LMFDB - Embedded newform 755.2.b.d.454.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [755,2,Mod(454,755)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(755, 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("755.454");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 755 = 5 \cdot 151 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	755.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:	$6.02870535261$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			454.11
Character	$\chi$	$=$	755.454
Dual form			755.2.b.d.454.34

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.84174i q^{2} -2.98474i q^{3} -1.39202 q^{4} +(-2.09409 + 0.784079i) q^{5} -5.49712 q^{6} +5.05690i q^{7} -1.11975i q^{8} -5.90867 q^{9} +O(q^{10})$	\(q-1.84174i q^{2} -2.98474i q^{3} -1.39202 q^{4} +(-2.09409 + 0.784079i) q^{5} -5.49712 q^{6} +5.05690i q^{7} -1.11975i q^{8} -5.90867 q^{9} +(1.44407 + 3.85678i) q^{10} -3.23202 q^{11} +4.15481i q^{12} +2.63821i q^{13} +9.31351 q^{14} +(2.34027 + 6.25032i) q^{15} -4.84632 q^{16} +0.962699i q^{17} +10.8823i q^{18} +2.66915 q^{19} +(2.91501 - 1.09145i) q^{20} +15.0935 q^{21} +5.95255i q^{22} -5.80633i q^{23} -3.34216 q^{24} +(3.77044 - 3.28387i) q^{25} +4.85890 q^{26} +8.68164i q^{27} -7.03930i q^{28} -2.13649 q^{29} +(11.5115 - 4.31018i) q^{30} -6.68690 q^{31} +6.68619i q^{32} +9.64675i q^{33} +1.77304 q^{34} +(-3.96501 - 10.5896i) q^{35} +8.22498 q^{36} +7.66357i q^{37} -4.91590i q^{38} +7.87437 q^{39} +(0.877970 + 2.34485i) q^{40} -9.30711 q^{41} -27.7984i q^{42} +5.98510i q^{43} +4.49903 q^{44} +(12.3733 - 4.63286i) q^{45} -10.6938 q^{46} +7.77804i q^{47} +14.4650i q^{48} -18.5723 q^{49} +(-6.04804 - 6.94418i) q^{50} +2.87341 q^{51} -3.67243i q^{52} -4.36855i q^{53} +15.9893 q^{54} +(6.76815 - 2.53416i) q^{55} +5.66245 q^{56} -7.96673i q^{57} +3.93486i q^{58} -11.8099 q^{59} +(-3.25770 - 8.70055i) q^{60} +6.78935 q^{61} +12.3155i q^{62} -29.8796i q^{63} +2.62159 q^{64} +(-2.06856 - 5.52465i) q^{65} +17.7668 q^{66} -2.79731i q^{67} -1.34009i q^{68} -17.3304 q^{69} +(-19.5034 + 7.30253i) q^{70} +14.5320 q^{71} +6.61622i q^{72} -11.7767i q^{73} +14.1143 q^{74} +(-9.80148 - 11.2538i) q^{75} -3.71551 q^{76} -16.3440i q^{77} -14.5026i q^{78} -4.34146 q^{79} +(10.1486 - 3.79990i) q^{80} +8.18641 q^{81} +17.1413i q^{82} +8.54220i q^{83} -21.0105 q^{84} +(-0.754831 - 2.01598i) q^{85} +11.0230 q^{86} +6.37686i q^{87} +3.61905i q^{88} -12.4688 q^{89} +(-8.53255 - 22.7885i) q^{90} -13.3412 q^{91} +8.08251i q^{92} +19.9587i q^{93} +14.3251 q^{94} +(-5.58945 + 2.09283i) q^{95} +19.9565 q^{96} -6.10100i q^{97} +34.2053i q^{98} +19.0970 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 50 q^{4} - q^{5} + 16 q^{6} - 70 q^{9}+O(q^{10}) $ 44 * q - 50 * q^4 - q^5 + 16 * q^6 - 70 * q^9	$ 44 q - 50 q^{4} - q^{5} + 16 q^{6} - 70 q^{9} - q^{10} + 20 q^{11} - 30 q^{14} + 6 q^{15} + 58 q^{16} - 18 q^{19} - q^{20} + 30 q^{21} - 56 q^{24} + 7 q^{25} + 68 q^{26} - 30 q^{29} + 2 q^{30} + 12 q^{31} - 32 q^{34} + 3 q^{35} + 106 q^{36} - 10 q^{39} - 3 q^{40} + 102 q^{41} - 30 q^{44} - 19 q^{45} - 4 q^{46} - 84 q^{49} - 59 q^{50} + 48 q^{51} - 22 q^{54} - 23 q^{55} + 110 q^{56} - 78 q^{59} - 105 q^{60} + 28 q^{61} - 24 q^{64} - 31 q^{65} + 48 q^{66} + 18 q^{69} - 51 q^{70} + 78 q^{71} - 14 q^{74} - 55 q^{75} + 34 q^{76} - 14 q^{79} - 51 q^{80} + 160 q^{81} + 52 q^{84} - 26 q^{85} + 76 q^{86} - 182 q^{89} - 120 q^{90} + 30 q^{91} + 170 q^{94} - 30 q^{95} + 130 q^{96} - 20 q^{99}+O(q^{100}) $ 44 * q - 50 * q^4 - q^5 + 16 * q^6 - 70 * q^9 - q^10 + 20 * q^11 - 30 * q^14 + 6 * q^15 + 58 * q^16 - 18 * q^19 - q^20 + 30 * q^21 - 56 * q^24 + 7 * q^25 + 68 * q^26 - 30 * q^29 + 2 * q^30 + 12 * q^31 - 32 * q^34 + 3 * q^35 + 106 * q^36 - 10 * q^39 - 3 * q^40 + 102 * q^41 - 30 * q^44 - 19 * q^45 - 4 * q^46 - 84 * q^49 - 59 * q^50 + 48 * q^51 - 22 * q^54 - 23 * q^55 + 110 * q^56 - 78 * q^59 - 105 * q^60 + 28 * q^61 - 24 * q^64 - 31 * q^65 + 48 * q^66 + 18 * q^69 - 51 * q^70 + 78 * q^71 - 14 * q^74 - 55 * q^75 + 34 * q^76 - 14 * q^79 - 51 * q^80 + 160 * q^81 + 52 * q^84 - 26 * q^85 + 76 * q^86 - 182 * q^89 - 120 * q^90 + 30 * q^91 + 170 * q^94 - 30 * q^95 + 130 * q^96 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/755\mathbb{Z}\right)^\times$.

$n$	$6$	$152$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	1.84174i		−	1.30231i	−0.758945	−	0.651154i	$-0.774285\pi$
$2$		−	1.84174i		−	1.30231i	0.758945	−	0.651154i	$-0.225715\pi$
$3$		−	2.98474i		−	1.72324i	−0.507553	−	0.861620i	$-0.669450\pi$
$3$		−	2.98474i		−	1.72324i	0.507553	−	0.861620i	$-0.330550\pi$
$4$	−1.39202			−0.696009
$5$	−2.09409	+	0.784079i	−0.936506	+	0.350651i
$5$	−2.09409	+	0.784079i	−0.936506	+	0.350651i
$6$	−5.49712			−2.24419
$7$			5.05690i			1.91133i	0.294457	+	0.955665i	$0.404861\pi$
$7$			5.05690i			1.91133i	−0.294457	+	0.955665i	$0.595139\pi$
$8$		−	1.11975i		−	0.395891i
$9$	−5.90867			−1.96956
$10$	1.44407	+	3.85678i	0.456655	+	1.21962i
$11$	−3.23202			−0.974491			−0.487246	−	0.873265i	$-0.661998\pi$
$11$	−3.23202			−0.974491			−0.487246	+	0.873265i	$0.661998\pi$
$12$			4.15481i			1.19939i
$13$			2.63821i			0.731707i	0.930672	+	0.365854i	$0.119223\pi$
$13$			2.63821i			0.731707i	−0.930672	+	0.365854i	$0.880777\pi$
$14$	9.31351			2.48914
$15$	2.34027	+	6.25032i	0.604255	+	1.61383i
$16$	−4.84632			−1.21158
$17$			0.962699i			0.233489i	0.993162	+	0.116744i	$0.0372458\pi$
$17$			0.962699i			0.233489i	−0.993162	+	0.116744i	$0.962754\pi$
$18$			10.8823i			2.56497i
$19$	2.66915			0.612346			0.306173	−	0.951976i	$-0.400951\pi$
$19$	2.66915			0.612346			0.306173	+	0.951976i	$0.400951\pi$
$20$	2.91501	−	1.09145i	0.651817	−	0.244056i
$21$	15.0935			3.29368
$22$			5.95255i			1.26909i
$23$		−	5.80633i		−	1.21070i	−0.795958	−	0.605351i	$-0.793033\pi$
$23$		−	5.80633i		−	1.21070i	0.795958	−	0.605351i	$-0.206967\pi$
$24$	−3.34216			−0.682215
$25$	3.77044	−	3.28387i	0.754088	−	0.656773i
$26$	4.85890			0.952909
$27$			8.68164i			1.67078i
$28$		−	7.03930i		−	1.33030i
$29$	−2.13649			−0.396736			−0.198368	−	0.980128i	$-0.563564\pi$
$29$	−2.13649			−0.396736			−0.198368	+	0.980128i	$0.563564\pi$
$30$	11.5115	−	4.31018i	2.10170	−	0.786927i
$31$	−6.68690			−1.20100			−0.600501	−	0.799624i	$-0.705032\pi$
$31$	−6.68690			−1.20100			−0.600501	+	0.799624i	$0.705032\pi$
$32$			6.68619i			1.18196i
$33$			9.64675i			1.67928i
$34$	1.77304			0.304074
$35$	−3.96501	−	10.5896i	−0.670209	−	1.78997i
$36$	8.22498			1.37083
$37$			7.66357i			1.25988i	0.776643	+	0.629941i	$0.216921\pi$
$37$			7.66357i			1.25988i	−0.776643	+	0.629941i	$0.783079\pi$
$38$		−	4.91590i		−	0.797464i
$39$	7.87437			1.26091
$40$	0.877970	+	2.34485i	0.138819	+	0.370754i
$41$	−9.30711			−1.45353			−0.726763	−	0.686888i	$-0.758976\pi$
$41$	−9.30711			−1.45353			−0.726763	+	0.686888i	$0.758976\pi$
$42$		−	27.7984i		−	4.28939i
$43$			5.98510i			0.912720i	0.889795	+	0.456360i	$0.150847\pi$
$43$			5.98510i			0.912720i	−0.889795	+	0.456360i	$0.849153\pi$
$44$	4.49903			0.678255
$45$	12.3733	−	4.63286i	1.84450	−	0.690627i
$46$	−10.6938			−1.57671
$47$			7.77804i			1.13454i	0.823531	+	0.567272i	$0.192001\pi$
$47$			7.77804i			1.13454i	−0.823531	+	0.567272i	$0.807999\pi$
$48$			14.4650i			2.08784i
$49$	−18.5723			−2.65318
$50$	−6.04804	−	6.94418i	−0.855321	−	0.982056i
$51$	2.87341			0.402357
$52$		−	3.67243i		−	0.509275i
$53$		−	4.36855i		−	0.600066i	−0.953929	−	0.300033i	$-0.903002\pi$
$53$		−	4.36855i		−	0.600066i	0.953929	−	0.300033i	$-0.0969977\pi$
$54$	15.9893			2.17587
$55$	6.76815	−	2.53416i	0.912617	−	0.341706i
$56$	5.66245			0.756677
$57$		−	7.96673i		−	1.05522i
$58$			3.93486i			0.516672i
$59$	−11.8099			−1.53752			−0.768761	−	0.639536i	$-0.779127\pi$
$59$	−11.8099			−1.53752			−0.768761	+	0.639536i	$0.779127\pi$
$60$	−3.25770	−	8.70055i	−0.420567	−	1.12324i
$61$	6.78935			0.869287			0.434644	−	0.900602i	$-0.356874\pi$
$61$	6.78935			0.869287			0.434644	+	0.900602i	$0.356874\pi$
$62$			12.3155i			1.56408i
$63$		−	29.8796i		−	3.76447i
$64$	2.62159			0.327699
$65$	−2.06856	−	5.52465i	−0.256574	−	0.685249i
$66$	17.7668			2.18695
$67$		−	2.79731i		−	0.341746i	−0.985293	−	0.170873i	$-0.945341\pi$
$67$		−	2.79731i		−	0.341746i	0.985293	−	0.170873i	$-0.0546588\pi$
$68$		−	1.34009i		−	0.162510i
$69$	−17.3304			−2.08633
$70$	−19.5034	+	7.30253i	−2.33110	+	0.872819i
$71$	14.5320			1.72463			0.862314	−	0.506375i	$-0.169015\pi$
$71$	14.5320			1.72463			0.862314	+	0.506375i	$0.169015\pi$
$72$			6.61622i			0.779730i
$73$		−	11.7767i		−	1.37836i	−0.724588	−	0.689182i	$-0.757970\pi$
$73$		−	11.7767i		−	1.37836i	0.724588	−	0.689182i	$-0.242030\pi$
$74$	14.1143			1.64076
$75$	−9.80148	−	11.2538i	−1.13178	−	1.29948i
$76$	−3.71551			−0.426198
$77$		−	16.3440i		−	1.86257i
$78$		−	14.5026i		−	1.64209i
$79$	−4.34146			−0.488453			−0.244226	−	0.969718i	$-0.578534\pi$
$79$	−4.34146			−0.488453			−0.244226	+	0.969718i	$0.578534\pi$
$80$	10.1486	−	3.79990i	1.13465	−	0.424841i
$81$	8.18641			0.909601
$82$			17.1413i			1.89294i
$83$			8.54220i			0.937628i	0.883297	+	0.468814i	$0.155319\pi$
$83$			8.54220i			0.937628i	−0.883297	+	0.468814i	$0.844681\pi$
$84$	−21.0105			−2.29243
$85$	−0.754831	−	2.01598i	−0.0818730	−	0.218664i
$86$	11.0230			1.18864
$87$			6.37686i			0.683671i
$88$			3.61905i			0.385792i
$89$	−12.4688			−1.32169			−0.660843	−	0.750524i	$-0.729801\pi$
$89$	−12.4688			−1.32169			−0.660843	+	0.750524i	$0.729801\pi$
$90$	−8.53255	−	22.7885i	−0.899409	−	2.40211i
$91$	−13.3412			−1.39853
$92$			8.08251i			0.842660i
$93$			19.9587i			2.06962i
$94$	14.3251			1.47753
$95$	−5.58945	+	2.09283i	−0.573466	+	0.214719i
$96$	19.9565			2.03680
$97$		−	6.10100i		−	0.619463i	−0.950824	−	0.309731i	$-0.899761\pi$
$97$		−	6.10100i		−	0.619463i	0.950824	−	0.309731i	$-0.100239\pi$
$98$			34.2053i			3.45526i
$99$	19.0970			1.91932
$100$	−5.24852	+	4.57120i	−0.524852	+	0.457120i
$101$	11.7363			1.16780			0.583901	−	0.811825i	$-0.301526\pi$
$101$	11.7363			1.16780			0.583901	+	0.811825i	$0.301526\pi$
$102$		−	5.29207i		−	0.523993i
$103$		−	0.313015i		−	0.0308423i	−0.999881	−	0.0154211i	$-0.995091\pi$
$103$		−	0.313015i		−	0.0308423i	0.999881	−	0.0154211i	$-0.00490890\pi$
$104$	2.95413			0.289676
$105$	−31.6073	+	11.8345i	−3.08455	+	1.15493i
$106$	−8.04574			−0.781471
$107$			1.41461i			0.136755i	0.997660	+	0.0683777i	$0.0217823\pi$
$107$			1.41461i			0.136755i	−0.997660	+	0.0683777i	$0.978218\pi$
$108$		−	12.0850i		−	1.16288i
$109$	−6.61740			−0.633832			−0.316916	−	0.948454i	$-0.602647\pi$
$109$	−6.61740			−0.633832			−0.316916	+	0.948454i	$0.602647\pi$
$110$	−4.66727	−	12.4652i	−0.445007	−	1.18851i
$111$	22.8738			2.17108
$112$		−	24.5074i		−	2.31573i
$113$		−	11.7937i		−	1.10946i	−0.832031	−	0.554729i	$-0.812822\pi$
$113$		−	11.7937i		−	1.10946i	0.832031	−	0.554729i	$-0.187178\pi$
$114$	−14.6727			−1.37422
$115$	4.55262	+	12.1590i	0.424534	+	1.13383i
$116$	2.97403			0.276131
$117$		−	15.5883i		−	1.44114i
$118$			21.7509i			2.00233i
$119$	−4.86827			−0.446274
$120$	6.99878	−	2.62051i	0.638898	−	0.239219i
$121$	−0.554031			−0.0503664
$122$		−	12.5042i		−	1.13208i
$123$			27.7793i			2.50478i
$124$	9.30828			0.835908
$125$	−5.32084	+	9.83304i	−0.475911	+	0.879494i
$126$	−55.0305			−4.90251
$127$		−	2.29727i		−	0.203849i	−0.994792	−	0.101925i	$-0.967500\pi$
$127$		−	2.29727i		−	0.203849i	0.994792	−	0.101925i	$-0.0325001\pi$
$128$			8.54407i			0.755197i
$129$	17.8640			1.57284
$130$	−10.1750	+	3.80976i	−0.892406	+	0.334138i
$131$	−10.1826			−0.889654			−0.444827	−	0.895617i	$-0.646735\pi$
$131$	−10.1826			−0.889654			−0.444827	+	0.895617i	$0.646735\pi$
$132$		−	13.4284i		−	1.16880i
$133$			13.4977i			1.17039i
$134$	−5.15193			−0.445059
$135$	−6.80709	−	18.1801i	−0.585861	−	1.56470i
$136$	1.07798			0.0924360
$137$			5.86906i			0.501427i	0.968061	+	0.250714i	$0.0806653\pi$
$137$			5.86906i			0.501427i	−0.968061	+	0.250714i	$0.919335\pi$
$138$			31.9181i			2.71705i
$139$	13.6708			1.15954			0.579772	−	0.814779i	$-0.303142\pi$
$139$	13.6708			1.15954			0.579772	+	0.814779i	$0.303142\pi$
$140$	5.51936	+	14.7409i	0.466471	+	1.24584i
$141$	23.2154			1.95509
$142$		−	26.7641i		−	2.24600i
$143$		−	8.52675i		−	0.713043i
$144$	28.6353			2.38628
$145$	4.47400	−	1.67517i	0.371545	−	0.139116i
$146$	−21.6897			−1.79506
$147$			55.4334i			4.57207i
$148$		−	10.6678i		−	0.876889i
$149$	−10.4548			−0.856487			−0.428243	−	0.903663i	$-0.640867\pi$
$149$	−10.4548			−0.856487			−0.428243	+	0.903663i	$0.640867\pi$
$150$	−20.7266	+	18.0518i	−1.69232	+	1.47392i
$151$	−1.00000			−0.0813788
$151$	−1.00000			−0.0813788
$152$		−	2.98878i		−	0.242422i
$153$		−	5.68827i		−	0.459870i
$154$	−30.1015			−2.42565
$155$	14.0030	−	5.24305i	1.12475	−	0.421132i
$156$	−10.9613			−0.877603
$157$		−	2.95170i		−	0.235571i	−0.993039	−	0.117786i	$-0.962420\pi$
$157$		−	2.95170i		−	0.235571i	0.993039	−	0.117786i	$-0.0375796\pi$
$158$			7.99586i			0.636116i
$159$	−13.0390			−1.03406
$160$	−5.24249	−	14.0015i	−0.414456	−	1.10691i
$161$	29.3620			2.31405
$162$		−	15.0773i		−	1.18458i
$163$			4.60377i			0.360595i	0.983612	+	0.180298i	$0.0577061\pi$
$163$			4.60377i			0.360595i	−0.983612	+	0.180298i	$0.942294\pi$
$164$	12.9557			1.01167
$165$	−7.56381	−	20.2012i	−0.588842	−	1.57266i
$166$	15.7325			1.22108
$167$			1.39733i			0.108129i	0.998537	+	0.0540643i	$0.0172176\pi$
$167$			1.39733i			0.108129i	−0.998537	+	0.0540643i	$0.982782\pi$
$168$		−	16.9010i		−	1.30394i
$169$	6.03985			0.464604
$170$	−3.71292	+	1.39021i	−0.284768	+	0.106624i
$171$	−15.7712			−1.20605
$172$		−	8.33137i		−	0.635261i
$173$			4.09454i			0.311302i	0.987812	+	0.155651i	$0.0497475\pi$
$173$			4.09454i			0.311302i	−0.987812	+	0.155651i	$0.950253\pi$
$174$	11.7445			0.890351
$175$	16.6062	+	19.0668i	1.25531	+	1.44131i
$176$	15.6634			1.18067
$177$			35.2496i			2.64952i
$178$			22.9642i			1.72124i
$179$	15.6301			1.16825			0.584124	−	0.811665i	$-0.301438\pi$
$179$	15.6301			1.16825			0.584124	+	0.811665i	$0.301438\pi$
$180$	−17.2239	+	6.44903i	−1.28379	+	0.480682i
$181$	−11.1225			−0.826728			−0.413364	−	0.910566i	$-0.635646\pi$
$181$	−11.1225			−0.826728			−0.413364	+	0.910566i	$0.635646\pi$
$182$			24.5710i			1.82132i
$183$		−	20.2645i		−	1.49799i
$184$	−6.50162			−0.479306
$185$	−6.00884	−	16.0482i	−0.441779	−	1.17989i
$186$	36.7587			2.69528
$187$		−	3.11146i		−	0.227533i
$188$		−	10.8272i		−	0.789652i
$189$	−43.9022			−3.19341
$190$	3.85445	+	10.2943i	0.279631	+	0.746830i
$191$	−26.7979			−1.93903			−0.969514	−	0.245036i	$-0.921200\pi$
$191$	−26.7979			−1.93903			−0.969514	+	0.245036i	$0.921200\pi$
$192$		−	7.82477i		−	0.564704i
$193$		−	3.39331i		−	0.244256i	−0.992514	−	0.122128i	$-0.961028\pi$
$193$		−	3.39331i		−	0.244256i	0.992514	−	0.122128i	$-0.0389718\pi$
$194$	−11.2365			−0.806732
$195$	−16.4896	+	6.17412i	−1.18085	+	0.442138i
$196$	25.8529			1.84664
$197$			0.815746i			0.0581195i	0.999578	+	0.0290598i	$0.00925131\pi$
$197$			0.815746i			0.0581195i	−0.999578	+	0.0290598i	$0.990749\pi$
$198$		−	35.1717i		−	2.49954i
$199$	−8.09639			−0.573938			−0.286969	−	0.957940i	$-0.592648\pi$
$199$	−8.09639			−0.573938			−0.286969	+	0.957940i	$0.592648\pi$
$200$	−3.67710	−	4.22194i	−0.260010	−	0.298536i
$201$	−8.34925			−0.588911
$202$		−	21.6152i		−	1.52084i
$203$		−	10.8040i		−	0.758292i
$204$	−3.99983			−0.280044
$205$	19.4900	−	7.29751i	1.36124	−	0.509680i
$206$	−0.576493			−0.0401662
$207$			34.3077i			2.38455i
$208$		−	12.7856i		−	0.886523i
$209$	−8.62677			−0.596726
$210$	21.7961	+	58.2124i	1.50408	+	4.01704i
$211$	−19.6219			−1.35083			−0.675413	−	0.737440i	$-0.736034\pi$
$211$	−19.6219			−1.35083			−0.675413	+	0.737440i	$0.736034\pi$
$212$			6.08109i			0.417651i
$213$		−	43.3741i		−	2.97195i
$214$	2.60535			0.178098
$215$	−4.69279	−	12.5334i	−0.320046	−	0.854768i
$216$	9.72124			0.661447
$217$		−	33.8150i		−	2.29551i
$218$			12.1875i			0.825445i
$219$	−35.1505			−2.37525
$220$	−9.42139	+	3.52759i	−0.635190	+	0.237830i
$221$	−2.53980			−0.170845
$222$		−	42.1276i		−	2.82742i
$223$			13.2702i			0.888638i	0.895869	+	0.444319i	$0.146554\pi$
$223$			13.2702i			0.888638i	−0.895869	+	0.444319i	$0.853446\pi$
$224$	−33.8114			−2.25912
$225$	−22.2783	+	19.4033i	−1.48522	+	1.29355i
$226$	−21.7210			−1.44486
$227$		−	24.0761i		−	1.59799i	−0.601340	−	0.798994i	$-0.705366\pi$
$227$		−	24.0761i		−	1.59799i	0.601340	−	0.798994i	$-0.294634\pi$
$228$			11.0898i			0.734442i
$229$	25.6629			1.69585			0.847926	−	0.530114i	$-0.177851\pi$
$229$	25.6629			1.69585			0.847926	+	0.530114i	$0.177851\pi$
$230$	22.3937	−	8.38475i	1.47660	−	0.552874i
$231$	−48.7827			−3.20966
$232$			2.39233i			0.157064i
$233$			3.17110i			0.207746i	0.994591	+	0.103873i	$0.0331235\pi$
$233$			3.17110i			0.207746i	−0.994591	+	0.103873i	$0.966876\pi$
$234$	−28.7097			−1.87681
$235$	−6.09859	−	16.2879i	−0.397828	−	1.06251i
$236$	16.4396			1.07013
$237$			12.9581i			0.841721i
$238$			8.96611i			0.581186i
$239$	−13.1419			−0.850080			−0.425040	−	0.905174i	$-0.639740\pi$
$239$	−13.1419			−0.850080			−0.425040	+	0.905174i	$0.639740\pi$
$240$	−11.3417	−	30.2911i	−0.732104	−	1.95528i
$241$	17.2892			1.11370			0.556848	−	0.830615i	$-0.312011\pi$
$241$	17.2892			1.11370			0.556848	+	0.830615i	$0.312011\pi$
$242$			1.02038i			0.0655926i
$243$			1.61061i			0.103320i
$244$	−9.45090			−0.605032
$245$	38.8920	−	14.5621i	2.48472	−	0.930339i
$246$	51.1624			3.26199
$247$			7.04179i			0.448058i
$248$			7.48764i			0.475466i
$249$	25.4962			1.61576
$250$	18.1099	+	9.79962i	1.14537	+	0.619783i
$251$	−8.40752			−0.530678			−0.265339	−	0.964155i	$-0.585484\pi$
$251$	−8.40752			−0.530678			−0.265339	+	0.964155i	$0.585484\pi$
$252$			41.5929i			2.62011i
$253$			18.7662i			1.17982i
$254$	−4.23097			−0.265475
$255$	−6.01718	+	2.25298i	−0.376810	+	0.141087i
$256$	20.9792			1.31120
$257$			10.4318i			0.650718i	0.945591	+	0.325359i	$0.105485\pi$
$257$			10.4318i			0.650718i	−0.945591	+	0.325359i	$0.894515\pi$
$258$		−	32.9009i		−	2.04832i
$259$	−38.7539			−2.40805
$260$	2.87948	+	7.69041i	0.178578	+	0.476939i
$261$	12.6238			0.781394
$262$			18.7536i			1.15860i
$263$		−	21.7382i		−	1.34043i	−0.742165	−	0.670217i	$-0.766201\pi$
$263$		−	21.7382i		−	1.34043i	0.742165	−	0.670217i	$-0.233799\pi$
$264$	10.8019			0.664812
$265$	3.42528	+	9.14814i	0.210414	+	0.561966i
$266$	24.8592			1.52422
$267$			37.2160i			2.27758i
$268$			3.89391i			0.237858i
$269$	−0.0727155			−0.00443354			−0.00221677	−	0.999998i	$-0.500706\pi$
$269$	−0.0727155			−0.00443354			−0.00221677	+	0.999998i	$0.500706\pi$
$270$	−33.4832	+	12.5369i	−2.03772	+	0.762972i
$271$	−1.67322			−0.101641			−0.0508204	−	0.998708i	$-0.516184\pi$
$271$	−1.67322			−0.101641			−0.0508204	+	0.998708i	$0.516184\pi$
$272$		−	4.66555i		−	0.282890i
$273$			39.8199i			2.41001i
$274$	10.8093			0.653013
$275$	−12.1862	+	10.6135i	−0.734853	+	0.640020i
$276$	24.1242			1.45211
$277$		−	28.5946i		−	1.71808i	−0.511907	−	0.859041i	$-0.671061\pi$
$277$		−	28.5946i		−	1.71808i	0.511907	−	0.859041i	$-0.328939\pi$
$278$		−	25.1781i		−	1.51008i
$279$	39.5107			2.36544
$280$	−11.8577	+	4.43981i	−0.708633	+	0.265329i
$281$	30.4961			1.81925			0.909623	−	0.415435i	$-0.136371\pi$
$281$	30.4961			1.81925			0.909623	+	0.415435i	$0.136371\pi$
$282$		−	42.7568i		−	2.54613i
$283$			18.9475i			1.12631i	0.826351	+	0.563156i	$0.190413\pi$
$283$			18.9475i			1.12631i	−0.826351	+	0.563156i	$0.809587\pi$
$284$	−20.2287			−1.20036
$285$	6.24654	+	16.6831i	0.370013	+	0.988220i
$286$	−15.7041			−0.928602
$287$		−	47.0652i		−	2.77817i
$288$		−	39.5065i		−	2.32794i
$289$	16.0732			0.945483
$290$	−3.08524	−	8.23996i	−0.181171	−	0.483867i
$291$	−18.2099			−1.06748
$292$			16.3934i			0.959353i
$293$			10.8300i			0.632695i	0.948643	+	0.316347i	$0.102457\pi$
$293$			10.8300i			0.632695i	−0.948643	+	0.316347i	$0.897543\pi$
$294$	102.094			5.95424
$295$	24.7311	−	9.25992i	1.43990	−	0.539133i
$296$	8.58126			0.498776
$297$		−	28.0592i		−	1.62816i
$298$			19.2550i			1.11541i
$299$	15.3183			0.885880
$300$	13.6438	+	15.6655i	0.787727	+	0.904446i
$301$	−30.2661			−1.74451
$302$			1.84174i			0.105980i
$303$		−	35.0297i		−	2.01240i
$304$	−12.9356			−0.741907
$305$	−14.2175	+	5.32339i	−0.814093	+	0.304816i
$306$	−10.4763			−0.598892
$307$			7.89410i			0.450540i	0.974296	+	0.225270i	$0.0723265\pi$
$307$			7.89410i			0.450540i	−0.974296	+	0.225270i	$0.927674\pi$
$308$			22.7512i			1.29637i
$309$	−0.934268			−0.0531487
$310$	−9.65636	−	25.7899i	−0.548444	−	1.46477i
$311$	16.1482			0.915678			0.457839	−	0.889035i	$-0.348624\pi$
$311$	16.1482			0.915678			0.457839	+	0.889035i	$0.348624\pi$
$312$		−	8.81730i		−	0.499182i
$313$		−	15.5790i		−	0.880577i	−0.897856	−	0.440288i	$-0.854876\pi$
$313$		−	15.5790i		−	0.880577i	0.897856	−	0.440288i	$-0.145124\pi$
$314$	−5.43628			−0.306787
$315$	23.4279	+	62.5706i	1.32002	+	3.52545i
$316$	6.04339			0.339967
$317$			10.0333i			0.563525i	0.959484	+	0.281763i	$0.0909191\pi$
$317$			10.0333i			0.563525i	−0.959484	+	0.281763i	$0.909081\pi$
$318$			24.0144i			1.34666i
$319$	6.90517			0.386615
$320$	−5.48985	+	2.05553i	−0.306892	+	0.114908i
$321$	4.22224			0.235662
$322$		−	54.0773i		−	3.01361i
$323$			2.56959i			0.142976i
$324$	−11.3956			−0.633090
$325$	8.66352	+	9.94721i	0.480566	+	0.551772i
$326$	8.47896			0.469606
$327$			19.7512i			1.09224i
$328$			10.4216i			0.575438i
$329$	−39.3328			−2.16849
$330$	−37.2054	+	13.9306i	−2.04809	+	0.766854i
$331$	−20.6883			−1.13713			−0.568565	−	0.822638i	$-0.692501\pi$
$331$	−20.6883			−1.13713			−0.568565	+	0.822638i	$0.692501\pi$
$332$		−	11.8909i		−	0.652597i
$333$		−	45.2815i		−	2.48141i
$334$	2.57352			0.140817
$335$	2.19331	+	5.85783i	0.119833	+	0.320047i
$336$	−73.1481			−3.99056
$337$		−	19.1195i		−	1.04150i	−0.853708	−	0.520752i	$-0.825652\pi$
$337$		−	19.1195i		−	1.04150i	0.853708	−	0.520752i	$-0.174348\pi$
$338$		−	11.1239i		−	0.605058i
$339$	−35.2012			−1.91186
$340$	1.05074	+	2.80628i	0.0569843	+	0.152192i
$341$	21.6122			1.17037
$342$			29.0464i			1.57065i
$343$		−	58.5198i		−	3.15977i
$344$	6.70181			0.361337
$345$	36.2914	−	13.5884i	1.95386	−	0.731574i
$346$	7.54108			0.405411
$347$			4.25871i			0.228619i	0.993445	+	0.114310i	$0.0364656\pi$
$347$			4.25871i			0.228619i	−0.993445	+	0.114310i	$0.963534\pi$
$348$		−	8.87669i		−	0.475841i
$349$	−13.9631			−0.747427			−0.373713	−	0.927544i	$-0.621916\pi$
$349$	−13.9631			−0.747427			−0.373713	+	0.927544i	$0.621916\pi$
$350$	35.1161	−	30.5843i	1.87703	−	1.63480i
$351$	−22.9040			−1.22252
$352$		−	21.6099i		−	1.15181i
$353$			31.6236i			1.68315i	0.540137	+	0.841577i	$0.318372\pi$
$353$			31.6236i			1.68315i	−0.540137	+	0.841577i	$0.681628\pi$
$354$	64.9207			3.45049
$355$	−30.4313	+	11.3942i	−1.61512	+	0.604742i
$356$	17.3567			0.919905
$357$			14.5305i			0.769037i
$358$		−	28.7866i		−	1.52142i
$359$	13.0795			0.690312			0.345156	−	0.938545i	$-0.387826\pi$
$359$	13.0795			0.690312			0.345156	+	0.938545i	$0.387826\pi$
$360$	−5.18764	−	13.8550i	−0.273413	−	0.730222i
$361$	−11.8756			−0.625032
$362$			20.4848i			1.07666i
$363$			1.65364i			0.0867935i
$364$	18.5711			0.973392
$365$	9.23389	+	24.6616i	0.483324	+	1.29085i
$366$	−37.3219			−1.95085
$367$		−	9.66558i		−	0.504539i	−0.967657	−	0.252270i	$-0.918823\pi$
$367$		−	9.66558i		−	0.504539i	0.967657	−	0.252270i	$-0.0811770\pi$
$368$			28.1393i			1.46686i
$369$	54.9927			2.86281
$370$	−29.5567	+	11.0667i	−1.53658	+	0.575332i
$371$	22.0913			1.14692
$372$		−	27.7828i		−	1.44047i
$373$		−	32.1466i		−	1.66449i	−0.554409	−	0.832244i	$-0.687056\pi$
$373$		−	32.1466i		−	1.66449i	0.554409	−	0.832244i	$-0.312944\pi$
$374$	−5.73052			−0.296318
$375$	29.3491	+	15.8813i	1.51558	+	0.820109i
$376$	8.70944			0.449155
$377$		−	5.63650i		−	0.290294i
$378$			80.8565i			4.15881i
$379$	−23.6225			−1.21341			−0.606704	−	0.794928i	$-0.707508\pi$
$379$	−23.6225			−1.21341			−0.606704	+	0.794928i	$0.707508\pi$
$380$	7.78062	−	2.91325i	0.399137	−	0.149447i
$381$	−6.85674			−0.351282
$382$			49.3548i			2.52521i
$383$		−	7.84289i		−	0.400753i	−0.979719	−	0.200376i	$-0.935784\pi$
$383$		−	7.84289i		−	0.400753i	0.979719	−	0.200376i	$-0.0642165\pi$
$384$	25.5018			1.30139
$385$	12.8150	+	34.2259i	0.653113	+	1.74431i
$386$	−6.24961			−0.318097
$387$		−	35.3640i		−	1.79765i
$388$			8.49270i			0.431152i
$389$	27.2278			1.38050			0.690252	−	0.723569i	$-0.257499\pi$
$389$	27.2278			1.38050			0.690252	+	0.723569i	$0.257499\pi$
$390$	11.3711	+	30.3697i	0.575800	+	1.53783i
$391$	5.58974			0.282685
$392$			20.7962i			1.05037i
$393$			30.3923i			1.53309i
$394$	1.50240			0.0756896
$395$	9.09142	−	3.40405i	0.457439	−	0.171276i
$396$	−26.5833			−1.33586
$397$			23.0313i			1.15591i	0.816069	+	0.577955i	$0.196149\pi$
$397$			23.0313i			1.15591i	−0.816069	+	0.577955i	$0.803851\pi$
$398$			14.9115i			0.747444i
$399$	40.2870			2.01687
$400$	−18.2728	+	15.9147i	−0.913639	+	0.795733i
$401$	−4.16770			−0.208125			−0.104062	−	0.994571i	$-0.533184\pi$
$401$	−4.16770			−0.208125			−0.104062	+	0.994571i	$0.533184\pi$
$402$			15.3772i			0.766944i
$403$		−	17.6414i		−	0.878782i
$404$	−16.3371			−0.812800
$405$	−17.1431	+	6.41879i	−0.851847	+	0.318952i
$406$	−19.8982			−0.987531
$407$		−	24.7688i		−	1.22774i
$408$		−	3.21749i		−	0.159289i
$409$	10.3041			0.509503			0.254751	−	0.967007i	$-0.418006\pi$
$409$	10.3041			0.509503			0.254751	+	0.967007i	$0.418006\pi$
$410$	−13.4401	−	35.8955i	−0.663761	−	1.77275i
$411$	17.5176			0.864080
$412$			0.435722i			0.0214665i
$413$		−	59.7217i		−	2.93871i
$414$	63.1860			3.10542
$415$	−6.69776	−	17.8882i	−0.328780	−	0.878095i
$416$	−17.6396			−0.864850
$417$		−	40.8039i		−	1.99817i
$418$			15.8883i			0.777122i
$419$	−7.34838			−0.358992			−0.179496	−	0.983759i	$-0.557447\pi$
$419$	−7.34838			−0.358992			−0.179496	+	0.983759i	$0.557447\pi$
$420$	43.9979	−	16.4739i	2.14688	−	0.803842i
$421$	−32.4387			−1.58096			−0.790482	−	0.612485i	$-0.790170\pi$
$421$	−32.4387			−1.58096			−0.790482	+	0.612485i	$0.790170\pi$
$422$			36.1384i			1.75919i
$423$		−	45.9579i		−	2.23455i
$424$	−4.89167			−0.237561
$425$	3.16137	+	3.62980i	0.153349	+	0.176071i
$426$	−79.8840			−3.87039
$427$			34.3331i			1.66149i
$428$		−	1.96916i		−	0.0951830i
$429$	−25.4501			−1.22874
$430$	−23.0832	+	8.64292i	−1.11317	+	0.416798i
$431$	−31.9662			−1.53976			−0.769880	−	0.638189i	$-0.779684\pi$
$431$	−31.9662			−1.53976			−0.769880	+	0.638189i	$0.779684\pi$
$432$		−	42.0740i		−	2.02429i
$433$		−	1.35734i		−	0.0652296i	−0.999468	−	0.0326148i	$-0.989617\pi$
$433$		−	1.35734i		−	0.0652296i	0.999468	−	0.0326148i	$-0.0103835\pi$
$434$	−62.2785			−2.98946
$435$	−4.99996	−	13.3537i	−0.239730	−	0.640262i
$436$	9.21153			0.441152
$437$		−	15.4980i		−	0.741369i
$438$			64.7382i			3.09331i
$439$	1.96228			0.0936546			0.0468273	−	0.998903i	$-0.485089\pi$
$439$	1.96228			0.0936546			0.0468273	+	0.998903i	$0.485089\pi$
$440$	−2.83762	−	7.57862i	−0.135278	−	0.361297i
$441$	109.737			5.22559
$442$			4.67766i			0.222494i
$443$		−	4.47227i		−	0.212484i	−0.994340	−	0.106242i	$-0.966118\pi$
$443$		−	4.47227i		−	0.212484i	0.994340	−	0.106242i	$-0.0338818\pi$
$444$	−31.8407			−1.51109
$445$	26.1107	−	9.77649i	1.23777	−	0.463450i
$446$	24.4403			1.15728
$447$			31.2047i			1.47593i
$448$			13.2571i			0.626340i
$449$	10.1325			0.478181			0.239091	−	0.970997i	$-0.423151\pi$
$449$	10.1325			0.478181			0.239091	+	0.970997i	$0.423151\pi$
$450$	35.7359	+	41.0309i	1.68461	+	1.93422i
$451$	30.0808			1.41645
$452$			16.4170i			0.772193i
$453$			2.98474i			0.140235i
$454$	−44.3420			−2.08107
$455$	27.9376	−	10.4605i	1.30974	−	0.490397i
$456$	−8.92073			−0.417751
$457$		−	12.1189i		−	0.566900i	−0.958987	−	0.283450i	$-0.908521\pi$
$457$		−	12.1189i		−	0.566900i	0.958987	−	0.283450i	$-0.0914789\pi$
$458$		−	47.2645i		−	2.20852i
$459$	−8.35780			−0.390109
$460$	−6.33732	−	16.9255i	−0.295479	−	0.789156i
$461$	6.25228			0.291198			0.145599	−	0.989344i	$-0.453489\pi$
$461$	6.25228			0.291198			0.145599	+	0.989344i	$0.453489\pi$
$462$			89.8451i			4.17997i
$463$			27.1143i			1.26011i	0.776552	+	0.630053i	$0.216967\pi$
$463$			27.1143i			1.26011i	−0.776552	+	0.630053i	$0.783033\pi$
$464$	10.3541			0.480677
$465$	−15.6492	−	41.7953i	−0.725712	−	1.93821i
$466$	5.84035			0.270549
$467$			35.8718i			1.65995i	0.557800	+	0.829976i	$0.311646\pi$
$467$			35.8718i			1.65995i	−0.557800	+	0.829976i	$0.688354\pi$
$468$			21.6992i			1.00305i
$469$	14.1457			0.653189
$470$	−29.9982	+	11.2320i	−1.38371	+	0.518095i
$471$	−8.81006			−0.405946
$472$			13.2241i			0.608691i
$473$		−	19.3440i		−	0.889437i
$474$	23.8656			1.09618
$475$	10.0639	−	8.76514i	0.461763	−	0.402172i
$476$	6.77672			0.310610
$477$			25.8123i			1.18186i
$478$			24.2040i			1.10707i
$479$	20.4413			0.933989			0.466994	−	0.884260i	$-0.345337\pi$
$479$	20.4413			0.933989			0.466994	+	0.884260i	$0.345337\pi$
$480$	−41.7908	+	15.6475i	−1.90748	+	0.714207i
$481$	−20.2181			−0.921866
$482$		−	31.8423i		−	1.45038i
$483$		−	87.6380i		−	3.98767i
$484$	0.771220			0.0350555
$485$	4.78367	+	12.7761i	0.217215	+	0.580131i
$486$	2.96632			0.134555
$487$			17.8978i			0.811026i	0.914089	+	0.405513i	$0.132907\pi$
$487$			17.8978i			0.811026i	−0.914089	+	0.405513i	$0.867093\pi$
$488$		−	7.60236i		−	0.344143i
$489$	13.7411			0.621392
$490$	−26.8197	−	71.6291i	−1.21159	−	3.23587i
$491$	−8.08986			−0.365090			−0.182545	−	0.983197i	$-0.558434\pi$
$491$	−8.08986			−0.365090			−0.182545	+	0.983197i	$0.558434\pi$
$492$		−	38.6693i		−	1.74335i
$493$		−	2.05679i		−	0.0926333i
$494$	12.9692			0.583510
$495$	−39.9908	+	14.9735i	−1.79745	+	0.673010i
$496$	32.4069			1.45511
$497$			73.4867i			3.29633i
$498$		−	46.9575i		−	2.10422i
$499$	−42.2623			−1.89192			−0.945961	−	0.324280i	$-0.894878\pi$
$499$	−42.2623			−1.89192			−0.945961	+	0.324280i	$0.894878\pi$
$500$	7.40671	−	13.6878i	0.331238	−	0.612135i
$501$	4.17067			0.186332
$502$			15.4845i			0.691107i
$503$			16.3610i			0.729503i	0.931105	+	0.364751i	$0.118846\pi$
$503$			16.3610i			0.729503i	−0.931105	+	0.364751i	$0.881154\pi$
$504$	−33.4576			−1.49032
$505$	−24.5768	+	9.20215i	−1.09365	+	0.409490i
$506$	34.5625			1.53649
$507$		−	18.0274i		−	0.800625i
$508$			3.19783i			0.141881i
$509$	−6.13034			−0.271722			−0.135861	−	0.990728i	$-0.543380\pi$
$509$	−6.13034			−0.271722			−0.135861	+	0.990728i	$0.543380\pi$
$510$	4.14940	+	11.0821i	0.183739	+	0.490723i
$511$	59.5538			2.63451
$512$		−	21.5501i		−	0.952389i
$513$			23.1726i			1.02310i
$514$	19.2127			0.847435
$515$	0.245428	+	0.655482i	0.0108149	+	0.0288840i
$516$	−24.8670			−1.09471
$517$		−	25.1388i		−	1.10560i
$518$			71.3747i			3.13603i
$519$	12.2211			0.536448
$520$	−6.18622	+	2.31627i	−0.271284	+	0.101575i
$521$	26.1954			1.14764			0.573821	−	0.818981i	$-0.305460\pi$
$521$	26.1954			1.14764			0.573821	+	0.818981i	$0.305460\pi$
$522$		−	23.2498i		−	1.01762i
$523$			37.9641i			1.66005i	0.557724	+	0.830026i	$0.311675\pi$
$523$			37.9641i			1.66005i	−0.557724	+	0.830026i	$0.688325\pi$
$524$	14.1743			0.619207
$525$	56.9093	−	49.5651i	2.48373	−	2.16320i
$526$	−40.0362			−1.74566
$527$		−	6.43747i		−	0.280421i
$528$		−	46.7512i		−	2.03459i
$529$	−10.7134			−0.465801
$530$	16.8485	−	6.30849i	0.731853	−	0.274023i
$531$	69.7810			3.02824
$532$		−	18.7890i		−	0.814605i
$533$		−	24.5541i		−	1.06356i
$534$	68.5423			2.96612
$535$	−1.10916	−	2.96232i	−0.0479534	−	0.128072i
$536$	−3.13228			−0.135294
$537$		−	46.6518i		−	2.01317i
$538$			0.133923i			0.00577384i
$539$	60.0259			2.58550
$540$	9.47558	+	25.3071i	0.407764	+	1.08904i
$541$	8.08392			0.347555			0.173777	−	0.984785i	$-0.444403\pi$
$541$	8.08392			0.347555			0.173777	+	0.984785i	$0.444403\pi$
$542$			3.08164i			0.132368i
$543$			33.1977i			1.42465i
$544$	−6.43678			−0.275975
$545$	13.8574	−	5.18856i	0.593587	−	0.222253i
$546$	73.3380			3.13858
$547$			17.5638i			0.750974i	0.926828	+	0.375487i	$0.122525\pi$
$547$			17.5638i			0.750974i	−0.926828	+	0.375487i	$0.877475\pi$
$548$		−	8.16983i		−	0.348998i
$549$	−40.1161			−1.71211
$550$	19.5474	+	22.4438i	0.833503	+	0.957005i
$551$	−5.70261			−0.242939
$552$			19.4056i			0.825959i
$553$		−	21.9543i		−	0.933594i
$554$	−52.6639			−2.23747
$555$	−47.8997	+	17.9348i	−2.03323	+	0.761291i
$556$	−19.0300			−0.807053
$557$		−	8.57515i		−	0.363341i	−0.983359	−	0.181670i	$-0.941850\pi$
$557$		−	8.57515i		−	0.363341i	0.983359	−	0.181670i	$-0.0581504\pi$
$558$		−	72.7686i		−	3.08054i
$559$	−15.7900			−0.667844
$560$	19.2157	+	51.3207i	0.812012	+	2.16870i
$561$	−9.28691			−0.392094
$562$		−	56.1660i		−	2.36922i
$563$			24.2805i			1.02330i	0.859194	+	0.511650i	$0.170966\pi$
$563$			24.2805i			1.02330i	−0.859194	+	0.511650i	$0.829034\pi$
$564$	−32.3163			−1.36076
$565$	9.24719	+	24.6971i	0.389032	+	1.03902i
$566$	34.8964			1.46681
$567$			41.3979i			1.73855i
$568$		−	16.2721i		−	0.682764i
$569$	4.37817			0.183543			0.0917713	−	0.995780i	$-0.470747\pi$
$569$	4.37817			0.183543			0.0917713	+	0.995780i	$0.470747\pi$
$570$	30.7259	−	11.5045i	1.28697	−	0.481872i
$571$	−14.6212			−0.611879			−0.305940	−	0.952051i	$-0.598971\pi$
$571$	−14.6212			−0.611879			−0.305940	+	0.952051i	$0.598971\pi$
$572$			11.8694i			0.496284i
$573$			79.9848i			3.34141i
$574$	−86.6819			−3.61803
$575$	−19.0672	−	21.8924i	−0.795157	−	0.912977i
$576$	−15.4901			−0.645422
$577$			6.08768i			0.253433i	0.991939	+	0.126717i	$0.0404439\pi$
$577$			6.08768i			0.253433i	−0.991939	+	0.126717i	$0.959556\pi$
$578$		−	29.6027i		−	1.23131i
$579$	−10.1282			−0.420912
$580$	−6.22788	+	2.33187i	−0.258599	+	0.0968256i
$581$	−43.1971			−1.79212
$582$			33.5380i			1.39019i
$583$			14.1192i			0.584759i
$584$	−13.1870			−0.545681
$585$	12.2225	+	32.6434i	0.505337	+	1.34964i
$586$	19.9461			0.823964
$587$		−	9.85615i		−	0.406807i	−0.979095	−	0.203403i	$-0.934800\pi$
$587$		−	9.85615i		−	0.406807i	0.979095	−	0.203403i	$-0.0652003\pi$
$588$		−	77.1642i		−	3.18220i
$589$	−17.8484			−0.735429
$590$	−17.0544	−	45.5483i	−0.702118	−	1.87519i
$591$	2.43479			0.100154
$592$		−	37.1401i		−	1.52645i
$593$			4.56494i			0.187460i	0.995598	+	0.0937298i	$0.0298790\pi$
$593$			4.56494i			0.187460i	−0.995598	+	0.0937298i	$0.970121\pi$
$594$	−51.6779			−2.12037
$595$	10.1946	−	3.81711i	0.417938	−	0.156486i
$596$	14.5532			0.596122
$597$			24.1656i			0.989032i
$598$		−	28.2124i		−	1.15369i
$599$	−16.4944			−0.673945			−0.336972	−	0.941515i	$-0.609403\pi$
$599$	−16.4944			−0.673945			−0.336972	+	0.941515i	$0.609403\pi$
$600$	−12.6014	+	10.9752i	−0.514450	+	0.448060i
$601$	14.2844			0.582671			0.291335	−	0.956621i	$-0.405900\pi$
$601$	14.2844			0.582671			0.291335	+	0.956621i	$0.405900\pi$
$602$			55.7423i			2.27189i
$603$			16.5284i			0.673089i
$604$	1.39202			0.0566404
$605$	1.16019	−	0.434404i	0.0471685	−	0.0176610i
$606$	−64.5157			−2.62077
$607$		−	38.0372i		−	1.54388i	−0.635695	−	0.771941i	$-0.719286\pi$
$607$		−	38.0372i		−	1.54388i	0.635695	−	0.771941i	$-0.280714\pi$
$608$			17.8465i			0.723770i
$609$	−32.2471			−1.30672
$610$	9.80431	+	26.1850i	0.396965	+	1.06020i
$611$	−20.5201			−0.830154
$612$			7.91818i			0.320073i
$613$			31.4630i			1.27078i	0.772192	+	0.635390i	$0.219161\pi$
$613$			31.4630i			1.27078i	−0.772192	+	0.635390i	$0.780839\pi$
$614$	14.5389			0.586743
$615$	−21.7812	−	58.1724i	−0.878301	−	2.34574i
$616$	−18.3012			−0.737375
$617$		−	40.1256i		−	1.61540i	−0.589596	−	0.807698i	$-0.700713\pi$
$617$		−	40.1256i		−	1.61540i	0.589596	−	0.807698i	$-0.299287\pi$
$618$			1.72068i			0.0692160i
$619$	9.35080			0.375840			0.187920	−	0.982184i	$-0.439825\pi$
$619$	9.35080			0.375840			0.187920	+	0.982184i	$0.439825\pi$
$620$	−19.4924	+	7.29842i	−0.782833	+	0.293112i
$621$	50.4084			2.02282
$622$		−	29.7407i		−	1.19250i
$623$		−	63.0533i		−	2.52618i
$624$	−38.1617			−1.52769
$625$	3.43246	−	24.7632i	0.137298	−	0.990530i
$626$	−28.6925			−1.14678
$627$			25.7487i			1.02830i
$628$			4.10882i			0.163960i
$629$	−7.37771			−0.294168
$630$	115.239	−	43.1483i	4.59123	−	1.71907i
$631$	24.0164			0.956078			0.478039	−	0.878339i	$-0.341348\pi$
$631$	24.0164			0.956078			0.478039	+	0.878339i	$0.341348\pi$
$632$			4.86134i			0.193374i
$633$			58.5662i			2.32780i
$634$	18.4787			0.733884
$635$	1.80124	+	4.81069i	0.0714799	+	0.190906i
$636$	18.1505			0.719714
$637$		−	48.9975i		−	1.94135i
$638$		−	12.7176i		−	0.503493i
$639$	−85.8647			−3.39675
$640$	−6.69923	−	17.8921i	−0.264810	−	0.707246i
$641$	−32.8506			−1.29752			−0.648760	−	0.760993i	$-0.724712\pi$
$641$	−32.8506			−1.29752			−0.648760	+	0.760993i	$0.724712\pi$
$642$		−	7.77628i		−	0.306905i
$643$			10.3100i			0.406587i	0.979118	+	0.203293i	$0.0651645\pi$
$643$			10.3100i			0.406587i	−0.979118	+	0.203293i	$0.934835\pi$
$644$	−40.8724			−1.61060
$645$	−37.4088	+	14.0068i	−1.47297	+	0.551516i
$646$	4.73253			0.186199
$647$			12.1202i			0.476492i	0.971205	+	0.238246i	$0.0765725\pi$
$647$			12.1202i			0.476492i	−0.971205	+	0.238246i	$0.923427\pi$
$648$		−	9.16671i		−	0.360102i
$649$	38.1700			1.49830
$650$	18.3202	−	15.9560i	0.718578	−	0.625845i
$651$	−100.929			−3.95572
$652$		−	6.40853i		−	0.250977i
$653$		−	8.64560i		−	0.338328i	−0.985588	−	0.169164i	$-0.945893\pi$
$653$		−	8.64560i		−	0.338328i	0.985588	−	0.169164i	$-0.0541068\pi$
$654$	36.3767			1.42244
$655$	21.3232	−	7.98392i	0.833166	−	0.311958i
$656$	45.1053			1.76106
$657$			69.5850i			2.71477i
$658$			72.4408i			2.82404i
$659$	−36.0416			−1.40398			−0.701992	−	0.712185i	$-0.747706\pi$
$659$	−36.0416			−1.40398			−0.701992	+	0.712185i	$0.747706\pi$
$660$	10.5290	+	28.1204i	0.409839	+	1.09458i
$661$	−8.03680			−0.312595			−0.156298	−	0.987710i	$-0.549956\pi$
$661$	−8.03680			−0.312595			−0.156298	+	0.987710i	$0.549956\pi$
$662$			38.1025i			1.48089i
$663$			7.58064i			0.294408i
$664$	9.56511			0.371198
$665$	−10.5832	−	28.2653i	−0.410400	−	1.09608i
$666$	−83.3969			−3.23157
$667$			12.4051i			0.480329i
$668$		−	1.94511i		−	0.0752585i
$669$	39.6081			1.53134
$670$	10.7886	−	4.03952i	0.416801	−	0.156060i
$671$	−21.9433			−0.847113
$672$			100.918i			3.89300i
$673$		−	27.8218i		−	1.07245i	−0.844074	−	0.536226i	$-0.819849\pi$
$673$		−	27.8218i		−	1.07245i	0.844074	−	0.536226i	$-0.180151\pi$
$674$	−35.2131			−1.35636
$675$	28.5093	+	32.7336i	1.09732	+	1.25992i
$676$	−8.40758			−0.323369
$677$			3.91258i			0.150373i	0.997169	+	0.0751864i	$0.0239552\pi$
$677$			3.91258i			0.150373i	−0.997169	+	0.0751864i	$0.976045\pi$
$678$			64.8315i			2.48984i
$679$	30.8522			1.18400
$680$	−2.25739	+	0.845221i	−0.0865669	+	0.0324127i
$681$	−71.8609			−2.75372
$682$		−	39.8041i		−	1.52418i
$683$		−	5.49668i		−	0.210325i	−0.994455	−	0.105162i	$-0.966464\pi$
$683$		−	5.49668i		−	0.210325i	0.994455	−	0.105162i	$-0.0335362\pi$
$684$	21.9537			0.839422
$685$	−4.60180	−	12.2903i	−0.175826	−	0.469590i
$686$	−107.778			−4.11500
$687$		−	76.5971i		−	2.92236i
$688$		−	29.0057i		−	1.10583i
$689$	11.5251			0.439073
$690$	−25.0263	−	66.8394i	−0.952735	−	2.54453i
$691$	12.9847			0.493963			0.246981	−	0.969020i	$-0.420561\pi$
$691$	12.9847			0.493963			0.246981	+	0.969020i	$0.420561\pi$
$692$		−	5.69967i		−	0.216669i
$693$			96.5715i			3.66845i
$694$	7.84344			0.297733
$695$	−28.6280	+	10.7190i	−1.08592	+	0.406595i
$696$	7.14047			0.270659
$697$		−	8.95995i		−	0.339382i
$698$			25.7164i			0.973381i
$699$	9.46491			0.357996
$700$	−23.1161	−	26.5413i	−0.873706	−	1.00317i
$701$	−14.2069			−0.536586			−0.268293	−	0.963337i	$-0.586460\pi$
$701$	−14.2069			−0.536586			−0.268293	+	0.963337i	$0.586460\pi$
$702$			42.1832i			1.59210i
$703$			20.4552i			0.771484i
$704$	−8.47304			−0.319340
$705$	−48.6152	+	18.2027i	−1.83096	+	0.685554i
$706$	58.2425			2.19199
$707$			59.3491i			2.23205i
$708$		−	49.0680i		−	1.84409i
$709$	45.0815			1.69307			0.846535	−	0.532333i	$-0.178684\pi$
$709$	45.0815			1.69307			0.846535	+	0.532333i	$0.178684\pi$
$710$	20.9852	+	56.0466i	0.787560	+	2.10339i
$711$	25.6523			0.962036
$712$			13.9619i			0.523243i
$713$			38.8263i			1.45406i
$714$	26.7615			1.00152
$715$	6.68564	+	17.8558i	0.250029	+	0.667769i
$716$	−21.7574			−0.813111
$717$			39.2252i			1.46489i
$718$		−	24.0892i		−	0.898999i
$719$	−0.923124			−0.0344267			−0.0172134	−	0.999852i	$-0.505479\pi$
$719$	−0.923124			−0.0344267			−0.0172134	+	0.999852i	$0.505479\pi$
$720$	−59.9650	+	22.4524i	−2.23476	+	0.836750i
$721$	1.58289			0.0589498
$722$			21.8718i			0.813985i
$723$		−	51.6038i		−	1.91917i
$724$	15.4827			0.575410
$725$	−8.05550	+	7.01593i	−0.299174	+	0.260565i
$726$	3.04558			0.113032
$727$		−	25.0566i		−	0.929297i	−0.885495	−	0.464648i	$-0.846181\pi$
$727$		−	25.0566i		−	0.929297i	0.885495	−	0.464648i	$-0.153819\pi$
$728$			14.9387i			0.553666i
$729$	29.3665			1.08765
$730$	45.4203	−	17.0065i	1.68108	−	0.629437i
$731$	−5.76185			−0.213110
$732$			28.2085i			1.04262i
$733$			26.5992i			0.982466i	0.871028	+	0.491233i	$0.163454\pi$
$733$			26.5992i			0.982466i	−0.871028	+	0.491233i	$0.836546\pi$
$734$	−17.8015			−0.657066
$735$	−43.4641	−	116.083i	−1.60320	−	4.28177i
$736$	38.8222			1.43100
$737$			9.04098i			0.333029i
$738$		−	101.282i		−	3.72826i
$739$	−13.8867			−0.510831			−0.255415	−	0.966831i	$-0.582212\pi$
$739$	−13.8867			−0.510831			−0.255415	+	0.966831i	$0.582212\pi$
$740$	8.36441	+	22.3394i	0.307482	+	0.821212i
$741$	21.0179			0.772112
$742$		−	40.6865i		−	1.49365i
$743$			11.0207i			0.404311i	0.979353	+	0.202156i	$0.0647947\pi$
$743$			11.0207i			0.404311i	−0.979353	+	0.202156i	$0.935205\pi$
$744$	22.3487			0.819341
$745$	21.8932	−	8.19735i	0.802106	−	0.300328i
$746$	−59.2058			−2.16768
$747$		−	50.4731i		−	1.84671i
$748$			4.33121i			0.158365i
$749$	−7.15354			−0.261385
$750$	29.2493	−	54.0534i	1.06803	−	1.97375i
$751$	37.3015			1.36115			0.680576	−	0.732677i	$-0.261730\pi$
$751$	37.3015			1.36115			0.680576	+	0.732677i	$0.261730\pi$
$752$		−	37.6949i		−	1.37459i
$753$			25.0943i			0.914486i
$754$	−10.3810			−0.378053
$755$	2.09409	−	0.784079i	0.0762118	−	0.0285355i
$756$	61.1126			2.22264
$757$			26.9904i			0.980982i	0.871446	+	0.490491i	$0.163183\pi$
$757$			26.9904i			0.980982i	−0.871446	+	0.490491i	$0.836817\pi$
$758$			43.5066i			1.58023i
$759$	56.0122			2.03311
$760$	2.34344	+	6.25878i	0.0850054	+	0.227030i
$761$	11.9483			0.433124			0.216562	−	0.976269i	$-0.430516\pi$
$761$	11.9483			0.433124			0.216562	+	0.976269i	$0.430516\pi$
$762$			12.6284i			0.457477i
$763$		−	33.4635i		−	1.21146i
$764$	37.3031			1.34958
$765$	4.46005	+	11.9118i	0.161254	+	0.430671i
$766$	−14.4446			−0.521904
$767$		−	31.1571i		−	1.12502i
$768$		−	62.6174i		−	2.25951i
$769$	−17.4212			−0.628224			−0.314112	−	0.949386i	$-0.601707\pi$
$769$	−17.4212			−0.628224			−0.314112	+	0.949386i	$0.601707\pi$
$770$	63.0353	−	23.6019i	2.27163	−	0.850555i
$771$	31.1362			1.12134
$772$			4.72355i			0.170004i
$773$		−	27.8315i		−	1.00103i	−0.865728	−	0.500514i	$-0.833144\pi$
$773$		−	27.8315i		−	1.00103i	0.865728	−	0.500514i	$-0.166856\pi$
$774$	−65.1314			−2.34110
$775$	−25.2126	+	21.9589i	−0.905662	+	0.788786i
$776$	−6.83158			−0.245240
$777$			115.670i			4.14965i
$778$		−	50.1466i		−	1.79784i
$779$	−24.8421			−0.890061
$780$	22.9539	−	8.59449i	0.821881	−	0.307732i
$781$	−46.9676			−1.68063
$782$		−	10.2949i		−	0.368144i
$783$		−	18.5482i		−	0.662858i
$784$	90.0071			3.21454
$785$	2.31437	+	6.18113i	0.0826033	+	0.220614i
$786$	55.9748			1.99655
$787$			18.8301i			0.671222i	0.942001	+	0.335611i	$0.108943\pi$
$787$			18.8301i			0.671222i	−0.942001	+	0.335611i	$0.891057\pi$
$788$		−	1.13553i		−	0.0404517i
$789$	−64.8829			−2.30989
$790$	−6.26938	−	16.7441i	−0.223054	−	0.595727i
$791$	59.6396			2.12054
$792$		−	21.3838i		−	0.759840i
$793$			17.9117i			0.636064i
$794$	42.4178			1.50535
$795$	27.3048	−	10.2236i	0.968402	−	0.362593i
$796$	11.2703			0.399466
$797$			28.9018i			1.02375i	0.859059	+	0.511877i	$0.171050\pi$
$797$			28.9018i			1.02375i	−0.859059	+	0.511877i	$0.828950\pi$
$798$		−	74.1983i		−	2.62659i
$799$	−7.48791			−0.264903
$800$	21.9565	+	25.2099i	0.776281	+	0.891304i
$801$	73.6738			2.60314
$802$			7.67582i			0.271043i
$803$			38.0627i			1.34320i
$804$	11.6223			0.409887
$805$	−61.4868	+	23.0221i	−2.16712	+	0.811424i
$806$	−32.4910			−1.14445
$807$			0.217037i			0.00764006i
$808$		−	13.1417i		−	0.462322i
$809$	25.1413			0.883921			0.441960	−	0.897035i	$-0.354283\pi$
$809$	25.1413			0.883921			0.441960	+	0.897035i	$0.354283\pi$
$810$	11.8218	+	31.5732i	0.415374	+	1.10937i
$811$	35.2646			1.23831			0.619153	−	0.785270i	$-0.287476\pi$
$811$	35.2646			1.23831			0.619153	+	0.785270i	$0.287476\pi$
$812$			15.0394i			0.527778i
$813$			4.99413i			0.175152i
$814$	−45.6178			−1.59890
$815$	−3.60972	−	9.64072i	−0.126443	−	0.337700i
$816$	−13.9254			−0.487488
$817$			15.9752i			0.558900i
$818$		−	18.9774i		−	0.663530i
$819$	78.8286			2.75449
$820$	−27.1304	+	10.1583i	−0.947433	+	0.354742i
$821$	−39.1724			−1.36713			−0.683564	−	0.729891i	$-0.739571\pi$
$821$	−39.1724			−1.36713			−0.683564	+	0.729891i	$0.739571\pi$
$822$		−	32.2629i		−	1.12530i
$823$		−	28.0532i		−	0.977872i	−0.872320	−	0.488936i	$-0.837385\pi$
$823$		−	28.0532i		−	0.977872i	0.872320	−	0.488936i	$-0.162615\pi$
$824$	−0.350498			−0.0122102
$825$	31.6786	+	36.3725i	1.10291	+	1.26633i
$826$	−109.992			−3.82711
$827$		−	34.0186i		−	1.18294i	−0.806326	−	0.591471i	$-0.798547\pi$
$827$		−	34.0186i		−	1.18294i	0.806326	−	0.591471i	$-0.201453\pi$
$828$		−	47.7569i		−	1.65967i
$829$	4.58863			0.159370			0.0796849	−	0.996820i	$-0.474609\pi$
$829$	4.58863			0.159370			0.0796849	+	0.996820i	$0.474609\pi$
$830$	−32.9454	+	12.3355i	−1.14355	+	0.428173i
$831$	−85.3474			−2.96067
$832$			6.91630i			0.239780i
$833$		−	17.8795i		−	0.619487i
$834$	−75.1502			−2.60224
$835$	−1.09562	−	2.92614i	−0.0379154	−	0.101263i
$836$	12.0086			0.415326
$837$		−	58.0532i		−	2.00661i
$838$			13.5338i			0.467518i
$839$	−1.73062			−0.0597477			−0.0298738	−	0.999554i	$-0.509511\pi$
$839$	−1.73062			−0.0597477			−0.0298738	+	0.999554i	$0.509511\pi$
$840$	13.2517	+	35.3921i	0.457226	+	1.22115i
$841$	−24.4354			−0.842601
$842$			59.7437i			2.05890i
$843$		−	91.0230i		−	3.13500i
$844$	27.3140			0.940186
$845$	−12.6480	+	4.73572i	−0.435105	+	0.162914i
$846$	−84.6426			−2.91007
$847$		−	2.80168i		−	0.0962668i
$848$			21.1714i			0.727028i
$849$	56.5533			1.94091
$850$	6.68516	−	5.82244i	0.229299	−	0.199708i
$851$	44.4972			1.52534
$852$			60.3776i			2.06850i
$853$		−	46.6751i		−	1.59812i	−0.601248	−	0.799062i	$-0.705330\pi$
$853$		−	46.6751i		−	1.59812i	0.601248	−	0.799062i	$-0.294670\pi$
$854$	63.2327			2.16378
$855$	33.0263	−	12.3658i	1.12947	−	0.422903i
$856$	1.58401			0.0541402
$857$		−	37.2608i		−	1.27280i	−0.771358	−	0.636402i	$-0.780422\pi$
$857$		−	37.2608i		−	1.27280i	0.771358	−	0.636402i	$-0.219578\pi$
$858$			46.8726i			1.60020i
$859$	26.7493			0.912676			0.456338	−	0.889807i	$-0.349161\pi$
$859$	26.7493			0.912676			0.456338	+	0.889807i	$0.349161\pi$
$860$	6.53245	+	17.4466i	0.222755	+	0.594926i
$861$	−140.477			−4.78745
$862$			58.8736i			2.00524i
$863$			28.3909i			0.966439i	0.875499	+	0.483219i	$0.160533\pi$
$863$			28.3909i			0.966439i	−0.875499	+	0.483219i	$0.839467\pi$
$864$	−58.0470			−1.97480
$865$	−3.21044	−	8.57434i	−0.109158	−	0.291536i
$866$	−2.49987			−0.0849491
$867$		−	47.9744i		−	1.62929i
$868$			47.0711i			1.59770i
$869$	14.0317			0.475993
$870$	−24.5941	+	9.20863i	−0.833819	+	0.312202i
$871$	7.37989			0.250058
$872$			7.40982i			0.250928i
$873$			36.0488i			1.22007i
$874$	−28.5433			−0.965491
$875$	−49.7247	−	26.9070i	−1.68100	−	0.909622i
$876$	48.9301			1.65320
$877$			7.98475i			0.269626i	0.990871	+	0.134813i	$0.0430433\pi$
$877$			7.98475i			0.269626i	−0.990871	+	0.134813i	$0.956957\pi$
$878$		−	3.61402i		−	0.121967i
$879$	32.3247			1.09029
$880$	−32.8006	+	12.2814i	−1.10571	+	0.414004i
$881$	40.8606			1.37663			0.688314	−	0.725413i	$-0.258351\pi$
$881$	40.8606			1.37663			0.688314	+	0.725413i	$0.258351\pi$
$882$		−	202.108i		−	6.80533i
$883$			44.5009i			1.49757i	0.662811	+	0.748787i	$0.269363\pi$
$883$			44.5009i			1.49757i	−0.662811	+	0.748787i	$0.730637\pi$
$884$	3.53545			0.118910
$885$	−27.6384	−	73.8159i	−0.929056	−	2.48129i
$886$	−8.23677			−0.276720
$887$		−	7.27016i		−	0.244108i	−0.992523	−	0.122054i	$-0.961052\pi$
$887$		−	7.27016i		−	0.244108i	0.992523	−	0.122054i	$-0.0389481\pi$
$888$		−	25.6128i		−	0.859510i
$889$	11.6170			0.389623
$890$	−18.0058	−	48.0892i	−0.603555	−	1.61196i
$891$	−26.4587			−0.886398
$892$		−	18.4724i		−	0.618500i
$893$			20.7608i			0.694733i
$894$	57.4711			1.92212
$895$	−32.7308	+	12.2552i	−1.09407	+	0.409647i
$896$	−43.2065			−1.44343
$897$		−	45.7211i		−	1.52658i
$898$		−	18.6614i		−	0.622740i
$899$	14.2865			0.476480
$900$	31.0118	−	27.0097i	1.03373	−	0.900324i
$901$	4.20559			0.140109
$902$		−	55.4011i		−	1.84465i
$903$			90.3364i			3.00621i
$904$	−13.2060			−0.439224
$905$	23.2915	−	8.72091i	0.774236	−	0.289893i
$906$	5.49712			0.182630
$907$		−	10.7924i		−	0.358356i	−0.983817	−	0.179178i	$-0.942656\pi$
$907$		−	10.7924i		−	0.358356i	0.983817	−	0.179178i	$-0.0573439\pi$
$908$			33.5144i			1.11221i
$909$	−69.3458			−2.30005
$910$	−19.2656	−	51.4539i	−0.638648	−	1.70568i
$911$	−56.8032			−1.88197			−0.940987	−	0.338442i	$-0.890100\pi$
$911$	−56.8032			−1.88197			−0.940987	+	0.338442i	$0.890100\pi$
$912$			38.6094i			1.27848i
$913$		−	27.6086i		−	0.913711i
$914$	−22.3200			−0.738278
$915$	15.8889	+	42.4356i	0.525272	+	1.40288i
$916$	−35.7232			−1.18033
$917$		−	51.4922i		−	1.70042i
$918$			15.3929i			0.508042i
$919$	−31.4818			−1.03849			−0.519244	−	0.854626i	$-0.673786\pi$
$919$	−31.4818			−1.03849			−0.519244	+	0.854626i	$0.673786\pi$
$920$	13.6150	−	5.09778i	0.448873	−	0.168069i
$921$	23.5619			0.776389
$922$		−	11.5151i		−	0.379229i
$923$			38.3384i			1.26192i
$924$	67.9063			2.23395
$925$	25.1661	+	28.8950i	0.827457	+	0.950063i
$926$	49.9375			1.64105
$927$			1.84950i			0.0607457i
$928$		−	14.2849i		−	0.468926i
$929$	−28.0659			−0.920813			−0.460406	−	0.887708i	$-0.652296\pi$
$929$	−28.0659			−0.920813			−0.460406	+	0.887708i	$0.652296\pi$
$930$	−76.9761	+	28.8217i	−2.52415	+	0.945101i
$931$	−49.5722			−1.62466
$932$		−	4.41423i		−	0.144593i
$933$		−	48.1980i		−	1.57793i
$934$	66.0667			2.16177
$935$	2.43963	+	6.51569i	0.0797845	+	0.213086i
$936$	−17.4550			−0.570534
$937$		−	3.72766i		−	0.121777i	−0.998145	−	0.0608886i	$-0.980607\pi$
$937$		−	3.72766i		−	0.121777i	0.998145	−	0.0608886i	$-0.0193934\pi$
$938$		−	26.0528i		−	0.850654i
$939$	−46.4993			−1.51745
$940$	8.48935	+	22.6731i	0.276892	+	0.739514i
$941$	29.4897			0.961336			0.480668	−	0.876903i	$-0.340394\pi$
$941$	29.4897			0.961336			0.480668	+	0.876903i	$0.340394\pi$
$942$			16.2259i			0.528667i
$943$			54.0401i			1.75979i
$944$	57.2347			1.86283
$945$	91.9352	−	34.4228i	2.99065	−	1.11977i
$946$	−35.6267			−1.15832
$947$			32.0418i			1.04122i	0.853795	+	0.520609i	$0.174295\pi$
$947$			32.0418i			1.04122i	−0.853795	+	0.520609i	$0.825705\pi$
$948$		−	18.0379i		−	0.585845i
$949$	31.0695			1.00856
$950$	−16.1431	−	18.5351i	−0.523753	−	0.601358i
$951$	29.9467			0.971090
$952$			5.45124i			0.176676i
$953$		−	13.1189i		−	0.424963i	−0.977165	−	0.212481i	$-0.931846\pi$
$953$		−	13.1189i		−	0.424963i	0.977165	−	0.212481i	$-0.0681545\pi$
$954$	47.5397			1.53915
$955$	56.1173	−	21.0117i	1.81591	−	0.679921i
$956$	18.2938			0.591663
$957$		−	20.6101i		−	0.666231i
$958$		−	37.6477i		−	1.21634i
$959$	−29.6792			−0.958393
$960$	6.13523	+	16.3858i	0.198014	+	0.528849i
$961$	13.7146			0.442407
$962$			37.2365i			1.20055i
$963$		−	8.35846i		−	0.269348i
$964$	−24.0669			−0.775142
$965$	2.66062	+	7.10591i	0.0856485	+	0.228747i
$966$	−161.407			−5.19317
$967$			14.7521i			0.474396i	0.971461	+	0.237198i	$0.0762290\pi$
$967$			14.7521i			0.474396i	−0.971461	+	0.237198i	$0.923771\pi$
$968$			0.620375i			0.0199396i
$969$	7.66956			0.246382
$970$	23.5302	−	8.81028i	0.755510	−	0.282881i
$971$	−16.2551			−0.521652			−0.260826	−	0.965386i	$-0.583995\pi$
$971$	−16.2551			−0.521652			−0.260826	+	0.965386i	$0.583995\pi$
$972$		−	2.24199i		−	0.0719120i
$973$			69.1320i			2.21627i
$974$	32.9631			1.05621
$975$	29.6898	−	25.8584i	0.950836	−	0.828130i
$976$	−32.9034			−1.05321
$977$		−	23.2033i		−	0.742341i	−0.928565	−	0.371170i	$-0.878957\pi$
$977$		−	23.2033i		−	0.742341i	0.928565	−	0.371170i	$-0.121043\pi$
$978$		−	25.3075i		−	0.809245i
$979$	40.2993			1.28797
$980$	−54.1384	+	20.2707i	−1.72939	+	0.647524i
$981$	39.1000			1.24837
$982$			14.8994i			0.475460i
$983$			6.05085i			0.192992i	0.995333	+	0.0964961i	$0.0307635\pi$
$983$			6.05085i			0.192992i	−0.995333	+	0.0964961i	$0.969236\pi$
$984$	31.1058			0.991617
$985$	−0.639609	−	1.70825i	−0.0203796	−	0.0544293i
$986$	−3.78808			−0.120637
$987$			117.398i			3.73682i
$988$		−	9.80229i		−	0.311852i
$989$	34.7515			1.10503
$990$	27.5774	+	73.6528i	0.876467	+	2.34084i
$991$	14.0363			0.445878			0.222939	−	0.974832i	$-0.428435\pi$
$991$	14.0363			0.445878			0.222939	+	0.974832i	$0.428435\pi$
$992$		−	44.7098i		−	1.41954i
$993$			61.7491i			1.95955i
$994$	135.344			4.29284
$995$	16.9546	−	6.34820i	0.537496	−	0.201252i
$996$	−35.4912			−1.12458
$997$			14.0139i			0.443825i	0.975067	+	0.221913i	$0.0712299\pi$
$997$			14.0139i			0.443825i	−0.975067	+	0.221913i	$0.928770\pi$
$998$			77.8364i			2.46387i
$999$	−66.5323			−2.10499

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	755.2.b.d.454.11	✓	44
5.2	odd	4		3775.2.a.x.1.34		44
5.3	odd	4		3775.2.a.x.1.11		44
5.4	even	2	inner	755.2.b.d.454.34	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
755.2.b.d.454.11	✓	44	1.1	even	1	trivial
755.2.b.d.454.34	yes	44	5.4	even	2	inner
3775.2.a.x.1.11		44	5.3	odd	4
3775.2.a.x.1.34		44	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:	\( N \)	\(=\)	\( 755 = 5 \cdot 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	755.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.84174i q^{2} -2.98474i q^{3} -1.39202 q^{4} +(-2.09409 + 0.784079i) q^{5} -5.49712 q^{6} +5.05690i q^{7} -1.11975i q^{8} -5.90867 q^{9} +O(q^{10})\)	\(q-1.84174i q^{2} -2.98474i q^{3} -1.39202 q^{4} +(-2.09409 + 0.784079i) q^{5} -5.49712 q^{6} +5.05690i q^{7} -1.11975i q^{8} -5.90867 q^{9} +(1.44407 + 3.85678i) q^{10} -3.23202 q^{11} +4.15481i q^{12} +2.63821i q^{13} +9.31351 q^{14} +(2.34027 + 6.25032i) q^{15} -4.84632 q^{16} +0.962699i q^{17} +10.8823i q^{18} +2.66915 q^{19} +(2.91501 - 1.09145i) q^{20} +15.0935 q^{21} +5.95255i q^{22} -5.80633i q^{23} -3.34216 q^{24} +(3.77044 - 3.28387i) q^{25} +4.85890 q^{26} +8.68164i q^{27} -7.03930i q^{28} -2.13649 q^{29} +(11.5115 - 4.31018i) q^{30} -6.68690 q^{31} +6.68619i q^{32} +9.64675i q^{33} +1.77304 q^{34} +(-3.96501 - 10.5896i) q^{35} +8.22498 q^{36} +7.66357i q^{37} -4.91590i q^{38} +7.87437 q^{39} +(0.877970 + 2.34485i) q^{40} -9.30711 q^{41} -27.7984i q^{42} +5.98510i q^{43} +4.49903 q^{44} +(12.3733 - 4.63286i) q^{45} -10.6938 q^{46} +7.77804i q^{47} +14.4650i q^{48} -18.5723 q^{49} +(-6.04804 - 6.94418i) q^{50} +2.87341 q^{51} -3.67243i q^{52} -4.36855i q^{53} +15.9893 q^{54} +(6.76815 - 2.53416i) q^{55} +5.66245 q^{56} -7.96673i q^{57} +3.93486i q^{58} -11.8099 q^{59} +(-3.25770 - 8.70055i) q^{60} +6.78935 q^{61} +12.3155i q^{62} -29.8796i q^{63} +2.62159 q^{64} +(-2.06856 - 5.52465i) q^{65} +17.7668 q^{66} -2.79731i q^{67} -1.34009i q^{68} -17.3304 q^{69} +(-19.5034 + 7.30253i) q^{70} +14.5320 q^{71} +6.61622i q^{72} -11.7767i q^{73} +14.1143 q^{74} +(-9.80148 - 11.2538i) q^{75} -3.71551 q^{76} -16.3440i q^{77} -14.5026i q^{78} -4.34146 q^{79} +(10.1486 - 3.79990i) q^{80} +8.18641 q^{81} +17.1413i q^{82} +8.54220i q^{83} -21.0105 q^{84} +(-0.754831 - 2.01598i) q^{85} +11.0230 q^{86} +6.37686i q^{87} +3.61905i q^{88} -12.4688 q^{89} +(-8.53255 - 22.7885i) q^{90} -13.3412 q^{91} +8.08251i q^{92} +19.9587i q^{93} +14.3251 q^{94} +(-5.58945 + 2.09283i) q^{95} +19.9565 q^{96} -6.10100i q^{97} +34.2053i q^{98} +19.0970 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 50 q^{4} - q^{5} + 16 q^{6} - 70 q^{9}+O(q^{10}) \) 44 * q - 50 * q^4 - q^5 + 16 * q^6 - 70 * q^9	\( 44 q - 50 q^{4} - q^{5} + 16 q^{6} - 70 q^{9} - q^{10} + 20 q^{11} - 30 q^{14} + 6 q^{15} + 58 q^{16} - 18 q^{19} - q^{20} + 30 q^{21} - 56 q^{24} + 7 q^{25} + 68 q^{26} - 30 q^{29} + 2 q^{30} + 12 q^{31} - 32 q^{34} + 3 q^{35} + 106 q^{36} - 10 q^{39} - 3 q^{40} + 102 q^{41} - 30 q^{44} - 19 q^{45} - 4 q^{46} - 84 q^{49} - 59 q^{50} + 48 q^{51} - 22 q^{54} - 23 q^{55} + 110 q^{56} - 78 q^{59} - 105 q^{60} + 28 q^{61} - 24 q^{64} - 31 q^{65} + 48 q^{66} + 18 q^{69} - 51 q^{70} + 78 q^{71} - 14 q^{74} - 55 q^{75} + 34 q^{76} - 14 q^{79} - 51 q^{80} + 160 q^{81} + 52 q^{84} - 26 q^{85} + 76 q^{86} - 182 q^{89} - 120 q^{90} + 30 q^{91} + 170 q^{94} - 30 q^{95} + 130 q^{96} - 20 q^{99}+O(q^{100}) \) 44 * q - 50 * q^4 - q^5 + 16 * q^6 - 70 * q^9 - q^10 + 20 * q^11 - 30 * q^14 + 6 * q^15 + 58 * q^16 - 18 * q^19 - q^20 + 30 * q^21 - 56 * q^24 + 7 * q^25 + 68 * q^26 - 30 * q^29 + 2 * q^30 + 12 * q^31 - 32 * q^34 + 3 * q^35 + 106 * q^36 - 10 * q^39 - 3 * q^40 + 102 * q^41 - 30 * q^44 - 19 * q^45 - 4 * q^46 - 84 * q^49 - 59 * q^50 + 48 * q^51 - 22 * q^54 - 23 * q^55 + 110 * q^56 - 78 * q^59 - 105 * q^60 + 28 * q^61 - 24 * q^64 - 31 * q^65 + 48 * q^66 + 18 * q^69 - 51 * q^70 + 78 * q^71 - 14 * q^74 - 55 * q^75 + 34 * q^76 - 14 * q^79 - 51 * q^80 + 160 * q^81 + 52 * q^84 - 26 * q^85 + 76 * q^86 - 182 * q^89 - 120 * q^90 + 30 * q^91 + 170 * q^94 - 30 * q^95 + 130 * q^96 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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