-0.213213\pi$
$264$		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	0.919285	−	0.393592i	$-0.128768\pi$
$269$	8.62201	+	8.62201i	0.525693	+	0.525693i	−0.393592	+	0.919285i	$0.628768\pi$
$270$		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	$-0.354380\pi$
$281$	14.8081			0.883375			0.441688	+	0.897169i	$0.354380\pi$
$282$		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	−0.268265	−	0.963345i	$-0.586450\pi$
$293$	11.8979	−	11.8979i	0.695080	−	0.695080i	0.963345	+	0.268265i	$0.0864503\pi$
$294$		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	$-0.799555\pi$
$311$		−	20.7712i		−	1.17783i	0.808195	−	0.588915i	$-0.200445\pi$
$312$		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	$-0.902096\pi$
$317$	−22.3592	−	22.3592i	−1.25582	−	1.25582i	−0.302749	−	0.953070i	$-0.597904\pi$
$318$		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	$0.0478471\pi$
$347$	21.2074	+	21.2074i	1.13847	+	1.13847i	0.149751	+	0.988724i	$0.452153\pi$
$348$		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	$0.0902892\pi$
$353$			10.5163i			0.559727i	−0.960040	+	0.279864i	$0.909711\pi$
$354$		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	$-0.899574\pi$
$359$		−	11.7583i		−	0.620578i	0.950642	−	0.310289i	$-0.100426\pi$
$360$		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	$-0.216865\pi$
$383$	30.4027			1.55351			0.776754	+	0.629805i	$0.216865\pi$
$384$		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	−0.999910	−	0.0133943i	$-0.995736\pi$
$389$	−19.4571	+	19.4571i	−0.986516	+	0.986516i	0.0133943	+	0.999910i	$0.495736\pi$
$390$		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	$0.190536\pi$
$401$			22.5671i			1.12695i	−0.826133	+	0.563475i	$0.809464\pi$
$402$		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	−0.449263	−	0.893400i	$-0.648313\pi$
$419$	9.09125	−	9.09125i	0.444137	−	0.444137i	0.893400	+	0.449263i	$0.148313\pi$
$420$		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	$-0.765689\pi$
$431$	−30.7707			−1.48217			−0.741085	+	0.671411i	$0.765689\pi$
$432$		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	0.939980	−	0.341230i	$-0.110843\pi$
$443$	12.6022	+	12.6022i	0.598750	+	0.598750i	−0.341230	+	0.939980i	$0.610843\pi$
$444$		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	$-0.924273\pi$
$449$		−	9.98731i		−	0.471330i	0.971834	−	0.235665i	$-0.0757268\pi$
$450$		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	0.957710	−	0.287734i	$-0.0929019\pi$
$461$	14.3850	+	14.3850i	0.669976	+	0.669976i	−0.287734	+	0.957710i	$0.592902\pi$
$462$		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	−0.809380	−	0.587285i	$-0.800197\pi$
$467$	−4.79951	+	4.79951i	−0.222095	+	0.222095i	0.587285	+	0.809380i	$0.300197\pi$
$468$		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	$-0.678502\pi$
$479$	−23.2801			−1.06369			−0.531847	+	0.846840i	$0.678502\pi$
$480$		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	$-0.935843\pi$
$491$	−26.1459	−	26.1459i	−1.17995	−	1.17995i	−0.200194	−	0.979756i	$-0.564157\pi$
$492$		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	$0.459488\pi$
$503$			44.4925i			1.98382i	−0.126929	+	0.991912i	$0.540512\pi$
$504$		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	0.918035	−	0.396499i	$-0.129775\pi$
$509$	11.7664	+	11.7664i	0.521536	+	0.521536i	−0.396499	+	0.918035i	$0.629775\pi$
$510$		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	$-0.724759\pi$
$521$	−29.6216			−1.29775			−0.648873	+	0.760897i	$0.724759\pi$
$522$		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	$-0.991016\pi$
$557$	−24.2575	−	24.2575i	−1.02782	−	1.02782i	−0.0282205	−	0.999602i	$-0.508984\pi$
$558$		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	−0.335055	−	0.942198i	$-0.608755\pi$
$563$	14.4061	−	14.4061i	0.607143	−	0.607143i	0.942198	+	0.335055i	$0.108755\pi$
$564$		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	$-0.251964\pi$
$569$	33.5254			1.40546			0.702729	+	0.711457i	$0.251964\pi$
$570$		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	0.968913	−	0.247401i	$-0.0795765\pi$
$587$	17.4809	+	17.4809i	0.721512	+	0.721512i	−0.247401	+	0.968913i	$0.579576\pi$
$588$		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	$0.176657\pi$
$593$			25.6632i			1.05386i	−0.849908	+	0.526930i	$0.823343\pi$
$594$		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	$-0.848225\pi$
$599$		−	22.4652i		−	0.917902i	0.888461	−	0.458951i	$-0.151775\pi$
$600$		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	$-0.684118\pi$
$617$	−27.1598			−1.09341			−0.546705	+	0.837325i	$0.684118\pi$
$618$		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	$-0.731772\pi$
$641$		−	37.7956i		−	1.49284i	0.665477	−	0.746418i	$-0.268228\pi$
$642$		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	$0.000629993\pi$
$647$			0.100686i			0.00395836i	−0.999998	+	0.00197918i	$0.999370\pi$
$648$		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	0.862446	−	0.506149i	$-0.168931\pi$
$653$	9.10477	+	9.10477i	0.356297	+	0.356297i	−0.506149	+	0.862446i	$0.668931\pi$
$654$		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	−0.931928	−	0.362643i	$-0.881874\pi$
$659$	−14.6141	+	14.6141i	−0.569285	+	0.569285i	0.362643	+	0.931928i	$0.381874\pi$
$660$		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	$0.572889\pi$
$677$	−31.2462	+	31.2462i	−1.20089	+	1.20089i	−0.973897	+	0.226992i	$0.927111\pi$
$678$		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	0.358228	−	0.933634i	$-0.383381\pi$
$683$	−15.0378	−	15.0378i	−0.575406	−	0.575406i	−0.933634	+	0.358228i	$0.883381\pi$
$684$		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	0.107971	−	0.994154i	$-0.465565\pi$
$701$	−23.4629	−	23.4629i	−0.886183	−	0.886183i	−0.994154	+	0.107971i	$0.965565\pi$
$702$		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	$-0.717153\pi$
$719$	−33.8130			−1.26101			−0.630507	+	0.776184i	$0.717153\pi$
$720$		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	$0.210586\pi$
$743$			33.4926i			1.22872i	−0.789025	+	0.614361i	$0.789414\pi$
$744$		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	$-0.493600\pi$
$761$	1.10917			0.0402073			0.0201037	+	0.999798i	$0.493600\pi$
$762$		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	−0.985237	−	0.171196i	$-0.945237\pi$
$773$	−22.6327	+	22.6327i	−0.814041	+	0.814041i	0.171196	+	0.985237i	$0.445237\pi$
$774$		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	$0.148108\pi$
$797$	37.8969	+	37.8969i	1.34238	+	1.34238i	0.448686	+	0.893689i	$0.351892\pi$
$798$		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	$-0.342123\pi$
$809$	27.0719			0.951799			0.475899	+	0.879500i	$0.342123\pi$
$810$		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	$0.627116\pi$
$821$	−37.5393	+	37.5393i	−1.31013	+	1.31013i	−0.921315	+	0.388817i	$0.872884\pi$
$822$		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	0.670715	−	0.741716i	$-0.265988\pi$
$827$	−2.04182	−	2.04182i	−0.0710011	−	0.0710011i	−0.741716	+	0.670715i	$0.765988\pi$
$828$		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	$0.00475701\pi$
$839$			0.865723i			0.0298881i	−0.999888	+	0.0149440i	$0.995243\pi$
$840$		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	$-0.722354\pi$
$857$	−37.6532			−1.28621			−0.643105	+	0.765778i	$0.722354\pi$
$858$		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	$-0.418569\pi$
$863$	14.8672			0.506085			0.253043	+	0.967455i	$0.418569\pi$
$864$		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	$0.112937\pi$
$881$			20.6232i			0.694812i	−0.937715	+	0.347406i	$0.887063\pi$
$882$		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	$-0.960120\pi$
$887$		−	7.44312i		−	0.249916i	0.992162	−	0.124958i	$-0.0398795\pi$
$888$		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	$-0.334557\pi$
$911$	29.9816			0.993334			0.496667	+	0.867941i	$0.334557\pi$
$912$		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	$0.0730851\pi$
$929$			13.8738i			0.455183i	−0.973757	+	0.227592i	$0.926915\pi$
$930$		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	0.622510	−	0.782612i	$-0.286113\pi$
$941$	−4.91123	−	4.91123i	−0.160102	−	0.160102i	−0.782612	+	0.622510i	$0.786113\pi$
$942$		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	−0.809507	−	0.587111i	$-0.800265\pi$
$947$	−6.84386	+	6.84386i	−0.222396	+	0.222396i	0.587111	+	0.809507i	$0.300265\pi$
$948$		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	$-0.477656\pi$
$953$	4.33045			0.140277			0.0701386	+	0.997537i	$0.477656\pi$
$954$		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	0.978556	−	0.205979i	$-0.0660379\pi$
$971$	24.0742	+	24.0742i	0.772577	+	0.772577i	−0.205979	+	0.978556i	$0.566038\pi$
$972$		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	$-0.890745\pi$
$977$		−	21.0381i		−	0.673068i	0.941671	−	0.336534i	$-0.109255\pi$
$978$		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	$-0.927700\pi$
$983$		−	14.1206i		−	0.450376i	0.974315	−	0.225188i	$-0.0722997\pi$
$984$		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.107.1	yes	16
3.2	odd	2	inner	144.2.l.a.107.8	yes	16
4.3	odd	2		576.2.l.a.143.2		16
8.3	odd	2		1152.2.l.b.287.7		16
8.5	even	2		1152.2.l.a.287.7		16
12.11	even	2		576.2.l.a.143.7		16
16.3	odd	4	inner	144.2.l.a.35.8	yes	16
16.5	even	4		1152.2.l.b.863.2		16
16.11	odd	4		1152.2.l.a.863.2		16
16.13	even	4		576.2.l.a.431.7		16
24.5	odd	2		1152.2.l.a.287.2		16
24.11	even	2		1152.2.l.b.287.2		16
48.5	odd	4		1152.2.l.b.863.7		16
48.11	even	4		1152.2.l.a.863.7		16
48.29	odd	4		576.2.l.a.431.2		16
48.35	even	4	inner	144.2.l.a.35.1	✓	16

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

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