LMFDB - Embedded newform 84.4.k.c.17.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [84,4,Mod(5,84)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(84, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("84.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	84.k (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.95616044048$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 14 x^{10} - 32 x^{9} + 70 x^{8} + 224 x^{7} - 50 x^{6} + 2016 x^{5} + 5670 x^{4} + \cdots + 531441 $ x^12 - 14x^10 - 32x^9 + 70x^8 + 224x^7 - 50x^6 + 2016x^5 + 5670x^4 - 23328x^3 - 91854*x^2 + 531441
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.5
Root			$2.88784 + 0.812653i$ of defining polynomial
Character	$\chi$	$=$	84.17
Dual form			84.4.k.c.5.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.62798 - 3.71992i) q^{3} +(9.68891 + 16.7817i) q^{5} +(-2.66851 + 18.3270i) q^{7} +(-0.675594 - 26.9915i) q^{9} +(36.3221 + 20.9706i) q^{11} -77.1820i q^{13} +(97.5776 + 24.8416i) q^{15} +(2.98415 - 5.16871i) q^{17} +(-59.0330 + 34.0827i) q^{19} +(58.4937 + 76.4166i) q^{21} +(30.8090 - 17.7876i) q^{23} +(-125.250 + 216.939i) q^{25} +(-102.857 - 95.4115i) q^{27} -228.525i q^{29} +(62.3989 + 36.0260i) q^{31} +(209.785 - 59.0346i) q^{33} +(-333.413 + 132.787i) q^{35} +(-34.6696 - 60.0496i) q^{37} +(-287.111 - 280.014i) q^{39} -132.789 q^{41} -366.304 q^{43} +(446.418 - 272.856i) q^{45} +(90.9542 + 157.537i) q^{47} +(-328.758 - 97.8116i) q^{49} +(-8.40073 - 29.8527i) q^{51} +(15.3092 + 8.83877i) q^{53} +812.728i q^{55} +(-87.3853 + 343.249i) q^{57} +(-247.185 + 428.137i) q^{59} +(498.419 - 287.763i) q^{61} +(496.477 + 59.6456i) q^{63} +(1295.24 - 747.810i) q^{65} +(202.162 - 350.154i) q^{67} +(45.6060 - 179.140i) q^{69} -489.797i q^{71} +(-336.670 - 194.377i) q^{73} +(352.593 + 1252.97i) q^{75} +(-481.254 + 609.715i) q^{77} +(-126.706 - 219.461i) q^{79} +(-728.087 + 36.4707i) q^{81} +356.881 q^{83} +115.653 q^{85} +(-850.096 - 829.084i) q^{87} +(711.578 + 1232.49i) q^{89} +(1414.51 + 205.961i) q^{91} +(360.395 - 101.417i) q^{93} +(-1143.93 - 660.449i) q^{95} -694.168i q^{97} +(541.489 - 994.557i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 42 q^{7} - 84 q^{9} + 132 q^{15} + 204 q^{19} - 378 q^{21} - 444 q^{25} + 1458 q^{31} - 108 q^{33} + 240 q^{37} - 432 q^{39} - 342 q^{45} - 1218 q^{49} - 300 q^{51} + 180 q^{57} + 2148 q^{61} + 1596 q^{63}+ \cdots + 9216 q^{99}+O(q^{100}) $ 12 * q - 42 * q^7 - 84 * q^9 + 132 * q^15 + 204 * q^19 - 378 * q^21 - 444 * q^25 + 1458 * q^31 - 108 * q^33 + 240 * q^37 - 432 * q^39 - 342 * q^45 - 1218 * q^49 - 300 * q^51 + 180 * q^57 + 2148 * q^61 + 1596 * q^63 + 1980 * q^67 - 3084 * q^73 - 3384 * q^75 - 438 * q^79 + 1008 * q^81 - 6144 * q^85 - 2898 * q^87 + 3780 * q^91 + 882 * q^93 + 9216 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	3.62798	−	3.71992i	0.698204	−	0.715899i
$3$	3.62798	−	3.71992i	0.698204	−	0.715899i
$4$		0			0
$5$	9.68891	+	16.7817i	0.866602	+	1.50100i	0.865447	+	0.501000i	$0.167034\pi$
$5$	9.68891	+	16.7817i	0.866602	+	1.50100i	0.00115523	+	0.999999i	$0.499632\pi$
$6$		0			0
$7$	−2.66851	+	18.3270i	−0.144086	+	0.989565i
$7$	−2.66851	+	18.3270i	−0.144086	+	0.989565i
$8$		0			0
$9$	−0.675594	−	26.9915i	−0.0250220	−	0.999687i
$10$		0			0
$11$	36.3221	+	20.9706i	0.995593	+	0.574806i	0.906942	−	0.421257i	$-0.138411\pi$
$11$	36.3221	+	20.9706i	0.995593	+	0.574806i	0.0886519	+	0.996063i	$0.471744\pi$
$12$		0			0
$13$		−	77.1820i		−	1.64665i	−0.567571	−	0.823325i	$-0.692117\pi$
$13$		−	77.1820i		−	1.64665i	0.567571	−	0.823325i	$-0.307883\pi$
$14$		0			0
$15$	97.5776	+	24.8416i	1.67963	+	0.427604i
$16$		0			0
$17$	2.98415	−	5.16871i	0.0425743	−	0.0737409i	−0.843953	−	0.536417i	$-0.819777\pi$
$17$	2.98415	−	5.16871i	0.0425743	−	0.0737409i	0.886527	+	0.462676i	$0.153111\pi$
$18$		0			0
$19$	−59.0330	+	34.0827i	−0.712794	+	0.411532i	−0.812095	−	0.583525i	$-0.801673\pi$
$19$	−59.0330	+	34.0827i	−0.712794	+	0.411532i	0.0993004	+	0.995057i	$0.468340\pi$
$20$		0			0
$21$	58.4937	+	76.4166i	0.607827	+	0.794069i
$22$		0			0
$23$	30.8090	−	17.7876i	0.279310	−	0.161260i	−0.353801	−	0.935321i	$-0.615111\pi$
$23$	30.8090	−	17.7876i	0.279310	−	0.161260i	0.633111	+	0.774061i	$0.281778\pi$
$24$		0			0
$25$	−125.250	+	216.939i	−1.00200	+	1.73551i
$26$		0			0
$27$	−102.857	−	95.4115i	−0.733145	−	0.680072i
$28$		0			0
$29$		−	228.525i		−	1.46331i	−0.681673	−	0.731657i	$-0.738747\pi$
$29$		−	228.525i		−	1.46331i	0.681673	−	0.731657i	$-0.261253\pi$
$30$		0			0
$31$	62.3989	+	36.0260i	0.361522	+	0.208725i	0.669748	−	0.742588i	$-0.266402\pi$
$31$	62.3989	+	36.0260i	0.361522	+	0.208725i	−0.308226	+	0.951313i	$0.599735\pi$
$32$		0			0
$33$	209.785	−	59.0346i	1.10663	−	0.311412i
$34$		0			0
$35$	−333.413	+	132.787i	−1.61020	+	0.641287i
$36$		0			0
$37$	−34.6696	−	60.0496i	−0.154045	−	0.266813i	0.778666	−	0.627439i	$-0.215897\pi$
$37$	−34.6696	−	60.0496i	−0.154045	−	0.266813i	−0.932711	+	0.360625i	$0.882563\pi$
$38$		0			0
$39$	−287.111	−	280.014i	−1.17883	−	1.14970i
$40$		0			0
$41$	−132.789			−0.505810			−0.252905	−	0.967491i	$-0.581386\pi$
$41$	−132.789			−0.505810			−0.252905	+	0.967491i	$0.581386\pi$
$42$		0			0
$43$	−366.304			−1.29909			−0.649544	−	0.760324i	$-0.725040\pi$
$43$	−366.304			−1.29909			−0.649544	+	0.760324i	$0.725040\pi$
$44$		0			0
$45$	446.418	−	272.856i	1.47885	−	0.903889i
$46$		0			0
$47$	90.9542	+	157.537i	0.282277	+	0.488919i	0.971945	−	0.235207i	$-0.0755768\pi$
$47$	90.9542	+	157.537i	0.282277	+	0.488919i	−0.689668	+	0.724126i	$0.742244\pi$
$48$		0			0
$49$	−328.758	−	97.8116i	−0.958478	−	0.285165i
$50$		0			0
$51$	−8.40073	−	29.8527i	−0.0230654	−	0.0819651i
$52$		0			0
$53$	15.3092	+	8.83877i	0.0396770	+	0.0229075i	0.519707	−	0.854344i	$-0.326041\pi$
$53$	15.3092	+	8.83877i	0.0396770	+	0.0229075i	−0.480030	+	0.877252i	$0.659374\pi$
$54$		0			0
$55$			812.728i			1.99251i
$56$		0			0
$57$	−87.3853	+	343.249i	−0.203061	+	0.797622i
$58$		0			0
$59$	−247.185	+	428.137i	−0.545437	+	0.944724i	0.453142	+	0.891438i	$0.350303\pi$
$59$	−247.185	+	428.137i	−0.545437	+	0.944724i	−0.998579	+	0.0532862i	$0.983030\pi$
$60$		0			0
$61$	498.419	−	287.763i	1.04617	−	0.604004i	0.124592	−	0.992208i	$-0.460238\pi$
$61$	498.419	−	287.763i	1.04617	−	0.604004i	0.921573	+	0.388204i	$0.126905\pi$
$62$		0			0
$63$	496.477	+	59.6456i	0.992861	+	0.119280i
$64$		0			0
$65$	1295.24	−	747.810i	2.47162	−	1.42699i
$66$		0			0
$67$	202.162	−	350.154i	0.368627	−	0.638480i	−0.620725	−	0.784029i	$-0.713161\pi$
$67$	202.162	−	350.154i	0.368627	−	0.638480i	0.989351	+	0.145549i	$0.0464948\pi$
$68$		0			0
$69$	45.6060	−	179.140i	0.0795697	−	0.312550i
$70$		0			0
$71$		−	489.797i		−	0.818707i	−0.912376	−	0.409353i	$-0.865754\pi$
$71$		−	489.797i		−	0.818707i	0.912376	−	0.409353i	$-0.134246\pi$
$72$		0			0
$73$	−336.670	−	194.377i	−0.539785	−	0.311645i	0.205207	−	0.978719i	$-0.434213\pi$
$73$	−336.670	−	194.377i	−0.539785	−	0.311645i	−0.744992	+	0.667074i	$0.767547\pi$
$74$		0			0
$75$	352.593	+	1252.97i	0.542852	+	1.92907i
$76$		0			0
$77$	−481.254	+	609.715i	−0.712259	+	0.902383i
$78$		0			0
$79$	−126.706	−	219.461i	−0.180449	−	0.312547i	0.761584	−	0.648066i	$-0.224422\pi$
$79$	−126.706	−	219.461i	−0.180449	−	0.312547i	−0.942034	+	0.335518i	$0.891089\pi$
$80$		0			0
$81$	−728.087	+	36.4707i	−0.998748	+	0.0500284i
$82$		0			0
$83$	356.881			0.471961			0.235981	−	0.971758i	$-0.424170\pi$
$83$	356.881			0.471961			0.235981	+	0.971758i	$0.424170\pi$
$84$		0			0
$85$	115.653			0.147580
$86$		0			0
$87$	−850.096	−	829.084i	−1.04758	−	1.02169i
$88$		0			0
$89$	711.578	+	1232.49i	0.847496	+	1.46791i	0.883436	+	0.468552i	$0.155224\pi$
$89$	711.578	+	1232.49i	0.847496	+	1.46791i	−0.0359398	+	0.999354i	$0.511442\pi$
$90$		0			0
$91$	1414.51	+	205.961i	1.62947	+	0.237259i
$92$		0			0
$93$	360.395	−	101.417i	0.401842	−	0.113080i
$94$		0			0
$95$	−1143.93	−	660.449i	−1.23542	−	0.713269i
$96$		0			0
$97$		−	694.168i		−	0.726619i	−0.931668	−	0.363310i	$-0.881647\pi$
$97$		−	694.168i		−	0.726619i	0.931668	−	0.363310i	$-0.118353\pi$
$98$		0			0
$99$	541.489	−	994.557i	0.549714	−	1.00966i
$100$		0			0
$101$	−7.67034	+	13.2854i	−0.00755671	+	0.0130886i	−0.869779	−	0.493441i	$-0.835739\pi$
$101$	−7.67034	+	13.2854i	−0.00755671	+	0.0130886i	0.862222	+	0.506530i	$0.169072\pi$
$102$		0			0
$103$	−305.835	+	176.574i	−0.292571	+	0.168916i	−0.639101	−	0.769123i	$-0.720693\pi$
$103$	−305.835	+	176.574i	−0.292571	+	0.168916i	0.346530	+	0.938039i	$0.387360\pi$
$104$		0			0
$105$	−715.659	+	1722.02i	−0.665154	+	1.60049i
$106$		0			0
$107$	−44.6169	+	25.7596i	−0.0403110	+	0.0232736i	−0.520020	−	0.854154i	$-0.674076\pi$
$107$	−44.6169	+	25.7596i	−0.0403110	+	0.0232736i	0.479709	+	0.877428i	$0.340742\pi$
$108$		0			0
$109$	335.314	−	580.781i	0.294654	−	0.510355i	−0.680250	−	0.732980i	$-0.738129\pi$
$109$	335.314	−	580.781i	0.294654	−	0.510355i	0.974904	+	0.222624i	$0.0714623\pi$
$110$		0			0
$111$	−349.160	−	88.8901i	−0.298566	−	0.0760097i
$112$		0			0
$113$		−	461.944i		−	0.384567i	−0.981339	−	0.192283i	$-0.938411\pi$
$113$		−	461.944i		−	0.384567i	0.981339	−	0.192283i	$-0.0615893\pi$
$114$		0			0
$115$	597.012	+	344.685i	0.484101	+	0.279496i
$116$		0			0
$117$	−2083.26	+	52.1437i	−1.64613	+	0.0412025i
$118$		0			0
$119$	86.7636	+	68.4833i	0.0668371	+	0.0527551i
$120$		0			0
$121$	214.030	+	370.711i	0.160804	+	0.278521i
$122$		0			0
$123$	−481.757	+	493.966i	−0.353159	+	0.362109i
$124$		0			0
$125$	−2431.91			−1.74014
$126$		0			0
$127$	−388.699			−0.271587			−0.135793	−	0.990737i	$-0.543358\pi$
$127$	−388.699			−0.271587			−0.135793	+	0.990737i	$0.543358\pi$
$128$		0			0
$129$	−1328.94	+	1362.62i	−0.907028	+	0.930015i
$130$		0			0
$131$	313.837	+	543.582i	0.209314	+	0.362542i	0.951499	−	0.307653i	$-0.0995437\pi$
$131$	313.837	+	543.582i	0.209314	+	0.362542i	−0.742185	+	0.670195i	$0.766210\pi$
$132$		0			0
$133$	−467.104	−	1172.85i	−0.304534	−	0.764653i
$134$		0			0
$135$	604.590	−	2650.55i	0.385443	−	1.68980i
$136$		0			0
$137$	−1822.30	−	1052.10i	−1.13642	−	0.656111i	−0.190877	−	0.981614i	$-0.561133\pi$
$137$	−1822.30	−	1052.10i	−1.13642	−	0.656111i	−0.945541	+	0.325502i	$0.894467\pi$
$138$		0			0
$139$			1030.03i			0.628533i	0.949335	+	0.314266i	$0.101759\pi$
$139$			1030.03i			0.628533i	−0.949335	+	0.314266i	$0.898241\pi$
$140$		0			0
$141$	916.005	+	233.199i	0.547103	+	0.139283i
$142$		0			0
$143$	1618.55	−	2803.41i	0.946504	−	1.63939i
$144$		0			0
$145$	3835.04	−	2214.16i	2.19643	−	1.26811i
$146$		0			0
$147$	−1556.58	+	868.095i	−0.873363	+	0.487070i
$148$		0			0
$149$	174.214	−	100.583i	0.0957866	−	0.0553024i	−0.451342	−	0.892351i	$-0.649054\pi$
$149$	174.214	−	100.583i	0.0957866	−	0.0553024i	0.547128	+	0.837049i	$0.315721\pi$
$150$		0			0
$151$	−596.238	+	1032.71i	−0.321332	+	0.556564i	−0.980763	−	0.195202i	$-0.937464\pi$
$151$	−596.238	+	1032.71i	−0.321332	+	0.556564i	0.659431	+	0.751765i	$0.270797\pi$
$152$		0			0
$153$	−141.527	−	77.0550i	−0.0747831	−	0.0407158i
$154$		0			0
$155$			1396.21i			0.723525i
$156$		0			0
$157$	945.892	+	546.111i	0.480830	+	0.277608i	0.720762	−	0.693182i	$-0.243792\pi$
$157$	945.892	+	546.111i	0.480830	+	0.277608i	−0.239932	+	0.970790i	$0.577125\pi$
$158$		0			0
$159$	88.4208	−	24.8821i	0.0441021	−	0.0124106i
$160$		0			0
$161$	243.779	+	612.104i	0.119332	+	0.299631i
$162$		0			0
$163$	289.802	+	501.952i	0.139258	+	0.241202i	0.927216	−	0.374527i	$-0.122195\pi$
$163$	289.802	+	501.952i	0.139258	+	0.241202i	−0.787958	+	0.615729i	$0.788862\pi$
$164$		0			0
$165$	3023.28	+	2948.56i	1.42644	+	1.39118i
$166$		0			0
$167$	3715.71			1.72174			0.860869	−	0.508827i	$-0.169921\pi$
$167$	3715.71			1.72174			0.860869	+	0.508827i	$0.169921\pi$
$168$		0			0
$169$	−3760.06			−1.71145
$170$		0			0
$171$	959.827	+	1570.37i	0.429239	+	0.702274i
$172$		0			0
$173$	669.204	+	1159.10i	0.294096	+	0.509390i	0.974774	−	0.223193i	$-0.0716480\pi$
$173$	669.204	+	1159.10i	0.294096	+	0.509390i	−0.680678	+	0.732583i	$0.738315\pi$
$174$		0			0
$175$	−3641.62	−	2874.36i	−1.57303	−	1.24161i
$176$		0			0
$177$	695.854	+	2472.78i	0.295501	+	1.05009i
$178$		0			0
$179$	2441.07	+	1409.35i	1.01930	+	0.588492i	0.913900	−	0.405938i	$-0.133055\pi$
$179$	2441.07	+	1409.35i	1.01930	+	0.588492i	0.105397	+	0.994430i	$0.466389\pi$
$180$		0			0
$181$			3688.28i			1.51463i	0.653050	+	0.757315i	$0.273489\pi$
$181$			3688.28i			1.51463i	−0.653050	+	0.757315i	$0.726511\pi$
$182$		0			0
$183$	737.800	−	2898.08i	0.298031	−	1.17067i
$184$		0			0
$185$	671.822	−	1163.63i	0.266991	−	0.462442i
$186$		0			0
$187$	216.781	−	125.159i	0.0847734	−	0.0489440i
$188$		0			0
$189$	2023.08	−	1630.46i	0.778612	−	0.627506i
$190$		0			0
$191$	−3905.03	+	2254.57i	−1.47936	+	0.854111i	−0.999727	−	0.0233572i	$-0.992564\pi$
$191$	−3905.03	+	2254.57i	−1.47936	+	0.854111i	−0.479636	+	0.877468i	$0.659231\pi$
$192$		0			0
$193$	1105.75	−	1915.21i	0.412401	−	0.714300i	−0.582751	−	0.812651i	$-0.698024\pi$
$193$	1105.75	−	1915.21i	0.412401	−	0.714300i	0.995152	+	0.0983513i	$0.0313569\pi$
$194$		0			0
$195$	1917.32	−	7531.24i	0.704114	−	2.76576i
$196$		0			0
$197$			4177.21i			1.51073i	0.655304	+	0.755365i	$0.272540\pi$
$197$			4177.21i			1.51073i	−0.655304	+	0.755365i	$0.727460\pi$
$198$		0			0
$199$	3823.65	+	2207.59i	1.36207	+	0.786391i	0.989899	−	0.141774i	$-0.0452807\pi$
$199$	3823.65	+	2207.59i	1.36207	+	0.786391i	0.372169	+	0.928165i	$0.378614\pi$
$200$		0			0
$201$	−569.108	−	2022.38i	−0.199710	−	0.709689i
$202$		0			0
$203$	4188.19	+	609.823i	1.44804	+	0.210843i
$204$		0			0
$205$	−1286.58	−	2228.43i	−0.438336	−	0.759221i
$206$		0			0
$207$	−500.929	−	819.566i	−0.168198	−	0.275187i
$208$		0			0
$209$	−2858.94			−0.946205
$210$		0			0
$211$	−2002.19			−0.653252			−0.326626	−	0.945154i	$-0.605912\pi$
$211$	−2002.19			−0.653252			−0.326626	+	0.945154i	$0.605912\pi$
$212$		0			0
$213$	−1822.00	−	1776.97i	−0.586111	−	0.571624i
$214$		0			0
$215$	−3549.08	−	6147.19i	−1.12579	−	1.94993i
$216$		0			0
$217$	−826.761	+	1047.45i	−0.258637	+	0.327675i
$218$		0			0
$219$	−1944.50	+	547.193i	−0.599986	+	0.168839i
$220$		0			0
$221$	−398.931	−	230.323i	−0.121425	−	0.0701050i
$222$		0			0
$223$			2122.04i			0.637230i	0.947884	+	0.318615i	$0.103218\pi$
$223$			2122.04i			0.637230i	−0.947884	+	0.318615i	$0.896782\pi$
$224$		0			0
$225$	5940.14	+	3234.13i	1.76004	+	0.958260i
$226$		0			0
$227$	−2431.41	+	4211.33i	−0.710918	+	1.23135i	0.253594	+	0.967311i	$0.418387\pi$
$227$	−2431.41	+	4211.33i	−0.710918	+	1.23135i	−0.964513	+	0.264036i	$0.914946\pi$
$228$		0			0
$229$	−4903.46	+	2831.01i	−1.41498	+	0.816937i	−0.995852	−	0.0909910i	$-0.970997\pi$
$229$	−4903.46	+	2831.01i	−1.41498	+	0.816937i	−0.419125	+	0.907928i	$0.637663\pi$
$230$		0			0
$231$	522.114	+	4002.26i	0.148713	+	1.13995i
$232$		0			0
$233$	2817.82	−	1626.87i	0.792280	−	0.457423i	−0.0484845	−	0.998824i	$-0.515439\pi$
$233$	2817.82	−	1626.87i	0.792280	−	0.457423i	0.840765	+	0.541401i	$0.182106\pi$
$234$		0			0
$235$	−1762.49	+	3052.73i	−0.489244	+	0.847396i
$236$		0			0
$237$	−1276.06	−	324.863i	−0.349743	−	0.0890385i
$238$		0			0
$239$		−	5823.69i		−	1.57616i	−0.615571	−	0.788082i	$-0.711074\pi$
$239$		−	5823.69i		−	1.57616i	0.615571	−	0.788082i	$-0.288926\pi$
$240$		0			0
$241$	−5349.06	−	3088.28i	−1.42972	−	0.825451i	−0.432624	−	0.901574i	$-0.642412\pi$
$241$	−5349.06	−	3088.28i	−1.42972	−	0.825451i	−0.997098	+	0.0761237i	$0.975746\pi$
$242$		0			0
$243$	−2505.81	+	2840.74i	−0.661515	+	0.749932i
$244$		0			0
$245$	−1543.86	−	6464.80i	−0.402587	−	1.68580i
$246$		0			0
$247$	2630.57	+	4556.28i	0.677649	+	1.17372i
$248$		0			0
$249$	1294.76	−	1327.57i	0.329525	−	0.337877i
$250$		0			0
$251$	−1648.38			−0.414522			−0.207261	−	0.978286i	$-0.566455\pi$
$251$	−1648.38			−0.414522			−0.207261	+	0.978286i	$0.566455\pi$
$252$		0			0
$253$	1492.07			0.370772
$254$		0			0
$255$	419.585	−	430.219i	0.103041	−	0.105652i
$256$		0			0
$257$	−1602.27	−	2775.22i	−0.388899	−	0.673592i	0.603403	−	0.797436i	$-0.293811\pi$
$257$	−1602.27	−	2775.22i	−0.388899	−	0.673592i	−0.992302	+	0.123844i	$0.960478\pi$
$258$		0			0
$259$	1193.04	−	475.147i	0.286225	−	0.113993i
$260$		0			0
$261$	−6168.25	+	154.390i	−1.46286	+	0.0366151i
$262$		0			0
$263$	2995.95	+	1729.71i	0.702426	+	0.405546i	0.808250	−	0.588839i	$-0.200415\pi$
$263$	2995.95	+	1729.71i	0.702426	+	0.405546i	−0.105824	+	0.994385i	$0.533748\pi$
$264$		0			0
$265$			342.552i			0.0794068i
$266$		0			0
$267$	7166.35	+	1824.43i	1.64260	+	0.418177i
$268$		0			0
$269$	−665.298	+	1152.33i	−0.150795	+	0.261185i	−0.931520	−	0.363690i	$-0.881517\pi$
$269$	−665.298	+	1152.33i	−0.150795	+	0.261185i	0.780725	+	0.624875i	$0.214850\pi$
$270$		0			0
$271$	2894.39	−	1671.08i	0.648789	−	0.374578i	−0.139203	−	0.990264i	$-0.544454\pi$
$271$	2894.39	−	1671.08i	0.648789	−	0.374578i	0.787992	+	0.615686i	$0.211121\pi$
$272$		0			0
$273$	5897.98	−	4514.66i	1.30755	−	1.00088i
$274$		0			0
$275$	−9098.68	+	5253.13i	−1.99517	+	1.15191i
$276$		0			0
$277$	2400.57	−	4157.91i	0.520709	−	0.901894i	−0.479001	−	0.877814i	$-0.659001\pi$
$277$	2400.57	−	4157.91i	0.520709	−	0.901894i	0.999710	−	0.0240796i	$-0.00766553\pi$
$278$		0			0
$279$	930.241	−	1708.58i	0.199613	−	0.366631i
$280$		0			0
$281$			4548.87i			0.965704i	0.875702	+	0.482852i	$0.160399\pi$
$281$			4548.87i			0.965704i	−0.875702	+	0.482852i	$0.839601\pi$
$282$		0			0
$283$	−3922.91	−	2264.89i	−0.824003	−	0.475739i	0.0277917	−	0.999614i	$-0.491152\pi$
$283$	−3922.91	−	2264.89i	−0.824003	−	0.475739i	−0.851795	+	0.523875i	$0.824486\pi$
$284$		0			0
$285$	−6606.97	+	1859.24i	−1.37320	+	0.386427i
$286$		0			0
$287$	354.350	−	2433.63i	0.0728802	−	0.500532i
$288$		0			0
$289$	2438.69	+	4223.93i	0.496375	+	0.859746i
$290$		0			0
$291$	−2582.25	−	2518.42i	−0.520186	−	0.507328i
$292$		0			0
$293$	9525.19			1.89921			0.949603	−	0.313454i	$-0.101486\pi$
$293$	9525.19			1.89921			0.949603	+	0.313454i	$0.101486\pi$
$294$		0			0
$295$	−9579.82			−1.89071
$296$		0			0
$297$	−1735.16	−	5622.53i	−0.339005	−	1.09849i
$298$		0			0
$299$	−1372.88	−	2377.90i	−0.265538	−	0.459925i
$300$		0			0
$301$	977.485	−	6713.25i	0.187180	−	1.28553i
$302$		0			0
$303$	21.5929	+	76.7322i	0.00409399	+	0.0145484i
$304$		0			0
$305$	9658.28	+	5576.21i	1.81322	+	1.04686i
$306$		0			0
$307$			3743.83i			0.696000i	0.937495	+	0.348000i	$0.113139\pi$
$307$			3743.83i			0.696000i	−0.937495	+	0.348000i	$0.886861\pi$
$308$		0			0
$309$	−452.720	+	1778.28i	−0.0833475	+	0.327389i
$310$		0			0
$311$	−5201.50	+	9009.27i	−0.948393	+	1.64266i	−0.199582	+	0.979881i	$0.563958\pi$
$311$	−5201.50	+	9009.27i	−0.948393	+	1.64266i	−0.748811	+	0.662783i	$0.769375\pi$
$312$		0			0
$313$	2850.12	−	1645.52i	0.514690	−	0.297157i	−0.220069	−	0.975484i	$-0.570628\pi$
$313$	2850.12	−	1645.52i	0.514690	−	0.297157i	0.734760	+	0.678328i	$0.237295\pi$
$314$		0			0
$315$	3809.37	+	8909.62i	0.681376	+	1.59365i
$316$		0			0
$317$	5177.79	−	2989.40i	0.917393	−	0.529657i	0.0345906	−	0.999402i	$-0.488987\pi$
$317$	5177.79	−	2989.40i	0.917393	−	0.529657i	0.882802	+	0.469744i	$0.155654\pi$
$318$		0			0
$319$	4792.31	−	8300.52i	0.841122	−	1.45687i
$320$		0			0
$321$	−66.0454	+	259.426i	−0.0114838	+	0.0451083i
$322$		0			0
$323$			406.832i			0.0700828i
$324$		0			0
$325$	16743.8	+	9667.04i	2.85778	+	1.64994i
$326$		0			0
$327$	−943.947	−	3354.40i	−0.159634	−	0.567275i
$328$		0			0
$329$	−3129.90	+	1246.53i	−0.524489	+	0.208885i
$330$		0			0
$331$	−20.9169	−	36.2291i	−0.00347340	−	0.00601611i	0.864283	−	0.503005i	$-0.167772\pi$
$331$	−20.9169	−	36.2291i	−0.00347340	−	0.00601611i	−0.867757	+	0.496989i	$0.834439\pi$
$332$		0			0
$333$	−1597.41	+	976.356i	−0.262875	+	0.160673i
$334$		0			0
$335$	7834.90			1.27781
$336$		0			0
$337$	−5477.82			−0.885447			−0.442723	−	0.896658i	$-0.645988\pi$
$337$	−5477.82			−0.885447			−0.442723	+	0.896658i	$0.645988\pi$
$338$		0			0
$339$	−1718.40	−	1675.92i	−0.275311	−	0.268506i
$340$		0			0
$341$	1510.97	+	2617.08i	0.239952	+	0.415610i
$342$		0			0
$343$	2669.89	−	5764.14i	0.420293	−	0.907389i
$344$		0			0
$345$	3448.14	−	970.327i	0.538092	−	0.151422i
$346$		0			0
$347$	−958.002	−	553.103i	−0.148208	−	0.0855681i	0.424062	−	0.905633i	$-0.360604\pi$
$347$	−958.002	−	553.103i	−0.148208	−	0.0855681i	−0.572270	+	0.820065i	$0.693937\pi$
$348$		0			0
$349$			7172.24i			1.10006i	0.835145	+	0.550030i	$0.185384\pi$
$349$			7172.24i			1.10006i	−0.835145	+	0.550030i	$0.814616\pi$
$350$		0			0
$351$	−7364.05	+	7938.74i	−1.11984	+	1.20723i
$352$		0			0
$353$	3686.86	−	6385.84i	0.555898	−	0.962843i	−0.441935	−	0.897047i	$-0.645708\pi$
$353$	3686.86	−	6385.84i	0.555898	−	0.962843i	0.997833	−	0.0657965i	$-0.0209588\pi$
$354$		0			0
$355$	8219.61	−	4745.60i	1.22888	−	0.709493i
$356$		0			0
$357$	569.529	−	74.2979i	0.0844332	−	0.0110147i
$358$		0			0
$359$	−827.565	+	477.795i	−0.121664	+	0.0702425i	−0.559597	−	0.828765i	$-0.689044\pi$
$359$	−827.565	+	477.795i	−0.121664	+	0.0702425i	0.437933	+	0.899008i	$0.355711\pi$
$360$		0			0
$361$	−1106.24	+	1916.06i	−0.161283	+	0.279350i
$362$		0			0
$363$	2155.51	+	548.756i	0.311667	+	0.0793450i
$364$		0			0
$365$		−	7533.19i		−	1.08029i
$366$		0			0
$367$	−4935.71	−	2849.63i	−0.702021	−	0.405312i	0.106079	−	0.994358i	$-0.466170\pi$
$367$	−4935.71	−	2849.63i	−0.702021	−	0.405312i	−0.808100	+	0.589046i	$0.799504\pi$
$368$		0			0
$369$	89.7118	+	3584.19i	0.0126564	+	0.505652i
$370$		0			0
$371$	−202.841	+	256.985i	−0.0283854	+	0.0359623i
$372$		0			0
$373$	−4957.03	−	8585.83i	−0.688111	−	1.19184i	−0.972448	−	0.233119i	$-0.925107\pi$
$373$	−4957.03	−	8585.83i	−0.688111	−	1.19184i	0.284337	−	0.958724i	$-0.408226\pi$
$374$		0			0
$375$	−8822.92	+	9046.52i	−1.21497	+	1.24576i
$376$		0			0
$377$	−17638.1			−2.40956
$378$		0			0
$379$	8051.92			1.09129			0.545646	−	0.838016i	$-0.316284\pi$
$379$	8051.92			1.09129			0.545646	+	0.838016i	$0.316284\pi$
$380$		0			0
$381$	−1410.19	+	1445.93i	−0.189623	+	0.194428i
$382$		0			0
$383$	−2184.21	−	3783.17i	−0.291405	−	0.504728i	0.682737	−	0.730664i	$-0.260789\pi$
$383$	−2184.21	−	3783.17i	−0.291405	−	0.504728i	−0.974142	+	0.225936i	$0.927456\pi$
$384$		0			0
$385$	−14894.9	−	2168.77i	−1.97172	−	0.287093i
$386$		0			0
$387$	247.473	+	9887.10i	0.0325058	+	1.29868i
$388$		0			0
$389$	2123.46	+	1225.98i	0.276770	+	0.159793i	0.631960	−	0.775001i	$-0.282251\pi$
$389$	2123.46	+	1225.98i	0.276770	+	0.159793i	−0.355190	+	0.934794i	$0.615584\pi$
$390$		0			0
$391$		−	212.324i		−	0.0274621i
$392$		0			0
$393$	3160.68	+	804.654i	0.405687	+	0.103281i
$394$		0			0
$395$	2455.28	−	4252.67i	0.312756	−	0.541709i
$396$		0			0
$397$	7282.29	−	4204.43i	0.920624	−	0.531523i	0.0367899	−	0.999323i	$-0.488287\pi$
$397$	7282.29	−	4204.43i	0.920624	−	0.531523i	0.883834	+	0.467801i	$0.154953\pi$
$398$		0			0
$399$	−6057.54	−	2517.47i	−0.760041	−	0.315868i
$400$		0			0
$401$	−6960.80	+	4018.82i	−0.866847	+	0.500474i	−0.866299	−	0.499526i	$-0.833508\pi$
$401$	−6960.80	+	4018.82i	−0.866847	+	0.500474i	−0.000547684		1.00000i	$0.500174\pi$
$402$		0			0
$403$	2780.56	−	4816.07i	0.343696	−	0.595299i
$404$		0			0
$405$	−7666.41	−	11865.2i	−0.940610	−	1.45577i
$406$		0			0
$407$		−	2908.17i		−	0.354183i
$408$		0			0
$409$	4257.86	+	2458.28i	0.514762	+	0.297198i	0.734789	−	0.678296i	$-0.237281\pi$
$409$	4257.86	+	2458.28i	0.514762	+	0.297198i	−0.220027	+	0.975494i	$0.570614\pi$
$410$		0			0
$411$	−10525.0	+	2961.79i	−1.26316	+	0.355461i
$412$		0			0
$413$	−7186.86	−	5672.65i	−0.856276	−	0.675867i
$414$		0			0
$415$	3457.79	+	5989.07i	0.409003	+	0.708414i
$416$		0			0
$417$	3831.63	+	3736.93i	0.449966	+	0.438844i
$418$		0			0
$419$	4713.84			0.549608			0.274804	−	0.961500i	$-0.411387\pi$
$419$	4713.84			0.549608			0.274804	+	0.961500i	$0.411387\pi$
$420$		0			0
$421$	9921.92			1.14861			0.574305	−	0.818641i	$-0.305272\pi$
$421$	9921.92			1.14861			0.574305	+	0.818641i	$0.305272\pi$
$422$		0			0
$423$	4190.73	−	2561.43i	0.481702	−	0.294423i
$424$		0			0
$425$	747.530	+	1294.76i	0.0853189	+	0.147777i
$426$		0			0
$427$	3943.79	+	9902.43i	0.446963	+	1.12228i
$428$		0			0
$429$	−4556.41	−	16191.6i	−0.512786	−	1.82223i
$430$		0			0
$431$	−10901.0	−	6293.70i	−1.21829	−	0.703380i	−0.253739	−	0.967273i	$-0.581660\pi$
$431$	−10901.0	−	6293.70i	−1.21829	−	0.703380i	−0.964552	+	0.263892i	$0.914994\pi$
$432$		0			0
$433$		−	3715.19i		−	0.412334i	−0.978517	−	0.206167i	$-0.933901\pi$
$433$		−	3715.19i		−	0.412334i	0.978517	−	0.206167i	$-0.0660989\pi$
$434$		0			0
$435$	5676.93	−	22299.0i	0.625719	−	2.45782i
$436$		0			0
$437$	−1212.50	+	2100.11i	−0.132727	+	0.229890i
$438$		0			0
$439$	−5079.47	+	2932.63i	−0.552232	+	0.318831i	−0.750022	−	0.661413i	$-0.769957\pi$
$439$	−5079.47	+	2932.63i	−0.552232	+	0.318831i	0.197790	+	0.980244i	$0.436624\pi$
$440$		0			0
$441$	−2417.98	+	8939.77i	−0.261093	+	0.965314i
$442$		0			0
$443$	13372.1	−	7720.38i	1.43415	−	0.828005i	0.436713	−	0.899601i	$-0.356142\pi$
$443$	13372.1	−	7720.38i	1.43415	−	0.828005i	0.997434	+	0.0715954i	$0.0228090\pi$
$444$		0			0
$445$	−13788.8	+	23883.0i	−1.46888	+	2.54418i
$446$		0			0
$447$	257.886	−	1012.98i	0.0272877	−	0.107186i
$448$		0			0
$449$			16373.4i			1.72095i	0.509491	+	0.860476i	$0.329834\pi$
$449$			16373.4i			1.72095i	−0.509491	+	0.860476i	$0.670166\pi$
$450$		0			0
$451$	−4823.19	−	2784.67i	−0.503581	−	0.290743i
$452$		0			0
$453$	1678.48	+	5964.62i	0.174088	+	0.618636i
$454$		0			0
$455$	10248.7	+	25733.5i	1.05597	+	2.65144i
$456$		0			0
$457$	−1377.21	−	2385.40i	−0.140970	−	0.244167i	0.786892	−	0.617090i	$-0.211689\pi$
$457$	−1377.21	−	2385.40i	−0.140970	−	0.244167i	−0.927862	+	0.372923i	$0.878355\pi$
$458$		0			0
$459$	−800.096	+	246.917i	−0.0813623	+	0.0251092i
$460$		0			0
$461$	−15142.3			−1.52982			−0.764909	−	0.644139i	$-0.777216\pi$
$461$	−15142.3			−1.52982			−0.764909	+	0.644139i	$0.777216\pi$
$462$		0			0
$463$	−10138.9			−1.01770			−0.508851	−	0.860855i	$-0.669930\pi$
$463$	−10138.9			−1.01770			−0.508851	+	0.860855i	$0.669930\pi$
$464$		0			0
$465$	5193.79	+	5065.42i	0.517971	+	0.505168i
$466$		0			0
$467$	8074.64	+	13985.7i	0.800106	+	1.38583i	0.919545	+	0.392984i	$0.128557\pi$
$467$	8074.64	+	13985.7i	0.800106	+	1.38583i	−0.119439	+	0.992842i	$0.538110\pi$
$468$		0			0
$469$	5877.81	+	4639.41i	0.578703	+	0.456776i
$470$		0			0
$471$	5463.16	−	1537.36i	0.534457	−	0.150399i
$472$		0			0
$473$	−13304.9	−	7681.60i	−1.29336	−	0.746724i
$474$		0			0
$475$		−	17075.4i		−	1.64942i
$476$		0			0
$477$	228.229	−	419.190i	0.0219075	−	0.0402377i
$478$		0			0
$479$	4209.90	−	7291.77i	0.401577	−	0.695552i	−0.592339	−	0.805689i	$-0.701796\pi$
$479$	4209.90	−	7291.77i	0.401577	−	0.695552i	0.993916	+	0.110137i	$0.0351289\pi$
$480$		0			0
$481$	−4634.75	+	2675.87i	−0.439348	+	0.253657i
$482$		0			0
$483$	3161.40	+	1313.86i	0.297823	+	0.123773i
$484$		0			0
$485$	11649.3	−	6725.73i	1.09065	−	0.629690i
$486$		0			0
$487$	7039.12	−	12192.1i	0.654975	−	1.13445i	−0.326925	−	0.945050i	$-0.606013\pi$
$487$	7039.12	−	12192.1i	0.654975	−	1.13445i	0.981900	−	0.189400i	$-0.0606541\pi$
$488$		0			0
$489$	2918.61	+	743.029i	0.269907	+	0.0687135i
$490$		0			0
$491$		−	17853.2i		−	1.64094i	−0.571688	−	0.820471i	$-0.693711\pi$
$491$		−	17853.2i		−	1.64094i	0.571688	−	0.820471i	$-0.306289\pi$
$492$		0			0
$493$	−1181.18	−	681.955i	−0.107906	−	0.0622996i
$494$		0			0
$495$	21936.8	−	549.075i	1.99189	−	0.0498567i
$496$		0			0
$497$	8976.51	+	1307.03i	0.810164	+	0.117964i
$498$		0			0
$499$	−6802.88	−	11782.9i	−0.610298	−	1.05707i	−0.991190	−	0.132447i	$-0.957716\pi$
$499$	−6802.88	−	11782.9i	−0.610298	−	1.05707i	0.380892	−	0.924619i	$-0.375617\pi$
$500$		0			0
$501$	13480.5	−	13822.1i	1.20212	−	1.23259i
$502$		0			0
$503$	7503.79			0.665164			0.332582	−	0.943074i	$-0.392080\pi$
$503$	7503.79			0.665164			0.332582	+	0.943074i	$0.392080\pi$
$504$		0			0
$505$	−297.269			−0.0261946
$506$		0			0
$507$	−13641.4	+	13987.1i	−1.19494	+	1.22523i
$508$		0			0
$509$	5239.61	+	9075.27i	0.456270	+	0.790283i	0.998760	−	0.0497789i	$-0.0158517\pi$
$509$	5239.61	+	9075.27i	0.456270	+	0.790283i	−0.542490	+	0.840062i	$0.682518\pi$
$510$		0			0
$511$	4460.75	−	5651.46i	0.386168	−	0.489248i
$512$		0			0
$513$	9323.86	+	2126.77i	0.802453	+	0.183039i
$514$		0			0
$515$	−5926.41	−	3421.61i	−0.507085	−	0.292766i
$516$		0			0
$517$			7629.45i			0.649019i
$518$		0			0
$519$	6739.60	+	1715.79i	0.570011	+	0.145115i
$520$		0			0
$521$	3647.88	−	6318.31i	0.306749	−	0.531305i	−0.670900	−	0.741548i	$-0.734092\pi$
$521$	3647.88	−	6318.31i	0.306749	−	0.531305i	0.977649	+	0.210243i	$0.0674254\pi$
$522$		0			0
$523$	−13159.3	+	7597.52i	−1.10022	+	0.635213i	−0.936279	−	0.351257i	$-0.885754\pi$
$523$	−13159.3	+	7597.52i	−1.10022	+	0.635213i	−0.163942	+	0.986470i	$0.552421\pi$
$524$		0			0
$525$	−23904.1	+	3118.41i	−1.98716	+	0.259235i
$526$		0			0
$527$	372.416	−	215.014i	0.0307831	−	0.0177726i
$528$		0			0
$529$	−5450.70	+	9440.89i	−0.447991	+	0.775943i
$530$		0			0
$531$	11723.1	+	6382.66i	0.958076	+	0.521627i
$532$		0			0
$533$			10249.0i			0.832892i
$534$		0			0
$535$	−864.578	−	499.164i	−0.0698672	−	0.0403378i
$536$		0			0
$537$	14098.8	−	3967.49i	1.13298	−	0.318827i
$538$		0			0
$539$	−9890.02	−	10447.0i	−0.790340	−	0.834848i
$540$		0			0
$541$	9186.61	+	15911.7i	0.730061	+	1.26450i	0.956857	+	0.290561i	$0.0938418\pi$
$541$	9186.61	+	15911.7i	0.730061	+	1.26450i	−0.226795	+	0.973942i	$0.572825\pi$
$542$		0			0
$543$	13720.1	+	13381.0i	1.08432	+	1.05752i
$544$		0			0
$545$	12995.3			1.02139
$546$		0			0
$547$	−20764.3			−1.62307			−0.811534	−	0.584305i	$-0.801367\pi$
$547$	−20764.3			−1.62307			−0.811534	+	0.584305i	$0.801367\pi$
$548$		0			0
$549$	−8103.89	−	13258.7i	−0.629992	−	1.03072i
$550$		0			0
$551$	7788.76	+	13490.5i	0.602201	+	1.04304i
$552$		0			0
$553$	4360.17	−	1736.50i	0.335286	−	0.133533i
$554$		0			0
$555$	−1891.25	−	6720.74i	−0.144647	−	0.514017i
$556$		0			0
$557$	−4512.21	−	2605.13i	−0.343247	−	0.198174i	0.318460	−	0.947936i	$-0.396834\pi$
$557$	−4512.21	−	2605.13i	−0.343247	−	0.198174i	−0.661707	+	0.749763i	$0.730168\pi$
$558$		0			0
$559$			28272.1i			2.13914i
$560$		0			0
$561$	320.897	−	1260.48i	0.0241502	−	0.0948621i
$562$		0			0
$563$	5094.34	−	8823.65i	0.381351	−	0.660520i	−0.609904	−	0.792475i	$-0.708792\pi$
$563$	5094.34	−	8823.65i	0.381351	−	0.660520i	0.991256	+	0.131955i	$0.0421255\pi$
$564$		0			0
$565$	7752.20	−	4475.74i	0.577235	−	0.333267i
$566$		0			0
$567$	1274.51	−	13441.0i	0.0943993	−	0.995534i
$568$		0			0
$569$	−1617.54	+	933.886i	−0.119175	+	0.0688059i	−0.558403	−	0.829570i	$-0.688586\pi$
$569$	−1617.54	+	933.886i	−0.119175	+	0.0688059i	0.439227	+	0.898376i	$0.355252\pi$
$570$		0			0
$571$	454.422	−	787.082i	0.0333047	−	0.0576854i	−0.848893	−	0.528565i	$-0.822730\pi$
$571$	454.422	−	787.082i	0.0333047	−	0.0576854i	0.882197	+	0.470880i	$0.156063\pi$
$572$		0			0
$573$	−5780.54	+	22705.9i	−0.421441	+	1.65542i
$574$		0			0
$575$			8911.59i			0.646328i
$576$		0			0
$577$	−13028.7	−	7522.10i	−0.940018	−	0.542720i	−0.0500521	−	0.998747i	$-0.515939\pi$
$577$	−13028.7	−	7522.10i	−0.940018	−	0.542720i	−0.889966	+	0.456027i	$0.849272\pi$
$578$		0			0
$579$	−3112.80	−	11061.6i	−0.223426	−	0.793965i
$580$		0			0
$581$	−952.341	+	6540.56i	−0.0680030	+	0.467036i
$582$		0			0
$583$	370.708	+	642.085i	0.0263347	+	0.0456131i
$584$		0			0
$585$	−21059.6	−	34455.4i	−1.48839	−	2.43514i
$586$		0			0
$587$	−22979.9			−1.61581			−0.807906	−	0.589312i	$-0.799399\pi$
$587$	−22979.9			−1.61581			−0.807906	+	0.589312i	$0.799399\pi$
$588$		0			0
$589$	−4911.46			−0.343587
$590$		0			0
$591$	15538.9	+	15154.8i	1.08153	+	1.05480i
$592$		0			0
$593$	2110.33	+	3655.20i	0.146140	+	0.253121i	0.929798	−	0.368071i	$-0.119982\pi$
$593$	2110.33	+	3655.20i	0.146140	+	0.253121i	−0.783658	+	0.621193i	$0.786648\pi$
$594$		0			0
$595$	−308.621	+	2119.57i	−0.0212642	+	0.146040i
$596$		0			0
$597$	22084.2	−	6214.61i	1.51398	−	0.426042i
$598$		0			0
$599$	−19538.6	−	11280.6i	−1.33276	−	0.769471i	−0.347041	−	0.937850i	$-0.612813\pi$
$599$	−19538.6	−	11280.6i	−1.33276	−	0.769471i	−0.985722	+	0.168379i	$0.946147\pi$
$600$		0			0
$601$		−	2004.06i		−	0.136019i	−0.997685	−	0.0680095i	$-0.978335\pi$
$601$		−	2004.06i		−	0.136019i	0.997685	−	0.0680095i	$-0.0216648\pi$
$602$		0			0
$603$	−9587.78	−	5220.09i	−0.647504	−	0.352535i
$604$		0			0
$605$	−4147.44	+	7183.58i	−0.278707	+	0.482734i
$606$		0			0
$607$	8503.70	−	4909.61i	0.568624	−	0.328295i	−0.187976	−	0.982174i	$-0.560193\pi$
$607$	8503.70	−	4909.61i	0.568624	−	0.328295i	0.756599	+	0.653879i	$0.226859\pi$
$608$		0			0
$609$	17463.1	−	13367.3i	1.16197	−	0.889442i
$610$		0			0
$611$	12159.0	−	7020.03i	0.805077	−	0.464812i
$612$		0			0
$613$	9496.72	−	16448.8i	0.625724	−	1.08379i	−0.362676	−	0.931915i	$-0.618137\pi$
$613$	9496.72	−	16448.8i	0.625724	−	1.08379i	0.988400	−	0.151871i	$-0.0485298\pi$
$614$		0			0
$615$	−12957.3	−	3298.70i	−0.849573	−	0.216287i
$616$		0			0
$617$		−	13306.4i		−	0.868223i	−0.900859	−	0.434112i	$-0.857062\pi$
$617$		−	13306.4i		−	0.868223i	0.900859	−	0.434112i	$-0.142938\pi$
$618$		0			0
$619$	−1611.02	−	930.120i	−0.104608	−	0.0603953i	0.446783	−	0.894642i	$-0.352569\pi$
$619$	−1611.02	−	930.120i	−0.104608	−	0.0603953i	−0.551391	+	0.834247i	$0.685903\pi$
$620$		0			0
$621$	−4866.08	−	1109.95i	−0.314443	−	0.0717242i
$622$		0			0
$623$	−24486.7	+	9752.19i	−1.57470	+	0.627148i
$624$		0			0
$625$	−7906.36	−	13694.2i	−0.506007	−	0.876429i
$626$		0			0
$627$	−10372.1	+	10635.0i	−0.660644	+	0.677387i
$628$		0			0
$629$	−413.838			−0.0262334
$630$		0			0
$631$	16908.2			1.06673			0.533364	−	0.845886i	$-0.320928\pi$
$631$	16908.2			1.06673			0.533364	+	0.845886i	$0.320928\pi$
$632$		0			0
$633$	−7263.88	+	7447.97i	−0.456103	+	0.467662i
$634$		0			0
$635$	−3766.07	−	6523.03i	−0.235358	−	0.407651i
$636$		0			0
$637$	−7549.30	+	25374.2i	−0.469567	+	1.57828i
$638$		0			0
$639$	−13220.4	+	330.904i	−0.818450	+	0.0204857i
$640$		0			0
$641$	4361.32	+	2518.01i	0.268739	+	0.155157i	0.628315	−	0.777959i	$-0.283745\pi$
$641$	4361.32	+	2518.01i	0.268739	+	0.155157i	−0.359575	+	0.933116i	$0.617078\pi$
$642$		0			0
$643$		−	7842.19i		−	0.480973i	−0.970652	−	0.240487i	$-0.922693\pi$
$643$		−	7842.19i		−	0.480973i	0.970652	−	0.240487i	$-0.0773070\pi$
$644$		0			0
$645$	−35743.0	−	9099.56i	−2.18199	−	0.555496i
$646$		0			0
$647$	−5238.32	+	9073.04i	−0.318299	+	0.551311i	−0.980133	−	0.198340i	$-0.936445\pi$
$647$	−5238.32	+	9073.04i	−0.318299	+	0.551311i	0.661834	+	0.749651i	$0.269778\pi$
$648$		0			0
$649$	−17956.6	+	10367.2i	−1.08607	+	0.627041i
$650$		0			0
$651$	896.956	+	6875.60i	0.0540008	+	0.413942i
$652$		0			0
$653$	−10925.7	+	6307.97i	−0.654758	+	0.378025i	−0.790277	−	0.612750i	$-0.790063\pi$
$653$	−10925.7	+	6307.97i	−0.654758	+	0.378025i	0.135519	+	0.990775i	$0.456730\pi$
$654$		0			0
$655$	−6081.49	+	10533.4i	−0.362784	+	0.628360i
$656$		0			0
$657$	−5019.08	+	9218.57i	−0.298041	+	0.547414i
$658$		0			0
$659$		−	1347.17i		−	0.0796334i	−0.999207	−	0.0398167i	$-0.987323\pi$
$659$		−	1347.17i		−	0.0796334i	0.999207	−	0.0398167i	$-0.0126774\pi$
$660$		0			0
$661$	−3269.64	−	1887.73i	−0.192397	−	0.111080i	0.400707	−	0.916206i	$-0.368764\pi$
$661$	−3269.64	−	1887.73i	−0.192397	−	0.111080i	−0.593104	+	0.805126i	$0.702098\pi$
$662$		0			0
$663$	−2304.09	+	648.385i	−0.134968	+	0.0379807i
$664$		0			0
$665$	15156.6	−	19202.4i	0.883833	−	1.11976i
$666$		0			0
$667$	−4064.92	−	7040.65i	−0.235973	−	0.408718i
$668$		0			0
$669$	7893.81	+	7698.70i	0.456192	+	0.444916i
$670$		0			0
$671$	24138.2			1.38874
$672$		0			0
$673$	27877.7			1.59674			0.798370	−	0.602167i	$-0.205696\pi$
$673$	27877.7			1.59674			0.798370	+	0.602167i	$0.205696\pi$
$674$		0			0
$675$	33581.4	−	10363.5i	1.91489	−	0.590952i
$676$		0			0
$677$	−10172.5	−	17619.3i	−0.577492	−	1.00024i	−0.995766	−	0.0919241i	$-0.970698\pi$
$677$	−10172.5	−	17619.3i	−0.577492	−	1.00024i	0.418274	−	0.908321i	$-0.362635\pi$
$678$		0			0
$679$	12722.0	+	1852.39i	0.719037	+	0.104696i
$680$		0			0
$681$	6844.70	+	24323.3i	0.385153	+	1.36868i
$682$		0			0
$683$	10909.0	+	6298.30i	0.611157	+	0.352852i	0.773418	−	0.633896i	$-0.218545\pi$
$683$	10909.0	+	6298.30i	0.611157	+	0.352852i	−0.162261	+	0.986748i	$0.551879\pi$
$684$		0			0
$685$		−	40774.9i		−	2.27435i
$686$		0			0
$687$	−7258.49	+	28511.3i	−0.403098	+	1.58337i
$688$		0			0
$689$	682.194	−	1181.59i	0.0377206	−	0.0653340i
$690$		0			0
$691$	−8495.72	+	4905.01i	−0.467717	+	0.270037i	−0.715284	−	0.698834i	$-0.753702\pi$
$691$	−8495.72	+	4905.01i	−0.467717	+	0.270037i	0.247567	+	0.968871i	$0.420369\pi$
$692$		0			0
$693$	16782.3	+	12577.9i	0.919923	+	0.689457i
$694$		0			0
$695$	−17285.6	+	9979.87i	−0.943427	+	0.544688i
$696$		0			0
$697$	−396.264	+	686.349i	−0.0215345	+	0.0372989i
$698$		0			0
$699$	4171.15	−	16384.3i	0.225705	−	0.886567i
$700$		0			0
$701$		−	21928.4i		−	1.18149i	−0.806858	−	0.590746i	$-0.798834\pi$
$701$		−	21928.4i		−	1.18149i	0.806858	−	0.590746i	$-0.201166\pi$
$702$		0			0
$703$	4093.30	+	2363.27i	0.219604	+	0.126789i
$704$		0			0
$705$	4961.62	+	17631.6i	0.265057	+	0.941905i
$706$		0			0
$707$	−223.014	−	176.027i	−0.0118632	−	0.00936374i
$708$		0			0
$709$	10010.9	+	17339.4i	0.530279	+	0.918471i	0.999376	+	0.0353240i	$0.0112463\pi$
$709$	10010.9	+	17339.4i	0.530279	+	0.918471i	−0.469096	+	0.883147i	$0.655420\pi$
$710$		0			0
$711$	−5837.98	+	3568.25i	−0.307934	+	0.188213i
$712$		0			0
$713$	2563.27			0.134635
$714$		0			0
$715$	62728.0			3.28097
$716$		0			0
$717$	−21663.6	−	21128.2i	−1.12837	−	1.10048i
$718$		0			0
$719$	6260.61	+	10843.7i	0.324731	+	0.562450i	0.981458	−	0.191678i	$-0.0613930\pi$
$719$	6260.61	+	10843.7i	0.324731	+	0.562450i	−0.656727	+	0.754128i	$0.728060\pi$
$720$		0			0
$721$	−2419.94	−	6076.22i	−0.124998	−	0.313856i
$722$		0			0
$723$	−30894.4	+	8693.86i	−1.58918	+	0.447203i
$724$		0			0
$725$	49576.1	+	28622.8i	2.53960	+	1.46624i
$726$		0			0
$727$		−	27158.2i		−	1.38547i	−0.721190	−	0.692737i	$-0.756405\pi$
$727$		−	27158.2i		−	1.38547i	0.721190	−	0.692737i	$-0.243595\pi$
$728$		0			0
$729$	1476.29	+	19627.6i	0.0750034	+	0.997183i
$730$		0			0
$731$	−1093.11	+	1893.32i	−0.0553078	+	0.0957959i
$732$		0			0
$733$	4714.05	−	2721.66i	0.237541	−	0.137144i	−0.376505	−	0.926415i	$-0.622874\pi$
$733$	4714.05	−	2721.66i	0.237541	−	0.137144i	0.614046	+	0.789270i	$0.289541\pi$
$734$		0			0
$735$	−29649.6	−	17711.1i	−1.48795	−	0.888821i
$736$		0			0
$737$	14685.9	−	8478.89i	0.734004	−	0.423778i
$738$		0			0
$739$	−13386.6	+	23186.2i	−0.666351	+	1.15415i	0.312566	+	0.949896i	$0.398811\pi$
$739$	−13386.6	+	23186.2i	−0.666351	+	1.15415i	−0.978917	+	0.204257i	$0.934522\pi$
$740$		0			0
$741$	26492.7	+	6744.57i	1.31340	+	0.334370i
$742$		0			0
$743$		−	6409.29i		−	0.316466i	−0.987402	−	0.158233i	$-0.949420\pi$
$743$		−	6409.29i		−	0.316466i	0.987402	−	0.158233i	$-0.0505797\pi$
$744$		0			0
$745$	3375.90	+	1949.07i	0.166018	+	0.0958504i
$746$		0			0
$747$	−241.107	−	9632.77i	−0.0118094	−	0.471814i
$748$		0			0
$749$	−353.035	−	886.433i	−0.0172225	−	0.0432437i
$750$		0			0
$751$	−9007.68	−	15601.8i	−0.437676	−	0.758078i	0.559834	−	0.828605i	$-0.310865\pi$
$751$	−9007.68	−	15601.8i	−0.437676	−	0.758078i	−0.997510	+	0.0705276i	$0.977532\pi$
$752$		0			0
$753$	−5980.30	+	6131.85i	−0.289421	+	0.296756i
$754$		0			0
$755$	−23107.6			−1.11387
$756$		0			0
$757$	4064.93			0.195168			0.0975840	−	0.995227i	$-0.468889\pi$
$757$	4064.93			0.195168			0.0975840	+	0.995227i	$0.468889\pi$
$758$		0			0
$759$	5413.18	−	5550.36i	0.258875	−	0.265435i
$760$		0			0
$761$	−10719.5	−	18566.8i	−0.510621	−	0.884421i	−0.999924	−	0.0123076i	$-0.996082\pi$
$761$	−10719.5	−	18566.8i	−0.510621	−	0.884421i	0.489303	−	0.872114i	$-0.337251\pi$
$762$		0			0
$763$	9749.19	+	7695.12i	0.462574	+	0.365114i
$764$		0			0
$765$	−78.1344	−	3121.65i	−0.00369275	−	0.147534i
$766$		0			0
$767$	33044.5	+	19078.3i	1.55563	+	0.898143i
$768$		0			0
$769$		−	18622.9i		−	0.873286i	−0.899635	−	0.436643i	$-0.856167\pi$
$769$		−	18622.9i		−	0.873286i	0.899635	−	0.436643i	$-0.143833\pi$
$770$		0			0
$771$	−16136.6	−	4108.09i	−0.753754	−	0.191893i
$772$		0			0
$773$	−20786.3	+	36002.9i	−0.967180	+	1.67520i	−0.263538	+	0.964649i	$0.584890\pi$
$773$	−20786.3	+	36002.9i	−0.967180	+	1.67520i	−0.703641	+	0.710555i	$0.748444\pi$
$774$		0			0
$775$	−15630.9	+	9024.51i	−0.724489	+	0.418284i
$776$		0			0
$777$	2560.83	−	6161.85i	0.118236	−	0.284498i
$778$		0			0
$779$	7838.95	−	4525.82i	0.360539	−	0.208157i
$780$		0			0
$781$	10271.3	−	17790.4i	0.470598	−	0.815099i
$782$		0			0
$783$	−21804.0	+	23505.5i	−0.995159	+	1.07282i
$784$		0			0
$785$			21164.9i			0.962301i
$786$		0			0
$787$	2973.05	+	1716.49i	0.134661	+	0.0777463i	0.565817	−	0.824531i	$-0.308561\pi$
$787$	2973.05	+	1716.49i	0.134661	+	0.0777463i	−0.431156	+	0.902277i	$0.641894\pi$
$788$		0			0
$789$	17303.6	−	4869.33i	0.780766	−	0.219712i
$790$		0			0
$791$	8466.05	+	1232.70i	0.380554	+	0.0554107i
$792$		0			0
$793$	−22210.1	−	38469.0i	−0.994582	−	1.72267i
$794$		0			0
$795$	1274.27	+	1242.77i	0.0568472	+	0.0554422i
$796$		0			0
$797$	9577.83			0.425676			0.212838	−	0.977087i	$-0.431729\pi$
$797$	9577.83			0.425676			0.212838	+	0.977087i	$0.431729\pi$
$798$		0			0
$799$	1085.69			0.0480711
$800$		0			0
$801$	32786.1	−	20039.3i	1.44624	−	0.883961i
$802$		0			0
$803$	−8152.38	−	14120.3i	−0.358271	−	0.620543i
$804$		0			0
$805$	−7910.17	+	10021.6i	−0.346332	+	0.438778i
$806$		0			0
$807$	1872.89	+	6655.48i	0.0816962	+	0.290315i
$808$		0			0
$809$	−12196.7	−	7041.78i	−0.530054	−	0.306027i	0.210984	−	0.977489i	$-0.432333\pi$
$809$	−12196.7	−	7041.78i	−0.530054	−	0.306027i	−0.741039	+	0.671463i	$0.765666\pi$
$810$		0			0
$811$		−	8029.38i		−	0.347657i	−0.984776	−	0.173828i	$-0.944386\pi$
$811$		−	8029.38i		−	0.347657i	0.984776	−	0.173828i	$-0.0556138\pi$
$812$		0			0
$813$	4284.50	−	16829.5i	0.184827	−	0.725999i
$814$		0			0
$815$	−5615.73	+	9726.73i	−0.241363	+	0.418052i
$816$		0			0
$817$	21624.0	−	12484.6i	0.925983	−	0.534616i
$818$		0			0
$819$	4603.57	−	38319.1i	0.196412	−	1.63489i
$820$		0			0
$821$	−15403.4	+	8893.18i	−0.654791	+	0.378044i	−0.790290	−	0.612734i	$-0.790070\pi$
$821$	−15403.4	+	8893.18i	−0.654791	+	0.378044i	0.135498	+	0.990778i	$0.456737\pi$
$822$		0			0
$823$	4759.27	−	8243.29i	0.201577	−	0.349141i	−0.747460	−	0.664307i	$-0.768727\pi$
$823$	4759.27	−	8243.29i	0.201577	−	0.349141i	0.949037	+	0.315166i	$0.102060\pi$
$824$		0			0
$825$	−13468.6	+	52904.6i	−0.568383	+	2.23261i
$826$		0			0
$827$			37498.5i			1.57672i	0.615212	+	0.788362i	$0.289071\pi$
$827$			37498.5i			1.57672i	−0.615212	+	0.788362i	$0.710929\pi$
$828$		0			0
$829$	23820.3	+	13752.7i	0.997967	+	0.576176i	0.907646	−	0.419736i	$-0.137877\pi$
$829$	23820.3	+	13752.7i	0.997967	+	0.576176i	0.0903208	+	0.995913i	$0.471211\pi$
$830$		0			0
$831$	−6757.88	−	24014.7i	−0.282104	−	1.00248i
$832$		0			0
$833$	−1486.62	+	1407.37i	−0.0618349	+	0.0585383i
$834$		0			0
$835$	36001.2	+	62355.8i	1.49206	+	2.58433i
$836$		0			0
$837$	−2980.89	−	9659.11i	−0.123100	−	0.398886i
$838$		0			0
$839$	2040.23			0.0839528			0.0419764	−	0.999119i	$-0.486635\pi$
$839$	2040.23			0.0839528			0.0419764	+	0.999119i	$0.486635\pi$
$840$		0			0
$841$	−27834.9			−1.14129
$842$		0			0
$843$	16921.4	+	16503.2i	0.691346	+	0.674259i
$844$		0			0
$845$	−36430.9	−	63100.2i	−1.48315	−	2.56889i
$846$		0			0
$847$	−7365.17	+	2933.29i	−0.298784	+	0.118995i
$848$		0			0
$849$	−22657.5	+	6375.94i	−0.915903	+	0.257740i
$850$		0			0
$851$	−2136.28	−	1233.38i	−0.0860524	−	0.0496824i
$852$		0			0
$853$		−	22267.7i		−	0.893825i	−0.894578	−	0.446913i	$-0.852524\pi$
$853$		−	22267.7i		−	0.893825i	0.894578	−	0.446913i	$-0.147476\pi$
$854$		0			0
$855$	−17053.7	+	31322.6i	−0.682133	+	1.25288i
$856$		0			0
$857$	13711.2	−	23748.5i	0.546517	−	0.946595i	−0.451993	−	0.892022i	$-0.649287\pi$
$857$	13711.2	−	23748.5i	0.546517	−	0.946595i	0.998510	−	0.0545736i	$-0.0173799\pi$
$858$		0			0
$859$	−37954.1	+	21912.8i	−1.50754	+	0.870380i	−0.507580	+	0.861605i	$0.669460\pi$
$859$	−37954.1	+	21912.8i	−1.50754	+	0.870380i	−0.999961	+	0.00877488i	$0.997207\pi$
$860$		0			0
$861$	−7767.34	−	10147.3i	−0.307445	−	0.401648i
$862$		0			0
$863$	−23255.2	+	13426.4i	−0.917286	+	0.529595i	−0.882768	−	0.469809i	$-0.844323\pi$
$863$	−23255.2	+	13426.4i	−0.917286	+	0.529595i	−0.0345178	+	0.999404i	$0.510990\pi$
$864$		0			0
$865$	−12967.7	+	22460.8i	−0.509729	+	0.882877i
$866$		0			0
$867$	24560.2	+	6252.60i	0.962062	+	0.244924i
$868$		0			0
$869$		−	10628.4i		−	0.414894i
$870$		0			0
$871$	−27025.6	−	15603.2i	−1.05135	−	0.606999i
$872$		0			0
$873$	−18736.7	+	468.976i	−0.726392	+	0.0181815i
$874$		0			0
$875$	6489.59	−	44569.7i	0.250729	−	1.72198i
$876$		0			0
$877$	19557.7	+	33874.9i	0.753039	+	1.30430i	0.946343	+	0.323163i	$0.104746\pi$
$877$	19557.7	+	33874.9i	0.753039	+	1.30430i	−0.193304	+	0.981139i	$0.561920\pi$
$878$		0			0
$879$	34557.2	−	35432.9i	1.32603	−	1.35964i
$880$		0			0
$881$	39685.7			1.51764			0.758822	−	0.651299i	$-0.225775\pi$
$881$	39685.7			1.51764			0.758822	+	0.651299i	$0.225775\pi$
$882$		0			0
$883$	−37785.0			−1.44005			−0.720026	−	0.693947i	$-0.755870\pi$
$883$	−37785.0			−1.44005			−0.720026	+	0.693947i	$0.755870\pi$
$884$		0			0
$885$	−34755.3	+	35636.2i	−1.32010	+	1.35356i
$886$		0			0
$887$	−7332.70	−	12700.6i	−0.277574	−	0.480772i	0.693207	−	0.720738i	$-0.256197\pi$
$887$	−7332.70	−	12700.6i	−0.277574	−	0.480772i	−0.970781	+	0.239966i	$0.922864\pi$
$888$		0			0
$889$	1037.25	−	7123.69i	0.0391318	−	0.268753i
$890$		0			0
$891$	−27210.5	−	13943.7i	−1.02310	−	0.524278i
$892$		0			0
$893$	−10738.6	−	6199.93i	−0.402411	−	0.232332i
$894$		0			0
$895$			54620.4i			2.03995i
$896$		0			0
$897$	−13826.4	−	3519.96i	−0.514660	−	0.131023i
$898$		0			0
$899$	8232.86	−	14259.7i	0.305430	−	0.529020i
$900$		0			0
$901$	91.3699	−	52.7525i	0.00337844	−	0.00195054i
$902$		0			0
$903$	−21426.4	−	27991.7i	−0.789621	−	1.03157i
$904$		0			0
$905$	−61895.6	+	35735.4i	−2.27346	+	1.31258i
$906$		0			0
$907$	19099.9	−	33081.9i	0.699229	−	1.21110i	−0.269505	−	0.962999i	$-0.586860\pi$
$907$	19099.9	−	33081.9i	0.699229	−	1.21110i	0.968734	−	0.248101i	$-0.0798066\pi$
$908$		0			0
$909$	363.776	+	198.059i	0.0132736	+	0.00722684i
$910$		0			0
$911$		−	41209.5i		−	1.49872i	−0.662165	−	0.749358i	$-0.730362\pi$
$911$		−	41209.5i		−	1.49872i	0.662165	−	0.749358i	$-0.269638\pi$
$912$		0			0
$913$	12962.7	+	7484.00i	0.469882	+	0.271286i
$914$		0			0
$915$	55783.1	−	15697.7i	2.01544	−	0.567157i
$916$		0			0
$917$	−10799.7	+	4301.14i	−0.388918	+	0.154892i
$918$		0			0
$919$	−17925.7	−	31048.1i	−0.643431	−	1.11445i	−0.984662	−	0.174475i	$-0.944177\pi$
$919$	−17925.7	−	31048.1i	−0.643431	−	1.11445i	0.341231	−	0.939979i	$-0.389156\pi$
$920$		0			0
$921$	13926.8	+	13582.5i	0.498265	+	0.485950i
$922$		0			0
$923$	−37803.5			−1.34812
$924$		0			0
$925$	17369.5			0.617411
$926$		0			0
$927$	4972.62	+	8135.65i	0.176184	+	0.288252i
$928$		0			0
$929$	19657.8	+	34048.3i	0.694243	+	1.20246i	0.970435	+	0.241361i	$0.0775938\pi$
$929$	19657.8	+	34048.3i	0.694243	+	1.20246i	−0.276193	+	0.961102i	$0.589073\pi$
$930$		0			0
$931$	22741.3	−	5430.85i	0.800553	−	0.191181i
$932$		0			0
$933$	14642.8	+	52034.6i	0.513810	+	1.82587i
$934$		0			0
$935$	4200.75	+	2425.31i	0.146930	+	0.0848299i
$936$		0			0
$937$		−	25396.6i		−	0.885455i	−0.896656	−	0.442728i	$-0.854011\pi$
$937$		−	25396.6i		−	0.885455i	0.896656	−	0.442728i	$-0.145989\pi$
$938$		0			0
$939$	4218.97	−	16572.1i	0.146625	−	0.575942i
$940$		0			0
$941$	−9088.06	+	15741.0i	−0.314838	+	0.545315i	−0.979403	−	0.201915i	$-0.935283\pi$
$941$	−9088.06	+	15741.0i	−0.314838	+	0.545315i	0.664565	+	0.747230i	$0.268617\pi$
$942$		0			0
$943$	−4091.11	+	2362.00i	−0.141278	+	0.0815668i
$944$		0			0
$945$	46963.4	+	18153.3i	1.61663	+	0.624898i
$946$		0			0
$947$	36468.5	−	21055.1i	1.25139	−	0.722491i	0.280005	−	0.959998i	$-0.409664\pi$
$947$	36468.5	−	21055.1i	1.25139	−	0.722491i	0.971386	+	0.237507i	$0.0763304\pi$
$948$		0			0
$949$	−15002.4	+	25984.9i	−0.513170	+	0.888836i
$950$		0			0
$951$	7664.57	−	30106.4i	0.261347	−	1.02657i
$952$		0			0
$953$			18521.2i			0.629551i	0.949166	+	0.314775i	$0.101929\pi$
$953$			18521.2i			0.629551i	−0.949166	+	0.314775i	$0.898071\pi$
$954$		0			0
$955$	−75671.0	−	43688.7i	−2.56404	−	1.48035i
$956$		0			0
$957$	−13490.9	−	47941.1i	−0.455694	−	1.61935i
$958$		0			0
$959$	24144.7	−	30589.7i	0.813007	−	1.03002i
$960$		0			0
$961$	−12299.8	−	21303.8i	−0.412868	−	0.715109i
$962$		0			0
$963$	725.433	+	1186.88i	0.0242749	+	0.0397160i
$964$		0			0
$965$	42853.9			1.42955
$966$		0			0
$967$	48504.3			1.61302			0.806512	−	0.591218i	$-0.201353\pi$
$967$	48504.3			1.61302			0.806512	+	0.591218i	$0.201353\pi$
$968$		0			0
$969$	1513.38	+	1475.98i	0.0501722	+	0.0489321i
$970$		0			0
$971$	16579.2	+	28716.0i	0.547943	+	0.949065i	0.998415	+	0.0562744i	$0.0179222\pi$
$971$	16579.2	+	28716.0i	0.547943	+	0.949065i	−0.450473	+	0.892790i	$0.648745\pi$
$972$		0			0
$973$	−18877.4	−	2748.65i	−0.621974	−	0.0905628i
$974$		0			0
$975$	96706.7	−	27213.8i	3.17651	−	0.893887i
$976$		0			0
$977$	−29562.2	−	17067.8i	−0.968045	−	0.558901i	−0.0694053	−	0.997589i	$-0.522110\pi$
$977$	−29562.2	−	17067.8i	−0.968045	−	0.558901i	−0.898640	+	0.438688i	$0.855443\pi$
$978$		0			0
$979$			59688.8i			1.94858i
$980$		0			0
$981$	−15902.7	−	8658.27i	−0.517568	−	0.281791i
$982$		0			0
$983$	169.731	−	293.983i	0.00550721	−	0.00953877i	−0.863259	−	0.504762i	$-0.831580\pi$
$983$	169.731	−	293.983i	0.00550721	−	0.00953877i	0.868766	+	0.495223i	$0.164914\pi$
$984$		0			0
$985$	−70100.6	+	40472.6i	−2.26761	+	1.30920i
$986$		0			0
$987$	−6718.21	+	16165.3i	−0.216660	+	0.521326i
$988$		0			0
$989$	−11285.5	+	6515.66i	−0.362848	+	0.209490i
$990$		0			0
$991$	279.970	−	484.922i	0.00897431	−	0.0155440i	−0.861503	−	0.507752i	$-0.830477\pi$
$991$	279.970	−	484.922i	0.00897431	−	0.0155440i	0.870478	+	0.492208i	$0.163810\pi$
$992$		0			0
$993$	−210.655	−	53.6292i	−0.00673207	−	0.00171387i
$994$		0			0
$995$			85556.5i			2.72595i
$996$		0			0
$997$	−11120.1	−	6420.22i	−0.353238	−	0.203942i	0.312872	−	0.949795i	$-0.398709\pi$
$997$	−11120.1	−	6420.22i	−0.353238	−	0.203942i	−0.666111	+	0.745853i	$0.732042\pi$
$998$		0			0
$999$	−2163.39	+	9484.42i	−0.0685151	+	0.300374i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.4.k.c.17.5	yes	12
3.2	odd	2	inner	84.4.k.c.17.2	yes	12
4.3	odd	2		336.4.bc.c.17.2		12
7.2	even	3		588.4.k.c.509.5		12
7.3	odd	6		588.4.f.c.293.12		12
7.4	even	3		588.4.f.c.293.1		12
7.5	odd	6	inner	84.4.k.c.5.2	✓	12
7.6	odd	2		588.4.k.c.521.2		12
12.11	even	2		336.4.bc.c.17.5		12
21.2	odd	6		588.4.k.c.509.2		12
21.5	even	6	inner	84.4.k.c.5.5	yes	12
21.11	odd	6		588.4.f.c.293.11		12
21.17	even	6		588.4.f.c.293.2		12
21.20	even	2		588.4.k.c.521.5		12
28.19	even	6		336.4.bc.c.257.5		12
84.47	odd	6		336.4.bc.c.257.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.4.k.c.5.2	✓	12	7.5	odd	6	inner
84.4.k.c.5.5	yes	12	21.5	even	6	inner
84.4.k.c.17.2	yes	12	3.2	odd	2	inner
84.4.k.c.17.5	yes	12	1.1	even	1	trivial
336.4.bc.c.17.2		12	4.3	odd	2
336.4.bc.c.17.5		12	12.11	even	2
336.4.bc.c.257.2		12	84.47	odd	6
336.4.bc.c.257.5		12	28.19	even	6
588.4.f.c.293.1		12	7.4	even	3
588.4.f.c.293.2		12	21.17	even	6
588.4.f.c.293.11		12	21.11	odd	6
588.4.f.c.293.12		12	7.3	odd	6
588.4.k.c.509.2		12	21.2	odd	6
588.4.k.c.509.5		12	7.2	even	3
588.4.k.c.521.2		12	7.6	odd	2
588.4.k.c.521.5		12	21.20	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:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	84.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.62798 - 3.71992i) q^{3} +(9.68891 + 16.7817i) q^{5} +(-2.66851 + 18.3270i) q^{7} +(-0.675594 - 26.9915i) q^{9} +(36.3221 + 20.9706i) q^{11} -77.1820i q^{13} +(97.5776 + 24.8416i) q^{15} +(2.98415 - 5.16871i) q^{17} +(-59.0330 + 34.0827i) q^{19} +(58.4937 + 76.4166i) q^{21} +(30.8090 - 17.7876i) q^{23} +(-125.250 + 216.939i) q^{25} +(-102.857 - 95.4115i) q^{27} -228.525i q^{29} +(62.3989 + 36.0260i) q^{31} +(209.785 - 59.0346i) q^{33} +(-333.413 + 132.787i) q^{35} +(-34.6696 - 60.0496i) q^{37} +(-287.111 - 280.014i) q^{39} -132.789 q^{41} -366.304 q^{43} +(446.418 - 272.856i) q^{45} +(90.9542 + 157.537i) q^{47} +(-328.758 - 97.8116i) q^{49} +(-8.40073 - 29.8527i) q^{51} +(15.3092 + 8.83877i) q^{53} +812.728i q^{55} +(-87.3853 + 343.249i) q^{57} +(-247.185 + 428.137i) q^{59} +(498.419 - 287.763i) q^{61} +(496.477 + 59.6456i) q^{63} +(1295.24 - 747.810i) q^{65} +(202.162 - 350.154i) q^{67} +(45.6060 - 179.140i) q^{69} -489.797i q^{71} +(-336.670 - 194.377i) q^{73} +(352.593 + 1252.97i) q^{75} +(-481.254 + 609.715i) q^{77} +(-126.706 - 219.461i) q^{79} +(-728.087 + 36.4707i) q^{81} +356.881 q^{83} +115.653 q^{85} +(-850.096 - 829.084i) q^{87} +(711.578 + 1232.49i) q^{89} +(1414.51 + 205.961i) q^{91} +(360.395 - 101.417i) q^{93} +(-1143.93 - 660.449i) q^{95} -694.168i q^{97} +(541.489 - 994.557i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 42 q^{7} - 84 q^{9} + 132 q^{15} + 204 q^{19} - 378 q^{21} - 444 q^{25} + 1458 q^{31} - 108 q^{33} + 240 q^{37} - 432 q^{39} - 342 q^{45} - 1218 q^{49} - 300 q^{51} + 180 q^{57} + 2148 q^{61} + 1596 q^{63}+ \cdots + 9216 q^{99}+O(q^{100}) \) 12 * q - 42 * q^7 - 84 * q^9 + 132 * q^15 + 204 * q^19 - 378 * q^21 - 444 * q^25 + 1458 * q^31 - 108 * q^33 + 240 * q^37 - 432 * q^39 - 342 * q^45 - 1218 * q^49 - 300 * q^51 + 180 * q^57 + 2148 * q^61 + 1596 * q^63 + 1980 * q^67 - 3084 * q^73 - 3384 * q^75 - 438 * q^79 + 1008 * q^81 - 6144 * q^85 - 2898 * q^87 + 3780 * q^91 + 882 * q^93 + 9216 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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