LMFDB - Embedded newform 1205.2.b.c.724.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1205,2,Mod(724,1205)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1205, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1205.724");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1205 = 5 \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1205.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:	$9.62197344356$
Analytic rank:	$0$
Dimension:	$46$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			724.6
Character	$\chi$	$=$	1205.724
Dual form			1205.2.b.c.724.41

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.95888i q^{2} -0.350465i q^{3} -1.83721 q^{4} +(-1.30176 - 1.81808i) q^{5} -0.686519 q^{6} +1.14869i q^{7} -0.318879i q^{8} +2.87717 q^{9} +O(q^{10})$	\(q-1.95888i q^{2} -0.350465i q^{3} -1.83721 q^{4} +(-1.30176 - 1.81808i) q^{5} -0.686519 q^{6} +1.14869i q^{7} -0.318879i q^{8} +2.87717 q^{9} +(-3.56141 + 2.54999i) q^{10} +0.395421 q^{11} +0.643879i q^{12} +0.595326i q^{13} +2.25014 q^{14} +(-0.637175 + 0.456220i) q^{15} -4.29907 q^{16} -7.79008i q^{17} -5.63604i q^{18} -3.25574 q^{19} +(2.39160 + 3.34021i) q^{20} +0.402575 q^{21} -0.774582i q^{22} -3.49975i q^{23} -0.111756 q^{24} +(-1.61086 + 4.73341i) q^{25} +1.16617 q^{26} -2.05974i q^{27} -2.11038i q^{28} -6.23795 q^{29} +(0.893680 + 1.24815i) q^{30} -9.01707 q^{31} +7.78361i q^{32} -0.138581i q^{33} -15.2598 q^{34} +(2.08841 - 1.49531i) q^{35} -5.28598 q^{36} +0.667693i q^{37} +6.37760i q^{38} +0.208641 q^{39} +(-0.579750 + 0.415103i) q^{40} +6.05766 q^{41} -0.788596i q^{42} -9.26190i q^{43} -0.726472 q^{44} +(-3.74538 - 5.23095i) q^{45} -6.85559 q^{46} +13.6965i q^{47} +1.50667i q^{48} +5.68052 q^{49} +(9.27218 + 3.15548i) q^{50} -2.73015 q^{51} -1.09374i q^{52} -0.719285i q^{53} -4.03479 q^{54} +(-0.514741 - 0.718908i) q^{55} +0.366293 q^{56} +1.14102i q^{57} +12.2194i q^{58} +10.8402 q^{59} +(1.17063 - 0.838173i) q^{60} +2.84725 q^{61} +17.6634i q^{62} +3.30498i q^{63} +6.64902 q^{64} +(1.08235 - 0.774969i) q^{65} -0.271464 q^{66} +1.17890i q^{67} +14.3120i q^{68} -1.22654 q^{69} +(-2.92914 - 4.09095i) q^{70} -14.0182 q^{71} -0.917471i q^{72} +4.89629i q^{73} +1.30793 q^{74} +(1.65889 + 0.564550i) q^{75} +5.98148 q^{76} +0.454215i q^{77} -0.408703i q^{78} -13.1124 q^{79} +(5.59635 + 7.81608i) q^{80} +7.90966 q^{81} -11.8662i q^{82} -5.86352i q^{83} -0.739616 q^{84} +(-14.1630 + 10.1408i) q^{85} -18.1429 q^{86} +2.18618i q^{87} -0.126092i q^{88} +11.3538 q^{89} +(-10.2468 + 7.33675i) q^{90} -0.683844 q^{91} +6.42979i q^{92} +3.16017i q^{93} +26.8298 q^{94} +(4.23818 + 5.91920i) q^{95} +2.72788 q^{96} +0.175389i q^{97} -11.1275i q^{98} +1.13769 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9}+O(q^{10}) $ 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9	$ 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9} - 7 q^{10} - 64 q^{11} + 66 q^{14} + 5 q^{15} + 22 q^{16} - 2 q^{20} - 14 q^{21} + 50 q^{24} + 30 q^{25} - 60 q^{26} + 36 q^{29} + 7 q^{30} - 36 q^{31} - 12 q^{34} + 3 q^{35} - 34 q^{36} + 88 q^{39} - 30 q^{40} - 76 q^{41} + 100 q^{44} - 17 q^{45} - 12 q^{46} - 22 q^{49} - 14 q^{50} - 112 q^{51} + 26 q^{54} - 5 q^{55} - 120 q^{56} + 84 q^{59} - 33 q^{60} - 78 q^{61} - 28 q^{64} + 9 q^{65} - 2 q^{66} + 24 q^{69} + 88 q^{70} - 172 q^{71} + 16 q^{74} + 59 q^{75} - 18 q^{76} + 54 q^{79} + 63 q^{80} - 42 q^{81} - 44 q^{84} + 30 q^{85} - 80 q^{86} + 86 q^{89} + 17 q^{90} - 88 q^{91} - 4 q^{94} + q^{95} - 122 q^{96} + 148 q^{99}+O(q^{100}) $ 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9 - 7 * q^10 - 64 * q^11 + 66 * q^14 + 5 * q^15 + 22 * q^16 - 2 * q^20 - 14 * q^21 + 50 * q^24 + 30 * q^25 - 60 * q^26 + 36 * q^29 + 7 * q^30 - 36 * q^31 - 12 * q^34 + 3 * q^35 - 34 * q^36 + 88 * q^39 - 30 * q^40 - 76 * q^41 + 100 * q^44 - 17 * q^45 - 12 * q^46 - 22 * q^49 - 14 * q^50 - 112 * q^51 + 26 * q^54 - 5 * q^55 - 120 * q^56 + 84 * q^59 - 33 * q^60 - 78 * q^61 - 28 * q^64 + 9 * q^65 - 2 * q^66 + 24 * q^69 + 88 * q^70 - 172 * q^71 + 16 * q^74 + 59 * q^75 - 18 * q^76 + 54 * q^79 + 63 * q^80 - 42 * q^81 - 44 * q^84 + 30 * q^85 - 80 * q^86 + 86 * q^89 + 17 * q^90 - 88 * q^91 - 4 * q^94 + q^95 - 122 * q^96 + 148 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1205\mathbb{Z}\right)^\times$.

$n$	$242$	$971$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	1.95888i		−	1.38514i	−0.721352	−	0.692569i	$-0.756479\pi$
$2$		−	1.95888i		−	1.38514i	0.721352	−	0.692569i	$-0.243521\pi$
$3$		−	0.350465i		−	0.202341i	−0.994869	−	0.101171i	$-0.967741\pi$
$3$		−	0.350465i		−	0.202341i	0.994869	−	0.101171i	$-0.0322588\pi$
$4$	−1.83721			−0.918607
$5$	−1.30176	−	1.81808i	−0.582163	−	0.813072i
$5$	−1.30176	−	1.81808i	−0.582163	−	0.813072i
$6$	−0.686519			−0.280270
$7$			1.14869i			0.434163i	0.976153	+	0.217082i	$0.0696538\pi$
$7$			1.14869i			0.434163i	−0.976153	+	0.217082i	$0.930346\pi$
$8$		−	0.318879i		−	0.112741i
$9$	2.87717			0.959058
$10$	−3.56141	+	2.54999i	−1.12622	+	0.806376i
$11$	0.395421			0.119224			0.0596119	−	0.998222i	$-0.481014\pi$
$11$	0.395421			0.119224			0.0596119	+	0.998222i	$0.481014\pi$
$12$			0.643879i			0.185872i
$13$			0.595326i			0.165114i	0.996586	+	0.0825569i	$0.0263086\pi$
$13$			0.595326i			0.165114i	−0.996586	+	0.0825569i	$0.973691\pi$
$14$	2.25014			0.601376
$15$	−0.637175	+	0.456220i	−0.164518	+	0.117795i
$16$	−4.29907			−1.07477
$17$		−	7.79008i		−	1.88937i	−0.327977	−	0.944686i	$-0.606367\pi$
$17$		−	7.79008i		−	1.88937i	0.327977	−	0.944686i	$-0.393633\pi$
$18$		−	5.63604i		−	1.32843i
$19$	−3.25574			−0.746917			−0.373459	−	0.927647i	$-0.621828\pi$
$19$	−3.25574			−0.746917			−0.373459	+	0.927647i	$0.621828\pi$
$20$	2.39160	+	3.34021i	0.534779	+	0.746893i
$21$	0.402575			0.0878490
$22$		−	0.774582i		−	0.165141i
$23$		−	3.49975i		−	0.729748i	−0.931057	−	0.364874i	$-0.881112\pi$
$23$		−	3.49975i		−	0.729748i	0.931057	−	0.364874i	$-0.118888\pi$
$24$	−0.111756			−0.0228121
$25$	−1.61086	+	4.73341i	−0.322172	+	0.946681i
$26$	1.16617			0.228705
$27$		−	2.05974i		−	0.396398i
$28$		−	2.11038i		−	0.398825i
$29$	−6.23795			−1.15836			−0.579179	−	0.815200i	$-0.696627\pi$
$29$	−6.23795			−1.15836			−0.579179	+	0.815200i	$0.696627\pi$
$30$	0.893680	+	1.24815i	0.163163	+	0.227880i
$31$	−9.01707			−1.61951			−0.809757	−	0.586766i	$-0.800401\pi$
$31$	−9.01707			−1.61951			−0.809757	+	0.586766i	$0.800401\pi$
$32$			7.78361i			1.37596i
$33$		−	0.138581i		−	0.0241239i
$34$	−15.2598			−2.61704
$35$	2.08841	−	1.49531i	0.353006	−	0.252754i
$36$	−5.28598			−0.880997
$37$			0.667693i			0.109768i	0.998493	+	0.0548840i	$0.0174789\pi$
$37$			0.667693i			0.109768i	−0.998493	+	0.0548840i	$0.982521\pi$
$38$			6.37760i			1.03458i
$39$	0.208641			0.0334093
$40$	−0.579750	+	0.415103i	−0.0916665	+	0.0656336i
$41$	6.05766			0.946048			0.473024	−	0.881050i	$-0.343162\pi$
$41$	6.05766			0.946048			0.473024	+	0.881050i	$0.343162\pi$
$42$		−	0.788596i		−	0.121683i
$43$		−	9.26190i		−	1.41243i	−0.707999	−	0.706213i	$-0.750402\pi$
$43$		−	9.26190i		−	1.41243i	0.707999	−	0.706213i	$-0.249598\pi$
$44$	−0.726472			−0.109520
$45$	−3.74538	−	5.23095i	−0.558328	−	0.779783i
$46$	−6.85559			−1.01080
$47$			13.6965i			1.99784i	0.0464433	+	0.998921i	$0.485211\pi$
$47$			13.6965i			1.99784i	−0.0464433	+	0.998921i	$0.514789\pi$
$48$			1.50667i			0.217470i
$49$	5.68052			0.811502
$50$	9.27218	+	3.15548i	1.31128	+	0.446253i
$51$	−2.73015			−0.382297
$52$		−	1.09374i		−	0.151675i
$53$		−	0.719285i		−	0.0988013i	−0.998779	−	0.0494007i	$-0.984269\pi$
$53$		−	0.719285i		−	0.0988013i	0.998779	−	0.0494007i	$-0.0157311\pi$
$54$	−4.03479			−0.549066
$55$	−0.514741	−	0.718908i	−0.0694077	−	0.0969376i
$56$	0.366293			0.0489479
$57$			1.14102i			0.151132i
$58$			12.2194i			1.60449i
$59$	10.8402			1.41127			0.705635	−	0.708576i	$-0.250662\pi$
$59$	10.8402			1.41127			0.705635	+	0.708576i	$0.250662\pi$
$60$	1.17063	−	0.838173i	0.151127	−	0.108208i
$61$	2.84725			0.364553			0.182276	−	0.983247i	$-0.441653\pi$
$61$	2.84725			0.364553			0.182276	+	0.983247i	$0.441653\pi$
$62$			17.6634i			2.24325i
$63$			3.30498i			0.416388i
$64$	6.64902			0.831128
$65$	1.08235	−	0.774969i	0.134249	−	0.0961231i
$66$	−0.271464			−0.0334149
$67$			1.17890i			0.144026i	0.997404	+	0.0720129i	$0.0229423\pi$
$67$			1.17890i			0.144026i	−0.997404	+	0.0720129i	$0.977058\pi$
$68$			14.3120i			1.73559i
$69$	−1.22654			−0.147658
$70$	−2.92914	−	4.09095i	−0.350099	−	0.488962i
$71$	−14.0182			−1.66366			−0.831828	−	0.555033i	$-0.812706\pi$
$71$	−14.0182			−1.66366			−0.831828	+	0.555033i	$0.812706\pi$
$72$		−	0.917471i		−	0.108125i
$73$			4.89629i			0.573067i	0.958070	+	0.286534i	$0.0925030\pi$
$73$			4.89629i			0.573067i	−0.958070	+	0.286534i	$0.907497\pi$
$74$	1.30793			0.152044
$75$	1.65889	+	0.564550i	0.191552	+	0.0651887i
$76$	5.98148			0.686123
$77$			0.454215i			0.0517626i
$78$		−	0.408703i		−	0.0462765i
$79$	−13.1124			−1.47526			−0.737632	−	0.675203i	$-0.764056\pi$
$79$	−13.1124			−1.47526			−0.737632	+	0.675203i	$0.764056\pi$
$80$	5.59635	+	7.81608i	0.625691	+	0.873864i
$81$	7.90966			0.878851
$82$		−	11.8662i		−	1.31041i
$83$		−	5.86352i		−	0.643604i	−0.946807	−	0.321802i	$-0.895711\pi$
$83$		−	5.86352i		−	0.643604i	0.946807	−	0.321802i	$-0.104289\pi$
$84$	−0.739616			−0.0806987
$85$	−14.1630	+	10.1408i	−1.53619	+	1.09992i
$86$	−18.1429			−1.95640
$87$			2.18618i			0.234383i
$88$		−	0.126092i		−	0.0134414i
$89$	11.3538			1.20350			0.601751	−	0.798683i	$-0.294470\pi$
$89$	11.3538			1.20350			0.601751	+	0.798683i	$0.294470\pi$
$90$	−10.2468	+	7.33675i	−1.08011	+	0.773362i
$91$	−0.683844			−0.0716863
$92$			6.42979i			0.670352i
$93$			3.16017i			0.327694i
$94$	26.8298			2.76729
$95$	4.23818	+	5.91920i	0.434828	+	0.607297i
$96$	2.72788			0.278413
$97$			0.175389i			0.0178081i	0.999960	+	0.00890404i	$0.00283428\pi$
$97$			0.175389i			0.0178081i	−0.999960	+	0.00890404i	$0.997166\pi$
$98$		−	11.1275i		−	1.12404i
$99$	1.13769			0.114343
$100$	2.95950	−	8.69628i	0.295950	−	0.869628i
$101$	−11.2535			−1.11976			−0.559882	−	0.828572i	$-0.689154\pi$
$101$	−11.2535			−1.11976			−0.559882	+	0.828572i	$0.689154\pi$
$102$			5.34804i			0.529534i
$103$		−	9.35760i		−	0.922032i	−0.887392	−	0.461016i	$-0.847485\pi$
$103$		−	9.35760i		−	0.922032i	0.887392	−	0.461016i	$-0.152515\pi$
$104$	0.189837			0.0186151
$105$	−0.524054	−	0.731915i	−0.0511425	−	0.0714276i
$106$	−1.40899			−0.136853
$107$		−	11.7603i		−	1.13691i	−0.822714	−	0.568456i	$-0.807541\pi$
$107$		−	11.7603i		−	1.13691i	0.822714	−	0.568456i	$-0.192459\pi$
$108$			3.78419i			0.364134i
$109$	4.89496			0.468852			0.234426	−	0.972134i	$-0.424679\pi$
$109$	4.89496			0.468852			0.234426	+	0.972134i	$0.424679\pi$
$110$	−1.40826	+	1.00832i	−0.134272	+	0.0961393i
$111$	0.234003			0.0222106
$112$		−	4.93829i		−	0.466625i
$113$		−	7.26082i		−	0.683041i	−0.939874	−	0.341520i	$-0.889058\pi$
$113$		−	7.26082i		−	0.683041i	0.939874	−	0.341520i	$-0.110942\pi$
$114$	2.23512			0.209339
$115$	−6.36284	+	4.55582i	−0.593338	+	0.424833i
$116$	11.4604			1.06408
$117$			1.71286i			0.158354i
$118$		−	21.2346i		−	1.95480i
$119$	8.94837			0.820296
$120$	0.145479	+	0.203182i	0.0132804	+	0.0185479i
$121$	−10.8436			−0.985786
$122$		−	5.57742i		−	0.504956i
$123$		−	2.12300i		−	0.191424i
$124$	16.5663			1.48770
$125$	10.7027	−	3.23306i	0.957277	−	0.289174i
$126$	6.47405			0.576754
$127$			12.5876i			1.11697i	0.829516	+	0.558483i	$0.188616\pi$
$127$			12.5876i			1.11697i	−0.829516	+	0.558483i	$0.811384\pi$
$128$			2.54258i			0.224735i
$129$	−3.24597			−0.285792
$130$	−1.51807	−	2.12020i	−0.133144	−	0.185954i
$131$	−14.3195			−1.25110			−0.625552	−	0.780182i	$-0.715126\pi$
$131$	−14.3195			−1.25110			−0.625552	+	0.780182i	$0.715126\pi$
$132$			0.254603i			0.0221604i
$133$		−	3.73982i		−	0.324284i
$134$	2.30933			0.199495
$135$	−3.74479	+	2.68128i	−0.322300	+	0.230768i
$136$	−2.48409			−0.213009
$137$		−	5.34099i		−	0.456312i	−0.973625	−	0.228156i	$-0.926730\pi$
$137$		−	5.34099i		−	0.456312i	0.973625	−	0.228156i	$-0.0732696\pi$
$138$			2.40264i			0.204527i
$139$	13.1396			1.11448			0.557241	−	0.830351i	$-0.311860\pi$
$139$	13.1396			1.11448			0.557241	+	0.830351i	$0.311860\pi$
$140$	−3.83686	+	2.74721i	−0.324274	+	0.232181i
$141$	4.80015			0.404245
$142$			27.4600i			2.30439i
$143$			0.235404i			0.0196855i
$144$	−12.3692			−1.03077
$145$	8.12029	+	11.3411i	0.674353	+	0.941828i
$146$	9.59125			0.793777
$147$		−	1.99082i		−	0.164200i
$148$		−	1.22669i		−	0.100834i
$149$	6.09589			0.499395			0.249697	−	0.968324i	$-0.419669\pi$
$149$	6.09589			0.499395			0.249697	+	0.968324i	$0.419669\pi$
$150$	1.10589	−	3.24957i	0.0902953	−	0.265327i
$151$	−2.45933			−0.200137			−0.100069	−	0.994981i	$-0.531906\pi$
$151$	−2.45933			−0.200137			−0.100069	+	0.994981i	$0.531906\pi$
$152$			1.03819i			0.0842081i
$153$		−	22.4134i		−	1.81202i
$154$	0.889753			0.0716983
$155$	11.7380	+	16.3938i	0.942821	+	1.31678i
$156$	−0.383318			−0.0306900
$157$		−	2.93713i		−	0.234409i	−0.993108	−	0.117204i	$-0.962607\pi$
$157$		−	2.93713i		−	0.234409i	0.993108	−	0.117204i	$-0.0373932\pi$
$158$			25.6857i			2.04344i
$159$	−0.252084			−0.0199916
$160$	14.1513	−	10.1324i	1.11876	−	0.801034i
$161$	4.02012			0.316830
$162$		−	15.4941i		−	1.21733i
$163$		−	23.5480i		−	1.84443i	−0.386683	−	0.922213i	$-0.626379\pi$
$163$		−	23.5480i		−	1.84443i	0.386683	−	0.922213i	$-0.373621\pi$
$164$	−11.1292			−0.869046
$165$	−0.251952	+	0.180399i	−0.0196144	+	0.0140440i
$166$	−11.4859			−0.891481
$167$		−	15.3378i		−	1.18688i	−0.804879	−	0.593439i	$-0.797770\pi$
$167$		−	15.3378i		−	1.18688i	0.804879	−	0.593439i	$-0.202230\pi$
$168$		−	0.128373i		−	0.00990418i
$169$	12.6456			0.972737
$170$	19.8646	+	27.7437i	1.52354	+	2.12784i
$171$	−9.36732			−0.716337
$172$			17.0161i			1.29746i
$173$			7.62958i			0.580066i	0.957017	+	0.290033i	$0.0936663\pi$
$173$			7.62958i			0.580066i	−0.957017	+	0.290033i	$0.906334\pi$
$174$	4.28247			0.324653
$175$	−5.43721	−	1.85038i	−0.411014	−	0.139875i
$176$	−1.69994			−0.128138
$177$		−	3.79910i		−	0.285558i
$178$		−	22.2408i		−	1.66702i
$179$	−13.4465			−1.00504			−0.502520	−	0.864566i	$-0.667594\pi$
$179$	−13.4465			−1.00504			−0.502520	+	0.864566i	$0.667594\pi$
$180$	6.88106	+	9.61036i	0.512884	+	0.716314i
$181$	24.3051			1.80658			0.903292	−	0.429027i	$-0.141144\pi$
$181$	24.3051			1.80658			0.903292	+	0.429027i	$0.141144\pi$
$182$			1.33957i			0.0992954i
$183$		−	0.997861i		−	0.0737640i
$184$	−1.11600			−0.0822725
$185$	1.21392	−	0.869173i	0.0892493	−	0.0639029i
$186$	6.19039			0.453901
$187$		−	3.08036i		−	0.225258i
$188$		−	25.1634i		−	1.83523i
$189$	2.36600			0.172101
$190$	11.5950	−	8.30208i	0.841191	−	0.602296i
$191$	16.5298			1.19605			0.598026	−	0.801476i	$-0.295952\pi$
$191$	16.5298			1.19605			0.598026	+	0.801476i	$0.295952\pi$
$192$		−	2.33025i		−	0.168171i
$193$			14.0074i			1.00828i	0.863623	+	0.504138i	$0.168190\pi$
$193$			14.0074i			1.00828i	−0.863623	+	0.504138i	$0.831810\pi$
$194$	0.343566			0.0246666
$195$	−0.271600	−	0.379327i	−0.0194496	−	0.0271641i
$196$	−10.4363			−0.745451
$197$		−	25.8379i		−	1.84087i	−0.390892	−	0.920437i	$-0.627833\pi$
$197$		−	25.8379i		−	1.84087i	0.390892	−	0.920437i	$-0.372167\pi$
$198$		−	2.22861i		−	0.158380i
$199$	5.06385			0.358967			0.179483	−	0.983761i	$-0.442557\pi$
$199$	5.06385			0.358967			0.179483	+	0.983761i	$0.442557\pi$
$200$	1.50939	+	0.513670i	0.106730	+	0.0363220i
$201$	0.413164			0.0291423
$202$			22.0443i			1.55103i
$203$		−	7.16546i		−	0.502916i
$204$	5.01587			0.351181
$205$	−7.88560	−	11.0133i	−0.550754	−	0.769205i
$206$	−18.3304			−1.27714
$207$		−	10.0694i		−	0.699871i
$208$		−	2.55935i		−	0.177459i
$209$	−1.28739			−0.0890503
$210$	−1.43373	+	1.02656i	−0.0989371	+	0.0708394i
$211$	−12.2747			−0.845026			−0.422513	−	0.906357i	$-0.638852\pi$
$211$	−12.2747			−0.845026			−0.422513	+	0.906357i	$0.638852\pi$
$212$			1.32148i			0.0907596i
$213$			4.91289i			0.336626i
$214$	−23.0370			−1.57478
$215$	−16.8389	+	12.0567i	−1.14840	+	0.822262i
$216$	−0.656810			−0.0446902
$217$		−	10.3578i		−	0.703133i
$218$		−	9.58864i		−	0.649425i
$219$	1.71598			0.115955
$220$	0.945690	+	1.32079i	0.0637584	+	0.0890475i
$221$	4.63764			0.311961
$222$		−	0.458384i		−	0.0307647i
$223$		−	20.5388i		−	1.37538i	−0.726005	−	0.687689i	$-0.758625\pi$
$223$		−	20.5388i		−	1.37538i	0.726005	−	0.687689i	$-0.241375\pi$
$224$	−8.94094			−0.597392
$225$	−4.63473	+	13.6188i	−0.308982	+	0.907922i
$226$	−14.2231			−0.946106
$227$			15.6294i			1.03736i	0.854969	+	0.518679i	$0.173576\pi$
$227$			15.6294i			1.03736i	−0.854969	+	0.518679i	$0.826424\pi$
$228$		−	2.09630i		−	0.138831i
$229$	7.68533			0.507861			0.253930	−	0.967222i	$-0.418277\pi$
$229$	7.68533			0.507861			0.253930	+	0.967222i	$0.418277\pi$
$230$	8.92431	+	12.4640i	0.588452	+	0.821855i
$231$	0.159186			0.0104737
$232$			1.98915i			0.130594i
$233$			28.4122i			1.86135i	0.365851	+	0.930673i	$0.380778\pi$
$233$			28.4122i			1.86135i	−0.365851	+	0.930673i	$0.619222\pi$
$234$	3.35528			0.219342
$235$	24.9014	−	17.8295i	1.62439	−	1.16307i
$236$	−19.9157			−1.29640
$237$			4.59545i			0.298507i
$238$		−	17.5288i		−	1.13622i
$239$	2.95254			0.190984			0.0954918	−	0.995430i	$-0.469558\pi$
$239$	2.95254			0.190984			0.0954918	+	0.995430i	$0.469558\pi$
$240$	2.73926	−	1.96132i	0.176819	−	0.126603i
$241$	1.00000			0.0644157
$241$	1.00000			0.0644157
$242$			21.2414i			1.36545i
$243$		−	8.95129i		−	0.574225i
$244$	−5.23100			−0.334881
$245$	−7.39465	−	10.3277i	−0.472427	−	0.659810i
$246$	−4.15870			−0.265149
$247$		−	1.93822i		−	0.123326i
$248$			2.87536i			0.182585i
$249$	−2.05496			−0.130228
$250$	−6.33318	−	20.9653i	−0.400545	−	1.32596i
$251$	12.1180			0.764879			0.382439	−	0.923981i	$-0.375084\pi$
$251$	12.1180			0.764879			0.382439	+	0.923981i	$0.375084\pi$
$252$		−	6.07195i		−	0.382497i
$253$		−	1.38387i		−	0.0870034i
$254$	24.6575			1.54715
$255$	3.55399	+	4.96364i	0.222559	+	0.310835i
$256$	18.2787			1.14242
$257$		−	28.0054i		−	1.74693i	−0.486888	−	0.873464i	$-0.661868\pi$
$257$		−	28.0054i		−	1.74693i	0.486888	−	0.873464i	$-0.338132\pi$
$258$			6.35847i			0.395861i
$259$	−0.766971			−0.0476572
$260$	−1.98851	+	1.42378i	−0.123322	+	0.0882993i
$261$	−17.9477			−1.11093
$262$			28.0503i			1.73295i
$263$			9.93706i			0.612746i	0.951912	+	0.306373i	$0.0991154\pi$
$263$			9.93706i			0.612746i	−0.951912	+	0.306373i	$0.900885\pi$
$264$	−0.0441907			−0.00271975
$265$	−1.30772	+	0.936333i	−0.0803326	+	0.0575185i
$266$	−7.32587			−0.449178
$267$		−	3.97912i		−	0.243518i
$268$		−	2.16589i		−	0.132303i
$269$	19.8870			1.21253			0.606266	−	0.795262i	$-0.292667\pi$
$269$	19.8870			1.21253			0.606266	+	0.795262i	$0.292667\pi$
$270$	5.25232	+	7.33559i	0.319646	+	0.446430i
$271$	7.60072			0.461711			0.230855	−	0.972988i	$-0.425848\pi$
$271$	7.60072			0.461711			0.230855	+	0.972988i	$0.425848\pi$
$272$			33.4901i			2.03064i
$273$			0.239663i			0.0145051i
$274$	−10.4624			−0.632055
$275$	−0.636968	+	1.87169i	−0.0384106	+	0.112867i
$276$	2.25342			0.135640
$277$		−	2.57322i		−	0.154610i	−0.997008	−	0.0773048i	$-0.975369\pi$
$277$		−	2.57322i		−	0.154610i	0.997008	−	0.0773048i	$-0.0246315\pi$
$278$		−	25.7388i		−	1.54371i
$279$	−25.9437			−1.55321
$280$	−0.476824	−	0.665951i	−0.0284957	−	0.0397982i
$281$	−4.36381			−0.260323			−0.130161	−	0.991493i	$-0.541550\pi$
$281$	−4.36381			−0.260323			−0.130161	+	0.991493i	$0.541550\pi$
$282$		−	9.40292i		−	0.559936i
$283$			9.97677i			0.593058i	0.955024	+	0.296529i	$0.0958291\pi$
$283$			9.97677i			0.593058i	−0.955024	+	0.296529i	$0.904171\pi$
$284$	25.7545			1.52825
$285$	2.07447	−	1.48533i	0.122881	−	0.0879835i
$286$	0.461129			0.0272671
$287$			6.95836i			0.410739i
$288$			22.3948i			1.31963i
$289$	−43.6853			−2.56972
$290$	22.2159	−	15.9067i	1.30456	−	0.934072i
$291$	0.0614678			0.00360330
$292$		−	8.99553i		−	0.526424i
$293$		−	8.13620i		−	0.475322i	−0.971348	−	0.237661i	$-0.923619\pi$
$293$		−	8.13620i		−	0.475322i	0.971348	−	0.237661i	$-0.0763807\pi$
$294$	−3.89978			−0.227440
$295$	−14.1113	−	19.7083i	−0.821589	−	1.14746i
$296$	0.212913			0.0123753
$297$		−	0.814465i		−	0.0472601i
$298$		−	11.9411i		−	0.691731i
$299$	2.08349			0.120491
$300$	−3.04774	−	1.03720i	−0.175961	−	0.0598827i
$301$	10.6390			0.613223
$302$			4.81753i			0.277217i
$303$			3.94396i			0.226574i
$304$	13.9967			0.802763
$305$	−3.70642	−	5.17654i	−0.212229	−	0.296408i
$306$	−43.9052			−2.50989
$307$		−	16.9541i		−	0.967624i	−0.875172	−	0.483812i	$-0.839252\pi$
$307$		−	16.9541i		−	0.967624i	0.875172	−	0.483812i	$-0.160748\pi$
$308$		−	0.834490i		−	0.0475495i
$309$	−3.27951			−0.186565
$310$	32.1135	−	22.9934i	1.82392	−	1.30594i
$311$	17.6072			0.998412			0.499206	−	0.866483i	$-0.333625\pi$
$311$	17.6072			0.998412			0.499206	+	0.866483i	$0.333625\pi$
$312$		−	0.0665313i		−	0.00376659i
$313$		−	0.775970i		−	0.0438604i	−0.999760	−	0.0219302i	$-0.993019\pi$
$313$		−	0.775970i		−	0.0438604i	0.999760	−	0.0219302i	$-0.00698116\pi$
$314$	−5.75349			−0.324688
$315$	6.00872	−	4.30227i	0.338553	−	0.242406i
$316$	24.0903			1.35519
$317$		−	20.2080i		−	1.13499i	−0.823376	−	0.567496i	$-0.807912\pi$
$317$		−	20.2080i		−	1.13499i	0.823376	−	0.567496i	$-0.192088\pi$
$318$			0.493803i			0.0276911i
$319$	−2.46661			−0.138104
$320$	−8.65541	−	12.0885i	−0.483852	−	0.675767i
$321$	−4.12157			−0.230044
$322$		−	7.87494i		−	0.438853i
$323$			25.3624i			1.41120i
$324$	−14.5317			−0.807318
$325$	−2.81792	−	0.958987i	−0.156310	−	0.0531950i
$326$	−46.1278			−2.55478
$327$		−	1.71551i		−	0.0948680i
$328$		−	1.93166i		−	0.106658i
$329$	−15.7330			−0.867389
$330$	0.353380	+	0.493544i	0.0194529	+	0.0271687i
$331$	3.47783			0.191159			0.0955794	−	0.995422i	$-0.469530\pi$
$331$	3.47783			0.191159			0.0955794	+	0.995422i	$0.469530\pi$
$332$			10.7725i			0.591219i
$333$			1.92107i			0.105274i
$334$	−30.0450			−1.64399
$335$	2.14334	−	1.53464i	0.117103	−	0.0838465i
$336$	−1.73070			−0.0944174
$337$		−	28.8161i		−	1.56971i	−0.619677	−	0.784857i	$-0.712737\pi$
$337$		−	28.8161i		−	1.56971i	0.619677	−	0.784857i	$-0.287263\pi$
$338$		−	24.7712i		−	1.34738i
$339$	−2.54466			−0.138207
$340$	26.0205	−	18.6308i	1.41116	−	1.01040i
$341$	−3.56554			−0.193085
$342$			18.3495i			0.992225i
$343$			14.5660i			0.786488i
$344$	−2.95343			−0.159238
$345$	1.59666	+	2.22995i	0.0859611	+	0.120057i
$346$	14.9454			0.803472
$347$		−	2.81946i		−	0.151356i	−0.997132	−	0.0756782i	$-0.975888\pi$
$347$		−	2.81946i		−	0.151356i	0.997132	−	0.0756782i	$-0.0241122\pi$
$348$		−	4.01648i		−	0.215306i
$349$	2.99211			0.160164			0.0800820	−	0.996788i	$-0.474482\pi$
$349$	2.99211			0.160164			0.0800820	+	0.996788i	$0.474482\pi$
$350$	−3.62467	+	10.6508i	−0.193747	+	0.569311i
$351$	1.22622			0.0654507
$352$			3.07780i			0.164047i
$353$		−	21.1653i		−	1.12652i	−0.826281	−	0.563259i	$-0.809547\pi$
$353$		−	21.1653i		−	1.12652i	0.826281	−	0.563259i	$-0.190453\pi$
$354$	−7.44198			−0.395537
$355$	18.2483	+	25.4863i	0.968520	+	1.35267i
$356$	−20.8594			−1.10555
$357$		−	3.13609i		−	0.165979i
$358$			26.3401i			1.39212i
$359$	21.1263			1.11500			0.557501	−	0.830176i	$-0.311760\pi$
$359$	21.1263			1.11500			0.557501	+	0.830176i	$0.311760\pi$
$360$	−1.66804	+	1.19432i	−0.0879135	+	0.0629464i
$361$	−8.40018			−0.442115
$362$		−	47.6108i		−	2.50237i
$363$			3.80032i			0.199465i
$364$	1.25637			0.0658515
$365$	8.90187	−	6.37378i	0.465945	−	0.333619i
$366$	−1.95469			−0.102173
$367$		−	7.88596i		−	0.411644i	−0.978589	−	0.205822i	$-0.934013\pi$
$367$		−	7.88596i		−	0.411644i	0.978589	−	0.205822i	$-0.0659868\pi$
$368$			15.0457i			0.784310i
$369$	17.4290			0.907315
$370$	−1.70261	−	2.37793i	−0.0885143	−	0.123623i
$371$	0.826233			0.0428959
$372$		−	5.80590i		−	0.301022i
$373$		−	37.2140i		−	1.92687i	−0.267944	−	0.963434i	$-0.586344\pi$
$373$		−	37.2140i		−	1.92687i	0.267944	−	0.963434i	$-0.413656\pi$
$374$	−6.03405			−0.312014
$375$	−1.13307	−	3.75091i	−0.0585117	−	0.193696i
$376$	4.36754			0.225238
$377$		−	3.71361i		−	0.191261i
$378$		−	4.63472i		−	0.238384i
$379$	2.84659			0.146219			0.0731097	−	0.997324i	$-0.476708\pi$
$379$	2.84659			0.146219			0.0731097	+	0.997324i	$0.476708\pi$
$380$	−7.78643	−	10.8748i	−0.399436	−	0.557868i
$381$	4.41150			0.226008
$382$		−	32.3799i		−	1.65670i
$383$		−	25.2530i		−	1.29037i	−0.764028	−	0.645183i	$-0.776781\pi$
$383$		−	25.2530i		−	1.29037i	0.764028	−	0.645183i	$-0.223219\pi$
$384$	0.891087			0.0454731
$385$	0.825801	−	0.591277i	0.0420867	−	0.0301343i
$386$	27.4388			1.39660
$387$		−	26.6481i		−	1.35460i
$388$		−	0.322227i		−	0.0163586i
$389$	24.4296			1.23863			0.619315	−	0.785143i	$-0.287411\pi$
$389$	24.4296			1.23863			0.619315	+	0.785143i	$0.287411\pi$
$390$	−0.743056	+	0.532031i	−0.0376261	+	0.0269404i
$391$	−27.2633			−1.37877
$392$		−	1.81140i		−	0.0914895i
$393$			5.01850i			0.253150i
$394$	−50.6133			−2.54986
$395$	17.0692	+	23.8395i	0.858845	+	1.19950i
$396$	−2.09019			−0.105036
$397$			38.2694i			1.92069i	0.278822	+	0.960343i	$0.410056\pi$
$397$			38.2694i			1.92069i	−0.278822	+	0.960343i	$0.589944\pi$
$398$		−	9.91947i		−	0.497218i
$399$	−1.31068			−0.0656159
$400$	6.92521	−	20.3493i	0.346260	−	1.01746i
$401$	−16.9783			−0.847856			−0.423928	−	0.905696i	$-0.639349\pi$
$401$	−16.9783			−0.847856			−0.423928	+	0.905696i	$0.639349\pi$
$402$		−	0.809338i		−	0.0403661i
$403$		−	5.36809i		−	0.267404i
$404$	20.6751			1.02862
$405$	−10.2964	−	14.3804i	−0.511634	−	0.714569i
$406$	−14.0363			−0.696609
$407$			0.264020i			0.0130870i
$408$			0.870588i			0.0431005i
$409$	22.7177			1.12332			0.561659	−	0.827369i	$-0.310163\pi$
$409$	22.7177			1.12332			0.561659	+	0.827369i	$0.310163\pi$
$410$	−21.5738	+	15.4470i	−1.06546	+	0.762871i
$411$	−1.87183			−0.0923306
$412$			17.1919i			0.846985i
$413$			12.4520i			0.612721i
$414$	−19.7247			−0.969418
$415$	−10.6604	+	7.63287i	−0.523297	+	0.374683i
$416$	−4.63379			−0.227190
$417$		−	4.60495i		−	0.225505i
$418$			2.52183i			0.123347i
$419$	16.7307			0.817346			0.408673	−	0.912681i	$-0.365992\pi$
$419$	16.7307			0.817346			0.408673	+	0.912681i	$0.365992\pi$
$420$	0.962800	+	1.34468i	0.0469798	+	0.0656139i
$421$	−24.0746			−1.17333			−0.586663	−	0.809831i	$-0.699559\pi$
$421$	−24.0746			−1.17333			−0.586663	+	0.809831i	$0.699559\pi$
$422$			24.0447i			1.17048i
$423$			39.4073i			1.91605i
$424$	−0.229365			−0.0111389
$425$	36.8736	+	12.5487i	1.78863	+	0.608703i
$426$	9.62377			0.466273
$427$			3.27060i			0.158275i
$428$			21.6062i			1.04437i
$429$	0.0825009			0.00398318
$430$	23.6177	+	32.9854i	1.13895	+	1.59070i
$431$	22.8880			1.10248			0.551239	−	0.834348i	$-0.314155\pi$
$431$	22.8880			1.10248			0.551239	+	0.834348i	$0.314155\pi$
$432$			8.85499i			0.426036i
$433$			27.4679i			1.32002i	0.751256	+	0.660011i	$0.229448\pi$
$433$			27.4679i			1.32002i	−0.751256	+	0.660011i	$0.770552\pi$
$434$	−20.2897			−0.973936
$435$	3.97466	−	2.84588i	0.190571	−	0.136449i
$436$	−8.99309			−0.430691
$437$			11.3943i			0.545062i
$438$		−	3.36140i		−	0.160614i
$439$	0.960670			0.0458503			0.0229251	−	0.999737i	$-0.492702\pi$
$439$	0.960670			0.0458503			0.0229251	+	0.999737i	$0.492702\pi$
$440$	−0.229245	+	0.164140i	−0.0109288	+	0.00782509i
$441$	16.3438			0.778278
$442$		−	9.08457i		−	0.432109i
$443$			22.0797i			1.04904i	0.851399	+	0.524519i	$0.175755\pi$
$443$			22.0797i			1.04904i	−0.851399	+	0.524519i	$0.824245\pi$
$444$	−0.429913			−0.0204028
$445$	−14.7799	−	20.6422i	−0.700635	−	0.978535i
$446$	−40.2330			−1.90509
$447$		−	2.13640i		−	0.101048i
$448$			7.63765i			0.360845i
$449$	−20.6202			−0.973128			−0.486564	−	0.873645i	$-0.661750\pi$
$449$	−20.6202			−0.973128			−0.486564	+	0.873645i	$0.661750\pi$
$450$	26.6777	+	9.07888i	1.25760	+	0.427982i
$451$	2.39533			0.112791
$452$			13.3397i			0.627446i
$453$			0.861907i			0.0404959i
$454$	30.6161			1.43689
$455$	0.890198	+	1.24329i	0.0417331	+	0.0582861i
$456$	0.363848			0.0170388
$457$			17.3096i			0.809711i	0.914381	+	0.404855i	$0.132678\pi$
$457$			17.3096i			0.809711i	−0.914381	+	0.404855i	$0.867322\pi$
$458$		−	15.0546i		−	0.703457i
$459$	−16.0456			−0.748943
$460$	11.6899	−	8.37002i	0.545044	−	0.390254i
$461$	9.15093			0.426201			0.213101	−	0.977030i	$-0.431644\pi$
$461$	9.15093			0.426201			0.213101	+	0.977030i	$0.431644\pi$
$462$		−	0.311827i		−	0.0145075i
$463$			14.2244i			0.661063i	0.943795	+	0.330532i	$0.107228\pi$
$463$			14.2244i			0.661063i	−0.943795	+	0.330532i	$0.892772\pi$
$464$	26.8174			1.24497
$465$	5.74545	−	4.11377i	0.266439	−	0.190771i
$466$	55.6562			2.57822
$467$		−	16.2381i		−	0.751411i	−0.926739	−	0.375705i	$-0.877400\pi$
$467$		−	16.2381i		−	0.751411i	0.926739	−	0.375705i	$-0.122600\pi$
$468$		−	3.14688i		−	0.145465i
$469$	−1.35419			−0.0625307
$470$	−34.9259	−	48.7789i	−1.61101	−	2.25000i
$471$	−1.02936			−0.0474305
$472$		−	3.45670i		−	0.159108i
$473$		−	3.66235i		−	0.168395i
$474$	9.00194			0.413473
$475$	5.24454	−	15.4107i	0.240636	−	0.707092i
$476$	−16.4401			−0.753529
$477$		−	2.06951i		−	0.0947562i
$478$		−	5.78367i		−	0.264539i
$479$	−32.4129			−1.48098			−0.740492	−	0.672066i	$-0.765407\pi$
$479$	−32.4129			−1.48098			−0.740492	+	0.672066i	$0.765407\pi$
$480$	−3.55104	−	4.95952i	−0.162082	−	0.226370i
$481$	−0.397495			−0.0181242
$482$		−	1.95888i		−	0.0892246i
$483$		−	1.40891i		−	0.0641077i
$484$	19.9221			0.905549
$485$	0.318872	−	0.228314i	0.0144792	−	0.0103672i
$486$	−17.5345			−0.795381
$487$			20.8714i			0.945772i	0.881123	+	0.472886i	$0.156788\pi$
$487$			20.8714i			0.945772i	−0.881123	+	0.472886i	$0.843212\pi$
$488$		−	0.907929i		−	0.0411000i
$489$	−8.25276			−0.373203
$490$	−20.2306	+	14.4852i	−0.913928	+	0.654376i
$491$	−1.44239			−0.0650941			−0.0325471	−	0.999470i	$-0.510362\pi$
$491$	−1.44239			−0.0650941			−0.0325471	+	0.999470i	$0.510362\pi$
$492$			3.90040i			0.175844i
$493$			48.5941i			2.18857i
$494$	−3.79675			−0.170824
$495$	−1.48100	−	2.06842i	−0.0665660	−	0.0929688i
$496$	38.7650			1.74060
$497$		−	16.1026i		−	0.722299i
$498$			4.02541i			0.180383i
$499$	−12.2754			−0.549524			−0.274762	−	0.961512i	$-0.588599\pi$
$499$	−12.2754			−0.549524			−0.274762	+	0.961512i	$0.588599\pi$
$500$	−19.6631	+	5.93982i	−0.879361	+	0.265637i
$501$	−5.37537			−0.240154
$502$		−	23.7376i		−	1.05946i
$503$			22.8011i			1.01665i	0.861165	+	0.508325i	$0.169735\pi$
$503$			22.8011i			1.01665i	−0.861165	+	0.508325i	$0.830265\pi$
$504$	1.05389			0.0469439
$505$	14.6493	+	20.4598i	0.651886	+	0.910450i
$506$	−2.71084			−0.120512
$507$		−	4.43183i		−	0.196825i
$508$		−	23.1260i		−	1.02605i
$509$	34.5559			1.53166			0.765831	−	0.643041i	$-0.222328\pi$
$509$	34.5559			1.53166			0.765831	+	0.643041i	$0.222328\pi$
$510$	9.72318	−	6.96184i	0.430550	−	0.308275i
$511$	−5.62431			−0.248805
$512$		−	30.7206i		−	1.35767i
$513$			6.70598i			0.296076i
$514$	−54.8592			−2.41974
$515$	−17.0129	+	12.1813i	−0.749678	+	0.536773i
$516$	5.96354			0.262530
$517$			5.41589i			0.238190i
$518$			1.50240i			0.0660118i
$519$	2.67390			0.117371
$520$	−0.247122	−	0.345140i	−0.0108370	−	0.0151354i
$521$	−16.4128			−0.719056			−0.359528	−	0.933134i	$-0.617062\pi$
$521$	−16.4128			−0.719056			−0.359528	+	0.933134i	$0.617062\pi$
$522$			35.1573i			1.53879i
$523$		−	22.5542i		−	0.986228i	−0.869965	−	0.493114i	$-0.835859\pi$
$523$		−	22.5542i		−	0.986228i	0.869965	−	0.493114i	$-0.164141\pi$
$524$	26.3081			1.14927
$525$	−0.648492	+	1.90555i	−0.0283025	+	0.0831650i
$526$	19.4655			0.848737
$527$			70.2437i			3.05986i
$528$			0.595770i			0.0259276i
$529$	10.7517			0.467467
$530$	1.83417	+	2.56167i	0.0796710	+	0.111272i
$531$	31.1890			1.35349
$532$			6.87086i			0.297889i
$533$			3.60628i			0.156205i
$534$	−7.79462			−0.337306
$535$	−21.3812	+	15.3090i	−0.924391	+	0.661868i
$536$	0.375927			0.0162376
$537$			4.71253i			0.203361i
$538$		−	38.9562i		−	1.67952i
$539$	2.24619			0.0967504
$540$	6.87997	−	4.92609i	0.296067	−	0.211985i
$541$	−23.0909			−0.992757			−0.496379	−	0.868106i	$-0.665337\pi$
$541$	−23.0909			−0.992757			−0.496379	+	0.868106i	$0.665337\pi$
$542$		−	14.8889i		−	0.639533i
$543$		−	8.51808i		−	0.365546i
$544$	60.6350			2.59970
$545$	−6.37205	−	8.89945i	−0.272948	−	0.381211i
$546$	0.469472			0.0200915
$547$		−	14.5566i		−	0.622395i	−0.950345	−	0.311198i	$-0.899270\pi$
$547$		−	14.5566i		−	0.622395i	0.950345	−	0.311198i	$-0.100730\pi$
$548$			9.81254i			0.419171i
$549$	8.19203			0.349627
$550$	3.66641	+	1.24774i	0.156336	+	0.0532040i
$551$	20.3091			0.865197
$552$			0.391118i			0.0166471i
$553$		−	15.0621i		−	0.640506i
$554$	−5.04063			−0.214156
$555$	−0.304615	−	0.425437i	−0.0129302	−	0.0180588i
$556$	−24.1402			−1.02377
$557$			8.58684i			0.363836i	0.983314	+	0.181918i	$0.0582306\pi$
$557$			8.58684i			0.363836i	−0.983314	+	0.181918i	$0.941769\pi$
$558$			50.8206i			2.15141i
$559$	5.51385			0.233211
$560$	−8.97823	+	6.42846i	−0.379400	+	0.271652i
$561$	−1.07956			−0.0455790
$562$			8.54818i			0.360583i
$563$			6.54355i			0.275778i	0.990448	+	0.137889i	$0.0440317\pi$
$563$			6.54355i			0.275778i	−0.990448	+	0.137889i	$0.955968\pi$
$564$	−8.81890			−0.371343
$565$	−13.2008	+	9.45182i	−0.555361	+	0.397641i
$566$	19.5433			0.821466
$567$			9.08573i			0.381565i
$568$			4.47012i			0.187562i
$569$	45.8495			1.92211			0.961056	−	0.276355i	$-0.0891265\pi$
$569$	45.8495			1.92211			0.961056	+	0.276355i	$0.0891265\pi$
$570$	−2.90959	−	4.06365i	−0.121869	−	0.170207i
$571$	−8.61219			−0.360409			−0.180205	−	0.983629i	$-0.557676\pi$
$571$	−8.61219			−0.360409			−0.180205	+	0.983629i	$0.557676\pi$
$572$		−	0.432488i		−	0.0180832i
$573$		−	5.79311i		−	0.242011i
$574$	13.6306			0.568930
$575$	16.5657	+	5.63761i	0.690839	+	0.235105i
$576$	19.1304			0.797100
$577$		−	8.25954i		−	0.343849i	−0.985110	−	0.171925i	$-0.945001\pi$
$577$		−	8.25954i		−	0.343849i	0.985110	−	0.171925i	$-0.0549986\pi$
$578$			85.5743i			3.55942i
$579$	4.90911			0.204015
$580$	−14.9187	−	20.8361i	−0.619465	−	0.865170i
$581$	6.73535			0.279429
$582$		−	0.120408i		−	0.00499107i
$583$		−	0.284420i		−	0.0117795i
$584$	1.56133			0.0646081
$585$	3.11412	−	2.22972i	0.128753	−	0.0921876i
$586$	−15.9378			−0.658386
$587$		−	9.63478i		−	0.397670i	−0.980033	−	0.198835i	$-0.936284\pi$
$587$		−	9.63478i		−	0.397670i	0.980033	−	0.198835i	$-0.0637158\pi$
$588$			3.65756i			0.150835i
$589$	29.3572			1.20964
$590$	−38.6063	+	27.6423i	−1.58940	+	1.13801i
$591$	−9.05527			−0.372484
$592$		−	2.87046i		−	0.117975i
$593$			22.0788i			0.906668i	0.891341	+	0.453334i	$0.149766\pi$
$593$			22.0788i			0.906668i	−0.891341	+	0.453334i	$0.850234\pi$
$594$	−1.59544			−0.0654617
$595$	−11.6486	−	16.2689i	−0.477546	−	0.666959i
$596$	−11.1995			−0.458747
$597$		−	1.77470i		−	0.0726337i
$598$		−	4.08131i		−	0.166897i
$599$	26.5132			1.08330			0.541650	−	0.840604i	$-0.317800\pi$
$599$	26.5132			1.08330			0.541650	+	0.840604i	$0.317800\pi$
$600$	0.180023	−	0.528987i	0.00734943	−	0.0215958i
$601$	31.0912			1.26823			0.634117	−	0.773237i	$-0.281364\pi$
$601$	31.0912			1.26823			0.634117	+	0.773237i	$0.281364\pi$
$602$		−	20.8406i		−	0.849399i
$603$			3.39190i			0.138129i
$604$	4.51831			0.183847
$605$	14.1158	+	19.7147i	0.573888	+	0.801515i
$606$	7.72574			0.313837
$607$		−	5.83591i		−	0.236872i	−0.992962	−	0.118436i	$-0.962212\pi$
$607$		−	5.83591i		−	0.236872i	0.992962	−	0.118436i	$-0.0377881\pi$
$608$		−	25.3414i		−	1.02773i
$609$	−2.51124			−0.101761
$610$	−10.1402	+	7.26044i	−0.410565	+	0.293967i
$611$	−8.15389			−0.329871
$612$			41.1782i			1.66453i
$613$		−	7.15782i		−	0.289101i	−0.989497	−	0.144551i	$-0.953826\pi$
$613$		−	7.15782i		−	0.289101i	0.989497	−	0.144551i	$-0.0461737\pi$
$614$	−33.2111			−1.34029
$615$	−3.85979	+	2.76363i	−0.155642	+	0.111440i
$616$	0.144840			0.00583576
$617$			7.92936i			0.319224i	0.987180	+	0.159612i	$0.0510243\pi$
$617$			7.92936i			0.319224i	−0.987180	+	0.159612i	$0.948976\pi$
$618$			6.42417i			0.258418i
$619$	27.1369			1.09072			0.545362	−	0.838200i	$-0.316392\pi$
$619$	27.1369			1.09072			0.545362	+	0.838200i	$0.316392\pi$
$620$	−21.5653	−	30.1189i	−0.866082	−	1.20960i
$621$	−7.20859			−0.289271
$622$		−	34.4904i		−	1.38294i
$623$			13.0420i			0.522517i
$624$	−0.896962			−0.0359072
$625$	−19.8103	−	15.2497i	−0.792410	−	0.609989i
$626$	−1.52003			−0.0607527
$627$			0.451184i			0.0180185i
$628$			5.39614i			0.215329i
$629$	5.20138			0.207393
$630$	−8.42764	−	11.7704i	−0.335765	−	0.468943i
$631$	21.9630			0.874333			0.437167	−	0.899380i	$-0.355982\pi$
$631$	21.9630			0.874333			0.437167	+	0.899380i	$0.355982\pi$
$632$			4.18129i			0.166323i
$633$			4.30185i			0.170983i
$634$	−39.5850			−1.57212
$635$	22.8853	−	16.3859i	0.908173	−	0.650256i
$636$	0.463132			0.0183644
$637$			3.38176i			0.133990i
$638$			4.83180i			0.191293i
$639$	−40.3329			−1.59554
$640$	4.62263	−	3.30983i	0.182726	−	0.130832i
$641$	8.90572			0.351755			0.175877	−	0.984412i	$-0.443724\pi$
$641$	8.90572			0.351755			0.175877	+	0.984412i	$0.443724\pi$
$642$			8.07367i			0.318642i
$643$			33.1787i			1.30844i	0.756303	+	0.654221i	$0.227003\pi$
$643$			33.1787i			1.30844i	−0.756303	+	0.654221i	$0.772997\pi$
$644$	−7.38582			−0.291042
$645$	4.22546	+	5.90145i	0.166377	+	0.232369i
$646$	49.6820			1.95471
$647$			45.8517i			1.80262i	0.433176	+	0.901309i	$0.357393\pi$
$647$			45.8517i			1.80262i	−0.433176	+	0.901309i	$0.642607\pi$
$648$		−	2.52223i		−	0.0990824i
$649$	4.28643			0.168257
$650$	−1.87854	+	5.51997i	−0.0736825	+	0.216511i
$651$	−3.63004			−0.142273
$652$			43.2628i			1.69430i
$653$			12.5825i			0.492390i	0.969220	+	0.246195i	$0.0791804\pi$
$653$			12.5825i			0.492390i	−0.969220	+	0.246195i	$0.920820\pi$
$654$	−3.36048			−0.131405
$655$	18.6406	+	26.0341i	0.728347	+	1.01724i
$656$	−26.0423			−1.01678
$657$			14.0875i			0.549605i
$658$			30.8191i			1.20145i
$659$	−47.3761			−1.84551			−0.922756	−	0.385385i	$-0.874069\pi$
$659$	−47.3761			−1.84551			−0.922756	+	0.385385i	$0.874069\pi$
$660$	0.462890	−	0.331431i	0.0180180	−	0.0129009i
$661$	14.2092			0.552675			0.276338	−	0.961061i	$-0.410879\pi$
$661$	14.2092			0.552675			0.276338	+	0.961061i	$0.410879\pi$
$662$		−	6.81266i		−	0.264781i
$663$		−	1.62533i		−	0.0631225i
$664$	−1.86975			−0.0725605
$665$	−6.79932	+	4.86834i	−0.263666	+	0.188786i
$666$	3.76314			0.145819
$667$			21.8313i			0.845310i
$668$			28.1789i			1.09027i
$669$	−7.19812			−0.278295
$670$	−3.00618	−	4.19855i	−0.116139	−	0.162204i
$671$	1.12586			0.0434634
$672$			3.13349i			0.120877i
$673$			4.54188i			0.175077i	0.996161	+	0.0875384i	$0.0279000\pi$
$673$			4.54188i			0.175077i	−0.996161	+	0.0875384i	$0.972100\pi$
$674$	−56.4473			−2.17427
$675$	9.74960	+	3.31796i	0.375262	+	0.127708i
$676$	−23.2326			−0.893563
$677$		−	33.7570i		−	1.29739i	−0.761050	−	0.648694i	$-0.775316\pi$
$677$		−	33.7570i		−	1.29739i	0.761050	−	0.648694i	$-0.224684\pi$
$678$			4.98469i			0.191436i
$679$	−0.201467			−0.00773161
$680$	3.23369	+	4.51629i	0.124006	+	0.173192i
$681$	5.47755			0.209900
$682$			6.98446i			0.267449i
$683$			17.9641i			0.687376i	0.939084	+	0.343688i	$0.111676\pi$
$683$			17.9641i			0.687376i	−0.939084	+	0.343688i	$0.888324\pi$
$684$	17.2098			0.658032
$685$	−9.71038	+	6.95267i	−0.371014	+	0.265648i
$686$	28.5330			1.08939
$687$		−	2.69344i		−	0.102761i
$688$			39.8176i			1.51803i
$689$	0.428209			0.0163135
$690$	4.36821	−	3.12766i	0.166295	−	0.119068i
$691$	−23.3108			−0.886785			−0.443392	−	0.896328i	$-0.646225\pi$
$691$	−23.3108			−0.886785			−0.443392	+	0.896328i	$0.646225\pi$
$692$		−	14.0172i		−	0.532853i
$693$			1.30686i			0.0496433i
$694$	−5.52298			−0.209650
$695$	−17.1045	−	23.8888i	−0.648810	−	0.906154i
$696$	0.697128			0.0264246
$697$		−	47.1897i		−	1.78744i
$698$		−	5.86119i		−	0.221849i
$699$	9.95749			0.376627
$700$	9.98931	+	3.39954i	0.377560	+	0.128490i
$701$	−31.4253			−1.18692			−0.593458	−	0.804865i	$-0.702238\pi$
$701$	−31.4253			−1.18692			−0.593458	+	0.804865i	$0.702238\pi$
$702$		−	2.40202i		−	0.0906583i
$703$		−	2.17383i		−	0.0819876i
$704$	2.62916			0.0990902
$705$	−6.24862	−	8.72707i	−0.235337	−	0.328681i
$706$	−41.4604			−1.56038
$707$		−	12.9268i		−	0.486161i
$708$			6.97975i			0.262315i
$709$	33.0144			1.23988			0.619941	−	0.784648i	$-0.287156\pi$
$709$	33.0144			1.23988			0.619941	+	0.784648i	$0.287156\pi$
$710$	49.9246	−	35.7463i	1.87364	−	1.34153i
$711$	−37.7268			−1.41486
$712$		−	3.62050i		−	0.135684i
$713$			31.5575i			1.18184i
$714$	−6.14322			−0.229904
$715$	0.427985	−	0.306439i	0.0160057	−	0.0114602i
$716$	24.7041			0.923236
$717$		−	1.03476i		−	0.0386438i
$718$		−	41.3839i		−	1.54443i
$719$	−29.1086			−1.08557			−0.542785	−	0.839872i	$-0.682630\pi$
$719$	−29.1086			−1.08557			−0.542785	+	0.839872i	$0.682630\pi$
$720$	16.1017	+	22.4882i	0.600074	+	0.838086i
$721$	10.7490			0.400312
$722$			16.4550i			0.612390i
$723$		−	0.350465i		−	0.0130339i
$724$	−44.6536			−1.65954
$725$	10.0485	−	29.5267i	0.373191	−	1.09660i
$726$	7.44437			0.276286
$727$			38.7905i			1.43866i	0.694668	+	0.719330i	$0.255551\pi$
$727$			38.7905i			1.43866i	−0.694668	+	0.719330i	$0.744449\pi$
$728$			0.218064i			0.00808198i
$729$	20.5919			0.762661
$730$	−12.4855	−	17.4377i	−0.462108	−	0.645398i
$731$	−72.1509			−2.66860
$732$			1.83328i			0.0677601i
$733$		−	41.6461i		−	1.53823i	−0.639108	−	0.769117i	$-0.720696\pi$
$733$		−	41.6461i		−	1.53823i	0.639108	−	0.769117i	$-0.279304\pi$
$734$	−15.4477			−0.570183
$735$	−3.61948	+	2.59156i	−0.133507	+	0.0955913i
$736$	27.2407			1.00411
$737$			0.466162i			0.0171713i
$738$		−	34.1412i		−	1.25676i
$739$	27.7225			1.01979			0.509894	−	0.860237i	$-0.329685\pi$
$739$	27.7225			1.01979			0.509894	+	0.860237i	$0.329685\pi$
$740$	−2.23023	+	1.59686i	−0.0819850	+	0.0587016i
$741$	−0.679280			−0.0249540
$742$		−	1.61849i		−	0.0594167i
$743$		−	0.633484i		−	0.0232403i	−0.999932	−	0.0116201i	$-0.996301\pi$
$743$		−	0.633484i		−	0.0232403i	0.999932	−	0.0116201i	$-0.00369889\pi$
$744$	1.00771			0.0369445
$745$	−7.93536	−	11.0828i	−0.290729	−	0.406044i
$746$	−72.8978			−2.66898
$747$		−	16.8704i		−	0.617254i
$748$			5.65928i			0.206924i
$749$	13.5089			0.493605
$750$	−7.34759	+	2.21956i	−0.268296	+	0.0810468i
$751$	−42.8427			−1.56335			−0.781677	−	0.623684i	$-0.785635\pi$
$751$	−42.8427			−1.56335			−0.781677	+	0.623684i	$0.785635\pi$
$752$		−	58.8823i		−	2.14722i
$753$		−	4.24692i		−	0.154766i
$754$	−7.27452			−0.264923
$755$	3.20144	+	4.47126i	0.116512	+	0.162726i
$756$	−4.34685			−0.158093
$757$		−	52.4715i		−	1.90711i	−0.301221	−	0.953554i	$-0.597394\pi$
$757$		−	52.4715i		−	1.90711i	0.301221	−	0.953554i	$-0.402606\pi$
$758$		−	5.57612i		−	0.202534i
$759$	−0.484999			−0.0176044
$760$	1.88751	−	1.35147i	0.0684672	−	0.0490228i
$761$	18.1523			0.658022			0.329011	−	0.944326i	$-0.393285\pi$
$761$	18.1523			0.658022			0.329011	+	0.944326i	$0.393285\pi$
$762$		−	8.64160i		−	0.313052i
$763$			5.62278i			0.203558i
$764$	−30.3687			−1.09870
$765$	−40.7495	+	29.1768i	−1.47330	+	1.05489i
$766$	−49.4676			−1.78734
$767$			6.45343i			0.233020i
$768$		−	6.40603i		−	0.231158i
$769$	1.59167			0.0573971			0.0286986	−	0.999588i	$-0.490864\pi$
$769$	1.59167			0.0573971			0.0286986	+	0.999588i	$0.490864\pi$
$770$	−1.15824	−	1.61765i	−0.0417401	−	0.0582959i
$771$	−9.81491			−0.353475
$772$		−	25.7346i		−	0.926209i
$773$			8.08891i			0.290938i	0.989363	+	0.145469i	$0.0464691\pi$
$773$			8.08891i			0.290938i	−0.989363	+	0.145469i	$0.953531\pi$
$774$	−52.2004			−1.87631
$775$	14.5252	−	42.6814i	0.521762	−	1.53316i
$776$	0.0559280			0.00200770
$777$			0.268796i			0.00964302i
$778$		−	47.8547i		−	1.71567i
$779$	−19.7222			−0.706619
$780$	0.498986	+	0.696904i	0.0178666	+	0.0249532i
$781$	−5.54310			−0.198348
$782$			53.4056i			1.90978i
$783$			12.8486i			0.459171i
$784$	−24.4210			−0.872177
$785$	−5.33995	+	3.82343i	−0.190591	+	0.136464i
$786$	9.83064			0.350647
$787$			13.2956i			0.473936i	0.971518	+	0.236968i	$0.0761536\pi$
$787$			13.2956i			0.473936i	−0.971518	+	0.236968i	$0.923846\pi$
$788$			47.4697i			1.69104i
$789$	3.48259			0.123984
$790$	46.6988	−	33.4365i	1.66147	−	1.18962i
$791$	8.34042			0.296551
$792$		−	0.362787i		−	0.0128911i
$793$			1.69504i			0.0601927i
$794$	74.9652			2.66041
$795$	0.328152	+	0.458310i	0.0116384	+	0.0162546i
$796$	−9.30337			−0.329749
$797$			15.6546i			0.554515i	0.960796	+	0.277258i	$0.0894255\pi$
$797$			15.6546i			0.554515i	−0.960796	+	0.277258i	$0.910574\pi$
$798$			2.56746i			0.0908871i
$799$	106.697			3.77467
$800$	−36.8430	−	12.5383i	−1.30260	−	0.443297i
$801$	32.6669			1.15423
$802$			33.2585i			1.17440i
$803$			1.93609i			0.0683233i
$804$	−0.759070			−0.0267703
$805$	−5.23322	−	7.30892i	−0.184447	−	0.257606i
$806$	−10.5155			−0.370391
$807$		−	6.96969i		−	0.245345i
$808$			3.58851i			0.126243i
$809$	52.3375			1.84009			0.920045	−	0.391813i	$-0.128152\pi$
$809$	52.3375			1.84009			0.920045	+	0.391813i	$0.128152\pi$
$810$	−28.1695	+	20.1695i	−0.989776	+	0.708684i
$811$	32.0875			1.12675			0.563373	−	0.826203i	$-0.309504\pi$
$811$	32.0875			1.12675			0.563373	+	0.826203i	$0.309504\pi$
$812$			13.1645i			0.461982i
$813$		−	2.66378i		−	0.0934230i
$814$	0.517183			0.0181273
$815$	−42.8123	+	30.6538i	−1.49965	+	1.07376i
$816$	11.7371			0.410881
$817$			30.1543i			1.05497i
$818$		−	44.5013i		−	1.55595i
$819$	−1.96754			−0.0687513
$820$	14.4875	+	20.2339i	0.505927	+	0.706597i
$821$	−37.5310			−1.30984			−0.654920	−	0.755698i	$-0.727298\pi$
$821$	−37.5310			−1.30984			−0.654920	+	0.755698i	$0.727298\pi$
$822$			3.66669i			0.127891i
$823$			36.0696i			1.25731i	0.777685	+	0.628654i	$0.216394\pi$
$823$			36.0696i			1.25731i	−0.777685	+	0.628654i	$0.783606\pi$
$824$	−2.98395			−0.103951
$825$	0.655961	+	0.223235i	0.0228376	+	0.00777204i
$826$	24.3919			0.848703
$827$		−	40.8256i		−	1.41964i	−0.704381	−	0.709822i	$-0.748775\pi$
$827$		−	40.8256i		−	1.41964i	0.704381	−	0.709822i	$-0.251225\pi$
$828$			18.4996i			0.642906i
$829$	−9.33570			−0.324242			−0.162121	−	0.986771i	$-0.551834\pi$
$829$	−9.33570			−0.324242			−0.162121	+	0.986771i	$0.551834\pi$
$830$	14.9519	+	20.8824i	0.518987	+	0.724838i
$831$	−0.901823			−0.0312839
$832$			3.95834i			0.137231i
$833$		−	44.2517i		−	1.53323i
$834$	−9.02055			−0.312356
$835$	−27.8855	+	19.9661i	−0.965017	+	0.690956i
$836$	2.36520			0.0818022
$837$			18.5728i			0.641971i
$838$		−	32.7733i		−	1.13214i
$839$	38.9297			1.34400			0.672002	−	0.740549i	$-0.265435\pi$
$839$	38.9297			1.34400			0.672002	+	0.740549i	$0.265435\pi$
$840$	−0.233393	+	0.167110i	−0.00805281	+	0.00576585i
$841$	9.91200			0.341793
$842$			47.1593i			1.62522i
$843$			1.52936i			0.0526740i
$844$	22.5513			0.776246
$845$	−16.4615	−	22.9907i	−0.566292	−	0.790906i
$846$	77.1941			2.65399
$847$		−	12.4560i		−	0.427992i
$848$			3.09226i			0.106189i
$849$	3.49651			0.120000
$850$	24.5815	−	72.2310i	0.843137	−	2.47750i
$851$	2.33676			0.0801030
$852$		−	9.02604i		−	0.309227i
$853$			18.9683i			0.649462i	0.945806	+	0.324731i	$0.105274\pi$
$853$			18.9683i			0.649462i	−0.945806	+	0.324731i	$0.894726\pi$
$854$	6.40671			0.219233
$855$	12.1940	+	17.0306i	0.417025	+	0.582434i
$856$	−3.75012			−0.128176
$857$		−	9.99880i		−	0.341552i	−0.985310	−	0.170776i	$-0.945372\pi$
$857$		−	9.99880i		−	0.341552i	0.985310	−	0.170776i	$-0.0546275\pi$
$858$		−	0.161609i		−	0.00551726i
$859$	−38.2098			−1.30370			−0.651852	−	0.758347i	$-0.726007\pi$
$859$	−38.2098			−1.30370			−0.651852	+	0.758347i	$0.726007\pi$
$860$	30.9367	−	22.1508i	1.05493	−	0.755336i
$861$	2.43866			0.0831094
$862$		−	44.8349i		−	1.52708i
$863$			30.2182i			1.02864i	0.857598	+	0.514320i	$0.171956\pi$
$863$			30.2182i			1.02864i	−0.857598	+	0.514320i	$0.828044\pi$
$864$	16.0322			0.545428
$865$	13.8712	−	9.93185i	0.471636	−	0.337693i
$866$	53.8063			1.82841
$867$			15.3102i			0.519961i
$868$			19.0295i			0.645903i
$869$	−5.18493			−0.175887
$870$	−5.57473	−	7.78589i	−0.189001	−	0.263966i
$871$	−0.701831			−0.0237806
$872$		−	1.56090i		−	0.0528588i
$873$			0.504625i			0.0170790i
$874$	22.3200			0.754985
$875$	3.71378	+	12.2940i	0.125549	+	0.415614i
$876$	−3.15262			−0.106517
$877$		−	51.3849i		−	1.73515i	−0.497310	−	0.867573i	$-0.665679\pi$
$877$		−	51.3849i		−	1.73515i	0.497310	−	0.867573i	$-0.334321\pi$
$878$		−	1.88184i		−	0.0635090i
$879$	−2.85145			−0.0961771
$880$	2.21291	+	3.09064i	0.0745972	+	0.104185i
$881$	−37.5670			−1.26566			−0.632832	−	0.774289i	$-0.718107\pi$
$881$	−37.5670			−1.26566			−0.632832	+	0.774289i	$0.718107\pi$
$882$		−	32.0156i		−	1.07802i
$883$			33.6934i			1.13387i	0.823761	+	0.566937i	$0.191872\pi$
$883$			33.6934i			1.13387i	−0.823761	+	0.566937i	$0.808128\pi$
$884$	−8.52033			−0.286570
$885$	−6.90708	+	4.94550i	−0.232179	+	0.166241i
$886$	43.2515			1.45306
$887$			3.08274i			0.103508i	0.998660	+	0.0517541i	$0.0164812\pi$
$887$			3.08274i			0.103508i	−0.998660	+	0.0517541i	$0.983519\pi$
$888$		−	0.0746187i		−	0.00250404i
$889$	−14.4592			−0.484945
$890$	−40.4356	+	28.9521i	−1.35541	+	0.970476i
$891$	3.12764			0.104780
$892$			37.7341i			1.26343i
$893$		−	44.5922i		−	1.49222i
$894$	−4.18494			−0.139965
$895$	17.5041	+	24.4469i	0.585097	+	0.817170i
$896$	−2.92064			−0.0975716
$897$		−	0.730191i		−	0.0243804i
$898$			40.3926i			1.34792i
$899$	56.2480			1.87598
$900$	8.51498	−	25.0207i	0.283833	−	0.834023i
$901$	−5.60328			−0.186672
$902$		−	4.69216i		−	0.156232i
$903$		−	3.72861i		−	0.124080i
$904$	−2.31533			−0.0770066
$905$	−31.6393	−	44.1887i	−1.05173	−	1.46888i
$906$	1.68837			0.0560925
$907$		−	15.3474i		−	0.509603i	−0.966993	−	0.254801i	$-0.917990\pi$
$907$		−	15.3474i		−	0.509603i	0.966993	−	0.254801i	$-0.0820101\pi$
$908$		−	28.7145i		−	0.952925i
$909$	−32.3783			−1.07392
$910$	2.43545	−	1.74379i	0.0807343	−	0.0578061i
$911$	1.34862			0.0446818			0.0223409	−	0.999750i	$-0.492888\pi$
$911$	1.34862			0.0446818			0.0223409	+	0.999750i	$0.492888\pi$
$912$		−	4.90534i		−	0.162432i
$913$		−	2.31856i		−	0.0767330i
$914$	33.9075			1.12156
$915$	−1.81419	+	1.29897i	−0.0599754	+	0.0429427i
$916$	−14.1196			−0.466525
$917$		−	16.4487i		−	0.543184i
$918$			31.4313i			1.03739i
$919$	−34.5210			−1.13874			−0.569371	−	0.822081i	$-0.692813\pi$
$919$	−34.5210			−1.13874			−0.569371	+	0.822081i	$0.692813\pi$
$920$	1.45276	+	2.02898i	0.0478960	+	0.0668934i
$921$	−5.94183			−0.195790
$922$		−	17.9256i		−	0.590348i
$923$		−	8.34541i		−	0.274693i
$924$	−0.292459			−0.00962121
$925$	−3.16046	−	1.07556i	−0.103915	−	0.0353642i
$926$	27.8639			0.915663
$927$		−	26.9234i		−	0.884282i
$928$		−	48.5538i		−	1.59386i
$929$	−25.8554			−0.848287			−0.424144	−	0.905595i	$-0.639425\pi$
$929$	−25.8554			−0.848287			−0.424144	+	0.905595i	$0.639425\pi$
$930$	−8.05838	−	11.2546i	−0.264245	−	0.369054i
$931$	−18.4943			−0.606125
$932$		−	52.1993i		−	1.70985i
$933$		−	6.17070i		−	0.202020i
$934$	−31.8086			−1.04081
$935$	−5.60035	+	4.00988i	−0.183151	+	0.131137i
$936$	0.546195			0.0178529
$937$			7.11017i			0.232279i	0.993233	+	0.116140i	$0.0370520\pi$
$937$			7.11017i			0.232279i	−0.993233	+	0.116140i	$0.962948\pi$
$938$			2.65270i			0.0866136i
$939$	−0.271950			−0.00887476
$940$	−45.7492	+	32.7566i	−1.49217	+	1.06840i
$941$	−16.9120			−0.551317			−0.275658	−	0.961256i	$-0.588896\pi$
$941$	−16.9120			−0.551317			−0.275658	+	0.961256i	$0.588896\pi$
$942$			2.01640i			0.0656978i
$943$		−	21.2003i		−	0.690377i
$944$	−46.6027			−1.51679
$945$	−3.07996	−	4.30159i	−0.100191	−	0.139931i
$946$	−7.17410			−0.233250
$947$		−	44.2056i		−	1.43649i	−0.695791	−	0.718244i	$-0.744946\pi$
$947$		−	44.2056i		−	1.43649i	0.695791	−	0.718244i	$-0.255054\pi$
$948$		−	8.44282i		−	0.274210i
$949$	−2.91489			−0.0946213
$950$	−30.1878	−	10.2734i	−0.979420	−	0.333314i
$951$	−7.08218			−0.229655
$952$		−	2.85345i		−	0.0924808i
$953$			39.1355i			1.26772i	0.773446	+	0.633862i	$0.218531\pi$
$953$			39.1355i			1.26772i	−0.773446	+	0.633862i	$0.781469\pi$
$954$	−4.05392			−0.131250
$955$	−21.5177	−	30.0525i	−0.696298	−	0.972477i
$956$	−5.42444			−0.175439
$957$			0.864462i			0.0279441i
$958$			63.4930i			2.05137i
$959$	6.13513			0.198114
$960$	−4.23659	+	3.03342i	−0.136735	+	0.0979031i
$961$	50.3075			1.62282
$962$			0.778645i			0.0251045i
$963$		−	33.8364i		−	1.09036i
$964$	−1.83721			−0.0591727
$965$	25.4666	−	18.2342i	0.819800	−	0.586981i
$966$	−2.75989			−0.0887980
$967$			38.7564i			1.24632i	0.782094	+	0.623161i	$0.214152\pi$
$967$			38.7564i			1.24632i	−0.782094	+	0.623161i	$0.785848\pi$
$968$			3.45781i			0.111138i
$969$	8.88865			0.285544
$970$	−0.447240	−	0.624633i	−0.0143600	−	0.0200558i
$971$	−35.9268			−1.15295			−0.576473	−	0.817116i	$-0.695572\pi$
$971$	−35.9268			−1.15295			−0.576473	+	0.817116i	$0.695572\pi$
$972$			16.4454i			0.527487i
$973$			15.0932i			0.483867i
$974$	40.8845			1.31003
$975$	−0.336091	+	0.987582i	−0.0107635	+	0.0316279i
$976$	−12.2405			−0.391810
$977$			1.39554i			0.0446474i	0.999751	+	0.0223237i	$0.00710644\pi$
$977$			1.39554i			0.0446474i	−0.999751	+	0.0223237i	$0.992894\pi$
$978$			16.1662i			0.516937i
$979$	4.48954			0.143486
$980$	13.5855	+	18.9741i	0.433974	+	0.606106i
$981$	14.0837			0.449656
$982$			2.82547i			0.0901643i
$983$		−	3.40982i		−	0.108756i	−0.998520	−	0.0543782i	$-0.982682\pi$
$983$		−	3.40982i		−	0.108756i	0.998520	−	0.0543782i	$-0.0173177\pi$
$984$	−0.676980			−0.0215813
$985$	−46.9755	+	33.6346i	−1.49676	+	1.07169i
$986$	95.1900			3.03147
$987$			5.51387i			0.175508i
$988$			3.56093i			0.113288i
$989$	−32.4143			−1.03072
$990$	−4.05180	+	2.90110i	−0.128775	+	0.0922031i
$991$	−21.1169			−0.670799			−0.335400	−	0.942076i	$-0.608871\pi$
$991$	−21.1169			−0.670799			−0.335400	+	0.942076i	$0.608871\pi$
$992$		−	70.1854i		−	2.22839i
$993$		−	1.21886i		−	0.0386793i
$994$	−31.5430			−1.00048
$995$	−6.59189	−	9.20650i	−0.208977	−	0.291866i
$996$	3.77539			0.119628
$997$			12.2441i			0.387775i	0.981024	+	0.193888i	$0.0621097\pi$
$997$			12.2441i			0.387775i	−0.981024	+	0.193888i	$0.937890\pi$
$998$			24.0461i			0.761166i
$999$	1.37528			0.0435118

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1205.2.b.c.724.6	✓	46
5.2	odd	4		6025.2.a.p.1.41		46
5.3	odd	4		6025.2.a.p.1.6		46
5.4	even	2	inner	1205.2.b.c.724.41	yes	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.b.c.724.6	✓	46	1.1	even	1	trivial
1205.2.b.c.724.41	yes	46	5.4	even	2	inner
6025.2.a.p.1.6		46	5.3	odd	4
6025.2.a.p.1.41		46	5.2	odd	4

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:	\( N \)	\(=\)	\( 1205 = 5 \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1205.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.95888i q^{2} -0.350465i q^{3} -1.83721 q^{4} +(-1.30176 - 1.81808i) q^{5} -0.686519 q^{6} +1.14869i q^{7} -0.318879i q^{8} +2.87717 q^{9} +O(q^{10})\)	\(q-1.95888i q^{2} -0.350465i q^{3} -1.83721 q^{4} +(-1.30176 - 1.81808i) q^{5} -0.686519 q^{6} +1.14869i q^{7} -0.318879i q^{8} +2.87717 q^{9} +(-3.56141 + 2.54999i) q^{10} +0.395421 q^{11} +0.643879i q^{12} +0.595326i q^{13} +2.25014 q^{14} +(-0.637175 + 0.456220i) q^{15} -4.29907 q^{16} -7.79008i q^{17} -5.63604i q^{18} -3.25574 q^{19} +(2.39160 + 3.34021i) q^{20} +0.402575 q^{21} -0.774582i q^{22} -3.49975i q^{23} -0.111756 q^{24} +(-1.61086 + 4.73341i) q^{25} +1.16617 q^{26} -2.05974i q^{27} -2.11038i q^{28} -6.23795 q^{29} +(0.893680 + 1.24815i) q^{30} -9.01707 q^{31} +7.78361i q^{32} -0.138581i q^{33} -15.2598 q^{34} +(2.08841 - 1.49531i) q^{35} -5.28598 q^{36} +0.667693i q^{37} +6.37760i q^{38} +0.208641 q^{39} +(-0.579750 + 0.415103i) q^{40} +6.05766 q^{41} -0.788596i q^{42} -9.26190i q^{43} -0.726472 q^{44} +(-3.74538 - 5.23095i) q^{45} -6.85559 q^{46} +13.6965i q^{47} +1.50667i q^{48} +5.68052 q^{49} +(9.27218 + 3.15548i) q^{50} -2.73015 q^{51} -1.09374i q^{52} -0.719285i q^{53} -4.03479 q^{54} +(-0.514741 - 0.718908i) q^{55} +0.366293 q^{56} +1.14102i q^{57} +12.2194i q^{58} +10.8402 q^{59} +(1.17063 - 0.838173i) q^{60} +2.84725 q^{61} +17.6634i q^{62} +3.30498i q^{63} +6.64902 q^{64} +(1.08235 - 0.774969i) q^{65} -0.271464 q^{66} +1.17890i q^{67} +14.3120i q^{68} -1.22654 q^{69} +(-2.92914 - 4.09095i) q^{70} -14.0182 q^{71} -0.917471i q^{72} +4.89629i q^{73} +1.30793 q^{74} +(1.65889 + 0.564550i) q^{75} +5.98148 q^{76} +0.454215i q^{77} -0.408703i q^{78} -13.1124 q^{79} +(5.59635 + 7.81608i) q^{80} +7.90966 q^{81} -11.8662i q^{82} -5.86352i q^{83} -0.739616 q^{84} +(-14.1630 + 10.1408i) q^{85} -18.1429 q^{86} +2.18618i q^{87} -0.126092i q^{88} +11.3538 q^{89} +(-10.2468 + 7.33675i) q^{90} -0.683844 q^{91} +6.42979i q^{92} +3.16017i q^{93} +26.8298 q^{94} +(4.23818 + 5.91920i) q^{95} +2.72788 q^{96} +0.175389i q^{97} -11.1275i q^{98} +1.13769 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9}+O(q^{10}) \) 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9	\( 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9} - 7 q^{10} - 64 q^{11} + 66 q^{14} + 5 q^{15} + 22 q^{16} - 2 q^{20} - 14 q^{21} + 50 q^{24} + 30 q^{25} - 60 q^{26} + 36 q^{29} + 7 q^{30} - 36 q^{31} - 12 q^{34} + 3 q^{35} - 34 q^{36} + 88 q^{39} - 30 q^{40} - 76 q^{41} + 100 q^{44} - 17 q^{45} - 12 q^{46} - 22 q^{49} - 14 q^{50} - 112 q^{51} + 26 q^{54} - 5 q^{55} - 120 q^{56} + 84 q^{59} - 33 q^{60} - 78 q^{61} - 28 q^{64} + 9 q^{65} - 2 q^{66} + 24 q^{69} + 88 q^{70} - 172 q^{71} + 16 q^{74} + 59 q^{75} - 18 q^{76} + 54 q^{79} + 63 q^{80} - 42 q^{81} - 44 q^{84} + 30 q^{85} - 80 q^{86} + 86 q^{89} + 17 q^{90} - 88 q^{91} - 4 q^{94} + q^{95} - 122 q^{96} + 148 q^{99}+O(q^{100}) \) 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9 - 7 * q^10 - 64 * q^11 + 66 * q^14 + 5 * q^15 + 22 * q^16 - 2 * q^20 - 14 * q^21 + 50 * q^24 + 30 * q^25 - 60 * q^26 + 36 * q^29 + 7 * q^30 - 36 * q^31 - 12 * q^34 + 3 * q^35 - 34 * q^36 + 88 * q^39 - 30 * q^40 - 76 * q^41 + 100 * q^44 - 17 * q^45 - 12 * q^46 - 22 * q^49 - 14 * q^50 - 112 * q^51 + 26 * q^54 - 5 * q^55 - 120 * q^56 + 84 * q^59 - 33 * q^60 - 78 * q^61 - 28 * q^64 + 9 * q^65 - 2 * q^66 + 24 * q^69 + 88 * q^70 - 172 * q^71 + 16 * q^74 + 59 * q^75 - 18 * q^76 + 54 * q^79 + 63 * q^80 - 42 * q^81 - 44 * q^84 + 30 * q^85 - 80 * q^86 + 86 * q^89 + 17 * q^90 - 88 * q^91 - 4 * q^94 + q^95 - 122 * q^96 + 148 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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