LMFDB - Embedded newform 990.2.n.h.91.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [990,2,Mod(91,990)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(990, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("990.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.n (of order $5$, degree $4$, 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:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 330)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	990.91
Dual form			990.2.n.h.631.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.809017 - 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 0.587785i) q^{5} +(-0.427051 + 1.31433i) q^{7} +(-0.309017 - 0.951057i) q^{8} +1.00000 q^{10} +(-1.69098 + 2.85317i) q^{11} +(3.92705 - 2.85317i) q^{13} +(0.427051 + 1.31433i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(5.23607 + 3.80423i) q^{17} +(-1.50000 - 4.61653i) q^{19} +(0.809017 - 0.587785i) q^{20} +(0.309017 + 3.30220i) q^{22} +8.61803 q^{23} +(0.309017 + 0.951057i) q^{25} +(1.50000 - 4.61653i) q^{26} +(1.11803 + 0.812299i) q^{28} +(-2.23607 + 6.88191i) q^{29} +(5.85410 - 4.25325i) q^{31} -1.00000 q^{32} +6.47214 q^{34} +(-1.11803 + 0.812299i) q^{35} +(-0.972136 + 2.99193i) q^{37} +(-3.92705 - 2.85317i) q^{38} +(0.309017 - 0.951057i) q^{40} +(0.336881 + 1.03681i) q^{41} +1.23607 q^{43} +(2.19098 + 2.48990i) q^{44} +(6.97214 - 5.06555i) q^{46} +(-3.64590 - 11.2209i) q^{47} +(4.11803 + 2.99193i) q^{49} +(0.809017 + 0.587785i) q^{50} +(-1.50000 - 4.61653i) q^{52} +(-10.5902 + 7.69421i) q^{53} +(-3.04508 + 1.31433i) q^{55} +1.38197 q^{56} +(2.23607 + 6.88191i) q^{58} +(2.88197 - 8.86978i) q^{59} +(3.00000 + 2.17963i) q^{61} +(2.23607 - 6.88191i) q^{62} +(-0.809017 + 0.587785i) q^{64} +4.85410 q^{65} -15.7082 q^{67} +(5.23607 - 3.80423i) q^{68} +(-0.427051 + 1.31433i) q^{70} +(6.61803 + 4.80828i) q^{71} +(0.618034 - 1.90211i) q^{73} +(0.972136 + 2.99193i) q^{74} -4.85410 q^{76} +(-3.02786 - 3.44095i) q^{77} +(2.85410 - 2.07363i) q^{79} +(-0.309017 - 0.951057i) q^{80} +(0.881966 + 0.640786i) q^{82} +(-5.23607 - 3.80423i) q^{83} +(2.00000 + 6.15537i) q^{85} +(1.00000 - 0.726543i) q^{86} +(3.23607 + 0.726543i) q^{88} -11.5623 q^{89} +(2.07295 + 6.37988i) q^{91} +(2.66312 - 8.19624i) q^{92} +(-9.54508 - 6.93491i) q^{94} +(1.50000 - 4.61653i) q^{95} +(1.61803 - 1.17557i) q^{97} +5.09017 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - q^{4} + q^{5} + 5 q^{7} + q^{8} + 4 q^{10} - 9 q^{11} + 9 q^{13} - 5 q^{14} - q^{16} + 12 q^{17} - 6 q^{19} + q^{20} - q^{22} + 30 q^{23} - q^{25} + 6 q^{26} + 10 q^{31} - 4 q^{32}+ \cdots - 2 q^{98}+O(q^{100}) $ 4 * q + q^2 - q^4 + q^5 + 5 * q^7 + q^8 + 4 * q^10 - 9 * q^11 + 9 * q^13 - 5 * q^14 - q^16 + 12 * q^17 - 6 * q^19 + q^20 - q^22 + 30 * q^23 - q^25 + 6 * q^26 + 10 * q^31 - 4 * q^32 + 8 * q^34 + 14 * q^37 - 9 * q^38 - q^40 + 17 * q^41 - 4 * q^43 + 11 * q^44 + 10 * q^46 - 28 * q^47 + 12 * q^49 + q^50 - 6 * q^52 - 20 * q^53 - q^55 + 10 * q^56 + 16 * q^59 + 12 * q^61 - q^64 + 6 * q^65 - 36 * q^67 + 12 * q^68 + 5 * q^70 + 22 * q^71 - 2 * q^73 - 14 * q^74 - 6 * q^76 - 30 * q^77 - 2 * q^79 + q^80 + 8 * q^82 - 12 * q^83 + 8 * q^85 + 4 * q^86 + 4 * q^88 - 6 * q^89 + 15 * q^91 - 5 * q^92 - 27 * q^94 + 6 * q^95 + 2 * q^97 - 2 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$		0			0
$3$		0			0
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$6$		0			0
$7$	−0.427051	+	1.31433i	−0.161410	+	0.496769i	−0.998754	−	0.0499075i	$-0.984107\pi$
$7$	−0.427051	+	1.31433i	−0.161410	+	0.496769i	0.837344	+	0.546677i	$0.184107\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$		0			0
$10$	1.00000			0.316228
$11$	−1.69098	+	2.85317i	−0.509851	+	0.860263i
$11$	−1.69098	+	2.85317i	−0.509851	+	0.860263i
$12$		0			0
$13$	3.92705	−	2.85317i	1.08917	−	0.791327i	0.109909	−	0.993942i	$-0.464944\pi$
$13$	3.92705	−	2.85317i	1.08917	−	0.791327i	0.979259	+	0.202615i	$0.0649439\pi$
$14$	0.427051	+	1.31433i	0.114134	+	0.351269i
$15$		0			0
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	5.23607	+	3.80423i	1.26993	+	0.922660i	0.999200	−	0.0399941i	$-0.0127339\pi$
$17$	5.23607	+	3.80423i	1.26993	+	0.922660i	0.270733	+	0.962654i	$0.412734\pi$
$18$		0			0
$19$	−1.50000	−	4.61653i	−0.344124	−	1.05910i	−0.962051	−	0.272869i	$-0.912028\pi$
$19$	−1.50000	−	4.61653i	−0.344124	−	1.05910i	0.617928	−	0.786235i	$-0.287972\pi$
$20$	0.809017	−	0.587785i	0.180902	−	0.131433i
$21$		0			0
$22$	0.309017	+	3.30220i	0.0658826	+	0.704031i
$23$	8.61803			1.79698			0.898492	−	0.438990i	$-0.144664\pi$
$23$	8.61803			1.79698			0.898492	+	0.438990i	$0.144664\pi$
$24$		0			0
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	1.50000	−	4.61653i	0.294174	−	0.905375i
$27$		0			0
$28$	1.11803	+	0.812299i	0.211289	+	0.153510i
$29$	−2.23607	+	6.88191i	−0.415227	+	1.27794i	0.496820	+	0.867854i	$0.334501\pi$
$29$	−2.23607	+	6.88191i	−0.415227	+	1.27794i	−0.912047	+	0.410085i	$0.865499\pi$
$30$		0			0
$31$	5.85410	−	4.25325i	1.05143	−	0.763907i	0.0789443	−	0.996879i	$-0.474845\pi$
$31$	5.85410	−	4.25325i	1.05143	−	0.763907i	0.972483	+	0.232972i	$0.0748451\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	6.47214			1.10996
$35$	−1.11803	+	0.812299i	−0.188982	+	0.137304i
$36$		0			0
$37$	−0.972136	+	2.99193i	−0.159818	+	0.491870i	−0.998617	−	0.0525715i	$-0.983258\pi$
$37$	−0.972136	+	2.99193i	−0.159818	+	0.491870i	0.838799	+	0.544441i	$0.183258\pi$
$38$	−3.92705	−	2.85317i	−0.637052	−	0.462845i
$39$		0			0
$40$	0.309017	−	0.951057i	0.0488599	−	0.150375i
$41$	0.336881	+	1.03681i	0.0526120	+	0.161923i	0.973910	−	0.226934i	$-0.0728701\pi$
$41$	0.336881	+	1.03681i	0.0526120	+	0.161923i	−0.921298	+	0.388857i	$0.872870\pi$
$42$		0			0
$43$	1.23607			0.188499			0.0942493	−	0.995549i	$-0.469955\pi$
$43$	1.23607			0.188499			0.0942493	+	0.995549i	$0.469955\pi$
$44$	2.19098	+	2.48990i	0.330303	+	0.375366i
$45$		0			0
$46$	6.97214	−	5.06555i	1.02799	−	0.746875i
$47$	−3.64590	−	11.2209i	−0.531809	−	1.63674i	−0.750445	−	0.660933i	$-0.770161\pi$
$47$	−3.64590	−	11.2209i	−0.531809	−	1.63674i	0.218636	−	0.975806i	$-0.429839\pi$
$48$		0			0
$49$	4.11803	+	2.99193i	0.588291	+	0.427418i
$50$	0.809017	+	0.587785i	0.114412	+	0.0831254i
$51$		0			0
$52$	−1.50000	−	4.61653i	−0.208013	−	0.640197i
$53$	−10.5902	+	7.69421i	−1.45467	+	1.05688i	−0.469960	+	0.882688i	$0.655732\pi$
$53$	−10.5902	+	7.69421i	−1.45467	+	1.05688i	−0.984711	+	0.174193i	$0.944268\pi$
$54$		0			0
$55$	−3.04508	+	1.31433i	−0.410599	+	0.177224i
$56$	1.38197			0.184673
$57$		0			0
$58$	2.23607	+	6.88191i	0.293610	+	0.903639i
$59$	2.88197	−	8.86978i	0.375200	−	1.15475i	−0.568144	−	0.822929i	$-0.692338\pi$
$59$	2.88197	−	8.86978i	0.375200	−	1.15475i	0.943344	−	0.331817i	$-0.107662\pi$
$60$		0			0
$61$	3.00000	+	2.17963i	0.384111	+	0.279073i	0.763038	−	0.646354i	$-0.223707\pi$
$61$	3.00000	+	2.17963i	0.384111	+	0.279073i	−0.378927	+	0.925426i	$0.623707\pi$
$62$	2.23607	−	6.88191i	0.283981	−	0.874003i
$63$		0			0
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	4.85410			0.602077
$66$		0			0
$67$	−15.7082			−1.91906			−0.959531	−	0.281602i	$-0.909134\pi$
$67$	−15.7082			−1.91906			−0.959531	+	0.281602i	$0.909134\pi$
$68$	5.23607	−	3.80423i	0.634967	−	0.461330i
$69$		0			0
$70$	−0.427051	+	1.31433i	−0.0510424	+	0.157092i
$71$	6.61803	+	4.80828i	0.785416	+	0.570638i	0.906600	−	0.421992i	$-0.138669\pi$
$71$	6.61803	+	4.80828i	0.785416	+	0.570638i	−0.121183	+	0.992630i	$0.538669\pi$
$72$		0			0
$73$	0.618034	−	1.90211i	0.0723354	−	0.222625i	−0.908352	−	0.418206i	$-0.862659\pi$
$73$	0.618034	−	1.90211i	0.0723354	−	0.222625i	0.980688	+	0.195580i	$0.0626591\pi$
$74$	0.972136	+	2.99193i	0.113009	+	0.347804i
$75$		0			0
$76$	−4.85410			−0.556804
$77$	−3.02786	−	3.44095i	−0.345057	−	0.392133i
$78$		0			0
$79$	2.85410	−	2.07363i	0.321112	−	0.233301i	−0.415538	−	0.909576i	$-0.636407\pi$
$79$	2.85410	−	2.07363i	0.321112	−	0.233301i	0.736650	+	0.676275i	$0.236407\pi$
$80$	−0.309017	−	0.951057i	−0.0345492	−	0.106331i
$81$		0			0
$82$	0.881966	+	0.640786i	0.0973969	+	0.0707630i
$83$	−5.23607	−	3.80423i	−0.574733	−	0.417568i	0.262088	−	0.965044i	$-0.415589\pi$
$83$	−5.23607	−	3.80423i	−0.574733	−	0.417568i	−0.836822	+	0.547476i	$0.815589\pi$
$84$		0			0
$85$	2.00000	+	6.15537i	0.216930	+	0.667643i
$86$	1.00000	−	0.726543i	0.107833	−	0.0783451i
$87$		0			0
$88$	3.23607	+	0.726543i	0.344966	+	0.0774497i
$89$	−11.5623			−1.22560			−0.612801	−	0.790237i	$-0.709957\pi$
$89$	−11.5623			−1.22560			−0.612801	+	0.790237i	$0.709957\pi$
$90$		0			0
$91$	2.07295	+	6.37988i	0.217304	+	0.668793i
$92$	2.66312	−	8.19624i	0.277649	−	0.854517i
$93$		0			0
$94$	−9.54508	−	6.93491i	−0.984500	−	0.715281i
$95$	1.50000	−	4.61653i	0.153897	−	0.473646i
$96$		0			0
$97$	1.61803	−	1.17557i	0.164286	−	0.119361i	−0.502604	−	0.864517i	$-0.667625\pi$
$97$	1.61803	−	1.17557i	0.164286	−	0.119361i	0.666891	+	0.745155i	$0.267625\pi$
$98$	5.09017			0.514185
$99$		0			0
$100$	1.00000			0.100000
$101$	6.00000	−	4.35926i	0.597022	−	0.433762i	−0.247798	−	0.968812i	$-0.579707\pi$
$101$	6.00000	−	4.35926i	0.597022	−	0.433762i	0.844821	+	0.535050i	$0.179707\pi$
$102$		0			0
$103$	−1.50000	+	4.61653i	−0.147799	+	0.454880i	−0.997360	−	0.0726107i	$-0.976867\pi$
$103$	−1.50000	+	4.61653i	−0.147799	+	0.454880i	0.849561	+	0.527490i	$0.176867\pi$
$104$	−3.92705	−	2.85317i	−0.385079	−	0.279776i
$105$		0			0
$106$	−4.04508	+	12.4495i	−0.392893	+	1.20920i
$107$	−0.472136	−	1.45309i	−0.0456431	−	0.140475i	0.925638	−	0.378411i	$-0.123529\pi$
$107$	−0.472136	−	1.45309i	−0.0456431	−	0.140475i	−0.971281	+	0.237936i	$0.923529\pi$
$108$		0			0
$109$	7.41641			0.710363			0.355182	−	0.934797i	$-0.384419\pi$
$109$	7.41641			0.710363			0.355182	+	0.934797i	$0.384419\pi$
$110$	−1.69098	+	2.85317i	−0.161229	+	0.272039i
$111$		0			0
$112$	1.11803	−	0.812299i	0.105644	−	0.0767551i
$113$	1.09017	+	3.35520i	0.102555	+	0.315630i	0.989149	−	0.146918i	$-0.0469352\pi$
$113$	1.09017	+	3.35520i	0.102555	+	0.315630i	−0.886594	+	0.462548i	$0.846935\pi$
$114$		0			0
$115$	6.97214	+	5.06555i	0.650155	+	0.472365i
$116$	5.85410	+	4.25325i	0.543540	+	0.394905i
$117$		0			0
$118$	−2.88197	−	8.86978i	−0.265306	−	0.816529i
$119$	−7.23607	+	5.25731i	−0.663329	+	0.481937i
$120$		0			0
$121$	−5.28115	−	9.64932i	−0.480105	−	0.877211i
$122$	3.70820			0.335725
$123$		0			0
$124$	−2.23607	−	6.88191i	−0.200805	−	0.618014i
$125$	−0.309017	+	0.951057i	−0.0276393	+	0.0850651i
$126$		0			0
$127$	−8.54508	−	6.20837i	−0.758254	−	0.550904i	0.140121	−	0.990134i	$-0.455251\pi$
$127$	−8.54508	−	6.20837i	−0.758254	−	0.550904i	−0.898374	+	0.439231i	$0.855251\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$		0			0
$130$	3.92705	−	2.85317i	0.344425	−	0.250240i
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$		0			0
$133$	6.70820			0.581675
$134$	−12.7082	+	9.23305i	−1.09782	+	0.797614i
$135$		0			0
$136$	2.00000	−	6.15537i	0.171499	−	0.527818i
$137$	−15.7082	−	11.4127i	−1.34204	−	0.975051i	−0.999366	−	0.0355973i	$-0.988667\pi$
$137$	−15.7082	−	11.4127i	−1.34204	−	0.975051i	−0.342676	−	0.939454i	$-0.611333\pi$
$138$		0			0
$139$	−6.42705	+	19.7804i	−0.545135	+	1.67775i	0.175533	+	0.984474i	$0.443835\pi$
$139$	−6.42705	+	19.7804i	−0.545135	+	1.67775i	−0.720668	+	0.693280i	$0.756165\pi$
$140$	0.427051	+	1.31433i	0.0360924	+	0.111081i
$141$		0			0
$142$	8.18034			0.686479
$143$	1.50000	+	16.0292i	0.125436	+	1.34043i
$144$		0			0
$145$	−5.85410	+	4.25325i	−0.486157	+	0.353214i
$146$	−0.618034	−	1.90211i	−0.0511489	−	0.157420i
$147$		0			0
$148$	2.54508	+	1.84911i	0.209205	+	0.151996i
$149$	−2.00000	−	1.45309i	−0.163846	−	0.119041i	0.502841	−	0.864379i	$-0.332288\pi$
$149$	−2.00000	−	1.45309i	−0.163846	−	0.119041i	−0.666687	+	0.745338i	$0.732288\pi$
$150$		0			0
$151$	−3.56231	−	10.9637i	−0.289896	−	0.892209i	−0.984888	−	0.173192i	$-0.944592\pi$
$151$	−3.56231	−	10.9637i	−0.289896	−	0.892209i	0.694992	−	0.719018i	$-0.255408\pi$
$152$	−3.92705	+	2.85317i	−0.318526	+	0.231423i
$153$		0			0
$154$	−4.47214	−	1.00406i	−0.360375	−	0.0809092i
$155$	7.23607			0.581215
$156$		0			0
$157$	−0.663119	−	2.04087i	−0.0529227	−	0.162879i	0.921102	−	0.389322i	$-0.127291\pi$
$157$	−0.663119	−	2.04087i	−0.0529227	−	0.162879i	−0.974025	+	0.226442i	$0.927291\pi$
$158$	1.09017	−	3.35520i	0.0867293	−	0.266925i
$159$		0			0
$160$	−0.809017	−	0.587785i	−0.0639584	−	0.0464685i
$161$	−3.68034	+	11.3269i	−0.290051	+	0.892686i
$162$		0			0
$163$	2.76393	−	2.00811i	0.216488	−	0.157288i	−0.474256	−	0.880387i	$-0.657283\pi$
$163$	2.76393	−	2.00811i	0.216488	−	0.157288i	0.690744	+	0.723099i	$0.257283\pi$
$164$	1.09017			0.0851280
$165$		0			0
$166$	−6.47214			−0.502335
$167$	−18.6353	+	13.5393i	−1.44204	+	1.04770i	−0.454428	+	0.890784i	$0.650156\pi$
$167$	−18.6353	+	13.5393i	−1.44204	+	1.04770i	−0.987611	+	0.156919i	$0.949844\pi$
$168$		0			0
$169$	3.26393	−	10.0453i	0.251072	−	0.772719i
$170$	5.23607	+	3.80423i	0.401588	+	0.291771i
$171$		0			0
$172$	0.381966	−	1.17557i	0.0291246	−	0.0896364i
$173$	4.51722	+	13.9026i	0.343438	+	1.05699i	0.962415	+	0.271584i	$0.0875475\pi$
$173$	4.51722	+	13.9026i	0.343438	+	1.05699i	−0.618977	+	0.785409i	$0.712453\pi$
$174$		0			0
$175$	−1.38197			−0.104467
$176$	3.04508	−	1.31433i	0.229532	−	0.0990712i
$177$		0			0
$178$	−9.35410	+	6.79615i	−0.701120	+	0.509393i
$179$	−3.42705	−	10.5474i	−0.256150	−	0.788348i	−0.993601	−	0.112948i	$-0.963971\pi$
$179$	−3.42705	−	10.5474i	−0.256150	−	0.788348i	0.737451	−	0.675400i	$-0.236029\pi$
$180$		0			0
$181$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$181$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$182$	5.42705	+	3.94298i	0.402280	+	0.292273i
$183$		0			0
$184$	−2.66312	−	8.19624i	−0.196328	−	0.604235i
$185$	−2.54508	+	1.84911i	−0.187118	+	0.135949i
$186$		0			0
$187$	−19.7082	+	8.50651i	−1.44121	+	0.622057i
$188$	−11.7984			−0.860485
$189$		0			0
$190$	−1.50000	−	4.61653i	−0.108821	−	0.334918i
$191$	1.90983	−	5.87785i	0.138190	−	0.425306i	−0.857882	−	0.513846i	$-0.828220\pi$
$191$	1.90983	−	5.87785i	0.138190	−	0.425306i	0.996073	+	0.0885400i	$0.0282201\pi$
$192$		0			0
$193$	1.38197	+	1.00406i	0.0994761	+	0.0722736i	0.636411	−	0.771350i	$-0.280418\pi$
$193$	1.38197	+	1.00406i	0.0994761	+	0.0722736i	−0.536935	+	0.843623i	$0.680418\pi$
$194$	0.618034	−	1.90211i	0.0443723	−	0.136564i
$195$		0			0
$196$	4.11803	−	2.99193i	0.294145	−	0.213709i
$197$	−14.6180			−1.04149			−0.520746	−	0.853712i	$-0.674346\pi$
$197$	−14.6180			−1.04149			−0.520746	+	0.853712i	$0.674346\pi$
$198$		0			0
$199$	2.47214			0.175245			0.0876225	−	0.996154i	$-0.472073\pi$
$199$	2.47214			0.175245			0.0876225	+	0.996154i	$0.472073\pi$
$200$	0.809017	−	0.587785i	0.0572061	−	0.0415627i
$201$		0			0
$202$	2.29180	−	7.05342i	0.161250	−	0.496277i
$203$	−8.09017	−	5.87785i	−0.567819	−	0.412544i
$204$		0			0
$205$	−0.336881	+	1.03681i	−0.0235288	+	0.0724142i
$206$	1.50000	+	4.61653i	0.104510	+	0.321649i
$207$		0			0
$208$	−4.85410			−0.336571
$209$	15.7082	+	3.52671i	1.08656	+	0.243948i
$210$		0			0
$211$	−11.7082	+	8.50651i	−0.806026	+	0.585612i	−0.912676	−	0.408684i	$-0.865988\pi$
$211$	−11.7082	+	8.50651i	−0.806026	+	0.585612i	0.106650	+	0.994297i	$0.465988\pi$
$212$	4.04508	+	12.4495i	0.277818	+	0.855035i
$213$		0			0
$214$	−1.23607	−	0.898056i	−0.0844959	−	0.0613898i
$215$	1.00000	+	0.726543i	0.0681994	+	0.0495498i
$216$		0			0
$217$	3.09017	+	9.51057i	0.209774	+	0.645619i
$218$	6.00000	−	4.35926i	0.406371	−	0.295246i
$219$		0			0
$220$	0.309017	+	3.30220i	0.0208339	+	0.222634i
$221$	31.4164			2.11330
$222$		0			0
$223$	−2.60739	−	8.02472i	−0.174604	−	0.537375i	0.825011	−	0.565116i	$-0.191169\pi$
$223$	−2.60739	−	8.02472i	−0.174604	−	0.537375i	−0.999615	+	0.0277409i	$0.991169\pi$
$224$	0.427051	−	1.31433i	0.0285335	−	0.0878172i
$225$		0			0
$226$	2.85410	+	2.07363i	0.189852	+	0.137936i
$227$	−4.85410	+	14.9394i	−0.322178	+	0.991562i	0.650520	+	0.759489i	$0.274551\pi$
$227$	−4.85410	+	14.9394i	−0.322178	+	0.991562i	−0.972698	+	0.232073i	$0.925449\pi$
$228$		0			0
$229$	−4.09017	+	2.97168i	−0.270286	+	0.196374i	−0.714669	−	0.699462i	$-0.753423\pi$
$229$	−4.09017	+	2.97168i	−0.270286	+	0.196374i	0.444383	+	0.895837i	$0.353423\pi$
$230$	8.61803			0.568256
$231$		0			0
$232$	7.23607			0.475071
$233$	−2.61803	+	1.90211i	−0.171513	+	0.124612i	−0.670230	−	0.742153i	$-0.733805\pi$
$233$	−2.61803	+	1.90211i	−0.171513	+	0.124612i	0.498717	+	0.866765i	$0.333805\pi$
$234$		0			0
$235$	3.64590	−	11.2209i	0.237832	−	0.731972i
$236$	−7.54508	−	5.48183i	−0.491143	−	0.356836i
$237$		0			0
$238$	−2.76393	+	8.50651i	−0.179159	+	0.551395i
$239$	−3.76393	−	11.5842i	−0.243469	−	0.749319i	−0.995885	−	0.0906309i	$-0.971112\pi$
$239$	−3.76393	−	11.5842i	−0.243469	−	0.749319i	0.752416	−	0.658688i	$-0.228888\pi$
$240$		0			0
$241$	5.56231			0.358300			0.179150	−	0.983822i	$-0.442665\pi$
$241$	5.56231			0.358300			0.179150	+	0.983822i	$0.442665\pi$
$242$	−9.94427	−	4.70228i	−0.639242	−	0.302274i
$243$		0			0
$244$	3.00000	−	2.17963i	0.192055	−	0.139536i
$245$	1.57295	+	4.84104i	0.100492	+	0.309283i
$246$		0			0
$247$	−19.0623	−	13.8496i	−1.21291	−	0.881227i
$248$	−5.85410	−	4.25325i	−0.371736	−	0.270082i
$249$		0			0
$250$	0.309017	+	0.951057i	0.0195440	+	0.0601501i
$251$	−2.97214	+	2.15938i	−0.187600	+	0.136299i	−0.677621	−	0.735411i	$-0.736989\pi$
$251$	−2.97214	+	2.15938i	−0.187600	+	0.136299i	0.490021	+	0.871710i	$0.336989\pi$
$252$		0			0
$253$	−14.5729	+	24.5887i	−0.916193	+	1.54588i
$254$	−10.5623			−0.662738
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	6.03444	−	18.5721i	0.376418	−	1.15850i	−0.566099	−	0.824337i	$-0.691548\pi$
$257$	6.03444	−	18.5721i	0.376418	−	1.15850i	0.942517	−	0.334158i	$-0.108452\pi$
$258$		0			0
$259$	−3.51722	−	2.55541i	−0.218549	−	0.158785i
$260$	1.50000	−	4.61653i	0.0930261	−	0.286305i
$261$		0			0
$262$		0			0
$263$	−0.381966			−0.0235530			−0.0117765	−	0.999931i	$-0.503749\pi$
$263$	−0.381966			−0.0235530			−0.0117765	+	0.999931i	$0.503749\pi$
$264$		0			0
$265$	−13.0902			−0.804123
$266$	5.42705	−	3.94298i	0.332754	−	0.241760i
$267$		0			0
$268$	−4.85410	+	14.9394i	−0.296511	+	0.912568i
$269$	−17.4721	−	12.6942i	−1.06529	−	0.773982i	−0.0902343	−	0.995921i	$-0.528762\pi$
$269$	−17.4721	−	12.6942i	−1.06529	−	0.773982i	−0.975061	+	0.221938i	$0.928762\pi$
$270$		0			0
$271$	−1.94427	+	5.98385i	−0.118106	+	0.363493i	−0.992582	−	0.121575i	$-0.961205\pi$
$271$	−1.94427	+	5.98385i	−0.118106	+	0.363493i	0.874476	+	0.485069i	$0.161205\pi$
$272$	−2.00000	−	6.15537i	−0.121268	−	0.373224i
$273$		0			0
$274$	−19.4164			−1.17299
$275$	−3.23607	−	0.726543i	−0.195142	−	0.0438122i
$276$		0			0
$277$	9.50000	−	6.90215i	0.570800	−	0.414710i	−0.264596	−	0.964359i	$-0.585239\pi$
$277$	9.50000	−	6.90215i	0.570800	−	0.414710i	0.835396	+	0.549649i	$0.185239\pi$
$278$	6.42705	+	19.7804i	0.385469	+	1.18635i
$279$		0			0
$280$	1.11803	+	0.812299i	0.0668153	+	0.0485442i
$281$	21.7984	+	15.8374i	1.30038	+	0.944783i	0.999959	−	0.00902337i	$-0.00287227\pi$
$281$	21.7984	+	15.8374i	1.30038	+	0.944783i	0.300423	+	0.953806i	$0.402872\pi$
$282$		0			0
$283$	−5.29180	−	16.2865i	−0.314565	−	0.968130i	−0.975933	−	0.218069i	$-0.930024\pi$
$283$	−5.29180	−	16.2865i	−0.314565	−	0.968130i	0.661369	−	0.750061i	$-0.269976\pi$
$284$	6.61803	−	4.80828i	0.392708	−	0.285319i
$285$		0			0
$286$	10.6353	+	12.0862i	0.628876	+	0.714673i
$287$	−1.50658			−0.0889305
$288$		0			0
$289$	7.69098	+	23.6704i	0.452411	+	1.39238i
$290$	−2.23607	+	6.88191i	−0.131306	+	0.404120i
$291$		0			0
$292$	−1.61803	−	1.17557i	−0.0946883	−	0.0687951i
$293$	3.37132	−	10.3759i	0.196955	−	0.606165i	−0.802993	−	0.595988i	$-0.796761\pi$
$293$	3.37132	−	10.3759i	0.196955	−	0.606165i	0.999948	−	0.0101766i	$-0.00323938\pi$
$294$		0			0
$295$	7.54508	−	5.48183i	0.439292	−	0.319164i
$296$	3.14590			0.182852
$297$		0			0
$298$	−2.47214			−0.143207
$299$	33.8435	−	24.5887i	1.95722	−	1.42200i
$300$		0			0
$301$	−0.527864	+	1.62460i	−0.0304256	+	0.0936403i
$302$	−9.32624	−	6.77591i	−0.536665	−	0.389910i
$303$		0			0
$304$	−1.50000	+	4.61653i	−0.0860309	+	0.264776i
$305$	1.14590	+	3.52671i	0.0656139	+	0.201939i
$306$		0			0
$307$	26.8328			1.53143			0.765715	−	0.643180i	$-0.222385\pi$
$307$	26.8328			1.53143			0.765715	+	0.643180i	$0.222385\pi$
$308$	−4.20820	+	1.81636i	−0.239785	+	0.103497i
$309$		0			0
$310$	5.85410	−	4.25325i	0.332491	−	0.241569i
$311$	−3.67376	−	11.3067i	−0.208320	−	0.641143i	−0.999561	−	0.0296381i	$-0.990565\pi$
$311$	−3.67376	−	11.3067i	−0.208320	−	0.641143i	0.791241	−	0.611505i	$-0.209435\pi$
$312$		0			0
$313$	6.23607	+	4.53077i	0.352483	+	0.256094i	0.749910	−	0.661540i	$-0.230097\pi$
$313$	6.23607	+	4.53077i	0.352483	+	0.256094i	−0.397427	+	0.917634i	$0.630097\pi$
$314$	−1.73607	−	1.26133i	−0.0979720	−	0.0711808i
$315$		0			0
$316$	−1.09017	−	3.35520i	−0.0613269	−	0.188745i
$317$	−17.8713	+	12.9843i	−1.00375	+	0.729270i	−0.962890	−	0.269895i	$-0.913011\pi$
$317$	−17.8713	+	12.9843i	−1.00375	+	0.729270i	−0.0408638	+	0.999165i	$0.513011\pi$
$318$		0			0
$319$	−15.8541	−	18.0171i	−0.887659	−	1.00876i
$320$	−1.00000			−0.0559017
$321$		0			0
$322$	3.68034	+	11.3269i	0.205097	+	0.631225i
$323$	9.70820	−	29.8788i	0.540179	−	1.66250i
$324$		0			0
$325$	3.92705	+	2.85317i	0.217834	+	0.158265i
$326$	1.05573	−	3.24920i	0.0584714	−	0.179956i
$327$		0			0
$328$	0.881966	−	0.640786i	0.0486984	−	0.0353815i
$329$	16.3050			0.898921
$330$		0			0
$331$	16.8541			0.926385			0.463193	−	0.886258i	$-0.346704\pi$
$331$	16.8541			0.926385			0.463193	+	0.886258i	$0.346704\pi$
$332$	−5.23607	+	3.80423i	−0.287367	+	0.208784i
$333$		0			0
$334$	−7.11803	+	21.9071i	−0.389481	+	1.19870i
$335$	−12.7082	−	9.23305i	−0.694323	−	0.504455i
$336$		0			0
$337$	−1.05573	+	3.24920i	−0.0575092	+	0.176995i	−0.975685	−	0.219179i	$-0.929662\pi$
$337$	−1.05573	+	3.24920i	−0.0575092	+	0.176995i	0.918176	+	0.396174i	$0.129662\pi$
$338$	−3.26393	−	10.0453i	−0.177534	−	0.546395i
$339$		0			0
$340$	6.47214			0.351001
$341$	2.23607	+	23.8949i	0.121090	+	1.29398i
$342$		0			0
$343$	−13.5172	+	9.82084i	−0.729861	+	0.530275i
$344$	−0.381966	−	1.17557i	−0.0205942	−	0.0633825i
$345$		0			0
$346$	11.8262	+	8.59226i	0.635782	+	0.461923i
$347$	3.00000	+	2.17963i	0.161048	+	0.117009i	0.665391	−	0.746495i	$-0.268265\pi$
$347$	3.00000	+	2.17963i	0.161048	+	0.117009i	−0.504342	+	0.863504i	$0.668265\pi$
$348$		0			0
$349$	−4.14590	−	12.7598i	−0.221925	−	0.683014i	−0.998589	−	0.0530998i	$-0.983090\pi$
$349$	−4.14590	−	12.7598i	−0.221925	−	0.683014i	0.776664	−	0.629915i	$-0.216910\pi$
$350$	−1.11803	+	0.812299i	−0.0597614	+	0.0434192i
$351$		0			0
$352$	1.69098	−	2.85317i	0.0901297	−	0.152074i
$353$	−3.23607			−0.172239			−0.0861193	−	0.996285i	$-0.527447\pi$
$353$	−3.23607			−0.172239			−0.0861193	+	0.996285i	$0.527447\pi$
$354$		0			0
$355$	2.52786	+	7.77997i	0.134165	+	0.412918i
$356$	−3.57295	+	10.9964i	−0.189366	+	0.582808i
$357$		0			0
$358$	−8.97214	−	6.51864i	−0.474192	−	0.344521i
$359$	−7.65248	+	23.5519i	−0.403882	+	1.24302i	0.517943	+	0.855415i	$0.326698\pi$
$359$	−7.65248	+	23.5519i	−0.403882	+	1.24302i	−0.921825	+	0.387606i	$0.873302\pi$
$360$		0			0
$361$	−3.69098	+	2.68166i	−0.194262	+	0.141140i
$362$		0			0
$363$		0			0
$364$	6.70820			0.351605
$365$	1.61803	−	1.17557i	0.0846918	−	0.0615322i
$366$		0			0
$367$	2.65248	−	8.16348i	0.138458	−	0.426130i	−0.857654	−	0.514228i	$-0.828079\pi$
$367$	2.65248	−	8.16348i	0.138458	−	0.426130i	0.996112	+	0.0880974i	$0.0280787\pi$
$368$	−6.97214	−	5.06555i	−0.363448	−	0.264060i
$369$		0			0
$370$	−0.972136	+	2.99193i	−0.0505389	+	0.155543i
$371$	−5.59017	−	17.2048i	−0.290227	−	0.893227i
$372$		0			0
$373$	34.5623			1.78957			0.894784	−	0.446499i	$-0.147329\pi$
$373$	34.5623			1.78957			0.894784	+	0.446499i	$0.147329\pi$
$374$	−10.9443	+	18.4661i	−0.565915	+	0.954859i
$375$		0			0
$376$	−9.54508	+	6.93491i	−0.492250	+	0.357641i
$377$	10.8541	+	33.4055i	0.559015	+	1.72047i
$378$		0			0
$379$	3.64590	+	2.64890i	0.187277	+	0.136065i	0.677473	−	0.735547i	$-0.263075\pi$
$379$	3.64590	+	2.64890i	0.187277	+	0.136065i	−0.490196	+	0.871612i	$0.663075\pi$
$380$	−3.92705	−	2.85317i	−0.201453	−	0.146365i
$381$		0			0
$382$	−1.90983	−	5.87785i	−0.0977154	−	0.300737i
$383$	12.7361	−	9.25330i	0.650783	−	0.472821i	−0.212755	−	0.977106i	$-0.568244\pi$
$383$	12.7361	−	9.25330i	0.650783	−	0.472821i	0.863538	+	0.504284i	$0.168244\pi$
$384$		0			0
$385$	−0.427051	−	4.56352i	−0.0217645	−	0.232579i
$386$	1.70820			0.0869453
$387$		0			0
$388$	−0.618034	−	1.90211i	−0.0313759	−	0.0965652i
$389$	−1.85410	+	5.70634i	−0.0940067	+	0.289323i	−0.986994	−	0.160760i	$-0.948606\pi$
$389$	−1.85410	+	5.70634i	−0.0940067	+	0.289323i	0.892987	+	0.450083i	$0.148606\pi$
$390$		0			0
$391$	45.1246	+	32.7849i	2.28205	+	1.65801i
$392$	1.57295	−	4.84104i	0.0794459	−	0.244509i
$393$		0			0
$394$	−11.8262	+	8.59226i	−0.595797	+	0.432872i
$395$	3.52786			0.177506
$396$		0			0
$397$	−35.7426			−1.79387			−0.896936	−	0.442160i	$-0.854212\pi$
$397$	−35.7426			−1.79387			−0.896936	+	0.442160i	$0.854212\pi$
$398$	2.00000	−	1.45309i	0.100251	−	0.0728366i
$399$		0			0
$400$	0.309017	−	0.951057i	0.0154508	−	0.0475528i
$401$	8.16312	+	5.93085i	0.407647	+	0.296173i	0.772648	−	0.634834i	$-0.218932\pi$
$401$	8.16312	+	5.93085i	0.407647	+	0.296173i	−0.365002	+	0.931007i	$0.618932\pi$
$402$		0			0
$403$	10.8541	−	33.4055i	0.540681	−	1.66405i
$404$	−2.29180	−	7.05342i	−0.114021	−	0.350921i
$405$		0			0
$406$	−10.0000			−0.496292
$407$	−6.89261	−	7.83297i	−0.341654	−	0.388266i
$408$		0			0
$409$	−18.2533	+	13.2618i	−0.902567	+	0.655753i	−0.939124	−	0.343578i	$-0.888361\pi$
$409$	−18.2533	+	13.2618i	−0.902567	+	0.655753i	0.0365570	+	0.999332i	$0.488361\pi$
$410$	0.336881	+	1.03681i	0.0166374	+	0.0512046i
$411$		0			0
$412$	3.92705	+	2.85317i	0.193472	+	0.140566i
$413$	10.4271	+	7.57570i	0.513082	+	0.372776i
$414$		0			0
$415$	−2.00000	−	6.15537i	−0.0981761	−	0.302155i
$416$	−3.92705	+	2.85317i	−0.192540	+	0.139888i
$417$		0			0
$418$	14.7812	−	6.37988i	0.722970	−	0.312050i
$419$	3.79837			0.185563			0.0927814	−	0.995687i	$-0.470424\pi$
$419$	3.79837			0.185563			0.0927814	+	0.995687i	$0.470424\pi$
$420$		0			0
$421$	−12.3262	−	37.9363i	−0.600744	−	1.84890i	−0.523756	−	0.851868i	$-0.675470\pi$
$421$	−12.3262	−	37.9363i	−0.600744	−	1.84890i	−0.0769877	−	0.997032i	$-0.524530\pi$
$422$	−4.47214	+	13.7638i	−0.217700	+	0.670012i
$423$		0			0
$424$	10.5902	+	7.69421i	0.514304	+	0.373664i
$425$	−2.00000	+	6.15537i	−0.0970143	+	0.298579i
$426$		0			0
$427$	−4.14590	+	3.01217i	−0.200634	+	0.145769i
$428$	−1.52786			−0.0738521
$429$		0			0
$430$	1.23607			0.0596085
$431$	−28.0344	+	20.3682i	−1.35037	+	0.981102i	−0.351379	+	0.936233i	$0.614287\pi$
$431$	−28.0344	+	20.3682i	−1.35037	+	0.981102i	−0.998993	+	0.0448689i	$0.985713\pi$
$432$		0			0
$433$	8.38197	−	25.7970i	0.402812	−	1.23973i	−0.519897	−	0.854229i	$-0.674030\pi$
$433$	8.38197	−	25.7970i	0.402812	−	1.23973i	0.922709	−	0.385498i	$-0.125970\pi$
$434$	8.09017	+	5.87785i	0.388341	+	0.282146i
$435$		0			0
$436$	2.29180	−	7.05342i	0.109757	−	0.337798i
$437$	−12.9271	−	39.7854i	−0.618385	−	1.90319i
$438$		0			0
$439$	20.2918			0.968475			0.484237	−	0.874937i	$-0.339097\pi$
$439$	20.2918			0.968475			0.484237	+	0.874937i	$0.339097\pi$
$440$	2.19098	+	2.48990i	0.104451	+	0.118701i
$441$		0			0
$442$	25.4164	−	18.4661i	1.20894	−	0.878343i
$443$	−2.61803	−	8.05748i	−0.124387	−	0.382822i	0.869402	−	0.494105i	$-0.164504\pi$
$443$	−2.61803	−	8.05748i	−0.124387	−	0.382822i	−0.993789	+	0.111283i	$0.964504\pi$
$444$		0			0
$445$	−9.35410	−	6.79615i	−0.443427	−	0.322169i
$446$	−6.82624	−	4.95955i	−0.323232	−	0.234842i
$447$		0			0
$448$	−0.427051	−	1.31433i	−0.0201763	−	0.0620962i
$449$	30.8156	−	22.3888i	1.45428	−	1.05659i	0.469470	−	0.882949i	$-0.344445\pi$
$449$	30.8156	−	22.3888i	1.45428	−	1.05659i	0.984808	−	0.173646i	$-0.0555549\pi$
$450$		0			0
$451$	−3.52786	−	0.792055i	−0.166121	−	0.0372964i
$452$	3.52786			0.165937
$453$		0			0
$454$	4.85410	+	14.9394i	0.227814	+	0.701140i
$455$	−2.07295	+	6.37988i	−0.0971813	+	0.299093i
$456$		0			0
$457$	−28.1803	−	20.4742i	−1.31822	−	0.957743i	−0.999953	−	0.00974267i	$-0.996899\pi$
$457$	−28.1803	−	20.4742i	−1.31822	−	0.957743i	−0.318268	−	0.948001i	$-0.603101\pi$
$458$	−1.56231	+	4.80828i	−0.0730018	+	0.224676i
$459$		0			0
$460$	6.97214	−	5.06555i	0.325078	−	0.236183i
$461$	15.7082			0.731604			0.365802	−	0.930693i	$-0.380795\pi$
$461$	15.7082			0.731604			0.365802	+	0.930693i	$0.380795\pi$
$462$		0			0
$463$	−4.27051			−0.198467			−0.0992337	−	0.995064i	$-0.531639\pi$
$463$	−4.27051			−0.198467			−0.0992337	+	0.995064i	$0.531639\pi$
$464$	5.85410	−	4.25325i	0.271770	−	0.197452i
$465$		0			0
$466$	−1.00000	+	3.07768i	−0.0463241	+	0.142571i
$467$	−7.70820	−	5.60034i	−0.356693	−	0.259153i	0.394978	−	0.918690i	$-0.370752\pi$
$467$	−7.70820	−	5.60034i	−0.356693	−	0.259153i	−0.751671	+	0.659538i	$0.770752\pi$
$468$		0			0
$469$	6.70820	−	20.6457i	0.309756	−	0.953331i
$470$	−3.64590	−	11.2209i	−0.168173	−	0.517582i
$471$		0			0
$472$	−9.32624			−0.429275
$473$	−2.09017	+	3.52671i	−0.0961061	+	0.162158i
$474$		0			0
$475$	3.92705	−	2.85317i	0.180185	−	0.130912i
$476$	2.76393	+	8.50651i	0.126685	+	0.389895i
$477$		0			0
$478$	−9.85410	−	7.15942i	−0.450716	−	0.327464i
$479$	−2.23607	−	1.62460i	−0.102169	−	0.0742298i	0.535528	−	0.844517i	$-0.320113\pi$
$479$	−2.23607	−	1.62460i	−0.102169	−	0.0742298i	−0.637697	+	0.770288i	$0.720113\pi$
$480$		0			0
$481$	4.71885	+	14.5231i	0.215161	+	0.662197i
$482$	4.50000	−	3.26944i	0.204969	−	0.148919i
$483$		0			0
$484$	−10.8090	+	2.04087i	−0.491319	+	0.0927668i
$485$	2.00000			0.0908153
$486$		0			0
$487$	−7.23607	−	22.2703i	−0.327898	−	1.00916i	−0.970116	−	0.242643i	$-0.921986\pi$
$487$	−7.23607	−	22.2703i	−0.327898	−	1.00916i	0.642218	−	0.766522i	$-0.278014\pi$
$488$	1.14590	−	3.52671i	0.0518724	−	0.159647i
$489$		0			0
$490$	4.11803	+	2.99193i	0.186034	+	0.135161i
$491$	3.29837	−	10.1514i	0.148854	−	0.458124i	−0.848633	−	0.528982i	$-0.822574\pi$
$491$	3.29837	−	10.1514i	0.148854	−	0.458124i	0.997486	+	0.0708582i	$0.0225738\pi$
$492$		0			0
$493$	−37.8885	+	27.5276i	−1.70641	+	1.23978i
$494$	−23.5623			−1.06012
$495$		0			0
$496$	−7.23607			−0.324909
$497$	−9.14590	+	6.64488i	−0.410250	+	0.298064i
$498$		0			0
$499$	3.84346	−	11.8290i	0.172057	−	0.529537i	−0.827430	−	0.561569i	$-0.810198\pi$
$499$	3.84346	−	11.8290i	0.172057	−	0.529537i	0.999487	+	0.0320324i	$0.0101980\pi$
$500$	0.809017	+	0.587785i	0.0361803	+	0.0262866i
$501$		0			0
$502$	−1.13525	+	3.49396i	−0.0506689	+	0.155943i
$503$	−4.46556	−	13.7436i	−0.199109	−	0.612796i	−0.999904	−	0.0138566i	$-0.995589\pi$
$503$	−4.46556	−	13.7436i	−0.199109	−	0.612796i	0.800795	−	0.598939i	$-0.204411\pi$
$504$		0			0
$505$	7.41641			0.330026
$506$	2.66312	+	28.4585i	0.118390	+	1.26513i
$507$		0			0
$508$	−8.54508	+	6.20837i	−0.379127	+	0.275452i
$509$	−8.14590	−	25.0705i	−0.361061	−	1.11123i	−0.952411	−	0.304816i	$-0.901405\pi$
$509$	−8.14590	−	25.0705i	−0.361061	−	1.11123i	0.591351	−	0.806414i	$-0.298595\pi$
$510$		0			0
$511$	2.23607	+	1.62460i	0.0989178	+	0.0718680i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$		0			0
$514$	−6.03444	−	18.5721i	−0.266168	−	0.819180i
$515$	−3.92705	+	2.85317i	−0.173047	+	0.125726i
$516$		0			0
$517$	38.1803	+	8.57202i	1.67917	+	0.376997i
$518$	−4.34752			−0.191019
$519$		0			0
$520$	−1.50000	−	4.61653i	−0.0657794	−	0.202448i
$521$	3.95492	−	12.1720i	0.173268	−	0.533264i	−0.826282	−	0.563256i	$-0.809548\pi$
$521$	3.95492	−	12.1720i	0.173268	−	0.533264i	0.999550	+	0.0299924i	$0.00954832\pi$
$522$		0			0
$523$	23.9443	+	17.3965i	1.04701	+	0.760697i	0.971642	−	0.236459i	$-0.0759867\pi$
$523$	23.9443	+	17.3965i	1.04701	+	0.760697i	0.0753683	+	0.997156i	$0.475987\pi$
$524$		0			0
$525$		0			0
$526$	−0.309017	+	0.224514i	−0.0134738	+	0.00978928i
$527$	46.8328			2.04007
$528$		0			0
$529$	51.2705			2.22915
$530$	−10.5902	+	7.69421i	−0.460008	+	0.334215i
$531$		0			0
$532$	2.07295	−	6.37988i	0.0898737	−	0.276603i
$533$	4.28115	+	3.11044i	0.185437	+	0.134728i
$534$		0			0
$535$	0.472136	−	1.45309i	0.0204122	−	0.0628223i
$536$	4.85410	+	14.9394i	0.209665	+	0.645283i
$537$		0			0
$538$	−21.5967			−0.931102
$539$	−15.5000	+	6.69015i	−0.667632	+	0.288165i
$540$		0			0
$541$	12.4721	−	9.06154i	0.536219	−	0.389586i	−0.286460	−	0.958092i	$-0.592479\pi$
$541$	12.4721	−	9.06154i	0.536219	−	0.389586i	0.822679	+	0.568506i	$0.192479\pi$
$542$	1.94427	+	5.98385i	0.0835136	+	0.257029i
$543$		0			0
$544$	−5.23607	−	3.80423i	−0.224495	−	0.163105i
$545$	6.00000	+	4.35926i	0.257012	+	0.186730i
$546$		0			0
$547$	8.56231	+	26.3521i	0.366098	+	1.12673i	0.949291	+	0.314399i	$0.101803\pi$
$547$	8.56231	+	26.3521i	0.366098	+	1.12673i	−0.583193	+	0.812334i	$0.698197\pi$
$548$	−15.7082	+	11.4127i	−0.671021	+	0.487525i
$549$		0			0
$550$	−3.04508	+	1.31433i	−0.129843	+	0.0560431i
$551$	35.1246			1.49636
$552$		0			0
$553$	1.50658	+	4.63677i	0.0640662	+	0.197176i
$554$	3.62868	−	11.1679i	0.154168	−	0.474479i
$555$		0			0
$556$	16.8262	+	12.2250i	0.713591	+	0.518455i
$557$	−12.8262	+	39.4751i	−0.543465	+	1.67261i	0.181146	+	0.983456i	$0.442019\pi$
$557$	−12.8262	+	39.4751i	−0.543465	+	1.67261i	−0.724612	+	0.689158i	$0.757981\pi$
$558$		0			0
$559$	4.85410	−	3.52671i	0.205307	−	0.149164i
$560$	1.38197			0.0583987
$561$		0			0
$562$	26.9443			1.13658
$563$	−14.1803	+	10.3026i	−0.597630	+	0.434204i	−0.845037	−	0.534708i	$-0.820422\pi$
$563$	−14.1803	+	10.3026i	−0.597630	+	0.434204i	0.247407	+	0.968912i	$0.420422\pi$
$564$		0			0
$565$	−1.09017	+	3.35520i	−0.0458638	+	0.141154i
$566$	−13.8541	−	10.0656i	−0.582331	−	0.423088i
$567$		0			0
$568$	2.52786	−	7.77997i	0.106067	−	0.326440i
$569$	0.718847	+	2.21238i	0.0301356	+	0.0927480i	0.964993	−	0.262275i	$-0.0844729\pi$
$569$	0.718847	+	2.21238i	0.0301356	+	0.0927480i	−0.934857	+	0.355023i	$0.884473\pi$
$570$		0			0
$571$	18.9787			0.794234			0.397117	−	0.917768i	$-0.370011\pi$
$571$	18.9787			0.794234			0.397117	+	0.917768i	$0.370011\pi$
$572$	15.7082	+	3.52671i	0.656793	+	0.147459i
$573$		0			0
$574$	−1.21885	+	0.885544i	−0.0508737	+	0.0369619i
$575$	2.66312	+	8.19624i	0.111060	+	0.341807i
$576$		0			0
$577$	14.3262	+	10.4086i	0.596409	+	0.433317i	0.844602	−	0.535394i	$-0.179837\pi$
$577$	14.3262	+	10.4086i	0.596409	+	0.433317i	−0.248193	+	0.968711i	$0.579837\pi$
$578$	20.1353	+	14.6291i	0.837516	+	0.608491i
$579$		0			0
$580$	2.23607	+	6.88191i	0.0928477	+	0.285756i
$581$	7.23607	−	5.25731i	0.300203	−	0.218110i
$582$		0			0
$583$	−4.04508	−	43.2263i	−0.167530	−	1.79025i
$584$	−2.00000			−0.0827606
$585$		0			0
$586$	−3.37132	−	10.3759i	−0.139268	−	0.428623i
$587$	0.944272	−	2.90617i	0.0389743	−	0.119950i	−0.929676	−	0.368377i	$-0.879914\pi$
$587$	0.944272	−	2.90617i	0.0389743	−	0.119950i	0.968651	+	0.248427i	$0.0799135\pi$
$588$		0			0
$589$	−28.4164	−	20.6457i	−1.17088	−	0.850692i
$590$	2.88197	−	8.86978i	0.118649	−	0.365163i
$591$		0			0
$592$	2.54508	−	1.84911i	0.104602	−	0.0759981i
$593$	23.8885			0.980985			0.490492	−	0.871445i	$-0.336817\pi$
$593$	23.8885			0.980985			0.490492	+	0.871445i	$0.336817\pi$
$594$		0			0
$595$	−8.94427			−0.366679
$596$	−2.00000	+	1.45309i	−0.0819232	+	0.0595207i
$597$		0			0
$598$	12.9271	−	39.7854i	0.528626	−	1.62694i
$599$	0.145898	+	0.106001i	0.00596123	+	0.00433109i	0.590762	−	0.806846i	$-0.298827\pi$
$599$	0.145898	+	0.106001i	0.00596123	+	0.00433109i	−0.584801	+	0.811177i	$0.698827\pi$
$600$		0			0
$601$	−5.50000	+	16.9273i	−0.224350	+	0.690477i	0.774007	+	0.633177i	$0.218249\pi$
$601$	−5.50000	+	16.9273i	−0.224350	+	0.690477i	−0.998357	+	0.0573006i	$0.981751\pi$
$602$	0.527864	+	1.62460i	0.0215141	+	0.0662137i
$603$		0			0
$604$	−11.5279			−0.469062
$605$	1.39919	−	10.9106i	0.0568850	−	0.443581i
$606$		0			0
$607$	18.9443	−	13.7638i	0.768924	−	0.558656i	−0.132710	−	0.991155i	$-0.542368\pi$
$607$	18.9443	−	13.7638i	0.768924	−	0.558656i	0.901635	+	0.432499i	$0.142368\pi$
$608$	1.50000	+	4.61653i	0.0608330	+	0.187225i
$609$		0			0
$610$	3.00000	+	2.17963i	0.121466	+	0.0882505i
$611$	−46.3328	−	33.6628i	−1.87443	−	1.36185i
$612$		0			0
$613$	4.50658	+	13.8698i	0.182019	+	0.560197i	0.999884	−	0.0152129i	$-0.00484262\pi$
$613$	4.50658	+	13.8698i	0.182019	+	0.560197i	−0.817865	+	0.575410i	$0.804843\pi$
$614$	21.7082	−	15.7719i	0.876072	−	0.636503i
$615$		0			0
$616$	−2.33688	+	3.94298i	−0.0941556	+	0.158867i
$617$	24.0000			0.966204			0.483102	−	0.875564i	$-0.339510\pi$
$617$	24.0000			0.966204			0.483102	+	0.875564i	$0.339510\pi$
$618$		0			0
$619$	8.20820	+	25.2623i	0.329916	+	1.01538i	0.969173	+	0.246383i	$0.0792420\pi$
$619$	8.20820	+	25.2623i	0.329916	+	1.01538i	−0.639257	+	0.768993i	$0.720758\pi$
$620$	2.23607	−	6.88191i	0.0898027	−	0.276384i
$621$		0			0
$622$	−9.61803	−	6.98791i	−0.385648	−	0.280190i
$623$	4.93769	−	15.1967i	0.197825	−	0.608841i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	7.70820			0.308082
$627$		0			0
$628$	−2.14590			−0.0856307
$629$	−16.4721	+	11.9677i	−0.656787	+	0.477184i
$630$		0			0
$631$	4.09017	−	12.5882i	0.162827	−	0.501130i	−0.836043	−	0.548665i	$-0.815136\pi$
$631$	4.09017	−	12.5882i	0.162827	−	0.501130i	0.998870	+	0.0475344i	$0.0151364\pi$
$632$	−2.85410	−	2.07363i	−0.113530	−	0.0824844i
$633$		0			0
$634$	−6.82624	+	21.0090i	−0.271105	+	0.834374i
$635$	−3.26393	−	10.0453i	−0.129525	−	0.398638i
$636$		0			0
$637$	24.7082			0.978975
$638$	−23.4164	−	5.25731i	−0.927064	−	0.208139i
$639$		0			0
$640$	−0.809017	+	0.587785i	−0.0319792	+	0.0232343i
$641$	−14.4098	−	44.3489i	−0.569154	−	1.75168i	−0.655274	−	0.755391i	$-0.727447\pi$
$641$	−14.4098	−	44.3489i	−0.569154	−	1.75168i	0.0861199	−	0.996285i	$-0.472553\pi$
$642$		0			0
$643$	−32.3607	−	23.5114i	−1.27618	−	0.927200i	−0.276750	−	0.960942i	$-0.589257\pi$
$643$	−32.3607	−	23.5114i	−1.27618	−	0.927200i	−0.999431	+	0.0337424i	$0.989257\pi$
$644$	9.63525	+	7.00042i	0.379682	+	0.275855i
$645$		0			0
$646$	−9.70820	−	29.8788i	−0.381964	−	1.17556i
$647$	−11.4164	+	8.29451i	−0.448825	+	0.326091i	−0.789132	−	0.614224i	$-0.789469\pi$
$647$	−11.4164	+	8.29451i	−0.448825	+	0.326091i	0.340306	+	0.940315i	$0.389469\pi$
$648$		0			0
$649$	20.4336	+	23.2214i	0.802090	+	0.911519i
$650$	4.85410			0.190394
$651$		0			0
$652$	−1.05573	−	3.24920i	−0.0413455	−	0.127248i
$653$	4.22949	−	13.0170i	0.165513	−	0.509396i	−0.833561	−	0.552427i	$-0.813702\pi$
$653$	4.22949	−	13.0170i	0.165513	−	0.509396i	0.999074	+	0.0430316i	$0.0137016\pi$
$654$		0			0
$655$		0			0
$656$	0.336881	−	1.03681i	0.0131530	−	0.0404808i
$657$		0			0
$658$	13.1910	−	9.58381i	0.514238	−	0.373616i
$659$	24.3262			0.947616			0.473808	−	0.880628i	$-0.342879\pi$
$659$	24.3262			0.947616			0.473808	+	0.880628i	$0.342879\pi$
$660$		0			0
$661$	20.6525			0.803288			0.401644	−	0.915796i	$-0.368439\pi$
$661$	20.6525			0.803288			0.401644	+	0.915796i	$0.368439\pi$
$662$	13.6353	−	9.90659i	0.529949	−	0.385031i
$663$		0			0
$664$	−2.00000	+	6.15537i	−0.0776151	+	0.238875i
$665$	5.42705	+	3.94298i	0.210452	+	0.152902i
$666$		0			0
$667$	−19.2705	+	59.3085i	−0.746157	+	2.29644i
$668$	7.11803	+	21.9071i	0.275405	+	0.847609i
$669$		0			0
$670$	−15.7082			−0.606861
$671$	−11.2918	+	4.87380i	−0.435915	+	0.188151i
$672$		0			0
$673$	−16.7984	+	12.2047i	−0.647530	+	0.470458i	−0.862429	−	0.506178i	$-0.831058\pi$
$673$	−16.7984	+	12.2047i	−0.647530	+	0.470458i	0.214899	+	0.976636i	$0.431058\pi$
$674$	1.05573	+	3.24920i	0.0406651	+	0.125154i
$675$		0			0
$676$	−8.54508	−	6.20837i	−0.328657	−	0.238783i
$677$	−8.38197	−	6.08985i	−0.322145	−	0.234052i	0.414945	−	0.909846i	$-0.363801\pi$
$677$	−8.38197	−	6.08985i	−0.322145	−	0.234052i	−0.737090	+	0.675794i	$0.763801\pi$
$678$		0			0
$679$	0.854102	+	2.62866i	0.0327774	+	0.100879i
$680$	5.23607	−	3.80423i	0.200794	−	0.145885i
$681$		0			0
$682$	15.8541	+	18.0171i	0.607085	+	0.689909i
$683$	−43.0132			−1.64585			−0.822926	−	0.568148i	$-0.807660\pi$
$683$	−43.0132			−1.64585			−0.822926	+	0.568148i	$0.807660\pi$
$684$		0			0
$685$	−6.00000	−	18.4661i	−0.229248	−	0.705553i
$686$	−5.16312	+	15.8904i	−0.197129	+	0.606700i
$687$		0			0
$688$	−1.00000	−	0.726543i	−0.0381246	−	0.0276992i
$689$	−19.6353	+	60.4311i	−0.748044	+	2.30224i
$690$		0			0
$691$	−9.06231	+	6.58415i	−0.344746	+	0.250473i	−0.746662	−	0.665204i	$-0.768345\pi$
$691$	−9.06231	+	6.58415i	−0.344746	+	0.250473i	0.401915	+	0.915677i	$0.368345\pi$
$692$	14.6180			0.555694
$693$		0			0
$694$	3.70820			0.140761
$695$	−16.8262	+	12.2250i	−0.638256	+	0.463720i
$696$		0			0
$697$	−2.18034	+	6.71040i	−0.0825863	+	0.254174i
$698$	−10.8541	−	7.88597i	−0.410834	−	0.298488i
$699$		0			0
$700$	−0.427051	+	1.31433i	−0.0161410	+	0.0496769i
$701$	3.11146	+	9.57608i	0.117518	+	0.361683i	0.992464	−	0.122537i	$-0.0391031\pi$
$701$	3.11146	+	9.57608i	0.117518	+	0.361683i	−0.874946	+	0.484221i	$0.839103\pi$
$702$		0			0
$703$	15.2705			0.575938
$704$	−0.309017	−	3.30220i	−0.0116465	−	0.124456i
$705$		0			0
$706$	−2.61803	+	1.90211i	−0.0985310	+	0.0715870i
$707$	3.16718	+	9.74759i	0.119114	+	0.366596i
$708$		0			0
$709$	−12.3262	−	8.95554i	−0.462922	−	0.336332i	0.331755	−	0.943366i	$-0.392359\pi$
$709$	−12.3262	−	8.95554i	−0.462922	−	0.336332i	−0.794676	+	0.607033i	$0.792359\pi$
$710$	6.61803	+	4.80828i	0.248370	+	0.180452i
$711$		0			0
$712$	3.57295	+	10.9964i	0.133902	+	0.412108i
$713$	50.4508	−	36.6547i	1.88940	−	1.37273i
$714$		0			0
$715$	−8.20820	+	13.8496i	−0.306969	+	0.517945i
$716$	−11.0902			−0.414459
$717$		0			0
$718$	7.65248	+	23.5519i	0.285588	+	0.878949i
$719$	−10.0344	+	30.8828i	−0.374222	+	1.15174i	0.569781	+	0.821797i	$0.307028\pi$
$719$	−10.0344	+	30.8828i	−0.374222	+	1.15174i	−0.944002	+	0.329939i	$0.892972\pi$
$720$		0			0
$721$	−5.42705	−	3.94298i	−0.202114	−	0.146844i
$722$	−1.40983	+	4.33901i	−0.0524684	+	0.161481i
$723$		0			0
$724$		0			0
$725$	−7.23607			−0.268741
$726$		0			0
$727$	−10.6869			−0.396356			−0.198178	−	0.980166i	$-0.563502\pi$
$727$	−10.6869			−0.396356			−0.198178	+	0.980166i	$0.563502\pi$
$728$	5.42705	−	3.94298i	0.201140	−	0.146137i
$729$		0			0
$730$	0.618034	−	1.90211i	0.0228745	−	0.0704004i
$731$	6.47214	+	4.70228i	0.239381	+	0.173920i
$732$		0			0
$733$	−3.27051	+	10.0656i	−0.120799	+	0.371781i	−0.993112	−	0.117166i	$-0.962619\pi$
$733$	−3.27051	+	10.0656i	−0.120799	+	0.371781i	0.872313	+	0.488947i	$0.162619\pi$
$734$	−2.65248	−	8.16348i	−0.0979047	−	0.301320i
$735$		0			0
$736$	−8.61803			−0.317665
$737$	26.5623	−	44.8182i	0.978435	−	1.65090i
$738$		0			0
$739$	3.35410	−	2.43690i	0.123383	−	0.0896427i	−0.524383	−	0.851483i	$-0.675704\pi$
$739$	3.35410	−	2.43690i	0.123383	−	0.0896427i	0.647765	+	0.761840i	$0.275704\pi$
$740$	0.972136	+	2.99193i	0.0357364	+	0.109985i
$741$		0			0
$742$	−14.6353	−	10.6331i	−0.537277	−	0.390355i
$743$	−10.2082	−	7.41669i	−0.374503	−	0.272092i	0.384573	−	0.923095i	$-0.374349\pi$
$743$	−10.2082	−	7.41669i	−0.374503	−	0.272092i	−0.759076	+	0.651002i	$0.774349\pi$
$744$		0			0
$745$	−0.763932	−	2.35114i	−0.0279883	−	0.0861391i
$746$	27.9615	−	20.3152i	1.02374	−	0.743793i
$747$		0			0
$748$	2.00000	+	21.3723i	0.0731272	+	0.781448i
$749$	2.11146			0.0771509
$750$		0			0
$751$	2.65248	+	8.16348i	0.0967902	+	0.297890i	0.987716	−	0.156259i	$-0.0499435\pi$
$751$	2.65248	+	8.16348i	0.0967902	+	0.297890i	−0.890926	+	0.454149i	$0.849943\pi$
$752$	−3.64590	+	11.2209i	−0.132952	+	0.409185i
$753$		0			0
$754$	28.4164	+	20.6457i	1.03486	+	0.751873i
$755$	3.56231	−	10.9637i	0.129646	−	0.399008i
$756$		0			0
$757$	−40.5795	+	29.4828i	−1.47489	+	1.07157i	−0.495728	+	0.868478i	$0.665099\pi$
$757$	−40.5795	+	29.4828i	−1.47489	+	1.07157i	−0.979160	+	0.203091i	$0.934901\pi$
$758$	4.50658			0.163686
$759$		0			0
$760$	−4.85410			−0.176077
$761$	29.0344	−	21.0948i	1.05250	−	0.764684i	0.0798119	−	0.996810i	$-0.474568\pi$
$761$	29.0344	−	21.0948i	1.05250	−	0.764684i	0.972686	+	0.232126i	$0.0745680\pi$
$762$		0			0
$763$	−3.16718	+	9.74759i	−0.114660	+	0.352886i
$764$	−5.00000	−	3.63271i	−0.180894	−	0.131427i
$765$		0			0
$766$	4.86475	−	14.9721i	0.175770	−	0.540966i
$767$	−13.9894	−	43.0548i	−0.505126	−	1.55462i
$768$		0			0
$769$	35.9098			1.29494			0.647471	−	0.762090i	$-0.275827\pi$
$769$	35.9098			1.29494			0.647471	+	0.762090i	$0.275827\pi$
$770$	−3.02786	−	3.44095i	−0.109117	−	0.124003i
$771$		0			0
$772$	1.38197	−	1.00406i	0.0497380	−	0.0361368i
$773$	−3.37132	−	10.3759i	−0.121258	−	0.373194i	0.871943	−	0.489608i	$-0.162860\pi$
$773$	−3.37132	−	10.3759i	−0.121258	−	0.373194i	−0.993201	+	0.116414i	$0.962860\pi$
$774$		0			0
$775$	5.85410	+	4.25325i	0.210286	+	0.152781i
$776$	−1.61803	−	1.17557i	−0.0580840	−	0.0422005i
$777$		0			0
$778$	1.85410	+	5.70634i	0.0664728	+	0.204582i
$779$	4.28115	−	3.11044i	0.153388	−	0.111443i
$780$		0			0
$781$	−24.9098	+	10.7516i	−0.891344	+	0.384724i
$782$	55.7771			1.99458
$783$		0			0
$784$	−1.57295	−	4.84104i	−0.0561768	−	0.172894i
$785$	0.663119	−	2.04087i	0.0236677	−	0.0728418i
$786$		0			0
$787$	−5.09017	−	3.69822i	−0.181445	−	0.131827i	0.493355	−	0.869828i	$-0.335770\pi$
$787$	−5.09017	−	3.69822i	−0.181445	−	0.131827i	−0.674800	+	0.738000i	$0.735770\pi$
$788$	−4.51722	+	13.9026i	−0.160919	+	0.495259i
$789$		0			0
$790$	2.85410	−	2.07363i	0.101544	−	0.0737763i
$791$	−4.87539			−0.173349
$792$		0			0
$793$	18.0000			0.639199
$794$	−28.9164	+	21.0090i	−1.02620	+	0.745582i
$795$		0			0
$796$	0.763932	−	2.35114i	0.0270769	−	0.0833340i
$797$	17.7254	+	12.8783i	0.627867	+	0.456172i	0.855661	−	0.517537i	$-0.173151\pi$
$797$	17.7254	+	12.8783i	0.627867	+	0.456172i	−0.227794	+	0.973709i	$0.573151\pi$
$798$		0			0
$799$	23.5967	−	72.6233i	0.834793	−	2.56923i
$800$	−0.309017	−	0.951057i	−0.0109254	−	0.0336249i
$801$		0			0
$802$	10.0902			0.356296
$803$	4.38197	+	4.97980i	0.154636	+	0.175733i
$804$		0			0
$805$	−9.63525	+	7.00042i	−0.339598	+	0.246732i
$806$	−10.8541	−	33.4055i	−0.382319	−	1.17666i
$807$		0			0
$808$	−6.00000	−	4.35926i	−0.211079	−	0.153358i
$809$	13.5451	+	9.84108i	0.476220	+	0.345994i	0.799860	−	0.600186i	$-0.204907\pi$
$809$	13.5451	+	9.84108i	0.476220	+	0.345994i	−0.323641	+	0.946180i	$0.604907\pi$
$810$		0			0
$811$	11.1008	+	34.1648i	0.389802	+	1.19969i	0.932936	+	0.360042i	$0.117238\pi$
$811$	11.1008	+	34.1648i	0.389802	+	1.19969i	−0.543134	+	0.839646i	$0.682762\pi$
$812$	−8.09017	+	5.87785i	−0.283909	+	0.206272i
$813$		0			0
$814$	−10.1803	−	2.28563i	−0.356821	−	0.0801112i
$815$	3.41641			0.119672
$816$		0			0
$817$	−1.85410	−	5.70634i	−0.0648668	−	0.199640i
$818$	−6.97214	+	21.4580i	−0.243775	+	0.750262i
$819$		0			0
$820$	0.881966	+	0.640786i	0.0307996	+	0.0223772i
$821$	−13.9098	+	42.8101i	−0.485456	+	1.49408i	0.345862	+	0.938285i	$0.387586\pi$
$821$	−13.9098	+	42.8101i	−0.485456	+	1.49408i	−0.831319	+	0.555796i	$0.812414\pi$
$822$		0			0
$823$	5.78115	−	4.20025i	0.201518	−	0.146412i	−0.482450	−	0.875924i	$-0.660253\pi$
$823$	5.78115	−	4.20025i	0.201518	−	0.146412i	0.683968	+	0.729512i	$0.260253\pi$
$824$	4.85410			0.169101
$825$		0			0
$826$	12.8885			0.448450
$827$	2.70820	−	1.96763i	0.0941735	−	0.0684210i	−0.539702	−	0.841856i	$-0.681463\pi$
$827$	2.70820	−	1.96763i	0.0941735	−	0.0684210i	0.633876	+	0.773435i	$0.281463\pi$
$828$		0			0
$829$	−9.56231	+	29.4298i	−0.332113	+	1.02214i	0.636014	+	0.771677i	$0.280582\pi$
$829$	−9.56231	+	29.4298i	−0.332113	+	1.02214i	−0.968127	+	0.250460i	$0.919418\pi$
$830$	−5.23607	−	3.80423i	−0.181747	−	0.132047i
$831$		0			0
$832$	−1.50000	+	4.61653i	−0.0520031	+	0.160049i
$833$	10.1803	+	31.3319i	0.352728	+	1.08558i
$834$		0			0
$835$	−23.0344			−0.797140
$836$	8.20820	−	13.8496i	0.283887	−	0.478998i
$837$		0			0
$838$	3.07295	−	2.23263i	0.106153	−	0.0771249i
$839$	13.4377	+	41.3570i	0.463921	+	1.42780i	0.860335	+	0.509729i	$0.170254\pi$
$839$	13.4377	+	41.3570i	0.463921	+	1.42780i	−0.396414	+	0.918072i	$0.629746\pi$
$840$		0			0
$841$	−18.8992	−	13.7311i	−0.651696	−	0.473485i
$842$	−32.2705	−	23.4459i	−1.11212	−	0.807999i
$843$		0			0
$844$	4.47214	+	13.7638i	0.153937	+	0.473770i
$845$	8.54508	−	6.20837i	0.293960	−	0.213574i
$846$		0			0
$847$	14.9377	−	2.82041i	0.513265	−	0.0969106i
$848$	13.0902			0.449518
$849$		0			0
$850$	2.00000	+	6.15537i	0.0685994	+	0.211127i
$851$	−8.37790	+	25.7845i	−0.287191	+	0.883882i
$852$		0			0
$853$	25.3885	+	18.4459i	0.869287	+	0.631574i	0.930396	−	0.366557i	$-0.119464\pi$
$853$	25.3885	+	18.4459i	0.869287	+	0.631574i	−0.0611084	+	0.998131i	$0.519464\pi$
$854$	−1.58359	+	4.87380i	−0.0541894	+	0.166778i
$855$		0			0
$856$	−1.23607	+	0.898056i	−0.0422479	+	0.0306949i
$857$	−37.5967			−1.28428			−0.642140	−	0.766587i	$-0.721953\pi$
$857$	−37.5967			−1.28428			−0.642140	+	0.766587i	$0.721953\pi$
$858$		0			0
$859$	−12.5066			−0.426719			−0.213359	−	0.976974i	$-0.568441\pi$
$859$	−12.5066			−0.426719			−0.213359	+	0.976974i	$0.568441\pi$
$860$	1.00000	−	0.726543i	0.0340997	−	0.0247749i
$861$		0			0
$862$	−10.7082	+	32.9565i	−0.364723	+	1.12250i
$863$	−28.6353	−	20.8047i	−0.974755	−	0.708201i	−0.0182250	−	0.999834i	$-0.505802\pi$
$863$	−28.6353	−	20.8047i	−0.974755	−	0.708201i	−0.956530	+	0.291633i	$0.905802\pi$
$864$		0			0
$865$	−4.51722	+	13.9026i	−0.153590	+	0.472702i
$866$	−8.38197	−	25.7970i	−0.284831	−	0.876619i
$867$		0			0
$868$	10.0000			0.339422
$869$	1.09017	+	11.6497i	0.0369815	+	0.395189i
$870$		0			0
$871$	−61.6869	+	44.8182i	−2.09018	+	1.51861i
$872$	−2.29180	−	7.05342i	−0.0776100	−	0.238859i
$873$		0			0
$874$	−33.8435	−	24.5887i	−1.14477	−	0.831726i
$875$	−1.11803	−	0.812299i	−0.0377964	−	0.0274607i
$876$		0			0
$877$	3.44427	+	10.6004i	0.116305	+	0.357949i	0.992217	−	0.124521i	$-0.0397395\pi$
$877$	3.44427	+	10.6004i	0.116305	+	0.357949i	−0.875912	+	0.482471i	$0.839740\pi$
$878$	16.4164	−	11.9272i	0.554027	−	0.402524i
$879$		0			0
$880$	3.23607	+	0.726543i	0.109088	+	0.0244917i
$881$	−8.50658			−0.286594			−0.143297	−	0.989680i	$-0.545770\pi$
$881$	−8.50658			−0.286594			−0.143297	+	0.989680i	$0.545770\pi$
$882$		0			0
$883$	4.76393	+	14.6619i	0.160319	+	0.493411i	0.998661	−	0.0517335i	$-0.0164746\pi$
$883$	4.76393	+	14.6619i	0.160319	+	0.493411i	−0.838342	+	0.545145i	$0.816475\pi$
$884$	9.70820	−	29.8788i	0.326522	−	1.00493i
$885$		0			0
$886$	−6.85410	−	4.97980i	−0.230268	−	0.167300i
$887$	4.75329	−	14.6291i	0.159600	−	0.491198i	−0.838998	−	0.544134i	$-0.816858\pi$
$887$	4.75329	−	14.6291i	0.159600	−	0.491198i	0.998598	+	0.0529367i	$0.0168581\pi$
$888$		0			0
$889$	11.8090	−	8.57975i	0.396062	−	0.287756i
$890$	−11.5623			−0.387569
$891$		0			0
$892$	−8.43769			−0.282515
$893$	−46.3328	+	33.6628i	−1.55047	+	1.12648i
$894$		0			0
$895$	3.42705	−	10.5474i	0.114554	−	0.352560i
$896$	−1.11803	−	0.812299i	−0.0373509	−	0.0271370i
$897$		0			0
$898$	11.7705	−	36.2259i	0.392787	−	1.20887i
$899$	16.1803	+	49.7980i	0.539645	+	1.66086i
$900$		0			0
$901$	−84.7214			−2.82248
$902$	−3.31966	+	1.43284i	−0.110533	+	0.0477084i
$903$		0			0
$904$	2.85410	−	2.07363i	0.0949260	−	0.0689678i
$905$		0			0
$906$		0			0
$907$	−47.1246	−	34.2380i	−1.56475	−	1.13686i	−0.931978	−	0.362515i	$-0.881918\pi$
$907$	−47.1246	−	34.2380i	−1.56475	−	1.13686i	−0.632769	−	0.774341i	$-0.718082\pi$
$908$	12.7082	+	9.23305i	0.421737	+	0.306410i
$909$		0			0
$910$	2.07295	+	6.37988i	0.0687176	+	0.211491i
$911$	−33.1803	+	24.1069i	−1.09931	+	0.798698i	−0.980948	−	0.194272i	$-0.937766\pi$
$911$	−33.1803	+	24.1069i	−1.09931	+	0.798698i	−0.118366	+	0.992970i	$0.537766\pi$
$912$		0			0
$913$	19.7082	−	8.50651i	0.652246	−	0.281524i
$914$	−34.8328			−1.15217
$915$		0			0
$916$	1.56231	+	4.80828i	0.0516200	+	0.158870i
$917$		0			0
$918$		0			0
$919$	−7.00000	−	5.08580i	−0.230909	−	0.167765i	0.466315	−	0.884619i	$-0.345581\pi$
$919$	−7.00000	−	5.08580i	−0.230909	−	0.167765i	−0.697223	+	0.716854i	$0.745581\pi$
$920$	2.66312	−	8.19624i	0.0878004	−	0.270222i
$921$		0			0
$922$	12.7082	−	9.23305i	0.418522	−	0.304074i
$923$	39.7082			1.30701
$924$		0			0
$925$	−3.14590			−0.103436
$926$	−3.45492	+	2.51014i	−0.113536	+	0.0824884i
$927$		0			0
$928$	2.23607	−	6.88191i	0.0734025	−	0.225910i
$929$	−10.0623	−	7.31069i	−0.330134	−	0.239856i	0.410354	−	0.911926i	$-0.365405\pi$
$929$	−10.0623	−	7.31069i	−0.330134	−	0.239856i	−0.740487	+	0.672070i	$0.765405\pi$
$930$		0			0
$931$	7.63525	−	23.4989i	0.250235	−	0.770145i
$932$	1.00000	+	3.07768i	0.0327561	+	0.100813i
$933$		0			0
$934$	−9.52786			−0.311761
$935$	−20.9443	−	4.70228i	−0.684951	−	0.153781i
$936$		0			0
$937$	12.0000	−	8.71851i	0.392023	−	0.284821i	−0.374261	−	0.927323i	$-0.622104\pi$
$937$	12.0000	−	8.71851i	0.392023	−	0.284821i	0.766284	+	0.642502i	$0.222104\pi$
$938$	−6.70820	−	20.6457i	−0.219031	−	0.674107i
$939$		0			0
$940$	−9.54508	−	6.93491i	−0.311326	−	0.226192i
$941$	−28.9443	−	21.0292i	−0.943556	−	0.685534i	0.00571778	−	0.999984i	$-0.498180\pi$
$941$	−28.9443	−	21.0292i	−0.943556	−	0.685534i	−0.949274	+	0.314450i	$0.898180\pi$
$942$		0			0
$943$	2.90325	+	8.93529i	0.0945429	+	0.290973i
$944$	−7.54508	+	5.48183i	−0.245572	+	0.178418i
$945$		0			0
$946$	0.381966	+	4.08174i	0.0124188	+	0.132709i
$947$	26.9443			0.875571			0.437786	−	0.899079i	$-0.355763\pi$
$947$	26.9443			0.875571			0.437786	+	0.899079i	$0.355763\pi$
$948$		0			0
$949$	−3.00000	−	9.23305i	−0.0973841	−	0.299718i
$950$	1.50000	−	4.61653i	0.0486664	−	0.149780i
$951$		0			0
$952$	7.23607	+	5.25731i	0.234522	+	0.170390i
$953$	−11.4377	+	35.2016i	−0.370503	+	1.14029i	0.575959	+	0.817478i	$0.304629\pi$
$953$	−11.4377	+	35.2016i	−0.370503	+	1.14029i	−0.946463	+	0.322813i	$0.895371\pi$
$954$		0			0
$955$	5.00000	−	3.63271i	0.161796	−	0.117552i
$956$	−12.1803			−0.393940
$957$		0			0
$958$	−2.76393			−0.0892986
$959$	21.7082	−	15.7719i	0.700994	−	0.509302i
$960$		0			0
$961$	6.60081	−	20.3152i	0.212929	−	0.655329i
$962$	12.3541	+	8.97578i	0.398312	+	0.289391i
$963$		0			0
$964$	1.71885	−	5.29007i	0.0553603	−	0.170382i
$965$	0.527864	+	1.62460i	0.0169925	+	0.0522977i
$966$		0			0
$967$	−57.9787			−1.86447			−0.932235	−	0.361854i	$-0.882144\pi$
$967$	−57.9787			−1.86447			−0.932235	+	0.361854i	$0.882144\pi$
$968$	−7.54508	+	8.00448i	−0.242508	+	0.257274i
$969$		0			0
$970$	1.61803	−	1.17557i	0.0519519	−	0.0377453i
$971$	−1.24671	−	3.83698i	−0.0400089	−	0.123135i	0.929057	−	0.369936i	$-0.120620\pi$
$971$	−1.24671	−	3.83698i	−0.0400089	−	0.123135i	−0.969066	+	0.246802i	$0.920620\pi$
$972$		0			0
$973$	−23.2533	−	16.8945i	−0.745466	−	0.541613i
$974$	−18.9443	−	13.7638i	−0.607014	−	0.441021i
$975$		0			0
$976$	−1.14590	−	3.52671i	−0.0366793	−	0.112887i
$977$	0.854102	−	0.620541i	0.0273251	−	0.0198529i	−0.574039	−	0.818828i	$-0.694624\pi$
$977$	0.854102	−	0.620541i	0.0273251	−	0.0198529i	0.601364	+	0.798975i	$0.294624\pi$
$978$		0			0
$979$	19.5517	−	32.9892i	0.624874	−	1.05434i
$980$	5.09017			0.162600
$981$		0			0
$982$	−3.29837	−	10.1514i	−0.105255	−	0.323943i
$983$	−6.57295	+	20.2295i	−0.209645	+	0.645219i	0.789846	+	0.613305i	$0.210160\pi$
$983$	−6.57295	+	20.2295i	−0.209645	+	0.645219i	−0.999491	+	0.0319144i	$0.989840\pi$
$984$		0			0
$985$	−11.8262	−	8.59226i	−0.376815	−	0.273772i
$986$	−14.4721	+	44.5407i	−0.460887	+	1.41846i
$987$		0			0
$988$	−19.0623	+	13.8496i	−0.606453	+	0.440614i
$989$	10.6525			0.338729
$990$		0			0
$991$	−12.0000			−0.381193			−0.190596	−	0.981669i	$-0.561042\pi$
$991$	−12.0000			−0.381193			−0.190596	+	0.981669i	$0.561042\pi$
$992$	−5.85410	+	4.25325i	−0.185868	+	0.135041i
$993$		0			0
$994$	−3.49342	+	10.7516i	−0.110805	+	0.341022i
$995$	2.00000	+	1.45309i	0.0634043	+	0.0460659i
$996$		0			0
$997$	−6.79837	+	20.9232i	−0.215307	+	0.662646i	0.783825	+	0.620982i	$0.213266\pi$
$997$	−6.79837	+	20.9232i	−0.215307	+	0.662646i	−0.999132	+	0.0416640i	$0.986734\pi$
$998$	−3.84346	−	11.8290i	−0.121663	−	0.374439i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.n.h.91.1		4
3.2	odd	2		330.2.m.a.91.1	✓	4
11.4	even	5	inner	990.2.n.h.631.1		4
33.2	even	10		3630.2.a.bf.1.1		2
33.20	odd	10		3630.2.a.bl.1.2		2
33.26	odd	10		330.2.m.a.301.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.m.a.91.1	✓	4	3.2	odd	2
330.2.m.a.301.1	yes	4	33.26	odd	10
990.2.n.h.91.1		4	1.1	even	1	trivial
990.2.n.h.631.1		4	11.4	even	5	inner
3630.2.a.bf.1.1		2	33.2	even	10
3630.2.a.bl.1.2		2	33.20	odd	10

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:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 0.587785i) q^{5} +(-0.427051 + 1.31433i) q^{7} +(-0.309017 - 0.951057i) q^{8} +1.00000 q^{10} +(-1.69098 + 2.85317i) q^{11} +(3.92705 - 2.85317i) q^{13} +(0.427051 + 1.31433i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(5.23607 + 3.80423i) q^{17} +(-1.50000 - 4.61653i) q^{19} +(0.809017 - 0.587785i) q^{20} +(0.309017 + 3.30220i) q^{22} +8.61803 q^{23} +(0.309017 + 0.951057i) q^{25} +(1.50000 - 4.61653i) q^{26} +(1.11803 + 0.812299i) q^{28} +(-2.23607 + 6.88191i) q^{29} +(5.85410 - 4.25325i) q^{31} -1.00000 q^{32} +6.47214 q^{34} +(-1.11803 + 0.812299i) q^{35} +(-0.972136 + 2.99193i) q^{37} +(-3.92705 - 2.85317i) q^{38} +(0.309017 - 0.951057i) q^{40} +(0.336881 + 1.03681i) q^{41} +1.23607 q^{43} +(2.19098 + 2.48990i) q^{44} +(6.97214 - 5.06555i) q^{46} +(-3.64590 - 11.2209i) q^{47} +(4.11803 + 2.99193i) q^{49} +(0.809017 + 0.587785i) q^{50} +(-1.50000 - 4.61653i) q^{52} +(-10.5902 + 7.69421i) q^{53} +(-3.04508 + 1.31433i) q^{55} +1.38197 q^{56} +(2.23607 + 6.88191i) q^{58} +(2.88197 - 8.86978i) q^{59} +(3.00000 + 2.17963i) q^{61} +(2.23607 - 6.88191i) q^{62} +(-0.809017 + 0.587785i) q^{64} +4.85410 q^{65} -15.7082 q^{67} +(5.23607 - 3.80423i) q^{68} +(-0.427051 + 1.31433i) q^{70} +(6.61803 + 4.80828i) q^{71} +(0.618034 - 1.90211i) q^{73} +(0.972136 + 2.99193i) q^{74} -4.85410 q^{76} +(-3.02786 - 3.44095i) q^{77} +(2.85410 - 2.07363i) q^{79} +(-0.309017 - 0.951057i) q^{80} +(0.881966 + 0.640786i) q^{82} +(-5.23607 - 3.80423i) q^{83} +(2.00000 + 6.15537i) q^{85} +(1.00000 - 0.726543i) q^{86} +(3.23607 + 0.726543i) q^{88} -11.5623 q^{89} +(2.07295 + 6.37988i) q^{91} +(2.66312 - 8.19624i) q^{92} +(-9.54508 - 6.93491i) q^{94} +(1.50000 - 4.61653i) q^{95} +(1.61803 - 1.17557i) q^{97} +5.09017 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - q^{4} + q^{5} + 5 q^{7} + q^{8} + 4 q^{10} - 9 q^{11} + 9 q^{13} - 5 q^{14} - q^{16} + 12 q^{17} - 6 q^{19} + q^{20} - q^{22} + 30 q^{23} - q^{25} + 6 q^{26} + 10 q^{31} - 4 q^{32}+ \cdots - 2 q^{98}+O(q^{100}) \) 4 * q + q^2 - q^4 + q^5 + 5 * q^7 + q^8 + 4 * q^10 - 9 * q^11 + 9 * q^13 - 5 * q^14 - q^16 + 12 * q^17 - 6 * q^19 + q^20 - q^22 + 30 * q^23 - q^25 + 6 * q^26 + 10 * q^31 - 4 * q^32 + 8 * q^34 + 14 * q^37 - 9 * q^38 - q^40 + 17 * q^41 - 4 * q^43 + 11 * q^44 + 10 * q^46 - 28 * q^47 + 12 * q^49 + q^50 - 6 * q^52 - 20 * q^53 - q^55 + 10 * q^56 + 16 * q^59 + 12 * q^61 - q^64 + 6 * q^65 - 36 * q^67 + 12 * q^68 + 5 * q^70 + 22 * q^71 - 2 * q^73 - 14 * q^74 - 6 * q^76 - 30 * q^77 - 2 * q^79 + q^80 + 8 * q^82 - 12 * q^83 + 8 * q^85 + 4 * q^86 + 4 * q^88 - 6 * q^89 + 15 * q^91 - 5 * q^92 - 27 * q^94 + 6 * q^95 + 2 * q^97 - 2 * q^98

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