LMFDB - Embedded newform 1890.2.bi.a.899.16

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			899.16
Character	$\chi$	$=$	1890.899
Dual form			1890.2.bi.a.719.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{4} +(0.834189 - 2.07464i) q^{5} +(-1.94702 - 1.79140i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{4} +(0.834189 - 2.07464i) q^{5} +(-1.94702 - 1.79140i) q^{7} -1.00000 q^{8} +(-0.834189 + 2.07464i) q^{10} +(3.95349 - 2.28255i) q^{11} +(0.341322 + 0.591187i) q^{13} +(1.94702 + 1.79140i) q^{14} +1.00000 q^{16} +(-5.72947 - 3.30791i) q^{17} +(-6.76346 + 3.90489i) q^{19} +(0.834189 - 2.07464i) q^{20} +(-3.95349 + 2.28255i) q^{22} +(1.75447 - 3.03883i) q^{23} +(-3.60826 - 3.46128i) q^{25} +(-0.341322 - 0.591187i) q^{26} +(-1.94702 - 1.79140i) q^{28} +(4.33820 + 2.50466i) q^{29} -5.21945i q^{31} -1.00000 q^{32} +(5.72947 + 3.30791i) q^{34} +(-5.34069 + 2.54500i) q^{35} +(1.37526 - 0.794006i) q^{37} +(6.76346 - 3.90489i) q^{38} +(-0.834189 + 2.07464i) q^{40} +(-3.41784 - 5.91987i) q^{41} +(2.05488 + 1.18639i) q^{43} +(3.95349 - 2.28255i) q^{44} +(-1.75447 + 3.03883i) q^{46} +3.81589i q^{47} +(0.581771 + 6.97578i) q^{49} +(3.60826 + 3.46128i) q^{50} +(0.341322 + 0.591187i) q^{52} +(-0.983879 + 1.70413i) q^{53} +(-1.43751 - 10.1061i) q^{55} +(1.94702 + 1.79140i) q^{56} +(-4.33820 - 2.50466i) q^{58} -9.36589 q^{59} +14.3153i q^{61} +5.21945i q^{62} +1.00000 q^{64} +(1.51123 - 0.214959i) q^{65} +7.26234i q^{67} +(-5.72947 - 3.30791i) q^{68} +(5.34069 - 2.54500i) q^{70} -8.48088i q^{71} +(-0.735176 + 1.27336i) q^{73} +(-1.37526 + 0.794006i) q^{74} +(-6.76346 + 3.90489i) q^{76} +(-11.7865 - 2.63812i) q^{77} +1.17562 q^{79} +(0.834189 - 2.07464i) q^{80} +(3.41784 + 5.91987i) q^{82} +(-9.77023 - 5.64084i) q^{83} +(-11.6422 + 9.12717i) q^{85} +(-2.05488 - 1.18639i) q^{86} +(-3.95349 + 2.28255i) q^{88} +(0.739183 + 1.28030i) q^{89} +(0.394492 - 1.76250i) q^{91} +(1.75447 - 3.03883i) q^{92} -3.81589i q^{94} +(2.45923 + 17.2892i) q^{95} +(4.40260 - 7.62553i) q^{97} +(-0.581771 - 6.97578i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 12 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} - 12 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 + 12 * 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 - 12 * 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 $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

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

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
$5$	0.834189	−	2.07464i	0.373060	−	0.927807i
$5$	0.834189	−	2.07464i	0.373060	−	0.927807i
$6$		0			0
$7$	−1.94702	−	1.79140i	−0.735904	−	0.677086i
$7$	−1.94702	−	1.79140i	−0.735904	−	0.677086i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−0.834189	+	2.07464i	−0.263794	+	0.656059i
$11$	3.95349	−	2.28255i	1.19202	−	0.688214i	0.233257	−	0.972415i	$-0.425062\pi$
$11$	3.95349	−	2.28255i	1.19202	−	0.688214i	0.958765	+	0.284201i	$0.0917283\pi$
$12$		0			0
$13$	0.341322	+	0.591187i	0.0946657	+	0.163966i	0.909469	−	0.415772i	$-0.136488\pi$
$13$	0.341322	+	0.591187i	0.0946657	+	0.163966i	−0.814803	+	0.579737i	$0.803155\pi$
$14$	1.94702	+	1.79140i	0.520363	+	0.478772i
$15$		0			0
$16$	1.00000			0.250000
$17$	−5.72947	−	3.30791i	−1.38960	−	0.802287i	−0.396332	−	0.918107i	$-0.629717\pi$
$17$	−5.72947	−	3.30791i	−1.38960	−	0.802287i	−0.993270	+	0.115821i	$0.963050\pi$
$18$		0			0
$19$	−6.76346	+	3.90489i	−1.55165	+	0.895843i	−0.553637	+	0.832758i	$0.686761\pi$
$19$	−6.76346	+	3.90489i	−1.55165	+	0.895843i	−0.998008	+	0.0630848i	$0.979906\pi$
$20$	0.834189	−	2.07464i	0.186530	−	0.463904i
$21$		0			0
$22$	−3.95349	+	2.28255i	−0.842887	+	0.486641i
$23$	1.75447	−	3.03883i	0.365832	−	0.633640i	−0.623077	−	0.782160i	$-0.714118\pi$
$23$	1.75447	−	3.03883i	0.365832	−	0.633640i	0.988909	+	0.148520i	$0.0474511\pi$
$24$		0			0
$25$	−3.60826	−	3.46128i	−0.721652	−	0.692256i
$26$	−0.341322	−	0.591187i	−0.0669388	−	0.115941i
$27$		0			0
$28$	−1.94702	−	1.79140i	−0.367952	−	0.338543i
$29$	4.33820	+	2.50466i	0.805583	+	0.465104i	0.845420	−	0.534103i	$-0.179350\pi$
$29$	4.33820	+	2.50466i	0.805583	+	0.465104i	−0.0398366	+	0.999206i	$0.512684\pi$
$30$		0			0
$31$		−	5.21945i		−	0.937441i	−0.883346	−	0.468721i	$-0.844715\pi$
$31$		−	5.21945i		−	0.937441i	0.883346	−	0.468721i	$-0.155285\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	5.72947	+	3.30791i	0.982597	+	0.567303i
$35$	−5.34069	+	2.54500i	−0.902742	+	0.430183i
$36$		0			0
$37$	1.37526	−	0.794006i	0.226091	−	0.130534i	−0.382676	−	0.923882i	$-0.624998\pi$
$37$	1.37526	−	0.794006i	0.226091	−	0.130534i	0.608767	+	0.793349i	$0.291664\pi$
$38$	6.76346	−	3.90489i	1.09718	−	0.633457i
$39$		0			0
$40$	−0.834189	+	2.07464i	−0.131897	+	0.328029i
$41$	−3.41784	−	5.91987i	−0.533777	−	0.924528i	−0.999221	−	0.0394513i	$-0.987439\pi$
$41$	−3.41784	−	5.91987i	−0.533777	−	0.924528i	0.465445	−	0.885077i	$-0.345894\pi$
$42$		0			0
$43$	2.05488	+	1.18639i	0.313366	+	0.180922i	0.648432	−	0.761273i	$-0.275425\pi$
$43$	2.05488	+	1.18639i	0.313366	+	0.180922i	−0.335066	+	0.942195i	$0.608758\pi$
$44$	3.95349	−	2.28255i	0.596011	−	0.344107i
$45$		0			0
$46$	−1.75447	+	3.03883i	−0.258682	+	0.448051i
$47$			3.81589i			0.556605i	0.960493	+	0.278303i	$0.0897718\pi$
$47$			3.81589i			0.556605i	−0.960493	+	0.278303i	$0.910228\pi$
$48$		0			0
$49$	0.581771	+	6.97578i	0.0831101	+	0.996540i
$50$	3.60826	+	3.46128i	0.510285	+	0.489499i
$51$		0			0
$52$	0.341322	+	0.591187i	0.0473329	+	0.0819829i
$53$	−0.983879	+	1.70413i	−0.135146	+	0.234080i	−0.925653	−	0.378373i	$-0.876484\pi$
$53$	−0.983879	+	1.70413i	−0.135146	+	0.234080i	0.790507	+	0.612453i	$0.209817\pi$
$54$		0			0
$55$	−1.43751	−	10.1061i	−0.193834	−	1.36271i
$56$	1.94702	+	1.79140i	0.260181	+	0.239386i
$57$		0			0
$58$	−4.33820	−	2.50466i	−0.569633	−	0.328878i
$59$	−9.36589			−1.21934			−0.609668	−	0.792657i	$-0.708697\pi$
$59$	−9.36589			−1.21934			−0.609668	+	0.792657i	$0.708697\pi$
$60$		0			0
$61$			14.3153i			1.83288i	0.400172	+	0.916440i	$0.368951\pi$
$61$			14.3153i			1.83288i	−0.400172	+	0.916440i	$0.631049\pi$
$62$			5.21945i			0.662871i
$63$		0			0
$64$	1.00000			0.125000
$65$	1.51123	−	0.214959i	0.187445	−	0.0266623i
$66$		0			0
$67$			7.26234i			0.887236i	0.896216	+	0.443618i	$0.146305\pi$
$67$			7.26234i			0.887236i	−0.896216	+	0.443618i	$0.853695\pi$
$68$	−5.72947	−	3.30791i	−0.694801	−	0.401143i
$69$		0			0
$70$	5.34069	−	2.54500i	0.638335	−	0.304185i
$71$		−	8.48088i		−	1.00650i	−0.864142	−	0.503248i	$-0.832138\pi$
$71$		−	8.48088i		−	1.00650i	0.864142	−	0.503248i	$-0.167862\pi$
$72$		0			0
$73$	−0.735176	+	1.27336i	−0.0860458	+	0.149036i	−0.905836	−	0.423628i	$-0.860756\pi$
$73$	−0.735176	+	1.27336i	−0.0860458	+	0.149036i	0.819791	+	0.572663i	$0.194090\pi$
$74$	−1.37526	+	0.794006i	−0.159871	+	0.0923013i
$75$		0			0
$76$	−6.76346	+	3.90489i	−0.775823	+	0.447921i
$77$	−11.7865	−	2.63812i	−1.34319	−	0.300641i
$78$		0			0
$79$	1.17562			0.132268			0.0661339	−	0.997811i	$-0.478934\pi$
$79$	1.17562			0.132268			0.0661339	+	0.997811i	$0.478934\pi$
$80$	0.834189	−	2.07464i	0.0932651	−	0.231952i
$81$		0			0
$82$	3.41784	+	5.91987i	0.377437	+	0.653740i
$83$	−9.77023	−	5.64084i	−1.07242	−	0.619163i	−0.143580	−	0.989639i	$-0.545861\pi$
$83$	−9.77023	−	5.64084i	−1.07242	−	0.619163i	−0.928842	+	0.370476i	$0.879195\pi$
$84$		0			0
$85$	−11.6422	+	9.12717i	−1.26277	+	0.989981i
$86$	−2.05488	−	1.18639i	−0.221583	−	0.127931i
$87$		0			0
$88$	−3.95349	+	2.28255i	−0.421443	+	0.243320i
$89$	0.739183	+	1.28030i	0.0783532	+	0.135712i	0.902540	−	0.430607i	$-0.141700\pi$
$89$	0.739183	+	1.28030i	0.0783532	+	0.135712i	−0.824186	+	0.566319i	$0.808367\pi$
$90$		0			0
$91$	0.394492	−	1.76250i	0.0413540	−	0.184760i
$92$	1.75447	−	3.03883i	0.182916	−	0.316820i
$93$		0			0
$94$		−	3.81589i		−	0.393579i
$95$	2.45923	+	17.2892i	0.252312	+	1.77383i
$96$		0			0
$97$	4.40260	−	7.62553i	0.447017	−	0.774255i	−0.551174	−	0.834391i	$-0.685820\pi$
$97$	4.40260	−	7.62553i	0.447017	−	0.774255i	0.998190	+	0.0601352i	$0.0191532\pi$
$98$	−0.581771	−	6.97578i	−0.0587677	−	0.704660i
$99$		0			0
$100$	−3.60826	−	3.46128i	−0.360826	−	0.346128i
$101$	−0.447091	−	0.774384i	−0.0444872	−	0.0770541i	0.842924	−	0.538032i	$-0.180832\pi$
$101$	−0.447091	−	0.774384i	−0.0444872	−	0.0770541i	−0.887412	+	0.460978i	$0.847499\pi$
$102$		0			0
$103$	−6.77551	+	11.7355i	−0.667611	+	1.15634i	0.310959	+	0.950423i	$0.399350\pi$
$103$	−6.77551	+	11.7355i	−0.667611	+	1.15634i	−0.978570	+	0.205913i	$0.933984\pi$
$104$	−0.341322	−	0.591187i	−0.0334694	−	0.0579707i
$105$		0			0
$106$	0.983879	−	1.70413i	0.0955628	−	0.165520i
$107$	2.12855	+	3.68676i	0.205775	+	0.356412i	0.950379	−	0.311094i	$-0.100695\pi$
$107$	2.12855	+	3.68676i	0.205775	+	0.356412i	−0.744605	+	0.667506i	$0.767362\pi$
$108$		0			0
$109$	3.35599	−	5.81274i	0.321445	−	0.556760i	−0.659341	−	0.751844i	$-0.729165\pi$
$109$	3.35599	−	5.81274i	0.321445	−	0.556760i	0.980786	+	0.195084i	$0.0624980\pi$
$110$	1.43751	+	10.1061i	0.137061	+	0.963583i
$111$		0			0
$112$	−1.94702	−	1.79140i	−0.183976	−	0.169271i
$113$	−3.41846	−	5.92094i	−0.321581	−	0.556995i	0.659233	−	0.751939i	$-0.270881\pi$
$113$	−3.41846	−	5.92094i	−0.321581	−	0.556995i	−0.980814	+	0.194943i	$0.937548\pi$
$114$		0			0
$115$	−4.84092	−	6.17485i	−0.451418	−	0.575808i
$116$	4.33820	+	2.50466i	0.402792	+	0.232552i
$117$		0			0
$118$	9.36589			0.862200
$119$	5.22960	+	16.7044i	0.479397	+	1.53129i
$120$		0			0
$121$	4.92005	−	8.52177i	0.447277	−	0.774707i
$122$		−	14.3153i		−	1.29604i
$123$		0			0
$124$		−	5.21945i		−	0.468721i
$125$	−10.1909	+	4.59847i	−0.911500	+	0.411300i
$126$		0			0
$127$		−	11.2278i		−	0.996304i	−0.867090	−	0.498152i	$-0.834012\pi$
$127$		−	11.2278i		−	0.996304i	0.867090	−	0.498152i	$-0.165988\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$	−1.51123	+	0.214959i	−0.132543	+	0.0188531i
$131$	1.13293	−	1.96229i	0.0989842	−	0.171446i	−0.812280	−	0.583267i	$-0.801774\pi$
$131$	1.13293	−	1.96229i	0.0989842	−	0.171446i	0.911264	+	0.411822i	$0.135107\pi$
$132$		0			0
$133$	20.1638	+	4.51318i	1.74842	+	0.391342i
$134$		−	7.26234i		−	0.627371i
$135$		0			0
$136$	5.72947	+	3.30791i	0.491298	+	0.283651i
$137$	1.93119	+	3.34491i	0.164992	+	0.285775i	0.936653	−	0.350260i	$-0.113907\pi$
$137$	1.93119	+	3.34491i	0.164992	+	0.285775i	−0.771660	+	0.636035i	$0.780573\pi$
$138$		0			0
$139$	−11.4418	+	6.60593i	−0.970482	+	0.560308i	−0.899383	−	0.437161i	$-0.855984\pi$
$139$	−11.4418	+	6.60593i	−0.970482	+	0.560308i	−0.0710985	+	0.997469i	$0.522650\pi$
$140$	−5.34069	+	2.54500i	−0.451371	+	0.215092i
$141$		0			0
$142$			8.48088i			0.711700i
$143$	2.69883	+	1.55817i	0.225687	+	0.130301i
$144$		0			0
$145$	8.81514	−	6.91084i	0.732058	−	0.573914i
$146$	0.735176	−	1.27336i	0.0608436	−	0.105384i
$147$		0			0
$148$	1.37526	−	0.794006i	0.113046	−	0.0652669i
$149$	−3.72883	−	2.15284i	−0.305477	−	0.176367i	0.339424	−	0.940634i	$-0.389768\pi$
$149$	−3.72883	−	2.15284i	−0.305477	−	0.176367i	−0.644901	+	0.764266i	$0.723101\pi$
$150$		0			0
$151$	−8.02202	−	13.8945i	−0.652823	−	1.13072i	−0.982435	−	0.186605i	$-0.940251\pi$
$151$	−8.02202	−	13.8945i	−0.652823	−	1.13072i	0.329612	−	0.944116i	$-0.393082\pi$
$152$	6.76346	−	3.90489i	0.548589	−	0.316728i
$153$		0			0
$154$	11.7865	+	2.63812i	0.949781	+	0.212585i
$155$	−10.8285	−	4.35401i	−0.869764	−	0.349722i
$156$		0			0
$157$	10.1182			0.807517			0.403759	−	0.914866i	$-0.367704\pi$
$157$	10.1182			0.807517			0.403759	+	0.914866i	$0.367704\pi$
$158$	−1.17562			−0.0935275
$159$		0			0
$160$	−0.834189	+	2.07464i	−0.0659484	+	0.164015i
$161$	−8.85975	+	2.77371i	−0.698246	+	0.218599i
$162$		0			0
$163$	−19.6914	+	11.3688i	−1.54235	+	0.890476i	−0.543660	+	0.839306i	$0.682962\pi$
$163$	−19.6914	+	11.3688i	−1.54235	+	0.890476i	−0.998690	+	0.0511701i	$0.983705\pi$
$164$	−3.41784	−	5.91987i	−0.266888	−	0.462264i
$165$		0			0
$166$	9.77023	+	5.64084i	0.758317	+	0.437814i
$167$	11.3198	−	6.53552i	0.875956	−	0.505733i	0.00663315	−	0.999978i	$-0.497889\pi$
$167$	11.3198	−	6.53552i	0.875956	−	0.505733i	0.869323	+	0.494245i	$0.164555\pi$
$168$		0			0
$169$	6.26700	−	10.8548i	0.482077	−	0.834982i
$170$	11.6422	−	9.12717i	0.892915	−	0.700022i
$171$		0			0
$172$	2.05488	+	1.18639i	0.156683	+	0.0904611i
$173$			0.697127i			0.0530016i	0.999649	+	0.0265008i	$0.00843645\pi$
$173$			0.697127i			0.0530016i	−0.999649	+	0.0265008i	$0.991564\pi$
$174$		0			0
$175$	0.824810	+	13.2030i	0.0623498	+	0.998054i
$176$	3.95349	−	2.28255i	0.298005	−	0.172054i
$177$		0			0
$178$	−0.739183	−	1.28030i	−0.0554041	−	0.0959627i
$179$	−10.6754	−	6.16342i	−0.797913	−	0.460675i	0.0448277	−	0.998995i	$-0.485726\pi$
$179$	−10.6754	−	6.16342i	−0.797913	−	0.460675i	−0.842741	+	0.538319i	$0.819059\pi$
$180$		0			0
$181$			11.6266i			0.864199i	0.901826	+	0.432100i	$0.142227\pi$
$181$			11.6266i			0.864199i	−0.901826	+	0.432100i	$0.857773\pi$
$182$	−0.394492	+	1.76250i	−0.0292417	+	0.130645i
$183$		0			0
$184$	−1.75447	+	3.03883i	−0.129341	+	0.224026i
$185$	−0.500051	−	3.51552i	−0.0367645	−	0.258466i
$186$		0			0
$187$	−30.2019			−2.20858
$188$			3.81589i			0.278303i
$189$		0			0
$190$	−2.45923	−	17.2892i	−0.178411	−	1.25429i
$191$			0.589056i			0.0426226i	0.999773	+	0.0213113i	$0.00678411\pi$
$191$			0.589056i			0.0426226i	−0.999773	+	0.0213113i	$0.993216\pi$
$192$		0			0
$193$		−	14.0161i		−	1.00890i	−0.863440	−	0.504452i	$-0.831695\pi$
$193$		−	14.0161i		−	1.00890i	0.863440	−	0.504452i	$-0.168305\pi$
$194$	−4.40260	+	7.62553i	−0.316088	+	0.547481i
$195$		0			0
$196$	0.581771	+	6.97578i	0.0415550	+	0.498270i
$197$	−10.4933			−0.747615			−0.373808	−	0.927506i	$-0.621948\pi$
$197$	−10.4933			−0.747615			−0.373808	+	0.927506i	$0.621948\pi$
$198$		0			0
$199$	−19.0237	−	10.9833i	−1.34855	−	0.778587i	−0.360508	−	0.932756i	$-0.617397\pi$
$199$	−19.0237	−	10.9833i	−1.34855	−	0.778587i	−0.988045	+	0.154169i	$0.950730\pi$
$200$	3.60826	+	3.46128i	0.255142	+	0.244750i
$201$		0			0
$202$	0.447091	+	0.774384i	0.0314572	+	0.0544855i
$203$	−3.95971	−	12.6481i	−0.277917	−	0.887720i
$204$		0			0
$205$	−15.1327	+	2.15249i	−1.05691	+	0.150337i
$206$	6.77551	−	11.7355i	0.472072	−	0.817653i
$207$		0			0
$208$	0.341322	+	0.591187i	0.0236664	+	0.0409915i
$209$	−17.8262	+	30.8759i	−1.23306	+	2.13573i
$210$		0			0
$211$	−6.82852	−	11.8273i	−0.470095	−	0.814228i	0.529320	−	0.848422i	$-0.322447\pi$
$211$	−6.82852	−	11.8273i	−0.470095	−	0.814228i	−0.999415	+	0.0341938i	$0.989114\pi$
$212$	−0.983879	+	1.70413i	−0.0675731	+	0.117040i
$213$		0			0
$214$	−2.12855	−	3.68676i	−0.145505	−	0.252022i
$215$	4.17548	−	3.27347i	0.284765	−	0.223249i
$216$		0			0
$217$	−9.35013	+	10.1624i	−0.634728	+	0.689867i
$218$	−3.35599	+	5.81274i	−0.227296	+	0.393689i
$219$		0			0
$220$	−1.43751	−	10.1061i	−0.0969168	−	0.681356i
$221$		−	4.51626i		−	0.303796i
$222$		0			0
$223$	13.5359	−	23.4449i	0.906433	−	1.56999i	0.0874521	−	0.996169i	$-0.472128\pi$
$223$	13.5359	−	23.4449i	0.906433	−	1.56999i	0.818981	−	0.573820i	$-0.194539\pi$
$224$	1.94702	+	1.79140i	0.130091	+	0.119693i
$225$		0			0
$226$	3.41846	+	5.92094i	0.227392	+	0.393855i
$227$	−6.72233	+	3.88114i	−0.446177	+	0.257600i	−0.706214	−	0.707998i	$-0.749598\pi$
$227$	−6.72233	+	3.88114i	−0.446177	+	0.257600i	0.260038	+	0.965599i	$0.416265\pi$
$228$		0			0
$229$	0.431712	+	0.249249i	0.0285283	+	0.0164708i	0.514196	−	0.857673i	$-0.328090\pi$
$229$	0.431712	+	0.249249i	0.0285283	+	0.0164708i	−0.485668	+	0.874143i	$0.661424\pi$
$230$	4.84092	+	6.17485i	0.319201	+	0.407158i
$231$		0			0
$232$	−4.33820	−	2.50466i	−0.284817	−	0.164439i
$233$	−8.94844	−	15.4992i	−0.586232	−	1.01538i	−0.994721	−	0.102620i	$-0.967277\pi$
$233$	−8.94844	−	15.4992i	−0.586232	−	1.01538i	0.408489	−	0.912763i	$-0.366056\pi$
$234$		0			0
$235$	7.91660	+	3.18317i	0.516422	+	0.207647i
$236$	−9.36589			−0.609668
$237$		0			0
$238$	−5.22960	−	16.7044i	−0.338985	−	1.08278i
$239$	−23.9059	+	13.8021i	−1.54634	+	0.892781i	−0.547925	+	0.836527i	$0.684582\pi$
$239$	−23.9059	+	13.8021i	−1.54634	+	0.892781i	−0.998417	+	0.0562537i	$0.982084\pi$
$240$		0			0
$241$	−12.1606	+	7.02092i	−0.783332	+	0.452257i	−0.837610	−	0.546269i	$-0.816048\pi$
$241$	−12.1606	+	7.02092i	−0.783332	+	0.452257i	0.0542778	+	0.998526i	$0.482714\pi$
$242$	−4.92005	+	8.52177i	−0.316273	+	0.547800i
$243$		0			0
$244$			14.3153i			0.916440i
$245$	14.9575	+	4.61215i	0.955602	+	0.294660i
$246$		0			0
$247$	−4.61704	−	2.66565i	−0.293775	−	0.169611i
$248$			5.21945i			0.331436i
$249$		0			0
$250$	10.1909	−	4.59847i	0.644528	−	0.290833i
$251$	16.0764			1.01473			0.507367	−	0.861730i	$-0.330619\pi$
$251$	16.0764			1.01473			0.507367	+	0.861730i	$0.330619\pi$
$252$		0			0
$253$		−	16.0186i		−	1.00708i
$254$			11.2278i			0.704493i
$255$		0			0
$256$	1.00000			0.0625000
$257$	22.0687	+	12.7414i	1.37661	+	0.794785i	0.991750	−	0.128190i	$-0.0409167\pi$
$257$	22.0687	+	12.7414i	1.37661	+	0.794785i	0.384859	+	0.922975i	$0.374250\pi$
$258$		0			0
$259$	−4.10004	−	0.917693i	−0.254764	−	0.0570227i
$260$	1.51123	−	0.214959i	0.0937224	−	0.0133312i
$261$		0			0
$262$	−1.13293	+	1.96229i	−0.0699924	+	0.121230i
$263$	−12.7152	−	22.0234i	−0.784054	−	1.35802i	−0.929563	−	0.368664i	$-0.879815\pi$
$263$	−12.7152	−	22.0234i	−0.784054	−	1.35802i	0.145509	−	0.989357i	$-0.453518\pi$
$264$		0			0
$265$	2.71471	+	3.46276i	0.166763	+	0.212716i
$266$	−20.1638	−	4.51318i	−1.23632	−	0.276721i
$267$		0			0
$268$			7.26234i			0.443618i
$269$	12.2442	−	21.2076i	0.746544	−	1.29305i	−0.202926	−	0.979194i	$-0.565045\pi$
$269$	12.2442	−	21.2076i	0.746544	−	1.29305i	0.949470	−	0.313858i	$-0.101621\pi$
$270$		0			0
$271$	−17.8062	+	10.2804i	−1.08165	+	0.624492i	−0.931342	−	0.364147i	$-0.881361\pi$
$271$	−17.8062	+	10.2804i	−1.08165	+	0.624492i	−0.150311	+	0.988639i	$0.548027\pi$
$272$	−5.72947	−	3.30791i	−0.347400	−	0.200572i
$273$		0			0
$274$	−1.93119	−	3.34491i	−0.116667	−	0.202074i
$275$	−22.1658	−	5.44811i	−1.33665	−	0.328534i
$276$		0			0
$277$	1.70051	−	0.981792i	0.102174	−	0.0589902i	−0.448042	−	0.894012i	$-0.647879\pi$
$277$	1.70051	−	0.981792i	0.102174	−	0.0589902i	0.550216	+	0.835022i	$0.314545\pi$
$278$	11.4418	−	6.60593i	0.686234	−	0.396197i
$279$		0			0
$280$	5.34069	−	2.54500i	0.319167	−	0.152093i
$281$	25.5282	+	14.7387i	1.52288	+	0.879237i	0.999634	+	0.0270583i	$0.00861399\pi$
$281$	25.5282	+	14.7387i	1.52288	+	0.879237i	0.523250	+	0.852179i	$0.324719\pi$
$282$		0			0
$283$	25.1313			1.49390			0.746951	−	0.664879i	$-0.231517\pi$
$283$	25.1313			1.49390			0.746951	+	0.664879i	$0.231517\pi$
$284$		−	8.48088i		−	0.503248i
$285$		0			0
$286$	−2.69883	−	1.55817i	−0.159585	−	0.0921364i
$287$	−3.95026	+	17.6488i	−0.233176	+	1.04178i
$288$		0			0
$289$	13.3846	+	23.1828i	0.787329	+	1.36369i
$290$	−8.81514	+	6.91084i	−0.517643	+	0.405818i
$291$		0			0
$292$	−0.735176	+	1.27336i	−0.0430229	+	0.0745179i
$293$	−26.8539	+	15.5041i	−1.56882	+	0.905761i	−0.572517	+	0.819893i	$0.694033\pi$
$293$	−26.8539	+	15.5041i	−1.56882	+	0.905761i	−0.996307	+	0.0858678i	$0.972634\pi$
$294$		0			0
$295$	−7.81292	+	19.4309i	−0.454886	+	1.13131i
$296$	−1.37526	+	0.794006i	−0.0799353	+	0.0461507i
$297$		0			0
$298$	3.72883	+	2.15284i	0.216005	+	0.124711i
$299$	2.39536			0.138527
$300$		0			0
$301$	−1.87560	−	5.99103i	−0.108108	−	0.345317i
$302$	8.02202	+	13.8945i	0.461615	+	0.799541i
$303$		0			0
$304$	−6.76346	+	3.90489i	−0.387911	+	0.223961i
$305$	29.6990	+	11.9416i	1.70056	+	0.683775i
$306$		0			0
$307$	−4.89776			−0.279530			−0.139765	−	0.990185i	$-0.544635\pi$
$307$	−4.89776			−0.279530			−0.139765	+	0.990185i	$0.544635\pi$
$308$	−11.7865	−	2.63812i	−0.671597	−	0.150321i
$309$		0			0
$310$	10.8285	+	4.35401i	0.615016	+	0.247291i
$311$	−9.06956			−0.514288			−0.257144	−	0.966373i	$-0.582781\pi$
$311$	−9.06956			−0.514288			−0.257144	+	0.966373i	$0.582781\pi$
$312$		0			0
$313$	30.0835			1.70042			0.850209	−	0.526445i	$-0.176475\pi$
$313$	30.0835			1.70042			0.850209	+	0.526445i	$0.176475\pi$
$314$	−10.1182			−0.571001
$315$		0			0
$316$	1.17562			0.0661339
$317$	3.37219			0.189401			0.0947006	−	0.995506i	$-0.469811\pi$
$317$	3.37219			0.189401			0.0947006	+	0.995506i	$0.469811\pi$
$318$		0			0
$319$	22.8680			1.28036
$320$	0.834189	−	2.07464i	0.0466326	−	0.115976i
$321$		0			0
$322$	8.85975	−	2.77371i	0.493734	−	0.154573i
$323$	51.6681			2.87489
$324$		0			0
$325$	0.814687	−	3.31457i	0.0451907	−	0.183859i
$326$	19.6914	−	11.3688i	1.09061	−	0.629662i
$327$		0			0
$328$	3.41784	+	5.91987i	0.188719	+	0.326870i
$329$	6.83579	−	7.42962i	0.376869	−	0.409608i
$330$		0			0
$331$	10.9348			0.601033			0.300516	−	0.953777i	$-0.402841\pi$
$331$	10.9348			0.601033			0.300516	+	0.953777i	$0.402841\pi$
$332$	−9.77023	−	5.64084i	−0.536211	−	0.309582i
$333$		0			0
$334$	−11.3198	+	6.53552i	−0.619394	+	0.357608i
$335$	15.0667	+	6.05816i	0.823184	+	0.330993i
$336$		0			0
$337$	−1.26189	+	0.728550i	−0.0687393	+	0.0396867i	−0.533976	−	0.845500i	$-0.679303\pi$
$337$	−1.26189	+	0.728550i	−0.0687393	+	0.0396867i	0.465236	+	0.885186i	$0.345969\pi$
$338$	−6.26700	+	10.8548i	−0.340880	+	0.590421i
$339$		0			0
$340$	−11.6422	+	9.12717i	−0.631386	+	0.494990i
$341$	−11.9136	−	20.6350i	−0.645160	−	1.11745i
$342$		0			0
$343$	11.3637	−	14.6242i	0.613582	−	0.789631i
$344$	−2.05488	−	1.18639i	−0.110792	−	0.0639656i
$345$		0			0
$346$		−	0.697127i		−	0.0374778i
$347$	35.8194			1.92289			0.961443	−	0.275003i	$-0.0886789\pi$
$347$	35.8194			1.92289			0.961443	+	0.275003i	$0.0886789\pi$
$348$		0			0
$349$	2.63799	+	1.52304i	0.141208	+	0.0815266i	0.568940	−	0.822379i	$-0.307354\pi$
$349$	2.63799	+	1.52304i	0.141208	+	0.0815266i	−0.427731	+	0.903906i	$0.640687\pi$
$350$	−0.824810	−	13.2030i	−0.0440879	−	0.705731i
$351$		0			0
$352$	−3.95349	+	2.28255i	−0.210722	+	0.121660i
$353$	29.5595	−	17.0662i	1.57329	−	0.908342i	0.577533	−	0.816368i	$-0.304016\pi$
$353$	29.5595	−	17.0662i	1.57329	−	0.908342i	0.995761	−	0.0919742i	$-0.0293177\pi$
$354$		0			0
$355$	−17.5948	−	7.07465i	−0.933833	−	0.375484i
$356$	0.739183	+	1.28030i	0.0391766	+	0.0678559i
$357$		0			0
$358$	10.6754	+	6.16342i	0.564210	+	0.325747i
$359$	−21.0726	+	12.1663i	−1.11217	+	0.642110i	−0.939390	−	0.342851i	$-0.888608\pi$
$359$	−21.0726	+	12.1663i	−1.11217	+	0.642110i	−0.172778	+	0.984961i	$0.555274\pi$
$360$		0			0
$361$	20.9963	−	36.3667i	1.10507	−	1.91404i
$362$		−	11.6266i		−	0.611081i
$363$		0			0
$364$	0.394492	−	1.76250i	0.0206770	−	0.0923800i
$365$	2.02849	+	2.58745i	0.106176	+	0.135433i
$366$		0			0
$367$	6.72343	+	11.6453i	0.350960	+	0.607881i	0.986418	−	0.164255i	$-0.0525218\pi$
$367$	6.72343	+	11.6453i	0.350960	+	0.607881i	−0.635458	+	0.772136i	$0.719188\pi$
$368$	1.75447	−	3.03883i	0.0914581	−	0.158410i
$369$		0			0
$370$	0.500051	+	3.51552i	0.0259964	+	0.182763i
$371$	4.96841	−	1.55545i	0.257947	−	0.0807550i
$372$		0			0
$373$	−2.42626	−	1.40080i	−0.125627	−	0.0725306i	0.435870	−	0.900010i	$-0.356441\pi$
$373$	−2.42626	−	1.40080i	−0.125627	−	0.0725306i	−0.561496	+	0.827479i	$0.689774\pi$
$374$	30.2019			1.56170
$375$		0			0
$376$		−	3.81589i		−	0.196790i
$377$			3.41958i			0.176117i
$378$		0			0
$379$	−13.2036			−0.678225			−0.339112	−	0.940746i	$-0.610127\pi$
$379$	−13.2036			−0.678225			−0.339112	+	0.940746i	$0.610127\pi$
$380$	2.45923	+	17.2892i	0.126156	+	0.886915i
$381$		0			0
$382$		−	0.589056i		−	0.0301387i
$383$	−2.77030	−	1.59943i	−0.141556	−	0.0817272i	0.427550	−	0.903992i	$-0.359377\pi$
$383$	−2.77030	−	1.59943i	−0.141556	−	0.0817272i	−0.569105	+	0.822265i	$0.692710\pi$
$384$		0			0
$385$	−15.3053	+	22.2520i	−0.780029	+	1.13407i
$386$			14.0161i			0.713403i
$387$		0			0
$388$	4.40260	−	7.62553i	0.223508	−	0.387128i
$389$	16.1572	−	9.32835i	0.819201	−	0.472966i	−0.0309398	−	0.999521i	$-0.509850\pi$
$389$	16.1572	−	9.32835i	0.819201	−	0.472966i	0.850141	+	0.526555i	$0.176517\pi$
$390$		0			0
$391$	−20.1044	+	11.6073i	−1.01672	+	0.587005i
$392$	−0.581771	−	6.97578i	−0.0293838	−	0.352330i
$393$		0			0
$394$	10.4933			0.528644
$395$	0.980691	−	2.43899i	0.0493439	−	0.122719i
$396$		0			0
$397$	5.38403	+	9.32542i	0.270217	+	0.468029i	0.968917	−	0.247385i	$-0.0795713\pi$
$397$	5.38403	+	9.32542i	0.270217	+	0.468029i	−0.698700	+	0.715414i	$0.746238\pi$
$398$	19.0237	+	10.9833i	0.953571	+	0.550544i
$399$		0			0
$400$	−3.60826	−	3.46128i	−0.180413	−	0.173064i
$401$	2.84720	+	1.64383i	0.142183	+	0.0820891i	0.569404	−	0.822058i	$-0.307174\pi$
$401$	2.84720	+	1.64383i	0.142183	+	0.0820891i	−0.427221	+	0.904147i	$0.640507\pi$
$402$		0			0
$403$	3.08567	−	1.78151i	0.153708	−	0.0887436i
$404$	−0.447091	−	0.774384i	−0.0222436	−	0.0385271i
$405$		0			0
$406$	3.95971	+	12.6481i	0.196517	+	0.627713i
$407$	3.62471	−	6.27819i	0.179670	−	0.311198i
$408$		0			0
$409$			28.9897i			1.43345i	0.697355	+	0.716725i	$0.254360\pi$
$409$			28.9897i			1.43345i	−0.697355	+	0.716725i	$0.745640\pi$
$410$	15.1327	−	2.15249i	0.747352	−	0.106304i
$411$		0			0
$412$	−6.77551	+	11.7355i	−0.333805	+	0.578168i
$413$	18.2356	+	16.7781i	0.897314	+	0.825594i
$414$		0			0
$415$	−19.8529	+	15.5642i	−0.974542	+	0.764015i
$416$	−0.341322	−	0.591187i	−0.0167347	−	0.0289853i
$417$		0			0
$418$	17.8262	−	30.8759i	0.871907	−	1.51019i
$419$	−15.2535	−	26.4199i	−0.745183	−	1.29069i	−0.950109	−	0.311917i	$-0.899029\pi$
$419$	−15.2535	−	26.4199i	−0.745183	−	1.29069i	0.204926	−	0.978777i	$-0.434305\pi$
$420$		0			0
$421$	3.34147	−	5.78760i	0.162853	−	0.282070i	−0.773038	−	0.634360i	$-0.781264\pi$
$421$	3.34147	−	5.78760i	0.162853	−	0.282070i	0.935891	+	0.352290i	$0.114597\pi$
$422$	6.82852	+	11.8273i	0.332407	+	0.575746i
$423$		0			0
$424$	0.983879	−	1.70413i	0.0477814	−	0.0827598i
$425$	9.22381	+	31.7671i	0.447420	+	1.54093i
$426$		0			0
$427$	25.6444	−	27.8721i	1.24102	−	1.34882i
$428$	2.12855	+	3.68676i	0.102887	+	0.178206i
$429$		0			0
$430$	−4.17548	+	3.27347i	−0.201360	+	0.157861i
$431$	16.7004	+	9.64197i	0.804429	+	0.464437i	0.845017	−	0.534739i	$-0.179590\pi$
$431$	16.7004	+	9.64197i	0.804429	+	0.464437i	−0.0405887	+	0.999176i	$0.512923\pi$
$432$		0			0
$433$	−12.0085			−0.577094			−0.288547	−	0.957466i	$-0.593172\pi$
$433$	−12.0085			−0.577094			−0.288547	+	0.957466i	$0.593172\pi$
$434$	9.35013	−	10.1624i	0.448820	−	0.487810i
$435$		0			0
$436$	3.35599	−	5.81274i	0.160723	−	0.278380i
$437$			27.4040i			1.31091i
$438$		0			0
$439$		−	13.4721i		−	0.642989i	−0.946911	−	0.321495i	$-0.895815\pi$
$439$		−	13.4721i		−	0.642989i	0.946911	−	0.321495i	$-0.104185\pi$
$440$	1.43751	+	10.1061i	0.0685305	+	0.481791i
$441$		0			0
$442$			4.51626i			0.214816i
$443$	−7.01072			−0.333090			−0.166545	−	0.986034i	$-0.553261\pi$
$443$	−7.01072			−0.333090			−0.166545	+	0.986034i	$0.553261\pi$
$444$		0			0
$445$	3.27278	−	0.465524i	0.155145	−	0.0220680i
$446$	−13.5359	+	23.4449i	−0.640945	+	1.11015i
$447$		0			0
$448$	−1.94702	−	1.79140i	−0.0919880	−	0.0846357i
$449$		−	12.1011i		−	0.571086i	−0.958366	−	0.285543i	$-0.907826\pi$
$449$		−	12.1011i		−	0.571086i	0.958366	−	0.285543i	$-0.0921740\pi$
$450$		0			0
$451$	−27.0248	−	15.6028i	−1.27255	−	0.734705i
$452$	−3.41846	−	5.92094i	−0.160791	−	0.278498i
$453$		0			0
$454$	6.72233	−	3.88114i	0.315494	−	0.182151i
$455$	−3.32747	−	2.28868i	−0.155994	−	0.107295i
$456$		0			0
$457$		−	19.0392i		−	0.890617i	−0.895377	−	0.445309i	$-0.853094\pi$
$457$		−	19.0392i		−	0.890617i	0.895377	−	0.445309i	$-0.146906\pi$
$458$	−0.431712	−	0.249249i	−0.0201726	−	0.0116466i
$459$		0			0
$460$	−4.84092	−	6.17485i	−0.225709	−	0.287904i
$461$	−6.78876	+	11.7585i	−0.316184	+	0.547647i	−0.979689	−	0.200525i	$-0.935735\pi$
$461$	−6.78876	+	11.7585i	−0.316184	+	0.547647i	0.663504	+	0.748172i	$0.269068\pi$
$462$		0			0
$463$	29.4895	−	17.0258i	1.37049	−	0.791254i	0.379502	−	0.925191i	$-0.376095\pi$
$463$	29.4895	−	17.0258i	1.37049	−	0.791254i	0.990990	+	0.133937i	$0.0427619\pi$
$464$	4.33820	+	2.50466i	0.201396	+	0.116276i
$465$		0			0
$466$	8.94844	+	15.4992i	0.414529	+	0.717985i
$467$	12.7222	−	7.34517i	0.588714	−	0.339894i	−0.175875	−	0.984412i	$-0.556275\pi$
$467$	12.7222	−	7.34517i	0.588714	−	0.339894i	0.764589	+	0.644519i	$0.222942\pi$
$468$		0			0
$469$	13.0098	−	14.1399i	0.600735	−	0.652921i
$470$	−7.91660	−	3.18317i	−0.365166	−	0.146829i
$471$		0			0
$472$	9.36589			0.431100
$473$	10.8319			0.498053
$474$		0			0
$475$	37.9202	+	9.32041i	1.73990	+	0.427650i
$476$	5.22960	+	16.7044i	0.239698	+	0.765643i
$477$		0			0
$478$	23.9059	−	13.8021i	1.09343	−	0.631291i
$479$	−2.51204	−	4.35098i	−0.114778	−	0.198801i	0.802913	−	0.596096i	$-0.203282\pi$
$479$	−2.51204	−	4.35098i	−0.114778	−	0.198801i	−0.917691	+	0.397295i	$0.869949\pi$
$480$		0			0
$481$	0.938812	+	0.542024i	0.0428062	+	0.0247141i
$482$	12.1606	−	7.02092i	0.553899	−	0.319794i
$483$		0			0
$484$	4.92005	−	8.52177i	0.223639	−	0.387353i
$485$	−12.1476	−	15.4949i	−0.551595	−	0.703589i
$486$		0			0
$487$	−12.8332	−	7.40923i	−0.581526	−	0.335744i	0.180213	−	0.983628i	$-0.442321\pi$
$487$	−12.8332	−	7.40923i	−0.581526	−	0.335744i	−0.761740	+	0.647883i	$0.775654\pi$
$488$		−	14.3153i		−	0.648021i
$489$		0			0
$490$	−14.9575	−	4.61215i	−0.675713	−	0.208356i
$491$	7.03712	−	4.06288i	0.317581	−	0.183355i	−0.332733	−	0.943021i	$-0.607971\pi$
$491$	7.03712	−	4.06288i	0.317581	−	0.183355i	0.650314	+	0.759666i	$0.274637\pi$
$492$		0			0
$493$	−16.5704	−	28.7008i	−0.746293	−	1.29262i
$494$	4.61704	+	2.66565i	0.207730	+	0.119933i
$495$		0			0
$496$		−	5.21945i		−	0.234360i
$497$	−15.1926	+	16.5124i	−0.681483	+	0.740684i
$498$		0			0
$499$	−0.852478	+	1.47654i	−0.0381622	+	0.0660988i	−0.884476	−	0.466586i	$-0.845484\pi$
$499$	−0.852478	+	1.47654i	−0.0381622	+	0.0660988i	0.846313	+	0.532685i	$0.178817\pi$
$500$	−10.1909	+	4.59847i	−0.455750	+	0.205650i
$501$		0			0
$502$	−16.0764			−0.717526
$503$		−	33.2589i		−	1.48294i	−0.670985	−	0.741471i	$-0.734129\pi$
$503$		−	33.2589i		−	1.48294i	0.670985	−	0.741471i	$-0.265871\pi$
$504$		0			0
$505$	−1.97953	+	0.281570i	−0.0880878	+	0.0125297i
$506$			16.0186i			0.712116i
$507$		0			0
$508$		−	11.2278i		−	0.498152i
$509$	−3.37974	+	5.85388i	−0.149804	+	0.259469i	−0.931155	−	0.364623i	$-0.881198\pi$
$509$	−3.37974	+	5.85388i	−0.149804	+	0.259469i	0.781351	+	0.624092i	$0.214531\pi$
$510$		0			0
$511$	3.71250	−	1.16227i	0.164231	−	0.0514156i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−22.0687	−	12.7414i	−0.973409	−	0.561998i
$515$	18.6949	+	23.8464i	0.823797	+	1.05080i
$516$		0			0
$517$	8.70996	+	15.0861i	0.383063	+	0.663485i
$518$	4.10004	+	0.917693i	0.180145	+	0.0403211i
$519$		0			0
$520$	−1.51123	+	0.214959i	−0.0662717	+	0.00942656i
$521$	20.1496	−	34.9001i	0.882770	−	1.52900i	0.0345209	−	0.999404i	$-0.489009\pi$
$521$	20.1496	−	34.9001i	0.882770	−	1.52900i	0.848249	−	0.529598i	$-0.177657\pi$
$522$		0			0
$523$	6.81446	+	11.8030i	0.297975	+	0.516109i	0.975673	−	0.219233i	$-0.0703553\pi$
$523$	6.81446	+	11.8030i	0.297975	+	0.516109i	−0.677697	+	0.735341i	$0.737022\pi$
$524$	1.13293	−	1.96229i	0.0494921	−	0.0857228i
$525$		0			0
$526$	12.7152	+	22.0234i	0.554410	+	0.960266i
$527$	−17.2655	+	29.9047i	−0.752097	+	1.30267i
$528$		0			0
$529$	5.34367	+	9.25551i	0.232334	+	0.402414i
$530$	−2.71471	−	3.46276i	−0.117920	−	0.150413i
$531$		0			0
$532$	20.1638	+	4.51318i	0.874212	+	0.195671i
$533$	2.33317	−	4.04116i	0.101061	−	0.175042i
$534$		0			0
$535$	9.42431	−	1.34052i	0.407448	−	0.0579559i
$536$		−	7.26234i		−	0.313685i
$537$		0			0
$538$	−12.2442	+	21.2076i	−0.527886	+	0.914326i
$539$	18.2226	+	26.2508i	0.784902	+	1.13070i
$540$		0			0
$541$	4.14554	+	7.18028i	0.178231	+	0.308704i	0.941275	−	0.337642i	$-0.109629\pi$
$541$	4.14554	+	7.18028i	0.178231	+	0.308704i	−0.763044	+	0.646347i	$0.776296\pi$
$542$	17.8062	−	10.2804i	0.764844	−	0.441583i
$543$		0			0
$544$	5.72947	+	3.30791i	0.245649	+	0.141826i
$545$	−9.25982	−	11.8114i	−0.396647	−	0.505944i
$546$		0			0
$547$	13.0289	+	7.52224i	0.557076	+	0.321628i	0.751971	−	0.659196i	$-0.229103\pi$
$547$	13.0289	+	7.52224i	0.557076	+	0.321628i	−0.194895	+	0.980824i	$0.562437\pi$
$548$	1.93119	+	3.34491i	0.0824962	+	0.142888i
$549$		0			0
$550$	22.1658	+	5.44811i	0.945151	+	0.232308i
$551$	−39.1217			−1.66664
$552$		0			0
$553$	−2.28896	−	2.10601i	−0.0973365	−	0.0895567i
$554$	−1.70051	+	0.981792i	−0.0722479	+	0.0417124i
$555$		0			0
$556$	−11.4418	+	6.60593i	−0.485241	+	0.280154i
$557$	−6.05011	+	10.4791i	−0.256352	+	0.444014i	−0.965262	−	0.261285i	$-0.915854\pi$
$557$	−6.05011	+	10.4791i	−0.256352	+	0.444014i	0.708910	+	0.705299i	$0.249187\pi$
$558$		0			0
$559$			1.61976i			0.0685085i
$560$	−5.34069	+	2.54500i	−0.225685	+	0.107546i
$561$		0			0
$562$	−25.5282	−	14.7387i	−1.07684	−	0.621715i
$563$		−	27.6595i		−	1.16571i	−0.812577	−	0.582854i	$-0.801936\pi$
$563$		−	27.6595i		−	1.16571i	0.812577	−	0.582854i	$-0.198064\pi$
$564$		0			0
$565$	−15.1355	+	2.15288i	−0.636753	+	0.0905725i
$566$	−25.1313			−1.05635
$567$		0			0
$568$			8.48088i			0.355850i
$569$		−	23.8789i		−	1.00105i	−0.865721	−	0.500527i	$-0.833140\pi$
$569$		−	23.8789i		−	1.00105i	0.865721	−	0.500527i	$-0.166860\pi$
$570$		0			0
$571$	29.5138			1.23511			0.617556	−	0.786527i	$-0.288123\pi$
$571$	29.5138			1.23511			0.617556	+	0.786527i	$0.288123\pi$
$572$	2.69883	+	1.55817i	0.112844	+	0.0651503i
$573$		0			0
$574$	3.95026	−	17.6488i	0.164881	−	0.736647i
$575$	−16.8488	+	4.89217i	−0.702645	+	0.204018i
$576$		0			0
$577$	10.1979	−	17.6634i	0.424546	−	0.735335i	−0.571832	−	0.820371i	$-0.693767\pi$
$577$	10.1979	−	17.6634i	0.424546	−	0.735335i	0.996378	+	0.0850355i	$0.0271004\pi$
$578$	−13.3846	−	23.1828i	−0.556725	−	0.964277i
$579$		0			0
$580$	8.81514	−	6.91084i	0.366029	−	0.286957i
$581$	8.91782	+	28.4852i	0.369973	+	1.18177i
$582$		0			0
$583$			8.98301i			0.372038i
$584$	0.735176	−	1.27336i	0.0304218	−	0.0526921i
$585$		0			0
$586$	26.8539	−	15.5041i	1.10933	−	0.640470i
$587$	−32.0984	−	18.5320i	−1.32484	−	0.764899i	−0.340346	−	0.940300i	$-0.610544\pi$
$587$	−32.0984	−	18.5320i	−1.32484	−	0.764899i	−0.984497	+	0.175401i	$0.943878\pi$
$588$		0			0
$589$	20.3814	+	35.3016i	0.839800	+	1.45458i
$590$	7.81292	−	19.4309i	0.321653	−	0.799955i
$591$		0			0
$592$	1.37526	−	0.794006i	0.0565228	−	0.0326334i
$593$	9.28698	−	5.36184i	0.381371	−	0.220184i	−0.297044	−	0.954864i	$-0.596001\pi$
$593$	9.28698	−	5.36184i	0.381371	−	0.220184i	0.678414	+	0.734679i	$0.262667\pi$
$594$		0			0
$595$	39.0180	+	3.08504i	1.59958	+	0.126474i
$596$	−3.72883	−	2.15284i	−0.152739	−	0.0881837i
$597$		0			0
$598$	−2.39536			−0.0979535
$599$			17.1036i			0.698832i	0.936968	+	0.349416i	$0.113620\pi$
$599$			17.1036i			0.698832i	−0.936968	+	0.349416i	$0.886380\pi$
$600$		0			0
$601$	20.0797	+	11.5930i	0.819069	+	0.472890i	0.850095	−	0.526629i	$-0.176544\pi$
$601$	20.0797	+	11.5930i	0.819069	+	0.472890i	−0.0310264	+	0.999519i	$0.509878\pi$
$602$	1.87560	+	5.99103i	0.0764438	+	0.244176i
$603$		0			0
$604$	−8.02202	−	13.8945i	−0.326411	−	0.565361i
$605$	−13.5754	−	17.3161i	−0.551917	−	0.703999i
$606$		0			0
$607$	−10.1717	+	17.6179i	−0.412857	+	0.715089i	−0.995201	−	0.0978537i	$-0.968802\pi$
$607$	−10.1717	+	17.6179i	−0.412857	+	0.715089i	0.582344	+	0.812942i	$0.302136\pi$
$608$	6.76346	−	3.90489i	0.274295	−	0.158364i
$609$		0			0
$610$	−29.6990	−	11.9416i	−1.20248	−	0.483502i
$611$	−2.25591	+	1.30245i	−0.0912642	+	0.0526914i
$612$		0			0
$613$	−5.31424	−	3.06818i	−0.214640	−	0.123922i	0.388826	−	0.921311i	$-0.372881\pi$
$613$	−5.31424	−	3.06818i	−0.214640	−	0.123922i	−0.603466	+	0.797389i	$0.706214\pi$
$614$	4.89776			0.197658
$615$		0			0
$616$	11.7865	+	2.63812i	0.474891	+	0.106293i
$617$	−10.4874	−	18.1648i	−0.422208	−	0.731286i	0.573947	−	0.818892i	$-0.305412\pi$
$617$	−10.4874	−	18.1648i	−0.422208	−	0.731286i	−0.996155	+	0.0876065i	$0.972078\pi$
$618$		0			0
$619$	19.5443	−	11.2839i	0.785550	−	0.453538i	−0.0528436	−	0.998603i	$-0.516828\pi$
$619$	19.5443	−	11.2839i	0.785550	−	0.453538i	0.838394	+	0.545065i	$0.183495\pi$
$620$	−10.8285	−	4.35401i	−0.434882	−	0.174861i
$621$		0			0
$622$	9.06956			0.363656
$623$	0.854330	−	3.81695i	0.0342280	−	0.152923i
$624$		0			0
$625$	1.03906	+	24.9784i	0.0415624	+	0.999136i
$626$	−30.0835			−1.20238
$627$		0			0
$628$	10.1182			0.403759
$629$	−10.5060			−0.418902
$630$		0			0
$631$	15.1577			0.603418			0.301709	−	0.953400i	$-0.402443\pi$
$631$	15.1577			0.603418			0.301709	+	0.953400i	$0.402443\pi$
$632$	−1.17562			−0.0467637
$633$		0			0
$634$	−3.37219			−0.133927
$635$	−23.2936	−	9.36608i	−0.924378	−	0.371682i
$636$		0			0
$637$	−3.92542	+	2.72492i	−0.155531	+	0.107965i
$638$	−22.8680			−0.905354
$639$		0			0
$640$	−0.834189	+	2.07464i	−0.0329742	+	0.0820073i
$641$	13.5794	−	7.84005i	0.536353	−	0.309663i	−0.207247	−	0.978289i	$-0.566450\pi$
$641$	13.5794	−	7.84005i	0.536353	−	0.309663i	0.743599	+	0.668625i	$0.233117\pi$
$642$		0			0
$643$	−9.19102	−	15.9193i	−0.362458	−	0.627796i	0.625906	−	0.779898i	$-0.284729\pi$
$643$	−9.19102	−	15.9193i	−0.362458	−	0.627796i	−0.988365	+	0.152102i	$0.951396\pi$
$644$	−8.85975	+	2.77371i	−0.349123	+	0.109299i
$645$		0			0
$646$	−51.6681			−2.03286
$647$	−2.50834	−	1.44819i	−0.0986129	−	0.0569342i	0.449883	−	0.893088i	$-0.351466\pi$
$647$	−2.50834	−	1.44819i	−0.0986129	−	0.0569342i	−0.548495	+	0.836154i	$0.684799\pi$
$648$		0			0
$649$	−37.0279	+	21.3781i	−1.45347	+	0.839164i
$650$	−0.814687	+	3.31457i	−0.0319547	+	0.130008i
$651$		0			0
$652$	−19.6914	+	11.3688i	−0.771175	+	0.445238i
$653$	−12.9351	+	22.4042i	−0.506189	+	0.876744i	0.493786	+	0.869584i	$0.335613\pi$
$653$	−12.9351	+	22.4042i	−0.506189	+	0.876744i	−0.999974	+	0.00716072i	$0.997721\pi$
$654$		0			0
$655$	−3.12596	−	3.98733i	−0.122141	−	0.155798i
$656$	−3.41784	−	5.91987i	−0.133444	−	0.231132i
$657$		0			0
$658$	−6.83579	+	7.42962i	−0.266487	+	0.289637i
$659$	−3.49291	−	2.01663i	−0.136064	−	0.0785568i	0.430423	−	0.902627i	$-0.358365\pi$
$659$	−3.49291	−	2.01663i	−0.136064	−	0.0785568i	−0.566487	+	0.824071i	$0.691698\pi$
$660$		0			0
$661$		−	48.8240i		−	1.89903i	−0.313719	−	0.949516i	$-0.601575\pi$
$661$		−	48.8240i		−	1.89903i	0.313719	−	0.949516i	$-0.398425\pi$
$662$	−10.9348			−0.424994
$663$		0			0
$664$	9.77023	+	5.64084i	0.379158	+	0.218907i
$665$	26.1836	−	38.0678i	1.01536	−	1.47621i
$666$		0			0
$667$	15.2225	−	8.78870i	0.589417	−	0.340300i
$668$	11.3198	−	6.53552i	0.437978	−	0.252867i
$669$		0			0
$670$	−15.0667	−	6.05816i	−0.582079	−	0.234047i
$671$	32.6753	+	56.5952i	1.26141	+	2.18483i
$672$		0			0
$673$	26.8527	+	15.5034i	1.03509	+	0.597612i	0.918440	−	0.395560i	$-0.129450\pi$
$673$	26.8527	+	15.5034i	1.03509	+	0.597612i	0.116655	+	0.993173i	$0.462783\pi$
$674$	1.26189	−	0.728550i	0.0486060	−	0.0280627i
$675$		0			0
$676$	6.26700	−	10.8548i	0.241038	−	0.417491i
$677$			35.3766i			1.35963i	0.733383	+	0.679816i	$0.237940\pi$
$677$			35.3766i			1.35963i	−0.733383	+	0.679816i	$0.762060\pi$
$678$		0			0
$679$	−22.2323	+	6.96024i	−0.853199	+	0.267109i
$680$	11.6422	−	9.12717i	0.446458	−	0.350011i
$681$		0			0
$682$	11.9136	+	20.6350i	0.456197	+	0.790157i
$683$	−16.9554	+	29.3676i	−0.648780	+	1.12372i	0.334635	+	0.942348i	$0.391387\pi$
$683$	−16.9554	+	29.3676i	−0.648780	+	1.12372i	−0.983415	+	0.181371i	$0.941946\pi$
$684$		0			0
$685$	8.55046	−	1.21623i	0.326696	−	0.0464697i
$686$	−11.3637	+	14.6242i	−0.433868	+	0.558353i
$687$		0			0
$688$	2.05488	+	1.18639i	0.0783416	+	0.0452305i
$689$	−1.34328			−0.0511749
$690$		0			0
$691$		−	12.2957i		−	0.467751i	−0.972267	−	0.233875i	$-0.924859\pi$
$691$		−	12.2957i		−	0.467751i	0.972267	−	0.233875i	$-0.0751407\pi$
$692$			0.697127i			0.0265008i
$693$		0			0
$694$	−35.8194			−1.35969
$695$	4.16030	+	29.2482i	0.157809	+	1.10945i
$696$		0			0
$697$			45.2236i			1.71297i
$698$	−2.63799	−	1.52304i	−0.0998493	−	0.0576480i
$699$		0			0
$700$	0.824810	+	13.2030i	0.0311749	+	0.499027i
$701$		−	15.9333i		−	0.601791i	−0.953657	−	0.300895i	$-0.902714\pi$
$701$		−	15.9333i		−	0.601791i	0.953657	−	0.300895i	$-0.0972855\pi$
$702$		0			0
$703$	−6.20101	+	10.7405i	−0.233875	+	0.405084i
$704$	3.95349	−	2.28255i	0.149003	−	0.0860268i
$705$		0			0
$706$	−29.5595	+	17.0662i	−1.11249	+	0.642295i
$707$	−0.516737	+	2.30866i	−0.0194339	+	0.0868261i
$708$		0			0
$709$	9.80213			0.368127			0.184063	−	0.982914i	$-0.441075\pi$
$709$	9.80213			0.368127			0.184063	+	0.982914i	$0.441075\pi$
$710$	17.5948	+	7.07465i	0.660320	+	0.265507i
$711$		0			0
$712$	−0.739183	−	1.28030i	−0.0277020	−	0.0479814i
$713$	−15.8610	−	9.15737i	−0.594000	−	0.342946i
$714$		0			0
$715$	5.48397	−	4.29929i	0.205089	−	0.160784i
$716$	−10.6754	−	6.16342i	−0.398957	−	0.230338i
$717$		0			0
$718$	21.0726	−	12.1663i	0.786421	−	0.454040i
$719$	10.7248	+	18.5760i	0.399969	+	0.692767i	0.993722	−	0.111881i	$-0.0356874\pi$
$719$	10.7248	+	18.5760i	0.399969	+	0.692767i	−0.593752	+	0.804648i	$0.702354\pi$
$720$		0			0
$721$	34.2151	−	10.7117i	1.27424	−	0.398923i
$722$	−20.9963	+	36.3667i	−0.781402	+	1.35343i
$723$		0			0
$724$			11.6266i			0.432100i
$725$	−6.98401	−	24.0532i	−0.259380	−	0.893313i
$726$		0			0
$727$	1.49310	−	2.58612i	0.0553760	−	0.0959140i	−0.837009	−	0.547190i	$-0.815698\pi$
$727$	1.49310	−	2.58612i	0.0553760	−	0.0959140i	0.892385	+	0.451276i	$0.149031\pi$
$728$	−0.394492	+	1.76250i	−0.0146209	+	0.0653225i
$729$		0			0
$730$	−2.02849	−	2.58745i	−0.0750778	−	0.0957658i
$731$	−7.84892	−	13.5947i	−0.290303	−	0.502819i
$732$		0			0
$733$	23.3598	−	40.4604i	0.862816	−	1.49444i	−0.00638426	−	0.999980i	$-0.502032\pi$
$733$	23.3598	−	40.4604i	0.862816	−	1.49444i	0.869200	−	0.494461i	$-0.164634\pi$
$734$	−6.72343	−	11.6453i	−0.248166	−	0.429837i
$735$		0			0
$736$	−1.75447	+	3.03883i	−0.0646706	+	0.112013i
$737$	16.5766	+	28.7116i	0.610608	+	1.05760i
$738$		0			0
$739$	−3.52514	+	6.10572i	−0.129674	+	0.224603i	−0.923550	−	0.383477i	$-0.874727\pi$
$739$	−3.52514	+	6.10572i	−0.129674	+	0.224603i	0.793876	+	0.608080i	$0.208060\pi$
$740$	−0.500051	−	3.51552i	−0.0183822	−	0.129233i
$741$		0			0
$742$	−4.96841	+	1.55545i	−0.182396	+	0.0571024i
$743$	−7.76460	−	13.4487i	−0.284856	−	0.493384i	0.687719	−	0.725977i	$-0.258612\pi$
$743$	−7.76460	−	13.4487i	−0.284856	−	0.493384i	−0.972574	+	0.232593i	$0.925279\pi$
$744$		0			0
$745$	−7.57691	+	5.94010i	−0.277596	+	0.217628i
$746$	2.42626	+	1.40080i	0.0888315	+	0.0512869i
$747$		0			0
$748$	−30.2019			−1.10429
$749$	2.46013	−	10.9913i	0.0898912	−	0.401612i
$750$		0			0
$751$	10.1062	−	17.5044i	0.368779	−	0.638744i	−0.620596	−	0.784131i	$-0.713109\pi$
$751$	10.1062	−	17.5044i	0.368779	−	0.638744i	0.989375	+	0.145387i	$0.0464426\pi$
$752$			3.81589i			0.139151i
$753$		0			0
$754$		−	3.41958i		−	0.124534i
$755$	−35.5180	+	5.05213i	−1.29263	+	0.183866i
$756$		0			0
$757$			6.00333i			0.218195i	0.994031	+	0.109097i	$0.0347960\pi$
$757$			6.00333i			0.218195i	−0.994031	+	0.109097i	$0.965204\pi$
$758$	13.2036			0.479577
$759$		0			0
$760$	−2.45923	−	17.2892i	−0.0892057	−	0.627144i
$761$	21.1958	−	36.7123i	0.768349	−	1.33082i	−0.170109	−	0.985425i	$-0.554412\pi$
$761$	21.1958	−	36.7123i	0.768349	−	1.33082i	0.938458	−	0.345394i	$-0.112255\pi$
$762$		0			0
$763$	−16.9471	+	5.30560i	−0.613527	+	0.192076i
$764$			0.589056i			0.0213113i
$765$		0			0
$766$	2.77030	+	1.59943i	0.100095	+	0.0577899i
$767$	−3.19679	−	5.53700i	−0.115429	−	0.199929i
$768$		0			0
$769$	33.6414	−	19.4229i	1.21314	−	0.700406i	0.249697	−	0.968324i	$-0.419669\pi$
$769$	33.6414	−	19.4229i	1.21314	−	0.700406i	0.963442	+	0.267918i	$0.0863356\pi$
$770$	15.3053	−	22.2520i	0.551564	−	0.801907i
$771$		0			0
$772$		−	14.0161i		−	0.504452i
$773$	−16.6613	−	9.61939i	−0.599265	−	0.345986i	0.169488	−	0.985532i	$-0.445789\pi$
$773$	−16.6613	−	9.61939i	−0.599265	−	0.345986i	−0.768752	+	0.639547i	$0.779122\pi$
$774$		0			0
$775$	−18.0660	+	18.8331i	−0.648950	+	0.676506i
$776$	−4.40260	+	7.62553i	−0.158044	+	0.273741i
$777$		0			0
$778$	−16.1572	+	9.32835i	−0.579263	+	0.334437i
$779$	46.2329	+	26.6925i	1.65646	+	0.956360i
$780$		0			0
$781$	−19.3580	−	33.5291i	−0.692684	−	1.19976i
$782$	20.1044	−	11.6073i	0.718931	−	0.415075i
$783$		0			0
$784$	0.581771	+	6.97578i	0.0207775	+	0.249135i
$785$	8.44046	−	20.9915i	0.301253	−	0.749220i
$786$		0			0
$787$	−32.0859			−1.14374			−0.571869	−	0.820345i	$-0.693781\pi$
$787$	−32.0859			−1.14374			−0.571869	+	0.820345i	$0.693781\pi$
$788$	−10.4933			−0.373808
$789$		0			0
$790$	−0.980691	+	2.43899i	−0.0348914	+	0.0867755i
$791$	−3.95097	+	17.6520i	−0.140480	+	0.627633i
$792$		0			0
$793$	−8.46300	+	4.88611i	−0.300530	+	0.173511i
$794$	−5.38403	−	9.32542i	−0.191072	−	0.330947i
$795$		0			0
$796$	−19.0237	−	10.9833i	−0.674276	−	0.389294i
$797$	39.6425	−	22.8876i	1.40421	−	0.810721i	0.409389	−	0.912360i	$-0.365742\pi$
$797$	39.6425	−	22.8876i	1.40421	−	0.810721i	0.994821	+	0.101639i	$0.0324086\pi$
$798$		0			0
$799$	12.6226	−	21.8631i	0.446557	−	0.773459i
$800$	3.60826	+	3.46128i	0.127571	+	0.122375i
$801$		0			0
$802$	−2.84720	−	1.64383i	−0.100538	−	0.0580458i
$803$			6.71230i			0.236872i
$804$		0			0
$805$	−1.63626	+	20.6946i	−0.0576707	+	0.729388i
$806$	−3.08567	+	1.78151i	−0.108688	+	0.0627512i
$807$		0			0
$808$	0.447091	+	0.774384i	0.0157286	+	0.0272428i
$809$	15.0301	+	8.67763i	0.528430	+	0.305089i	0.740377	−	0.672192i	$-0.234647\pi$
$809$	15.0301	+	8.67763i	0.528430	+	0.305089i	−0.211947	+	0.977281i	$0.567980\pi$
$810$		0			0
$811$			42.8371i			1.50421i	0.659041	+	0.752107i	$0.270962\pi$
$811$			42.8371i			1.50421i	−0.659041	+	0.752107i	$0.729038\pi$
$812$	−3.95971	−	12.6481i	−0.138959	−	0.443860i
$813$		0			0
$814$	−3.62471	+	6.27819i	−0.127046	+	0.220050i
$815$	7.15989	+	50.3363i	0.250800	+	1.76320i
$816$		0			0
$817$	−18.5308			−0.648311
$818$		−	28.9897i		−	1.01360i
$819$		0			0
$820$	−15.1327	+	2.15249i	−0.528457	+	0.0751684i
$821$			8.28288i			0.289074i	0.989499	+	0.144537i	$0.0461693\pi$
$821$			8.28288i			0.289074i	−0.989499	+	0.144537i	$0.953831\pi$
$822$		0			0
$823$			27.0685i			0.943549i	0.881719	+	0.471775i	$0.156386\pi$
$823$			27.0685i			0.943549i	−0.881719	+	0.471775i	$0.843614\pi$
$824$	6.77551	−	11.7355i	0.236036	−	0.408827i
$825$		0			0
$826$	−18.2356	−	16.7781i	−0.634497	−	0.583783i
$827$	−35.7680			−1.24377			−0.621887	−	0.783107i	$-0.713634\pi$
$827$	−35.7680			−1.24377			−0.621887	+	0.783107i	$0.713634\pi$
$828$		0			0
$829$	2.71605	+	1.56811i	0.0943322	+	0.0544627i	0.546424	−	0.837509i	$-0.315989\pi$
$829$	2.71605	+	1.56811i	0.0943322	+	0.0544627i	−0.452092	+	0.891971i	$0.649322\pi$
$830$	19.8529	−	15.5642i	0.689105	−	0.540240i
$831$		0			0
$832$	0.341322	+	0.591187i	0.0118332	+	0.0204957i
$833$	19.7420	−	41.8920i	0.684021	−	1.45147i
$834$		0			0
$835$	−4.11595	−	28.9365i	−0.142438	−	1.00139i
$836$	−17.8262	+	30.8759i	−0.616532	+	1.06786i
$837$		0			0
$838$	15.2535	+	26.4199i	0.526924	+	0.912659i
$839$	10.4737	−	18.1410i	0.361593	−	0.626298i	−0.626630	−	0.779317i	$-0.715566\pi$
$839$	10.4737	−	18.1410i	0.361593	−	0.626298i	0.988223	+	0.153019i	$0.0488996\pi$
$840$		0			0
$841$	−1.95336	−	3.38332i	−0.0673573	−	0.116666i
$842$	−3.34147	+	5.78760i	−0.115155	+	0.199454i
$843$		0			0
$844$	−6.82852	−	11.8273i	−0.235047	−	0.407114i
$845$	−17.2919	−	22.0567i	−0.594858	−	0.758773i
$846$		0			0
$847$	−24.8453	+	7.77829i	−0.853696	+	0.267265i
$848$	−0.983879	+	1.70413i	−0.0337866	+	0.0585200i
$849$		0			0
$850$	−9.22381	−	31.7671i	−0.316374	−	1.08960i
$851$		−	5.57224i		−	0.191014i
$852$		0			0
$853$	−5.19207	+	8.99293i	−0.177773	+	0.307912i	−0.941117	−	0.338080i	$-0.890223\pi$
$853$	−5.19207	+	8.99293i	−0.177773	+	0.307912i	0.763344	+	0.645992i	$0.223556\pi$
$854$	−25.6444	+	27.8721i	−0.877532	+	0.953763i
$855$		0			0
$856$	−2.12855	−	3.68676i	−0.0727524	−	0.126011i
$857$	−10.6711	+	6.16097i	−0.364518	+	0.210455i	−0.671061	−	0.741402i	$-0.734161\pi$
$857$	−10.6711	+	6.16097i	−0.364518	+	0.210455i	0.306543	+	0.951857i	$0.400828\pi$
$858$		0			0
$859$	−2.83794	−	1.63848i	−0.0968291	−	0.0559043i	0.450804	−	0.892623i	$-0.351138\pi$
$859$	−2.83794	−	1.63848i	−0.0968291	−	0.0559043i	−0.547633	+	0.836719i	$0.684471\pi$
$860$	4.17548	−	3.27347i	0.142383	−	0.111624i
$861$		0			0
$862$	−16.7004	−	9.64197i	−0.568817	−	0.328407i
$863$	−13.9352	−	24.1365i	−0.474361	−	0.821617i	0.525208	−	0.850974i	$-0.323987\pi$
$863$	−13.9352	−	24.1365i	−0.474361	−	0.821617i	−0.999569	+	0.0293570i	$0.990654\pi$
$864$		0			0
$865$	1.44629	+	0.581536i	0.0491753	+	0.0197728i
$866$	12.0085			0.408067
$867$		0			0
$868$	−9.35013	+	10.1624i	−0.317364	+	0.344933i
$869$	4.64781	−	2.68341i	0.157666	−	0.0910286i
$870$		0			0
$871$	−4.29340	+	2.47880i	−0.145476	+	0.0839909i
$872$	−3.35599	+	5.81274i	−0.113648	+	0.196844i
$873$		0			0
$874$		−	27.4040i		−	0.926955i
$875$	28.0796	+	9.30262i	0.949262	+	0.314486i
$876$		0			0
$877$	−28.6808	−	16.5588i	−0.968481	−	0.559153i	−0.0697079	−	0.997567i	$-0.522207\pi$
$877$	−28.6808	−	16.5588i	−0.968481	−	0.559153i	−0.898773	+	0.438415i	$0.855540\pi$
$878$			13.4721i			0.454662i
$879$		0			0
$880$	−1.43751	−	10.1061i	−0.0484584	−	0.340678i
$881$	5.13912			0.173141			0.0865707	−	0.996246i	$-0.472409\pi$
$881$	5.13912			0.173141			0.0865707	+	0.996246i	$0.472409\pi$
$882$		0			0
$883$			54.5450i			1.83559i	0.397060	+	0.917793i	$0.370031\pi$
$883$			54.5450i			1.83559i	−0.397060	+	0.917793i	$0.629969\pi$
$884$		−	4.51626i		−	0.151898i
$885$		0			0
$886$	7.01072			0.235530
$887$	−40.7398	−	23.5211i	−1.36791	−	0.789762i	−0.377247	−	0.926113i	$-0.623129\pi$
$887$	−40.7398	−	23.5211i	−1.36791	−	0.789762i	−0.990661	+	0.136351i	$0.956463\pi$
$888$		0			0
$889$	−20.1134	+	21.8607i	−0.674583	+	0.733184i
$890$	−3.27278	+	0.465524i	−0.109704	+	0.0156044i
$891$		0			0
$892$	13.5359	−	23.4449i	0.453217	−	0.784994i
$893$	−14.9006	−	25.8087i	−0.498631	−	0.863654i
$894$		0			0
$895$	−21.6921	+	17.0061i	−0.725088	+	0.568450i
$896$	1.94702	+	1.79140i	0.0650454	+	0.0598465i
$897$		0			0
$898$			12.1011i			0.403819i
$899$	13.0729	−	22.6430i	0.436007	−	0.755187i
$900$		0			0
$901$	11.2742	−	6.50918i	0.375599	−	0.216852i
$902$	27.0248	+	15.6028i	0.899826	+	0.519515i
$903$		0			0
$904$	3.41846	+	5.92094i	0.113696	+	0.196927i
$905$	24.1210	+	9.69879i	0.801810	+	0.322399i
$906$		0			0
$907$	10.2762	−	5.93299i	0.341217	−	0.197002i	−0.319593	−	0.947555i	$-0.603546\pi$
$907$	10.2762	−	5.93299i	0.341217	−	0.197002i	0.660810	+	0.750553i	$0.270213\pi$
$908$	−6.72233	+	3.88114i	−0.223088	+	0.128800i
$909$		0			0
$910$	3.32747	+	2.28868i	0.110304	+	0.0758692i
$911$	−28.3773	−	16.3837i	−0.940182	−	0.542815i	−0.0501649	−	0.998741i	$-0.515975\pi$
$911$	−28.3773	−	16.3837i	−0.940182	−	0.542815i	−0.890017	+	0.455926i	$0.849308\pi$
$912$		0			0
$913$	−51.5020			−1.70447
$914$			19.0392i			0.629762i
$915$		0			0
$916$	0.431712	+	0.249249i	0.0142642	+	0.00823542i
$917$	−5.72107	+	1.79108i	−0.188926	+	0.0591468i
$918$		0			0
$919$	10.3565	+	17.9380i	0.341630	+	0.591720i	0.984736	−	0.174057i	$-0.0556878\pi$
$919$	10.3565	+	17.9380i	0.341630	+	0.591720i	−0.643106	+	0.765777i	$0.722354\pi$
$920$	4.84092	+	6.17485i	0.159600	+	0.203579i
$921$		0			0
$922$	6.78876	−	11.7585i	0.223576	−	0.387245i
$923$	5.01379	−	2.89471i	0.165031	−	0.0952806i
$924$		0			0
$925$	−7.71057	−	1.89518i	−0.253522	−	0.0623131i
$926$	−29.4895	+	17.0258i	−0.969084	+	0.559501i
$927$		0			0
$928$	−4.33820	−	2.50466i	−0.142408	−	0.0822195i
$929$	−27.8564			−0.913938			−0.456969	−	0.889483i	$-0.651065\pi$
$929$	−27.8564			−0.913938			−0.456969	+	0.889483i	$0.651065\pi$
$930$		0			0
$931$	−31.1744	−	44.9087i	−1.02170	−	1.47182i
$932$	−8.94844	−	15.4992i	−0.293116	−	0.507692i
$933$		0			0
$934$	−12.7222	+	7.34517i	−0.416283	+	0.240341i
$935$	−25.1941	+	62.6580i	−0.823934	+	2.04914i
$936$		0			0
$937$	−47.7529			−1.56002			−0.780009	−	0.625768i	$-0.784785\pi$
$937$	−47.7529			−1.56002			−0.780009	+	0.625768i	$0.784785\pi$
$938$	−13.0098	+	14.1399i	−0.424784	+	0.461685i
$939$		0			0
$940$	7.91660	+	3.18317i	0.258211	+	0.103824i
$941$	24.1319			0.786677			0.393338	−	0.919394i	$-0.371320\pi$
$941$	24.1319			0.786677			0.393338	+	0.919394i	$0.371320\pi$
$942$		0			0
$943$	−23.9860			−0.781091
$944$	−9.36589			−0.304834
$945$		0			0
$946$	−10.8319			−0.352176
$947$	37.1817			1.20824			0.604122	−	0.796892i	$-0.293524\pi$
$947$	37.1817			1.20824			0.604122	+	0.796892i	$0.293524\pi$
$948$		0			0
$949$	−1.00373			−0.0325824
$950$	−37.9202	−	9.32041i	−1.23030	−	0.302394i
$951$		0			0
$952$	−5.22960	−	16.7044i	−0.169492	−	0.541391i
$953$	−20.4203			−0.661478			−0.330739	−	0.943722i	$-0.607298\pi$
$953$	−20.4203			−0.661478			−0.330739	+	0.943722i	$0.607298\pi$
$954$		0			0
$955$	1.22208	+	0.491384i	0.0395456	+	0.0159008i
$956$	−23.9059	+	13.8021i	−0.773171	+	0.446390i
$957$		0			0
$958$	2.51204	+	4.35098i	0.0811604	+	0.140574i
$959$	2.23202	−	9.97214i	0.0720757	−	0.322017i
$960$		0			0
$961$	3.75733			0.121204
$962$	−0.938812	−	0.542024i	−0.0302685	−	0.0174755i
$963$		0			0
$964$	−12.1606	+	7.02092i	−0.391666	+	0.226129i
$965$	−29.0784	−	11.6921i	−0.936068	−	0.376382i
$966$		0			0
$967$	26.8470	−	15.5001i	0.863341	−	0.498450i	−0.00178853	−	0.999998i	$-0.500569\pi$
$967$	26.8470	−	15.5001i	0.863341	−	0.498450i	0.865130	+	0.501548i	$0.167236\pi$
$968$	−4.92005	+	8.52177i	−0.158136	+	0.273900i
$969$		0			0
$970$	12.1476	+	15.4949i	0.390037	+	0.497513i
$971$	2.43683	+	4.22071i	0.0782015	+	0.135449i	0.902474	−	0.430744i	$-0.141749\pi$
$971$	2.43683	+	4.22071i	0.0782015	+	0.135449i	−0.824273	+	0.566193i	$0.808416\pi$
$972$		0			0
$973$	34.1113	+	7.63498i	1.09356	+	0.244766i
$974$	12.8332	+	7.40923i	0.411201	+	0.237407i
$975$		0			0
$976$			14.3153i			0.458220i
$977$	17.4304			0.557647			0.278823	−	0.960342i	$-0.410056\pi$
$977$	17.4304			0.557647			0.278823	+	0.960342i	$0.410056\pi$
$978$		0			0
$979$	5.84470	+	3.37444i	0.186797	+	0.107848i
$980$	14.9575	+	4.61215i	0.477801	+	0.147330i
$981$		0			0
$982$	−7.03712	+	4.06288i	−0.224563	+	0.129652i
$983$	−10.9451	+	6.31918i	−0.349096	+	0.201551i	−0.664287	−	0.747478i	$-0.731265\pi$
$983$	−10.9451	+	6.31918i	−0.349096	+	0.201551i	0.315191	+	0.949028i	$0.397931\pi$
$984$		0			0
$985$	−8.75338	+	21.7698i	−0.278906	+	0.693643i
$986$	16.5704	+	28.7008i	0.527709	+	0.914019i
$987$		0			0
$988$	−4.61704	−	2.66565i	−0.146888	−	0.0848056i
$989$	7.21045	−	4.16296i	0.229279	−	0.132374i
$990$		0			0
$991$	−5.82563	+	10.0903i	−0.185057	+	0.320529i	−0.943596	−	0.331099i	$-0.892580\pi$
$991$	−5.82563	+	10.0903i	−0.185057	+	0.320529i	0.758538	+	0.651628i	$0.225914\pi$
$992$			5.21945i			0.165718i
$993$		0			0
$994$	15.1926	−	16.5124i	0.481882	−	0.523743i
$995$	−38.6558	+	30.3051i	−1.22547	+	0.960736i
$996$		0			0
$997$	12.1993	+	21.1298i	0.386355	+	0.669186i	0.991956	−	0.126582i	$-0.0404007\pi$
$997$	12.1993	+	21.1298i	0.386355	+	0.669186i	−0.605601	+	0.795768i	$0.707067\pi$
$998$	0.852478	−	1.47654i	0.0269847	−	0.0467389i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.bi.a.899.16		48
3.2	odd	2		630.2.bi.b.479.10	yes	48
5.4	even	2		1890.2.bi.b.899.16		48
7.5	odd	6		1890.2.r.b.89.24		48
9.4	even	3		630.2.r.b.59.7	yes	48
9.5	odd	6		1890.2.r.a.1529.24		48
15.14	odd	2		630.2.bi.a.479.15	yes	48
21.5	even	6		630.2.r.a.299.18	yes	48
35.19	odd	6		1890.2.r.a.89.24		48
45.4	even	6		630.2.r.a.59.18	✓	48
45.14	odd	6		1890.2.r.b.1529.24		48
63.5	even	6		1890.2.bi.b.719.16		48
63.40	odd	6		630.2.bi.a.509.15	yes	48
105.89	even	6		630.2.r.b.299.7	yes	48
315.194	even	6	inner	1890.2.bi.a.719.16		48
315.229	odd	6		630.2.bi.b.509.10	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.r.a.59.18	✓	48	45.4	even	6
630.2.r.a.299.18	yes	48	21.5	even	6
630.2.r.b.59.7	yes	48	9.4	even	3
630.2.r.b.299.7	yes	48	105.89	even	6
630.2.bi.a.479.15	yes	48	15.14	odd	2
630.2.bi.a.509.15	yes	48	63.40	odd	6
630.2.bi.b.479.10	yes	48	3.2	odd	2
630.2.bi.b.509.10	yes	48	315.229	odd	6
1890.2.r.a.89.24		48	35.19	odd	6
1890.2.r.a.1529.24		48	9.5	odd	6
1890.2.r.b.89.24		48	7.5	odd	6
1890.2.r.b.1529.24		48	45.14	odd	6
1890.2.bi.a.719.16		48	315.194	even	6	inner
1890.2.bi.a.899.16		48	1.1	even	1	trivial
1890.2.bi.b.719.16		48	63.5	even	6
1890.2.bi.b.899.16		48	5.4	even	2

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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(0.834189 - 2.07464i) q^{5} +(-1.94702 - 1.79140i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(0.834189 - 2.07464i) q^{5} +(-1.94702 - 1.79140i) q^{7} -1.00000 q^{8} +(-0.834189 + 2.07464i) q^{10} +(3.95349 - 2.28255i) q^{11} +(0.341322 + 0.591187i) q^{13} +(1.94702 + 1.79140i) q^{14} +1.00000 q^{16} +(-5.72947 - 3.30791i) q^{17} +(-6.76346 + 3.90489i) q^{19} +(0.834189 - 2.07464i) q^{20} +(-3.95349 + 2.28255i) q^{22} +(1.75447 - 3.03883i) q^{23} +(-3.60826 - 3.46128i) q^{25} +(-0.341322 - 0.591187i) q^{26} +(-1.94702 - 1.79140i) q^{28} +(4.33820 + 2.50466i) q^{29} -5.21945i q^{31} -1.00000 q^{32} +(5.72947 + 3.30791i) q^{34} +(-5.34069 + 2.54500i) q^{35} +(1.37526 - 0.794006i) q^{37} +(6.76346 - 3.90489i) q^{38} +(-0.834189 + 2.07464i) q^{40} +(-3.41784 - 5.91987i) q^{41} +(2.05488 + 1.18639i) q^{43} +(3.95349 - 2.28255i) q^{44} +(-1.75447 + 3.03883i) q^{46} +3.81589i q^{47} +(0.581771 + 6.97578i) q^{49} +(3.60826 + 3.46128i) q^{50} +(0.341322 + 0.591187i) q^{52} +(-0.983879 + 1.70413i) q^{53} +(-1.43751 - 10.1061i) q^{55} +(1.94702 + 1.79140i) q^{56} +(-4.33820 - 2.50466i) q^{58} -9.36589 q^{59} +14.3153i q^{61} +5.21945i q^{62} +1.00000 q^{64} +(1.51123 - 0.214959i) q^{65} +7.26234i q^{67} +(-5.72947 - 3.30791i) q^{68} +(5.34069 - 2.54500i) q^{70} -8.48088i q^{71} +(-0.735176 + 1.27336i) q^{73} +(-1.37526 + 0.794006i) q^{74} +(-6.76346 + 3.90489i) q^{76} +(-11.7865 - 2.63812i) q^{77} +1.17562 q^{79} +(0.834189 - 2.07464i) q^{80} +(3.41784 + 5.91987i) q^{82} +(-9.77023 - 5.64084i) q^{83} +(-11.6422 + 9.12717i) q^{85} +(-2.05488 - 1.18639i) q^{86} +(-3.95349 + 2.28255i) q^{88} +(0.739183 + 1.28030i) q^{89} +(0.394492 - 1.76250i) q^{91} +(1.75447 - 3.03883i) q^{92} -3.81589i q^{94} +(2.45923 + 17.2892i) q^{95} +(4.40260 - 7.62553i) q^{97} +(-0.581771 - 6.97578i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{2} + 48 q^{4} + 3 q^{7} - 48 q^{8}+O(q^{10}) \) 48 * q - 48 * q^2 + 48 * q^4 + 3 * q^7 - 48 * q^8	\( 48 q - 48 q^{2} + 48 q^{4} + 3 q^{7} - 48 q^{8} - 6 q^{11} - 3 q^{14} + 48 q^{16} + 6 q^{22} - 3 q^{23} - 18 q^{25} + 3 q^{28} + 3 q^{29} - 48 q^{32} + 12 q^{35} + 3 q^{41} - 6 q^{44} + 3 q^{46} + 3 q^{49} + 18 q^{50} - 42 q^{55} - 3 q^{56} - 3 q^{58} + 48 q^{64} - 12 q^{65} - 12 q^{70} - 18 q^{73} + 12 q^{77} - 3 q^{82} - 9 q^{83} - 33 q^{85} + 6 q^{88} + 33 q^{89} - 3 q^{92} - 24 q^{97} - 3 q^{98}+O(q^{100}) \) 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 + 12 * 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 - 12 * 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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