LMFDB - Embedded newform 1890.2.bi.b.719.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(719,1890)]

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([5, 3, 5]))

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

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

chi := DirichletCharacter("1890.719");

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.bi (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:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			719.19
Character	$\chi$	$=$	1890.719
Dual form			1890.2.bi.b.899.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{4} +(1.79580 + 1.33234i) q^{5} +(-2.61687 - 0.389830i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{4} +(1.79580 + 1.33234i) q^{5} +(-2.61687 - 0.389830i) q^{7} +1.00000 q^{8} +(1.79580 + 1.33234i) q^{10} +(1.98187 + 1.14423i) q^{11} +(2.02055 - 3.49969i) q^{13} +(-2.61687 - 0.389830i) q^{14} +1.00000 q^{16} +(5.58838 - 3.22645i) q^{17} +(-0.177623 - 0.102551i) q^{19} +(1.79580 + 1.33234i) q^{20} +(1.98187 + 1.14423i) q^{22} +(-1.00425 - 1.73941i) q^{23} +(1.44977 + 4.78520i) q^{25} +(2.02055 - 3.49969i) q^{26} +(-2.61687 - 0.389830i) q^{28} +(-2.95397 + 1.70547i) q^{29} +0.975100i q^{31} +1.00000 q^{32} +(5.58838 - 3.22645i) q^{34} +(-4.17999 - 4.18661i) q^{35} +(7.40520 + 4.27539i) q^{37} +(-0.177623 - 0.102551i) q^{38} +(1.79580 + 1.33234i) q^{40} +(1.15662 - 2.00333i) q^{41} +(2.12736 - 1.22823i) q^{43} +(1.98187 + 1.14423i) q^{44} +(-1.00425 - 1.73941i) q^{46} +4.77784i q^{47} +(6.69607 + 2.04027i) q^{49} +(1.44977 + 4.78520i) q^{50} +(2.02055 - 3.49969i) q^{52} +(-2.35928 - 4.08640i) q^{53} +(2.03453 + 4.69532i) q^{55} +(-2.61687 - 0.389830i) q^{56} +(-2.95397 + 1.70547i) q^{58} +9.07146 q^{59} +10.7821i q^{61} +0.975100i q^{62} +1.00000 q^{64} +(8.29125 - 3.59268i) q^{65} +6.05164i q^{67} +(5.58838 - 3.22645i) q^{68} +(-4.17999 - 4.18661i) q^{70} -11.0359i q^{71} +(7.78631 + 13.4863i) q^{73} +(7.40520 + 4.27539i) q^{74} +(-0.177623 - 0.102551i) q^{76} +(-4.74025 - 3.76691i) q^{77} -7.23402 q^{79} +(1.79580 + 1.33234i) q^{80} +(1.15662 - 2.00333i) q^{82} +(-9.91029 + 5.72171i) q^{83} +(14.3343 + 1.65154i) q^{85} +(2.12736 - 1.22823i) q^{86} +(1.98187 + 1.14423i) q^{88} +(-5.08916 + 8.81469i) q^{89} +(-6.65180 + 8.37059i) q^{91} +(-1.00425 - 1.73941i) q^{92} +4.77784i q^{94} +(-0.182343 - 0.420814i) q^{95} +(-4.24029 - 7.34440i) q^{97} +(6.69607 + 2.04027i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 48 q^{2} + 48 q^{4} - 3 q^{7} + 48 q^{8}+O(q^{10}) $ 48 * q + 48 * q^2 + 48 * q^4 - 3 * q^7 + 48 * q^8	$ 48 q + 48 q^{2} + 48 q^{4} - 3 q^{7} + 48 q^{8} - 6 q^{11} - 3 q^{14} + 48 q^{16} - 6 q^{22} + 3 q^{23} + 18 q^{25} - 3 q^{28} + 3 q^{29} + 48 q^{32} + 18 q^{35} + 3 q^{41} - 6 q^{44} + 3 q^{46} + 3 q^{49} + 18 q^{50} + 42 q^{55} - 3 q^{56} + 3 q^{58} + 48 q^{64} + 12 q^{65} + 18 q^{70} + 18 q^{73} - 12 q^{77} + 3 q^{82} + 9 q^{83} + 33 q^{85} - 6 q^{88} + 33 q^{89} + 3 q^{92} + 24 q^{97} + 3 q^{98}+O(q^{100}) $ 48 * q + 48 * q^2 + 48 * q^4 - 3 * q^7 + 48 * q^8 - 6 * q^11 - 3 * q^14 + 48 * q^16 - 6 * q^22 + 3 * q^23 + 18 * q^25 - 3 * q^28 + 3 * q^29 + 48 * q^32 + 18 * q^35 + 3 * q^41 - 6 * q^44 + 3 * q^46 + 3 * q^49 + 18 * q^50 + 42 * q^55 - 3 * q^56 + 3 * q^58 + 48 * q^64 + 12 * q^65 + 18 * q^70 + 18 * q^73 - 12 * q^77 + 3 * q^82 + 9 * q^83 + 33 * q^85 - 6 * q^88 + 33 * q^89 + 3 * q^92 + 24 * q^97 + 3 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$757$	$1081$	$1541$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	1.79580	+	1.33234i	0.803104	+	0.595838i
$5$	1.79580	+	1.33234i	0.803104	+	0.595838i
$6$		0			0
$7$	−2.61687	−	0.389830i	−0.989086	−	0.147342i
$7$	−2.61687	−	0.389830i	−0.989086	−	0.147342i
$8$	1.00000			0.353553
$9$		0			0
$10$	1.79580	+	1.33234i	0.567881	+	0.421321i
$11$	1.98187	+	1.14423i	0.597556	+	0.344999i	0.768080	−	0.640354i	$-0.221213\pi$
$11$	1.98187	+	1.14423i	0.597556	+	0.344999i	−0.170523	+	0.985354i	$0.554546\pi$
$12$		0			0
$13$	2.02055	−	3.49969i	0.560399	−	0.970640i	−0.437062	−	0.899431i	$-0.643981\pi$
$13$	2.02055	−	3.49969i	0.560399	−	0.970640i	0.997461	−	0.0712086i	$-0.0226856\pi$
$14$	−2.61687	−	0.389830i	−0.699389	−	0.104186i
$15$		0			0
$16$	1.00000			0.250000
$17$	5.58838	−	3.22645i	1.35538	−	0.782529i	0.366383	−	0.930464i	$-0.380596\pi$
$17$	5.58838	−	3.22645i	1.35538	−	0.782529i	0.988997	+	0.147935i	$0.0472626\pi$
$18$		0			0
$19$	−0.177623	−	0.102551i	−0.0407496	−	0.0235268i	0.479487	−	0.877549i	$-0.340823\pi$
$19$	−0.177623	−	0.102551i	−0.0407496	−	0.0235268i	−0.520236	+	0.854022i	$0.674156\pi$
$20$	1.79580	+	1.33234i	0.401552	+	0.297919i
$21$		0			0
$22$	1.98187	+	1.14423i	0.422536	+	0.243951i
$23$	−1.00425	−	1.73941i	−0.209400	−	0.362692i	0.742126	−	0.670261i	$-0.233818\pi$
$23$	−1.00425	−	1.73941i	−0.209400	−	0.362692i	−0.951526	+	0.307569i	$0.900484\pi$
$24$		0			0
$25$	1.44977	+	4.78520i	0.289953	+	0.957041i
$26$	2.02055	−	3.49969i	0.396262	−	0.686346i
$27$		0			0
$28$	−2.61687	−	0.389830i	−0.494543	−	0.0736709i
$29$	−2.95397	+	1.70547i	−0.548538	+	0.316698i	−0.748532	−	0.663099i	$-0.769241\pi$
$29$	−2.95397	+	1.70547i	−0.548538	+	0.316698i	0.199994	+	0.979797i	$0.435908\pi$
$30$		0			0
$31$			0.975100i			0.175133i	0.996159	+	0.0875665i	$0.0279090\pi$
$31$			0.975100i			0.175133i	−0.996159	+	0.0875665i	$0.972091\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	5.58838	−	3.22645i	0.958399	−	0.553332i
$35$	−4.17999	−	4.18661i	−0.706547	−	0.707666i
$36$		0			0
$37$	7.40520	+	4.27539i	1.21741	+	0.702870i	0.964363	−	0.264584i	$-0.0852348\pi$
$37$	7.40520	+	4.27539i	1.21741	+	0.702870i	0.253045	+	0.967455i	$0.418568\pi$
$38$	−0.177623	−	0.102551i	−0.0288143	−	0.0166359i
$39$		0			0
$40$	1.79580	+	1.33234i	0.283940	+	0.210661i
$41$	1.15662	−	2.00333i	0.180634	−	0.312867i	−0.761463	−	0.648209i	$-0.775518\pi$
$41$	1.15662	−	2.00333i	0.180634	−	0.312867i	0.942097	+	0.335342i	$0.108852\pi$
$42$		0			0
$43$	2.12736	−	1.22823i	0.324419	−	0.187303i	−0.328942	−	0.944350i	$-0.606692\pi$
$43$	2.12736	−	1.22823i	0.324419	−	0.187303i	0.653360	+	0.757047i	$0.273359\pi$
$44$	1.98187	+	1.14423i	0.298778	+	0.172500i
$45$		0			0
$46$	−1.00425	−	1.73941i	−0.148068	−	0.256462i
$47$			4.77784i			0.696920i	0.937324	+	0.348460i	$0.113295\pi$
$47$			4.77784i			0.696920i	−0.937324	+	0.348460i	$0.886705\pi$
$48$		0			0
$49$	6.69607	+	2.04027i	0.956581	+	0.291467i
$50$	1.44977	+	4.78520i	0.205028	+	0.676730i
$51$		0			0
$52$	2.02055	−	3.49969i	0.280200	−	0.485320i
$53$	−2.35928	−	4.08640i	−0.324072	−	0.561310i	0.657252	−	0.753671i	$-0.271719\pi$
$53$	−2.35928	−	4.08640i	−0.324072	−	0.561310i	−0.981324	+	0.192361i	$0.938385\pi$
$54$		0			0
$55$	2.03453	+	4.69532i	0.274336	+	0.633117i
$56$	−2.61687	−	0.389830i	−0.349695	−	0.0520932i
$57$		0			0
$58$	−2.95397	+	1.70547i	−0.387875	+	0.223940i
$59$	9.07146			1.18100			0.590502	−	0.807036i	$-0.298930\pi$
$59$	9.07146			1.18100			0.590502	+	0.807036i	$0.298930\pi$
$60$		0			0
$61$			10.7821i			1.38051i	0.723568	+	0.690253i	$0.242501\pi$
$61$			10.7821i			1.38051i	−0.723568	+	0.690253i	$0.757499\pi$
$62$			0.975100i			0.123838i
$63$		0			0
$64$	1.00000			0.125000
$65$	8.29125	−	3.59268i	1.02840	−	0.445618i
$66$		0			0
$67$			6.05164i			0.739325i	0.929166	+	0.369662i	$0.120527\pi$
$67$			6.05164i			0.739325i	−0.929166	+	0.369662i	$0.879473\pi$
$68$	5.58838	−	3.22645i	0.677690	−	0.391265i
$69$		0			0
$70$	−4.17999	−	4.18661i	−0.499604	−	0.500395i
$71$		−	11.0359i		−	1.30973i	−0.755748	−	0.654863i	$-0.772726\pi$
$71$		−	11.0359i		−	1.30973i	0.755748	−	0.654863i	$-0.227274\pi$
$72$		0			0
$73$	7.78631	+	13.4863i	0.911318	+	1.57845i	0.812204	+	0.583373i	$0.198268\pi$
$73$	7.78631	+	13.4863i	0.911318	+	1.57845i	0.0991142	+	0.995076i	$0.468399\pi$
$74$	7.40520	+	4.27539i	0.860837	+	0.497004i
$75$		0			0
$76$	−0.177623	−	0.102551i	−0.0203748	−	0.0117634i
$77$	−4.74025	−	3.76691i	−0.540201	−	0.429279i
$78$		0			0
$79$	−7.23402			−0.813891			−0.406946	−	0.913452i	$-0.633406\pi$
$79$	−7.23402			−0.813891			−0.406946	+	0.913452i	$0.633406\pi$
$80$	1.79580	+	1.33234i	0.200776	+	0.148960i
$81$		0			0
$82$	1.15662	−	2.00333i	0.127728	−	0.221231i
$83$	−9.91029	+	5.72171i	−1.08780	+	0.628039i	−0.932989	−	0.359906i	$-0.882809\pi$
$83$	−9.91029	+	5.72171i	−1.08780	+	0.628039i	−0.154807	+	0.987945i	$0.549476\pi$
$84$		0			0
$85$	14.3343	+	1.65154i	1.55477	+	0.179135i
$86$	2.12736	−	1.22823i	0.229399	−	0.132443i
$87$		0			0
$88$	1.98187	+	1.14423i	0.211268	+	0.121976i
$89$	−5.08916	+	8.81469i	−0.539450	+	0.934355i	0.459483	+	0.888186i	$0.348035\pi$
$89$	−5.08916	+	8.81469i	−0.539450	+	0.934355i	−0.998934	+	0.0461690i	$0.985299\pi$
$90$		0			0
$91$	−6.65180	+	8.37059i	−0.697299	+	0.877476i
$92$	−1.00425	−	1.73941i	−0.104700	−	0.181346i
$93$		0			0
$94$			4.77784i			0.492797i
$95$	−0.182343	−	0.420814i	−0.0187080	−	0.0431746i
$96$		0			0
$97$	−4.24029	−	7.34440i	−0.430536	−	0.745711i	0.566383	−	0.824142i	$-0.308342\pi$
$97$	−4.24029	−	7.34440i	−0.430536	−	0.745711i	−0.996920	+	0.0784313i	$0.975009\pi$
$98$	6.69607	+	2.04027i	0.676405	+	0.206098i
$99$		0			0
$100$	1.44977	+	4.78520i	0.144977	+	0.478520i
$101$	0.757545	−	1.31211i	0.0753785	−	0.130559i	−0.825872	−	0.563857i	$-0.809317\pi$
$101$	0.757545	−	1.31211i	0.0753785	−	0.130559i	0.901251	+	0.433298i	$0.142650\pi$
$102$		0			0
$103$	−9.38804	−	16.2606i	−0.925031	−	1.60220i	−0.791511	−	0.611155i	$-0.790705\pi$
$103$	−9.38804	−	16.2606i	−0.925031	−	1.60220i	−0.133520	−	0.991046i	$-0.542628\pi$
$104$	2.02055	−	3.49969i	0.198131	−	0.343173i
$105$		0			0
$106$	−2.35928	−	4.08640i	−0.229154	−	0.396906i
$107$	9.00357	−	15.5946i	0.870408	−	1.50759i	0.00883183	−	0.999961i	$-0.497189\pi$
$107$	9.00357	−	15.5946i	0.870408	−	1.50759i	0.861576	−	0.507629i	$-0.169478\pi$
$108$		0			0
$109$	−8.13785	−	14.0952i	−0.779464	−	1.35007i	−0.932251	−	0.361813i	$-0.882158\pi$
$109$	−8.13785	−	14.0952i	−0.779464	−	1.35007i	0.152786	−	0.988259i	$-0.451175\pi$
$110$	2.03453	+	4.69532i	0.193985	+	0.447682i
$111$		0			0
$112$	−2.61687	−	0.389830i	−0.247271	−	0.0368354i
$113$	2.98673	−	5.17317i	0.280968	−	0.486651i	−0.690655	−	0.723184i	$-0.742678\pi$
$113$	2.98673	−	5.17317i	0.280968	−	0.486651i	0.971623	+	0.236533i	$0.0760112\pi$
$114$		0			0
$115$	0.514051	−	4.46162i	0.0479355	−	0.416048i
$116$	−2.95397	+	1.70547i	−0.274269	+	0.158349i
$117$		0			0
$118$	9.07146			0.835096
$119$	−15.8818	+	6.26470i	−1.45589	+	0.574284i
$120$		0			0
$121$	−2.88146	−	4.99084i	−0.261951	−	0.453713i
$122$			10.7821i			0.976166i
$123$		0			0
$124$			0.975100i			0.0875665i
$125$	−3.77201	+	10.5248i	−0.337379	+	0.941369i
$126$		0			0
$127$			11.8327i			1.04998i	0.851108	+	0.524991i	$0.175931\pi$
$127$			11.8327i			1.04998i	−0.851108	+	0.524991i	$0.824069\pi$
$128$	1.00000			0.0883883
$129$		0			0
$130$	8.29125	−	3.59268i	0.727191	−	0.315099i
$131$	1.47813	+	2.56020i	0.129145	+	0.223685i	0.923346	−	0.383970i	$-0.125443\pi$
$131$	1.47813	+	2.56020i	0.129145	+	0.223685i	−0.794201	+	0.607656i	$0.792110\pi$
$132$		0			0
$133$	0.424840	+	0.337605i	0.0368383	+	0.0292741i
$134$			6.05164i			0.522782i
$135$		0			0
$136$	5.58838	−	3.22645i	0.479199	−	0.276666i
$137$	3.43092	−	5.94252i	0.293123	−	0.507704i	−0.681423	−	0.731889i	$-0.738639\pi$
$137$	3.43092	−	5.94252i	0.293123	−	0.507704i	0.974547	+	0.224185i	$0.0719721\pi$
$138$		0			0
$139$	−1.44024	−	0.831524i	−0.122160	−	0.0705289i	0.437675	−	0.899133i	$-0.355802\pi$
$139$	−1.44024	−	0.831524i	−0.122160	−	0.0705289i	−0.559835	+	0.828604i	$0.689135\pi$
$140$	−4.17999	−	4.18661i	−0.353274	−	0.353833i
$141$		0			0
$142$		−	11.0359i		−	0.926116i
$143$	8.00893	−	4.62396i	0.669740	−	0.386675i
$144$		0			0
$145$	−7.57698	−	0.872991i	−0.629234	−	0.0724980i
$146$	7.78631	+	13.4863i	0.644399	+	1.11613i
$147$		0			0
$148$	7.40520	+	4.27539i	0.608704	+	0.351435i
$149$	10.1542	−	5.86255i	0.831867	−	0.480278i	−0.0226246	−	0.999744i	$-0.507202\pi$
$149$	10.1542	−	5.86255i	0.831867	−	0.480278i	0.854491	+	0.519466i	$0.173869\pi$
$150$		0			0
$151$	−1.68168	+	2.91276i	−0.136853	+	0.237037i	−0.926304	−	0.376777i	$-0.877032\pi$
$151$	−1.68168	+	2.91276i	−0.136853	+	0.237037i	0.789451	+	0.613814i	$0.210366\pi$
$152$	−0.177623	−	0.102551i	−0.0144071	−	0.00831797i
$153$		0			0
$154$	−4.74025	−	3.76691i	−0.381980	−	0.303546i
$155$	−1.29916	+	1.75108i	−0.104351	+	0.140650i
$156$		0			0
$157$	−2.58329			−0.206169			−0.103084	−	0.994673i	$-0.532871\pi$
$157$	−2.58329			−0.206169			−0.103084	+	0.994673i	$0.532871\pi$
$158$	−7.23402			−0.575508
$159$		0			0
$160$	1.79580	+	1.33234i	0.141970	+	0.105330i
$161$	1.94992	+	4.94330i	0.153675	+	0.389587i
$162$		0			0
$163$	−21.1464	−	12.2089i	−1.65631	−	0.956272i	−0.974395	−	0.224841i	$-0.927814\pi$
$163$	−21.1464	−	12.2089i	−1.65631	−	0.956272i	−0.681916	−	0.731431i	$-0.738853\pi$
$164$	1.15662	−	2.00333i	0.0903170	−	0.156434i
$165$		0			0
$166$	−9.91029	+	5.72171i	−0.769188	+	0.444091i
$167$	−0.00904075	−	0.00521968i	−0.000699594	−	0.000403911i	0.499650	−	0.866227i	$-0.333462\pi$
$167$	−0.00904075	−	0.00521968i	−0.000699594	−	0.000403911i	−0.500350	+	0.865823i	$0.666795\pi$
$168$		0			0
$169$	−1.66523	−	2.88426i	−0.128094	−	0.221866i
$170$	14.3343	+	1.65154i	1.09939	+	0.126668i
$171$		0			0
$172$	2.12736	−	1.22823i	0.162209	−	0.0936516i
$173$		−	18.2330i		−	1.38623i	−0.720826	−	0.693116i	$-0.756237\pi$
$173$		−	18.2330i		−	1.38623i	0.720826	−	0.693116i	$-0.243763\pi$
$174$		0			0
$175$	−1.92844	−	13.0874i	−0.145776	−	0.989318i
$176$	1.98187	+	1.14423i	0.149389	+	0.0862498i
$177$		0			0
$178$	−5.08916	+	8.81469i	−0.381449	+	0.660689i
$179$	−13.5399	+	7.81725i	−1.01202	+	0.584289i	−0.911782	−	0.410675i	$-0.865293\pi$
$179$	−13.5399	+	7.81725i	−1.01202	+	0.584289i	−0.100236	+	0.994964i	$0.531960\pi$
$180$		0			0
$181$			24.3098i			1.80693i	0.428659	+	0.903467i	$0.358986\pi$
$181$			24.3098i			1.80693i	−0.428659	+	0.903467i	$0.641014\pi$
$182$	−6.65180	+	8.37059i	−0.493065	+	0.620469i
$183$		0			0
$184$	−1.00425	−	1.73941i	−0.0740342	−	0.128231i
$185$	7.60197	+	17.5439i	0.558908	+	1.28986i
$186$		0			0
$187$	14.7672			1.07989
$188$			4.77784i			0.348460i
$189$		0			0
$190$	−0.182343	−	0.420814i	−0.0132286	−	0.0305291i
$191$			11.9399i			0.863943i	0.901887	+	0.431972i	$0.142182\pi$
$191$			11.9399i			0.863943i	−0.901887	+	0.431972i	$0.857818\pi$
$192$		0			0
$193$		−	12.4417i		−	0.895572i	−0.894141	−	0.447786i	$-0.852213\pi$
$193$		−	12.4417i		−	0.895572i	0.894141	−	0.447786i	$-0.147787\pi$
$194$	−4.24029	−	7.34440i	−0.304435	−	0.527297i
$195$		0			0
$196$	6.69607	+	2.04027i	0.478290	+	0.145734i
$197$	−23.0465			−1.64199			−0.820996	−	0.570934i	$-0.806581\pi$
$197$	−23.0465			−1.64199			−0.820996	+	0.570934i	$0.806581\pi$
$198$		0			0
$199$	−6.98847	+	4.03479i	−0.495399	+	0.286019i	−0.726812	−	0.686837i	$-0.758999\pi$
$199$	−6.98847	+	4.03479i	−0.495399	+	0.286019i	0.231412	+	0.972856i	$0.425665\pi$
$200$	1.44977	+	4.78520i	0.102514	+	0.338365i
$201$		0			0
$202$	0.757545	−	1.31211i	0.0533007	−	0.0923195i
$203$	8.39500	−	3.31147i	0.589214	−	0.232419i
$204$		0			0
$205$	4.74616	−	2.05656i	0.331486	−	0.143636i
$206$	−9.38804	−	16.2606i	−0.654096	−	1.13293i
$207$		0			0
$208$	2.02055	−	3.49969i	0.140100	−	0.242660i
$209$	−0.234684	−	0.406485i	−0.0162334	−	0.0281171i
$210$		0			0
$211$	−9.23801	+	16.0007i	−0.635971	+	1.10153i	0.350338	+	0.936623i	$0.386067\pi$
$211$	−9.23801	+	16.0007i	−0.635971	+	1.10153i	−0.986309	+	0.164910i	$0.947266\pi$
$212$	−2.35928	−	4.08640i	−0.162036	−	0.280655i
$213$		0			0
$214$	9.00357	−	15.5946i	0.615471	−	1.06603i
$215$	5.45671	+	0.628702i	0.372145	+	0.0428771i
$216$		0			0
$217$	0.380123	−	2.55171i	0.0258044	−	0.173222i
$218$	−8.13785	−	14.0952i	−0.551165	−	0.954645i
$219$		0			0
$220$	2.03453	+	4.69532i	0.137168	+	0.316559i
$221$		−	26.0768i		−	1.75411i
$222$		0			0
$223$	2.10769	+	3.65063i	0.141142	+	0.244464i	0.927927	−	0.372763i	$-0.121589\pi$
$223$	2.10769	+	3.65063i	0.141142	+	0.244464i	−0.786785	+	0.617227i	$0.788256\pi$
$224$	−2.61687	−	0.389830i	−0.174847	−	0.0260466i
$225$		0			0
$226$	2.98673	−	5.17317i	0.198674	−	0.344114i
$227$	16.0856	+	9.28700i	1.06764	+	0.616400i	0.927535	−	0.373737i	$-0.121924\pi$
$227$	16.0856	+	9.28700i	1.06764	+	0.616400i	0.140102	+	0.990137i	$0.455257\pi$
$228$		0			0
$229$	1.36101	−	0.785777i	0.0899378	−	0.0519256i	−0.454357	−	0.890820i	$-0.650131\pi$
$229$	1.36101	−	0.785777i	0.0899378	−	0.0519256i	0.544294	+	0.838894i	$0.316797\pi$
$230$	0.514051	−	4.46162i	0.0338955	−	0.294190i
$231$		0			0
$232$	−2.95397	+	1.70547i	−0.193937	+	0.111970i
$233$	3.77904	−	6.54549i	0.247573	−	0.428809i	−0.715279	−	0.698839i	$-0.753700\pi$
$233$	3.77904	−	6.54549i	0.247573	−	0.428809i	0.962852	+	0.270030i	$0.0870336\pi$
$234$		0			0
$235$	−6.36569	+	8.58003i	−0.415252	+	0.559699i
$236$	9.07146			0.590502
$237$		0			0
$238$	−15.8818	+	6.26470i	−1.02947	+	0.406080i
$239$	−14.4459	−	8.34037i	−0.934430	−	0.539494i	−0.0462202	−	0.998931i	$-0.514718\pi$
$239$	−14.4459	−	8.34037i	−0.934430	−	0.539494i	−0.888210	+	0.459438i	$0.848051\pi$
$240$		0			0
$241$	24.5697	+	14.1853i	1.58267	+	0.913757i	0.994467	+	0.105047i	$0.0334994\pi$
$241$	24.5697	+	14.1853i	1.58267	+	0.913757i	0.588207	+	0.808710i	$0.299834\pi$
$242$	−2.88146	−	4.99084i	−0.185227	−	0.320823i
$243$		0			0
$244$			10.7821i			0.690253i
$245$	9.30644	+	12.5853i	0.594567	+	0.804046i
$246$		0			0
$247$	−0.717793	+	0.414418i	−0.0456720	+	0.0263688i
$248$			0.975100i			0.0619189i
$249$		0			0
$250$	−3.77201	+	10.5248i	−0.238563	+	0.665648i
$251$	−9.95552			−0.628387			−0.314193	−	0.949359i	$-0.601734\pi$
$251$	−9.95552			−0.628387			−0.314193	+	0.949359i	$0.601734\pi$
$252$		0			0
$253$		−	4.59638i		−	0.288972i
$254$			11.8327i			0.742450i
$255$		0			0
$256$	1.00000			0.0625000
$257$	16.2504	−	9.38216i	1.01367	−	0.585243i	0.101406	−	0.994845i	$-0.467666\pi$
$257$	16.2504	−	9.38216i	1.01367	−	0.585243i	0.912264	+	0.409602i	$0.134332\pi$
$258$		0			0
$259$	−17.7118	−	14.0749i	−1.10056	−	0.874574i
$260$	8.29125	−	3.59268i	0.514202	−	0.222809i
$261$		0			0
$262$	1.47813	+	2.56020i	0.0913192	+	0.158170i
$263$	1.47472	−	2.55429i	0.0909351	−	0.157504i	−0.816970	−	0.576681i	$-0.804348\pi$
$263$	1.47472	−	2.55429i	0.0909351	−	0.157504i	0.907905	+	0.419176i	$0.137681\pi$
$264$		0			0
$265$	1.20766	−	10.4817i	0.0741861	−	0.643885i
$266$	0.424840	+	0.337605i	0.0260486	+	0.0206999i
$267$		0			0
$268$			6.05164i			0.369662i
$269$	−13.8077	−	23.9156i	−0.841869	−	1.45816i	−0.888313	−	0.459239i	$-0.848122\pi$
$269$	−13.8077	−	23.9156i	−0.841869	−	1.45816i	0.0464436	−	0.998921i	$-0.485211\pi$
$270$		0			0
$271$	12.8142	+	7.39828i	0.778407	+	0.449413i	0.835865	−	0.548935i	$-0.184966\pi$
$271$	12.8142	+	7.39828i	0.778407	+	0.449413i	−0.0574587	+	0.998348i	$0.518300\pi$
$272$	5.58838	−	3.22645i	0.338845	−	0.195632i
$273$		0			0
$274$	3.43092	−	5.94252i	0.207269	−	0.359001i
$275$	−2.60214	+	11.1425i	−0.156915	+	0.671919i
$276$		0			0
$277$	6.88813	+	3.97687i	0.413868	+	0.238947i	0.692450	−	0.721466i	$-0.256531\pi$
$277$	6.88813	+	3.97687i	0.413868	+	0.238947i	−0.278582	+	0.960412i	$0.589865\pi$
$278$	−1.44024	−	0.831524i	−0.0863799	−	0.0498715i
$279$		0			0
$280$	−4.17999	−	4.18661i	−0.249802	−	0.250198i
$281$	12.9850	−	7.49690i	0.774621	−	0.447228i	−0.0598996	−	0.998204i	$-0.519078\pi$
$281$	12.9850	−	7.49690i	0.774621	−	0.447228i	0.834521	+	0.550977i	$0.185745\pi$
$282$		0			0
$283$	−29.8023			−1.77156			−0.885780	−	0.464105i	$-0.846376\pi$
$283$	−29.8023			−1.77156			−0.885780	+	0.464105i	$0.846376\pi$
$284$		−	11.0359i		−	0.654863i
$285$		0			0
$286$	8.00893	−	4.62396i	0.473578	−	0.273420i
$287$	−3.80769	+	4.79157i	−0.224761	+	0.282838i
$288$		0			0
$289$	12.3200	−	21.3388i	0.724704	−	1.25522i
$290$	−7.57698	−	0.872991i	−0.444936	−	0.0512638i
$291$		0			0
$292$	7.78631	+	13.4863i	0.455659	+	0.789225i
$293$	2.19993	+	1.27013i	0.128522	+	0.0742019i	0.562882	−	0.826537i	$-0.309692\pi$
$293$	2.19993	+	1.27013i	0.128522	+	0.0742019i	−0.434361	+	0.900739i	$0.643026\pi$
$294$		0			0
$295$	16.2905	+	12.0862i	0.948469	+	0.703688i
$296$	7.40520	+	4.27539i	0.430418	+	0.248502i
$297$		0			0
$298$	10.1542	−	5.86255i	0.588219	−	0.339608i
$299$	−8.11653			−0.469391
$300$		0			0
$301$	−6.04582	+	2.38482i	−0.348476	+	0.137459i
$302$	−1.68168	+	2.91276i	−0.0967699	+	0.167610i
$303$		0			0
$304$	−0.177623	−	0.102551i	−0.0101874	−	0.00588169i
$305$	−14.3654	+	19.3625i	−0.822559	+	1.10869i
$306$		0			0
$307$	−8.06299			−0.460179			−0.230089	−	0.973169i	$-0.573902\pi$
$307$	−8.06299			−0.460179			−0.230089	+	0.973169i	$0.573902\pi$
$308$	−4.74025	−	3.76691i	−0.270101	−	0.214639i
$309$		0			0
$310$	−1.29916	+	1.75108i	−0.0737873	+	0.0994547i
$311$	0.763625			0.0433012			0.0216506	−	0.999766i	$-0.493108\pi$
$311$	0.763625			0.0433012			0.0216506	+	0.999766i	$0.493108\pi$
$312$		0			0
$313$	−3.83737			−0.216901			−0.108450	−	0.994102i	$-0.534589\pi$
$313$	−3.83737			−0.216901			−0.108450	+	0.994102i	$0.534589\pi$
$314$	−2.58329			−0.145783
$315$		0			0
$316$	−7.23402			−0.406946
$317$	−17.3289			−0.973288			−0.486644	−	0.873600i	$-0.661779\pi$
$317$	−17.3289			−0.973288			−0.486644	+	0.873600i	$0.661779\pi$
$318$		0			0
$319$	−7.80583			−0.437043
$320$	1.79580	+	1.33234i	0.100388	+	0.0744798i
$321$		0			0
$322$	1.94992	+	4.94330i	0.108665	+	0.275479i
$323$	−1.32350			−0.0736416
$324$		0			0
$325$	19.6761	+	4.59500i	1.09143	+	0.254885i
$326$	−21.1464	−	12.2089i	−1.17119	−	0.676186i
$327$		0			0
$328$	1.15662	−	2.00333i	0.0638638	−	0.110615i
$329$	1.86254	−	12.5030i	0.102685	−	0.689313i
$330$		0			0
$331$	−4.95873			−0.272556			−0.136278	−	0.990671i	$-0.543514\pi$
$331$	−4.95873			−0.272556			−0.136278	+	0.990671i	$0.543514\pi$
$332$	−9.91029	+	5.72171i	−0.543898	+	0.314020i
$333$		0			0
$334$	−0.00904075	−	0.00521968i	−0.000494688	−	0.000285608i
$335$	−8.06281	+	10.8675i	−0.440518	+	0.593755i
$336$		0			0
$337$	1.58895	+	0.917381i	0.0865557	+	0.0499729i	0.542653	−	0.839957i	$-0.317420\pi$
$337$	1.58895	+	0.917381i	0.0865557	+	0.0499729i	−0.456097	+	0.889930i	$0.650753\pi$
$338$	−1.66523	−	2.88426i	−0.0905765	−	0.156883i
$339$		0			0
$340$	14.3343	+	1.65154i	0.777386	+	0.0895676i
$341$	−1.11574	+	1.93252i	−0.0604208	+	0.104652i
$342$		0			0
$343$	−16.7274	−	7.94946i	−0.903195	−	0.429230i
$344$	2.12736	−	1.22823i	0.114699	−	0.0662217i
$345$		0			0
$346$		−	18.2330i		−	0.980214i
$347$	6.78486			0.364230			0.182115	−	0.983277i	$-0.441706\pi$
$347$	6.78486			0.364230			0.182115	+	0.983277i	$0.441706\pi$
$348$		0			0
$349$	−11.4343	+	6.60159i	−0.612064	+	0.353375i	−0.773773	−	0.633463i	$-0.781633\pi$
$349$	−11.4343	+	6.60159i	−0.612064	+	0.353375i	0.161709	+	0.986838i	$0.448299\pi$
$350$	−1.92844	−	13.0874i	−0.103079	−	0.699553i
$351$		0			0
$352$	1.98187	+	1.14423i	0.105634	+	0.0609878i
$353$	−26.8650	−	15.5105i	−1.42988	−	0.825543i	−0.432771	−	0.901504i	$-0.642464\pi$
$353$	−26.8650	−	15.5105i	−1.42988	−	0.825543i	−0.997111	+	0.0759611i	$0.975798\pi$
$354$		0			0
$355$	14.7036	−	19.8183i	0.780385	−	1.05185i
$356$	−5.08916	+	8.81469i	−0.269725	+	0.467178i
$357$		0			0
$358$	−13.5399	+	7.81725i	−0.715605	+	0.413155i
$359$	−24.9912	−	14.4287i	−1.31899	−	0.761517i	−0.335420	−	0.942069i	$-0.608878\pi$
$359$	−24.9912	−	14.4287i	−1.31899	−	0.761517i	−0.983565	+	0.180552i	$0.942212\pi$
$360$		0			0
$361$	−9.47897	−	16.4181i	−0.498893	−	0.864108i
$362$			24.3098i			1.27769i
$363$		0			0
$364$	−6.65180	+	8.37059i	−0.348649	+	0.438738i
$365$	−3.98563	+	34.5926i	−0.208617	+	1.81066i
$366$		0			0
$367$	−6.18161	+	10.7069i	−0.322677	+	0.558893i	−0.981040	−	0.193808i	$-0.937916\pi$
$367$	−6.18161	+	10.7069i	−0.322677	+	0.558893i	0.658362	+	0.752701i	$0.271250\pi$
$368$	−1.00425	−	1.73941i	−0.0523501	−	0.0906730i
$369$		0			0
$370$	7.60197	+	17.5439i	0.395207	+	0.912066i
$371$	4.58095	+	11.6133i	0.237831	+	0.602933i
$372$		0			0
$373$	−31.7495	+	18.3306i	−1.64393	+	0.949123i	−0.664512	+	0.747278i	$0.731360\pi$
$373$	−31.7495	+	18.3306i	−1.64393	+	0.949123i	−0.979417	+	0.201845i	$0.935306\pi$
$374$	14.7672			0.763596
$375$		0			0
$376$			4.77784i			0.246398i
$377$			13.7840i			0.709910i
$378$		0			0
$379$	19.2906			0.990893			0.495446	−	0.868639i	$-0.335004\pi$
$379$	19.2906			0.990893			0.495446	+	0.868639i	$0.335004\pi$
$380$	−0.182343	−	0.420814i	−0.00935400	−	0.0215873i
$381$		0			0
$382$			11.9399i			0.610900i
$383$	7.09201	−	4.09457i	0.362385	−	0.209223i	−0.307742	−	0.951470i	$-0.599573\pi$
$383$	7.09201	−	4.09457i	0.362385	−	0.209223i	0.670126	+	0.742247i	$0.266240\pi$
$384$		0			0
$385$	−3.49374	−	13.0802i	−0.178057	−	0.666628i
$386$		−	12.4417i		−	0.633265i
$387$		0			0
$388$	−4.24029	−	7.34440i	−0.215268	−	0.372855i
$389$	−7.64611	−	4.41449i	−0.387673	−	0.223823i	0.293478	−	0.955966i	$-0.405187\pi$
$389$	−7.64611	−	4.41449i	−0.387673	−	0.223823i	−0.681152	+	0.732142i	$0.738521\pi$
$390$		0			0
$391$	−11.2242	−	6.48032i	−0.567634	−	0.327724i
$392$	6.69607	+	2.04027i	0.338202	+	0.103049i
$393$		0			0
$394$	−23.0465			−1.16106
$395$	−12.9908	−	9.63815i	−0.653640	−	0.484948i
$396$		0			0
$397$	−5.82466	+	10.0886i	−0.292332	+	0.506333i	−0.974361	−	0.224992i	$-0.927764\pi$
$397$	−5.82466	+	10.0886i	−0.292332	+	0.506333i	0.682029	+	0.731325i	$0.261098\pi$
$398$	−6.98847	+	4.03479i	−0.350300	+	0.202246i
$399$		0			0
$400$	1.44977	+	4.78520i	0.0724883	+	0.239260i
$401$	2.28763	−	1.32076i	0.114239	−	0.0659557i	−0.441792	−	0.897118i	$-0.645657\pi$
$401$	2.28763	−	1.32076i	0.114239	−	0.0659557i	0.556031	+	0.831162i	$0.312324\pi$
$402$		0			0
$403$	3.41255	+	1.97024i	0.169991	+	0.0981444i
$404$	0.757545	−	1.31211i	0.0376893	−	0.0652797i
$405$		0			0
$406$	8.39500	−	3.31147i	0.416637	−	0.164345i
$407$	9.78409	+	16.9465i	0.484979	+	0.840009i
$408$		0			0
$409$			4.00359i			0.197965i	0.995089	+	0.0989824i	$0.0315588\pi$
$409$			4.00359i			0.197965i	−0.995089	+	0.0989824i	$0.968441\pi$
$410$	4.74616	−	2.05656i	0.234396	−	0.101566i
$411$		0			0
$412$	−9.38804	−	16.2606i	−0.462516	−	0.801100i
$413$	−23.7389	−	3.53633i	−1.16811	−	0.174011i
$414$		0			0
$415$	−25.4201	−	2.92881i	−1.24782	−	0.143770i
$416$	2.02055	−	3.49969i	0.0990655	−	0.171587i
$417$		0			0
$418$	−0.234684	−	0.406485i	−0.0114788	−	0.0198818i
$419$	−10.3156	+	17.8671i	−0.503949	+	0.872865i	0.496040	+	0.868299i	$0.334787\pi$
$419$	−10.3156	+	17.8671i	−0.503949	+	0.872865i	−0.999990	+	0.00456603i	$0.998547\pi$
$420$		0			0
$421$	−2.08360	−	3.60891i	−0.101549	−	0.175887i	0.810774	−	0.585359i	$-0.199046\pi$
$421$	−2.08360	−	3.60891i	−0.101549	−	0.175887i	−0.912323	+	0.409472i	$0.865713\pi$
$422$	−9.23801	+	16.0007i	−0.449699	+	0.778902i
$423$		0			0
$424$	−2.35928	−	4.08640i	−0.114577	−	0.198453i
$425$	23.5411	+	22.0639i	1.14191	+	1.07026i
$426$		0			0
$427$	4.20318	−	28.2154i	0.203406	−	1.36544i
$428$	9.00357	−	15.5946i	0.435204	−	0.753795i
$429$		0			0
$430$	5.45671	+	0.628702i	0.263146	+	0.0303187i
$431$	1.89577	−	1.09452i	0.0913159	−	0.0527213i	−0.453647	−	0.891182i	$-0.649877\pi$
$431$	1.89577	−	1.09452i	0.0913159	−	0.0527213i	0.544963	+	0.838460i	$0.316544\pi$
$432$		0			0
$433$	−23.8117			−1.14432			−0.572158	−	0.820143i	$-0.693894\pi$
$433$	−23.8117			−1.14432			−0.572158	+	0.820143i	$0.693894\pi$
$434$	0.380123	−	2.55171i	0.0182465	−	0.122486i
$435$		0			0
$436$	−8.13785	−	14.0952i	−0.389732	−	0.675036i
$437$			0.411946i			0.0197060i
$438$		0			0
$439$			14.3892i			0.686758i	0.939197	+	0.343379i	$0.111572\pi$
$439$			14.3892i			0.686758i	−0.939197	+	0.343379i	$0.888428\pi$
$440$	2.03453	+	4.69532i	0.0969925	+	0.223841i
$441$		0			0
$442$		−	26.0768i		−	1.24035i
$443$	−36.6080			−1.73930			−0.869649	−	0.493670i	$-0.835655\pi$
$443$	−36.6080			−1.73930			−0.869649	+	0.493670i	$0.835655\pi$
$444$		0			0
$445$	−20.8832	+	9.04891i	−0.989960	+	0.428960i
$446$	2.10769	+	3.65063i	0.0998021	+	0.172862i
$447$		0			0
$448$	−2.61687	−	0.389830i	−0.123636	−	0.0184177i
$449$			0.350689i			0.0165500i	0.999966	+	0.00827501i	$0.00263405\pi$
$449$			0.350689i			0.0165500i	−0.999966	+	0.00827501i	$0.997366\pi$
$450$		0			0
$451$	4.58455	−	2.64689i	0.215878	−	0.124637i
$452$	2.98673	−	5.17317i	0.140484	−	0.243325i
$453$		0			0
$454$	16.0856	+	9.28700i	0.754933	+	0.435861i
$455$	−23.0977	+	6.16943i	−1.08284	+	0.289227i
$456$		0			0
$457$			1.91541i			0.0895992i	0.998996	+	0.0447996i	$0.0142649\pi$
$457$			1.91541i			0.0895992i	−0.998996	+	0.0447996i	$0.985735\pi$
$458$	1.36101	−	0.785777i	0.0635956	−	0.0367169i
$459$		0			0
$460$	0.514051	−	4.46162i	0.0239678	−	0.208024i
$461$	12.2091	+	21.1468i	0.568636	+	0.984906i	0.996701	+	0.0811583i	$0.0258619\pi$
$461$	12.2091	+	21.1468i	0.568636	+	0.984906i	−0.428065	+	0.903748i	$0.640805\pi$
$462$		0			0
$463$	−4.09771	−	2.36581i	−0.190437	−	0.109949i	0.401750	−	0.915749i	$-0.368402\pi$
$463$	−4.09771	−	2.36581i	−0.190437	−	0.109949i	−0.592187	+	0.805801i	$0.701735\pi$
$464$	−2.95397	+	1.70547i	−0.137134	+	0.0791746i
$465$		0			0
$466$	3.77904	−	6.54549i	0.175061	−	0.303214i
$467$	−29.9337	−	17.2822i	−1.38517	−	0.799726i	−0.392401	−	0.919794i	$-0.628355\pi$
$467$	−29.9337	−	17.2822i	−1.38517	−	0.799726i	−0.992766	+	0.120068i	$0.961689\pi$
$468$		0			0
$469$	2.35911	−	15.8364i	0.108933	−	0.731256i
$470$	−6.36569	+	8.58003i	−0.293627	+	0.395767i
$471$		0			0
$472$	9.07146			0.417548
$473$	5.62152			0.258478
$474$		0			0
$475$	0.233215	−	0.998638i	0.0107006	−	0.0458207i
$476$	−15.8818	+	6.26470i	−0.727943	+	0.287142i
$477$		0			0
$478$	−14.4459	−	8.34037i	−0.660742	−	0.381480i
$479$	20.7765	−	35.9860i	0.949303	−	1.64424i	0.202404	−	0.979302i	$-0.435125\pi$
$479$	20.7765	−	35.9860i	0.949303	−	1.64424i	0.746898	−	0.664938i	$-0.231542\pi$
$480$		0			0
$481$	29.9251	−	17.2773i	1.36447	−	0.787776i
$482$	24.5697	+	14.1853i	1.11912	+	0.646124i
$483$		0			0
$484$	−2.88146	−	4.99084i	−0.130976	−	0.226856i
$485$	2.17050	−	18.8385i	0.0985576	−	0.855413i
$486$		0			0
$487$	8.25200	−	4.76429i	0.373934	−	0.215891i	−0.301242	−	0.953548i	$-0.597401\pi$
$487$	8.25200	−	4.76429i	0.373934	−	0.215891i	0.675176	+	0.737657i	$0.264068\pi$
$488$			10.7821i			0.488083i
$489$		0			0
$490$	9.30644	+	12.5853i	0.420422	+	0.568547i
$491$	−3.87273	−	2.23592i	−0.174774	−	0.100906i	0.410061	−	0.912058i	$-0.365507\pi$
$491$	−3.87273	−	2.23592i	−0.174774	−	0.100906i	−0.584835	+	0.811152i	$0.698841\pi$
$492$		0			0
$493$	−11.0052	+	19.0616i	−0.495651	+	0.858493i
$494$	−0.717793	+	0.414418i	−0.0322950	+	0.0186455i
$495$		0			0
$496$			0.975100i			0.0437833i
$497$	−4.30214	+	28.8797i	−0.192977	+	1.29543i
$498$		0			0
$499$	17.8598	+	30.9342i	0.799516	+	1.38480i	0.919931	+	0.392079i	$0.128244\pi$
$499$	17.8598	+	30.9342i	0.799516	+	1.38480i	−0.120415	+	0.992724i	$0.538423\pi$
$500$	−3.77201	+	10.5248i	−0.168690	+	0.470684i
$501$		0			0
$502$	−9.95552			−0.444337
$503$			2.25896i			0.100722i	0.998731	+	0.0503609i	$0.0160372\pi$
$503$			2.25896i			0.100722i	−0.998731	+	0.0503609i	$0.983963\pi$
$504$		0			0
$505$	3.10856	−	1.34697i	0.138329	−	0.0599394i
$506$		−	4.59638i		−	0.204334i
$507$		0			0
$508$			11.8327i			0.524991i
$509$	19.7072	+	34.1338i	0.873506	+	1.51296i	0.858346	+	0.513071i	$0.171492\pi$
$509$	19.7072	+	34.1338i	0.873506	+	1.51296i	0.0151595	+	0.999885i	$0.495174\pi$
$510$		0			0
$511$	−15.1184	−	38.3272i	−0.668800	−	1.69550i
$512$	1.00000			0.0441942
$513$		0			0
$514$	16.2504	−	9.38216i	0.716774	−	0.413829i
$515$	4.80552	−	41.7087i	0.211756	−	1.83790i
$516$		0			0
$517$	−5.46696	+	9.46906i	−0.240437	+	0.416449i
$518$	−17.7118	−	14.0749i	−0.778212	−	0.618417i
$519$		0			0
$520$	8.29125	−	3.59268i	0.363596	−	0.157550i
$521$	19.9940	+	34.6307i	0.875954	+	1.51720i	0.855743	+	0.517401i	$0.173100\pi$
$521$	19.9940	+	34.6307i	0.875954	+	1.51720i	0.0202106	+	0.999796i	$0.493566\pi$
$522$		0			0
$523$	14.4859	−	25.0903i	0.633424	−	1.09712i	−0.353422	−	0.935464i	$-0.614982\pi$
$523$	14.4859	−	25.0903i	0.633424	−	1.09712i	0.986847	−	0.161659i	$-0.0516846\pi$
$524$	1.47813	+	2.56020i	0.0645724	+	0.111843i
$525$		0			0
$526$	1.47472	−	2.55429i	0.0643008	−	0.111372i
$527$	3.14611	+	5.44922i	0.137047	+	0.237372i
$528$		0			0
$529$	9.48297	−	16.4250i	0.412303	−	0.714130i
$530$	1.20766	−	10.4817i	0.0524575	−	0.455296i
$531$		0			0
$532$	0.424840	+	0.337605i	0.0184192	+	0.0146371i
$533$	−4.67402	−	8.09564i	−0.202454	−	0.350661i
$534$		0			0
$535$	36.9458	−	16.0090i	1.59731	−	0.692130i
$536$			6.05164i			0.261391i
$537$		0			0
$538$	−13.8077	−	23.9156i	−0.595291	−	1.03107i
$539$	10.9362	+	11.7054i	0.471055	+	0.504188i
$540$		0			0
$541$	2.46717	−	4.27326i	0.106072	−	0.183722i	−0.808104	−	0.589040i	$-0.799506\pi$
$541$	2.46717	−	4.27326i	0.106072	−	0.183722i	0.914176	+	0.405318i	$0.132839\pi$
$542$	12.8142	+	7.39828i	0.550417	+	0.317783i
$543$		0			0
$544$	5.58838	−	3.22645i	0.239600	−	0.138333i
$545$	4.16557	−	36.1544i	0.178434	−	1.54868i
$546$		0			0
$547$	−12.6990	+	7.33178i	−0.542971	+	0.313484i	−0.746282	−	0.665630i	$-0.768163\pi$
$547$	−12.6990	+	7.33178i	−0.542971	+	0.313484i	0.203311	+	0.979114i	$0.434830\pi$
$548$	3.43092	−	5.94252i	0.146562	−	0.253852i
$549$		0			0
$550$	−2.60214	+	11.1425i	−0.110956	+	0.475119i
$551$	0.699591			0.0298036
$552$		0			0
$553$	18.9305	+	2.82004i	0.805008	+	0.119920i
$554$	6.88813	+	3.97687i	0.292649	+	0.168961i
$555$		0			0
$556$	−1.44024	−	0.831524i	−0.0610798	−	0.0352645i
$557$	13.3908	+	23.1936i	0.567387	+	0.982743i	0.996823	+	0.0796459i	$0.0253790\pi$
$557$	13.3908	+	23.1936i	0.567387	+	0.982743i	−0.429436	+	0.903097i	$0.641288\pi$
$558$		0			0
$559$		−	9.92679i		−	0.419858i
$560$	−4.17999	−	4.18661i	−0.176637	−	0.176917i
$561$		0			0
$562$	12.9850	−	7.49690i	0.547740	−	0.316238i
$563$			18.5309i			0.780986i	0.920606	+	0.390493i	$0.127695\pi$
$563$			18.5309i			0.780986i	−0.920606	+	0.390493i	$0.872305\pi$
$564$		0			0
$565$	12.2560	−	5.31063i	0.515612	−	0.223420i
$566$	−29.8023			−1.25268
$567$		0			0
$568$		−	11.0359i		−	0.463058i
$569$			23.8266i			0.998863i	0.866353	+	0.499431i	$0.166458\pi$
$569$			23.8266i			0.998863i	−0.866353	+	0.499431i	$0.833542\pi$
$570$		0			0
$571$	44.5452			1.86416			0.932079	−	0.362255i	$-0.117993\pi$
$571$	44.5452			1.86416			0.932079	+	0.362255i	$0.117993\pi$
$572$	8.00893	−	4.62396i	0.334870	−	0.193337i
$573$		0			0
$574$	−3.80769	+	4.79157i	−0.158930	+	0.199996i
$575$	6.86750	−	7.32727i	0.286395	−	0.305568i
$576$		0			0
$577$	−1.24045	−	2.14853i	−0.0516407	−	0.0894443i	0.839050	−	0.544055i	$-0.183112\pi$
$577$	−1.24045	−	2.14853i	−0.0516407	−	0.0894443i	−0.890690	+	0.454611i	$0.849778\pi$
$578$	12.3200	−	21.3388i	0.512443	−	0.887578i
$579$		0			0
$580$	−7.57698	−	0.872991i	−0.314617	−	0.0362490i
$581$	28.1645	−	11.1097i	1.16846	−	0.460907i
$582$		0			0
$583$		−	10.7983i		−	0.447219i
$584$	7.78631	+	13.4863i	0.322200	+	0.558066i
$585$		0			0
$586$	2.19993	+	1.27013i	0.0908784	+	0.0524687i
$587$	−9.73573	+	5.62093i	−0.401837	+	0.232001i	−0.687276	−	0.726396i	$-0.741194\pi$
$587$	−9.73573	+	5.62093i	−0.401837	+	0.232001i	0.285439	+	0.958397i	$0.407860\pi$
$588$		0			0
$589$	0.0999973	−	0.173200i	0.00412032	−	0.00713660i
$590$	16.2905	+	12.0862i	0.670669	+	0.497582i
$591$		0			0
$592$	7.40520	+	4.27539i	0.304352	+	0.175718i
$593$	25.3760	+	14.6508i	1.04207	+	0.601638i	0.920418	−	0.390935i	$-0.127848\pi$
$593$	25.3760	+	14.6508i	1.04207	+	0.601638i	0.121649	+	0.992573i	$0.461182\pi$
$594$		0			0
$595$	−36.8672	−	9.90982i	−1.51141	−	0.406263i
$596$	10.1542	−	5.86255i	0.415933	−	0.240139i
$597$		0			0
$598$	−8.11653			−0.331909
$599$		−	13.5005i		−	0.551614i	−0.961213	−	0.275807i	$-0.911055\pi$
$599$		−	13.5005i		−	0.551614i	0.961213	−	0.275807i	$-0.0889451\pi$
$600$		0			0
$601$	−13.5297	+	7.81138i	−0.551889	+	0.318633i	−0.749883	−	0.661570i	$-0.769890\pi$
$601$	−13.5297	+	7.81138i	−0.551889	+	0.318633i	0.197995	+	0.980203i	$0.436557\pi$
$602$	−6.04582	+	2.38482i	−0.246409	+	0.0971979i
$603$		0			0
$604$	−1.68168	+	2.91276i	−0.0684266	+	0.118518i
$605$	1.47495	−	12.8016i	0.0599654	−	0.520459i
$606$		0			0
$607$	4.07061	+	7.05051i	0.165221	+	0.286171i	0.936734	−	0.350043i	$-0.113833\pi$
$607$	4.07061	+	7.05051i	0.165221	+	0.286171i	−0.771513	+	0.636214i	$0.780500\pi$
$608$	−0.177623	−	0.102551i	−0.00720357	−	0.00415899i
$609$		0			0
$610$	−14.3654	+	19.3625i	−0.581637	+	0.783963i
$611$	16.7210	+	9.65386i	0.676458	+	0.390553i
$612$		0			0
$613$	14.5475	−	8.39900i	0.587568	−	0.339232i	−0.176567	−	0.984289i	$-0.556499\pi$
$613$	14.5475	−	8.39900i	0.587568	−	0.339232i	0.764135	+	0.645056i	$0.223166\pi$
$614$	−8.06299			−0.325396
$615$		0			0
$616$	−4.74025	−	3.76691i	−0.190990	−	0.151773i
$617$	−13.7676	+	23.8461i	−0.554262	+	0.960009i	0.443699	+	0.896176i	$0.353666\pi$
$617$	−13.7676	+	23.8461i	−0.554262	+	0.960009i	−0.997961	+	0.0638334i	$0.979667\pi$
$618$		0			0
$619$	8.09495	+	4.67362i	0.325363	+	0.187849i	0.653781	−	0.756684i	$-0.273182\pi$
$619$	8.09495	+	4.67362i	0.325363	+	0.187849i	−0.328417	+	0.944533i	$0.606515\pi$
$620$	−1.29916	+	1.75108i	−0.0521755	+	0.0703251i
$621$		0			0
$622$	0.763625			0.0306186
$623$	16.7539	−	21.0830i	0.671232	−	0.844674i
$624$		0			0
$625$	−20.7964	+	13.8748i	−0.831854	+	0.554994i
$626$	−3.83737			−0.153372
$627$		0			0
$628$	−2.58329			−0.103084
$629$	55.1774			2.20007
$630$		0			0
$631$	−45.9246			−1.82823			−0.914115	−	0.405454i	$-0.867113\pi$
$631$	−45.9246			−1.82823			−0.914115	+	0.405454i	$0.867113\pi$
$632$	−7.23402			−0.287754
$633$		0			0
$634$	−17.3289			−0.688218
$635$	−15.7651	+	21.2491i	−0.625620	+	0.843245i
$636$		0			0
$637$	20.6700	−	19.3117i	0.818977	−	0.765157i
$638$	−7.80583			−0.309036
$639$		0			0
$640$	1.79580	+	1.33234i	0.0709851	+	0.0526652i
$641$	−16.2569	−	9.38590i	−0.642107	−	0.370721i	0.143318	−	0.989677i	$-0.454223\pi$
$641$	−16.2569	−	9.38590i	−0.642107	−	0.370721i	−0.785426	+	0.618956i	$0.787556\pi$
$642$		0			0
$643$	−11.5123	+	19.9399i	−0.454001	+	0.786353i	−0.998630	−	0.0523244i	$-0.983337\pi$
$643$	−11.5123	+	19.9399i	−0.454001	+	0.786353i	0.544629	+	0.838677i	$0.316670\pi$
$644$	1.94992	+	4.94330i	0.0768376	+	0.194793i
$645$		0			0
$646$	−1.32350			−0.0520724
$647$	14.6259	−	8.44426i	0.575003	−	0.331978i	−0.184142	−	0.982900i	$-0.558951\pi$
$647$	14.6259	−	8.44426i	0.575003	−	0.331978i	0.759145	+	0.650922i	$0.225617\pi$
$648$		0			0
$649$	17.9785	+	10.3799i	0.705716	+	0.407445i
$650$	19.6761	+	4.59500i	0.771759	+	0.180231i
$651$		0			0
$652$	−21.1464	−	12.2089i	−0.828156	−	0.478136i
$653$	−10.8831	−	18.8501i	−0.425888	−	0.737660i	0.570615	−	0.821218i	$-0.306705\pi$
$653$	−10.8831	−	18.8501i	−0.425888	−	0.737660i	−0.996503	+	0.0835580i	$0.973372\pi$
$654$		0			0
$655$	−0.756620	+	6.56696i	−0.0295636	+	0.256592i
$656$	1.15662	−	2.00333i	0.0451585	−	0.0782168i
$657$		0			0
$658$	1.86254	−	12.5030i	0.0726095	−	0.487418i
$659$	21.0718	−	12.1658i	0.820841	−	0.473913i	−0.0298654	−	0.999554i	$-0.509508\pi$
$659$	21.0718	−	12.1658i	0.820841	−	0.473913i	0.850706	+	0.525641i	$0.176175\pi$
$660$		0			0
$661$		−	25.9481i		−	1.00926i	−0.863335	−	0.504632i	$-0.831628\pi$
$661$		−	25.9481i		−	1.00926i	0.863335	−	0.504632i	$-0.168372\pi$
$662$	−4.95873			−0.192727
$663$		0			0
$664$	−9.91029	+	5.72171i	−0.384594	+	0.222045i
$665$	0.313123	+	1.17230i	0.0121424	+	0.0454599i
$666$		0			0
$667$	5.93303	+	3.42544i	0.229728	+	0.132633i
$668$	−0.00904075	−	0.00521968i	−0.000349797	−	0.000201955i
$669$		0			0
$670$	−8.06281	+	10.8675i	−0.311493	+	0.419848i
$671$	−12.3372	+	21.3687i	−0.476274	+	0.824930i
$672$		0			0
$673$	−3.32531	+	1.91987i	−0.128181	+	0.0740054i	−0.562719	−	0.826648i	$-0.690245\pi$
$673$	−3.32531	+	1.91987i	−0.128181	+	0.0740054i	0.434538	+	0.900653i	$0.356912\pi$
$674$	1.58895	+	0.917381i	0.0612041	+	0.0353362i
$675$		0			0
$676$	−1.66523	−	2.88426i	−0.0640472	−	0.110933i
$677$		−	16.2326i		−	0.623868i	−0.950104	−	0.311934i	$-0.899023\pi$
$677$		−	16.2326i		−	0.623868i	0.950104	−	0.311934i	$-0.100977\pi$
$678$		0			0
$679$	8.23324	+	20.8724i	0.315963	+	0.801008i
$680$	14.3343	+	1.65154i	0.549695	+	0.0633338i
$681$		0			0
$682$	−1.11574	+	1.93252i	−0.0427239	+	0.0740000i
$683$	4.73579	+	8.20262i	0.181210	+	0.313865i	0.942293	−	0.334790i	$-0.108665\pi$
$683$	4.73579	+	8.20262i	0.181210	+	0.313865i	−0.761083	+	0.648655i	$0.775332\pi$
$684$		0			0
$685$	14.0787	−	6.10043i	0.537918	−	0.233085i
$686$	−16.7274	−	7.94946i	−0.638655	−	0.303512i
$687$		0			0
$688$	2.12736	−	1.22823i	0.0811047	−	0.0468258i
$689$	−19.0682			−0.726440
$690$		0			0
$691$		−	15.7754i		−	0.600123i	−0.953920	−	0.300062i	$-0.902993\pi$
$691$		−	15.7754i		−	0.600123i	0.953920	−	0.300062i	$-0.0970072\pi$
$692$		−	18.2330i		−	0.693116i
$693$		0			0
$694$	6.78486			0.257550
$695$	−1.47851	−	3.41213i	−0.0560831	−	0.129430i
$696$		0			0
$697$		−	14.9271i		−	0.565405i
$698$	−11.4343	+	6.60159i	−0.432794	+	0.249874i
$699$		0			0
$700$	−1.92844	−	13.0874i	−0.0728882	−	0.494659i
$701$			3.43541i			0.129754i	0.997893	+	0.0648769i	$0.0206655\pi$
$701$			3.43541i			0.129754i	−0.997893	+	0.0648769i	$0.979335\pi$
$702$		0			0
$703$	−0.876890	−	1.51882i	−0.0330725	−	0.0572833i
$704$	1.98187	+	1.14423i	0.0746945	+	0.0431249i
$705$		0			0
$706$	−26.8650	−	15.5105i	−1.01108	−	0.583747i
$707$	−2.49390	+	3.13830i	−0.0937927	+	0.118028i
$708$		0			0
$709$	−25.8612			−0.971239			−0.485620	−	0.874170i	$-0.661406\pi$
$709$	−25.8612			−0.971239			−0.485620	+	0.874170i	$0.661406\pi$
$710$	14.7036	−	19.8183i	0.551816	−	0.743768i
$711$		0			0
$712$	−5.08916	+	8.81469i	−0.190724	+	0.330345i
$713$	1.69610	−	0.979242i	0.0635193	−	0.0366729i
$714$		0			0
$715$	20.5431	+	2.36689i	0.768267	+	0.0885168i
$716$	−13.5399	+	7.81725i	−0.506009	+	0.292144i
$717$		0			0
$718$	−24.9912	−	14.4287i	−0.932664	−	0.538474i
$719$	20.8858	−	36.1753i	0.778909	−	1.34911i	−0.153663	−	0.988123i	$-0.549107\pi$
$719$	20.8858	−	36.1753i	0.778909	−	1.34911i	0.932571	−	0.360986i	$-0.117560\pi$
$720$		0			0
$721$	18.2285	+	46.2116i	0.678864	+	1.72101i
$722$	−9.47897	−	16.4181i	−0.352771	−	0.611017i
$723$		0			0
$724$			24.3098i			0.903467i
$725$	−12.4436	−	11.6628i	−0.462143	−	0.433145i
$726$		0			0
$727$	21.4490	+	37.1508i	0.795499	+	1.37785i	0.922522	+	0.385945i	$0.126125\pi$
$727$	21.4490	+	37.1508i	0.795499	+	1.37785i	−0.127022	+	0.991900i	$0.540542\pi$
$728$	−6.65180	+	8.37059i	−0.246532	+	0.310235i
$729$		0			0
$730$	−3.98563	+	34.5926i	−0.147515	+	1.28033i
$731$	7.92564	−	13.7276i	0.293141	−	0.507734i
$732$		0			0
$733$	2.36946	+	4.10402i	0.0875179	+	0.151586i	0.906461	−	0.422289i	$-0.138773\pi$
$733$	2.36946	+	4.10402i	0.0875179	+	0.151586i	−0.818943	+	0.573874i	$0.805440\pi$
$734$	−6.18161	+	10.7069i	−0.228167	+	0.395197i
$735$		0			0
$736$	−1.00425	−	1.73941i	−0.0370171	−	0.0641155i
$737$	−6.92448	+	11.9936i	−0.255067	+	0.441788i
$738$		0			0
$739$	−14.6252	−	25.3317i	−0.537998	−	0.931841i	−0.999012	−	0.0444475i	$-0.985847\pi$
$739$	−14.6252	−	25.3317i	−0.537998	−	0.931841i	0.461013	−	0.887393i	$-0.347486\pi$
$740$	7.60197	+	17.5439i	0.279454	+	0.644928i
$741$		0			0
$742$	4.58095	+	11.6133i	0.168172	+	0.426338i
$743$	16.2571	−	28.1581i	0.596415	−	1.03302i	−0.396930	−	0.917849i	$-0.629925\pi$
$743$	16.2571	−	28.1581i	0.596415	−	1.03302i	0.993346	−	0.115173i	$-0.0367421\pi$
$744$		0			0
$745$	26.0458	+	3.00090i	0.954244	+	0.109944i
$746$	−31.7495	+	18.3306i	−1.16243	+	0.671131i
$747$		0			0
$748$	14.7672			0.539944
$749$	−29.6405	+	37.2993i	−1.08304	+	1.36289i
$750$		0			0
$751$	16.5978	+	28.7482i	0.605662	+	1.04904i	0.991946	+	0.126658i	$0.0404251\pi$
$751$	16.5978	+	28.7482i	0.605662	+	1.04904i	−0.386284	+	0.922380i	$0.626242\pi$
$752$			4.77784i			0.174230i
$753$		0			0
$754$			13.7840i			0.501982i
$755$	−6.90072	+	2.99015i	−0.251143	+	0.108823i
$756$		0			0
$757$			1.30712i			0.0475082i	0.999718	+	0.0237541i	$0.00756188\pi$
$757$			1.30712i			0.0475082i	−0.999718	+	0.0237541i	$0.992438\pi$
$758$	19.2906			0.700667
$759$		0			0
$760$	−0.182343	−	0.420814i	−0.00661428	−	0.0152645i
$761$	11.3771	+	19.7057i	0.412420	+	0.714332i	0.995154	−	0.0983312i	$-0.0313504\pi$
$761$	11.3771	+	19.7057i	0.412420	+	0.714332i	−0.582734	+	0.812663i	$0.698017\pi$
$762$		0			0
$763$	15.8010	+	40.0577i	0.572035	+	1.45018i
$764$			11.9399i			0.431972i
$765$		0			0
$766$	7.09201	−	4.09457i	0.256245	−	0.147943i
$767$	18.3293	−	31.7473i	0.661834	−	1.14633i
$768$		0			0
$769$	−34.4497	−	19.8896i	−1.24229	−	0.717236i	−0.272729	−	0.962091i	$-0.587926\pi$
$769$	−34.4497	−	19.8896i	−1.24229	−	0.717236i	−0.969560	+	0.244855i	$0.921260\pi$
$770$	−3.49374	−	13.0802i	−0.125906	−	0.471377i
$771$		0			0
$772$		−	12.4417i		−	0.447786i
$773$	−31.3729	+	18.1132i	−1.12841	+	0.651486i	−0.943534	−	0.331277i	$-0.892521\pi$
$773$	−31.3729	+	18.1132i	−1.12841	+	0.651486i	−0.184872	+	0.982763i	$0.559187\pi$
$774$		0			0
$775$	−4.66605	+	1.41367i	−0.167610	+	0.0507804i
$776$	−4.24029	−	7.34440i	−0.152218	−	0.263649i
$777$		0			0
$778$	−7.64611	−	4.41449i	−0.274126	−	0.158267i
$779$	−0.410886	+	0.237225i	−0.0147215	+	0.00849947i
$780$		0			0
$781$	12.6277	−	21.8718i	0.451854	−	0.782635i
$782$	−11.2242	−	6.48032i	−0.401378	−	0.231736i
$783$		0			0
$784$	6.69607	+	2.04027i	0.239145	+	0.0728668i
$785$	−4.63905	−	3.44180i	−0.165575	−	0.122843i
$786$		0			0
$787$	17.1289			0.610581			0.305290	−	0.952259i	$-0.401246\pi$
$787$	17.1289			0.610581			0.305290	+	0.952259i	$0.401246\pi$
$788$	−23.0465			−0.820996
$789$		0			0
$790$	−12.9908	−	9.63815i	−0.462193	−	0.342910i
$791$	−9.83255	+	12.3732i	−0.349605	+	0.439941i
$792$		0			0
$793$	37.7340	+	21.7858i	1.33997	+	0.773635i
$794$	−5.82466	+	10.0886i	−0.206710	+	0.358032i
$795$		0			0
$796$	−6.98847	+	4.03479i	−0.247700	+	0.143010i
$797$	−35.9212	−	20.7391i	−1.27239	−	0.734616i	−0.296955	−	0.954891i	$-0.595971\pi$
$797$	−35.9212	−	20.7391i	−1.27239	−	0.734616i	−0.975438	+	0.220275i	$0.929305\pi$
$798$		0			0
$799$	15.4155	+	26.7004i	0.545360	+	0.944591i
$800$	1.44977	+	4.78520i	0.0512570	+	0.169183i
$801$		0			0
$802$	2.28763	−	1.32076i	0.0807788	−	0.0466377i
$803$			35.6374i			1.25762i
$804$		0			0
$805$	−3.08448	+	11.4751i	−0.108714	+	0.404444i
$806$	3.41255	+	1.97024i	0.120202	+	0.0693986i
$807$		0			0
$808$	0.757545	−	1.31211i	0.0266503	−	0.0461597i
$809$	−5.30390	+	3.06221i	−0.186475	+	0.107661i	−0.590331	−	0.807161i	$-0.701003\pi$
$809$	−5.30390	+	3.06221i	−0.186475	+	0.107661i	0.403856	+	0.914822i	$0.367670\pi$
$810$		0			0
$811$			51.1448i			1.79594i	0.440059	+	0.897969i	$0.354957\pi$
$811$			51.1448i			1.79594i	−0.440059	+	0.897969i	$0.645043\pi$
$812$	8.39500	−	3.31147i	0.294607	−	0.116210i
$813$		0			0
$814$	9.78409	+	16.9465i	0.342932	+	0.593976i
$815$	−21.7083	−	50.0987i	−0.760407	−	1.75488i
$816$		0			0
$817$	−0.503824			−0.0176266
$818$			4.00359i			0.139982i
$819$		0			0
$820$	4.74616	−	2.05656i	0.165743	−	0.0718182i
$821$			9.10905i			0.317908i	0.987286	+	0.158954i	$0.0508121\pi$
$821$			9.10905i			0.317908i	−0.987286	+	0.158954i	$0.949188\pi$
$822$		0			0
$823$		−	44.7216i		−	1.55890i	−0.626466	−	0.779449i	$-0.715499\pi$
$823$		−	44.7216i		−	1.55890i	0.626466	−	0.779449i	$-0.284501\pi$
$824$	−9.38804	−	16.2606i	−0.327048	−	0.566464i
$825$		0			0
$826$	−23.7389	−	3.53633i	−0.825981	−	0.123044i
$827$	34.3286			1.19372			0.596860	−	0.802345i	$-0.296415\pi$
$827$	34.3286			1.19372			0.596860	+	0.802345i	$0.296415\pi$
$828$		0			0
$829$	40.7898	−	23.5500i	1.41669	−	0.817925i	0.420682	−	0.907208i	$-0.361791\pi$
$829$	40.7898	−	23.5500i	1.41669	−	0.817925i	0.996006	+	0.0892828i	$0.0284575\pi$
$830$	−25.4201	−	2.92881i	−0.882344	−	0.101660i
$831$		0			0
$832$	2.02055	−	3.49969i	0.0700499	−	0.121330i
$833$	44.0030	−	10.2027i	1.52461	−	0.353504i
$834$		0			0
$835$	−0.00928098	−	0.0214188i	−0.000321181	−	0.000741228i
$836$	−0.234684	−	0.406485i	−0.00811672	−	0.0140586i
$837$		0			0
$838$	−10.3156	+	17.8671i	−0.356346	+	0.617209i
$839$	7.97922	+	13.8204i	0.275473	+	0.477134i	0.970254	−	0.242087i	$-0.0778321\pi$
$839$	7.97922	+	13.8204i	0.275473	+	0.477134i	−0.694781	+	0.719221i	$0.744499\pi$
$840$		0			0
$841$	−8.68273	+	15.0389i	−0.299404	+	0.518583i
$842$	−2.08360	−	3.60891i	−0.0718058	−	0.124371i
$843$		0			0
$844$	−9.23801	+	16.0007i	−0.317985	+	0.550767i
$845$	0.852391	−	7.39818i	0.0293231	−	0.254505i
$846$		0			0
$847$	5.59485	+	14.1837i	0.192241	+	0.487357i
$848$	−2.35928	−	4.08640i	−0.0810181	−	0.140327i
$849$		0			0
$850$	23.5411	+	22.0639i	0.807452	+	0.756786i
$851$		−	17.1742i		−	0.588725i
$852$		0			0
$853$	4.85434	+	8.40796i	0.166209	+	0.287883i	0.937084	−	0.349104i	$-0.113514\pi$
$853$	4.85434	+	8.40796i	0.166209	+	0.287883i	−0.770875	+	0.636987i	$0.780181\pi$
$854$	4.20318	−	28.2154i	0.143830	−	0.965511i
$855$		0			0
$856$	9.00357	−	15.5946i	0.307736	−	0.533014i
$857$	27.0181	+	15.5989i	0.922921	+	0.532849i	0.884566	−	0.466415i	$-0.154455\pi$
$857$	27.0181	+	15.5989i	0.922921	+	0.532849i	0.0383555	+	0.999264i	$0.487788\pi$
$858$		0			0
$859$	−13.8087	+	7.97243i	−0.471145	+	0.272016i	−0.716719	−	0.697362i	$-0.754357\pi$
$859$	−13.8087	+	7.97243i	−0.471145	+	0.272016i	0.245574	+	0.969378i	$0.421024\pi$
$860$	5.45671	+	0.628702i	0.186072	+	0.0214386i
$861$		0			0
$862$	1.89577	−	1.09452i	0.0645701	−	0.0372796i
$863$	21.8059	−	37.7689i	0.742281	−	1.28567i	−0.209174	−	0.977879i	$-0.567077\pi$
$863$	21.8059	−	37.7689i	0.742281	−	1.28567i	0.951454	−	0.307790i	$-0.0995893\pi$
$864$		0			0
$865$	24.2925	−	32.7428i	0.825971	−	1.11329i
$866$	−23.8117			−0.809154
$867$		0			0
$868$	0.380123	−	2.55171i	0.0129022	−	0.0866108i
$869$	−14.3369	−	8.27741i	−0.486346	−	0.280792i
$870$		0			0
$871$	21.1789	+	12.2276i	0.717618	+	0.414317i
$872$	−8.13785	−	14.0952i	−0.275582	−	0.477323i
$873$		0			0
$874$			0.411946i			0.0139343i
$875$	13.9738	−	26.0717i	0.472400	−	0.881384i
$876$		0			0
$877$	32.8047	−	18.9398i	1.10774	−	0.639552i	0.169494	−	0.985531i	$-0.445787\pi$
$877$	32.8047	−	18.9398i	1.10774	−	0.639552i	0.938242	+	0.345980i	$0.112453\pi$
$878$			14.3892i			0.485611i
$879$		0			0
$880$	2.03453	+	4.69532i	0.0685840	+	0.158279i
$881$	16.7367			0.563872			0.281936	−	0.959433i	$-0.409023\pi$
$881$	16.7367			0.563872			0.281936	+	0.959433i	$0.409023\pi$
$882$		0			0
$883$		−	5.43664i		−	0.182957i	−0.995807	−	0.0914787i	$-0.970841\pi$
$883$		−	5.43664i		−	0.182957i	0.995807	−	0.0914787i	$-0.0291593\pi$
$884$		−	26.0768i		−	0.877057i
$885$		0			0
$886$	−36.6080			−1.22987
$887$	33.7618	−	19.4924i	1.13361	−	0.654490i	0.188770	−	0.982021i	$-0.439550\pi$
$887$	33.7618	−	19.4924i	1.13361	−	0.654490i	0.944840	+	0.327531i	$0.106217\pi$
$888$		0			0
$889$	4.61274	−	30.9647i	0.154706	−	1.03852i
$890$	−20.8832	+	9.04891i	−0.700007	+	0.303320i
$891$		0			0
$892$	2.10769	+	3.65063i	0.0705708	+	0.122232i
$893$	0.489972	−	0.848656i	0.0163963	−	0.0283992i
$894$		0			0
$895$	−34.7301	−	4.00147i	−1.16090	−	0.133754i
$896$	−2.61687	−	0.389830i	−0.0874236	−	0.0130233i
$897$		0			0
$898$			0.350689i			0.0117026i
$899$	−1.66301	−	2.88041i	−0.0554644	−	0.0960671i
$900$		0			0
$901$	−26.3691	−	15.2242i	−0.878483	−	0.507192i
$902$	4.58455	−	2.64689i	0.152649	−	0.0881318i
$903$		0			0
$904$	2.98673	−	5.17317i	0.0993372	−	0.172057i
$905$	−32.3888	+	43.6554i	−1.07664	+	1.45116i
$906$		0			0
$907$	−2.39252	−	1.38132i	−0.0794424	−	0.0458661i	0.459753	−	0.888047i	$-0.347938\pi$
$907$	−2.39252	−	1.38132i	−0.0794424	−	0.0458661i	−0.539195	+	0.842181i	$0.681271\pi$
$908$	16.0856	+	9.28700i	0.533818	+	0.308200i
$909$		0			0
$910$	−23.0977	+	6.16943i	−0.765682	+	0.204515i
$911$	−36.0610	+	20.8198i	−1.19475	+	0.689792i	−0.959381	−	0.282113i	$-0.908965\pi$
$911$	−36.0610	+	20.8198i	−1.19475	+	0.689792i	−0.235373	+	0.971905i	$0.575631\pi$
$912$		0			0
$913$	−26.1879			−0.866692
$914$			1.91541i			0.0633562i
$915$		0			0
$916$	1.36101	−	0.785777i	0.0449689	−	0.0259628i
$917$	−2.87004	−	7.27593i	−0.0947771	−	0.240273i
$918$		0			0
$919$	−11.8470	+	20.5196i	−0.390797	+	0.676880i	−0.992555	−	0.121798i	$-0.961134\pi$
$919$	−11.8470	+	20.5196i	−0.390797	+	0.676880i	0.601758	+	0.798679i	$0.294467\pi$
$920$	0.514051	−	4.46162i	0.0169478	−	0.147095i
$921$		0			0
$922$	12.2091	+	21.1468i	0.402086	+	0.696434i
$923$	−38.6224	−	22.2987i	−1.27127	−	0.733969i
$924$		0			0
$925$	−9.72283	+	41.6337i	−0.319685	+	1.36891i
$926$	−4.09771	−	2.36581i	−0.134659	−	0.0777454i
$927$		0			0
$928$	−2.95397	+	1.70547i	−0.0969687	+	0.0559849i
$929$	6.44893			0.211583			0.105791	−	0.994388i	$-0.466262\pi$
$929$	6.44893			0.211583			0.105791	+	0.994388i	$0.466262\pi$
$930$		0			0
$931$	−0.980146	−	1.04909i	−0.0321230	−	0.0343824i
$932$	3.77904	−	6.54549i	0.123787	−	0.214405i
$933$		0			0
$934$	−29.9337	−	17.2822i	−0.979461	−	0.565492i
$935$	26.5190	+	19.6749i	0.867263	+	0.643439i
$936$		0			0
$937$	−38.6081			−1.26127			−0.630635	−	0.776079i	$-0.717206\pi$
$937$	−38.6081			−1.26127			−0.630635	+	0.776079i	$0.717206\pi$
$938$	2.35911	−	15.8364i	0.0770276	−	0.517076i
$939$		0			0
$940$	−6.36569	+	8.58003i	−0.207626	+	0.279850i
$941$	10.4321			0.340077			0.170039	−	0.985437i	$-0.445611\pi$
$941$	10.4321			0.340077			0.170039	+	0.985437i	$0.445611\pi$
$942$		0			0
$943$	−4.64614			−0.151299
$944$	9.07146			0.295251
$945$		0			0
$946$	5.62152			0.182771
$947$	−34.1258			−1.10894			−0.554470	−	0.832204i	$-0.687079\pi$
$947$	−34.1258			−1.10894			−0.554470	+	0.832204i	$0.687079\pi$
$948$		0			0
$949$	62.9304			2.04281
$950$	0.233215	−	0.998638i	0.00756648	−	0.0324001i
$951$		0			0
$952$	−15.8818	+	6.26470i	−0.514734	+	0.203040i
$953$	44.3067			1.43523			0.717617	−	0.696438i	$-0.245233\pi$
$953$	44.3067			1.43523			0.717617	+	0.696438i	$0.245233\pi$
$954$		0			0
$955$	−15.9080	+	21.4417i	−0.514771	+	0.693837i
$956$	−14.4459	−	8.34037i	−0.467215	−	0.269747i
$957$		0			0
$958$	20.7765	−	35.9860i	0.671258	−	1.16265i
$959$	−11.2949	+	14.2134i	−0.364730	+	0.458973i
$960$		0			0
$961$	30.0492			0.969328
$962$	29.9251	−	17.2773i	0.964824	−	0.557042i
$963$		0			0
$964$	24.5697	+	14.1853i	0.791337	+	0.456879i
$965$	16.5765	−	22.3427i	0.533616	−	0.719237i
$966$		0			0
$967$	14.0448	+	8.10875i	0.451649	+	0.260760i	0.708526	−	0.705684i	$-0.249360\pi$
$967$	14.0448	+	8.10875i	0.451649	+	0.260760i	−0.256877	+	0.966444i	$0.582694\pi$
$968$	−2.88146	−	4.99084i	−0.0926137	−	0.160412i
$969$		0			0
$970$	2.17050	−	18.8385i	0.0696907	−	0.604869i
$971$	18.1313	−	31.4043i	0.581861	−	1.00781i	−0.413397	−	0.910551i	$-0.635658\pi$
$971$	18.1313	−	31.4043i	0.581861	−	1.00781i	0.995259	−	0.0972627i	$-0.0310087\pi$
$972$		0			0
$973$	3.44478	+	2.73744i	0.110435	+	0.0877584i
$974$	8.25200	−	4.76429i	0.264411	−	0.152658i
$975$		0			0
$976$			10.7821i			0.345127i
$977$	−8.70634			−0.278541			−0.139270	−	0.990254i	$-0.544476\pi$
$977$	−8.70634			−0.278541			−0.139270	+	0.990254i	$0.544476\pi$
$978$		0			0
$979$	−20.1721	+	11.6464i	−0.644704	+	0.372220i
$980$	9.30644	+	12.5853i	0.297283	+	0.402023i
$981$		0			0
$982$	−3.87273	−	2.23592i	−0.123584	−	0.0713512i
$983$	9.66469	+	5.57991i	0.308256	+	0.177972i	0.646146	−	0.763214i	$-0.276380\pi$
$983$	9.66469	+	5.57991i	0.308256	+	0.177972i	−0.337890	+	0.941186i	$0.609713\pi$
$984$		0			0
$985$	−41.3867	−	30.7056i	−1.31869	−	0.978362i
$986$	−11.0052	+	19.0616i	−0.350478	+	0.607047i
$987$		0			0
$988$	−0.717793	+	0.414418i	−0.0228360	+	0.0131844i
$989$	−4.27279	−	2.46689i	−0.135867	−	0.0784427i
$990$		0			0
$991$	−24.4098	−	42.2790i	−0.775402	−	1.34304i	−0.934568	−	0.355785i	$-0.884214\pi$
$991$	−24.4098	−	42.2790i	−0.775402	−	1.34304i	0.159165	−	0.987252i	$-0.449120\pi$
$992$			0.975100i			0.0309594i
$993$		0			0
$994$	−4.30214	+	28.8797i	−0.136456	+	0.916008i
$995$	−17.9256	−	2.06532i	−0.568279	−	0.0654749i
$996$		0			0
$997$	−8.97969	+	15.5533i	−0.284390	+	0.492577i	−0.972461	−	0.233066i	$-0.925124\pi$
$997$	−8.97969	+	15.5533i	−0.284390	+	0.492577i	0.688071	+	0.725643i	$0.258458\pi$
$998$	17.8598	+	30.9342i	0.565343	+	0.979204i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.bi.b.719.19		48
3.2	odd	2		630.2.bi.a.509.6	yes	48
5.4	even	2		1890.2.bi.a.719.14		48
7.3	odd	6		1890.2.r.a.1529.22		48
9.2	odd	6		1890.2.r.b.89.22		48
9.7	even	3		630.2.r.a.299.10	yes	48
15.14	odd	2		630.2.bi.b.509.19	yes	48
21.17	even	6		630.2.r.b.59.15	yes	48
35.24	odd	6		1890.2.r.b.1529.22		48
45.29	odd	6		1890.2.r.a.89.22		48
45.34	even	6		630.2.r.b.299.15	yes	48
63.38	even	6		1890.2.bi.a.899.14		48
63.52	odd	6		630.2.bi.b.479.19	yes	48
105.59	even	6		630.2.r.a.59.10	✓	48
315.164	even	6	inner	1890.2.bi.b.899.19		48
315.304	odd	6		630.2.bi.a.479.6	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.r.a.59.10	✓	48	105.59	even	6
630.2.r.a.299.10	yes	48	9.7	even	3
630.2.r.b.59.15	yes	48	21.17	even	6
630.2.r.b.299.15	yes	48	45.34	even	6
630.2.bi.a.479.6	yes	48	315.304	odd	6
630.2.bi.a.509.6	yes	48	3.2	odd	2
630.2.bi.b.479.19	yes	48	63.52	odd	6
630.2.bi.b.509.19	yes	48	15.14	odd	2
1890.2.r.a.89.22		48	45.29	odd	6
1890.2.r.a.1529.22		48	7.3	odd	6
1890.2.r.b.89.22		48	9.2	odd	6
1890.2.r.b.1529.22		48	35.24	odd	6
1890.2.bi.a.719.14		48	5.4	even	2
1890.2.bi.a.899.14		48	63.38	even	6
1890.2.bi.b.719.19		48	1.1	even	1	trivial
1890.2.bi.b.899.19		48	315.164	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.bi (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(1.79580 + 1.33234i) q^{5} +(-2.61687 - 0.389830i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(1.79580 + 1.33234i) q^{5} +(-2.61687 - 0.389830i) q^{7} +1.00000 q^{8} +(1.79580 + 1.33234i) q^{10} +(1.98187 + 1.14423i) q^{11} +(2.02055 - 3.49969i) q^{13} +(-2.61687 - 0.389830i) q^{14} +1.00000 q^{16} +(5.58838 - 3.22645i) q^{17} +(-0.177623 - 0.102551i) q^{19} +(1.79580 + 1.33234i) q^{20} +(1.98187 + 1.14423i) q^{22} +(-1.00425 - 1.73941i) q^{23} +(1.44977 + 4.78520i) q^{25} +(2.02055 - 3.49969i) q^{26} +(-2.61687 - 0.389830i) q^{28} +(-2.95397 + 1.70547i) q^{29} +0.975100i q^{31} +1.00000 q^{32} +(5.58838 - 3.22645i) q^{34} +(-4.17999 - 4.18661i) q^{35} +(7.40520 + 4.27539i) q^{37} +(-0.177623 - 0.102551i) q^{38} +(1.79580 + 1.33234i) q^{40} +(1.15662 - 2.00333i) q^{41} +(2.12736 - 1.22823i) q^{43} +(1.98187 + 1.14423i) q^{44} +(-1.00425 - 1.73941i) q^{46} +4.77784i q^{47} +(6.69607 + 2.04027i) q^{49} +(1.44977 + 4.78520i) q^{50} +(2.02055 - 3.49969i) q^{52} +(-2.35928 - 4.08640i) q^{53} +(2.03453 + 4.69532i) q^{55} +(-2.61687 - 0.389830i) q^{56} +(-2.95397 + 1.70547i) q^{58} +9.07146 q^{59} +10.7821i q^{61} +0.975100i q^{62} +1.00000 q^{64} +(8.29125 - 3.59268i) q^{65} +6.05164i q^{67} +(5.58838 - 3.22645i) q^{68} +(-4.17999 - 4.18661i) q^{70} -11.0359i q^{71} +(7.78631 + 13.4863i) q^{73} +(7.40520 + 4.27539i) q^{74} +(-0.177623 - 0.102551i) q^{76} +(-4.74025 - 3.76691i) q^{77} -7.23402 q^{79} +(1.79580 + 1.33234i) q^{80} +(1.15662 - 2.00333i) q^{82} +(-9.91029 + 5.72171i) q^{83} +(14.3343 + 1.65154i) q^{85} +(2.12736 - 1.22823i) q^{86} +(1.98187 + 1.14423i) q^{88} +(-5.08916 + 8.81469i) q^{89} +(-6.65180 + 8.37059i) q^{91} +(-1.00425 - 1.73941i) q^{92} +4.77784i q^{94} +(-0.182343 - 0.420814i) q^{95} +(-4.24029 - 7.34440i) q^{97} +(6.69607 + 2.04027i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 48 q^{2} + 48 q^{4} - 3 q^{7} + 48 q^{8}+O(q^{10}) \) 48 * q + 48 * q^2 + 48 * q^4 - 3 * q^7 + 48 * q^8	\( 48 q + 48 q^{2} + 48 q^{4} - 3 q^{7} + 48 q^{8} - 6 q^{11} - 3 q^{14} + 48 q^{16} - 6 q^{22} + 3 q^{23} + 18 q^{25} - 3 q^{28} + 3 q^{29} + 48 q^{32} + 18 q^{35} + 3 q^{41} - 6 q^{44} + 3 q^{46} + 3 q^{49} + 18 q^{50} + 42 q^{55} - 3 q^{56} + 3 q^{58} + 48 q^{64} + 12 q^{65} + 18 q^{70} + 18 q^{73} - 12 q^{77} + 3 q^{82} + 9 q^{83} + 33 q^{85} - 6 q^{88} + 33 q^{89} + 3 q^{92} + 24 q^{97} + 3 q^{98}+O(q^{100}) \) 48 * q + 48 * q^2 + 48 * q^4 - 3 * q^7 + 48 * q^8 - 6 * q^11 - 3 * q^14 + 48 * q^16 - 6 * q^22 + 3 * q^23 + 18 * q^25 - 3 * q^28 + 3 * q^29 + 48 * q^32 + 18 * q^35 + 3 * q^41 - 6 * q^44 + 3 * q^46 + 3 * q^49 + 18 * q^50 + 42 * q^55 - 3 * q^56 + 3 * q^58 + 48 * q^64 + 12 * q^65 + 18 * q^70 + 18 * q^73 - 12 * q^77 + 3 * q^82 + 9 * q^83 + 33 * q^85 - 6 * q^88 + 33 * q^89 + 3 * q^92 + 24 * q^97 + 3 * q^98

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