LMFDB - Embedded newform 287.2.c.b.204.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(204,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("287.204");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.c (of order $2$, degree $1$, 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:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$12$
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} + 18x^{10} + 113x^{8} + 290x^{6} + 258x^{4} + 49x^{2} + 1 $ x^12 + 18x^10 + 113x^8 + 290x^6 + 258x^4 + 49*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			204.5
Root			$-0.473876i$ of defining polynomial
Character	$\chi$	$=$	287.204
Dual form			287.2.c.b.204.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.473876 q^{2} -0.526124i q^{3} -1.77544 q^{4} -1.62273 q^{5} +0.249318i q^{6} +1.00000i q^{7} +1.78909 q^{8} +2.72319 q^{9} +O(q^{10})$	\(q-0.473876 q^{2} -0.526124i q^{3} -1.77544 q^{4} -1.62273 q^{5} +0.249318i q^{6} +1.00000i q^{7} +1.78909 q^{8} +2.72319 q^{9} +0.768972 q^{10} +2.76897i q^{11} +0.934102i q^{12} +1.63638i q^{13} -0.473876i q^{14} +0.853755i q^{15} +2.70307 q^{16} +7.37322i q^{17} -1.29046 q^{18} +2.49217i q^{19} +2.88106 q^{20} +0.526124 q^{21} -1.31215i q^{22} +3.50118 q^{23} -0.941284i q^{24} -2.36675 q^{25} -0.775441i q^{26} -3.01111i q^{27} -1.77544i q^{28} -2.41900i q^{29} -0.404574i q^{30} -2.57048 q^{31} -4.85911 q^{32} +1.45682 q^{33} -3.49400i q^{34} -1.62273i q^{35} -4.83487 q^{36} +0.867407 q^{37} -1.18098i q^{38} +0.860938 q^{39} -2.90321 q^{40} +(5.83345 + 2.64024i) q^{41} -0.249318 q^{42} +0.398169 q^{43} -4.91615i q^{44} -4.41900 q^{45} -1.65913 q^{46} +2.68348i q^{47} -1.42215i q^{48} -1.00000 q^{49} +1.12155 q^{50} +3.87923 q^{51} -2.90529i q^{52} +6.59778i q^{53} +1.42689i q^{54} -4.49329i q^{55} +1.78909i q^{56} +1.31119 q^{57} +1.14631i q^{58} -7.62273 q^{59} -1.51579i q^{60} -2.70472 q^{61} +1.21809 q^{62} +2.72319i q^{63} -3.10353 q^{64} -2.65540i q^{65} -0.690353 q^{66} -8.44637i q^{67} -13.0907i q^{68} -1.84205i q^{69} +0.768972i q^{70} +7.09398i q^{71} +4.87205 q^{72} +1.93724 q^{73} -0.411043 q^{74} +1.24521i q^{75} -4.42469i q^{76} -2.76897 q^{77} -0.407978 q^{78} -11.7714i q^{79} -4.38635 q^{80} +6.58537 q^{81} +(-2.76433 - 1.25115i) q^{82} +3.79392 q^{83} -0.934102 q^{84} -11.9647i q^{85} -0.188683 q^{86} -1.27269 q^{87} +4.95395i q^{88} +5.41058i q^{89} +2.09406 q^{90} -1.63638 q^{91} -6.21614 q^{92} +1.35239i q^{93} -1.27164i q^{94} -4.04411i q^{95} +2.55649i q^{96} +3.74428i q^{97} +0.473876 q^{98} +7.54045i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} + 12 q^{4} + 2 q^{5} - 24 q^{8} - 4 q^{9}+O(q^{10}) $ 12 * q - 4 * q^2 + 12 * q^4 + 2 * q^5 - 24 * q^8 - 4 * q^9	$ 12 q - 4 q^{2} + 12 q^{4} + 2 q^{5} - 24 q^{8} - 4 q^{9} - 4 q^{10} + 28 q^{16} - 40 q^{18} + 2 q^{20} + 8 q^{21} + 16 q^{23} + 34 q^{25} - 6 q^{31} - 42 q^{32} + 18 q^{33} - 36 q^{36} - 10 q^{37} + 10 q^{39} + 38 q^{40} - 2 q^{41} + 32 q^{42} - 50 q^{43} + 6 q^{45} - 8 q^{46} - 12 q^{49} + 18 q^{50} - 2 q^{51} - 50 q^{57} - 70 q^{59} + 52 q^{61} + 68 q^{62} + 8 q^{64} + 92 q^{66} + 2 q^{72} - 64 q^{73} + 18 q^{74} - 20 q^{77} - 12 q^{78} - 32 q^{80} - 4 q^{81} - 56 q^{82} + 60 q^{83} - 20 q^{84} + 48 q^{86} - 20 q^{87} - 42 q^{90} + 14 q^{91} + 56 q^{92} + 4 q^{98}+O(q^{100}) $ 12 * q - 4 * q^2 + 12 * q^4 + 2 * q^5 - 24 * q^8 - 4 * q^9 - 4 * q^10 + 28 * q^16 - 40 * q^18 + 2 * q^20 + 8 * q^21 + 16 * q^23 + 34 * q^25 - 6 * q^31 - 42 * q^32 + 18 * q^33 - 36 * q^36 - 10 * q^37 + 10 * q^39 + 38 * q^40 - 2 * q^41 + 32 * q^42 - 50 * q^43 + 6 * q^45 - 8 * q^46 - 12 * q^49 + 18 * q^50 - 2 * q^51 - 50 * q^57 - 70 * q^59 + 52 * q^61 + 68 * q^62 + 8 * q^64 + 92 * q^66 + 2 * q^72 - 64 * q^73 + 18 * q^74 - 20 * q^77 - 12 * q^78 - 32 * q^80 - 4 * q^81 - 56 * q^82 + 60 * q^83 - 20 * q^84 + 48 * q^86 - 20 * q^87 - 42 * q^90 + 14 * q^91 + 56 * q^92 + 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$1$	$-1$

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 $

$2$	−0.473876			−0.335081			−0.167541	−	0.985865i	$-0.553583\pi$
$2$	−0.473876			−0.335081			−0.167541	+	0.985865i	$0.553583\pi$
$3$		−	0.526124i		−	0.303758i	−0.988399	−	0.151879i	$-0.951468\pi$
$3$		−	0.526124i		−	0.303758i	0.988399	−	0.151879i	$-0.0485323\pi$
$4$	−1.77544			−0.887721
$5$	−1.62273			−0.725706			−0.362853	−	0.931846i	$-0.618197\pi$
$5$	−1.62273			−0.725706			−0.362853	+	0.931846i	$0.618197\pi$
$6$			0.249318i			0.101783i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	1.78909			0.632540
$9$	2.72319			0.907731
$10$	0.768972			0.243170
$11$			2.76897i			0.834877i	0.908705	+	0.417438i	$0.137072\pi$
$11$			2.76897i			0.834877i	−0.908705	+	0.417438i	$0.862928\pi$
$12$			0.934102i			0.269652i
$13$			1.63638i			0.453850i	0.973912	+	0.226925i	$0.0728672\pi$
$13$			1.63638i			0.453850i	−0.973912	+	0.226925i	$0.927133\pi$
$14$		−	0.473876i		−	0.126649i
$15$			0.853755i			0.220439i
$16$	2.70307			0.675768
$17$			7.37322i			1.78827i	0.447798	+	0.894135i	$0.352208\pi$
$17$			7.37322i			1.78827i	−0.447798	+	0.894135i	$0.647792\pi$
$18$	−1.29046			−0.304164
$19$			2.49217i			0.571742i	0.958268	+	0.285871i	$0.0922829\pi$
$19$			2.49217i			0.571742i	−0.958268	+	0.285871i	$0.907717\pi$
$20$	2.88106			0.644224
$21$	0.526124			0.114810
$22$		−	1.31215i		−	0.279751i
$23$	3.50118			0.730046			0.365023	−	0.930998i	$-0.381061\pi$
$23$	3.50118			0.730046			0.365023	+	0.930998i	$0.381061\pi$
$24$		−	0.941284i		−	0.192139i
$25$	−2.36675			−0.473351
$26$		−	0.775441i		−	0.152077i
$27$		−	3.01111i		−	0.579488i
$28$		−	1.77544i		−	0.335527i
$29$		−	2.41900i		−	0.449197i	−0.974451	−	0.224599i	$-0.927893\pi$
$29$		−	2.41900i		−	0.449197i	0.974451	−	0.224599i	$-0.0721071\pi$
$30$		−	0.404574i		−	0.0738649i
$31$	−2.57048			−0.461672			−0.230836	−	0.972993i	$-0.574146\pi$
$31$	−2.57048			−0.461672			−0.230836	+	0.972993i	$0.574146\pi$
$32$	−4.85911			−0.858977
$33$	1.45682			0.253600
$34$		−	3.49400i		−	0.599215i
$35$		−	1.62273i		−	0.274291i
$36$	−4.83487			−0.805812
$37$	0.867407			0.142601			0.0713004	−	0.997455i	$-0.477285\pi$
$37$	0.867407			0.142601			0.0713004	+	0.997455i	$0.477285\pi$
$38$		−	1.18098i		−	0.191580i
$39$	0.860938			0.137860
$40$	−2.90321			−0.459038
$41$	5.83345	+	2.64024i	0.911032	+	0.412336i
$41$	5.83345	+	2.64024i	0.911032	+	0.412336i
$42$	−0.249318			−0.0384705
$43$	0.398169			0.0607202			0.0303601	−	0.999539i	$-0.490335\pi$
$43$	0.398169			0.0607202			0.0303601	+	0.999539i	$0.490335\pi$
$44$		−	4.91615i		−	0.741137i
$45$	−4.41900			−0.658746
$46$	−1.65913			−0.244625
$47$			2.68348i			0.391425i	0.980661	+	0.195713i	$0.0627020\pi$
$47$			2.68348i			0.391425i	−0.980661	+	0.195713i	$0.937298\pi$
$48$		−	1.42215i		−	0.205270i
$49$	−1.00000			−0.142857
$50$	1.12155			0.158611
$51$	3.87923			0.543200
$52$		−	2.90529i		−	0.402892i
$53$			6.59778i			0.906275i	0.891441	+	0.453138i	$0.149695\pi$
$53$			6.59778i			0.906275i	−0.891441	+	0.453138i	$0.850305\pi$
$54$			1.42689i			0.194176i
$55$		−	4.49329i		−	0.605875i
$56$			1.78909i			0.239078i
$57$	1.31119			0.173671
$58$			1.14631i			0.150518i
$59$	−7.62273			−0.992395			−0.496197	−	0.868210i	$-0.665271\pi$
$59$	−7.62273			−0.992395			−0.496197	+	0.868210i	$0.665271\pi$
$60$		−	1.51579i		−	0.195688i
$61$	−2.70472			−0.346304			−0.173152	−	0.984895i	$-0.555395\pi$
$61$	−2.70472			−0.346304			−0.173152	+	0.984895i	$0.555395\pi$
$62$	1.21809			0.154698
$63$			2.72319i			0.343090i
$64$	−3.10353			−0.387941
$65$		−	2.65540i		−	0.329361i
$66$	−0.690353			−0.0849766
$67$		−	8.44637i		−	1.03189i	−0.856622	−	0.515944i	$-0.827441\pi$
$67$		−	8.44637i		−	1.03189i	0.856622	−	0.515944i	$-0.172559\pi$
$68$		−	13.0907i		−	1.58748i
$69$		−	1.84205i		−	0.221757i
$70$			0.768972i			0.0919098i
$71$			7.09398i			0.841900i	0.907084	+	0.420950i	$0.138303\pi$
$71$			7.09398i			0.841900i	−0.907084	+	0.420950i	$0.861697\pi$
$72$	4.87205			0.574176
$73$	1.93724			0.226736			0.113368	−	0.993553i	$-0.463836\pi$
$73$	1.93724			0.226736			0.113368	+	0.993553i	$0.463836\pi$
$74$	−0.411043			−0.0477828
$75$			1.24521i			0.143784i
$76$		−	4.42469i		−	0.507547i
$77$	−2.76897			−0.315554
$78$	−0.407978			−0.0461944
$79$		−	11.7714i		−	1.32439i	−0.749334	−	0.662193i	$-0.769626\pi$
$79$		−	11.7714i		−	1.32439i	0.749334	−	0.662193i	$-0.230374\pi$
$80$	−4.38635			−0.490409
$81$	6.58537			0.731707
$82$	−2.76433	−	1.25115i	−0.305270	−	0.138166i
$83$	3.79392			0.416437			0.208218	−	0.978082i	$-0.433234\pi$
$83$	3.79392			0.416437			0.208218	+	0.978082i	$0.433234\pi$
$84$	−0.934102			−0.101919
$85$		−	11.9647i		−	1.29776i
$86$	−0.188683			−0.0203462
$87$	−1.27269			−0.136447
$88$			4.95395i			0.528093i
$89$			5.41058i			0.573521i	0.958002	+	0.286760i	$0.0925784\pi$
$89$			5.41058i			0.573521i	−0.958002	+	0.286760i	$0.907422\pi$
$90$	2.09406			0.220733
$91$	−1.63638			−0.171539
$92$	−6.21614			−0.648077
$93$			1.35239i			0.140236i
$94$		−	1.27164i		−	0.131159i
$95$		−	4.04411i		−	0.414917i
$96$			2.55649i			0.260921i
$97$			3.74428i			0.380174i	0.981767	+	0.190087i	$0.0608770\pi$
$97$			3.74428i			0.380174i	−0.981767	+	0.190087i	$0.939123\pi$
$98$	0.473876			0.0478687
$99$			7.54045i			0.757844i
$100$	4.20203			0.420203
$101$			7.61739i			0.757959i	0.925405	+	0.378979i	$0.123725\pi$
$101$			7.61739i			0.757959i	−0.925405	+	0.378979i	$0.876275\pi$
$102$	−1.83827			−0.182016
$103$	−13.0221			−1.28311			−0.641554	−	0.767078i	$-0.721710\pi$
$103$	−13.0221			−1.28311			−0.641554	+	0.767078i	$0.721710\pi$
$104$			2.92763i			0.287078i
$105$	−0.853755			−0.0833180
$106$		−	3.12653i		−	0.303676i
$107$	11.3784			1.09999			0.549994	−	0.835168i	$-0.314630\pi$
$107$	11.3784			1.09999			0.549994	+	0.835168i	$0.314630\pi$
$108$			5.34604i			0.514423i
$109$		−	18.7191i		−	1.79297i	−0.443075	−	0.896484i	$-0.646113\pi$
$109$		−	18.7191i		−	1.79297i	0.443075	−	0.896484i	$-0.353887\pi$
$110$			2.12926i			0.203017i
$111$		−	0.456363i		−	0.0433161i
$112$			2.70307i			0.255416i
$113$	4.06651			0.382545			0.191272	−	0.981537i	$-0.438739\pi$
$113$	4.06651			0.382545			0.191272	+	0.981537i	$0.438739\pi$
$114$	−0.621341			−0.0581939
$115$	−5.68146			−0.529799
$116$			4.29480i			0.398762i
$117$			4.45618i			0.411974i
$118$	3.61223			0.332533
$119$	−7.37322			−0.675902
$120$			1.52745i			0.139436i
$121$	3.33279			0.302981
$122$	1.28170			0.116040
$123$	1.38909	−	3.06912i	0.125250	−	0.276733i
$124$	4.56374			0.409836
$125$	11.9542			1.06922
$126$		−	1.29046i		−	0.114963i
$127$	13.4221			1.19102			0.595511	−	0.803347i	$-0.296950\pi$
$127$	13.4221			1.19102			0.595511	+	0.803347i	$0.296950\pi$
$128$	11.1889			0.988969
$129$		−	0.209486i		−	0.0184442i
$130$			1.25833i			0.110363i
$131$	−3.09642			−0.270535			−0.135268	−	0.990809i	$-0.543189\pi$
$131$	−3.09642			−0.270535			−0.135268	+	0.990809i	$0.543189\pi$
$132$	−2.58650			−0.225126
$133$	−2.49217			−0.216098
$134$			4.00253i			0.345766i
$135$			4.88621i			0.420538i
$136$			13.1914i			1.13115i
$137$			17.7753i			1.51865i	0.650713	+	0.759324i	$0.274470\pi$
$137$			17.7753i			1.51865i	−0.650713	+	0.759324i	$0.725530\pi$
$138$			0.872905i			0.0743066i
$139$	−17.1904			−1.45807			−0.729036	−	0.684475i	$-0.760031\pi$
$139$	−17.1904			−1.45807			−0.729036	+	0.684475i	$0.760031\pi$
$140$			2.88106i			0.243494i
$141$	1.41184			0.118898
$142$		−	3.36167i		−	0.282105i
$143$	−4.53109			−0.378909
$144$	7.36099			0.613416
$145$			3.92538i			0.325985i
$146$	−0.918010			−0.0759750
$147$			0.526124i			0.0433939i
$148$	−1.54003			−0.126590
$149$		−	1.20888i		−	0.0990350i	−0.998773	−	0.0495175i	$-0.984232\pi$
$149$		−	1.20888i		−	0.0990350i	0.998773	−	0.0495175i	$-0.0157684\pi$
$150$		−	0.590074i		−	0.0481793i
$151$			17.0168i			1.38481i	0.721511	+	0.692403i	$0.243448\pi$
$151$			17.0168i			1.38481i	−0.721511	+	0.692403i	$0.756552\pi$
$152$			4.45872i			0.361650i
$153$			20.0787i			1.62327i
$154$	1.31215			0.105736
$155$	4.17119			0.335038
$156$	−1.52854			−0.122381
$157$		−	13.9985i		−	1.11720i	−0.829436	−	0.558601i	$-0.811338\pi$
$157$		−	13.9985i		−	1.11720i	0.829436	−	0.558601i	$-0.188662\pi$
$158$			5.57818i			0.443777i
$159$	3.47125			0.275288
$160$	7.88501			0.623365
$161$			3.50118i			0.275932i
$162$	−3.12065			−0.245181
$163$	−0.561017			−0.0439422			−0.0219711	−	0.999759i	$-0.506994\pi$
$163$	−0.561017			−0.0439422			−0.0219711	+	0.999759i	$0.506994\pi$
$164$	−10.3569	−	4.68759i	−0.808742	−	0.366039i
$165$	−2.36403			−0.184039
$166$	−1.79785			−0.139540
$167$		−	15.4597i		−	1.19631i	−0.801382	−	0.598154i	$-0.795901\pi$
$167$		−	15.4597i		−	1.19631i	0.801382	−	0.598154i	$-0.204099\pi$
$168$	0.941284			0.0726216
$169$	10.3223			0.794020
$170$			5.66980i			0.434854i
$171$			6.78665i			0.518988i
$172$	−0.706925			−0.0539026
$173$	9.11098			0.692695			0.346347	−	0.938106i	$-0.387422\pi$
$173$	9.11098			0.692695			0.346347	+	0.938106i	$0.387422\pi$
$174$	0.603100			0.0457209
$175$		−	2.36675i		−	0.178910i
$176$			7.48474i			0.564183i
$177$			4.01050i			0.301447i
$178$		−	2.56395i		−	0.192176i
$179$		−	15.6357i		−	1.16866i	−0.811515	−	0.584332i	$-0.801356\pi$
$179$		−	15.6357i		−	1.16866i	0.811515	−	0.584332i	$-0.198644\pi$
$180$	7.84568			0.584782
$181$			12.1485i			0.902989i	0.892274	+	0.451495i	$0.149109\pi$
$181$			12.1485i			0.902989i	−0.892274	+	0.451495i	$0.850891\pi$
$182$	0.775441			0.0574795
$183$			1.42302i			0.105192i
$184$	6.26393			0.461783
$185$	−1.40756			−0.103486
$186$		−	0.640866i		−	0.0469906i
$187$	−20.4163			−1.49298
$188$		−	4.76435i		−	0.347476i
$189$	3.01111			0.219026
$190$			1.91641i			0.139031i
$191$		−	12.2282i		−	0.884804i	−0.896817	−	0.442402i	$-0.854126\pi$
$191$		−	12.2282i		−	0.884804i	0.896817	−	0.442402i	$-0.145874\pi$
$192$			1.63284i			0.117840i
$193$			15.4360i			1.11111i	0.831481	+	0.555553i	$0.187493\pi$
$193$			15.4360i			1.11111i	−0.831481	+	0.555553i	$0.812507\pi$
$194$		−	1.77432i		−	0.127389i
$195$	−1.39707			−0.100046
$196$	1.77544			0.126817
$197$	9.28850			0.661779			0.330889	−	0.943670i	$-0.392651\pi$
$197$	9.28850			0.661779			0.330889	+	0.943670i	$0.392651\pi$
$198$		−	3.57324i		−	0.253939i
$199$		−	25.1389i		−	1.78205i	−0.453953	−	0.891026i	$-0.649987\pi$
$199$		−	25.1389i		−	1.78205i	0.453953	−	0.891026i	$-0.350013\pi$
$200$	−4.23434			−0.299413
$201$	−4.44383			−0.313444
$202$		−	3.60970i		−	0.253978i
$203$	2.41900			0.169781
$204$	−6.88734			−0.482210
$205$	−9.46610	−	4.28439i	−0.661141	−	0.299235i
$206$	6.17088			0.429946
$207$	9.53439			0.662686
$208$			4.42325i			0.306697i
$209$	−6.90074			−0.477334
$210$	0.404574			0.0279183
$211$		−	23.2073i		−	1.59766i	−0.601560	−	0.798828i	$-0.705454\pi$
$211$		−	23.2073i		−	1.59766i	0.601560	−	0.798828i	$-0.294546\pi$
$212$		−	11.7140i		−	0.804519i
$213$	3.73231			0.255734
$214$	−5.39194			−0.368586
$215$	−0.646120			−0.0440650
$216$		−	5.38715i		−	0.366549i
$217$		−	2.57048i		−	0.174496i
$218$			8.87056i			0.600790i
$219$		−	1.01923i		−	0.0688729i
$220$			7.97757i			0.537848i
$221$	−12.0654			−0.811606
$222$			0.216260i			0.0145144i
$223$	2.85382			0.191106			0.0955529	−	0.995424i	$-0.469538\pi$
$223$	2.85382			0.191106			0.0955529	+	0.995424i	$0.469538\pi$
$224$		−	4.85911i		−	0.324663i
$225$	−6.44513			−0.429675
$226$	−1.92702			−0.128184
$227$			14.2283i			0.944365i	0.881501	+	0.472183i	$0.156534\pi$
$227$			14.2283i			0.944365i	−0.881501	+	0.472183i	$0.843466\pi$
$228$	−2.32794			−0.154171
$229$		−	20.0492i		−	1.32489i	−0.749111	−	0.662444i	$-0.769519\pi$
$229$		−	20.0492i		−	1.32489i	0.749111	−	0.662444i	$-0.230481\pi$
$230$	2.69231			0.177526
$231$			1.45682i			0.0958518i
$232$		−	4.32782i		−	0.284135i
$233$			26.2688i			1.72093i	0.509512	+	0.860463i	$0.329826\pi$
$233$			26.2688i			1.72093i	−0.509512	+	0.860463i	$0.670174\pi$
$234$		−	2.11168i		−	0.138045i
$235$		−	4.35455i		−	0.284060i
$236$	13.5337			0.880969
$237$	−6.19321			−0.402292
$238$	3.49400			0.226482
$239$		−	18.1487i		−	1.17394i	−0.809607	−	0.586972i	$-0.800320\pi$
$239$		−	18.1487i		−	1.17394i	0.809607	−	0.586972i	$-0.199680\pi$
$240$			2.30776i			0.148966i
$241$	15.5782			1.00348			0.501740	−	0.865019i	$-0.332694\pi$
$241$	15.5782			1.00348			0.501740	+	0.865019i	$0.332694\pi$
$242$	−1.57933			−0.101523
$243$		−	12.4980i		−	0.801750i
$244$	4.80207			0.307421
$245$	1.62273			0.103672
$246$	−0.658258	+	1.45438i	−0.0419690	+	0.0927280i
$247$	−4.07813			−0.259485
$248$	−4.59883			−0.292026
$249$		−	1.99607i		−	0.126496i
$250$	−5.66483			−0.358275
$251$	−20.0363			−1.26468			−0.632339	−	0.774692i	$-0.717905\pi$
$251$	−20.0363			−1.26468			−0.632339	+	0.774692i	$0.717905\pi$
$252$		−	4.83487i		−	0.304568i
$253$			9.69467i			0.609498i
$254$	−6.36043			−0.399089
$255$	−6.29493			−0.394204
$256$	0.904906			0.0565566
$257$			9.37988i			0.585101i	0.956250	+	0.292550i	$0.0945039\pi$
$257$			9.37988i			0.585101i	−0.956250	+	0.292550i	$0.905496\pi$
$258$			0.0992705i			0.00618031i
$259$			0.867407i			0.0538980i
$260$			4.71450i			0.292381i
$261$		−	6.58741i		−	0.407751i
$262$	1.46732			0.0906513
$263$		−	19.4633i		−	1.20016i	−0.799941	−	0.600079i	$-0.795136\pi$
$263$		−	19.4633i		−	1.20016i	0.799941	−	0.600079i	$-0.204864\pi$
$264$	2.60639			0.160412
$265$		−	10.7064i		−	0.657689i
$266$	1.18098			0.0724104
$267$	2.84664			0.174211
$268$			14.9960i			0.916028i
$269$	14.7533			0.899524			0.449762	−	0.893149i	$-0.351509\pi$
$269$	14.7533			0.899524			0.449762	+	0.893149i	$0.351509\pi$
$270$		−	2.31546i		−	0.140914i
$271$	−4.77670			−0.290164			−0.145082	−	0.989420i	$-0.546345\pi$
$271$	−4.77670			−0.290164			−0.145082	+	0.989420i	$0.546345\pi$
$272$			19.9304i			1.20846i
$273$			0.860938i			0.0521063i
$274$		−	8.42331i		−	0.508870i
$275$		−	6.55348i		−	0.395190i
$276$			3.27046i			0.196858i
$277$	−28.3040			−1.70062			−0.850311	−	0.526281i	$-0.823586\pi$
$277$	−28.3040			−1.70062			−0.850311	+	0.526281i	$0.823586\pi$
$278$	8.14613			0.488572
$279$	−6.99992			−0.419074
$280$		−	2.90321i		−	0.173500i
$281$		−	11.0245i		−	0.657667i	−0.944388	−	0.328834i	$-0.893344\pi$
$281$		−	11.0245i		−	0.657667i	0.944388	−	0.328834i	$-0.106656\pi$
$282$	−0.669038			−0.0398406
$283$	23.8172			1.41579			0.707894	−	0.706318i	$-0.249645\pi$
$283$	23.8172			1.41579			0.707894	+	0.706318i	$0.249645\pi$
$284$		−	12.5949i		−	0.747372i
$285$	−2.12770			−0.126034
$286$	2.14718			0.126965
$287$	−2.64024	+	5.83345i	−0.155848	+	0.344338i
$288$	−13.2323			−0.779720
$289$	−37.3644			−2.19791
$290$		−	1.86015i		−	0.109232i
$291$	1.96995			0.115481
$292$	−3.43945			−0.201278
$293$		−	18.7645i		−	1.09624i	−0.836401	−	0.548118i	$-0.815344\pi$
$293$		−	18.7645i		−	1.09624i	0.836401	−	0.548118i	$-0.184656\pi$
$294$		−	0.249318i		−	0.0145405i
$295$	12.3696			0.720187
$296$	1.55187			0.0902006
$297$	8.33767			0.483801
$298$			0.572858i			0.0331848i
$299$			5.72925i			0.331331i
$300$		−	2.21079i		−	0.127640i
$301$			0.398169i			0.0229501i
$302$		−	8.06385i		−	0.464023i
$303$	4.00769			0.230236
$304$			6.73651i			0.386365i
$305$	4.38902			0.251315
$306$		−	9.51483i		−	0.543927i
$307$	10.2881			0.587170			0.293585	−	0.955933i	$-0.405152\pi$
$307$	10.2881			0.587170			0.293585	+	0.955933i	$0.405152\pi$
$308$	4.91615			0.280123
$309$			6.85125i			0.389754i
$310$	−1.97663			−0.112265
$311$		−	31.5063i		−	1.78656i	−0.449500	−	0.893280i	$-0.648398\pi$
$311$		−	31.5063i		−	1.78656i	0.449500	−	0.893280i	$-0.351602\pi$
$312$	1.54030			0.0872021
$313$			10.0313i			0.567004i	0.958972	+	0.283502i	$0.0914963\pi$
$313$			10.0313i			0.567004i	−0.958972	+	0.283502i	$0.908504\pi$
$314$			6.63356i			0.374353i
$315$		−	4.41900i		−	0.248983i
$316$			20.8994i			1.17568i
$317$			15.5061i			0.870912i	0.900210	+	0.435456i	$0.143413\pi$
$317$			15.5061i			0.870912i	−0.900210	+	0.435456i	$0.856587\pi$
$318$	−1.64494			−0.0922438
$319$	6.69815			0.375024
$320$	5.03619			0.281531
$321$		−	5.98643i		−	0.334130i
$322$		−	1.65913i		−	0.0924595i
$323$	−18.3753			−1.02243
$324$	−11.6919			−0.649552
$325$		−	3.87291i		−	0.214830i
$326$	0.265852			0.0147242
$327$	−9.84859			−0.544628
$328$	10.4366	+	4.72363i	0.576264	+	0.260819i
$329$	−2.68348			−0.147945
$330$	1.12026			0.0616680
$331$			3.93053i			0.216042i	0.994149	+	0.108021i	$0.0344513\pi$
$331$			3.93053i			0.216042i	−0.994149	+	0.108021i	$0.965549\pi$
$332$	−6.73588			−0.369679
$333$	2.36212			0.129443
$334$			7.32598i			0.400860i
$335$			13.7062i			0.748847i
$336$	1.42215			0.0775847
$337$	33.4956			1.82462			0.912310	−	0.409499i	$-0.134297\pi$
$337$	33.4956			1.82462			0.912310	+	0.409499i	$0.134297\pi$
$338$	−4.89148			−0.266061
$339$		−	2.13949i		−	0.116201i
$340$			21.2427i			1.15205i
$341$		−	7.11759i		−	0.385439i
$342$		−	3.21603i		−	0.173903i
$343$		−	1.00000i		−	0.0539949i
$344$	0.712361			0.0384079
$345$			2.98915i			0.160930i
$346$	−4.31748			−0.232109
$347$		−	0.0992811i		−	0.00532969i	−0.999996	−	0.00266484i	$-0.999152\pi$
$347$		−	0.0992811i		−	0.00532969i	0.999996	−	0.00266484i	$-0.000848247\pi$
$348$	2.25959			0.121127
$349$	−15.3145			−0.819766			−0.409883	−	0.912138i	$-0.634430\pi$
$349$	−15.3145			−0.819766			−0.409883	+	0.912138i	$0.634430\pi$
$350$			1.12155i			0.0599493i
$351$	4.92731			0.263000
$352$		−	13.4547i		−	0.717140i
$353$	−14.8252			−0.789065			−0.394533	−	0.918882i	$-0.629094\pi$
$353$	−14.8252			−0.789065			−0.394533	+	0.918882i	$0.629094\pi$
$354$		−	1.90048i		−	0.101009i
$355$		−	11.5116i		−	0.610972i
$356$		−	9.60618i		−	0.509126i
$357$			3.87923i			0.205310i
$358$			7.40937i			0.391597i
$359$	−7.26402			−0.383380			−0.191690	−	0.981456i	$-0.561397\pi$
$359$	−7.26402			−0.383380			−0.191690	+	0.981456i	$0.561397\pi$
$360$	−7.90600			−0.416683
$361$	12.7891			0.673111
$362$		−	5.75688i		−	0.302575i
$363$		−	1.75346i		−	0.0920328i
$364$	2.90529			0.152279
$365$	−3.14361			−0.164544
$366$		−	0.674334i		−	0.0352480i
$367$	33.0949			1.72754			0.863770	−	0.503886i	$-0.168097\pi$
$367$	33.0949			1.72754			0.863770	+	0.503886i	$0.168097\pi$
$368$	9.46394			0.493342
$369$	15.8856	+	7.18989i	0.826972	+	0.374291i
$370$	0.667012			0.0346763
$371$	−6.59778			−0.342540
$372$		−	2.40109i		−	0.124491i
$373$	−7.60423			−0.393732			−0.196866	−	0.980430i	$-0.563076\pi$
$373$	−7.60423			−0.393732			−0.196866	+	0.980430i	$0.563076\pi$
$374$	9.67478			0.500271
$375$		−	6.28941i		−	0.324784i
$376$			4.80099i			0.247592i
$377$	3.95840			0.203868
$378$	−1.42689			−0.0733914
$379$	−25.0468			−1.28657			−0.643285	−	0.765627i	$-0.722429\pi$
$379$	−25.0468			−1.28657			−0.643285	+	0.765627i	$0.722429\pi$
$380$			7.18007i			0.368330i
$381$		−	7.06170i		−	0.361782i
$382$			5.79467i			0.296481i
$383$			4.59766i			0.234929i	0.993077	+	0.117465i	$0.0374767\pi$
$383$			4.59766i			0.234929i	−0.993077	+	0.117465i	$0.962523\pi$
$384$		−	5.88675i		−	0.300407i
$385$	4.49329			0.228999
$386$		−	7.31475i		−	0.372311i
$387$	1.08429			0.0551176
$388$		−	6.64774i		−	0.337488i
$389$	24.7421			1.25447			0.627236	−	0.778829i	$-0.284186\pi$
$389$	24.7421			1.25447			0.627236	+	0.778829i	$0.284186\pi$
$390$	0.662037			0.0335236
$391$			25.8150i			1.30552i
$392$	−1.78909			−0.0903628
$393$			1.62910i			0.0821772i
$394$	−4.40160			−0.221750
$395$			19.1018i			0.961114i
$396$		−	13.3876i		−	0.672753i
$397$			37.4163i			1.87787i	0.344092	+	0.938936i	$0.388187\pi$
$397$			37.4163i			1.87787i	−0.344092	+	0.938936i	$0.611813\pi$
$398$			11.9127i			0.597132i
$399$			1.31119i			0.0656415i
$400$	−6.39751			−0.319876
$401$	−14.4664			−0.722417			−0.361209	−	0.932485i	$-0.617636\pi$
$401$	−14.4664			−0.722417			−0.361209	+	0.932485i	$0.617636\pi$
$402$	2.10583			0.105029
$403$		−	4.20628i		−	0.209530i
$404$		−	13.5242i		−	0.672856i
$405$	−10.6863			−0.531004
$406$	−1.14631			−0.0568903
$407$			2.40182i			0.119054i
$408$	6.94030			0.343596
$409$	20.7285			1.02496			0.512479	−	0.858700i	$-0.328727\pi$
$409$	20.7285			1.02496			0.512479	+	0.858700i	$0.328727\pi$
$410$	4.48576	+	2.03027i	0.221536	+	0.100268i
$411$	9.35202			0.461301
$412$	23.1200			1.13904
$413$		−	7.62273i		−	0.375090i
$414$	−4.51812			−0.222054
$415$	−6.15649			−0.302210
$416$		−	7.95134i		−	0.389847i
$417$			9.04428i			0.442900i
$418$	3.27010			0.159946
$419$	−35.2228			−1.72075			−0.860374	−	0.509663i	$-0.829770\pi$
$419$	−35.2228			−1.72075			−0.860374	+	0.509663i	$0.829770\pi$
$420$	1.51579			0.0739631
$421$		−	7.33000i		−	0.357242i	−0.983918	−	0.178621i	$-0.942836\pi$
$421$		−	7.33000i		−	0.357242i	0.983918	−	0.178621i	$-0.0571636\pi$
$422$			10.9974i			0.535344i
$423$			7.30763i			0.355309i
$424$			11.8040i			0.573255i
$425$		−	17.4506i		−	0.846479i
$426$	−1.76865			−0.0856915
$427$		−	2.70472i		−	0.130890i
$428$	−20.2016			−0.976483
$429$			2.38391i			0.115096i
$430$	0.306181			0.0147654
$431$	25.6015			1.23318			0.616591	−	0.787284i	$-0.288513\pi$
$431$	25.6015			1.23318			0.616591	+	0.787284i	$0.288513\pi$
$432$		−	8.13925i		−	0.391600i
$433$	1.59949			0.0768666			0.0384333	−	0.999261i	$-0.487763\pi$
$433$	1.59949			0.0768666			0.0384333	+	0.999261i	$0.487763\pi$
$434$			1.21809i			0.0584702i
$435$	2.06524			0.0990205
$436$			33.2347i			1.59166i
$437$			8.72552i			0.417398i
$438$			0.482987i			0.0230780i
$439$			3.95270i			0.188652i	0.995541	+	0.0943260i	$0.0300696\pi$
$439$			3.95270i			0.188652i	−0.995541	+	0.0943260i	$0.969930\pi$
$440$		−	8.03891i		−	0.383240i
$441$	−2.72319			−0.129676
$442$	5.71750			0.271954
$443$	−8.59951			−0.408575			−0.204288	−	0.978911i	$-0.565488\pi$
$443$	−8.59951			−0.408575			−0.204288	+	0.978911i	$0.565488\pi$
$444$			0.810246i			0.0384526i
$445$		−	8.77991i		−	0.416207i
$446$	−1.35236			−0.0640360
$447$	−0.636018			−0.0300826
$448$		−	3.10353i		−	0.146628i
$449$	−21.9764			−1.03713			−0.518565	−	0.855038i	$-0.673534\pi$
$449$	−21.9764			−1.03713			−0.518565	+	0.855038i	$0.673534\pi$
$450$	3.05420			0.143976
$451$	−7.31075	+	16.1527i	−0.344250	+	0.760599i
$452$	−7.21985			−0.339593
$453$	8.95293			0.420645
$454$		−	6.74245i		−	0.316439i
$455$	2.65540			0.124487
$456$	2.34584			0.109854
$457$			2.60673i			0.121938i	0.998140	+	0.0609688i	$0.0194190\pi$
$457$			2.60673i			0.121938i	−0.998140	+	0.0609688i	$0.980581\pi$
$458$			9.50084i			0.443945i
$459$	22.2016			1.03628
$460$	10.0871			0.470313
$461$	16.4133			0.764443			0.382221	−	0.924071i	$-0.375159\pi$
$461$	16.4133			0.764443			0.382221	+	0.924071i	$0.375159\pi$
$462$		−	0.690353i		−	0.0321181i
$463$			25.9499i			1.20600i	0.797743	+	0.602998i	$0.206027\pi$
$463$			25.9499i			1.20600i	−0.797743	+	0.602998i	$0.793973\pi$
$464$		−	6.53874i		−	0.303553i
$465$		−	2.19456i		−	0.101770i
$466$		−	12.4482i		−	0.576650i
$467$	31.1512			1.44151			0.720753	−	0.693192i	$-0.243796\pi$
$467$	31.1512			1.44151			0.720753	+	0.693192i	$0.243796\pi$
$468$		−	7.91168i		−	0.365718i
$469$	8.44637			0.390017
$470$			2.06352i			0.0951830i
$471$	−7.36494			−0.339359
$472$	−13.6378			−0.627729
$473$			1.10252i			0.0506939i
$474$	2.93481			0.134801
$475$		−	5.89835i		−	0.270635i
$476$	13.0907			0.600012
$477$			17.9670i			0.822654i
$478$			8.60025i			0.393366i
$479$			20.0950i			0.918165i	0.888394	+	0.459083i	$0.151822\pi$
$479$			20.0950i			0.918165i	−0.888394	+	0.459083i	$0.848178\pi$
$480$		−	4.14849i		−	0.189352i
$481$			1.41941i			0.0647193i
$482$	−7.38213			−0.336247
$483$	1.84205			0.0838163
$484$	−5.91718			−0.268963
$485$		−	6.07594i		−	0.275894i
$486$			5.92253i			0.268651i
$487$	−2.24229			−0.101608			−0.0508040	−	0.998709i	$-0.516178\pi$
$487$	−2.24229			−0.101608			−0.0508040	+	0.998709i	$0.516178\pi$
$488$	−4.83899			−0.219051
$489$			0.295164i			0.0133478i
$490$	−0.768972			−0.0347386
$491$	−14.8211			−0.668869			−0.334434	−	0.942419i	$-0.608545\pi$
$491$	−14.8211			−0.668869			−0.334434	+	0.942419i	$0.608545\pi$
$492$	−2.46625	+	5.44903i	−0.111187	+	0.245661i
$493$	17.8358			0.803286
$494$	1.93253			0.0869486
$495$		−	12.2361i		−	0.549972i
$496$	−6.94820			−0.311983
$497$	−7.09398			−0.318208
$498$			0.945890i			0.0423864i
$499$			41.5418i			1.85966i	0.367983	+	0.929832i	$0.380048\pi$
$499$			41.5418i			1.85966i	−0.367983	+	0.929832i	$0.619952\pi$
$500$	−21.2240			−0.949168
$501$	−8.13371			−0.363387
$502$	9.49471			0.423770
$503$			22.1621i			0.988160i	0.869416	+	0.494080i	$0.164495\pi$
$503$			22.1621i			0.988160i	−0.869416	+	0.494080i	$0.835505\pi$
$504$			4.87205i			0.217018i
$505$		−	12.3610i		−	0.550055i
$506$		−	4.59407i		−	0.204231i
$507$		−	5.43079i		−	0.241190i
$508$	−23.8302			−1.05729
$509$		−	30.7968i		−	1.36504i	−0.730865	−	0.682522i	$-0.760883\pi$
$509$		−	30.7968i		−	1.36504i	0.730865	−	0.682522i	$-0.239117\pi$
$510$	2.98302			0.132090
$511$			1.93724i			0.0856982i
$512$	−22.8066			−1.00792
$513$	7.50418			0.331318
$514$		−	4.44490i		−	0.196056i
$515$	21.1314			0.931160
$516$			0.371930i			0.0163733i
$517$	−7.43047			−0.326792
$518$		−	0.411043i		−	0.0180602i
$519$		−	4.79350i		−	0.210411i
$520$		−	4.75075i		−	0.208334i
$521$		−	15.6052i		−	0.683678i	−0.939759	−	0.341839i	$-0.888950\pi$
$521$		−	15.6052i		−	0.683678i	0.939759	−	0.341839i	$-0.111050\pi$
$522$			3.12162i			0.136630i
$523$	43.9461			1.92163			0.960814	−	0.277193i	$-0.0894040\pi$
$523$	43.9461			1.92163			0.960814	+	0.277193i	$0.0894040\pi$
$524$	5.49751			0.240160
$525$	−1.24521			−0.0543452
$526$			9.22319i			0.402150i
$527$		−	18.9527i		−	0.825594i
$528$	3.93790			0.171375
$529$	−10.7417			−0.467033
$530$			5.07351i			0.220379i
$531$	−20.7582			−0.900828
$532$	4.42469			0.191835
$533$	−4.32043	+	9.54573i	−0.187139	+	0.413472i
$534$	−1.34895			−0.0583749
$535$	−18.4640			−0.798268
$536$		−	15.1113i		−	0.652710i
$537$	−8.22629			−0.354991
$538$	−6.99123			−0.301413
$539$		−	2.76897i		−	0.119268i
$540$		−	8.67517i		−	0.373320i
$541$	−23.6069			−1.01494			−0.507469	−	0.861670i	$-0.669419\pi$
$541$	−23.6069			−1.01494			−0.507469	+	0.861670i	$0.669419\pi$
$542$	2.26356			0.0972284
$543$	6.39160			0.274290
$544$		−	35.8273i		−	1.53608i
$545$			30.3761i			1.30117i
$546$		−	0.407978i		−	0.0174598i
$547$			12.5626i			0.537136i	0.963261	+	0.268568i	$0.0865504\pi$
$547$			12.5626i			0.537136i	−0.963261	+	0.268568i	$0.913450\pi$
$548$		−	31.5590i		−	1.34814i
$549$	−7.36547			−0.314351
$550$			3.10554i			0.132421i
$551$	6.02856			0.256825
$552$		−	3.29560i		−	0.140270i
$553$	11.7714			0.500571
$554$	13.4126			0.569846
$555$			0.740553i			0.0314347i
$556$	30.5206			1.29436
$557$		−	28.0468i		−	1.18838i	−0.804324	−	0.594191i	$-0.797472\pi$
$557$		−	28.0468i		−	1.18838i	0.804324	−	0.594191i	$-0.202528\pi$
$558$	3.31709			0.140424
$559$			0.651555i			0.0275578i
$560$		−	4.38635i		−	0.185357i
$561$			10.7415i			0.453505i
$562$			5.22425i			0.220372i
$563$		−	32.2134i		−	1.35763i	−0.734308	−	0.678816i	$-0.762493\pi$
$563$		−	32.2134i		−	1.35763i	0.734308	−	0.678816i	$-0.237507\pi$
$564$	−2.50664			−0.105549
$565$	−6.59884			−0.277615
$566$	−11.2864			−0.474404
$567$			6.58537i			0.276559i
$568$			12.6918i			0.532535i
$569$	22.2672			0.933490			0.466745	−	0.884392i	$-0.345427\pi$
$569$	22.2672			0.933490			0.466745	+	0.884392i	$0.345427\pi$
$570$	1.00827			0.0422317
$571$			18.8917i			0.790593i	0.918554	+	0.395296i	$0.129358\pi$
$571$			18.8917i			0.790593i	−0.918554	+	0.395296i	$0.870642\pi$
$572$	8.04468			0.336365
$573$	−6.43356			−0.268766
$574$	1.25115	−	2.76433i	0.0522219	−	0.115381i
$575$	−8.28643			−0.345568
$576$	−8.45152			−0.352147
$577$		−	14.6460i		−	0.609721i	−0.952397	−	0.304860i	$-0.901390\pi$
$577$		−	14.6460i		−	0.609721i	0.952397	−	0.304860i	$-0.0986098\pi$
$578$	17.7061			0.736477
$579$	8.12124			0.337507
$580$		−	6.96928i		−	0.289384i
$581$			3.79392i			0.157398i
$582$	−0.933514			−0.0386954
$583$	−18.2691			−0.756628
$584$	3.46589			0.143420
$585$		−	7.23116i		−	0.298972i
$586$			8.89207i			0.367328i
$587$			9.09391i			0.375346i	0.982232	+	0.187673i	$0.0600945\pi$
$587$			9.09391i			0.375346i	−0.982232	+	0.187673i	$0.939906\pi$
$588$		−	0.934102i		−	0.0385217i
$589$		−	6.40606i		−	0.263957i
$590$	−5.86167			−0.241321
$591$		−	4.88690i		−	0.201020i
$592$	2.34466			0.0963651
$593$			11.7054i			0.480684i	0.970688	+	0.240342i	$0.0772595\pi$
$593$			11.7054i			0.480684i	−0.970688	+	0.240342i	$0.922740\pi$
$594$	−3.95103			−0.162113
$595$	11.9647			0.490506
$596$			2.14629i			0.0879154i
$597$	−13.2262			−0.541312
$598$		−	2.71496i		−	0.111023i
$599$	18.9668			0.774963			0.387482	−	0.921877i	$-0.373345\pi$
$599$	18.9668			0.774963			0.387482	+	0.921877i	$0.373345\pi$
$600$			2.22779i			0.0909491i
$601$		−	21.3210i		−	0.869702i	−0.900503	−	0.434851i	$-0.856801\pi$
$601$		−	21.3210i		−	0.869702i	0.900503	−	0.434851i	$-0.143199\pi$
$602$		−	0.188683i		−	0.00769014i
$603$		−	23.0011i		−	0.936677i
$604$		−	30.2123i		−	1.22932i
$605$	−5.40821			−0.219875
$606$	−1.89915			−0.0771477
$607$	−36.5519			−1.48360			−0.741798	−	0.670624i	$-0.766027\pi$
$607$	−36.5519			−1.48360			−0.741798	+	0.670624i	$0.766027\pi$
$608$		−	12.1097i		−	0.491113i
$609$		−	1.27269i		−	0.0515722i
$610$	−2.07985			−0.0842108
$611$	−4.39118			−0.177648
$612$		−	35.6486i		−	1.44101i
$613$	−42.8925			−1.73241			−0.866207	−	0.499686i	$-0.833449\pi$
$613$	−42.8925			−1.73241			−0.866207	+	0.499686i	$0.833449\pi$
$614$	−4.87526			−0.196750
$615$	−2.25412	+	4.98034i	−0.0908949	+	0.200827i
$616$	−4.95395			−0.199600
$617$	40.8459			1.64439			0.822196	−	0.569204i	$-0.192749\pi$
$617$	40.8459			1.64439			0.822196	+	0.569204i	$0.192749\pi$
$618$		−	3.24665i		−	0.130599i
$619$	24.8379			0.998321			0.499160	−	0.866510i	$-0.333642\pi$
$619$	24.8379			0.998321			0.499160	+	0.866510i	$0.333642\pi$
$620$	−7.40570			−0.297420
$621$		−	10.5424i		−	0.423053i
$622$			14.9301i			0.598643i
$623$	−5.41058			−0.216770
$624$	2.32718			0.0931617
$625$	−7.56470			−0.302588
$626$		−	4.75361i		−	0.189992i
$627$			3.63064i			0.144994i
$628$			24.8535i			0.991764i
$629$			6.39558i			0.255009i
$630$			2.09406i			0.0834294i
$631$	20.6114			0.820528			0.410264	−	0.911967i	$-0.365437\pi$
$631$	20.6114			0.820528			0.410264	+	0.911967i	$0.365437\pi$
$632$		−	21.0601i		−	0.837726i
$633$	−12.2099			−0.485300
$634$		−	7.34799i		−	0.291826i
$635$	−21.7805			−0.864332
$636$	−6.16300			−0.244379
$637$		−	1.63638i		−	0.0648357i
$638$	−3.17409			−0.125664
$639$			19.3183i			0.764219i
$640$	−18.1565			−0.717700
$641$			28.8053i			1.13774i	0.822427	+	0.568871i	$0.192619\pi$
$641$			28.8053i			1.13774i	−0.822427	+	0.568871i	$0.807381\pi$
$642$			2.83683i			0.111961i
$643$			26.2977i			1.03708i	0.855054	+	0.518539i	$0.173524\pi$
$643$			26.2977i			1.03708i	−0.855054	+	0.518539i	$0.826476\pi$
$644$		−	6.21614i		−	0.244950i
$645$			0.339939i			0.0133851i
$646$	8.70762			0.342597
$647$	−12.6930			−0.499012			−0.249506	−	0.968373i	$-0.580268\pi$
$647$	−12.6930			−0.499012			−0.249506	+	0.968373i	$0.580268\pi$
$648$	11.7818			0.462834
$649$		−	21.1071i		−	0.828527i
$650$			1.83528i			0.0719856i
$651$	−1.35239			−0.0530044
$652$	0.996052			0.0390084
$653$		−	0.434120i		−	0.0169884i	−0.999964	−	0.00849422i	$-0.997296\pi$
$653$		−	0.434120i		−	0.0169884i	0.999964	−	0.00849422i	$-0.00270383\pi$
$654$	4.66701			0.182495
$655$	5.02464			0.196329
$656$	15.7682	+	7.13677i	0.615646	+	0.278644i
$657$	5.27547			0.205816
$658$	1.27164			0.0495735
$659$		−	19.6777i		−	0.766533i	−0.923638	−	0.383266i	$-0.874799\pi$
$659$		−	19.6777i		−	0.766533i	0.923638	−	0.383266i	$-0.125201\pi$
$660$	4.19719			0.163375
$661$	35.7186			1.38929			0.694647	−	0.719351i	$-0.255561\pi$
$661$	35.7186			1.38929			0.694647	+	0.719351i	$0.255561\pi$
$662$		−	1.86259i		−	0.0723915i
$663$			6.34789i			0.246531i
$664$	6.78767			0.263413
$665$	4.04411			0.156824
$666$	−1.11935			−0.0433740
$667$		−	8.46936i		−	0.327935i
$668$			27.4478i			1.06199i
$669$		−	1.50146i		−	0.0580499i
$670$		−	6.49502i		−	0.250925i
$671$		−	7.48929i		−	0.289121i
$672$	−2.55649			−0.0986188
$673$		−	8.94138i		−	0.344665i	−0.985039	−	0.172332i	$-0.944870\pi$
$673$		−	8.94138i		−	0.344665i	0.985039	−	0.172332i	$-0.0551303\pi$
$674$	−15.8728			−0.611396
$675$			7.12655i			0.274301i
$676$	−18.3266			−0.704868
$677$	−41.2411			−1.58502			−0.792512	−	0.609856i	$-0.791227\pi$
$677$	−41.2411			−1.58502			−0.792512	+	0.609856i	$0.791227\pi$
$678$			1.01385i			0.0389368i
$679$	−3.74428			−0.143692
$680$		−	21.4060i		−	0.820883i
$681$	7.48584			0.286858
$682$			3.37286i			0.129153i
$683$			10.2803i			0.393363i	0.980467	+	0.196682i	$0.0630166\pi$
$683$			10.2803i			0.393363i	−0.980467	+	0.196682i	$0.936983\pi$
$684$		−	12.0493i		−	0.460717i
$685$		−	28.8445i		−	1.10209i
$686$			0.473876i			0.0180927i
$687$	−10.5484			−0.402445
$688$	1.07628			0.0410328
$689$	−10.7965			−0.411313
$690$		−	1.41649i		−	0.0539248i
$691$		−	16.1153i		−	0.613053i	−0.951862	−	0.306527i	$-0.900833\pi$
$691$		−	16.1153i		−	0.613053i	0.951862	−	0.306527i	$-0.0991669\pi$
$692$	−16.1760			−0.614920
$693$	−7.54045			−0.286438
$694$			0.0470470i			0.00178588i
$695$	27.8954			1.05813
$696$	−2.27697			−0.0863082
$697$	−19.4671	+	43.0113i	−0.737369	+	1.62917i
$698$	7.25717			0.274688
$699$	13.8206			0.522745
$700$			4.20203i			0.158822i
$701$	22.9744			0.867730			0.433865	−	0.900978i	$-0.357150\pi$
$701$	22.9744			0.867730			0.433865	+	0.900978i	$0.357150\pi$
$702$	−2.33494			−0.0881265
$703$			2.16172i			0.0815309i
$704$		−	8.59359i		−	0.323883i
$705$	−2.29103			−0.0862853
$706$	7.02531			0.264401
$707$	−7.61739			−0.286481
$708$		−	7.12040i		−	0.267601i
$709$			7.09797i			0.266570i	0.991078	+	0.133285i	$0.0425525\pi$
$709$			7.09797i			0.266570i	−0.991078	+	0.133285i	$0.957447\pi$
$710$			5.45507i			0.204725i
$711$		−	32.0558i		−	1.20219i
$712$			9.68004i			0.362775i
$713$	−8.99971			−0.337042
$714$		−	1.83827i		−	0.0687957i
$715$	7.35272			0.274976
$716$			27.7602i			1.03745i
$717$	−9.54848			−0.356594
$718$	3.44225			0.128463
$719$			28.2361i			1.05303i	0.850166	+	0.526515i	$0.176502\pi$
$719$			28.2361i			1.05303i	−0.850166	+	0.526515i	$0.823498\pi$
$720$	−11.9449			−0.445160
$721$		−	13.0221i		−	0.484970i
$722$	−6.06046			−0.225547
$723$		−	8.19605i		−	0.304814i
$724$		−	21.5689i		−	0.801602i
$725$			5.72519i			0.212628i
$726$			0.830924i			0.0308385i
$727$		−	29.7753i		−	1.10431i	−0.833743	−	0.552153i	$-0.813807\pi$
$727$		−	29.7753i		−	1.10431i	0.833743	−	0.552153i	$-0.186193\pi$
$728$	−2.92763			−0.108505
$729$	13.1806			0.488170
$730$	1.48968			0.0551355
$731$			2.93579i			0.108584i
$732$		−	2.52648i		−	0.0933814i
$733$	16.7299			0.617933			0.308967	−	0.951073i	$-0.400017\pi$
$733$	16.7299			0.617933			0.308967	+	0.951073i	$0.400017\pi$
$734$	−15.6829			−0.578866
$735$		−	0.853755i		−	0.0314912i
$736$	−17.0126			−0.627093
$737$	23.3878			0.861499
$738$	−7.52782	−	3.40712i	−0.277103	−	0.125418i
$739$	−19.5911			−0.720672			−0.360336	−	0.932823i	$-0.617338\pi$
$739$	−19.5911			−0.720672			−0.360336	+	0.932823i	$0.617338\pi$
$740$	2.49905			0.0918668
$741$			2.14560i			0.0788206i
$742$	3.12653			0.114779
$743$	−5.10296			−0.187209			−0.0936047	−	0.995609i	$-0.529839\pi$
$743$	−5.10296			−0.187209			−0.0936047	+	0.995609i	$0.529839\pi$
$744$			2.41955i			0.0887051i
$745$			1.96168i			0.0718703i
$746$	3.60347			0.131932
$747$	10.3316			0.378012
$748$	36.2479			1.32535
$749$			11.3784i			0.415757i
$750$			2.98040i			0.108829i
$751$			33.7578i			1.23184i	0.787809	+	0.615919i	$0.211215\pi$
$751$			33.7578i			1.23184i	−0.787809	+	0.615919i	$0.788785\pi$
$752$			7.25363i			0.264513i
$753$			10.5416i			0.384156i
$754$	−1.87579			−0.0683124
$755$		−	27.6136i		−	1.00496i
$756$	−5.34604			−0.194434
$757$		−	50.0488i		−	1.81905i	−0.415645	−	0.909527i	$-0.636444\pi$
$757$		−	50.0488i		−	1.81905i	0.415645	−	0.909527i	$-0.363556\pi$
$758$	11.8691			0.431105
$759$	5.10059			0.185140
$760$		−	7.23528i		−	0.262451i
$761$	−39.0545			−1.41572			−0.707862	−	0.706351i	$-0.750340\pi$
$761$	−39.0545			−1.41572			−0.707862	+	0.706351i	$0.750340\pi$
$762$			3.34637i			0.121226i
$763$	18.7191			0.677679
$764$			21.7105i			0.785459i
$765$		−	32.5823i		−	1.17802i
$766$		−	2.17872i		−	0.0787204i
$767$		−	12.4737i		−	0.450398i
$768$		−	0.476092i		−	0.0171795i
$769$	27.0882			0.976826			0.488413	−	0.872612i	$-0.337576\pi$
$769$	27.0882			0.976826			0.488413	+	0.872612i	$0.337576\pi$
$770$	−2.12926			−0.0767333
$771$	4.93498			0.177729
$772$		−	27.4057i		−	0.986352i
$773$			13.8039i			0.496492i	0.968697	+	0.248246i	$0.0798541\pi$
$773$			13.8039i			0.496492i	−0.968697	+	0.248246i	$0.920146\pi$
$774$	−0.513820			−0.0184689
$775$	6.08370			0.218533
$776$			6.69886i			0.240475i
$777$	0.456363			0.0163719
$778$	−11.7247			−0.420350
$779$	−6.57992	+	14.5379i	−0.235750	+	0.520875i
$780$	2.48041			0.0888130
$781$	−19.6430			−0.702883
$782$		−	12.2331i		−	0.437455i
$783$	−7.28388			−0.260304
$784$	−2.70307			−0.0965384
$785$			22.7158i			0.810760i
$786$		−	0.771991i		−	0.0275360i
$787$	−29.0789			−1.03655			−0.518275	−	0.855214i	$-0.673426\pi$
$787$	−29.0789			−1.03655			−0.518275	+	0.855214i	$0.673426\pi$
$788$	−16.4912			−0.587474
$789$	−10.2401			−0.364557
$790$		−	9.05187i		−	0.322051i
$791$			4.06651i			0.144588i
$792$			13.4906i			0.479366i
$793$		−	4.42594i		−	0.157170i
$794$		−	17.7307i		−	0.629240i
$795$	−5.63289			−0.199778
$796$			44.6327i			1.58196i
$797$	41.6629			1.47578			0.737888	−	0.674924i	$-0.235823\pi$
$797$	41.6629			1.47578			0.737888	+	0.674924i	$0.235823\pi$
$798$		−	0.621341i		−	0.0219952i
$799$	−19.7859			−0.699974
$800$	11.5003			0.406598
$801$			14.7341i			0.520603i
$802$	6.85528			0.242068
$803$			5.36415i			0.189297i
$804$	7.88977			0.278251
$805$		−	5.68146i		−	0.200245i
$806$			1.99326i			0.0702095i
$807$		−	7.76205i		−	0.273237i
$808$			13.6282i			0.479439i
$809$			40.3766i			1.41957i	0.704420	+	0.709783i	$0.251207\pi$
$809$			40.3766i			1.41957i	−0.704420	+	0.709783i	$0.748793\pi$
$810$	5.06396			0.177930
$811$	24.9792			0.877138			0.438569	−	0.898698i	$-0.355486\pi$
$811$	24.9792			0.877138			0.438569	+	0.898698i	$0.355486\pi$
$812$	−4.29480			−0.150718
$813$			2.51313i			0.0881394i
$814$		−	1.13817i		−	0.0398928i
$815$	0.910377			0.0318891
$816$	10.4858			0.367078
$817$			0.992303i			0.0347163i
$818$	−9.82274			−0.343444
$819$	−4.45618			−0.155711
$820$	16.8065	+	7.60669i	0.586909	+	0.265637i
$821$	18.5347			0.646865			0.323432	−	0.946251i	$-0.395163\pi$
$821$	18.5347			0.646865			0.323432	+	0.946251i	$0.395163\pi$
$822$	−4.43170			−0.154573
$823$		−	4.61445i		−	0.160850i	−0.996761	−	0.0804249i	$-0.974372\pi$
$823$		−	4.61445i		−	0.160850i	0.996761	−	0.0804249i	$-0.0256277\pi$
$824$	−23.2978			−0.811617
$825$	−3.44794			−0.120042
$826$			3.61223i			0.125686i
$827$			32.0375i			1.11405i	0.830495	+	0.557026i	$0.188058\pi$
$827$			32.0375i			1.11405i	−0.830495	+	0.557026i	$0.811942\pi$
$828$	−16.9277			−0.588280
$829$	−19.9446			−0.692704			−0.346352	−	0.938105i	$-0.612580\pi$
$829$	−19.9446			−0.692704			−0.346352	+	0.938105i	$0.612580\pi$
$830$	2.91742			0.101265
$831$			14.8914i			0.516577i
$832$		−	5.07855i		−	0.176067i
$833$		−	7.37322i		−	0.255467i
$834$		−	4.28587i		−	0.148408i
$835$			25.0869i			0.868167i
$836$	12.2519			0.423739
$837$			7.73999i			0.267533i
$838$	16.6913			0.576590
$839$		−	1.14755i		−	0.0396178i	−0.999804	−	0.0198089i	$-0.993694\pi$
$839$		−	1.14755i		−	0.0396178i	0.999804	−	0.0198089i	$-0.00630577\pi$
$840$	−1.52745			−0.0527019
$841$	23.1484			0.798222
$842$			3.47351i			0.119705i
$843$	−5.80025			−0.199771
$844$			41.2032i			1.41827i
$845$	−16.7502			−0.576225
$846$		−	3.46291i		−	0.119057i
$847$			3.33279i			0.114516i
$848$			17.8343i			0.612432i
$849$		−	12.5308i		−	0.430057i
$850$			8.26943i			0.283639i
$851$	3.03695			0.104105
$852$	−6.62650			−0.227020
$853$	55.2524			1.89181			0.945903	−	0.324449i	$-0.105179\pi$
$853$	55.2524			1.89181			0.945903	+	0.324449i	$0.105179\pi$
$854$			1.28170i			0.0438589i
$855$		−	11.0129i		−	0.376633i
$856$	20.3570			0.695787
$857$	50.0018			1.70803			0.854015	−	0.520249i	$-0.174161\pi$
$857$	50.0018			1.70803			0.854015	+	0.520249i	$0.174161\pi$
$858$		−	1.12968i		−	0.0385666i
$859$	6.84952			0.233703			0.116851	−	0.993149i	$-0.462720\pi$
$859$	6.84952			0.233703			0.116851	+	0.993149i	$0.462720\pi$
$860$	1.14715			0.0391174
$861$	3.06912	+	1.38909i	0.104595	+	0.0473402i
$862$	−12.1320			−0.413216
$863$	−20.1480			−0.685847			−0.342924	−	0.939363i	$-0.611417\pi$
$863$	−20.1480			−0.685847			−0.342924	+	0.939363i	$0.611417\pi$
$864$			14.6313i			0.497767i
$865$	−14.7846			−0.502693
$866$	−0.757960			−0.0257565
$867$			19.6583i			0.667631i
$868$			4.56374i			0.154903i
$869$	32.5947			1.10570
$870$	−0.978667			−0.0331799
$871$	13.8215			0.468322
$872$		−	33.4903i		−	1.13412i
$873$			10.1964i			0.345096i
$874$		−	4.13482i		−	0.139862i
$875$			11.9542i			0.404127i
$876$			1.80957i			0.0611399i
$877$	37.8677			1.27870			0.639350	−	0.768916i	$-0.279203\pi$
$877$	37.8677			1.27870			0.639350	+	0.768916i	$0.279203\pi$
$878$		−	1.87309i		−	0.0632137i
$879$	−9.87247			−0.332990
$880$		−	12.1457i		−	0.409431i
$881$	20.6698			0.696383			0.348192	−	0.937423i	$-0.386796\pi$
$881$	20.6698			0.696383			0.348192	+	0.937423i	$0.386796\pi$
$882$	1.29046			0.0434520
$883$			21.9744i			0.739497i	0.929132	+	0.369748i	$0.120556\pi$
$883$			21.9744i			0.739497i	−0.929132	+	0.369748i	$0.879444\pi$
$884$	21.4214			0.720479
$885$		−	6.50795i		−	0.218762i
$886$	4.07510			0.136906
$887$			8.84733i			0.297064i	0.988908	+	0.148532i	$0.0474548\pi$
$887$			8.84733i			0.297064i	−0.988908	+	0.148532i	$0.952545\pi$
$888$		−	0.816476i		−	0.0273991i
$889$			13.4221i			0.450164i
$890$			4.16059i			0.139463i
$891$			18.2347i			0.610885i
$892$	−5.06679			−0.169649
$893$	−6.68767			−0.223794
$894$	0.301394			0.0100801
$895$			25.3724i			0.848107i
$896$			11.1889i			0.373795i
$897$	3.01430			0.100644
$898$	10.4141			0.347523
$899$			6.21800i			0.207382i
$900$	11.4430			0.381432
$901$	−48.6469			−1.62066
$902$	3.46439	−	7.65436i	0.115352	−	0.254862i
$903$	0.209486			0.00697126
$904$	7.27536			0.241975
$905$		−	19.7137i		−	0.655305i
$906$	−4.24258			−0.140950
$907$	−12.5151			−0.415558			−0.207779	−	0.978176i	$-0.566623\pi$
$907$	−12.5151			−0.415558			−0.207779	+	0.978176i	$0.566623\pi$
$908$		−	25.2615i		−	0.838333i
$909$			20.7436i			0.688023i
$910$	−1.25833			−0.0417132
$911$	40.3465			1.33674			0.668370	−	0.743829i	$-0.266992\pi$
$911$	40.3465			1.33674			0.668370	+	0.743829i	$0.266992\pi$
$912$	3.54424			0.117361
$913$			10.5053i			0.347673i
$914$		−	1.23527i		−	0.0408590i
$915$		−	2.30917i		−	0.0763387i
$916$			35.5962i			1.17613i
$917$		−	3.09642i		−	0.102253i
$918$	−10.5208			−0.347238
$919$			17.6800i			0.583209i	0.956539	+	0.291605i	$0.0941892\pi$
$919$			17.6800i			0.583209i	−0.956539	+	0.291605i	$0.905811\pi$
$920$	−10.1647			−0.335119
$921$		−	5.41279i		−	0.178357i
$922$	−7.77787			−0.256150
$923$	−11.6084			−0.382096
$924$		−	2.58650i		−	0.0850897i
$925$	−2.05294			−0.0675002
$926$		−	12.2971i		−	0.404106i
$927$	−35.4618			−1.16472
$928$			11.7542i			0.385850i
$929$			42.1887i			1.38417i	0.721818	+	0.692083i	$0.243307\pi$
$929$			42.1887i			1.38417i	−0.721818	+	0.692083i	$0.756693\pi$
$930$			1.03995i			0.0341013i
$931$		−	2.49217i		−	0.0816774i
$932$		−	46.6387i		−	1.52770i
$933$	−16.5762			−0.542681
$934$	−14.7618			−0.483022
$935$	33.1300			1.08347
$936$			7.97251i			0.260590i
$937$		−	22.3644i		−	0.730614i	−0.930887	−	0.365307i	$-0.880964\pi$
$937$		−	22.3644i		−	0.730614i	0.930887	−	0.365307i	$-0.119036\pi$
$938$	−4.00253			−0.130687
$939$	5.27772			0.172232
$940$			7.73125i			0.252166i
$941$	5.01189			0.163383			0.0816916	−	0.996658i	$-0.473968\pi$
$941$	5.01189			0.163383			0.0816916	+	0.996658i	$0.473968\pi$
$942$	3.49007			0.113713
$943$	20.4239	+	9.24395i	0.665095	+	0.301025i
$944$	−20.6048			−0.670629
$945$	−4.88621			−0.158948
$946$		−	0.522458i		−	0.0169866i
$947$	27.6955			0.899984			0.449992	−	0.893033i	$-0.351427\pi$
$947$	27.6955			0.899984			0.449992	+	0.893033i	$0.351427\pi$
$948$	10.9957			0.357123
$949$			3.17005i			0.102904i
$950$			2.79509i			0.0906846i
$951$	8.15815			0.264546
$952$	−13.1914			−0.427535
$953$	−56.2519			−1.82218			−0.911089	−	0.412209i	$-0.864757\pi$
$953$	−56.2519			−1.82218			−0.911089	+	0.412209i	$0.864757\pi$
$954$		−	8.51416i		−	0.275656i
$955$			19.8431i			0.642107i
$956$			32.2220i			1.04213i
$957$		−	3.52406i		−	0.113917i
$958$		−	9.52256i		−	0.307660i
$959$	−17.7753			−0.573995
$960$		−	2.64966i		−	0.0855173i
$961$	−24.3926			−0.786859
$962$		−	0.672623i		−	0.0216862i
$963$	30.9855			0.998494
$964$	−27.6582			−0.890809
$965$		−	25.0484i		−	0.806336i
$966$	−0.872905			−0.0280853
$967$			20.7989i			0.668849i	0.942423	+	0.334424i	$0.108542\pi$
$967$			20.7989i			0.668849i	−0.942423	+	0.334424i	$0.891458\pi$
$968$	5.96267			0.191648
$969$			9.66768i			0.310571i
$970$			2.87925i			0.0924470i
$971$		−	14.4769i		−	0.464585i	−0.972646	−	0.232292i	$-0.925377\pi$
$971$		−	14.4769i		−	0.464585i	0.972646	−	0.232292i	$-0.0746226\pi$
$972$			22.1895i			0.711730i
$973$		−	17.1904i		−	0.551099i
$974$	1.06257			0.0340469
$975$	−2.03763			−0.0652563
$976$	−7.31105			−0.234021
$977$		−	58.2925i		−	1.86494i	−0.361243	−	0.932472i	$-0.617648\pi$
$977$		−	58.2925i		−	1.86494i	0.361243	−	0.932472i	$-0.382352\pi$
$978$		−	0.139871i		−	0.00447259i
$979$	−14.9818			−0.478819
$980$	−2.88106			−0.0920320
$981$		−	50.9759i		−	1.62753i
$982$	7.02339			0.224125
$983$	−16.3324			−0.520923			−0.260461	−	0.965484i	$-0.583875\pi$
$983$	−16.3324			−0.520923			−0.260461	+	0.965484i	$0.583875\pi$
$984$	2.48522	−	5.49093i	0.0792258	−	0.175044i
$985$	−15.0727			−0.480257
$986$	−8.45198			−0.269166
$987$			1.41184i			0.0449394i
$988$	7.24048			0.230350
$989$	1.39406			0.0443285
$990$			5.79840i			0.184285i
$991$			7.50614i			0.238440i	0.992868	+	0.119220i	$0.0380395\pi$
$991$			7.50614i			0.238440i	−0.992868	+	0.119220i	$0.961961\pi$
$992$	12.4902			0.396566
$993$	2.06795			0.0656243
$994$	3.36167			0.106626
$995$			40.7936i			1.29324i
$996$			3.54390i			0.112293i
$997$		−	22.9800i		−	0.727784i	−0.931441	−	0.363892i	$-0.881448\pi$
$997$		−	22.9800i		−	0.727784i	0.931441	−	0.363892i	$-0.118552\pi$
$998$		−	19.6857i		−	0.623139i
$999$		−	2.61185i		−	0.0826354i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.c.b.204.5	✓	12
41.40	even	2	inner	287.2.c.b.204.6	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.c.b.204.5	✓	12	1.1	even	1	trivial
287.2.c.b.204.6	yes	12	41.40	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.473876 q^{2} -0.526124i q^{3} -1.77544 q^{4} -1.62273 q^{5} +0.249318i q^{6} +1.00000i q^{7} +1.78909 q^{8} +2.72319 q^{9} +O(q^{10})\)	\(q-0.473876 q^{2} -0.526124i q^{3} -1.77544 q^{4} -1.62273 q^{5} +0.249318i q^{6} +1.00000i q^{7} +1.78909 q^{8} +2.72319 q^{9} +0.768972 q^{10} +2.76897i q^{11} +0.934102i q^{12} +1.63638i q^{13} -0.473876i q^{14} +0.853755i q^{15} +2.70307 q^{16} +7.37322i q^{17} -1.29046 q^{18} +2.49217i q^{19} +2.88106 q^{20} +0.526124 q^{21} -1.31215i q^{22} +3.50118 q^{23} -0.941284i q^{24} -2.36675 q^{25} -0.775441i q^{26} -3.01111i q^{27} -1.77544i q^{28} -2.41900i q^{29} -0.404574i q^{30} -2.57048 q^{31} -4.85911 q^{32} +1.45682 q^{33} -3.49400i q^{34} -1.62273i q^{35} -4.83487 q^{36} +0.867407 q^{37} -1.18098i q^{38} +0.860938 q^{39} -2.90321 q^{40} +(5.83345 + 2.64024i) q^{41} -0.249318 q^{42} +0.398169 q^{43} -4.91615i q^{44} -4.41900 q^{45} -1.65913 q^{46} +2.68348i q^{47} -1.42215i q^{48} -1.00000 q^{49} +1.12155 q^{50} +3.87923 q^{51} -2.90529i q^{52} +6.59778i q^{53} +1.42689i q^{54} -4.49329i q^{55} +1.78909i q^{56} +1.31119 q^{57} +1.14631i q^{58} -7.62273 q^{59} -1.51579i q^{60} -2.70472 q^{61} +1.21809 q^{62} +2.72319i q^{63} -3.10353 q^{64} -2.65540i q^{65} -0.690353 q^{66} -8.44637i q^{67} -13.0907i q^{68} -1.84205i q^{69} +0.768972i q^{70} +7.09398i q^{71} +4.87205 q^{72} +1.93724 q^{73} -0.411043 q^{74} +1.24521i q^{75} -4.42469i q^{76} -2.76897 q^{77} -0.407978 q^{78} -11.7714i q^{79} -4.38635 q^{80} +6.58537 q^{81} +(-2.76433 - 1.25115i) q^{82} +3.79392 q^{83} -0.934102 q^{84} -11.9647i q^{85} -0.188683 q^{86} -1.27269 q^{87} +4.95395i q^{88} +5.41058i q^{89} +2.09406 q^{90} -1.63638 q^{91} -6.21614 q^{92} +1.35239i q^{93} -1.27164i q^{94} -4.04411i q^{95} +2.55649i q^{96} +3.74428i q^{97} +0.473876 q^{98} +7.54045i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} + 12 q^{4} + 2 q^{5} - 24 q^{8} - 4 q^{9}+O(q^{10}) \) 12 * q - 4 * q^2 + 12 * q^4 + 2 * q^5 - 24 * q^8 - 4 * q^9	\( 12 q - 4 q^{2} + 12 q^{4} + 2 q^{5} - 24 q^{8} - 4 q^{9} - 4 q^{10} + 28 q^{16} - 40 q^{18} + 2 q^{20} + 8 q^{21} + 16 q^{23} + 34 q^{25} - 6 q^{31} - 42 q^{32} + 18 q^{33} - 36 q^{36} - 10 q^{37} + 10 q^{39} + 38 q^{40} - 2 q^{41} + 32 q^{42} - 50 q^{43} + 6 q^{45} - 8 q^{46} - 12 q^{49} + 18 q^{50} - 2 q^{51} - 50 q^{57} - 70 q^{59} + 52 q^{61} + 68 q^{62} + 8 q^{64} + 92 q^{66} + 2 q^{72} - 64 q^{73} + 18 q^{74} - 20 q^{77} - 12 q^{78} - 32 q^{80} - 4 q^{81} - 56 q^{82} + 60 q^{83} - 20 q^{84} + 48 q^{86} - 20 q^{87} - 42 q^{90} + 14 q^{91} + 56 q^{92} + 4 q^{98}+O(q^{100}) \) 12 * q - 4 * q^2 + 12 * q^4 + 2 * q^5 - 24 * q^8 - 4 * q^9 - 4 * q^10 + 28 * q^16 - 40 * q^18 + 2 * q^20 + 8 * q^21 + 16 * q^23 + 34 * q^25 - 6 * q^31 - 42 * q^32 + 18 * q^33 - 36 * q^36 - 10 * q^37 + 10 * q^39 + 38 * q^40 - 2 * q^41 + 32 * q^42 - 50 * q^43 + 6 * q^45 - 8 * q^46 - 12 * q^49 + 18 * q^50 - 2 * q^51 - 50 * q^57 - 70 * q^59 + 52 * q^61 + 68 * q^62 + 8 * q^64 + 92 * q^66 + 2 * q^72 - 64 * q^73 + 18 * q^74 - 20 * q^77 - 12 * q^78 - 32 * q^80 - 4 * q^81 - 56 * q^82 + 60 * q^83 - 20 * q^84 + 48 * q^86 - 20 * q^87 - 42 * q^90 + 14 * q^91 + 56 * q^92 + 4 * q^98

Introduction

L-functions

Modular forms

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Database

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