LMFDB - Embedded newform 1890.2.bq.a.289.42

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(289,1890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1890, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 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("1890.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.bq (of order $6$, degree $2$, not 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:	$15.0917259820$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			289.42
Character	$\chi$	$=$	1890.289
Dual form			1890.2.bq.a.739.42

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.82669 + 1.28965i) q^{5} +(2.61855 - 0.378415i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.82669 + 1.28965i) q^{5} +(2.61855 - 0.378415i) q^{7} -1.00000i q^{8} +(-0.937140 + 2.03021i) q^{10} -1.86045 q^{11} +(-2.13798 + 1.23436i) q^{13} +(2.07852 - 1.63699i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(6.17648 - 3.56599i) q^{17} +(2.57424 - 4.45871i) q^{19} +(0.203520 + 2.22679i) q^{20} +(-1.61120 + 0.930226i) q^{22} +4.03065i q^{23} +(1.67362 - 4.71158i) q^{25} +(-1.23436 + 2.13798i) q^{26} +(0.981558 - 2.45694i) q^{28} +(0.563512 - 0.976031i) q^{29} +(-0.0124464 + 0.0215578i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(3.56599 - 6.17648i) q^{34} +(-4.29527 + 4.06825i) q^{35} +(-0.142548 - 0.0823004i) q^{37} -5.14848i q^{38} +(1.28965 + 1.82669i) q^{40} +(2.73422 + 4.73581i) q^{41} +(5.90484 + 3.40916i) q^{43} +(-0.930226 + 1.61120i) q^{44} +(2.01533 + 3.49065i) q^{46} +(10.8449 - 6.26132i) q^{47} +(6.71360 - 1.98179i) q^{49} +(-0.906392 - 4.91716i) q^{50} +2.46872i q^{52} +(2.19776 - 1.26888i) q^{53} +(3.39848 - 2.39933i) q^{55} +(-0.378415 - 2.61855i) q^{56} -1.12702i q^{58} +(4.32390 - 7.48921i) q^{59} +(3.21768 + 5.57318i) q^{61} +0.0248928i q^{62} -1.00000 q^{64} +(2.31354 - 5.01203i) q^{65} +(-13.6342 - 7.87168i) q^{67} -7.13199i q^{68} +(-1.68568 + 5.67084i) q^{70} +10.0316 q^{71} +(8.79348 - 5.07692i) q^{73} -0.164601 q^{74} +(-2.57424 - 4.45871i) q^{76} +(-4.87169 + 0.704022i) q^{77} +(6.33233 + 10.9679i) q^{79} +(2.03021 + 0.937140i) q^{80} +(4.73581 + 2.73422i) q^{82} +(-14.2772 - 8.24296i) q^{83} +(-6.68367 + 14.4795i) q^{85} +6.81832 q^{86} +1.86045i q^{88} +(-2.70604 + 4.68699i) q^{89} +(-5.13130 + 4.04128i) q^{91} +(3.49065 + 2.01533i) q^{92} +(6.26132 - 10.8449i) q^{94} +(1.04782 + 11.4646i) q^{95} +(-3.56475 - 2.05811i) q^{97} +(4.82326 - 5.07309i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 48 q^{4}+O(q^{10}) $ 96 * q + 48 * q^4	$ 96 q + 48 q^{4} + 8 q^{11} + 2 q^{14} - 48 q^{16} - 24 q^{26} - 10 q^{29} + 34 q^{35} - 30 q^{41} + 4 q^{44} - 6 q^{46} + 12 q^{49} + 12 q^{50} + 12 q^{55} + 4 q^{56} + 24 q^{59} - 6 q^{61} - 96 q^{64} - 18 q^{65} + 6 q^{70} + 32 q^{71} + 8 q^{86} + 66 q^{89} - 12 q^{94} - 30 q^{95}+O(q^{100}) $ 96 * q + 48 * q^4 + 8 * q^11 + 2 * q^14 - 48 * q^16 - 24 * q^26 - 10 * q^29 + 34 * q^35 - 30 * q^41 + 4 * q^44 - 6 * q^46 + 12 * q^49 + 12 * q^50 + 12 * q^55 + 4 * q^56 + 24 * q^59 - 6 * q^61 - 96 * q^64 - 18 * q^65 + 6 * q^70 + 32 * q^71 + 8 * q^86 + 66 * q^89 - 12 * q^94 - 30 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.82669	+	1.28965i	−0.816922	+	0.576748i
$5$	−1.82669	+	1.28965i	−0.816922	+	0.576748i
$6$		0			0
$7$	2.61855	−	0.378415i	0.989719	−	0.143027i
$7$	2.61855	−	0.378415i	0.989719	−	0.143027i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−0.937140	+	2.03021i	−0.296350	+	0.642010i
$11$	−1.86045			−0.560947			−0.280474	−	0.959862i	$-0.590492\pi$
$11$	−1.86045			−0.560947			−0.280474	+	0.959862i	$0.590492\pi$
$12$		0			0
$13$	−2.13798	+	1.23436i	−0.592968	+	0.342350i	−0.766270	−	0.642519i	$-0.777890\pi$
$13$	−2.13798	+	1.23436i	−0.592968	+	0.342350i	0.173302	+	0.984869i	$0.444556\pi$
$14$	2.07852	−	1.63699i	0.555509	−	0.437504i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	6.17648	−	3.56599i	1.49802	−	0.864881i	0.498020	−	0.867166i	$-0.334061\pi$
$17$	6.17648	−	3.56599i	1.49802	−	0.864881i	0.999997	+	0.00228505i	$0.000727355\pi$
$18$		0			0
$19$	2.57424	−	4.45871i	0.590571	−	1.02290i	−0.403585	−	0.914942i	$-0.632236\pi$
$19$	2.57424	−	4.45871i	0.590571	−	1.02290i	0.994156	−	0.107956i	$-0.0344307\pi$
$20$	0.203520	+	2.22679i	0.0455085	+	0.497925i
$21$		0			0
$22$	−1.61120	+	0.930226i	−0.343509	+	0.198325i
$23$			4.03065i			0.840449i	0.907420	+	0.420224i	$0.138049\pi$
$23$			4.03065i			0.840449i	−0.907420	+	0.420224i	$0.861951\pi$
$24$		0			0
$25$	1.67362	−	4.71158i	0.334724	−	0.942316i
$26$	−1.23436	+	2.13798i	−0.242078	+	0.419291i
$27$		0			0
$28$	0.981558	−	2.45694i	0.185497	−	0.464318i
$29$	0.563512	−	0.976031i	0.104641	−	0.181244i	−0.808950	−	0.587877i	$-0.799964\pi$
$29$	0.563512	−	0.976031i	0.104641	−	0.181244i	0.913592	+	0.406633i	$0.133297\pi$
$30$		0			0
$31$	−0.0124464	+	0.0215578i	−0.00223544	+	0.00387189i	−0.867141	−	0.498063i	$-0.834045\pi$
$31$	−0.0124464	+	0.0215578i	−0.00223544	+	0.00387189i	0.864906	+	0.501935i	$0.167378\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$	3.56599	−	6.17648i	0.611563	−	1.05926i
$35$	−4.29527	+	4.06825i	−0.726033	+	0.687660i
$36$		0			0
$37$	−0.142548	−	0.0823004i	−0.0234348	−	0.0135301i	0.488237	−	0.872711i	$-0.337640\pi$
$37$	−0.142548	−	0.0823004i	−0.0234348	−	0.0135301i	−0.511672	+	0.859181i	$0.670974\pi$
$38$		−	5.14848i		−	0.835193i
$39$		0			0
$40$	1.28965	+	1.82669i	0.203911	+	0.288826i
$41$	2.73422	+	4.73581i	0.427013	+	0.739609i	0.996606	−	0.0823184i	$-0.0262325\pi$
$41$	2.73422	+	4.73581i	0.427013	+	0.739609i	−0.569593	+	0.821927i	$0.692899\pi$
$42$		0			0
$43$	5.90484	+	3.40916i	0.900480	+	0.519892i	0.877356	−	0.479840i	$-0.159305\pi$
$43$	5.90484	+	3.40916i	0.900480	+	0.519892i	0.0231240	+	0.999733i	$0.492639\pi$
$44$	−0.930226	+	1.61120i	−0.140237	+	0.242897i
$45$		0			0
$46$	2.01533	+	3.49065i	0.297144	+	0.514668i
$47$	10.8449	−	6.26132i	1.58189	−	0.913307i	0.587311	−	0.809361i	$-0.300187\pi$
$47$	10.8449	−	6.26132i	1.58189	−	0.913307i	0.994583	−	0.103946i	$-0.0331468\pi$
$48$		0			0
$49$	6.71360	−	1.98179i	0.959086	−	0.283114i
$50$	−0.906392	−	4.91716i	−0.128183	−	0.695391i
$51$		0			0
$52$			2.46872i			0.342350i
$53$	2.19776	−	1.26888i	0.301885	−	0.174294i	−0.341404	−	0.939917i	$-0.610902\pi$
$53$	2.19776	−	1.26888i	0.301885	−	0.174294i	0.643290	+	0.765623i	$0.277569\pi$
$54$		0			0
$55$	3.39848	−	2.39933i	0.458251	−	0.323525i
$56$	−0.378415	−	2.61855i	−0.0505678	−	0.349918i
$57$		0			0
$58$		−	1.12702i		−	0.147985i
$59$	4.32390	−	7.48921i	0.562923	−	0.975012i	−0.434316	−	0.900760i	$-0.643010\pi$
$59$	4.32390	−	7.48921i	0.562923	−	0.975012i	0.997240	−	0.0742513i	$-0.0236567\pi$
$60$		0			0
$61$	3.21768	+	5.57318i	0.411981	+	0.713572i	0.995106	−	0.0988099i	$-0.0315036\pi$
$61$	3.21768	+	5.57318i	0.411981	+	0.713572i	−0.583125	+	0.812382i	$0.698170\pi$
$62$			0.0248928i			0.00316139i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	2.31354	−	5.01203i	0.286959	−	0.621666i
$66$		0			0
$67$	−13.6342	−	7.87168i	−1.66568	−	0.961679i	−0.969927	−	0.243394i	$-0.921739\pi$
$67$	−13.6342	−	7.87168i	−1.66568	−	0.961679i	−0.695749	−	0.718285i	$-0.744928\pi$
$68$		−	7.13199i		−	0.864881i
$69$		0			0
$70$	−1.68568	+	5.67084i	−0.201478	+	0.677795i
$71$	10.0316			1.19053			0.595264	−	0.803531i	$-0.297048\pi$
$71$	10.0316			1.19053			0.595264	+	0.803531i	$0.297048\pi$
$72$		0			0
$73$	8.79348	−	5.07692i	1.02920	−	0.594208i	0.112444	−	0.993658i	$-0.464132\pi$
$73$	8.79348	−	5.07692i	1.02920	−	0.594208i	0.916755	+	0.399450i	$0.130799\pi$
$74$	−0.164601			−0.0191344
$75$		0			0
$76$	−2.57424	−	4.45871i	−0.295285	−	0.511449i
$77$	−4.87169	+	0.704022i	−0.555180	+	0.0802308i
$78$		0			0
$79$	6.33233	+	10.9679i	0.712443	+	1.23399i	0.963938	+	0.266129i	$0.0857446\pi$
$79$	6.33233	+	10.9679i	0.712443	+	1.23399i	−0.251495	+	0.967859i	$0.580922\pi$
$80$	2.03021	+	0.937140i	0.226985	+	0.104775i
$81$		0			0
$82$	4.73581	+	2.73422i	0.522982	+	0.301944i
$83$	−14.2772	−	8.24296i	−1.56713	−	0.904783i	−0.996502	−	0.0835738i	$-0.973367\pi$
$83$	−14.2772	−	8.24296i	−1.56713	−	0.904783i	−0.570628	−	0.821209i	$-0.693300\pi$
$84$		0			0
$85$	−6.68367	+	14.4795i	−0.724946	+	1.57052i
$86$	6.81832			0.735239
$87$		0			0
$88$			1.86045i			0.198325i
$89$	−2.70604	+	4.68699i	−0.286839	+	0.496820i	−0.973054	−	0.230579i	$-0.925938\pi$
$89$	−2.70604	+	4.68699i	−0.286839	+	0.496820i	0.686214	+	0.727400i	$0.259271\pi$
$90$		0			0
$91$	−5.13130	+	4.04128i	−0.537906	+	0.423641i
$92$	3.49065	+	2.01533i	0.363925	+	0.210112i
$93$		0			0
$94$	6.26132	−	10.8449i	0.645806	−	1.11857i
$95$	1.04782	+	11.4646i	0.107504	+	1.17624i
$96$		0			0
$97$	−3.56475	−	2.05811i	−0.361945	−	0.208969i	0.307989	−	0.951390i	$-0.400344\pi$
$97$	−3.56475	−	2.05811i	−0.361945	−	0.208969i	−0.669934	+	0.742421i	$0.733677\pi$
$98$	4.82326	−	5.07309i	0.487222	−	0.512459i
$99$		0			0
$100$	−3.24354	−	3.80519i	−0.324354	−	0.380519i
$101$	3.17312			0.315737			0.157868	−	0.987460i	$-0.449538\pi$
$101$	3.17312			0.315737			0.157868	+	0.987460i	$0.449538\pi$
$102$		0			0
$103$		−	9.69673i		−	0.955447i	−0.878510	−	0.477724i	$-0.841462\pi$
$103$		−	9.69673i		−	0.955447i	0.878510	−	0.477724i	$-0.158538\pi$
$104$	1.23436	+	2.13798i	0.121039	+	0.209646i
$105$		0			0
$106$	1.26888	−	2.19776i	0.123244	−	0.213465i
$107$	−3.50826	−	2.02550i	−0.339156	−	0.195812i	0.320743	−	0.947166i	$-0.396068\pi$
$107$	−3.50826	−	2.02550i	−0.339156	−	0.195812i	−0.659899	+	0.751354i	$0.729401\pi$
$108$		0			0
$109$	−3.82986	−	6.63352i	−0.366835	−	0.635376i	0.622234	−	0.782831i	$-0.286225\pi$
$109$	−3.82986	−	6.63352i	−0.366835	−	0.635376i	−0.989069	+	0.147455i	$0.952892\pi$
$110$	1.74350	−	3.77712i	0.166237	−	0.360134i
$111$		0			0
$112$	−1.63699	−	2.07852i	−0.154681	−	0.196402i
$113$	−13.1907	+	7.61565i	−1.24088	+	0.716420i	−0.969273	−	0.245989i	$-0.920887\pi$
$113$	−13.1907	+	7.61565i	−1.24088	+	0.716420i	−0.271604	+	0.962409i	$0.587554\pi$
$114$		0			0
$115$	−5.19812	−	7.36276i	−0.484727	−	0.686581i
$116$	−0.563512	−	0.976031i	−0.0523207	−	0.0906222i
$117$		0			0
$118$		−	8.64779i		−	0.796094i
$119$	14.8240	−	11.6750i	1.35891	−	1.07025i
$120$		0			0
$121$	−7.53872			−0.685338
$122$	5.57318	+	3.21768i	0.504572	+	0.291315i
$123$		0			0
$124$	0.0124464	+	0.0215578i	0.00111772	+	0.00193595i
$125$	3.01908	+	10.7650i	0.270035	+	0.962850i
$126$		0			0
$127$			5.86205i			0.520173i	0.965585	+	0.260087i	$0.0837511\pi$
$127$			5.86205i			0.520173i	−0.965585	+	0.260087i	$0.916249\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	−0.502435	−	5.49732i	−0.0440664	−	0.482147i
$131$	16.8954			1.47616			0.738079	−	0.674714i	$-0.235733\pi$
$131$	16.8954			1.47616			0.738079	+	0.674714i	$0.235733\pi$
$132$		0			0
$133$	5.05353	−	12.6495i	0.438197	−	1.09685i
$134$	−15.7434			−1.36002
$135$		0			0
$136$	−3.56599	−	6.17648i	−0.305781	−	0.529629i
$137$			4.78193i			0.408548i	0.978914	+	0.204274i	$0.0654833\pi$
$137$			4.78193i			0.408548i	−0.978914	+	0.204274i	$0.934517\pi$
$138$		0			0
$139$	0.819319	+	1.41910i	0.0694937	+	0.120367i	0.898679	−	0.438608i	$-0.144528\pi$
$139$	0.819319	+	1.41910i	0.0694937	+	0.120367i	−0.829185	+	0.558975i	$0.811195\pi$
$140$	1.37558	+	5.75394i	0.116257	+	0.486296i
$141$		0			0
$142$	8.68759	−	5.01578i	0.729046	−	0.420915i
$143$	3.97760	−	2.29647i	0.332624	−	0.192040i
$144$		0			0
$145$	0.229372	+	2.50964i	0.0190483	+	0.208414i
$146$	5.07692	−	8.79348i	0.420169	−	0.727754i
$147$		0			0
$148$	−0.142548	+	0.0823004i	−0.0117174	+	0.00676505i
$149$	−1.13238			−0.0927679			−0.0463840	−	0.998924i	$-0.514770\pi$
$149$	−1.13238			−0.0927679			−0.0463840	+	0.998924i	$0.514770\pi$
$150$		0			0
$151$	1.52957			0.124474			0.0622372	−	0.998061i	$-0.480176\pi$
$151$	1.52957			0.124474			0.0622372	+	0.998061i	$0.480176\pi$
$152$	−4.45871	−	2.57424i	−0.361649	−	0.208798i
$153$		0			0
$154$	−3.86699	+	3.04554i	−0.311611	+	0.245417i
$155$	−0.00506618	−	0.0554309i	−0.000406926	−	0.00445232i
$156$		0			0
$157$	1.60931	+	0.929138i	0.128437	+	0.0741533i	0.562842	−	0.826564i	$-0.309708\pi$
$157$	1.60931	+	0.929138i	0.128437	+	0.0741533i	−0.434405	+	0.900718i	$0.643041\pi$
$158$	10.9679	+	6.33233i	0.872561	+	0.503773i
$159$		0			0
$160$	2.22679	−	0.203520i	0.176043	−	0.0160897i
$161$	1.52526	+	10.5545i	0.120207	+	0.831808i
$162$		0			0
$163$	−19.5044	−	11.2609i	−1.52771	−	0.882021i	−0.999458	−	0.0329304i	$-0.989516\pi$
$163$	−19.5044	−	11.2609i	−1.52771	−	0.882021i	−0.528247	−	0.849090i	$-0.677151\pi$
$164$	5.46844			0.427013
$165$		0			0
$166$	−16.4859			−1.27956
$167$	1.38259	−	0.798239i	0.106988	−	0.0617696i	−0.445551	−	0.895256i	$-0.646992\pi$
$167$	1.38259	−	0.798239i	0.106988	−	0.0617696i	0.552539	+	0.833487i	$0.313659\pi$
$168$		0			0
$169$	−3.45271	+	5.98026i	−0.265593	+	0.460020i
$170$	1.45150	+	15.8814i	0.111325	+	1.21805i
$171$		0			0
$172$	5.90484	−	3.40916i	0.450240	−	0.259946i
$173$	19.5135	−	11.2661i	1.48359	−	0.856549i	0.483760	−	0.875201i	$-0.339271\pi$
$173$	19.5135	−	11.2661i	1.48359	−	0.856549i	0.999826	+	0.0186515i	$0.00593731\pi$
$174$		0			0
$175$	2.59953	−	12.9708i	0.196506	−	0.980503i
$176$	0.930226	+	1.61120i	0.0701184	+	0.121449i
$177$		0			0
$178$			5.41207i			0.405652i
$179$	7.22646	+	12.5166i	0.540131	+	0.935534i	0.998896	+	0.0469763i	$0.0149585\pi$
$179$	7.22646	+	12.5166i	0.540131	+	0.935534i	−0.458765	+	0.888557i	$0.651708\pi$
$180$		0			0
$181$	3.56702			0.265134			0.132567	−	0.991174i	$-0.457678\pi$
$181$	3.56702			0.265134			0.132567	+	0.991174i	$0.457678\pi$
$182$	−2.42319	+	6.06550i	−0.179619	+	0.449604i
$183$		0			0
$184$	4.03065			0.297144
$185$	0.366531	−	0.0334996i	0.0269479	−	0.00246294i
$186$		0			0
$187$	−11.4911	+	6.63436i	−0.840309	+	0.485153i
$188$		−	12.5226i		−	0.913307i
$189$		0			0
$190$	6.63972	+	9.40469i	0.481696	+	0.682288i
$191$	−0.958731	−	1.66057i	−0.0693713	−	0.120155i	0.829253	−	0.558873i	$-0.188766\pi$
$191$	−0.958731	−	1.66057i	−0.0693713	−	0.120155i	−0.898625	+	0.438718i	$0.855433\pi$
$192$		0			0
$193$	12.3389	+	7.12386i	0.888173	+	0.512787i	0.873344	−	0.487103i	$-0.161946\pi$
$193$	12.3389	+	7.12386i	0.888173	+	0.512787i	0.0148283	+	0.999890i	$0.495280\pi$
$194$	−4.11621			−0.295527
$195$		0			0
$196$	1.64052	−	6.80505i	0.117180	−	0.486075i
$197$			13.4264i			0.956590i	0.878199	+	0.478295i	$0.158745\pi$
$197$			13.4264i			0.956590i	−0.878199	+	0.478295i	$0.841255\pi$
$198$		0			0
$199$	−3.33319	−	5.77325i	−0.236283	−	0.409255i	0.723361	−	0.690470i	$-0.242596\pi$
$199$	−3.33319	−	5.77325i	−0.236283	−	0.409255i	−0.959645	+	0.281215i	$0.909263\pi$
$200$	−4.71158	−	1.67362i	−0.333159	−	0.118343i
$201$		0			0
$202$	2.74800	−	1.58656i	0.193349	−	0.111630i
$203$	1.10624	−	2.76903i	0.0776428	−	0.194348i
$204$		0			0
$205$	−11.1021	−	5.12469i	−0.775404	−	0.357924i
$206$	−4.84836	−	8.39761i	−0.337802	−	0.585089i
$207$		0			0
$208$	2.13798	+	1.23436i	0.148242	+	0.0855875i
$209$	−4.78925	+	8.29522i	−0.331279	+	0.573792i
$210$		0			0
$211$	2.20274	+	3.81526i	0.151643	+	0.262653i	0.931832	−	0.362891i	$-0.118210\pi$
$211$	2.20274	+	3.81526i	0.151643	+	0.262653i	−0.780189	+	0.625544i	$0.784877\pi$
$212$		−	2.53775i		−	0.174294i
$213$		0			0
$214$	−4.05099			−0.276920
$215$	−15.1830	+	1.38767i	−1.03547	+	0.0946381i
$216$		0			0
$217$	−0.0244337	+	0.0611600i	−0.00165867	+	0.00415181i
$218$	−6.63352	−	3.82986i	−0.449279	−	0.259391i
$219$		0			0
$220$	−0.378640	−	4.14283i	−0.0255279	−	0.279310i
$221$	−8.80345	+	15.2480i	−0.592184	+	1.02569i
$222$		0			0
$223$	−10.8925	−	6.28877i	−0.729413	−	0.421127i	0.0887942	−	0.996050i	$-0.471699\pi$
$223$	−10.8925	−	6.28877i	−0.729413	−	0.421127i	−0.818207	+	0.574923i	$0.805032\pi$
$224$	−2.45694	−	0.981558i	−0.164161	−	0.0655831i
$225$		0			0
$226$	−7.61565	+	13.1907i	−0.506586	+	0.877432i
$227$		−	3.41232i		−	0.226483i	−0.993567	−	0.113242i	$-0.963877\pi$
$227$		−	3.41232i		−	0.226483i	0.993567	−	0.113242i	$-0.0361234\pi$
$228$		0			0
$229$	−24.0667			−1.59037			−0.795187	−	0.606364i	$-0.792628\pi$
$229$	−24.0667			−1.59037			−0.795187	+	0.606364i	$0.792628\pi$
$230$	−8.18308	−	3.77728i	−0.539577	−	0.249067i
$231$		0			0
$232$	−0.976031	−	0.563512i	−0.0640796	−	0.0369964i
$233$	−20.5971	−	11.8917i	−1.34936	−	0.779054i	−0.361202	−	0.932487i	$-0.617634\pi$
$233$	−20.5971	−	11.8917i	−1.34936	−	0.779054i	−0.988159	+	0.153433i	$0.950967\pi$
$234$		0			0
$235$	−11.7355	+	25.4236i	−0.765537	+	1.65845i
$236$	−4.32390	−	7.48921i	−0.281462	−	0.487506i
$237$		0			0
$238$	7.00046	−	17.5229i	0.453773	−	1.13584i
$239$	11.4772	+	19.8792i	0.742401	+	1.28588i	0.951399	+	0.307960i	$0.0996464\pi$
$239$	11.4772	+	19.8792i	0.742401	+	1.28588i	−0.208998	+	0.977916i	$0.567020\pi$
$240$		0			0
$241$	−12.1600			−0.783295			−0.391647	−	0.920115i	$-0.628095\pi$
$241$	−12.1600			−0.783295			−0.391647	+	0.920115i	$0.628095\pi$
$242$	−6.52872	+	3.76936i	−0.419682	+	0.242304i
$243$		0			0
$244$	6.43535			0.411981
$245$	−9.70788	+	12.2783i	−0.620214	+	0.784433i
$246$		0			0
$247$			12.7102i			0.808728i
$248$	0.0215578	+	0.0124464i	0.00136892	+	0.000790346i
$249$		0			0
$250$	7.99710	+	7.81322i	0.505781	+	0.494151i
$251$	−26.7127			−1.68609			−0.843046	−	0.537841i	$-0.819240\pi$
$251$	−26.7127			−1.68609			−0.843046	+	0.537841i	$0.819240\pi$
$252$		0			0
$253$		−	7.49883i		−	0.471448i
$254$	2.93103	+	5.07669i	0.183909	+	0.318540i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$		−	12.9891i		−	0.810236i	−0.914264	−	0.405118i	$-0.867230\pi$
$257$		−	12.9891i		−	0.810236i	0.914264	−	0.405118i	$-0.132770\pi$
$258$		0			0
$259$	−0.404414	−	0.161565i	−0.0251290	−	0.0100392i
$260$	−3.18378	−	4.50960i	−0.197450	−	0.279673i
$261$		0			0
$262$	14.6319	−	8.44770i	0.903959	−	0.521901i
$263$			8.84342i			0.545308i	0.962112	+	0.272654i	$0.0879015\pi$
$263$			8.84342i			0.545308i	−0.962112	+	0.272654i	$0.912099\pi$
$264$		0			0
$265$	−2.37823	+	5.15218i	−0.146093	+	0.316496i
$266$	−1.94826	−	13.4815i	−0.119455	−	0.826607i
$267$		0			0
$268$	−13.6342	+	7.87168i	−0.832838	+	0.480839i
$269$	0.396645	+	0.687010i	0.0241839	+	0.0418877i	0.877864	−	0.478910i	$-0.158968\pi$
$269$	0.396645	+	0.687010i	0.0241839	+	0.0418877i	−0.853680	+	0.520798i	$0.825635\pi$
$270$		0			0
$271$	−15.0428	+	26.0548i	−0.913783	+	1.58272i	−0.105110	+	0.994461i	$0.533519\pi$
$271$	−15.0428	+	26.0548i	−0.913783	+	1.58272i	−0.808673	+	0.588258i	$0.799814\pi$
$272$	−6.17648	−	3.56599i	−0.374504	−	0.216220i
$273$		0			0
$274$	2.39097	+	4.14127i	0.144444	+	0.250184i
$275$	−3.11369	+	8.76567i	−0.187763	+	0.528590i
$276$		0			0
$277$		−	10.7131i		−	0.643689i	−0.946793	−	0.321844i	$-0.895697\pi$
$277$		−	10.7131i		−	0.643689i	0.946793	−	0.321844i	$-0.104303\pi$
$278$	1.41910	+	0.819319i	0.0851121	+	0.0491395i
$279$		0			0
$280$	4.06825	+	4.29527i	0.243125	+	0.256691i
$281$	−7.78912	+	13.4911i	−0.464660	+	0.804814i	−0.999186	−	0.0403376i	$-0.987157\pi$
$281$	−7.78912	+	13.4911i	−0.464660	+	0.804814i	0.534526	+	0.845152i	$0.320490\pi$
$282$		0			0
$283$	16.7746	+	9.68484i	0.997149	+	0.575704i	0.907403	−	0.420261i	$-0.138061\pi$
$283$	16.7746	+	9.68484i	0.997149	+	0.575704i	0.0897455	+	0.995965i	$0.471395\pi$
$284$	5.01578	−	8.68759i	0.297632	−	0.515513i
$285$		0			0
$286$	2.29647	−	3.97760i	0.135793	−	0.235201i
$287$	8.95178	+	11.3663i	0.528407	+	0.670930i
$288$		0			0
$289$	16.9326	−	29.3282i	0.996037	−	1.72519i
$290$	1.45346	+	2.05873i	0.0853502	+	0.120893i
$291$		0			0
$292$		−	10.1538i		−	0.594208i
$293$	−5.22984	+	3.01945i	−0.305530	+	0.176398i	−0.644925	−	0.764246i	$-0.723111\pi$
$293$	−5.22984	+	3.01945i	−0.305530	+	0.176398i	0.339394	+	0.940644i	$0.389778\pi$
$294$		0			0
$295$	1.76000	+	19.2568i	0.102471	+	1.12117i
$296$	−0.0823004	+	0.142548i	−0.00478361	+	0.00828546i
$297$		0			0
$298$	−0.980667	+	0.566188i	−0.0568085	+	0.0327984i
$299$	−4.97528	−	8.61743i	−0.287728	−	0.498359i
$300$		0			0
$301$	16.7522	+	6.69258i	0.965581	+	0.385754i
$302$	1.32464	−	0.764783i	0.0762247	−	0.0440083i
$303$		0			0
$304$	−5.14848			−0.295285
$305$	−13.0651	−	6.03082i	−0.748108	−	0.345324i
$306$		0			0
$307$			29.4814i			1.68260i	0.540572	+	0.841298i	$0.318208\pi$
$307$			29.4814i			1.68260i	−0.540572	+	0.841298i	$0.681792\pi$
$308$	−1.82614	+	4.57102i	−0.104054	+	0.260458i
$309$		0			0
$310$	−0.0321029	−	0.0454715i	−0.00182332	−	0.00258261i
$311$	4.12138	−	7.13843i	0.233702	−	0.404783i	−0.725193	−	0.688546i	$-0.758249\pi$
$311$	4.12138	−	7.13843i	0.233702	−	0.404783i	0.958895	+	0.283762i	$0.0915827\pi$
$312$		0			0
$313$	2.97043	−	1.71498i	0.167899	−	0.0969364i	−0.413696	−	0.910415i	$-0.635762\pi$
$313$	2.97043	−	1.71498i	0.167899	−	0.0969364i	0.581595	+	0.813479i	$0.302429\pi$
$314$	1.85828			0.104869
$315$		0			0
$316$	12.6647			0.712443
$317$	−23.0163	+	13.2885i	−1.29273	+	0.746355i	−0.979136	−	0.203204i	$-0.934865\pi$
$317$	−23.0163	+	13.2885i	−1.29273	+	0.746355i	−0.313589	+	0.949559i	$0.601531\pi$
$318$		0			0
$319$	−1.04839	+	1.81586i	−0.0586984	+	0.101669i
$320$	1.82669	−	1.28965i	0.102115	−	0.0720935i
$321$		0			0
$322$	6.59814	+	8.37780i	0.367700	+	0.466877i
$323$		−	36.7189i		−	2.04309i
$324$		0			0
$325$	2.23763	+	12.1391i	0.124121	+	0.673356i
$326$	−22.5218			−1.24737
$327$		0			0
$328$	4.73581	−	2.73422i	0.261491	−	0.150972i
$329$	26.0286	−	20.4994i	1.43500	−	1.13017i
$330$		0			0
$331$	1.15790	+	2.00554i	0.0636439	+	0.110235i	0.896092	−	0.443869i	$-0.146394\pi$
$331$	1.15790	+	2.00554i	0.0636439	+	0.110235i	−0.832448	+	0.554104i	$0.813061\pi$
$332$	−14.2772	+	8.24296i	−0.783565	+	0.452391i
$333$		0			0
$334$	0.798239	−	1.38259i	0.0436777	−	0.0756520i
$335$	35.0571	−	3.20409i	1.91537	−	0.175058i
$336$		0			0
$337$	9.27844	−	5.35691i	0.505429	−	0.291809i	−0.225524	−	0.974238i	$-0.572409\pi$
$337$	9.27844	−	5.35691i	0.505429	−	0.291809i	0.730953	+	0.682428i	$0.239076\pi$
$338$			6.90541i			0.375605i
$339$		0			0
$340$	9.19775	+	13.0280i	0.498818	+	0.706540i
$341$	0.0231559	−	0.0401072i	0.00125396	−	0.00217193i
$342$		0			0
$343$	16.8300	−	7.72995i	0.908733	−	0.417378i
$344$	3.40916	−	5.90484i	0.183810	−	0.318368i
$345$		0			0
$346$	11.2661	−	19.5135i	0.605672	−	1.04905i
$347$	2.25512	+	1.30199i	0.121061	+	0.0698946i	0.559308	−	0.828960i	$-0.311067\pi$
$347$	2.25512	+	1.30199i	0.121061	+	0.0698946i	−0.438247	+	0.898855i	$0.644400\pi$
$348$		0			0
$349$	8.68928	−	15.0503i	0.465126	−	0.805622i	−0.534081	−	0.845433i	$-0.679342\pi$
$349$	8.68928	−	15.0503i	0.465126	−	0.805622i	0.999207	+	0.0398110i	$0.0126756\pi$
$350$	−4.23416	−	12.5328i	−0.226325	−	0.669908i
$351$		0			0
$352$	1.61120	+	0.930226i	0.0858772	+	0.0495812i
$353$			1.56231i			0.0831532i	0.999135	+	0.0415766i	$0.0132381\pi$
$353$			1.56231i			0.0831532i	−0.999135	+	0.0415766i	$0.986762\pi$
$354$		0			0
$355$	−18.3246	+	12.9372i	−0.972568	+	0.686634i
$356$	2.70604	+	4.68699i	0.143420	+	0.248410i
$357$		0			0
$358$	12.5166	+	7.22646i	0.661522	+	0.381930i
$359$	4.26628	−	7.38941i	0.225166	−	0.389998i	−0.731203	−	0.682159i	$-0.761041\pi$
$359$	4.26628	−	7.38941i	0.225166	−	0.389998i	0.956369	+	0.292161i	$0.0943743\pi$
$360$		0			0
$361$	−3.75341	−	6.50110i	−0.197548	−	0.342163i
$362$	3.08913	−	1.78351i	0.162361	−	0.0937391i
$363$		0			0
$364$	0.934200	+	6.46447i	0.0489654	+	0.338830i
$365$	−9.51556	+	20.6145i	−0.498067	+	1.07901i
$366$		0			0
$367$			28.0528i			1.46434i	0.681121	+	0.732171i	$0.261493\pi$
$367$			28.0528i			1.46434i	−0.681121	+	0.732171i	$0.738507\pi$
$368$	3.49065	−	2.01533i	0.181962	−	0.105056i
$369$		0			0
$370$	0.300675	−	0.212277i	0.0156314	−	0.0110357i
$371$	5.27478	−	4.15428i	0.273853	−	0.215679i
$372$		0			0
$373$			14.0602i			0.728010i	0.931397	+	0.364005i	$0.118591\pi$
$373$			14.0602i			0.728010i	−0.931397	+	0.364005i	$0.881409\pi$
$374$	−6.63436	+	11.4911i	−0.343055	+	0.594188i
$375$		0			0
$376$	−6.26132	−	10.8449i	−0.322903	−	0.559284i
$377$			2.78231i			0.143296i
$378$		0			0
$379$	9.12176			0.468553			0.234277	−	0.972170i	$-0.424728\pi$
$379$	9.12176			0.468553			0.234277	+	0.972170i	$0.424728\pi$
$380$	10.4525	+	4.82484i	0.536203	+	0.247509i
$381$		0			0
$382$	−1.66057	−	0.958731i	−0.0849622	−	0.0490529i
$383$			10.0996i			0.516068i	0.966136	+	0.258034i	$0.0830746\pi$
$383$			10.0996i			0.516068i	−0.966136	+	0.258034i	$0.916925\pi$
$384$		0			0
$385$	7.99114	−	7.56879i	0.407266	−	0.385741i
$386$	14.2477			0.725190
$387$		0			0
$388$	−3.56475	+	2.05811i	−0.180973	+	0.104485i
$389$	−29.6454			−1.50308			−0.751540	−	0.659688i	$-0.770688\pi$
$389$	−29.6454			−1.50308			−0.751540	+	0.659688i	$0.770688\pi$
$390$		0			0
$391$	14.3733	+	24.8952i	0.726888	+	1.25901i
$392$	−1.98179	−	6.71360i	−0.100096	−	0.339088i
$393$		0			0
$394$	6.71319	+	11.6276i	0.338206	+	0.585789i
$395$	−25.7120	−	11.8686i	−1.29371	−	0.597172i
$396$		0			0
$397$	−23.6754	−	13.6690i	−1.18823	−	0.686027i	−0.230329	−	0.973113i	$-0.573980\pi$
$397$	−23.6754	−	13.6690i	−1.18823	−	0.686027i	−0.957905	+	0.287086i	$0.907313\pi$
$398$	−5.77325	−	3.33319i	−0.289387	−	0.167078i
$399$		0			0
$400$	−4.91716	+	0.906392i	−0.245858	+	0.0453196i
$401$	14.4629			0.722243			0.361122	−	0.932519i	$-0.382394\pi$
$401$	14.4629			0.722243			0.361122	+	0.932519i	$0.382394\pi$
$402$		0			0
$403$		−	0.0614533i		−	0.00306121i
$404$	1.58656	−	2.74800i	0.0789342	−	0.136718i
$405$		0			0
$406$	−0.426482	−	2.95117i	−0.0211659	−	0.146464i
$407$	0.265205	+	0.153116i	0.0131457	+	0.00758967i
$408$		0			0
$409$	−16.5873	+	28.7301i	−0.820191	+	1.42061i	0.0853491	+	0.996351i	$0.472799\pi$
$409$	−16.5873	+	28.7301i	−0.820191	+	1.42061i	−0.905540	+	0.424261i	$0.860534\pi$
$410$	−12.1770	+	1.11294i	−0.601381	+	0.0549641i
$411$		0			0
$412$	−8.39761	−	4.84836i	−0.413721	−	0.238862i
$413$	8.48831	−	21.2471i	0.417682	−	1.04550i
$414$		0			0
$415$	36.7106	−	3.35522i	1.80205	−	0.164701i
$416$	2.46872			0.121039
$417$		0			0
$418$			9.57850i			0.468500i
$419$	2.56007	+	4.43417i	0.125068	+	0.216623i	0.921759	−	0.387762i	$-0.126752\pi$
$419$	2.56007	+	4.43417i	0.125068	+	0.216623i	−0.796692	+	0.604386i	$0.793419\pi$
$420$		0			0
$421$	0.254924	−	0.441541i	0.0124242	−	0.0215194i	−0.859746	−	0.510721i	$-0.829378\pi$
$421$	0.254924	−	0.441541i	0.0124242	−	0.0215194i	0.872171	+	0.489202i	$0.162712\pi$
$422$	3.81526	+	2.20274i	0.185724	+	0.107228i
$423$		0			0
$424$	−1.26888	−	2.19776i	−0.0616221	−	0.106733i
$425$	−6.46438	−	35.0691i	−0.313568	−	1.70110i
$426$		0			0
$427$	10.5346	+	13.3760i	0.509806	+	0.647312i
$428$	−3.50826	+	2.02550i	−0.169578	+	0.0979060i
$429$		0			0
$430$	−12.4550	+	8.79323i	−0.600633	+	0.424047i
$431$	−6.19259	−	10.7259i	−0.298286	−	0.516647i	0.677458	−	0.735562i	$-0.263082\pi$
$431$	−6.19259	−	10.7259i	−0.298286	−	0.516647i	−0.975744	+	0.218915i	$0.929748\pi$
$432$		0			0
$433$		−	18.6516i		−	0.896339i	−0.893949	−	0.448169i	$-0.852076\pi$
$433$		−	18.6516i		−	0.896339i	0.893949	−	0.448169i	$-0.147924\pi$
$434$	0.00941979	+	0.0651830i	0.000452164	+	0.00312888i
$435$		0			0
$436$	−7.65973			−0.366835
$437$	17.9715	+	10.3759i	0.859694	+	0.496345i
$438$		0			0
$439$	−0.191909	−	0.332396i	−0.00915932	−	0.0158644i	0.861409	−	0.507911i	$-0.169582\pi$
$439$	−0.191909	−	0.332396i	−0.00915932	−	0.0158644i	−0.870569	+	0.492047i	$0.836249\pi$
$440$	−2.39933	−	3.39848i	−0.114383	−	0.162016i
$441$		0			0
$442$			17.6069i			0.837474i
$443$	−4.70125	+	2.71427i	−0.223363	+	0.128959i	−0.607506	−	0.794315i	$-0.707830\pi$
$443$	−4.70125	+	2.71427i	−0.223363	+	0.128959i	0.384143	+	0.923273i	$0.374497\pi$
$444$		0			0
$445$	−1.10147	−	12.0515i	−0.0522145	−	0.571298i
$446$	−12.5775			−0.595563
$447$		0			0
$448$	−2.61855	+	0.378415i	−0.123715	+	0.0178784i
$449$	−5.22072			−0.246381			−0.123191	−	0.992383i	$-0.539313\pi$
$449$	−5.22072			−0.246381			−0.123191	+	0.992383i	$0.539313\pi$
$450$		0			0
$451$	−5.08688	−	8.81074i	−0.239532	−	0.414882i
$452$			15.2313i			0.716420i
$453$		0			0
$454$	−1.70616	−	2.95515i	−0.0800740	−	0.138692i
$455$	4.16149	−	13.9997i	0.195093	−	0.656318i
$456$		0			0
$457$	10.6361	−	6.14074i	0.497535	−	0.287252i	−0.230160	−	0.973153i	$-0.573925\pi$
$457$	10.6361	−	6.14074i	0.497535	−	0.287252i	0.727695	+	0.685901i	$0.240592\pi$
$458$	−20.8424	+	12.0334i	−0.973902	+	0.562282i
$459$		0			0
$460$	−8.97540	+	0.820319i	−0.418480	+	0.0382476i
$461$	1.30604	−	2.26214i	0.0608286	−	0.105358i	−0.834007	−	0.551753i	$-0.813959\pi$
$461$	1.30604	−	2.26214i	0.0608286	−	0.105358i	0.894836	+	0.446395i	$0.147292\pi$
$462$		0			0
$463$	16.9779	−	9.80220i	0.789030	−	0.455547i	−0.0505907	−	0.998719i	$-0.516110\pi$
$463$	16.9779	−	9.80220i	0.789030	−	0.455547i	0.839621	+	0.543173i	$0.182777\pi$
$464$	−1.12702			−0.0523207
$465$		0			0
$466$	−23.7835			−1.10175
$467$	13.9721	+	8.06679i	0.646551	+	0.373287i	0.787134	−	0.616782i	$-0.211564\pi$
$467$	13.9721	+	8.06679i	0.646551	+	0.373287i	−0.140582	+	0.990069i	$0.544897\pi$
$468$		0			0
$469$	−38.6805	−	15.4530i	−1.78610	−	0.713554i
$470$	2.54861	+	27.8852i	0.117559	+	1.28625i
$471$		0			0
$472$	−7.48921	−	4.32390i	−0.344719	−	0.199023i
$473$	−10.9857	−	6.34258i	−0.505122	−	0.291632i
$474$		0			0
$475$	−16.6993	−	19.5909i	−0.766216	−	0.898893i
$476$	−2.69885	−	18.6755i	−0.123702	−	0.855989i
$477$		0			0
$478$	19.8792	+	11.4772i	0.909252	+	0.524957i
$479$	22.4504			1.02579			0.512894	−	0.858452i	$-0.328574\pi$
$479$	22.4504			1.02579			0.512894	+	0.858452i	$0.328574\pi$
$480$		0			0
$481$	0.406353			0.0185281
$482$	−10.5309	+	6.08000i	−0.479668	+	0.276937i
$483$		0			0
$484$	−3.76936	+	6.52872i	−0.171334	+	0.296760i
$485$	9.16593	−	0.837733i	0.416203	−	0.0380395i
$486$		0			0
$487$	−25.5573	+	14.7555i	−1.15811	+	0.668636i	−0.950851	−	0.309649i	$-0.899788\pi$
$487$	−25.5573	+	14.7555i	−1.15811	+	0.668636i	−0.207261	+	0.978286i	$0.566455\pi$
$488$	5.57318	−	3.21768i	0.252286	−	0.145657i
$489$		0			0
$490$	−2.26812	+	15.4873i	−0.102463	+	0.699644i
$491$	2.00136	+	3.46646i	0.0903202	+	0.156439i	0.907646	−	0.419737i	$-0.137878\pi$
$491$	2.00136	+	3.46646i	0.0903202	+	0.156439i	−0.817326	+	0.576176i	$0.804544\pi$
$492$		0			0
$493$		−	8.03792i		−	0.362010i
$494$	6.35508	+	11.0073i	0.285929	+	0.495243i
$495$		0			0
$496$	0.0248928			0.00111772
$497$	26.2681	−	3.79609i	1.17829	−	0.170278i
$498$		0			0
$499$	3.44048			0.154017			0.0770085	−	0.997030i	$-0.475463\pi$
$499$	3.44048			0.154017			0.0770085	+	0.997030i	$0.475463\pi$
$500$	10.8323	+	2.76789i	0.484435	+	0.123784i
$501$		0			0
$502$	−23.1339	+	13.3564i	−1.03252	+	0.596124i
$503$			26.9973i			1.20375i	0.798591	+	0.601875i	$0.205579\pi$
$503$			26.9973i			1.20375i	−0.798591	+	0.601875i	$0.794421\pi$
$504$		0			0
$505$	−5.79631	+	4.09220i	−0.257932	+	0.182100i
$506$	−3.74942	−	6.49418i	−0.166682	−	0.288702i
$507$		0			0
$508$	5.07669	+	2.93103i	0.225242	+	0.130043i
$509$	−33.3321			−1.47742			−0.738709	−	0.674024i	$-0.764564\pi$
$509$	−33.3321			−1.47742			−0.738709	+	0.674024i	$0.764564\pi$
$510$		0			0
$511$	21.1050	−	16.6217i	0.933630	−	0.735303i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−6.49454	−	11.2489i	−0.286462	−	0.496166i
$515$	12.5054	+	17.7130i	0.551052	+	0.780526i
$516$		0			0
$517$	−20.1765	+	11.6489i	−0.887359	+	0.512317i
$518$	−0.431015	+	0.0622873i	−0.0189377	+	0.00273675i
$519$		0			0
$520$	−5.01203	−	2.31354i	−0.219792	−	0.101455i
$521$	9.84067	+	17.0445i	0.431127	+	0.746735i	0.996971	−	0.0777783i	$-0.0247826\pi$
$521$	9.84067	+	17.0445i	0.431127	+	0.746735i	−0.565843	+	0.824513i	$0.691449\pi$
$522$		0			0
$523$	−6.77298	−	3.91038i	−0.296162	−	0.170989i	0.344556	−	0.938766i	$-0.388030\pi$
$523$	−6.77298	−	3.91038i	−0.296162	−	0.170989i	−0.640717	+	0.767777i	$0.721363\pi$
$524$	8.44770	−	14.6319i	0.369040	−	0.639195i
$525$		0			0
$526$	4.42171	+	7.65862i	0.192796	+	0.333932i
$527$			0.177535i			0.00773355i
$528$		0			0
$529$	6.75385			0.293646
$530$	0.516484	+	5.65103i	0.0224346	+	0.245465i
$531$		0			0
$532$	−8.42801	−	10.7012i	−0.365401	−	0.463957i
$533$	−11.6914	−	6.75002i	−0.506410	−	0.292376i
$534$		0			0
$535$	9.02069	−	0.824459i	0.389999	−	0.0356445i
$536$	−7.87168	+	13.6342i	−0.340005	+	0.588906i
$537$		0			0
$538$	0.687010	+	0.396645i	0.0296191	+	0.0171006i
$539$	−12.4903	+	3.68703i	−0.537997	+	0.158812i
$540$		0			0
$541$	11.7762	−	20.3970i	0.506299	−	0.876936i	−0.493674	−	0.869647i	$-0.664347\pi$
$541$	11.7762	−	20.3970i	0.506299	−	0.876936i	0.999973	−	0.00728876i	$-0.00232011\pi$
$542$			30.0855i			1.29228i
$543$		0			0
$544$	−7.13199			−0.305781
$545$	15.5509	+	7.17824i	0.666127	+	0.307482i
$546$		0			0
$547$	−8.50253	−	4.90894i	−0.363542	−	0.209891i	0.307091	−	0.951680i	$-0.400644\pi$
$547$	−8.50253	−	4.90894i	−0.363542	−	0.209891i	−0.670633	+	0.741789i	$0.733978\pi$
$548$	4.14127	+	2.39097i	0.176906	+	0.102137i
$549$		0			0
$550$	1.68630	+	9.14814i	0.0719041	+	0.390078i
$551$	−2.90123	−	5.02507i	−0.123596	−	0.214075i
$552$		0			0
$553$	20.7319	+	26.3238i	0.881612	+	1.11940i
$554$	−5.35656	−	9.27783i	−0.227578	−	0.394177i
$555$		0			0
$556$	1.63864			0.0694937
$557$	−14.2332	+	8.21754i	−0.603080	+	0.348188i	−0.770252	−	0.637739i	$-0.779870\pi$
$557$	−14.2332	+	8.21754i	−0.603080	+	0.348188i	0.167172	+	0.985928i	$0.446536\pi$
$558$		0			0
$559$	−16.8325			−0.711941
$560$	5.67084	+	1.68568i	0.239637	+	0.0712332i
$561$		0			0
$562$			15.5782i			0.657128i
$563$	27.6749	+	15.9781i	1.16636	+	0.673398i	0.952820	−	0.303536i	$-0.0981673\pi$
$563$	27.6749	+	15.9781i	1.16636	+	0.673398i	0.213540	+	0.976934i	$0.431501\pi$
$564$		0			0
$565$	14.2739	−	30.9228i	0.600506	−	1.30093i
$566$	19.3697			0.814169
$567$		0			0
$568$		−	10.0316i		−	0.420915i
$569$	−20.2164	−	35.0158i	−0.847515	−	1.46794i	−0.883419	−	0.468584i	$-0.844764\pi$
$569$	−20.2164	−	35.0158i	−0.847515	−	1.46794i	0.0359035	−	0.999355i	$-0.488569\pi$
$570$		0			0
$571$	−6.55212	+	11.3486i	−0.274198	+	0.474925i	−0.969932	−	0.243374i	$-0.921746\pi$
$571$	−6.55212	+	11.3486i	−0.274198	+	0.474925i	0.695735	+	0.718299i	$0.255079\pi$
$572$		−	4.59294i		−	0.192040i
$573$		0			0
$574$	13.4356	+	5.36759i	0.560792	+	0.224039i
$575$	18.9907	+	6.74578i	0.791968	+	0.281318i
$576$		0			0
$577$	13.1964	−	7.61896i	0.549374	−	0.317181i	−0.199495	−	0.979899i	$-0.563930\pi$
$577$	13.1964	−	7.61896i	0.549374	−	0.317181i	0.748870	+	0.662717i	$0.230597\pi$
$578$		−	33.8653i		−	1.40861i
$579$		0			0
$580$	2.28810	+	1.05618i	0.0950081	+	0.0438554i
$581$	−40.5049	−	16.1819i	−1.68043	−	0.671338i
$582$		0			0
$583$	−4.08882	+	2.36068i	−0.169342	+	0.0977695i
$584$	−5.07692	−	8.79348i	−0.210084	−	0.363877i
$585$		0			0
$586$	−3.01945	+	5.22984i	−0.124732	+	0.216043i
$587$	−30.9687	−	17.8798i	−1.27821	−	0.737978i	−0.301695	−	0.953405i	$-0.597552\pi$
$587$	−30.9687	−	17.8798i	−1.27821	−	0.737978i	−0.976520	+	0.215427i	$0.930886\pi$
$588$		0			0
$589$	0.0640799	+	0.110990i	0.00264037	+	0.00457325i
$590$	11.1526	+	15.7969i	0.459145	+	0.650347i
$591$		0			0
$592$			0.164601i			0.00676505i
$593$	−39.8145	−	22.9869i	−1.63499	−	0.943960i	−0.982523	−	0.186140i	$-0.940402\pi$
$593$	−39.8145	−	22.9869i	−1.63499	−	0.943960i	−0.652464	−	0.757820i	$-0.726264\pi$
$594$		0			0
$595$	−12.0223	+	40.4444i	−0.492865	+	1.65806i
$596$	−0.566188	+	0.980667i	−0.0231920	+	0.0401697i
$597$		0			0
$598$	−8.61743	−	4.97528i	−0.352393	−	0.203454i
$599$	10.6593	−	18.4624i	0.435527	−	0.754355i	−0.561812	−	0.827265i	$-0.689895\pi$
$599$	10.6593	−	18.4624i	0.435527	−	0.754355i	0.997338	+	0.0729106i	$0.0232288\pi$
$600$		0			0
$601$	−9.44816	+	16.3647i	−0.385398	+	0.667530i	−0.991824	−	0.127610i	$-0.959269\pi$
$601$	−9.44816	+	16.3647i	−0.385398	+	0.667530i	0.606426	+	0.795140i	$0.292603\pi$
$602$	17.8541	−	2.58015i	0.727680	−	0.105159i
$603$		0			0
$604$	0.764783	−	1.32464i	0.0311186	−	0.0538990i
$605$	13.7709	−	9.72228i	0.559868	−	0.395267i
$606$		0			0
$607$		−	14.0116i		−	0.568713i	−0.958719	−	0.284356i	$-0.908220\pi$
$607$		−	14.0116i		−	0.568713i	0.958719	−	0.284356i	$-0.0917799\pi$
$608$	−4.45871	+	2.57424i	−0.180825	+	0.104399i
$609$		0			0
$610$	−14.3302	+	1.30972i	−0.580211	+	0.0530292i
$611$	−15.4574	+	26.7731i	−0.625341	+	1.08312i
$612$		0			0
$613$	−5.46761	+	3.15673i	−0.220835	+	0.127499i	−0.606337	−	0.795208i	$-0.707362\pi$
$613$	−5.46761	+	3.15673i	−0.220835	+	0.127499i	0.385502	+	0.922707i	$0.374028\pi$
$614$	14.7407	+	25.5317i	0.594887	+	1.03037i
$615$		0			0
$616$	0.704022	+	4.87169i	0.0283659	+	0.196286i
$617$	−14.0939	+	8.13710i	−0.567398	+	0.327587i	−0.756109	−	0.654445i	$-0.772902\pi$
$617$	−14.0939	+	8.13710i	−0.567398	+	0.327587i	0.188712	+	0.982033i	$0.439569\pi$
$618$		0			0
$619$	28.3083			1.13781			0.568904	−	0.822404i	$-0.307368\pi$
$619$	28.3083			1.13781			0.568904	+	0.822404i	$0.307368\pi$
$620$	−0.0505377	−	0.0233280i	−0.00202964	−	0.000936875i
$621$		0			0
$622$		−	8.24275i		−	0.330504i
$623$	−5.31227	+	13.2971i	−0.212831	+	0.532738i
$624$		0			0
$625$	−19.3980	−	15.7708i	−0.775920	−	0.630832i
$626$	1.71498	−	2.97043i	0.0685444	−	0.118722i
$627$		0			0
$628$	1.60931	−	0.929138i	0.0642186	−	0.0370766i
$629$	−1.17393			−0.0468077
$630$		0			0
$631$	24.3538			0.969508			0.484754	−	0.874651i	$-0.338909\pi$
$631$	24.3538			0.969508			0.484754	+	0.874651i	$0.338909\pi$
$632$	10.9679	−	6.33233i	0.436280	−	0.251887i
$633$		0			0
$634$	−13.2885	+	23.0163i	−0.527753	+	0.914095i
$635$	−7.55998	−	10.7082i	−0.300009	−	0.424941i
$636$		0			0
$637$	−11.9073	+	12.5240i	−0.471783	+	0.496220i
$638$			2.09677i			0.0830120i
$639$		0			0
$640$	0.937140	−	2.03021i	0.0370437	−	0.0802513i
$641$	−25.9748			−1.02594			−0.512971	−	0.858406i	$-0.671455\pi$
$641$	−25.9748			−1.02594			−0.512971	+	0.858406i	$0.671455\pi$
$642$		0			0
$643$	34.8054	−	20.0949i	1.37259	−	0.792465i	0.381336	−	0.924436i	$-0.375464\pi$
$643$	34.8054	−	20.0949i	1.37259	−	0.792465i	0.991254	+	0.131971i	$0.0421306\pi$
$644$	9.90306	+	3.95632i	0.390235	+	0.155901i
$645$		0			0
$646$	−18.3594	−	31.7995i	−0.722343	−	1.25113i
$647$	−26.4801	+	15.2883i	−1.04104	+	0.601044i	−0.920127	−	0.391619i	$-0.871915\pi$
$647$	−26.4801	+	15.2883i	−1.04104	+	0.601044i	−0.120912	+	0.992663i	$0.538582\pi$
$648$		0			0
$649$	−8.04440	+	13.9333i	−0.315770	+	0.546930i
$650$	8.00739	+	9.39395i	0.314076	+	0.368461i
$651$		0			0
$652$	−19.5044	+	11.2609i	−0.763853	+	0.441010i
$653$		−	23.3755i		−	0.914756i	−0.889272	−	0.457378i	$-0.848789\pi$
$653$		−	23.3755i		−	0.914756i	0.889272	−	0.457378i	$-0.151211\pi$
$654$		0			0
$655$	−30.8627	+	21.7891i	−1.20591	+	0.851371i
$656$	2.73422	−	4.73581i	0.106753	−	0.184902i
$657$		0			0
$658$	12.2917	−	30.7673i	0.479180	−	1.19944i
$659$	−18.2243	+	31.5654i	−0.709917	+	1.22961i	0.254971	+	0.966949i	$0.417934\pi$
$659$	−18.2243	+	31.5654i	−0.709917	+	1.22961i	−0.964888	+	0.262663i	$0.915399\pi$
$660$		0			0
$661$	14.8884	−	25.7875i	0.579092	−	1.00302i	−0.416492	−	0.909139i	$-0.636741\pi$
$661$	14.8884	−	25.7875i	0.579092	−	1.00302i	0.995584	−	0.0938772i	$-0.0299261\pi$
$662$	2.00554	+	1.15790i	0.0779476	+	0.0450031i
$663$		0			0
$664$	−8.24296	+	14.2772i	−0.319889	+	0.554064i
$665$	7.08212	+	29.6240i	0.274633	+	1.14877i
$666$		0			0
$667$	3.93404	+	2.27132i	0.152327	+	0.0879458i
$668$		−	1.59648i		−	0.0617696i
$669$		0			0
$670$	28.7583	−	20.3034i	1.11103	−	0.784388i
$671$	−5.98633	−	10.3686i	−0.231100	−	0.400277i
$672$		0			0
$673$	−5.68572	−	3.28265i	−0.219168	−	0.126537i	0.386397	−	0.922333i	$-0.373720\pi$
$673$	−5.68572	−	3.28265i	−0.219168	−	0.126537i	−0.605565	+	0.795796i	$0.707053\pi$
$674$	5.35691	−	9.27844i	0.206340	−	0.357392i
$675$		0			0
$676$	3.45271	+	5.98026i	0.132796	+	0.230010i
$677$	−1.02368	+	0.591025i	−0.0393434	+	0.0227149i	−0.519543	−	0.854444i	$-0.673898\pi$
$677$	−1.02368	+	0.591025i	−0.0393434	+	0.0227149i	0.480199	+	0.877159i	$0.340564\pi$
$678$		0			0
$679$	−10.1133	−	4.04030i	−0.388112	−	0.155053i
$680$	14.4795	+	6.68367i	0.555262	+	0.256307i
$681$		0			0
$682$		−	0.0463118i		−	0.00177337i
$683$	33.5322	−	19.3599i	1.28308	−	0.740784i	0.305666	−	0.952139i	$-0.401121\pi$
$683$	33.5322	−	19.3599i	1.28308	−	0.740784i	0.977409	+	0.211355i	$0.0677875\pi$
$684$		0			0
$685$	−6.16700	−	8.73512i	−0.235629	−	0.333752i
$686$	10.7102	−	15.1093i	0.408917	−	0.576877i
$687$		0			0
$688$		−	6.81832i		−	0.259946i
$689$	−3.13250	+	5.42565i	−0.119339	+	0.206701i
$690$		0			0
$691$	24.5167	+	42.4642i	0.932661	+	1.61542i	0.778753	+	0.627331i	$0.215853\pi$
$691$	24.5167	+	42.4642i	0.932661	+	1.61542i	0.153908	+	0.988085i	$0.450814\pi$
$692$		−	22.5323i		−	0.856549i
$693$		0			0
$694$	2.60399			0.0988459
$695$	−3.32678	−	1.53563i	−0.126192	−	0.0582499i
$696$		0			0
$697$	33.7757	+	19.5004i	1.27935	+	0.738631i
$698$		−	17.3786i		−	0.657788i
$699$		0			0
$700$	−9.93331	−	8.73667i	−0.375444	−	0.330215i
$701$	−4.72481			−0.178454			−0.0892269	−	0.996011i	$-0.528440\pi$
$701$	−4.72481			−0.178454			−0.0892269	+	0.996011i	$0.528440\pi$
$702$		0			0
$703$	−0.733907	+	0.423722i	−0.0276798	+	0.0159810i
$704$	1.86045			0.0701184
$705$		0			0
$706$	0.781154	+	1.35300i	0.0293991	+	0.0509207i
$707$	8.30896	−	1.20075i	0.312491	−	0.0451590i
$708$		0			0
$709$	5.91387	+	10.2431i	0.222100	+	0.384688i	0.955445	−	0.295168i	$-0.0953756\pi$
$709$	5.91387	+	10.2431i	0.222100	+	0.384688i	−0.733346	+	0.679856i	$0.762042\pi$
$710$	−9.40097	+	20.3662i	−0.352812	+	0.764330i
$711$		0			0
$712$	4.68699	+	2.70604i	0.175653	+	0.101413i
$713$	−0.0868919	−	0.0501670i	−0.00325413	−	0.00187877i
$714$		0			0
$715$	−4.30423	+	9.32465i	−0.160969	+	0.348722i
$716$	14.4529			0.540131
$717$		0			0
$718$		−	8.53256i		−	0.318432i
$719$	21.5479	−	37.3220i	0.803600	−	1.39188i	−0.113633	−	0.993523i	$-0.536249\pi$
$719$	21.5479	−	37.3220i	0.803600	−	1.39188i	0.917232	−	0.398353i	$-0.130418\pi$
$720$		0			0
$721$	−3.66938	−	25.3914i	−0.136655	−	0.945624i
$722$	−6.50110	−	3.75341i	−0.241946	−	0.139687i
$723$		0			0
$724$	1.78351	−	3.08913i	0.0662836	−	0.114806i
$725$	−3.65554	−	4.28854i	−0.135763	−	0.159272i
$726$		0			0
$727$	14.3846	+	8.30493i	0.533494	+	0.308013i	0.742438	−	0.669915i	$-0.233669\pi$
$727$	14.3846	+	8.30493i	0.533494	+	0.308013i	−0.208944	+	0.977928i	$0.567003\pi$
$728$	4.04128	+	5.13130i	0.149780	+	0.190178i
$729$		0			0
$730$	2.06651	+	22.6104i	0.0764850	+	0.836850i
$731$	48.6282			1.79858
$732$		0			0
$733$		−	50.3737i		−	1.86059i	−0.366808	−	0.930297i	$-0.619549\pi$
$733$		−	50.3737i		−	1.86059i	0.366808	−	0.930297i	$-0.380451\pi$
$734$	14.0264	+	24.2944i	0.517723	+	0.896723i
$735$		0			0
$736$	2.01533	−	3.49065i	0.0742859	−	0.128667i
$737$	25.3657	+	14.6449i	0.934357	+	0.539451i
$738$		0			0
$739$	21.8633	+	37.8684i	0.804256	+	1.39301i	0.916792	+	0.399364i	$0.130769\pi$
$739$	21.8633	+	37.8684i	0.804256	+	1.39301i	−0.112537	+	0.993648i	$0.535898\pi$
$740$	0.154254	−	0.334175i	0.00567049	−	0.0122845i
$741$		0			0
$742$	2.49095	−	6.23510i	0.0914457	−	0.228898i
$743$	−31.4095	+	18.1343i	−1.15230	+	0.665282i	−0.949447	−	0.313926i	$-0.898356\pi$
$743$	−31.4095	+	18.1343i	−1.15230	+	0.665282i	−0.202856	+	0.979209i	$0.565022\pi$
$744$		0			0
$745$	2.06851	−	1.46037i	0.0757842	−	0.0535037i
$746$	7.03010	+	12.1765i	0.257390	+	0.445813i
$747$		0			0
$748$			13.2687i			0.485153i
$749$	−9.95303	−	3.97628i	−0.363676	−	0.145290i
$750$		0			0
$751$	44.0233			1.60643			0.803217	−	0.595687i	$-0.203120\pi$
$751$	44.0233			1.60643			0.803217	+	0.595687i	$0.203120\pi$
$752$	−10.8449	−	6.26132i	−0.395474	−	0.228327i
$753$		0			0
$754$	1.39115	+	2.40955i	0.0506628	+	0.0877506i
$755$	−2.79405	+	1.97260i	−0.101686	+	0.0717903i
$756$		0			0
$757$		−	14.2814i		−	0.519068i	−0.965734	−	0.259534i	$-0.916431\pi$
$757$		−	14.2814i		−	0.519068i	0.965734	−	0.259534i	$-0.0835689\pi$
$758$	7.89967	−	4.56088i	0.286929	−	0.165659i
$759$		0			0
$760$	11.4646	−	1.04782i	0.415863	−	0.0380084i
$761$	−5.64220			−0.204530			−0.102265	−	0.994757i	$-0.532609\pi$
$761$	−5.64220			−0.204530			−0.102265	+	0.994757i	$0.532609\pi$
$762$		0			0
$763$	−12.5389	−	15.9209i	−0.453939	−	0.576376i
$764$	−1.91746			−0.0693713
$765$		0			0
$766$	5.04982	+	8.74655i	0.182457	+	0.316026i
$767$			21.3490i			0.770867i
$768$		0			0
$769$	−2.47121	−	4.28027i	−0.0891143	−	0.154350i	0.818023	−	0.575186i	$-0.195070\pi$
$769$	−2.47121	−	4.28027i	−0.0891143	−	0.154350i	−0.907137	+	0.420835i	$0.861737\pi$
$770$	3.13614	−	10.5503i	0.113018	−	0.380208i
$771$		0			0
$772$	12.3389	−	7.12386i	0.444086	−	0.256393i
$773$	24.7596	−	14.2949i	0.890540	−	0.514153i	0.0164207	−	0.999865i	$-0.494773\pi$
$773$	24.7596	−	14.2949i	0.890540	−	0.514153i	0.874119	+	0.485712i	$0.161440\pi$
$774$		0			0
$775$	0.0807407	+	0.0947217i	0.00290029	+	0.00340250i
$776$	−2.05811	+	3.56475i	−0.0738817	+	0.127967i
$777$		0			0
$778$	−25.6736	+	14.8227i	−0.920444	+	0.531419i
$779$	28.1541			1.00873
$780$		0			0
$781$	−18.6632			−0.667823
$782$	24.8952	+	14.3733i	0.890252	+	0.513987i
$783$		0			0
$784$	−5.07309	−	4.82326i	−0.181182	−	0.172259i
$785$	−4.13798	+	0.378197i	−0.147691	+	0.0134984i
$786$		0			0
$787$	−22.0854	−	12.7510i	−0.787259	−	0.454524i	0.0517380	−	0.998661i	$-0.483524\pi$
$787$	−22.0854	−	12.7510i	−0.787259	−	0.454524i	−0.838997	+	0.544137i	$0.816857\pi$
$788$	11.6276	+	6.71319i	0.414216	+	0.239147i
$789$		0			0
$790$	−28.2015	+	2.57751i	−1.00336	+	0.0917039i
$791$	−31.6586	+	24.9335i	−1.12565	+	0.886534i
$792$		0			0
$793$	−13.7586	−	7.94355i	−0.488583	−	0.282084i
$794$	−27.3380			−0.970189
$795$		0			0
$796$	−6.66638			−0.236283
$797$	37.2901	−	21.5295i	1.32088	−	0.762612i	0.337014	−	0.941500i	$-0.390583\pi$
$797$	37.2901	−	21.5295i	1.32088	−	0.762612i	0.983870	+	0.178887i	$0.0572497\pi$
$798$		0			0
$799$	44.6556	−	77.3458i	1.57980	−	2.73630i
$800$	−3.80519	+	3.24354i	−0.134534	+	0.114676i
$801$		0			0
$802$	12.5252	−	7.23145i	0.442282	−	0.255352i
$803$	−16.3599	+	9.44536i	−0.577327	+	0.333320i
$804$		0			0
$805$	−16.3977	−	17.3127i	−0.577943	−	0.610193i
$806$	−0.0307267	−	0.0532201i	−0.00108230	−	0.00187460i
$807$		0			0
$808$		−	3.17312i		−	0.111630i
$809$	−0.417099	−	0.722437i	−0.0146644	−	0.0253995i	0.858600	−	0.512646i	$-0.171335\pi$
$809$	−0.417099	−	0.722437i	−0.0146644	−	0.0253995i	−0.873264	+	0.487246i	$0.838001\pi$
$810$		0			0
$811$	2.98741			0.104902			0.0524510	−	0.998623i	$-0.483297\pi$
$811$	2.98741			0.104902			0.0524510	+	0.998623i	$0.483297\pi$
$812$	−1.84493	−	2.34254i	−0.0647443	−	0.0822072i
$813$		0			0
$814$	0.306232			0.0107334
$815$	50.1512	−	4.58364i	1.75672	−	0.160558i
$816$		0			0
$817$	30.4009	−	17.5520i	1.06359	−	0.614066i
$818$			33.1747i			1.15993i
$819$		0			0
$820$	−9.98916	+	7.05235i	−0.348837	+	0.246279i
$821$	21.7323	+	37.6415i	0.758463	+	1.31370i	0.943634	+	0.330990i	$0.107383\pi$
$821$	21.7323	+	37.6415i	0.758463	+	1.31370i	−0.185171	+	0.982706i	$0.559284\pi$
$822$		0			0
$823$	−5.78559	−	3.34031i	−0.201673	−	0.116436i	0.395763	−	0.918353i	$-0.370480\pi$
$823$	−5.78559	−	3.34031i	−0.201673	−	0.116436i	−0.597436	+	0.801917i	$0.703814\pi$
$824$	−9.69673			−0.337802
$825$		0			0
$826$	−3.27245	−	22.6447i	−0.113863	−	0.787909i
$827$		−	21.5493i		−	0.749342i	−0.927158	−	0.374671i	$-0.877756\pi$
$827$		−	21.5493i		−	0.749342i	0.927158	−	0.374671i	$-0.122244\pi$
$828$		0			0
$829$	−20.3294	−	35.2115i	−0.706068	−	1.22295i	−0.966305	−	0.257401i	$-0.917134\pi$
$829$	−20.3294	−	35.2115i	−0.706068	−	1.22295i	0.260237	−	0.965545i	$-0.416199\pi$
$830$	30.1147	−	21.2610i	1.04530	−	0.737981i
$831$		0			0
$832$	2.13798	−	1.23436i	0.0741210	−	0.0427938i
$833$	34.3994	−	36.1812i	1.19187	−	1.25360i
$834$		0			0
$835$	−1.49612	+	3.24119i	−0.0517755	+	0.112166i
$836$	4.78925	+	8.29522i	0.165640	+	0.286896i
$837$		0			0
$838$	4.43417	+	2.56007i	0.153176	+	0.0884362i
$839$	−1.49547	+	2.59023i	−0.0516294	+	0.0894247i	−0.890685	−	0.454621i	$-0.849775\pi$
$839$	−1.49547	+	2.59023i	−0.0516294	+	0.0894247i	0.839056	+	0.544046i	$0.183108\pi$
$840$		0			0
$841$	13.8649	+	24.0147i	0.478100	+	0.828094i
$842$		−	0.509848i		−	0.0175705i
$843$		0			0
$844$	4.40548			0.151643
$845$	−1.40539	−	15.3769i	−0.0483469	−	0.528981i
$846$		0			0
$847$	−19.7405	+	2.85276i	−0.678292	+	0.0980220i
$848$	−2.19776	−	1.26888i	−0.0754713	−	0.0435734i
$849$		0			0
$850$	−23.1329	−	27.1386i	−0.793451	−	0.930845i
$851$	0.331724	−	0.574563i	0.0113714	−	0.0196958i
$852$		0			0
$853$	43.4957	+	25.1122i	1.48926	+	0.859827i	0.999925	−	0.0122673i	$-0.00390491\pi$
$853$	43.4957	+	25.1122i	1.48926	+	0.859827i	0.489339	+	0.872094i	$0.337238\pi$
$854$	15.8113	+	6.31667i	0.541050	+	0.216152i
$855$		0			0
$856$	−2.02550	+	3.50826i	−0.0692300	+	0.119910i
$857$		−	16.9016i		−	0.577347i	−0.957428	−	0.288673i	$-0.906786\pi$
$857$		−	16.9016i		−	0.577347i	0.957428	−	0.288673i	$-0.0932141\pi$
$858$		0			0
$859$	−29.1707			−0.995292			−0.497646	−	0.867380i	$-0.665802\pi$
$859$	−29.1707			−0.995292			−0.497646	+	0.867380i	$0.665802\pi$
$860$	−6.38972	+	13.8427i	−0.217888	+	0.472031i
$861$		0			0
$862$	−10.7259	−	6.19259i	−0.365325	−	0.210920i
$863$	−1.13286	−	0.654060i	−0.0385632	−	0.0222644i	0.480594	−	0.876943i	$-0.340421\pi$
$863$	−1.13286	−	0.654060i	−0.0385632	−	0.0222644i	−0.519158	+	0.854679i	$0.673754\pi$
$864$		0			0
$865$	−21.1159	+	45.7454i	−0.717962	+	1.55539i
$866$	−9.32580	−	16.1528i	−0.316904	−	0.548893i
$867$		0			0
$868$	0.0407493	+	0.0517402i	0.00138312	+	0.00175618i
$869$	−11.7810	−	20.4053i	−0.399643	−	0.692202i
$870$		0			0
$871$	38.8660			1.31692
$872$	−6.63352	+	3.82986i	−0.224639	+	0.129696i
$873$		0			0
$874$	20.7517			0.701937
$875$	11.9793	+	27.0462i	0.404973	+	0.914329i
$876$		0			0
$877$		−	4.95578i		−	0.167345i	−0.996493	−	0.0836724i	$-0.973335\pi$
$877$		−	4.95578i		−	0.167345i	0.996493	−	0.0836724i	$-0.0266649\pi$
$878$	−0.332396	−	0.191909i	−0.0112178	−	0.00647662i
$879$		0			0
$880$	−3.77712	−	1.74350i	−0.127327	−	0.0587735i
$881$	−20.8587			−0.702747			−0.351374	−	0.936235i	$-0.614285\pi$
$881$	−20.8587			−0.702747			−0.351374	+	0.936235i	$0.614285\pi$
$882$		0			0
$883$			7.31896i			0.246303i	0.992388	+	0.123151i	$0.0393001\pi$
$883$			7.31896i			0.246303i	−0.992388	+	0.123151i	$0.960700\pi$
$884$	8.80345	+	15.2480i	0.296092	+	0.512846i
$885$		0			0
$886$	−2.71427	+	4.70125i	−0.0911876	+	0.157941i
$887$		−	27.3875i		−	0.919584i	−0.888027	−	0.459792i	$-0.847924\pi$
$887$		−	27.3875i		−	0.919584i	0.888027	−	0.459792i	$-0.152076\pi$
$888$		0			0
$889$	2.21829	+	15.3501i	0.0743989	+	0.514825i
$890$	−6.97967	−	9.88620i	−0.233959	−	0.331386i
$891$		0			0
$892$	−10.8925	+	6.28877i	−0.364707	+	0.210563i
$893$		−	64.4725i		−	2.15749i
$894$		0			0
$895$	−29.3425	−	13.5444i	−0.980812	−	0.452739i
$896$	−2.07852	+	1.63699i	−0.0694386	+	0.0546880i
$897$		0			0
$898$	−4.52128	+	2.61036i	−0.150877	+	0.0871089i
$899$	0.0140274	+	0.0242961i	0.000467839	+	0.000810321i
$900$		0			0
$901$	9.04961	−	15.6744i	0.301486	−	0.522190i
$902$	−8.81074	−	5.08688i	−0.293366	−	0.169375i
$903$		0			0
$904$	7.61565	+	13.1907i	0.253293	+	0.438716i
$905$	−6.51585	+	4.60019i	−0.216594	+	0.152916i
$906$		0			0
$907$		−	51.7815i		−	1.71938i	−0.510819	−	0.859688i	$-0.670658\pi$
$907$		−	51.7815i		−	1.71938i	0.510819	−	0.859688i	$-0.329342\pi$
$908$	−2.95515	−	1.70616i	−0.0980702	−	0.0566209i
$909$		0			0
$910$	−3.39592	−	14.2049i	−0.112573	−	0.470887i
$911$	−8.58686	+	14.8729i	−0.284495	+	0.492760i	−0.972487	−	0.232959i	$-0.925159\pi$
$911$	−8.58686	+	14.8729i	−0.284495	+	0.492760i	0.687991	+	0.725719i	$0.258493\pi$
$912$		0			0
$913$	26.5621	+	15.3356i	0.879077	+	0.507536i
$914$	6.14074	−	10.6361i	0.203118	−	0.351810i
$915$		0			0
$916$	−12.0334	+	20.8424i	−0.397594	+	0.688653i
$917$	44.2415	−	6.39347i	1.46098	−	0.211131i
$918$		0			0
$919$	3.73425	−	6.46790i	0.123181	−	0.213356i	−0.797839	−	0.602870i	$-0.794024\pi$
$919$	3.73425	−	6.46790i	0.123181	−	0.213356i	0.921021	+	0.389514i	$0.127357\pi$
$920$	−7.36276	+	5.19812i	−0.242743	+	0.171377i
$921$		0			0
$922$		−	2.61209i		−	0.0860246i
$923$	−21.4472	+	12.3826i	−0.705944	+	0.407577i
$924$		0			0
$925$	−0.626337	+	0.533889i	−0.0205938	+	0.0175542i
$926$	9.80220	−	16.9779i	0.322120	−	0.557929i
$927$		0			0
$928$	−0.976031	+	0.563512i	−0.0320398	+	0.0184982i
$929$	−0.894243	−	1.54887i	−0.0293391	−	0.0508169i	0.850983	−	0.525193i	$-0.176007\pi$
$929$	−0.894243	−	1.54887i	−0.0293391	−	0.0508169i	−0.880322	+	0.474376i	$0.842674\pi$
$930$		0			0
$931$	8.44617	−	35.0356i	0.276812	−	1.14825i
$932$	−20.5971	+	11.8917i	−0.674681	+	0.389527i
$933$		0			0
$934$	16.1336			0.527907
$935$	12.4346	−	26.9383i	0.406656	−	0.880978i
$936$		0			0
$937$			37.8051i			1.23504i	0.786556	+	0.617519i	$0.211862\pi$
$937$			37.8051i			1.23504i	−0.786556	+	0.617519i	$0.788138\pi$
$938$	−41.2248	+	5.95752i	−1.34604	+	0.194520i
$939$		0			0
$940$	16.1498	+	22.8750i	0.526748	+	0.746101i
$941$	−11.6837	+	20.2368i	−0.380878	+	0.659700i	−0.991188	−	0.132463i	$-0.957712\pi$
$941$	−11.6837	+	20.2368i	−0.380878	+	0.659700i	0.610310	+	0.792163i	$0.291045\pi$
$942$		0			0
$943$	−19.0884	+	11.0207i	−0.621603	+	0.358883i
$944$	−8.64779			−0.281462
$945$		0			0
$946$	−12.6852			−0.412430
$947$	−42.2075	+	24.3685i	−1.37156	+	0.791870i	−0.991124	−	0.132937i	$-0.957559\pi$
$947$	−42.2075	+	24.3685i	−1.37156	+	0.791870i	−0.380435	+	0.924808i	$0.624226\pi$
$948$		0			0
$949$	−12.5335	+	21.7087i	−0.406855	+	0.704693i
$950$	−24.2575	−	8.61660i	−0.787016	−	0.279559i
$951$		0			0
$952$	−11.6750	−	14.8240i	−0.378389	−	0.480449i
$953$		−	41.3647i		−	1.33993i	−0.742391	−	0.669967i	$-0.766308\pi$
$953$		−	41.3647i		−	1.33993i	0.742391	−	0.669967i	$-0.233692\pi$
$954$		0			0
$955$	3.89286	+	1.79693i	0.125970	+	0.0581473i
$956$	22.9545			0.742401
$957$		0			0
$958$	19.4427	−	11.2252i	0.628164	−	0.362671i
$959$	1.80955	+	12.5217i	0.0584335	+	0.404348i
$960$		0			0
$961$	15.4997	+	26.8463i	0.499990	+	0.866008i
$962$	0.351912	−	0.203177i	0.0113461	−	0.00655068i
$963$		0			0
$964$	−6.08000	+	10.5309i	−0.195824	+	0.339177i
$965$	−31.7266	+	2.89970i	−1.02132	+	0.0933446i
$966$		0			0
$967$	1.14078	−	0.658630i	0.0366850	−	0.0211801i	−0.481545	−	0.876421i	$-0.659924\pi$
$967$	1.14078	−	0.658630i	0.0366850	−	0.0211801i	0.518230	+	0.855241i	$0.326591\pi$
$968$			7.53872i			0.242304i
$969$		0			0
$970$	7.51906	−	5.30846i	0.241423	−	0.170444i
$971$	−15.0115	+	26.0006i	−0.481741	+	0.834399i	−0.999780	−	0.0209572i	$-0.993329\pi$
$971$	−15.0115	+	26.0006i	−0.481741	+	0.834399i	0.518040	+	0.855357i	$0.326662\pi$
$972$		0			0
$973$	2.68244	+	3.40595i	0.0859949	+	0.109190i
$974$	−14.7555	+	25.5573i	−0.472797	+	0.818909i
$975$		0			0
$976$	3.21768	−	5.57318i	0.102995	−	0.178393i
$977$	−40.7626	−	23.5343i	−1.30411	−	0.752929i	−0.323005	−	0.946397i	$-0.604693\pi$
$977$	−40.7626	−	23.5343i	−1.30411	−	0.752929i	−0.981107	+	0.193468i	$0.938027\pi$
$978$		0			0
$979$	5.03445	−	8.71993i	0.160902	−	0.278690i
$980$	5.77939	+	14.5464i	0.184616	+	0.464669i
$981$		0			0
$982$	3.46646	+	2.00136i	0.110619	+	0.0638661i
$983$		−	43.6850i		−	1.39334i	−0.717394	−	0.696668i	$-0.754665\pi$
$983$		−	43.6850i		−	1.39334i	0.717394	−	0.696668i	$-0.245335\pi$
$984$		0			0
$985$	−17.3153	−	24.5259i	−0.551711	−	0.781460i
$986$	−4.01896	−	6.96104i	−0.127990	−	0.221685i
$987$		0			0
$988$	11.0073	+	6.35508i	0.350189	+	0.202182i
$989$	−13.7411	+	23.8004i	−0.436943	+	0.756807i
$990$		0			0
$991$	−16.5047	−	28.5870i	−0.524289	−	0.908095i	−0.999600	−	0.0282776i	$-0.990998\pi$
$991$	−16.5047	−	28.5870i	−0.524289	−	0.908095i	0.475311	−	0.879818i	$-0.342336\pi$
$992$	0.0215578	−	0.0124464i	0.000684460	−	0.000395173i
$993$		0			0
$994$	20.8508	−	16.4216i	0.661348	−	0.520861i
$995$	13.5342	+	6.24733i	0.429062	+	0.198054i
$996$		0			0
$997$		−	52.3005i		−	1.65637i	−0.560453	−	0.828186i	$-0.689373\pi$
$997$		−	52.3005i		−	1.65637i	0.560453	−	0.828186i	$-0.310627\pi$
$998$	2.97954	−	1.72024i	0.0943158	−	0.0544532i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.bq.a.289.42		96
3.2	odd	2		630.2.bq.a.79.21	yes	96
5.4	even	2	inner	1890.2.bq.a.289.16		96
7.4	even	3		1890.2.ba.a.1369.20		96
9.4	even	3		1890.2.ba.a.1549.31		96
9.5	odd	6		630.2.ba.a.499.12	✓	96
15.14	odd	2		630.2.bq.a.79.28	yes	96
21.11	odd	6		630.2.ba.a.529.13	yes	96
35.4	even	6		1890.2.ba.a.1369.31		96
45.4	even	6		1890.2.ba.a.1549.20		96
45.14	odd	6		630.2.ba.a.499.37	yes	96
63.4	even	3	inner	1890.2.bq.a.739.16		96
63.32	odd	6		630.2.bq.a.319.28	yes	96
105.74	odd	6		630.2.ba.a.529.36	yes	96
315.4	even	6	inner	1890.2.bq.a.739.42		96
315.284	odd	6		630.2.bq.a.319.21	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.ba.a.499.12	✓	96	9.5	odd	6
630.2.ba.a.499.37	yes	96	45.14	odd	6
630.2.ba.a.529.13	yes	96	21.11	odd	6
630.2.ba.a.529.36	yes	96	105.74	odd	6
630.2.bq.a.79.21	yes	96	3.2	odd	2
630.2.bq.a.79.28	yes	96	15.14	odd	2
630.2.bq.a.319.21	yes	96	315.284	odd	6
630.2.bq.a.319.28	yes	96	63.32	odd	6
1890.2.ba.a.1369.20		96	7.4	even	3
1890.2.ba.a.1369.31		96	35.4	even	6
1890.2.ba.a.1549.20		96	45.4	even	6
1890.2.ba.a.1549.31		96	9.4	even	3
1890.2.bq.a.289.16		96	5.4	even	2	inner
1890.2.bq.a.289.42		96	1.1	even	1	trivial
1890.2.bq.a.739.16		96	63.4	even	3	inner
1890.2.bq.a.739.42		96	315.4	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.bq (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.82669 + 1.28965i) q^{5} +(2.61855 - 0.378415i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.82669 + 1.28965i) q^{5} +(2.61855 - 0.378415i) q^{7} -1.00000i q^{8} +(-0.937140 + 2.03021i) q^{10} -1.86045 q^{11} +(-2.13798 + 1.23436i) q^{13} +(2.07852 - 1.63699i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(6.17648 - 3.56599i) q^{17} +(2.57424 - 4.45871i) q^{19} +(0.203520 + 2.22679i) q^{20} +(-1.61120 + 0.930226i) q^{22} +4.03065i q^{23} +(1.67362 - 4.71158i) q^{25} +(-1.23436 + 2.13798i) q^{26} +(0.981558 - 2.45694i) q^{28} +(0.563512 - 0.976031i) q^{29} +(-0.0124464 + 0.0215578i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(3.56599 - 6.17648i) q^{34} +(-4.29527 + 4.06825i) q^{35} +(-0.142548 - 0.0823004i) q^{37} -5.14848i q^{38} +(1.28965 + 1.82669i) q^{40} +(2.73422 + 4.73581i) q^{41} +(5.90484 + 3.40916i) q^{43} +(-0.930226 + 1.61120i) q^{44} +(2.01533 + 3.49065i) q^{46} +(10.8449 - 6.26132i) q^{47} +(6.71360 - 1.98179i) q^{49} +(-0.906392 - 4.91716i) q^{50} +2.46872i q^{52} +(2.19776 - 1.26888i) q^{53} +(3.39848 - 2.39933i) q^{55} +(-0.378415 - 2.61855i) q^{56} -1.12702i q^{58} +(4.32390 - 7.48921i) q^{59} +(3.21768 + 5.57318i) q^{61} +0.0248928i q^{62} -1.00000 q^{64} +(2.31354 - 5.01203i) q^{65} +(-13.6342 - 7.87168i) q^{67} -7.13199i q^{68} +(-1.68568 + 5.67084i) q^{70} +10.0316 q^{71} +(8.79348 - 5.07692i) q^{73} -0.164601 q^{74} +(-2.57424 - 4.45871i) q^{76} +(-4.87169 + 0.704022i) q^{77} +(6.33233 + 10.9679i) q^{79} +(2.03021 + 0.937140i) q^{80} +(4.73581 + 2.73422i) q^{82} +(-14.2772 - 8.24296i) q^{83} +(-6.68367 + 14.4795i) q^{85} +6.81832 q^{86} +1.86045i q^{88} +(-2.70604 + 4.68699i) q^{89} +(-5.13130 + 4.04128i) q^{91} +(3.49065 + 2.01533i) q^{92} +(6.26132 - 10.8449i) q^{94} +(1.04782 + 11.4646i) q^{95} +(-3.56475 - 2.05811i) q^{97} +(4.82326 - 5.07309i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 48 q^{4}+O(q^{10}) \) 96 * q + 48 * q^4	\( 96 q + 48 q^{4} + 8 q^{11} + 2 q^{14} - 48 q^{16} - 24 q^{26} - 10 q^{29} + 34 q^{35} - 30 q^{41} + 4 q^{44} - 6 q^{46} + 12 q^{49} + 12 q^{50} + 12 q^{55} + 4 q^{56} + 24 q^{59} - 6 q^{61} - 96 q^{64} - 18 q^{65} + 6 q^{70} + 32 q^{71} + 8 q^{86} + 66 q^{89} - 12 q^{94} - 30 q^{95}+O(q^{100}) \) 96 * q + 48 * q^4 + 8 * q^11 + 2 * q^14 - 48 * q^16 - 24 * q^26 - 10 * q^29 + 34 * q^35 - 30 * q^41 + 4 * q^44 - 6 * q^46 + 12 * q^49 + 12 * q^50 + 12 * q^55 + 4 * q^56 + 24 * q^59 - 6 * q^61 - 96 * q^64 - 18 * q^65 + 6 * q^70 + 32 * q^71 + 8 * q^86 + 66 * q^89 - 12 * q^94 - 30 * q^95

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