LMFDB - Embedded newform 418.2.b.c.417.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(417,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("418.417");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.b (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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.14584320320.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 4x^{6} + 11x^{5} - 11x^{4} + 32x^{3} + 44x^{2} - 18x + 46 $ x^8 - x^7 + 4x^6 + 11x^5 - 11x^4 + 32x^3 + 44x^2 - 18x + 46
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			417.8
Root			$0.274776 + 0.839339i$ of defining polynomial
Character	$\chi$	$=$	418.417
Dual form			418.2.b.c.417.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +3.37171i q^{3} +1.00000 q^{4} +0.549551 q^{5} -3.37171i q^{6} -2.61555i q^{7} -1.00000 q^{8} -8.36845 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +3.37171i q^{3} +1.00000 q^{4} +0.549551 q^{5} -3.37171i q^{6} -2.61555i q^{7} -1.00000 q^{8} -8.36845 q^{9} -0.549551 q^{10} +(-2.53057 + 2.14388i) q^{11} +3.37171i q^{12} -3.98957 q^{13} +2.61555i q^{14} +1.85293i q^{15} +1.00000 q^{16} +5.05039i q^{17} +8.36845 q^{18} +(-4.14844 - 1.33807i) q^{19} +0.549551 q^{20} +8.81890 q^{21} +(2.53057 - 2.14388i) q^{22} +3.67046 q^{23} -3.37171i q^{24} -4.69799 q^{25} +3.98957 q^{26} -18.1009i q^{27} -2.61555i q^{28} -4.22001 q^{29} -1.85293i q^{30} +4.52906i q^{31} -1.00000 q^{32} +(-7.22856 - 8.53234i) q^{33} -5.05039i q^{34} -1.43738i q^{35} -8.36845 q^{36} +8.93697i q^{37} +(4.14844 + 1.33807i) q^{38} -13.4517i q^{39} -0.549551 q^{40} +10.7591 q^{41} -8.81890 q^{42} -2.26059i q^{43} +(-2.53057 + 2.14388i) q^{44} -4.59889 q^{45} -3.67046 q^{46} +7.34091 q^{47} +3.37171i q^{48} +0.158876 q^{49} +4.69799 q^{50} -17.0285 q^{51} -3.98957 q^{52} -2.63638i q^{53} +18.1009i q^{54} +(-1.39068 + 1.17817i) q^{55} +2.61555i q^{56} +(4.51158 - 13.9874i) q^{57} +4.22001 q^{58} +5.14971i q^{59} +1.85293i q^{60} +11.7124i q^{61} -4.52906i q^{62} +21.8881i q^{63} +1.00000 q^{64} -2.19247 q^{65} +(7.22856 + 8.53234i) q^{66} -9.09686i q^{67} +5.05039i q^{68} +12.3757i q^{69} +1.43738i q^{70} -2.28930i q^{71} +8.36845 q^{72} +4.68896i q^{73} -8.93697i q^{74} -15.8403i q^{75} +(-4.14844 - 1.33807i) q^{76} +(5.60744 + 6.61883i) q^{77} +13.4517i q^{78} -10.5767 q^{79} +0.549551 q^{80} +35.9256 q^{81} -10.7591 q^{82} +0.876294i q^{83} +8.81890 q^{84} +2.77545i q^{85} +2.26059i q^{86} -14.2287i q^{87} +(2.53057 - 2.14388i) q^{88} +11.2646i q^{89} +4.59889 q^{90} +10.4349i q^{91} +3.67046 q^{92} -15.2707 q^{93} -7.34091 q^{94} +(-2.27978 - 0.735337i) q^{95} -3.37171i q^{96} -2.77545i q^{97} -0.158876 q^{98} +(21.1769 - 17.9410i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 8 q^{4} + 2 q^{5} - 8 q^{8} - 14 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 + 8 * q^4 + 2 * q^5 - 8 * q^8 - 14 * q^9	$ 8 q - 8 q^{2} + 8 q^{4} + 2 q^{5} - 8 q^{8} - 14 q^{9} - 2 q^{10} - 6 q^{11} + 10 q^{13} + 8 q^{16} + 14 q^{18} + 2 q^{20} + 20 q^{21} + 6 q^{22} + 12 q^{23} - 2 q^{25} - 10 q^{26} - 14 q^{29} - 8 q^{32} - 8 q^{33} - 14 q^{36} - 2 q^{40} + 22 q^{41} - 20 q^{42} - 6 q^{44} - 6 q^{45} - 12 q^{46} + 24 q^{47} + 10 q^{49} + 2 q^{50} - 24 q^{51} + 10 q^{52} + 10 q^{57} + 14 q^{58} + 8 q^{64} - 16 q^{65} + 8 q^{66} + 14 q^{72} - 16 q^{77} - 12 q^{79} + 2 q^{80} + 36 q^{81} - 22 q^{82} + 20 q^{84} + 6 q^{88} + 6 q^{90} + 12 q^{92} - 32 q^{93} - 24 q^{94} - 12 q^{95} - 10 q^{98} + 24 q^{99}+O(q^{100}) $ 8 * q - 8 * q^2 + 8 * q^4 + 2 * q^5 - 8 * q^8 - 14 * q^9 - 2 * q^10 - 6 * q^11 + 10 * q^13 + 8 * q^16 + 14 * q^18 + 2 * q^20 + 20 * q^21 + 6 * q^22 + 12 * q^23 - 2 * q^25 - 10 * q^26 - 14 * q^29 - 8 * q^32 - 8 * q^33 - 14 * q^36 - 2 * q^40 + 22 * q^41 - 20 * q^42 - 6 * q^44 - 6 * q^45 - 12 * q^46 + 24 * q^47 + 10 * q^49 + 2 * q^50 - 24 * q^51 + 10 * q^52 + 10 * q^57 + 14 * q^58 + 8 * q^64 - 16 * q^65 + 8 * q^66 + 14 * q^72 - 16 * q^77 - 12 * q^79 + 2 * q^80 + 36 * q^81 - 22 * q^82 + 20 * q^84 + 6 * q^88 + 6 * q^90 + 12 * q^92 - 32 * q^93 - 24 * q^94 - 12 * q^95 - 10 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$			3.37171i			1.94666i	0.229410	+	0.973330i	$0.426320\pi$
$3$			3.37171i			1.94666i	−0.229410	+	0.973330i	$0.573680\pi$
$4$	1.00000			0.500000
$5$	0.549551			0.245767			0.122883	−	0.992421i	$-0.460786\pi$
$5$	0.549551			0.245767			0.122883	+	0.992421i	$0.460786\pi$
$6$		−	3.37171i		−	1.37650i
$7$		−	2.61555i		−	0.988587i	−0.869295	−	0.494293i	$-0.835427\pi$
$7$		−	2.61555i		−	0.988587i	0.869295	−	0.494293i	$-0.164573\pi$
$8$	−1.00000			−0.353553
$9$	−8.36845			−2.78948
$10$	−0.549551			−0.173783
$11$	−2.53057	+	2.14388i	−0.762994	+	0.646405i
$11$	−2.53057	+	2.14388i	−0.762994	+	0.646405i
$12$			3.37171i			0.973330i
$13$	−3.98957			−1.10651			−0.553253	−	0.833013i	$-0.686614\pi$
$13$	−3.98957			−1.10651			−0.553253	+	0.833013i	$0.686614\pi$
$14$			2.61555i			0.699036i
$15$			1.85293i			0.478424i
$16$	1.00000			0.250000
$17$			5.05039i			1.22490i	0.790509	+	0.612450i	$0.209816\pi$
$17$			5.05039i			1.22490i	−0.790509	+	0.612450i	$0.790184\pi$
$18$	8.36845			1.97246
$19$	−4.14844	−	1.33807i	−0.951718	−	0.306974i
$19$	−4.14844	−	1.33807i	−0.951718	−	0.306974i
$20$	0.549551			0.122883
$21$	8.81890			1.92444
$22$	2.53057	−	2.14388i	0.539518	−	0.457077i
$23$	3.67046			0.765343			0.382672	−	0.923884i	$-0.375004\pi$
$23$	3.67046			0.765343			0.382672	+	0.923884i	$0.375004\pi$
$24$		−	3.37171i		−	0.688248i
$25$	−4.69799			−0.939599
$26$	3.98957			0.782418
$27$		−	18.1009i		−	3.48351i
$28$		−	2.61555i		−	0.494293i
$29$	−4.22001			−0.783636			−0.391818	−	0.920043i	$-0.628154\pi$
$29$	−4.22001			−0.783636			−0.391818	+	0.920043i	$0.628154\pi$
$30$		−	1.85293i		−	0.338297i
$31$			4.52906i			0.813444i	0.913552	+	0.406722i	$0.133328\pi$
$31$			4.52906i			0.813444i	−0.913552	+	0.406722i	$0.866672\pi$
$32$	−1.00000			−0.176777
$33$	−7.22856	−	8.53234i	−1.25833	−	1.48529i
$34$		−	5.05039i		−	0.866135i
$35$		−	1.43738i		−	0.242962i
$36$	−8.36845			−1.39474
$37$			8.93697i			1.46923i	0.678485	+	0.734614i	$0.262637\pi$
$37$			8.93697i			1.46923i	−0.678485	+	0.734614i	$0.737363\pi$
$38$	4.14844	+	1.33807i	0.672966	+	0.217063i
$39$		−	13.4517i		−	2.15399i
$40$	−0.549551			−0.0868917
$41$	10.7591			1.68029			0.840147	−	0.542359i	$-0.182469\pi$
$41$	10.7591			1.68029			0.840147	+	0.542359i	$0.182469\pi$
$42$	−8.81890			−1.36079
$43$		−	2.26059i		−	0.344736i	−0.985033	−	0.172368i	$-0.944858\pi$
$43$		−	2.26059i		−	0.344736i	0.985033	−	0.172368i	$-0.0551419\pi$
$44$	−2.53057	+	2.14388i	−0.381497	+	0.323203i
$45$	−4.59889			−0.685562
$46$	−3.67046			−0.541179
$47$	7.34091			1.07078			0.535391	−	0.844604i	$-0.320164\pi$
$47$	7.34091			1.07078			0.535391	+	0.844604i	$0.320164\pi$
$48$			3.37171i			0.486665i
$49$	0.158876			0.0226965
$50$	4.69799			0.664397
$51$	−17.0285			−2.38446
$52$	−3.98957			−0.553253
$53$		−	2.63638i		−	0.362134i	−0.983471	−	0.181067i	$-0.942045\pi$
$53$		−	2.63638i		−	0.362134i	0.983471	−	0.181067i	$-0.0579551\pi$
$54$			18.1009i			2.46322i
$55$	−1.39068	+	1.17817i	−0.187519	+	0.158865i
$56$			2.61555i			0.349518i
$57$	4.51158	−	13.9874i	0.597573	−	1.85267i
$58$	4.22001			0.554114
$59$			5.14971i			0.670434i	0.942141	+	0.335217i	$0.108810\pi$
$59$			5.14971i			0.670434i	−0.942141	+	0.335217i	$0.891190\pi$
$60$			1.85293i			0.239212i
$61$			11.7124i			1.49962i	0.661653	+	0.749811i	$0.269855\pi$
$61$			11.7124i			1.49962i	−0.661653	+	0.749811i	$0.730145\pi$
$62$		−	4.52906i		−	0.575192i
$63$			21.8881i			2.75765i
$64$	1.00000			0.125000
$65$	−2.19247			−0.271943
$66$	7.22856	+	8.53234i	0.889774	+	1.05026i
$67$		−	9.09686i		−	1.11136i	−0.831397	−	0.555679i	$-0.812458\pi$
$67$		−	9.09686i		−	1.11136i	0.831397	−	0.555679i	$-0.187542\pi$
$68$			5.05039i			0.612450i
$69$			12.3757i			1.48986i
$70$			1.43738i			0.171800i
$71$		−	2.28930i		−	0.271690i	−0.990730	−	0.135845i	$-0.956625\pi$
$71$		−	2.28930i		−	0.271690i	0.990730	−	0.135845i	$-0.0433749\pi$
$72$	8.36845			0.986231
$73$			4.68896i			0.548801i	0.961615	+	0.274401i	$0.0884794\pi$
$73$			4.68896i			0.548801i	−0.961615	+	0.274401i	$0.911521\pi$
$74$		−	8.93697i		−	1.03890i
$75$		−	15.8403i		−	1.82908i
$76$	−4.14844	−	1.33807i	−0.475859	−	0.153487i
$77$	5.60744	+	6.61883i	0.639027	+	0.754286i
$78$			13.4517i			1.52310i
$79$	−10.5767			−1.18997			−0.594984	−	0.803738i	$-0.702842\pi$
$79$	−10.5767			−1.18997			−0.594984	+	0.803738i	$0.702842\pi$
$80$	0.549551			0.0614417
$81$	35.9256			3.99173
$82$	−10.7591			−1.18815
$83$			0.876294i			0.0961858i	0.998843	+	0.0480929i	$0.0153144\pi$
$83$			0.876294i			0.0961858i	−0.998843	+	0.0480929i	$0.984686\pi$
$84$	8.81890			0.962221
$85$			2.77545i			0.301040i
$86$			2.26059i			0.243765i
$87$		−	14.2287i		−	1.52547i
$88$	2.53057	−	2.14388i	0.269759	−	0.228539i
$89$			11.2646i			1.19405i	0.802224	+	0.597023i	$0.203650\pi$
$89$			11.2646i			1.19405i	−0.802224	+	0.597023i	$0.796350\pi$
$90$	4.59889			0.484766
$91$			10.4349i			1.09388i
$92$	3.67046			0.382672
$93$	−15.2707			−1.58350
$94$	−7.34091			−0.757157
$95$	−2.27978	−	0.735337i	−0.233901	−	0.0754440i
$96$		−	3.37171i		−	0.344124i
$97$		−	2.77545i		−	0.281804i	−0.990024	−	0.140902i	$-0.955000\pi$
$97$		−	2.77545i		−	0.281804i	0.990024	−	0.140902i	$-0.0450003\pi$
$98$	−0.158876			−0.0160489
$99$	21.1769	−	17.9410i	2.12836	−	1.80314i
$100$	−4.69799			−0.469799
$101$			11.2646i			1.12087i	0.828198	+	0.560435i	$0.189366\pi$
$101$			11.2646i			1.12087i	−0.828198	+	0.560435i	$0.810634\pi$
$102$	17.0285			1.68607
$103$		−	5.86713i		−	0.578106i	−0.957313	−	0.289053i	$-0.906660\pi$
$103$		−	5.86713i		−	0.578106i	0.957313	−	0.289053i	$-0.0933403\pi$
$104$	3.98957			0.391209
$105$	4.84644			0.472964
$106$			2.63638i			0.256068i
$107$	−8.14844			−0.787740			−0.393870	−	0.919166i	$-0.628864\pi$
$107$	−8.14844			−0.787740			−0.393870	+	0.919166i	$0.628864\pi$
$108$		−	18.1009i		−	1.74176i
$109$	7.10441			0.680479			0.340240	−	0.940339i	$-0.389492\pi$
$109$	7.10441			0.680479			0.340240	+	0.940339i	$0.389492\pi$
$110$	1.39068	−	1.17817i	0.132596	−	0.112334i
$111$	−30.1329			−2.86009
$112$		−	2.61555i		−	0.247147i
$113$		−	5.80008i		−	0.545626i	−0.962067	−	0.272813i	$-0.912046\pi$
$113$		−	5.80008i		−	0.545626i	0.962067	−	0.272813i	$-0.0879540\pi$
$114$	−4.51158	+	13.9874i	−0.422548	+	1.31004i
$115$	2.01710			0.188096
$116$	−4.22001			−0.391818
$117$	33.3865			3.08658
$118$		−	5.14971i		−	0.474069i
$119$	13.2096			1.21092
$120$		−	1.85293i		−	0.169148i
$121$	1.80753	−	10.8505i	0.164321	−	0.986407i
$122$		−	11.7124i		−	1.06039i
$123$			36.2767i			3.27096i
$124$			4.52906i			0.406722i
$125$	−5.32954			−0.476689
$126$		−	21.8881i		−	1.94995i
$127$	12.3785			1.09841			0.549205	−	0.835687i	$-0.314930\pi$
$127$	12.3785			1.09841			0.549205	+	0.835687i	$0.314930\pi$
$128$	−1.00000			−0.0883883
$129$	7.62205			0.671084
$130$	2.19247			0.192292
$131$			6.73554i			0.588487i	0.955731	+	0.294243i	$0.0950676\pi$
$131$			6.73554i			0.588487i	−0.955731	+	0.294243i	$0.904932\pi$
$132$	−7.22856	−	8.53234i	−0.629165	−	0.742645i
$133$	−3.49979	+	10.8505i	−0.303470	+	0.940856i
$134$			9.09686i			0.785849i
$135$		−	9.94736i		−	0.856132i
$136$		−	5.05039i		−	0.433068i
$137$	−2.29021			−0.195666			−0.0978331	−	0.995203i	$-0.531191\pi$
$137$	−2.29021			−0.195666			−0.0978331	+	0.995203i	$0.531191\pi$
$138$		−	12.3757i		−	1.05349i
$139$		−	3.06983i		−	0.260380i	−0.991489	−	0.130190i	$-0.958441\pi$
$139$		−	3.06983i		−	0.260380i	0.991489	−	0.130190i	$-0.0415587\pi$
$140$		−	1.43738i		−	0.121481i
$141$			24.7515i			2.08445i
$142$			2.28930i			0.192114i
$143$	10.0959	−	8.55317i	0.844258	−	0.715252i
$144$	−8.36845			−0.697371
$145$	−2.31911			−0.192592
$146$		−	4.68896i		−	0.388061i
$147$			0.535683i			0.0441824i
$148$			8.93697i			0.734614i
$149$			21.4518i			1.75740i	0.477377	+	0.878699i	$0.341588\pi$
$149$			21.4518i			1.75740i	−0.477377	+	0.878699i	$0.658412\pi$
$150$			15.8403i			1.29335i
$151$	7.23575			0.588837			0.294419	−	0.955677i	$-0.404874\pi$
$151$	7.23575			0.588837			0.294419	+	0.955677i	$0.404874\pi$
$152$	4.14844	+	1.33807i	0.336483	+	0.108532i
$153$		−	42.2640i		−	3.41684i
$154$	−5.60744	−	6.61883i	−0.451861	−	0.533361i
$155$			2.48895i			0.199917i
$156$		−	13.4517i		−	1.07700i
$157$	−16.7849			−1.33958			−0.669790	−	0.742551i	$-0.733616\pi$
$157$	−16.7849			−1.33958			−0.669790	+	0.742551i	$0.733616\pi$
$158$	10.5767			0.841434
$159$	8.88911			0.704952
$160$	−0.549551			−0.0434458
$161$		−	9.60028i		−	0.756608i
$162$	−35.9256			−2.82258
$163$	−17.6549			−1.38284			−0.691419	−	0.722454i	$-0.743014\pi$
$163$	−17.6549			−1.38284			−0.691419	+	0.722454i	$0.743014\pi$
$164$	10.7591			0.840147
$165$	−3.97246	−	4.68896i	−0.309256	−	0.365035i
$166$		−	0.876294i		−	0.0680136i
$167$	8.10516			0.627196			0.313598	−	0.949556i	$-0.398466\pi$
$167$	8.10516			0.627196			0.313598	+	0.949556i	$0.398466\pi$
$168$	−8.81890			−0.680393
$169$	2.91664			0.224357
$170$		−	2.77545i		−	0.212867i
$171$	34.7160	+	11.1976i	2.65480	+	0.856298i
$172$		−	2.26059i		−	0.172368i
$173$	−7.70936			−0.586132			−0.293066	−	0.956092i	$-0.594676\pi$
$173$	−7.70936			−0.586132			−0.293066	+	0.956092i	$0.594676\pi$
$174$			14.2287i			1.07867i
$175$			12.2879i			0.928875i
$176$	−2.53057	+	2.14388i	−0.190749	+	0.161601i
$177$	−17.3633			−1.30511
$178$		−	11.2646i		−	0.844318i
$179$			7.66595i			0.572980i	0.958083	+	0.286490i	$0.0924885\pi$
$179$			7.66595i			0.572980i	−0.958083	+	0.286490i	$0.907512\pi$
$180$	−4.59889			−0.342781
$181$		−	0.440951i		−	0.0327757i	−0.999866	−	0.0163878i	$-0.994783\pi$
$181$		−	0.440951i		−	0.0327757i	0.999866	−	0.0163878i	$-0.00521664\pi$
$182$		−	10.4349i		−	0.773488i
$183$	−39.4909			−2.91925
$184$	−3.67046			−0.270590
$185$			4.91132i			0.361087i
$186$	15.2707			1.11970
$187$	−10.8275	−	12.7804i	−0.791782	−	0.934592i
$188$	7.34091			0.535391
$189$	−47.3438			−3.44376
$190$	2.27978	+	0.735337i	0.165393	+	0.0533469i
$191$	0.305959			0.0221384			0.0110692	−	0.999939i	$-0.496476\pi$
$191$	0.305959			0.0221384			0.0110692	+	0.999939i	$0.496476\pi$
$192$			3.37171i			0.243332i
$193$	−17.8024			−1.28145			−0.640723	−	0.767772i	$-0.721365\pi$
$193$	−17.8024			−1.28145			−0.640723	+	0.767772i	$0.721365\pi$
$194$			2.77545i			0.199266i
$195$		−	7.39238i		−	0.529380i
$196$	0.158876			0.0113483
$197$		−	13.4869i		−	0.960898i	−0.877023	−	0.480449i	$-0.840474\pi$
$197$		−	13.4869i		−	0.960898i	0.877023	−	0.480449i	$-0.159526\pi$
$198$	−21.1769	+	17.9410i	−1.50498	+	1.27501i
$199$	−6.72511			−0.476730			−0.238365	−	0.971176i	$-0.576612\pi$
$199$	−6.72511			−0.476730			−0.238365	+	0.971176i	$0.576612\pi$
$200$	4.69799			0.332198
$201$	30.6720			2.16344
$202$		−	11.2646i		−	0.792575i
$203$			11.0377i			0.774692i
$204$	−17.0285			−1.19223
$205$	5.91269			0.412960
$206$			5.86713i			0.408782i
$207$	−30.7160			−2.13491
$208$	−3.98957			−0.276627
$209$	13.3666	−	5.50771i	0.924585	−	0.380976i
$210$	−4.84644			−0.334436
$211$	14.0080			0.964352			0.482176	−	0.876074i	$-0.339846\pi$
$211$	14.0080			0.964352			0.482176	+	0.876074i	$0.339846\pi$
$212$		−	2.63638i		−	0.181067i
$213$	7.71886			0.528888
$214$	8.14844			0.557016
$215$		−	1.24231i		−	0.0847247i
$216$			18.1009i			1.23161i
$217$	11.8460			0.804160
$218$	−7.10441			−0.481172
$219$	−15.8098			−1.06833
$220$	−1.39068	+	1.17817i	−0.0937593	+	0.0794324i
$221$		−	20.1489i		−	1.35536i
$222$	30.1329			2.02239
$223$		−	4.40001i		−	0.294647i	−0.989088	−	0.147323i	$-0.952934\pi$
$223$		−	4.40001i		−	0.294647i	0.989088	−	0.147323i	$-0.0470658\pi$
$224$			2.61555i			0.174759i
$225$	39.3149			2.62100
$226$			5.80008i			0.385816i
$227$	2.32306			0.154187			0.0770936	−	0.997024i	$-0.475436\pi$
$227$	2.32306			0.154187			0.0770936	+	0.997024i	$0.475436\pi$
$228$	4.51158	−	13.9874i	0.298787	−	0.926335i
$229$	11.6600			0.770516			0.385258	−	0.922809i	$-0.374112\pi$
$229$	11.6600			0.770516			0.385258	+	0.922809i	$0.374112\pi$
$230$	−2.01710			−0.133004
$231$	−22.3168	+	18.9067i	−1.46834	+	1.24397i
$232$	4.22001			0.277057
$233$			7.57452i			0.496223i	0.968731	+	0.248112i	$0.0798100\pi$
$233$			7.57452i			0.496223i	−0.968731	+	0.248112i	$0.920190\pi$
$234$	−33.3865			−2.18254
$235$	4.03421			0.263163
$236$			5.14971i			0.335217i
$237$		−	35.6615i		−	2.31646i
$238$	−13.2096			−0.856250
$239$			6.81545i			0.440855i	0.975403	+	0.220427i	$0.0707452\pi$
$239$			6.81545i			0.440855i	−0.975403	+	0.220427i	$0.929255\pi$
$240$			1.85293i			0.119606i
$241$	−14.8529			−0.956760			−0.478380	−	0.878153i	$-0.658776\pi$
$241$	−14.8529			−0.956760			−0.478380	+	0.878153i	$0.658776\pi$
$242$	−1.80753	+	10.8505i	−0.116192	+	0.697495i
$243$			66.8282i			4.28703i
$244$			11.7124i			0.749811i
$245$	0.0873103			0.00557805
$246$		−	36.2767i		−	2.31292i
$247$	16.5505	+	5.33831i	1.05308	+	0.339669i
$248$		−	4.52906i		−	0.287596i
$249$	−2.95461			−0.187241
$250$	5.32954			0.337070
$251$	−15.7137			−0.991842			−0.495921	−	0.868368i	$-0.665170\pi$
$251$	−15.7137			−0.991842			−0.495921	+	0.868368i	$0.665170\pi$
$252$			21.8881i			1.37882i
$253$	−9.28833	+	7.86903i	−0.583952	+	0.494722i
$254$	−12.3785			−0.776694
$255$	−9.35802			−0.586022
$256$	1.00000			0.0625000
$257$		−	15.1780i		−	0.946778i	−0.880854	−	0.473389i	$-0.843031\pi$
$257$		−	15.1780i		−	0.946778i	0.880854	−	0.473389i	$-0.156969\pi$
$258$	−7.62205			−0.474528
$259$	23.3751			1.45246
$260$	−2.19247			−0.135971
$261$	35.3149			2.18594
$262$		−	6.73554i		−	0.416123i
$263$			17.3014i			1.06685i	0.845847	+	0.533425i	$0.179095\pi$
$263$			17.3014i			1.06685i	−0.845847	+	0.533425i	$0.820905\pi$
$264$	7.22856	+	8.53234i	0.444887	+	0.525129i
$265$		−	1.44882i		−	0.0890005i
$266$	3.49979	−	10.8505i	0.214586	−	0.665285i
$267$	−37.9810			−2.32440
$268$		−	9.09686i		−	0.555679i
$269$		−	2.68907i		−	0.163955i	−0.996634	−	0.0819777i	$-0.973876\pi$
$269$		−	2.68907i		−	0.163955i	0.996634	−	0.0819777i	$-0.0261236\pi$
$270$			9.94736i			0.605377i
$271$		−	14.9386i		−	0.907455i	−0.891141	−	0.453727i	$-0.850094\pi$
$271$		−	14.9386i		−	0.907455i	0.891141	−	0.453727i	$-0.149906\pi$
$272$			5.05039i			0.306225i
$273$	−35.1836			−2.12941
$274$	2.29021			0.138357
$275$	11.8886	−	10.0719i	0.716909	−	0.607361i
$276$			12.3757i			0.744931i
$277$		−	10.7978i		−	0.648776i	−0.945924	−	0.324388i	$-0.894842\pi$
$277$		−	10.7978i		−	0.648776i	0.945924	−	0.324388i	$-0.105158\pi$
$278$			3.06983i			0.184116i
$279$		−	37.9013i		−	2.26909i
$280$			1.43738i			0.0858999i
$281$	−6.80575			−0.405997			−0.202998	−	0.979179i	$-0.565069\pi$
$281$	−6.80575			−0.405997			−0.202998	+	0.979179i	$0.565069\pi$
$282$		−	24.7515i		−	1.47393i
$283$		−	32.3915i		−	1.92548i	−0.270434	−	0.962738i	$-0.587167\pi$
$283$		−	32.3915i		−	1.92548i	0.270434	−	0.962738i	$-0.412833\pi$
$284$		−	2.28930i		−	0.135845i
$285$	2.47934	−	7.68677i	0.146864	−	0.455325i
$286$	−10.0959	+	8.55317i	−0.596981	+	0.505759i
$287$		−	28.1411i		−	1.66112i
$288$	8.36845			0.493116
$289$	−8.50646			−0.500380
$290$	2.31911			0.136183
$291$	9.35802			0.548577
$292$			4.68896i			0.274401i
$293$	27.9451			1.63257			0.816286	−	0.577649i	$-0.196030\pi$
$293$	27.9451			1.63257			0.816286	+	0.577649i	$0.196030\pi$
$294$		−	0.535683i		−	0.0312417i
$295$			2.83003i			0.164770i
$296$		−	8.93697i		−	0.519451i
$297$	38.8062	+	45.8055i	2.25176	+	2.65790i
$298$		−	21.4518i		−	1.24267i
$299$	−14.6435			−0.846857
$300$		−	15.8403i		−	0.914539i
$301$	−5.91269			−0.340802
$302$	−7.23575			−0.416371
$303$	−37.9810			−2.18195
$304$	−4.14844	−	1.33807i	−0.237929	−	0.0767435i
$305$			6.43657i			0.368557i
$306$			42.2640i			2.41607i
$307$	8.48362			0.484186			0.242093	−	0.970253i	$-0.422166\pi$
$307$	8.48362			0.484186			0.242093	+	0.970253i	$0.422166\pi$
$308$	5.60744	+	6.61883i	0.319514	+	0.377143i
$309$	19.7823			1.12538
$310$		−	2.48895i		−	0.141363i
$311$	10.6492			0.603859			0.301929	−	0.953330i	$-0.402369\pi$
$311$	10.6492			0.603859			0.301929	+	0.953330i	$0.402369\pi$
$312$			13.4517i			0.761551i
$313$	24.2599			1.37125			0.685624	−	0.727956i	$-0.259529\pi$
$313$	24.2599			1.37125			0.685624	+	0.727956i	$0.259529\pi$
$314$	16.7849			0.947226
$315$			12.0286i			0.677738i
$316$	−10.5767			−0.594984
$317$			6.10196i			0.342720i	0.985208	+	0.171360i	$0.0548162\pi$
$317$			6.10196i			0.342720i	−0.985208	+	0.171360i	$0.945184\pi$
$318$	−8.88911			−0.498476
$319$	10.6790	−	9.04720i	0.597910	−	0.506546i
$320$	0.549551			0.0307208
$321$		−	27.4742i		−	1.53346i
$322$			9.60028i			0.535003i
$323$	6.75777	−	20.9513i	0.376012	−	1.16576i
$324$	35.9256			1.99587
$325$	18.7430			1.03967
$326$	17.6549			0.977815
$327$			23.9540i			1.32466i
$328$	−10.7591			−0.594073
$329$		−	19.2006i		−	1.05856i
$330$	3.97246	+	4.68896i	0.218677	+	0.258119i
$331$		−	13.5012i		−	0.742094i	−0.928614	−	0.371047i	$-0.878999\pi$
$331$		−	13.5012i		−	0.742094i	0.928614	−	0.371047i	$-0.121001\pi$
$332$			0.876294i			0.0480929i
$333$		−	74.7886i		−	4.09839i
$334$	−8.10516			−0.443495
$335$		−	4.99919i		−	0.273135i
$336$	8.81890			0.481110
$337$	11.2371			0.612124			0.306062	−	0.952012i	$-0.400988\pi$
$337$	11.2371			0.612124			0.306062	+	0.952012i	$0.400988\pi$
$338$	−2.91664			−0.158644
$339$	19.5562			1.06215
$340$			2.77545i			0.150520i
$341$	−9.70979	−	11.4611i	−0.525814	−	0.620653i
$342$	−34.7160	−	11.1976i	−1.87723	−	0.605494i
$343$		−	18.7244i		−	1.01102i
$344$			2.26059i			0.121883i
$345$			6.80109i			0.366159i
$346$	7.70936			0.414458
$347$			5.20240i			0.279279i	0.990202	+	0.139640i	$0.0445944\pi$
$347$			5.20240i			0.279279i	−0.990202	+	0.139640i	$0.955406\pi$
$348$		−	14.2287i		−	0.762736i
$349$			4.91132i			0.262897i	0.991323	+	0.131448i	$0.0419628\pi$
$349$			4.91132i			0.262897i	−0.991323	+	0.131448i	$0.958037\pi$
$350$		−	12.2879i		−	0.656814i
$351$			72.2146i			3.85453i
$352$	2.53057	−	2.14388i	0.134880	−	0.114269i
$353$	−8.82463			−0.469688			−0.234844	−	0.972033i	$-0.575458\pi$
$353$	−8.82463			−0.469688			−0.234844	+	0.972033i	$0.575458\pi$
$354$	17.3633			0.922851
$355$		−	1.25809i		−	0.0667723i
$356$			11.2646i			0.597023i
$357$			44.5389i			2.35725i
$358$		−	7.66595i		−	0.405158i
$359$			13.2564i			0.699644i	0.936816	+	0.349822i	$0.113758\pi$
$359$			13.2564i			0.699644i	−0.936816	+	0.349822i	$0.886242\pi$
$360$	4.59889			0.242383
$361$	15.4191	+	11.1018i	0.811534	+	0.584305i
$362$			0.440951i			0.0231759i
$363$	36.5847	+	6.09447i	1.92020	+	0.319877i
$364$			10.4349i			0.546939i
$365$			2.57682i			0.134877i
$366$	39.4909			2.06422
$367$	21.5733			1.12612			0.563059	−	0.826417i	$-0.309624\pi$
$367$	21.5733			1.12612			0.563059	+	0.826417i	$0.309624\pi$
$368$	3.67046			0.191336
$369$	−90.0372			−4.68715
$370$		−	4.91132i		−	0.255327i
$371$	−6.89559			−0.358001
$372$	−15.2707			−0.791749
$373$	5.97820			0.309539			0.154770	−	0.987951i	$-0.450536\pi$
$373$	5.97820			0.309539			0.154770	+	0.987951i	$0.450536\pi$
$374$	10.8275	+	12.7804i	0.559874	+	0.660856i
$375$		−	17.9697i		−	0.927951i
$376$	−7.34091			−0.378579
$377$	16.8360			0.867098
$378$	47.3438			2.43510
$379$			24.1506i			1.24053i	0.784391	+	0.620267i	$0.212976\pi$
$379$			24.1506i			1.24053i	−0.784391	+	0.620267i	$0.787024\pi$
$380$	−2.27978	−	0.735337i	−0.116950	−	0.0377220i
$381$			41.7366i			2.13823i
$382$	−0.305959			−0.0156542
$383$			12.1325i			0.619944i	0.950746	+	0.309972i	$0.100320\pi$
$383$			12.1325i			0.619944i	−0.950746	+	0.309972i	$0.899680\pi$
$384$		−	3.37171i		−	0.172062i
$385$	3.08158	+	3.63739i	0.157052	+	0.185378i
$386$	17.8024			0.906119
$387$			18.9176i			0.961636i
$388$		−	2.77545i		−	0.140902i
$389$	−30.9307			−1.56825			−0.784125	−	0.620603i	$-0.786888\pi$
$389$	−30.9307			−1.56825			−0.784125	+	0.620603i	$0.786888\pi$
$390$			7.39238i			0.374328i
$391$			18.5372i			0.937469i
$392$	−0.158876			−0.00802443
$393$	−22.7103			−1.14558
$394$			13.4869i			0.679458i
$395$	−5.81242			−0.292455
$396$	21.1769	−	17.9410i	1.06418	−	0.901568i
$397$	−34.3210			−1.72252			−0.861260	−	0.508164i	$-0.830324\pi$
$397$	−34.3210			−1.72252			−0.861260	+	0.508164i	$0.830324\pi$
$398$	6.72511			0.337099
$399$	−36.5847	−	11.8003i	−1.83153	−	0.590753i
$400$	−4.69799			−0.234900
$401$			28.5279i			1.42462i	0.701867	+	0.712308i	$0.252350\pi$
$401$			28.5279i			1.42462i	−0.701867	+	0.712308i	$0.747650\pi$
$402$	−30.6720			−1.52978
$403$		−	18.0690i		−	0.900081i
$404$			11.2646i			0.560435i
$405$	19.7430			0.981036
$406$		−	11.0377i		−	0.547790i
$407$	−19.1598	−	22.6156i	−0.949717	−	1.12101i
$408$	17.0285			0.843035
$409$	17.6593			0.873195			0.436598	−	0.899657i	$-0.356183\pi$
$409$	17.6593			0.873195			0.436598	+	0.899657i	$0.356183\pi$
$410$	−5.91269			−0.292007
$411$		−	7.72195i		−	0.380896i
$412$		−	5.86713i		−	0.289053i
$413$	13.4693			0.662783
$414$	30.7160			1.50961
$415$			0.481568i			0.0236393i
$416$	3.98957			0.195605
$417$	10.3506			0.506871
$418$	−13.3666	+	5.50771i	−0.653780	+	0.269391i
$419$	−14.3376			−0.700436			−0.350218	−	0.936668i	$-0.613893\pi$
$419$	−14.3376			−0.700436			−0.350218	+	0.936668i	$0.613893\pi$
$420$	4.84644			0.236482
$421$			17.9266i			0.873690i	0.899537	+	0.436845i	$0.143904\pi$
$421$			17.9266i			0.873690i	−0.899537	+	0.436845i	$0.856096\pi$
$422$	−14.0080			−0.681900
$423$	−61.4321			−2.98693
$424$			2.63638i			0.128034i
$425$		−	23.7267i		−	1.15091i
$426$	−7.71886			−0.373980
$427$	30.6345			1.48251
$428$	−8.14844			−0.393870
$429$	28.8388	+	34.0404i	1.39235	+	1.64348i
$430$			1.24231i			0.0599094i
$431$	−29.0015			−1.39695			−0.698475	−	0.715634i	$-0.746138\pi$
$431$	−29.0015			−1.39695			−0.698475	+	0.715634i	$0.746138\pi$
$432$		−	18.1009i		−	0.870879i
$433$		−	19.6742i		−	0.945483i	−0.881201	−	0.472742i	$-0.843264\pi$
$433$		−	19.6742i		−	0.945483i	0.881201	−	0.472742i	$-0.156736\pi$
$434$	−11.8460			−0.568627
$435$		−	7.81937i		−	0.374910i
$436$	7.10441			0.340240
$437$	−15.2267	−	4.91132i	−0.728391	−	0.234940i
$438$	15.8098			0.755423
$439$	21.3057			1.01686			0.508432	−	0.861102i	$-0.330225\pi$
$439$	21.3057			1.01686			0.508432	+	0.861102i	$0.330225\pi$
$440$	1.39068	−	1.17817i	0.0662979	−	0.0561672i
$441$	−1.32954			−0.0633116
$442$			20.1489i			0.958384i
$443$	38.0569			1.80814			0.904070	−	0.427384i	$-0.140565\pi$
$443$	38.0569			1.80814			0.904070	+	0.427384i	$0.140565\pi$
$444$	−30.1329			−1.43004
$445$			6.19047i			0.293457i
$446$			4.40001i			0.208347i
$447$	−72.3292			−3.42105
$448$		−	2.61555i		−	0.123573i
$449$			7.29947i			0.344483i	0.985055	+	0.172242i	$0.0551010\pi$
$449$			7.29947i			0.344483i	−0.985055	+	0.172242i	$0.944899\pi$
$450$	−39.3149			−1.85332
$451$	−27.2267	+	23.0663i	−1.28205	+	1.08615i
$452$		−	5.80008i		−	0.272813i
$453$			24.3969i			1.14627i
$454$	−2.32306			−0.109027
$455$			5.73453i			0.268839i
$456$	−4.51158	+	13.9874i	−0.211274	+	0.655018i
$457$			42.2044i			1.97424i	0.159986	+	0.987119i	$0.448855\pi$
$457$			42.2044i			1.97424i	−0.159986	+	0.987119i	$0.551145\pi$
$458$	−11.6600			−0.544837
$459$	91.4165			4.26696
$460$	2.01710			0.0940479
$461$			34.1868i			1.59224i	0.605140	+	0.796119i	$0.293117\pi$
$461$			34.1868i			1.59224i	−0.605140	+	0.796119i	$0.706883\pi$
$462$	22.3168	−	18.9067i	1.03827	−	0.879619i
$463$	23.9347			1.11234			0.556170	−	0.831069i	$-0.312271\pi$
$463$	23.9347			1.11234			0.556170	+	0.831069i	$0.312271\pi$
$464$	−4.22001			−0.195909
$465$	−8.39203			−0.389171
$466$		−	7.57452i		−	0.350883i
$467$	17.6443			0.816480			0.408240	−	0.912875i	$-0.366143\pi$
$467$	17.6443			0.816480			0.408240	+	0.912875i	$0.366143\pi$
$468$	33.3865			1.54329
$469$	−23.7933			−1.09867
$470$	−4.03421			−0.186084
$471$		−	56.5938i		−	2.60771i
$472$		−	5.14971i		−	0.237034i
$473$	4.84644	+	5.72057i	0.222839	+	0.263032i
$474$			35.6615i			1.63799i
$475$	19.4894	+	6.28623i	0.894233	+	0.288432i
$476$	13.2096			0.605460
$477$			22.0624i			1.01017i
$478$		−	6.81545i		−	0.311731i
$479$		−	32.9775i		−	1.50678i	−0.657575	−	0.753389i	$-0.728418\pi$
$479$		−	32.9775i		−	1.50678i	0.657575	−	0.753389i	$-0.271582\pi$
$480$		−	1.85293i		−	0.0845742i
$481$		−	35.6546i		−	1.62571i
$482$	14.8529			0.676532
$483$	32.3694			1.47286
$484$	1.80753	−	10.8505i	0.0821604	−	0.493203i
$485$		−	1.52525i		−	0.0692581i
$486$		−	66.8282i		−	3.03139i
$487$			38.0849i			1.72579i	0.505383	+	0.862895i	$0.331351\pi$
$487$			38.0849i			1.72579i	−0.505383	+	0.862895i	$0.668649\pi$
$488$		−	11.7124i		−	0.530196i
$489$		−	59.5273i		−	2.69192i
$490$	−0.0873103			−0.00394428
$491$		−	30.3390i		−	1.36918i	−0.728929	−	0.684589i	$-0.759982\pi$
$491$		−	30.3390i		−	1.36918i	0.728929	−	0.684589i	$-0.240018\pi$
$492$			36.2767i			1.63548i
$493$		−	21.3127i		−	0.959875i
$494$	−16.5505	−	5.33831i	−0.744642	−	0.240182i
$495$	11.6378	−	9.85949i	0.523080	−	0.443151i
$496$			4.52906i			0.203361i
$497$	−5.98779			−0.268589
$498$	2.95461			0.132399
$499$	−13.8596			−0.620440			−0.310220	−	0.950665i	$-0.600403\pi$
$499$	−13.8596			−0.620440			−0.310220	+	0.950665i	$0.600403\pi$
$500$	−5.32954			−0.238344
$501$			27.3283i			1.22094i
$502$	15.7137			0.701338
$503$		−	17.0503i		−	0.760237i	−0.924938	−	0.380118i	$-0.875883\pi$
$503$		−	17.0503i		−	0.760237i	0.924938	−	0.380118i	$-0.124117\pi$
$504$		−	21.8881i		−	0.974975i
$505$			6.19047i			0.275473i
$506$	9.28833	−	7.86903i	0.412917	−	0.349821i
$507$			9.83408i			0.436747i
$508$	12.3785			0.549205
$509$			12.6845i			0.562229i	0.959674	+	0.281115i	$0.0907041\pi$
$509$			12.6845i			0.562229i	−0.959674	+	0.281115i	$0.909296\pi$
$510$	9.35802			0.414380
$511$	12.2642			0.542537
$512$	−1.00000			−0.0441942
$513$	−24.2202	+	75.0904i	−1.06935	+	3.31532i
$514$			15.1780i			0.669473i
$515$		−	3.22429i		−	0.142079i
$516$	7.62205			0.335542
$517$	−18.5767	+	15.7381i	−0.817001	+	0.692159i
$518$	−23.3751			−1.02704
$519$		−	25.9938i		−	1.14100i
$520$	2.19247			0.0961462
$521$		−	37.5513i		−	1.64515i	−0.568656	−	0.822575i	$-0.692537\pi$
$521$		−	37.5513i		−	1.64515i	0.568656	−	0.822575i	$-0.307463\pi$
$522$	−35.3149			−1.54569
$523$	1.00489			0.0439408			0.0219704	−	0.999759i	$-0.493006\pi$
$523$	1.00489			0.0439408			0.0219704	+	0.999759i	$0.493006\pi$
$524$			6.73554i			0.294243i
$525$	−41.4311			−1.80820
$526$		−	17.3014i		−	0.754377i
$527$	−22.8736			−0.996388
$528$	−7.22856	−	8.53234i	−0.314583	−	0.371323i
$529$	−9.52775			−0.414250
$530$			1.44882i			0.0629329i
$531$		−	43.0951i		−	1.87017i
$532$	−3.49979	+	10.8505i	−0.151735	+	0.470428i
$533$	−42.9242			−1.85926
$534$	37.9810			1.64360
$535$	−4.47799			−0.193600
$536$			9.09686i			0.392925i
$537$	−25.8474			−1.11540
$538$			2.68907i			0.115934i
$539$	−0.402045	+	0.340611i	−0.0173173	+	0.0146712i
$540$		−	9.94736i		−	0.428066i
$541$		−	32.1921i		−	1.38405i	−0.721875	−	0.692024i	$-0.756719\pi$
$541$		−	32.1921i		−	1.38405i	0.721875	−	0.692024i	$-0.243281\pi$
$542$			14.9386i			0.641667i
$543$	1.48676			0.0638030
$544$		−	5.05039i		−	0.216534i
$545$	3.90424			0.167239
$546$	35.1836			1.50572
$547$	−7.40623			−0.316668			−0.158334	−	0.987386i	$-0.550612\pi$
$547$	−7.40623			−0.316668			−0.158334	+	0.987386i	$0.550612\pi$
$548$	−2.29021			−0.0978331
$549$		−	98.0148i		−	4.18317i
$550$	−11.8886	+	10.0719i	−0.506931	+	0.429469i
$551$	17.5065	+	5.64666i	0.745800	+	0.240556i
$552$		−	12.3757i		−	0.526746i
$553$			27.6638i			1.17639i
$554$			10.7978i			0.458754i
$555$	−16.5596			−0.702914
$556$		−	3.06983i		−	0.130190i
$557$			14.1333i			0.598847i	0.954120	+	0.299423i	$0.0967943\pi$
$557$			14.1333i			0.598847i	−0.954120	+	0.299423i	$0.903206\pi$
$558$			37.9013i			1.60449i
$559$			9.01877i			0.381453i
$560$		−	1.43738i		−	0.0607404i
$561$	43.0917	−	36.5071i	1.81933	−	1.54133i
$562$	6.80575			0.287083
$563$	36.0797			1.52058			0.760289	−	0.649585i	$-0.225057\pi$
$563$	36.0797			1.52058			0.760289	+	0.649585i	$0.225057\pi$
$564$			24.7515i			1.04222i
$565$		−	3.18744i		−	0.134097i
$566$			32.3915i			1.36152i
$567$		−	93.9654i		−	3.94618i
$568$			2.28930i			0.0960569i
$569$	5.05706			0.212003			0.106001	−	0.994366i	$-0.466195\pi$
$569$	5.05706			0.212003			0.106001	+	0.994366i	$0.466195\pi$
$570$	−2.47934	+	7.68677i	−0.103848	+	0.321963i
$571$			17.4759i			0.731344i	0.930744	+	0.365672i	$0.119161\pi$
$571$			17.4759i			0.731344i	−0.930744	+	0.365672i	$0.880839\pi$
$572$	10.0959	−	8.55317i	0.422129	−	0.357626i
$573$			1.03161i			0.0430960i
$574$			28.1411i			1.17459i
$575$	−17.2438			−0.719115
$576$	−8.36845			−0.348685
$577$	−34.5036			−1.43641			−0.718203	−	0.695834i	$-0.755035\pi$
$577$	−34.5036			−1.43641			−0.718203	+	0.695834i	$0.755035\pi$
$578$	8.50646			0.353822
$579$		−	60.0246i		−	2.49454i
$580$	−2.31911			−0.0962958
$581$	2.29200			0.0950880
$582$	−9.35802			−0.387902
$583$	5.65208	+	6.67153i	0.234085	+	0.276306i
$584$		−	4.68896i		−	0.194030i
$585$	18.3476			0.758579
$586$	−27.9451			−1.15440
$587$	−3.35154			−0.138333			−0.0691664	−	0.997605i	$-0.522034\pi$
$587$	−3.35154			−0.138333			−0.0691664	+	0.997605i	$0.522034\pi$
$588$			0.535683i			0.0220912i
$589$	6.06020	−	18.7886i	0.249706	−	0.774169i
$590$		−	2.83003i		−	0.116510i
$591$	45.4738			1.87054
$592$			8.93697i			0.367307i
$593$			14.0111i			0.575367i	0.957726	+	0.287683i	$0.0928851\pi$
$593$			14.0111i			0.575367i	−0.957726	+	0.287683i	$0.907115\pi$
$594$	−38.8062	−	45.8055i	−1.59224	−	1.87942i
$595$	7.25934			0.297604
$596$			21.4518i			0.878699i
$597$		−	22.6751i		−	0.928032i
$598$	14.6435			0.598819
$599$			15.1874i			0.620540i	0.950649	+	0.310270i	$0.100419\pi$
$599$			15.1874i			0.620540i	−0.950649	+	0.310270i	$0.899581\pi$
$600$			15.8403i			0.646677i
$601$	−39.7522			−1.62153			−0.810764	−	0.585374i	$-0.800948\pi$
$601$	−39.7522			−1.62153			−0.810764	+	0.585374i	$0.800948\pi$
$602$	5.91269			0.240983
$603$			76.1266i			3.10012i
$604$	7.23575			0.294419
$605$	0.993330	−	5.96289i	0.0403846	−	0.242426i
$606$	37.9810			1.54287
$607$	10.3196			0.418861			0.209430	−	0.977824i	$-0.432839\pi$
$607$	10.3196			0.418861			0.209430	+	0.977824i	$0.432839\pi$
$608$	4.14844	+	1.33807i	0.168242	+	0.0542658i
$609$	−37.2158			−1.50806
$610$		−	6.43657i		−	0.260609i
$611$	−29.2871			−1.18483
$612$		−	42.2640i		−	1.70842i
$613$			3.01777i			0.121887i	0.998141	+	0.0609434i	$0.0194109\pi$
$613$			3.01777i			0.121887i	−0.998141	+	0.0609434i	$0.980589\pi$
$614$	−8.48362			−0.342371
$615$			19.9359i			0.803893i
$616$	−5.60744	−	6.61883i	−0.225930	−	0.266680i
$617$	20.9072			0.841694			0.420847	−	0.907132i	$-0.361733\pi$
$617$	20.9072			0.841694			0.420847	+	0.907132i	$0.361733\pi$
$618$	−19.7823			−0.795760
$619$	−4.43082			−0.178090			−0.0890448	−	0.996028i	$-0.528381\pi$
$619$	−4.43082			−0.178090			−0.0890448	+	0.996028i	$0.528381\pi$
$620$			2.48895i			0.0999587i
$621$		−	66.4385i		−	2.66608i
$622$	−10.6492			−0.426993
$623$	29.4632			1.18042
$624$		−	13.4517i		−	0.538498i
$625$	20.5611			0.822444
$626$	−24.2599			−0.969619
$627$	18.5704	+	45.0682i	0.741631	+	1.79985i
$628$	−16.7849			−0.669790
$629$	−45.1352			−1.79966
$630$		−	12.0286i		−	0.479233i
$631$	39.6614			1.57889			0.789447	−	0.613818i	$-0.210367\pi$
$631$	39.6614			1.57889			0.789447	+	0.613818i	$0.210367\pi$
$632$	10.5767			0.420717
$633$			47.2311i			1.87727i
$634$		−	6.10196i		−	0.242340i
$635$	6.80260			0.269953
$636$	8.88911			0.352476
$637$	−0.633845			−0.0251139
$638$	−10.6790	+	9.04720i	−0.422786	+	0.358182i
$639$			19.1579i			0.757874i
$640$	−0.549551			−0.0217229
$641$			33.9734i			1.34187i	0.741516	+	0.670935i	$0.234107\pi$
$641$			33.9734i			1.34187i	−0.741516	+	0.670935i	$0.765893\pi$
$642$			27.4742i			1.08432i
$643$	2.27414			0.0896835			0.0448418	−	0.998994i	$-0.485722\pi$
$643$	2.27414			0.0896835			0.0448418	+	0.998994i	$0.485722\pi$
$644$		−	9.60028i		−	0.378304i
$645$	4.18871			0.164930
$646$	−6.75777	+	20.9513i	−0.265881	+	0.824316i
$647$	−44.2461			−1.73949			−0.869746	−	0.493499i	$-0.835718\pi$
$647$	−44.2461			−1.73949			−0.869746	+	0.493499i	$0.835718\pi$
$648$	−35.9256			−1.41129
$649$	−11.0404	−	13.0317i	−0.433372	−	0.511538i
$650$	−18.7430			−0.735159
$651$			39.9414i			1.56543i
$652$	−17.6549			−0.691419
$653$	31.5131			1.23320			0.616602	−	0.787275i	$-0.288509\pi$
$653$	31.5131			1.23320			0.616602	+	0.787275i	$0.288509\pi$
$654$		−	23.9540i		−	0.936677i
$655$			3.70152i			0.144630i
$656$	10.7591			0.420073
$657$		−	39.2393i		−	1.53087i
$658$			19.2006i			0.748516i
$659$	−12.0612			−0.469839			−0.234919	−	0.972015i	$-0.575483\pi$
$659$	−12.0612			−0.469839			−0.234919	+	0.972015i	$0.575483\pi$
$660$	−3.97246	−	4.68896i	−0.154628	−	0.182517i
$661$		−	21.7536i		−	0.846119i	−0.906102	−	0.423059i	$-0.860956\pi$
$661$		−	21.7536i		−	0.846119i	0.906102	−	0.423059i	$-0.139044\pi$
$662$			13.5012i			0.524739i
$663$	67.9362			2.63842
$664$		−	0.876294i		−	0.0340068i
$665$	−1.92331	+	5.96289i	−0.0745829	+	0.231231i
$666$			74.7886i			2.89800i
$667$	−15.4894			−0.599750
$668$	8.10516			0.313598
$669$	14.8356			0.573577
$670$			4.99919i			0.193136i
$671$	−25.1101	−	29.6390i	−0.969363	−	1.14420i
$672$	−8.81890			−0.340196
$673$	−0.138009			−0.00531986			−0.00265993	−	0.999996i	$-0.500847\pi$
$673$	−0.138009			−0.00531986			−0.00265993	+	0.999996i	$0.500847\pi$
$674$	−11.2371			−0.432837
$675$			85.0378i			3.27311i
$676$	2.91664			0.112179
$677$	26.2333			1.00823			0.504115	−	0.863637i	$-0.331819\pi$
$677$	26.2333			1.00823			0.504115	+	0.863637i	$0.331819\pi$
$678$	−19.5562			−0.751052
$679$	−7.25934			−0.278588
$680$		−	2.77545i		−	0.106434i
$681$			7.83270i			0.300150i
$682$	9.70979	+	11.4611i	0.371807	+	0.438868i
$683$		−	21.9562i		−	0.840131i	−0.907494	−	0.420066i	$-0.862007\pi$
$683$		−	21.9562i		−	0.840131i	0.907494	−	0.420066i	$-0.137993\pi$
$684$	34.7160	+	11.1976i	1.32740	+	0.428149i
$685$	−1.25859			−0.0480883
$686$			18.7244i			0.714902i
$687$			39.3143i			1.49993i
$688$		−	2.26059i		−	0.0861841i
$689$			10.5180i			0.400704i
$690$		−	6.80109i		−	0.258913i
$691$	18.1093			0.688910			0.344455	−	0.938803i	$-0.388064\pi$
$691$	18.1093			0.688910			0.344455	+	0.938803i	$0.388064\pi$
$692$	−7.70936			−0.293066
$693$	−46.9256	−	55.3894i	−1.78256	−	2.10407i
$694$		−	5.20240i		−	0.197480i
$695$		−	1.68703i		−	0.0639927i
$696$			14.2287i			0.539336i
$697$			54.3378i			2.05819i
$698$		−	4.91132i		−	0.185896i
$699$	−25.5391			−0.965978
$700$			12.2879i			0.464437i
$701$		−	11.1851i		−	0.422455i	−0.977437	−	0.211227i	$-0.932254\pi$
$701$		−	11.1851i		−	0.422455i	0.977437	−	0.211227i	$-0.0677461\pi$
$702$		−	72.2146i		−	2.72557i
$703$	11.9583	−	37.0745i	0.451015	−	1.39829i
$704$	−2.53057	+	2.14388i	−0.0953743	+	0.0808006i
$705$			13.6022i			0.512288i
$706$	8.82463			0.332119
$707$	29.4632			1.10808
$708$	−17.3633			−0.652554
$709$	46.8540			1.75964			0.879820	−	0.475307i	$-0.157663\pi$
$709$	46.8540			1.75964			0.879820	+	0.475307i	$0.157663\pi$
$710$			1.25809i			0.0472152i
$711$	88.5103			3.31940
$712$		−	11.2646i		−	0.422159i
$713$			16.6237i			0.622564i
$714$		−	44.5389i		−	1.66683i
$715$	5.54819	−	4.70040i	0.207491	−	0.175785i
$716$			7.66595i			0.286490i
$717$	−22.9797			−0.858194
$718$		−	13.2564i		−	0.494723i
$719$	−41.2438			−1.53813			−0.769067	−	0.639168i	$-0.779279\pi$
$719$	−41.2438			−1.53813			−0.769067	+	0.639168i	$0.779279\pi$
$720$	−4.59889			−0.171391
$721$	−15.3458			−0.571508
$722$	−15.4191	−	11.1018i	−0.573841	−	0.413166i
$723$		−	50.0798i		−	1.86249i
$724$		−	0.440951i		−	0.0163878i
$725$	19.8256			0.736303
$726$	−36.5847	−	6.09447i	−1.35779	−	0.226187i
$727$	18.5148			0.686675			0.343338	−	0.939212i	$-0.388442\pi$
$727$	18.5148			0.686675			0.343338	+	0.939212i	$0.388442\pi$
$728$		−	10.4349i		−	0.386744i
$729$	−117.549			−4.35366
$730$		−	2.57682i		−	0.0953725i
$731$	11.4169			0.422268
$732$	−39.4909			−1.45963
$733$			44.8982i			1.65835i	0.558987	+	0.829176i	$0.311190\pi$
$733$			44.8982i			1.65835i	−0.558987	+	0.829176i	$0.688810\pi$
$734$	−21.5733			−0.796286
$735$			0.294385i			0.0108586i
$736$	−3.67046			−0.135295
$737$	19.5026	+	23.0202i	0.718388	+	0.847960i
$738$	90.0372			3.31432
$739$		−	7.30885i		−	0.268860i	−0.990923	−	0.134430i	$-0.957080\pi$
$739$		−	7.30885i		−	0.268860i	0.990923	−	0.134430i	$-0.0429204\pi$
$740$			4.91132i			0.180544i
$741$	−17.9993	+	55.8035i	−0.661219	+	2.04999i
$742$	6.89559			0.253145
$743$	−39.0601			−1.43298			−0.716488	−	0.697600i	$-0.754251\pi$
$743$	−39.0601			−1.43298			−0.716488	+	0.697600i	$0.754251\pi$
$744$	15.2707			0.559851
$745$			11.7888i			0.431910i
$746$	−5.97820			−0.218877
$747$		−	7.33322i		−	0.268309i
$748$	−10.8275	−	12.7804i	−0.395891	−	0.467296i
$749$			21.3127i			0.778749i
$750$			17.9697i			0.656160i
$751$			29.3174i			1.06981i	0.844914	+	0.534903i	$0.179652\pi$
$751$			29.3174i			1.06981i	−0.844914	+	0.534903i	$0.820348\pi$
$752$	7.34091			0.267696
$753$		−	52.9822i		−	1.93078i
$754$	−16.8360			−0.613131
$755$	3.97642			0.144717
$756$	−47.3438			−1.72188
$757$	0.123922			0.00450401			0.00225201	−	0.999997i	$-0.499283\pi$
$757$	0.123922			0.00450401			0.00225201	+	0.999997i	$0.499283\pi$
$758$		−	24.1506i		−	0.877190i
$759$	−26.5321	−	31.3176i	−0.963055	−	1.13676i
$760$	2.27978	+	0.735337i	0.0826964	+	0.0266735i
$761$		−	39.6344i		−	1.43675i	−0.695657	−	0.718374i	$-0.744887\pi$
$761$		−	39.6344i		−	1.43675i	0.695657	−	0.718374i	$-0.255113\pi$
$762$		−	41.7366i		−	1.51196i
$763$		−	18.5820i		−	0.672713i
$764$	0.305959			0.0110692
$765$		−	23.2262i		−	0.839745i
$766$		−	12.1325i		−	0.438367i
$767$		−	20.5451i		−	0.741840i
$768$			3.37171i			0.121666i
$769$			48.0946i			1.73434i	0.498015	+	0.867168i	$0.334062\pi$
$769$			48.0946i			1.73434i	−0.498015	+	0.867168i	$0.665938\pi$
$770$	−3.08158	−	3.63739i	−0.111052	−	0.131082i
$771$	51.1759			1.84305
$772$	−17.8024			−0.640723
$773$			45.0990i			1.62210i	0.584979	+	0.811048i	$0.301103\pi$
$773$			45.0990i			1.62210i	−0.584979	+	0.811048i	$0.698897\pi$
$774$		−	18.9176i		−	0.679980i
$775$		−	21.2775i		−	0.764311i
$776$			2.77545i			0.0996328i
$777$			78.8142i			2.82744i
$778$	30.9307			1.10892
$779$	−44.6336	−	14.3964i	−1.59917	−	0.515806i
$780$		−	7.39238i		−	0.264690i
$781$	4.90799	+	5.79322i	0.175622	+	0.207298i
$782$		−	18.5372i		−	0.662891i
$783$			76.3858i			2.72981i
$784$	0.158876			0.00567413
$785$	−9.22415			−0.329224
$786$	22.7103			0.810050
$787$	−10.3124			−0.367599			−0.183799	−	0.982964i	$-0.558840\pi$
$787$	−10.3124			−0.367599			−0.183799	+	0.982964i	$0.558840\pi$
$788$		−	13.4869i		−	0.480449i
$789$	−58.3354			−2.07679
$790$	5.81242			0.206797
$791$	−15.1704			−0.539399
$792$	−21.1769	+	17.9410i	−0.752489	+	0.637505i
$793$		−	46.7275i		−	1.65934i
$794$	34.3210			1.21801
$795$	4.88502			0.173254
$796$	−6.72511			−0.238365
$797$			23.3363i			0.826615i	0.910592	+	0.413307i	$0.135627\pi$
$797$			23.3363i			0.826615i	−0.910592	+	0.413307i	$0.864373\pi$
$798$	36.5847	+	11.8003i	1.29508	+	0.417726i
$799$			37.0745i			1.31160i
$800$	4.69799			0.166099
$801$		−	94.2673i		−	3.33077i
$802$		−	28.5279i		−	1.00736i
$803$	−10.0526	−	11.8657i	−0.354748	−	0.418732i
$804$	30.6720			1.08172
$805$		−	5.27584i		−	0.185949i
$806$			18.0690i			0.636454i
$807$	9.06677			0.319165
$808$		−	11.2646i		−	0.396287i
$809$			31.6627i			1.11320i	0.830781	+	0.556600i	$0.187894\pi$
$809$			31.6627i			1.11320i	−0.830781	+	0.556600i	$0.812106\pi$
$810$	−19.7430			−0.693697
$811$	0.563001			0.0197696			0.00988481	−	0.999951i	$-0.496854\pi$
$811$	0.563001			0.0197696			0.00988481	+	0.999951i	$0.496854\pi$
$812$			11.0377i			0.387346i
$813$	50.3686			1.76651
$814$	19.1598	+	22.6156i	0.671551	+	0.792676i
$815$	−9.70227			−0.339856
$816$	−17.0285			−0.596116
$817$	−3.02482	+	9.37792i	−0.105825	+	0.328092i
$818$	−17.6593			−0.617442
$819$		−	87.3242i		−	3.05135i
$820$	5.91269			0.206480
$821$		−	12.2039i		−	0.425920i	−0.977061	−	0.212960i	$-0.931690\pi$
$821$		−	12.2039i		−	0.425920i	0.977061	−	0.212960i	$-0.0683104\pi$
$822$			7.72195i			0.269334i
$823$	−0.691745			−0.0241127			−0.0120564	−	0.999927i	$-0.503838\pi$
$823$	−0.691745			−0.0241127			−0.0120564	+	0.999927i	$0.503838\pi$
$824$			5.86713i			0.204391i
$825$	33.9597	+	40.0849i	1.18233	+	1.39558i
$826$	−13.4693			−0.468658
$827$	−5.10441			−0.177498			−0.0887489	−	0.996054i	$-0.528287\pi$
$827$	−5.10441			−0.177498			−0.0887489	+	0.996054i	$0.528287\pi$
$828$	−30.7160			−1.06746
$829$		−	41.3515i		−	1.43620i	−0.695942	−	0.718098i	$-0.745013\pi$
$829$		−	41.3515i		−	1.43620i	0.695942	−	0.718098i	$-0.254987\pi$
$830$		−	0.481568i		−	0.0167155i
$831$	36.4070			1.26295
$832$	−3.98957			−0.138313
$833$			0.802385i			0.0278010i
$834$	−10.3506			−0.358412
$835$	4.45420			0.154144
$836$	13.3666	−	5.50771i	0.462292	−	0.190488i
$837$	81.9800			2.83364
$838$	14.3376			0.495283
$839$			20.6329i			0.712327i	0.934424	+	0.356163i	$0.115915\pi$
$839$			20.6329i			0.712327i	−0.934424	+	0.356163i	$0.884085\pi$
$840$	−4.84644			−0.167218
$841$	−11.1915			−0.385915
$842$		−	17.9266i		−	0.617792i
$843$		−	22.9470i		−	0.790338i
$844$	14.0080			0.482176
$845$	1.60284			0.0551395
$846$	61.4321			2.11208
$847$	−28.3800	−	4.72769i	−0.975149	−	0.162445i
$848$		−	2.63638i		−	0.0905335i
$849$	109.215			3.74825
$850$			23.7267i			0.813819i
$851$			32.8027i			1.12446i
$852$	7.71886			0.264444
$853$			12.7678i			0.437160i	0.975819	+	0.218580i	$0.0701424\pi$
$853$			12.7678i			0.437160i	−0.975819	+	0.218580i	$0.929858\pi$
$854$	−30.6345			−1.04829
$855$	19.0782	+	6.15363i	0.652462	+	0.210450i
$856$	8.14844			0.278508
$857$	−37.8401			−1.29259			−0.646296	−	0.763087i	$-0.723683\pi$
$857$	−37.8401			−1.29259			−0.646296	+	0.763087i	$0.723683\pi$
$858$	−28.8388	−	34.0404i	−0.984541	−	1.16212i
$859$	−12.3728			−0.422155			−0.211078	−	0.977469i	$-0.567697\pi$
$859$	−12.3728			−0.422155			−0.211078	+	0.977469i	$0.567697\pi$
$860$		−	1.24231i		−	0.0423624i
$861$	94.8836			3.23363
$862$	29.0015			0.987793
$863$		−	57.3000i		−	1.95051i	−0.221075	−	0.975257i	$-0.570956\pi$
$863$		−	57.3000i		−	1.95051i	0.221075	−	0.975257i	$-0.429044\pi$
$864$			18.1009i			0.615804i
$865$	−4.23669			−0.144052
$866$			19.6742i			0.668558i
$867$		−	28.6813i		−	0.974069i
$868$	11.8460			0.402080
$869$	26.7650	−	22.6751i	0.907939	−	0.769201i
$870$			7.81937i			0.265102i
$871$			36.2925i			1.22973i
$872$	−7.10441			−0.240586
$873$			23.2262i			0.786088i
$874$	15.2267	+	4.91132i	0.515050	+	0.166128i
$875$			13.9397i			0.471248i
$876$	−15.8098			−0.534164
$877$	−17.2974			−0.584092			−0.292046	−	0.956404i	$-0.594336\pi$
$877$	−17.2974			−0.584092			−0.292046	+	0.956404i	$0.594336\pi$
$878$	−21.3057			−0.719031
$879$			94.2229i			3.17806i
$880$	−1.39068	+	1.17817i	−0.0468797	+	0.0397162i
$881$	−4.50293			−0.151708			−0.0758538	−	0.997119i	$-0.524168\pi$
$881$	−4.50293			−0.151708			−0.0758538	+	0.997119i	$0.524168\pi$
$882$	1.32954			0.0447681
$883$	−14.9153			−0.501939			−0.250970	−	0.967995i	$-0.580749\pi$
$883$	−14.9153			−0.501939			−0.250970	+	0.967995i	$0.580749\pi$
$884$		−	20.1489i		−	0.677680i
$885$	−9.54204			−0.320752
$886$	−38.0569			−1.27855
$887$	7.21760			0.242343			0.121172	−	0.992632i	$-0.461335\pi$
$887$	7.21760			0.242343			0.121172	+	0.992632i	$0.461335\pi$
$888$	30.1329			1.01119
$889$		−	32.3765i		−	1.08587i
$890$		−	6.19047i		−	0.207505i
$891$	−90.9121	+	77.0203i	−3.04567	+	2.58028i
$892$		−	4.40001i		−	0.147323i
$893$	−30.4534	−	9.82264i	−1.01908	−	0.328702i
$894$	72.3292			2.41905
$895$			4.21283i			0.140819i
$896$			2.61555i			0.0873795i
$897$		−	49.3738i		−	1.64854i
$898$		−	7.29947i		−	0.243586i
$899$		−	19.1127i		−	0.637444i
$900$	39.3149			1.31050
$901$	13.3147			0.443578
$902$	27.2267	−	23.0663i	0.906549	−	0.768024i
$903$		−	19.9359i		−	0.663425i
$904$			5.80008i			0.192908i
$905$		−	0.242325i		−	0.00805517i
$906$		−	24.3969i		−	0.810532i
$907$			20.9068i			0.694198i	0.937829	+	0.347099i	$0.112833\pi$
$907$			20.9068i			0.694198i	−0.937829	+	0.347099i	$0.887167\pi$
$908$	2.32306			0.0770936
$909$		−	94.2673i		−	3.12665i
$910$		−	5.73453i		−	0.190098i
$911$		−	8.14065i		−	0.269712i	−0.990865	−	0.134856i	$-0.956943\pi$
$911$		−	8.14065i		−	0.269712i	0.990865	−	0.134856i	$-0.0430572\pi$
$912$	4.51158	−	13.9874i	0.149393	−	0.463168i
$913$	−1.87867	−	2.21752i	−0.0621750	−	0.0733892i
$914$		−	42.2044i		−	1.39600i
$915$	−21.7023			−0.717455
$916$	11.6600			0.385258
$917$	17.6172			0.581770
$918$	−91.4165			−3.01719
$919$		−	40.9735i		−	1.35159i	−0.737089	−	0.675796i	$-0.763800\pi$
$919$		−	40.9735i		−	1.35159i	0.737089	−	0.675796i	$-0.236200\pi$
$920$	−2.01710			−0.0665019
$921$			28.6043i			0.942545i
$922$		−	34.1868i		−	1.12588i
$923$			9.13331i			0.300627i
$924$	−22.3168	+	18.9067i	−0.734169	+	0.621984i
$925$		−	41.9858i		−	1.38048i
$926$	−23.9347			−0.786542
$927$			49.0988i			1.61262i
$928$	4.22001			0.138529
$929$	7.14938			0.234564			0.117282	−	0.993099i	$-0.462582\pi$
$929$	7.14938			0.234564			0.117282	+	0.993099i	$0.462582\pi$
$930$	8.39203			0.275186
$931$	−0.659087	−	0.212586i	−0.0216007	−	0.00696724i
$932$			7.57452i			0.248112i
$933$			35.9059i			1.17551i
$934$	−17.6443			−0.577338
$935$	−5.95024	−	7.02346i	−0.194594	−	0.229692i
$936$	−33.3865			−1.09127
$937$		−	26.4991i		−	0.865687i	−0.901469	−	0.432843i	$-0.857510\pi$
$937$		−	26.4991i		−	0.865687i	0.901469	−	0.432843i	$-0.142490\pi$
$938$	23.7933			0.776880
$939$			81.7973i			2.66935i
$940$	4.03421			0.131581
$941$	32.4157			1.05672			0.528361	−	0.849020i	$-0.322807\pi$
$941$	32.4157			1.05672			0.528361	+	0.849020i	$0.322807\pi$
$942$			56.5938i			1.84393i
$943$	39.4909			1.28600
$944$			5.14971i			0.167609i
$945$	−26.0179			−0.846361
$946$	−4.84644	−	5.72057i	−0.157571	−	0.185992i
$947$	−21.1899			−0.688578			−0.344289	−	0.938864i	$-0.611880\pi$
$947$	−21.1899			−0.688578			−0.344289	+	0.938864i	$0.611880\pi$
$948$		−	35.6615i		−	1.15823i
$949$		−	18.7069i		−	0.607252i
$950$	−19.4894	−	6.28623i	−0.632318	−	0.203952i
$951$	−20.5741			−0.667160
$952$	−13.2096			−0.428125
$953$	33.9745			1.10054			0.550271	−	0.834986i	$-0.314524\pi$
$953$	33.9745			1.10054			0.550271	+	0.834986i	$0.314524\pi$
$954$		−	22.0624i		−	0.714296i
$955$	0.168140			0.00544089
$956$			6.81545i			0.220427i
$957$	30.5046	+	36.0066i	0.986073	+	1.16393i
$958$			32.9775i			1.06545i
$959$			5.99018i			0.193433i
$960$			1.85293i			0.0598030i
$961$	10.4876			0.338309
$962$			35.6546i			1.14955i
$963$	68.1898			2.19739
$964$	−14.8529			−0.478380
$965$	−9.78333			−0.314937
$966$	−32.3694			−1.04147
$967$		−	38.6701i		−	1.24355i	−0.783197	−	0.621773i	$-0.786413\pi$
$967$		−	38.6701i		−	1.24355i	0.783197	−	0.621773i	$-0.213587\pi$
$968$	−1.80753	+	10.8505i	−0.0580962	+	0.348748i
$969$	70.6416	+	22.7853i	2.26934	+	0.731968i
$970$			1.52525i			0.0489729i
$971$		−	13.6334i		−	0.437517i	−0.975779	−	0.218759i	$-0.929799\pi$
$971$		−	13.6334i		−	0.437517i	0.975779	−	0.218759i	$-0.0702007\pi$
$972$			66.8282i			2.14352i
$973$	−8.02932			−0.257408
$974$		−	38.0849i		−	1.22032i
$975$			63.1959i			2.02389i
$976$			11.7124i			0.374905i
$977$			39.4021i			1.26059i	0.776357	+	0.630293i	$0.217065\pi$
$977$			39.4021i			1.26059i	−0.776357	+	0.630293i	$0.782935\pi$
$978$			59.5273i			1.90347i
$979$	−24.1500	−	28.5058i	−0.771837	−	0.911050i
$980$	0.0873103			0.00278903
$981$	−59.4529			−1.89819
$982$			30.3390i			0.968155i
$983$			2.35737i			0.0751886i	0.999293	+	0.0375943i	$0.0119695\pi$
$983$			2.35737i			0.0751886i	−0.999293	+	0.0375943i	$0.988031\pi$
$984$		−	36.2767i		−	1.15646i
$985$		−	7.41172i		−	0.236157i
$986$			21.3127i			0.678734i
$987$	64.7388			2.06066
$988$	16.5505	+	5.33831i	0.526541	+	0.169834i
$989$		−	8.29739i		−	0.263842i
$990$	−11.6378	+	9.85949i	−0.369874	+	0.313355i
$991$			44.4844i			1.41309i	0.707667	+	0.706547i	$0.249748\pi$
$991$			44.4844i			1.41309i	−0.707667	+	0.706547i	$0.750252\pi$
$992$		−	4.52906i		−	0.143798i
$993$	45.5222			1.44460
$994$	5.98779			0.189921
$995$	−3.69579			−0.117164
$996$	−2.95461			−0.0936205
$997$		−	8.70938i		−	0.275829i	−0.990444	−	0.137914i	$-0.955960\pi$
$997$		−	8.70938i		−	0.275829i	0.990444	−	0.137914i	$-0.0440399\pi$
$998$	13.8596			0.438718
$999$	161.767			5.11808

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.b.c.417.8	yes	8
3.2	odd	2		3762.2.g.h.2089.5		8
11.10	odd	2		418.2.b.d.417.8	yes	8
19.18	odd	2		418.2.b.d.417.1	yes	8
33.32	even	2		3762.2.g.g.2089.6		8
57.56	even	2		3762.2.g.g.2089.5		8
209.208	even	2	inner	418.2.b.c.417.1	✓	8
627.626	odd	2		3762.2.g.h.2089.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.b.c.417.1	✓	8	209.208	even	2	inner
418.2.b.c.417.8	yes	8	1.1	even	1	trivial
418.2.b.d.417.1	yes	8	19.18	odd	2
418.2.b.d.417.8	yes	8	11.10	odd	2
3762.2.g.g.2089.5		8	57.56	even	2
3762.2.g.g.2089.6		8	33.32	even	2
3762.2.g.h.2089.5		8	3.2	odd	2
3762.2.g.h.2089.6		8	627.626	odd	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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +3.37171i q^{3} +1.00000 q^{4} +0.549551 q^{5} -3.37171i q^{6} -2.61555i q^{7} -1.00000 q^{8} -8.36845 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +3.37171i q^{3} +1.00000 q^{4} +0.549551 q^{5} -3.37171i q^{6} -2.61555i q^{7} -1.00000 q^{8} -8.36845 q^{9} -0.549551 q^{10} +(-2.53057 + 2.14388i) q^{11} +3.37171i q^{12} -3.98957 q^{13} +2.61555i q^{14} +1.85293i q^{15} +1.00000 q^{16} +5.05039i q^{17} +8.36845 q^{18} +(-4.14844 - 1.33807i) q^{19} +0.549551 q^{20} +8.81890 q^{21} +(2.53057 - 2.14388i) q^{22} +3.67046 q^{23} -3.37171i q^{24} -4.69799 q^{25} +3.98957 q^{26} -18.1009i q^{27} -2.61555i q^{28} -4.22001 q^{29} -1.85293i q^{30} +4.52906i q^{31} -1.00000 q^{32} +(-7.22856 - 8.53234i) q^{33} -5.05039i q^{34} -1.43738i q^{35} -8.36845 q^{36} +8.93697i q^{37} +(4.14844 + 1.33807i) q^{38} -13.4517i q^{39} -0.549551 q^{40} +10.7591 q^{41} -8.81890 q^{42} -2.26059i q^{43} +(-2.53057 + 2.14388i) q^{44} -4.59889 q^{45} -3.67046 q^{46} +7.34091 q^{47} +3.37171i q^{48} +0.158876 q^{49} +4.69799 q^{50} -17.0285 q^{51} -3.98957 q^{52} -2.63638i q^{53} +18.1009i q^{54} +(-1.39068 + 1.17817i) q^{55} +2.61555i q^{56} +(4.51158 - 13.9874i) q^{57} +4.22001 q^{58} +5.14971i q^{59} +1.85293i q^{60} +11.7124i q^{61} -4.52906i q^{62} +21.8881i q^{63} +1.00000 q^{64} -2.19247 q^{65} +(7.22856 + 8.53234i) q^{66} -9.09686i q^{67} +5.05039i q^{68} +12.3757i q^{69} +1.43738i q^{70} -2.28930i q^{71} +8.36845 q^{72} +4.68896i q^{73} -8.93697i q^{74} -15.8403i q^{75} +(-4.14844 - 1.33807i) q^{76} +(5.60744 + 6.61883i) q^{77} +13.4517i q^{78} -10.5767 q^{79} +0.549551 q^{80} +35.9256 q^{81} -10.7591 q^{82} +0.876294i q^{83} +8.81890 q^{84} +2.77545i q^{85} +2.26059i q^{86} -14.2287i q^{87} +(2.53057 - 2.14388i) q^{88} +11.2646i q^{89} +4.59889 q^{90} +10.4349i q^{91} +3.67046 q^{92} -15.2707 q^{93} -7.34091 q^{94} +(-2.27978 - 0.735337i) q^{95} -3.37171i q^{96} -2.77545i q^{97} -0.158876 q^{98} +(21.1769 - 17.9410i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 8 q^{4} + 2 q^{5} - 8 q^{8} - 14 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 + 8 * q^4 + 2 * q^5 - 8 * q^8 - 14 * q^9	\( 8 q - 8 q^{2} + 8 q^{4} + 2 q^{5} - 8 q^{8} - 14 q^{9} - 2 q^{10} - 6 q^{11} + 10 q^{13} + 8 q^{16} + 14 q^{18} + 2 q^{20} + 20 q^{21} + 6 q^{22} + 12 q^{23} - 2 q^{25} - 10 q^{26} - 14 q^{29} - 8 q^{32} - 8 q^{33} - 14 q^{36} - 2 q^{40} + 22 q^{41} - 20 q^{42} - 6 q^{44} - 6 q^{45} - 12 q^{46} + 24 q^{47} + 10 q^{49} + 2 q^{50} - 24 q^{51} + 10 q^{52} + 10 q^{57} + 14 q^{58} + 8 q^{64} - 16 q^{65} + 8 q^{66} + 14 q^{72} - 16 q^{77} - 12 q^{79} + 2 q^{80} + 36 q^{81} - 22 q^{82} + 20 q^{84} + 6 q^{88} + 6 q^{90} + 12 q^{92} - 32 q^{93} - 24 q^{94} - 12 q^{95} - 10 q^{98} + 24 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^4 + 2 * q^5 - 8 * q^8 - 14 * q^9 - 2 * q^10 - 6 * q^11 + 10 * q^13 + 8 * q^16 + 14 * q^18 + 2 * q^20 + 20 * q^21 + 6 * q^22 + 12 * q^23 - 2 * q^25 - 10 * q^26 - 14 * q^29 - 8 * q^32 - 8 * q^33 - 14 * q^36 - 2 * q^40 + 22 * q^41 - 20 * q^42 - 6 * q^44 - 6 * q^45 - 12 * q^46 + 24 * q^47 + 10 * q^49 + 2 * q^50 - 24 * q^51 + 10 * q^52 + 10 * q^57 + 14 * q^58 + 8 * q^64 - 16 * q^65 + 8 * q^66 + 14 * q^72 - 16 * q^77 - 12 * q^79 + 2 * q^80 + 36 * q^81 - 22 * q^82 + 20 * q^84 + 6 * q^88 + 6 * q^90 + 12 * q^92 - 32 * q^93 - 24 * q^94 - 12 * q^95 - 10 * q^98 + 24 * q^99

Introduction

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