LMFDB - Embedded newform 1110.2.h.e.961.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(961,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1110.961");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.h (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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{33})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 17x^{2} + 64 $ x^4 + 17*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			961.2
Root			$3.37228i$ of defining polynomial
Character	$\chi$	$=$	1110.961
Dual form			1110.2.h.e.961.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} -1.00000i q^{5} +1.00000i q^{6} +3.37228 q^{7} +1.00000i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} -1.00000i q^{5} +1.00000i q^{6} +3.37228 q^{7} +1.00000i q^{8} +1.00000 q^{9} -1.00000 q^{10} +0.627719 q^{11} +1.00000 q^{12} +6.74456i q^{13} -3.37228i q^{14} +1.00000i q^{15} +1.00000 q^{16} -5.37228i q^{17} -1.00000i q^{18} +6.00000i q^{19} +1.00000i q^{20} -3.37228 q^{21} -0.627719i q^{22} +2.74456i q^{23} -1.00000i q^{24} -1.00000 q^{25} +6.74456 q^{26} -1.00000 q^{27} -3.37228 q^{28} +9.37228i q^{29} +1.00000 q^{30} -2.62772i q^{31} -1.00000i q^{32} -0.627719 q^{33} -5.37228 q^{34} -3.37228i q^{35} -1.00000 q^{36} +(5.74456 + 2.00000i) q^{37} +6.00000 q^{38} -6.74456i q^{39} +1.00000 q^{40} +8.11684 q^{41} +3.37228i q^{42} +1.37228i q^{43} -0.627719 q^{44} -1.00000i q^{45} +2.74456 q^{46} -1.00000 q^{48} +4.37228 q^{49} +1.00000i q^{50} +5.37228i q^{51} -6.74456i q^{52} -2.62772 q^{53} +1.00000i q^{54} -0.627719i q^{55} +3.37228i q^{56} -6.00000i q^{57} +9.37228 q^{58} -8.00000i q^{59} -1.00000i q^{60} -11.3723i q^{61} -2.62772 q^{62} +3.37228 q^{63} -1.00000 q^{64} +6.74456 q^{65} +0.627719i q^{66} -2.74456 q^{67} +5.37228i q^{68} -2.74456i q^{69} -3.37228 q^{70} +2.74456 q^{71} +1.00000i q^{72} +14.0000 q^{73} +(2.00000 - 5.74456i) q^{74} +1.00000 q^{75} -6.00000i q^{76} +2.11684 q^{77} -6.74456 q^{78} +4.74456i q^{79} -1.00000i q^{80} +1.00000 q^{81} -8.11684i q^{82} +17.4891 q^{83} +3.37228 q^{84} -5.37228 q^{85} +1.37228 q^{86} -9.37228i q^{87} +0.627719i q^{88} -8.74456i q^{89} -1.00000 q^{90} +22.7446i q^{91} -2.74456i q^{92} +2.62772i q^{93} +6.00000 q^{95} +1.00000i q^{96} +10.1168i q^{97} -4.37228i q^{98} +0.627719 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} - 4 q^{4} + 2 q^{7} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^3 - 4 * q^4 + 2 * q^7 + 4 * q^9	$ 4 q - 4 q^{3} - 4 q^{4} + 2 q^{7} + 4 q^{9} - 4 q^{10} + 14 q^{11} + 4 q^{12} + 4 q^{16} - 2 q^{21} - 4 q^{25} + 4 q^{26} - 4 q^{27} - 2 q^{28} + 4 q^{30} - 14 q^{33} - 10 q^{34} - 4 q^{36} + 24 q^{38} + 4 q^{40} - 2 q^{41} - 14 q^{44} - 12 q^{46} - 4 q^{48} + 6 q^{49} - 22 q^{53} + 26 q^{58} - 22 q^{62} + 2 q^{63} - 4 q^{64} + 4 q^{65} + 12 q^{67} - 2 q^{70} - 12 q^{71} + 56 q^{73} + 8 q^{74} + 4 q^{75} - 26 q^{77} - 4 q^{78} + 4 q^{81} + 24 q^{83} + 2 q^{84} - 10 q^{85} - 6 q^{86} - 4 q^{90} + 24 q^{95} + 14 q^{99}+O(q^{100}) $ 4 * q - 4 * q^3 - 4 * q^4 + 2 * q^7 + 4 * q^9 - 4 * q^10 + 14 * q^11 + 4 * q^12 + 4 * q^16 - 2 * q^21 - 4 * q^25 + 4 * q^26 - 4 * q^27 - 2 * q^28 + 4 * q^30 - 14 * q^33 - 10 * q^34 - 4 * q^36 + 24 * q^38 + 4 * q^40 - 2 * q^41 - 14 * q^44 - 12 * q^46 - 4 * q^48 + 6 * q^49 - 22 * q^53 + 26 * q^58 - 22 * q^62 + 2 * q^63 - 4 * q^64 + 4 * q^65 + 12 * q^67 - 2 * q^70 - 12 * q^71 + 56 * q^73 + 8 * q^74 + 4 * q^75 - 26 * q^77 - 4 * q^78 + 4 * q^81 + 24 * q^83 + 2 * q^84 - 10 * q^85 - 6 * q^86 - 4 * q^90 + 24 * q^95 + 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−1.00000			−0.500000
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$			1.00000i			0.408248i
$7$	3.37228			1.27460			0.637301	−	0.770615i	$-0.280051\pi$
$7$	3.37228			1.27460			0.637301	+	0.770615i	$0.280051\pi$
$8$			1.00000i			0.353553i
$9$	1.00000			0.333333
$10$	−1.00000			−0.316228
$11$	0.627719			0.189264			0.0946322	−	0.995512i	$-0.469833\pi$
$11$	0.627719			0.189264			0.0946322	+	0.995512i	$0.469833\pi$
$12$	1.00000			0.288675
$13$			6.74456i			1.87061i	0.353849	+	0.935303i	$0.384873\pi$
$13$			6.74456i			1.87061i	−0.353849	+	0.935303i	$0.615127\pi$
$14$		−	3.37228i		−	0.901280i
$15$			1.00000i			0.258199i
$16$	1.00000			0.250000
$17$		−	5.37228i		−	1.30297i	−0.758662	−	0.651485i	$-0.774146\pi$
$17$		−	5.37228i		−	1.30297i	0.758662	−	0.651485i	$-0.225854\pi$
$18$		−	1.00000i		−	0.235702i
$19$			6.00000i			1.37649i	0.725476	+	0.688247i	$0.241620\pi$
$19$			6.00000i			1.37649i	−0.725476	+	0.688247i	$0.758380\pi$
$20$			1.00000i			0.223607i
$21$	−3.37228			−0.735892
$22$		−	0.627719i		−	0.133830i
$23$			2.74456i			0.572281i	0.958188	+	0.286140i	$0.0923724\pi$
$23$			2.74456i			0.572281i	−0.958188	+	0.286140i	$0.907628\pi$
$24$		−	1.00000i		−	0.204124i
$25$	−1.00000			−0.200000
$26$	6.74456			1.32272
$27$	−1.00000			−0.192450
$28$	−3.37228			−0.637301
$29$			9.37228i			1.74039i	0.492708	+	0.870194i	$0.336007\pi$
$29$			9.37228i			1.74039i	−0.492708	+	0.870194i	$0.663993\pi$
$30$	1.00000			0.182574
$31$		−	2.62772i		−	0.471952i	−0.971759	−	0.235976i	$-0.924171\pi$
$31$		−	2.62772i		−	0.471952i	0.971759	−	0.235976i	$-0.0758287\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−0.627719			−0.109272
$34$	−5.37228			−0.921339
$35$		−	3.37228i		−	0.570020i
$36$	−1.00000			−0.166667
$37$	5.74456	+	2.00000i	0.944400	+	0.328798i
$37$	5.74456	+	2.00000i	0.944400	+	0.328798i
$38$	6.00000			0.973329
$39$		−	6.74456i		−	1.07999i
$40$	1.00000			0.158114
$41$	8.11684			1.26764			0.633819	−	0.773481i	$-0.281486\pi$
$41$	8.11684			1.26764			0.633819	+	0.773481i	$0.281486\pi$
$42$			3.37228i			0.520354i
$43$			1.37228i			0.209271i	0.994511	+	0.104635i	$0.0333676\pi$
$43$			1.37228i			0.209271i	−0.994511	+	0.104635i	$0.966632\pi$
$44$	−0.627719			−0.0946322
$45$		−	1.00000i		−	0.149071i
$46$	2.74456			0.404664
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$	−1.00000			−0.144338
$49$	4.37228			0.624612
$50$			1.00000i			0.141421i
$51$			5.37228i			0.752270i
$52$		−	6.74456i		−	0.935303i
$53$	−2.62772			−0.360945			−0.180472	−	0.983580i	$-0.557763\pi$
$53$	−2.62772			−0.360945			−0.180472	+	0.983580i	$0.557763\pi$
$54$			1.00000i			0.136083i
$55$		−	0.627719i		−	0.0846416i
$56$			3.37228i			0.450640i
$57$		−	6.00000i		−	0.794719i
$58$	9.37228			1.23064
$59$		−	8.00000i		−	1.04151i	−0.853706	−	0.520756i	$-0.825650\pi$
$59$		−	8.00000i		−	1.04151i	0.853706	−	0.520756i	$-0.174350\pi$
$60$		−	1.00000i		−	0.129099i
$61$		−	11.3723i		−	1.45607i	−0.685539	−	0.728036i	$-0.740433\pi$
$61$		−	11.3723i		−	1.45607i	0.685539	−	0.728036i	$-0.259567\pi$
$62$	−2.62772			−0.333721
$63$	3.37228			0.424868
$64$	−1.00000			−0.125000
$65$	6.74456			0.836560
$66$			0.627719i			0.0772668i
$67$	−2.74456			−0.335302			−0.167651	−	0.985846i	$-0.553618\pi$
$67$	−2.74456			−0.335302			−0.167651	+	0.985846i	$0.553618\pi$
$68$			5.37228i			0.651485i
$69$		−	2.74456i		−	0.330407i
$70$	−3.37228			−0.403065
$71$	2.74456			0.325720			0.162860	−	0.986649i	$-0.447928\pi$
$71$	2.74456			0.325720			0.162860	+	0.986649i	$0.447928\pi$
$72$			1.00000i			0.117851i
$73$	14.0000			1.63858			0.819288	−	0.573382i	$-0.194369\pi$
$73$	14.0000			1.63858			0.819288	+	0.573382i	$0.194369\pi$
$74$	2.00000	−	5.74456i	0.232495	−	0.667792i
$75$	1.00000			0.115470
$76$		−	6.00000i		−	0.688247i
$77$	2.11684			0.241237
$78$	−6.74456			−0.763671
$79$			4.74456i			0.533805i	0.963724	+	0.266903i	$0.0860002\pi$
$79$			4.74456i			0.533805i	−0.963724	+	0.266903i	$0.914000\pi$
$80$		−	1.00000i		−	0.111803i
$81$	1.00000			0.111111
$82$		−	8.11684i		−	0.896355i
$83$	17.4891			1.91968			0.959840	−	0.280546i	$-0.0905157\pi$
$83$	17.4891			1.91968			0.959840	+	0.280546i	$0.0905157\pi$
$84$	3.37228			0.367946
$85$	−5.37228			−0.582706
$86$	1.37228			0.147977
$87$		−	9.37228i		−	1.00481i
$88$			0.627719i			0.0669150i
$89$		−	8.74456i		−	0.926922i	−0.886117	−	0.463461i	$-0.846607\pi$
$89$		−	8.74456i		−	0.926922i	0.886117	−	0.463461i	$-0.153393\pi$
$90$	−1.00000			−0.105409
$91$			22.7446i			2.38428i
$92$		−	2.74456i		−	0.286140i
$93$			2.62772i			0.272482i
$94$		0			0
$95$	6.00000			0.615587
$96$			1.00000i			0.102062i
$97$			10.1168i			1.02721i	0.858027	+	0.513605i	$0.171690\pi$
$97$			10.1168i			1.02721i	−0.858027	+	0.513605i	$0.828310\pi$
$98$		−	4.37228i		−	0.441667i
$99$	0.627719			0.0630881
$100$	1.00000			0.100000
$101$	−16.7446			−1.66615			−0.833073	−	0.553163i	$-0.813421\pi$
$101$	−16.7446			−1.66615			−0.833073	+	0.553163i	$0.813421\pi$
$102$	5.37228			0.531935
$103$			15.4891i			1.52619i	0.646287	+	0.763094i	$0.276321\pi$
$103$			15.4891i			1.52619i	−0.646287	+	0.763094i	$0.723679\pi$
$104$	−6.74456			−0.661359
$105$			3.37228i			0.329101i
$106$			2.62772i			0.255227i
$107$	14.7446			1.42541			0.712705	−	0.701464i	$-0.247470\pi$
$107$	14.7446			1.42541			0.712705	+	0.701464i	$0.247470\pi$
$108$	1.00000			0.0962250
$109$		−	14.1168i		−	1.35215i	−0.736834	−	0.676074i	$-0.763680\pi$
$109$		−	14.1168i		−	1.35215i	0.736834	−	0.676074i	$-0.236320\pi$
$110$	−0.627719			−0.0598506
$111$	−5.74456	−	2.00000i	−0.545250	−	0.189832i
$112$	3.37228			0.318651
$113$		−	18.8614i		−	1.77433i	−0.461451	−	0.887166i	$-0.652671\pi$
$113$		−	18.8614i		−	1.77433i	0.461451	−	0.887166i	$-0.347329\pi$
$114$	−6.00000			−0.561951
$115$	2.74456			0.255932
$116$		−	9.37228i		−	0.870194i
$117$			6.74456i			0.623535i
$118$	−8.00000			−0.736460
$119$		−	18.1168i		−	1.66077i
$120$	−1.00000			−0.0912871
$121$	−10.6060			−0.964179
$122$	−11.3723			−1.02960
$123$	−8.11684			−0.731871
$124$			2.62772i			0.235976i
$125$			1.00000i			0.0894427i
$126$		−	3.37228i		−	0.300427i
$127$	13.4891			1.19697			0.598483	−	0.801135i	$-0.295770\pi$
$127$	13.4891			1.19697			0.598483	+	0.801135i	$0.295770\pi$
$128$			1.00000i			0.0883883i
$129$		−	1.37228i		−	0.120823i
$130$		−	6.74456i		−	0.591537i
$131$			13.4891i			1.17855i	0.807932	+	0.589275i	$0.200587\pi$
$131$			13.4891i			1.17855i	−0.807932	+	0.589275i	$0.799413\pi$
$132$	0.627719			0.0546359
$133$			20.2337i			1.75448i
$134$			2.74456i			0.237094i
$135$			1.00000i			0.0860663i
$136$	5.37228			0.460669
$137$	8.74456			0.747098			0.373549	−	0.927610i	$-0.378141\pi$
$137$	8.74456			0.747098			0.373549	+	0.927610i	$0.378141\pi$
$138$	−2.74456			−0.233633
$139$	−7.37228			−0.625309			−0.312654	−	0.949867i	$-0.601218\pi$
$139$	−7.37228			−0.625309			−0.312654	+	0.949867i	$0.601218\pi$
$140$			3.37228i			0.285010i
$141$		0			0
$142$		−	2.74456i		−	0.230319i
$143$			4.23369i			0.354039i
$144$	1.00000			0.0833333
$145$	9.37228			0.778326
$146$		−	14.0000i		−	1.15865i
$147$	−4.37228			−0.360620
$148$	−5.74456	−	2.00000i	−0.472200	−	0.164399i
$149$	−11.4891			−0.941226			−0.470613	−	0.882340i	$-0.655967\pi$
$149$	−11.4891			−0.941226			−0.470613	+	0.882340i	$0.655967\pi$
$150$		−	1.00000i		−	0.0816497i
$151$	−22.7446			−1.85093			−0.925463	−	0.378838i	$-0.876324\pi$
$151$	−22.7446			−1.85093			−0.925463	+	0.378838i	$0.876324\pi$
$152$	−6.00000			−0.486664
$153$		−	5.37228i		−	0.434323i
$154$		−	2.11684i		−	0.170580i
$155$	−2.62772			−0.211063
$156$			6.74456i			0.539997i
$157$	−10.6277			−0.848184			−0.424092	−	0.905619i	$-0.639407\pi$
$157$	−10.6277			−0.848184			−0.424092	+	0.905619i	$0.639407\pi$
$158$	4.74456			0.377457
$159$	2.62772			0.208392
$160$	−1.00000			−0.0790569
$161$			9.25544i			0.729431i
$162$		−	1.00000i		−	0.0785674i
$163$			8.11684i			0.635760i	0.948131	+	0.317880i	$0.102971\pi$
$163$			8.11684i			0.635760i	−0.948131	+	0.317880i	$0.897029\pi$
$164$	−8.11684			−0.633819
$165$			0.627719i			0.0488678i
$166$		−	17.4891i		−	1.35742i
$167$			14.7446i			1.14097i	0.821309	+	0.570484i	$0.193244\pi$
$167$			14.7446i			1.14097i	−0.821309	+	0.570484i	$0.806756\pi$
$168$		−	3.37228i		−	0.260177i
$169$	−32.4891			−2.49916
$170$			5.37228i			0.412035i
$171$			6.00000i			0.458831i
$172$		−	1.37228i		−	0.104635i
$173$	−13.3723			−1.01668			−0.508338	−	0.861158i	$-0.669740\pi$
$173$	−13.3723			−1.01668			−0.508338	+	0.861158i	$0.669740\pi$
$174$	−9.37228			−0.710511
$175$	−3.37228			−0.254921
$176$	0.627719			0.0473161
$177$			8.00000i			0.601317i
$178$	−8.74456			−0.655433
$179$		−	2.74456i		−	0.205138i	−0.994726	−	0.102569i	$-0.967294\pi$
$179$		−	2.74456i		−	0.205138i	0.994726	−	0.102569i	$-0.0327063\pi$
$180$			1.00000i			0.0745356i
$181$	11.2554			0.836610			0.418305	−	0.908307i	$-0.362624\pi$
$181$	11.2554			0.836610			0.418305	+	0.908307i	$0.362624\pi$
$182$	22.7446			1.68594
$183$			11.3723i			0.840663i
$184$	−2.74456			−0.202332
$185$	2.00000	−	5.74456i	0.147043	−	0.422349i
$186$	2.62772			0.192674
$187$		−	3.37228i		−	0.246606i
$188$		0			0
$189$	−3.37228			−0.245297
$190$		−	6.00000i		−	0.435286i
$191$			10.1168i			0.732029i	0.930609	+	0.366015i	$0.119278\pi$
$191$			10.1168i			0.732029i	−0.930609	+	0.366015i	$0.880722\pi$
$192$	1.00000			0.0721688
$193$		−	16.2337i		−	1.16853i	−0.811564	−	0.584263i	$-0.801384\pi$
$193$		−	16.2337i		−	1.16853i	0.811564	−	0.584263i	$-0.198616\pi$
$194$	10.1168			0.726347
$195$	−6.74456			−0.482988
$196$	−4.37228			−0.312306
$197$	−7.48913			−0.533578			−0.266789	−	0.963755i	$-0.585963\pi$
$197$	−7.48913			−0.533578			−0.266789	+	0.963755i	$0.585963\pi$
$198$		−	0.627719i		−	0.0446100i
$199$			0.744563i			0.0527806i	0.999652	+	0.0263903i	$0.00840128\pi$
$199$			0.744563i			0.0527806i	−0.999652	+	0.0263903i	$0.991599\pi$
$200$		−	1.00000i		−	0.0707107i
$201$	2.74456			0.193587
$202$			16.7446i			1.17814i
$203$			31.6060i			2.21830i
$204$		−	5.37228i		−	0.376135i
$205$		−	8.11684i		−	0.566905i
$206$	15.4891			1.07918
$207$			2.74456i			0.190760i
$208$			6.74456i			0.467651i
$209$			3.76631i			0.260521i
$210$	3.37228			0.232710
$211$	−4.86141			−0.334673			−0.167337	−	0.985900i	$-0.553517\pi$
$211$	−4.86141			−0.334673			−0.167337	+	0.985900i	$0.553517\pi$
$212$	2.62772			0.180472
$213$	−2.74456			−0.188054
$214$		−	14.7446i		−	1.00792i
$215$	1.37228			0.0935888
$216$		−	1.00000i		−	0.0680414i
$217$		−	8.86141i		−	0.601551i
$218$	−14.1168			−0.956113
$219$	−14.0000			−0.946032
$220$			0.627719i			0.0423208i
$221$	36.2337			2.43734
$222$	−2.00000	+	5.74456i	−0.134231	+	0.385550i
$223$	12.6277			0.845615			0.422807	−	0.906220i	$-0.361045\pi$
$223$	12.6277			0.845615			0.422807	+	0.906220i	$0.361045\pi$
$224$		−	3.37228i		−	0.225320i
$225$	−1.00000			−0.0666667
$226$	−18.8614			−1.25464
$227$		−	0.627719i		−	0.0416632i	−0.999783	−	0.0208316i	$-0.993369\pi$
$227$		−	0.627719i		−	0.0416632i	0.999783	−	0.0208316i	$-0.00663138\pi$
$228$			6.00000i			0.397360i
$229$	27.4891			1.81653			0.908266	−	0.418393i	$-0.137406\pi$
$229$	27.4891			1.81653			0.908266	+	0.418393i	$0.137406\pi$
$230$		−	2.74456i		−	0.180971i
$231$	−2.11684			−0.139278
$232$	−9.37228			−0.615320
$233$	3.25544			0.213271			0.106635	−	0.994298i	$-0.465992\pi$
$233$	3.25544			0.213271			0.106635	+	0.994298i	$0.465992\pi$
$234$	6.74456			0.440906
$235$		0			0
$236$			8.00000i			0.520756i
$237$		−	4.74456i		−	0.308192i
$238$	−18.1168			−1.17434
$239$		−	20.8614i		−	1.34941i	−0.738086	−	0.674706i	$-0.764270\pi$
$239$		−	20.8614i		−	1.34941i	0.738086	−	0.674706i	$-0.235730\pi$
$240$			1.00000i			0.0645497i
$241$			1.48913i			0.0959230i	0.998849	+	0.0479615i	$0.0152725\pi$
$241$			1.48913i			0.0959230i	−0.998849	+	0.0479615i	$0.984728\pi$
$242$			10.6060i			0.681778i
$243$	−1.00000			−0.0641500
$244$			11.3723i			0.728036i
$245$		−	4.37228i		−	0.279335i
$246$			8.11684i			0.517511i
$247$	−40.4674			−2.57488
$248$	2.62772			0.166860
$249$	−17.4891			−1.10833
$250$	1.00000			0.0632456
$251$		−	4.00000i		−	0.252478i	−0.992000	−	0.126239i	$-0.959709\pi$
$251$		−	4.00000i		−	0.252478i	0.992000	−	0.126239i	$-0.0402906\pi$
$252$	−3.37228			−0.212434
$253$			1.72281i			0.108312i
$254$		−	13.4891i		−	0.846383i
$255$	5.37228			0.336425
$256$	1.00000			0.0625000
$257$		−	0.510875i		−	0.0318675i	−0.999873	−	0.0159337i	$-0.994928\pi$
$257$		−	0.510875i		−	0.0318675i	0.999873	−	0.0159337i	$-0.00507208\pi$
$258$	−1.37228			−0.0854345
$259$	19.3723	+	6.74456i	1.20373	+	0.419087i
$260$	−6.74456			−0.418280
$261$			9.37228i			0.580130i
$262$	13.4891			0.833361
$263$	−23.6060			−1.45561			−0.727803	−	0.685786i	$-0.759459\pi$
$263$	−23.6060			−1.45561			−0.727803	+	0.685786i	$0.759459\pi$
$264$		−	0.627719i		−	0.0386334i
$265$			2.62772i			0.161419i
$266$	20.2337			1.24061
$267$			8.74456i			0.535159i
$268$	2.74456			0.167651
$269$	6.23369			0.380075			0.190037	−	0.981777i	$-0.439139\pi$
$269$	6.23369			0.380075			0.190037	+	0.981777i	$0.439139\pi$
$270$	1.00000			0.0608581
$271$	−21.4891			−1.30537			−0.652686	−	0.757629i	$-0.726358\pi$
$271$	−21.4891			−1.30537			−0.652686	+	0.757629i	$0.726358\pi$
$272$		−	5.37228i		−	0.325742i
$273$		−	22.7446i		−	1.37656i
$274$		−	8.74456i		−	0.528278i
$275$	−0.627719			−0.0378529
$276$			2.74456i			0.165203i
$277$		−	13.4891i		−	0.810483i	−0.914210	−	0.405241i	$-0.867187\pi$
$277$		−	13.4891i		−	0.810483i	0.914210	−	0.405241i	$-0.132813\pi$
$278$			7.37228i			0.442160i
$279$		−	2.62772i		−	0.157317i
$280$	3.37228			0.201532
$281$		−	24.9783i		−	1.49008i	−0.667021	−	0.745039i	$-0.732431\pi$
$281$		−	24.9783i		−	1.49008i	0.667021	−	0.745039i	$-0.267569\pi$
$282$		0			0
$283$			19.2554i			1.14462i	0.820038	+	0.572308i	$0.193952\pi$
$283$			19.2554i			1.14462i	−0.820038	+	0.572308i	$0.806048\pi$
$284$	−2.74456			−0.162860
$285$	−6.00000			−0.355409
$286$	4.23369			0.250343
$287$	27.3723			1.61573
$288$		−	1.00000i		−	0.0589256i
$289$	−11.8614			−0.697730
$290$		−	9.37228i		−	0.550359i
$291$		−	10.1168i		−	0.593060i
$292$	−14.0000			−0.819288
$293$	4.11684			0.240509			0.120254	−	0.992743i	$-0.461629\pi$
$293$	4.11684			0.240509			0.120254	+	0.992743i	$0.461629\pi$
$294$			4.37228i			0.254997i
$295$	−8.00000			−0.465778
$296$	−2.00000	+	5.74456i	−0.116248	+	0.333896i
$297$	−0.627719			−0.0364239
$298$			11.4891i			0.665547i
$299$	−18.5109			−1.07051
$300$	−1.00000			−0.0577350
$301$			4.62772i			0.266737i
$302$			22.7446i			1.30880i
$303$	16.7446			0.961950
$304$			6.00000i			0.344124i
$305$	−11.3723			−0.651175
$306$	−5.37228			−0.307113
$307$	25.4891			1.45474			0.727371	−	0.686245i	$-0.240742\pi$
$307$	25.4891			1.45474			0.727371	+	0.686245i	$0.240742\pi$
$308$	−2.11684			−0.120618
$309$		−	15.4891i		−	0.881146i
$310$			2.62772i			0.149244i
$311$			8.86141i			0.502484i	0.967924	+	0.251242i	$0.0808390\pi$
$311$			8.86141i			0.502484i	−0.967924	+	0.251242i	$0.919161\pi$
$312$	6.74456			0.381836
$313$			16.2337i			0.917582i	0.888544	+	0.458791i	$0.151717\pi$
$313$			16.2337i			0.917582i	−0.888544	+	0.458791i	$0.848283\pi$
$314$			10.6277i			0.599757i
$315$		−	3.37228i		−	0.190007i
$316$		−	4.74456i		−	0.266903i
$317$	10.6277			0.596912			0.298456	−	0.954423i	$-0.403528\pi$
$317$	10.6277			0.596912			0.298456	+	0.954423i	$0.403528\pi$
$318$		−	2.62772i		−	0.147355i
$319$			5.88316i			0.329394i
$320$			1.00000i			0.0559017i
$321$	−14.7446			−0.822961
$322$	9.25544			0.515785
$323$	32.2337			1.79353
$324$	−1.00000			−0.0555556
$325$		−	6.74456i		−	0.374121i
$326$	8.11684			0.449550
$327$			14.1168i			0.780663i
$328$			8.11684i			0.448178i
$329$		0			0
$330$	0.627719			0.0345548
$331$			19.4891i			1.07122i	0.844466	+	0.535610i	$0.179918\pi$
$331$			19.4891i			1.07122i	−0.844466	+	0.535610i	$0.820082\pi$
$332$	−17.4891			−0.959840
$333$	5.74456	+	2.00000i	0.314800	+	0.109599i
$334$	14.7446			0.806787
$335$			2.74456i			0.149951i
$336$	−3.37228			−0.183973
$337$	−23.2554			−1.26680			−0.633402	−	0.773823i	$-0.718342\pi$
$337$	−23.2554			−1.26680			−0.633402	+	0.773823i	$0.718342\pi$
$338$			32.4891i			1.76718i
$339$			18.8614i			1.02441i
$340$	5.37228			0.291353
$341$		−	1.64947i		−	0.0893237i
$342$	6.00000			0.324443
$343$	−8.86141			−0.478471
$344$	−1.37228			−0.0739885
$345$	−2.74456			−0.147762
$346$			13.3723i			0.718898i
$347$			14.9783i			0.804075i	0.915623	+	0.402037i	$0.131698\pi$
$347$			14.9783i			0.804075i	−0.915623	+	0.402037i	$0.868302\pi$
$348$			9.37228i			0.502407i
$349$	−11.4891			−0.614999			−0.307499	−	0.951548i	$-0.599492\pi$
$349$	−11.4891			−0.614999			−0.307499	+	0.951548i	$0.599492\pi$
$350$			3.37228i			0.180256i
$351$		−	6.74456i		−	0.359998i
$352$		−	0.627719i		−	0.0334575i
$353$		−	12.1168i		−	0.644915i	−0.946584	−	0.322457i	$-0.895491\pi$
$353$		−	12.1168i		−	0.644915i	0.946584	−	0.322457i	$-0.104509\pi$
$354$	8.00000			0.425195
$355$		−	2.74456i		−	0.145666i
$356$			8.74456i			0.463461i
$357$			18.1168i			0.958845i
$358$	−2.74456			−0.145055
$359$	−8.00000			−0.422224			−0.211112	−	0.977462i	$-0.567708\pi$
$359$	−8.00000			−0.422224			−0.211112	+	0.977462i	$0.567708\pi$
$360$	1.00000			0.0527046
$361$	−17.0000			−0.894737
$362$		−	11.2554i		−	0.591573i
$363$	10.6060			0.556669
$364$		−	22.7446i		−	1.19214i
$365$		−	14.0000i		−	0.732793i
$366$	11.3723			0.594439
$367$	19.3723			1.01122			0.505612	−	0.862761i	$-0.331267\pi$
$367$	19.3723			1.01122			0.505612	+	0.862761i	$0.331267\pi$
$368$			2.74456i			0.143070i
$369$	8.11684			0.422546
$370$	−5.74456	−	2.00000i	−0.298646	−	0.103975i
$371$	−8.86141			−0.460061
$372$		−	2.62772i		−	0.136241i
$373$	−0.510875			−0.0264521			−0.0132260	−	0.999913i	$-0.504210\pi$
$373$	−0.510875			−0.0264521			−0.0132260	+	0.999913i	$0.504210\pi$
$374$	−3.37228			−0.174377
$375$		−	1.00000i		−	0.0516398i
$376$		0			0
$377$	−63.2119			−3.25558
$378$			3.37228i			0.173451i
$379$	28.0000			1.43826			0.719132	−	0.694874i	$-0.244540\pi$
$379$	28.0000			1.43826			0.719132	+	0.694874i	$0.244540\pi$
$380$	−6.00000			−0.307794
$381$	−13.4891			−0.691069
$382$	10.1168			0.517623
$383$		−	21.7228i		−	1.10998i	−0.831856	−	0.554992i	$-0.812721\pi$
$383$		−	21.7228i		−	1.10998i	0.831856	−	0.554992i	$-0.187279\pi$
$384$		−	1.00000i		−	0.0510310i
$385$		−	2.11684i		−	0.107884i
$386$	−16.2337			−0.826273
$387$			1.37228i			0.0697570i
$388$		−	10.1168i		−	0.513605i
$389$			22.8614i			1.15912i	0.814930	+	0.579560i	$0.196775\pi$
$389$			22.8614i			1.15912i	−0.814930	+	0.579560i	$0.803225\pi$
$390$			6.74456i			0.341524i
$391$	14.7446			0.745665
$392$			4.37228i			0.220834i
$393$		−	13.4891i		−	0.680436i
$394$			7.48913i			0.377297i
$395$	4.74456			0.238725
$396$	−0.627719			−0.0315441
$397$	−14.0000			−0.702640			−0.351320	−	0.936255i	$-0.614267\pi$
$397$	−14.0000			−0.702640			−0.351320	+	0.936255i	$0.614267\pi$
$398$	0.744563			0.0373216
$399$		−	20.2337i		−	1.01295i
$400$	−1.00000			−0.0500000
$401$		−	16.9783i		−	0.847853i	−0.905697	−	0.423927i	$-0.860651\pi$
$401$		−	16.9783i		−	0.847853i	0.905697	−	0.423927i	$-0.139349\pi$
$402$		−	2.74456i		−	0.136886i
$403$	17.7228			0.882836
$404$	16.7446			0.833073
$405$		−	1.00000i		−	0.0496904i
$406$	31.6060			1.56858
$407$	3.60597	+	1.25544i	0.178741	+	0.0622297i
$408$	−5.37228			−0.265968
$409$			1.48913i			0.0736325i	0.999322	+	0.0368163i	$0.0117216\pi$
$409$			1.48913i			0.0736325i	−0.999322	+	0.0368163i	$0.988278\pi$
$410$	−8.11684			−0.400862
$411$	−8.74456			−0.431337
$412$		−	15.4891i		−	0.763094i
$413$		−	26.9783i		−	1.32751i
$414$	2.74456			0.134888
$415$		−	17.4891i		−	0.858507i
$416$	6.74456			0.330679
$417$	7.37228			0.361022
$418$	3.76631			0.184216
$419$	−8.00000			−0.390826			−0.195413	−	0.980721i	$-0.562605\pi$
$419$	−8.00000			−0.390826			−0.195413	+	0.980721i	$0.562605\pi$
$420$		−	3.37228i		−	0.164550i
$421$			2.74456i			0.133762i	0.997761	+	0.0668809i	$0.0213048\pi$
$421$			2.74456i			0.133762i	−0.997761	+	0.0668809i	$0.978695\pi$
$422$			4.86141i			0.236650i
$423$		0			0
$424$		−	2.62772i		−	0.127613i
$425$			5.37228i			0.260594i
$426$			2.74456i			0.132974i
$427$		−	38.3505i		−	1.85591i
$428$	−14.7446			−0.712705
$429$		−	4.23369i		−	0.204404i
$430$		−	1.37228i		−	0.0661773i
$431$			19.3723i			0.933130i	0.884487	+	0.466565i	$0.154509\pi$
$431$			19.3723i			0.933130i	−0.884487	+	0.466565i	$0.845491\pi$
$432$	−1.00000			−0.0481125
$433$	11.4891			0.552132			0.276066	−	0.961139i	$-0.410969\pi$
$433$	11.4891			0.552132			0.276066	+	0.961139i	$0.410969\pi$
$434$	−8.86141			−0.425361
$435$	−9.37228			−0.449366
$436$			14.1168i			0.676074i
$437$	−16.4674			−0.787741
$438$			14.0000i			0.668946i
$439$			6.62772i			0.316324i	0.987413	+	0.158162i	$0.0505568\pi$
$439$			6.62772i			0.316324i	−0.987413	+	0.158162i	$0.949443\pi$
$440$	0.627719			0.0299253
$441$	4.37228			0.208204
$442$		−	36.2337i		−	1.72346i
$443$	4.00000			0.190046			0.0950229	−	0.995475i	$-0.469708\pi$
$443$	4.00000			0.190046			0.0950229	+	0.995475i	$0.469708\pi$
$444$	5.74456	+	2.00000i	0.272625	+	0.0949158i
$445$	−8.74456			−0.414532
$446$		−	12.6277i		−	0.597940i
$447$	11.4891			0.543417
$448$	−3.37228			−0.159325
$449$		−	8.97825i		−	0.423710i	−0.977301	−	0.211855i	$-0.932050\pi$
$449$		−	8.97825i		−	0.423710i	0.977301	−	0.211855i	$-0.0679504\pi$
$450$			1.00000i			0.0471405i
$451$	5.09509			0.239919
$452$			18.8614i			0.887166i
$453$	22.7446			1.06863
$454$	−0.627719			−0.0294603
$455$	22.7446			1.06628
$456$	6.00000			0.280976
$457$		−	11.3723i		−	0.531973i	−0.963977	−	0.265986i	$-0.914302\pi$
$457$		−	11.3723i		−	0.531973i	0.963977	−	0.265986i	$-0.0856976\pi$
$458$		−	27.4891i		−	1.28448i
$459$			5.37228i			0.250757i
$460$	−2.74456			−0.127966
$461$		−	25.6060i		−	1.19259i	−0.802766	−	0.596294i	$-0.796639\pi$
$461$		−	25.6060i		−	1.19259i	0.802766	−	0.596294i	$-0.203361\pi$
$462$			2.11684i			0.0984845i
$463$		−	22.2337i		−	1.03329i	−0.856201	−	0.516644i	$-0.827181\pi$
$463$		−	22.2337i		−	1.03329i	0.856201	−	0.516644i	$-0.172819\pi$
$464$			9.37228i			0.435097i
$465$	2.62772			0.121858
$466$		−	3.25544i		−	0.150805i
$467$			20.6277i			0.954537i	0.878758	+	0.477268i	$0.158373\pi$
$467$			20.6277i			0.954537i	−0.878758	+	0.477268i	$0.841627\pi$
$468$		−	6.74456i		−	0.311768i
$469$	−9.25544			−0.427376
$470$		0			0
$471$	10.6277			0.489699
$472$	8.00000			0.368230
$473$			0.861407i			0.0396075i
$474$	−4.74456			−0.217925
$475$		−	6.00000i		−	0.275299i
$476$			18.1168i			0.830384i
$477$	−2.62772			−0.120315
$478$	−20.8614			−0.954179
$479$		−	34.9783i		−	1.59820i	−0.601200	−	0.799099i	$-0.705311\pi$
$479$		−	34.9783i		−	1.59820i	0.601200	−	0.799099i	$-0.294689\pi$
$480$	1.00000			0.0456435
$481$	−13.4891	+	38.7446i	−0.615051	+	1.76660i
$482$	1.48913			0.0678278
$483$		−	9.25544i		−	0.421137i
$484$	10.6060			0.482090
$485$	10.1168			0.459382
$486$			1.00000i			0.0453609i
$487$		−	7.25544i		−	0.328775i	−0.986396	−	0.164388i	$-0.947435\pi$
$487$		−	7.25544i		−	0.328775i	0.986396	−	0.164388i	$-0.0525648\pi$
$488$	11.3723			0.514799
$489$		−	8.11684i		−	0.367056i
$490$	−4.37228			−0.197520
$491$	−32.4674			−1.46523			−0.732616	−	0.680642i	$-0.761701\pi$
$491$	−32.4674			−1.46523			−0.732616	+	0.680642i	$0.761701\pi$
$492$	8.11684			0.365936
$493$	50.3505			2.26767
$494$			40.4674i			1.82071i
$495$		−	0.627719i		−	0.0282139i
$496$		−	2.62772i		−	0.117988i
$497$	9.25544			0.415163
$498$			17.4891i			0.783706i
$499$			20.9783i			0.939115i	0.882902	+	0.469558i	$0.155587\pi$
$499$			20.9783i			0.939115i	−0.882902	+	0.469558i	$0.844413\pi$
$500$		−	1.00000i		−	0.0447214i
$501$		−	14.7446i		−	0.658738i
$502$	−4.00000			−0.178529
$503$		−	1.48913i		−	0.0663968i	−0.999449	−	0.0331984i	$-0.989431\pi$
$503$		−	1.48913i		−	0.0663968i	0.999449	−	0.0331984i	$-0.0105693\pi$
$504$			3.37228i			0.150213i
$505$			16.7446i			0.745123i
$506$	1.72281			0.0765884
$507$	32.4891			1.44289
$508$	−13.4891			−0.598483
$509$	−7.25544			−0.321592			−0.160796	−	0.986988i	$-0.551406\pi$
$509$	−7.25544			−0.321592			−0.160796	+	0.986988i	$0.551406\pi$
$510$		−	5.37228i		−	0.237889i
$511$	47.2119			2.08853
$512$		−	1.00000i		−	0.0441942i
$513$		−	6.00000i		−	0.264906i
$514$	−0.510875			−0.0225337
$515$	15.4891			0.682532
$516$			1.37228i			0.0604113i
$517$		0			0
$518$	6.74456	−	19.3723i	0.296339	−	0.851169i
$519$	13.3723			0.586978
$520$			6.74456i			0.295769i
$521$	−12.1168			−0.530849			−0.265424	−	0.964132i	$-0.585512\pi$
$521$	−12.1168			−0.530849			−0.265424	+	0.964132i	$0.585512\pi$
$522$	9.37228			0.410214
$523$		−	40.7446i		−	1.78164i	−0.454361	−	0.890818i	$-0.650132\pi$
$523$		−	40.7446i		−	1.78164i	0.454361	−	0.890818i	$-0.349868\pi$
$524$		−	13.4891i		−	0.589275i
$525$	3.37228			0.147178
$526$			23.6060i			1.02927i
$527$	−14.1168			−0.614939
$528$	−0.627719			−0.0273179
$529$	15.4674			0.672495
$530$	2.62772			0.114141
$531$		−	8.00000i		−	0.347170i
$532$		−	20.2337i		−	0.877242i
$533$			54.7446i			2.37125i
$534$	8.74456			0.378414
$535$		−	14.7446i		−	0.637463i
$536$		−	2.74456i		−	0.118547i
$537$			2.74456i			0.118437i
$538$		−	6.23369i		−	0.268753i
$539$	2.74456			0.118217
$540$		−	1.00000i		−	0.0430331i
$541$		−	29.7228i		−	1.27788i	−0.769255	−	0.638942i	$-0.779372\pi$
$541$		−	29.7228i		−	1.27788i	0.769255	−	0.638942i	$-0.220628\pi$
$542$			21.4891i			0.923037i
$543$	−11.2554			−0.483017
$544$	−5.37228			−0.230335
$545$	−14.1168			−0.604699
$546$	−22.7446			−0.973377
$547$		−	40.3505i		−	1.72526i	−0.505832	−	0.862632i	$-0.668814\pi$
$547$		−	40.3505i		−	1.72526i	0.505832	−	0.862632i	$-0.331186\pi$
$548$	−8.74456			−0.373549
$549$		−	11.3723i		−	0.485357i
$550$			0.627719i			0.0267660i
$551$	−56.2337			−2.39564
$552$	2.74456			0.116816
$553$			16.0000i			0.680389i
$554$	−13.4891			−0.573098
$555$	−2.00000	+	5.74456i	−0.0848953	+	0.243843i
$556$	7.37228			0.312654
$557$		−	10.2337i		−	0.433615i	−0.976214	−	0.216808i	$-0.930436\pi$
$557$		−	10.2337i		−	0.433615i	0.976214	−	0.216808i	$-0.0695644\pi$
$558$	−2.62772			−0.111240
$559$	−9.25544			−0.391463
$560$		−	3.37228i		−	0.142505i
$561$			3.37228i			0.142378i
$562$	−24.9783			−1.05364
$563$			24.8614i			1.04778i	0.851785	+	0.523892i	$0.175520\pi$
$563$			24.8614i			1.04778i	−0.851785	+	0.523892i	$0.824480\pi$
$564$		0			0
$565$	−18.8614			−0.793505
$566$	19.2554			0.809366
$567$	3.37228			0.141623
$568$			2.74456i			0.115159i
$569$		−	32.7446i		−	1.37272i	−0.727260	−	0.686362i	$-0.759207\pi$
$569$		−	32.7446i		−	1.37272i	0.727260	−	0.686362i	$-0.240793\pi$
$570$			6.00000i			0.251312i
$571$	−10.3505			−0.433156			−0.216578	−	0.976265i	$-0.569490\pi$
$571$	−10.3505			−0.433156			−0.216578	+	0.976265i	$0.569490\pi$
$572$		−	4.23369i		−	0.177019i
$573$		−	10.1168i		−	0.422637i
$574$		−	27.3723i		−	1.14250i
$575$		−	2.74456i		−	0.114456i
$576$	−1.00000			−0.0416667
$577$		−	21.7228i		−	0.904333i	−0.891934	−	0.452166i	$-0.850651\pi$
$577$		−	21.7228i		−	0.904333i	0.891934	−	0.452166i	$-0.149349\pi$
$578$			11.8614i			0.493369i
$579$			16.2337i			0.674649i
$580$	−9.37228			−0.389163
$581$	58.9783			2.44683
$582$	−10.1168			−0.419357
$583$	−1.64947			−0.0683140
$584$			14.0000i			0.579324i
$585$	6.74456			0.278853
$586$		−	4.11684i		−	0.170065i
$587$			7.37228i			0.304287i	0.988358	+	0.152143i	$0.0486175\pi$
$587$			7.37228i			0.304287i	−0.988358	+	0.152143i	$0.951382\pi$
$588$	4.37228			0.180310
$589$	15.7663			0.649640
$590$			8.00000i			0.329355i
$591$	7.48913			0.308061
$592$	5.74456	+	2.00000i	0.236100	+	0.0821995i
$593$	−5.76631			−0.236794			−0.118397	−	0.992966i	$-0.537776\pi$
$593$	−5.76631			−0.236794			−0.118397	+	0.992966i	$0.537776\pi$
$594$			0.627719i			0.0257556i
$595$	−18.1168			−0.742718
$596$	11.4891			0.470613
$597$		−	0.744563i		−	0.0304729i
$598$			18.5109i			0.756966i
$599$	−10.7446			−0.439011			−0.219505	−	0.975611i	$-0.570444\pi$
$599$	−10.7446			−0.439011			−0.219505	+	0.975611i	$0.570444\pi$
$600$			1.00000i			0.0408248i
$601$	34.6277			1.41249			0.706247	−	0.707965i	$-0.250387\pi$
$601$	34.6277			1.41249			0.706247	+	0.707965i	$0.250387\pi$
$602$	4.62772			0.188612
$603$	−2.74456			−0.111767
$604$	22.7446			0.925463
$605$			10.6060i			0.431194i
$606$		−	16.7446i		−	0.680201i
$607$			38.2337i			1.55186i	0.630821	+	0.775929i	$0.282718\pi$
$607$			38.2337i			1.55186i	−0.630821	+	0.775929i	$0.717282\pi$
$608$	6.00000			0.243332
$609$		−	31.6060i		−	1.28074i
$610$			11.3723i			0.460450i
$611$		0			0
$612$			5.37228i			0.217162i
$613$	20.3505			0.821950			0.410975	−	0.911647i	$-0.365188\pi$
$613$	20.3505			0.821950			0.410975	+	0.911647i	$0.365188\pi$
$614$		−	25.4891i		−	1.02866i
$615$			8.11684i			0.327303i
$616$			2.11684i			0.0852901i
$617$	−48.7446			−1.96238			−0.981191	−	0.193039i	$-0.938166\pi$
$617$	−48.7446			−1.96238			−0.981191	+	0.193039i	$0.938166\pi$
$618$	−15.4891			−0.623064
$619$	−15.3723			−0.617864			−0.308932	−	0.951084i	$-0.599972\pi$
$619$	−15.3723			−0.617864			−0.308932	+	0.951084i	$0.599972\pi$
$620$	2.62772			0.105532
$621$		−	2.74456i		−	0.110136i
$622$	8.86141			0.355310
$623$		−	29.4891i		−	1.18146i
$624$		−	6.74456i		−	0.269999i
$625$	1.00000			0.0400000
$626$	16.2337			0.648829
$627$		−	3.76631i		−	0.150412i
$628$	10.6277			0.424092
$629$	10.7446	−	30.8614i	0.428414	−	1.23052i
$630$	−3.37228			−0.134355
$631$		−	20.1168i		−	0.800839i	−0.916332	−	0.400419i	$-0.868864\pi$
$631$		−	20.1168i		−	0.800839i	0.916332	−	0.400419i	$-0.131136\pi$
$632$	−4.74456			−0.188729
$633$	4.86141			0.193224
$634$		−	10.6277i		−	0.422081i
$635$		−	13.4891i		−	0.535300i
$636$	−2.62772			−0.104196
$637$			29.4891i			1.16840i
$638$	5.88316			0.232916
$639$	2.74456			0.108573
$640$	1.00000			0.0395285
$641$	2.86141			0.113019			0.0565094	−	0.998402i	$-0.482003\pi$
$641$	2.86141			0.113019			0.0565094	+	0.998402i	$0.482003\pi$
$642$			14.7446i			0.581921i
$643$		−	11.8832i		−	0.468626i	−0.972161	−	0.234313i	$-0.924716\pi$
$643$		−	11.8832i		−	0.468626i	0.972161	−	0.234313i	$-0.0752840\pi$
$644$		−	9.25544i		−	0.364715i
$645$	−1.37228			−0.0540335
$646$		−	32.2337i		−	1.26822i
$647$			44.2337i			1.73901i	0.493928	+	0.869503i	$0.335561\pi$
$647$			44.2337i			1.73901i	−0.493928	+	0.869503i	$0.664439\pi$
$648$			1.00000i			0.0392837i
$649$		−	5.02175i		−	0.197121i
$650$	−6.74456			−0.264544
$651$			8.86141i			0.347306i
$652$		−	8.11684i		−	0.317880i
$653$			7.48913i			0.293072i	0.989205	+	0.146536i	$0.0468124\pi$
$653$			7.48913i			0.293072i	−0.989205	+	0.146536i	$0.953188\pi$
$654$	14.1168			0.552012
$655$	13.4891			0.527064
$656$	8.11684			0.316910
$657$	14.0000			0.546192
$658$		0			0
$659$	1.02175			0.0398017			0.0199009	−	0.999802i	$-0.493665\pi$
$659$	1.02175			0.0398017			0.0199009	+	0.999802i	$0.493665\pi$
$660$		−	0.627719i		−	0.0244339i
$661$			22.3505i			0.869335i	0.900591	+	0.434667i	$0.143134\pi$
$661$			22.3505i			0.869335i	−0.900591	+	0.434667i	$0.856866\pi$
$662$	19.4891			0.757466
$663$	−36.2337			−1.40720
$664$			17.4891i			0.678710i
$665$	20.2337			0.784629
$666$	2.00000	−	5.74456i	0.0774984	−	0.222597i
$667$	−25.7228			−0.995991
$668$		−	14.7446i		−	0.570484i
$669$	−12.6277			−0.488216
$670$	2.74456			0.106032
$671$		−	7.13859i		−	0.275582i
$672$			3.37228i			0.130089i
$673$	−2.00000			−0.0770943			−0.0385472	−	0.999257i	$-0.512273\pi$
$673$	−2.00000			−0.0770943			−0.0385472	+	0.999257i	$0.512273\pi$
$674$			23.2554i			0.895766i
$675$	1.00000			0.0384900
$676$	32.4891			1.24958
$677$	−12.9783			−0.498795			−0.249397	−	0.968401i	$-0.580233\pi$
$677$	−12.9783			−0.498795			−0.249397	+	0.968401i	$0.580233\pi$
$678$	18.8614			0.724368
$679$			34.1168i			1.30928i
$680$		−	5.37228i		−	0.206018i
$681$			0.627719i			0.0240542i
$682$	−1.64947			−0.0631614
$683$		−	12.6277i		−	0.483186i	−0.970378	−	0.241593i	$-0.922330\pi$
$683$		−	12.6277i		−	0.483186i	0.970378	−	0.241593i	$-0.0776699\pi$
$684$		−	6.00000i		−	0.229416i
$685$		−	8.74456i		−	0.334113i
$686$			8.86141i			0.338330i
$687$	−27.4891			−1.04878
$688$			1.37228i			0.0523177i
$689$		−	17.7228i		−	0.675185i
$690$			2.74456i			0.104484i
$691$	39.3723			1.49779			0.748896	−	0.662687i	$-0.230584\pi$
$691$	39.3723			1.49779			0.748896	+	0.662687i	$0.230584\pi$
$692$	13.3723			0.508338
$693$	2.11684			0.0804123
$694$	14.9783			0.568567
$695$			7.37228i			0.279647i
$696$	9.37228			0.355255
$697$		−	43.6060i		−	1.65169i
$698$			11.4891i			0.434870i
$699$	−3.25544			−0.123132
$700$	3.37228			0.127460
$701$			16.9783i			0.641260i	0.947205	+	0.320630i	$0.103895\pi$
$701$			16.9783i			0.641260i	−0.947205	+	0.320630i	$0.896105\pi$
$702$	−6.74456			−0.254557
$703$	−12.0000	+	34.4674i	−0.452589	+	1.29996i
$704$	−0.627719			−0.0236580
$705$		0			0
$706$	−12.1168			−0.456023
$707$	−56.4674			−2.12367
$708$		−	8.00000i		−	0.300658i
$709$		−	11.1386i		−	0.418319i	−0.977882	−	0.209159i	$-0.932927\pi$
$709$		−	11.1386i		−	0.418319i	0.977882	−	0.209159i	$-0.0670727\pi$
$710$	−2.74456			−0.103002
$711$			4.74456i			0.177935i
$712$	8.74456			0.327716
$713$	7.21194			0.270089
$714$	18.1168			0.678006
$715$	4.23369			0.158331
$716$			2.74456i			0.102569i
$717$			20.8614i			0.779084i
$718$			8.00000i			0.298557i
$719$	48.0000			1.79010			0.895049	−	0.445968i	$-0.147140\pi$
$719$	48.0000			1.79010			0.895049	+	0.445968i	$0.147140\pi$
$720$		−	1.00000i		−	0.0372678i
$721$			52.2337i			1.94528i
$722$			17.0000i			0.632674i
$723$		−	1.48913i		−	0.0553812i
$724$	−11.2554			−0.418305
$725$		−	9.37228i		−	0.348078i
$726$		−	10.6060i		−	0.393624i
$727$		−	50.4674i		−	1.87173i	−0.352357	−	0.935866i	$-0.614620\pi$
$727$		−	50.4674i		−	1.87173i	0.352357	−	0.935866i	$-0.385380\pi$
$728$	−22.7446			−0.842970
$729$	1.00000			0.0370370
$730$	−14.0000			−0.518163
$731$	7.37228			0.272674
$732$		−	11.3723i		−	0.420332i
$733$	−1.60597			−0.0593178			−0.0296589	−	0.999560i	$-0.509442\pi$
$733$	−1.60597			−0.0593178			−0.0296589	+	0.999560i	$0.509442\pi$
$734$		−	19.3723i		−	0.715044i
$735$			4.37228i			0.161274i
$736$	2.74456			0.101166
$737$	−1.72281			−0.0634606
$738$		−	8.11684i		−	0.298785i
$739$	−26.3505			−0.969320			−0.484660	−	0.874703i	$-0.661057\pi$
$739$	−26.3505			−0.969320			−0.484660	+	0.874703i	$0.661057\pi$
$740$	−2.00000	+	5.74456i	−0.0735215	+	0.211174i
$741$	40.4674			1.48661
$742$			8.86141i			0.325312i
$743$	−31.6060			−1.15951			−0.579755	−	0.814791i	$-0.696852\pi$
$743$	−31.6060			−1.15951			−0.579755	+	0.814791i	$0.696852\pi$
$744$	−2.62772			−0.0963368
$745$			11.4891i			0.420929i
$746$			0.510875i			0.0187045i
$747$	17.4891			0.639894
$748$			3.37228i			0.123303i
$749$	49.7228			1.81683
$750$	−1.00000			−0.0365148
$751$	−14.7446			−0.538037			−0.269018	−	0.963135i	$-0.586699\pi$
$751$	−14.7446			−0.538037			−0.269018	+	0.963135i	$0.586699\pi$
$752$		0			0
$753$			4.00000i			0.145768i
$754$			63.2119i			2.30204i
$755$			22.7446i			0.827759i
$756$	3.37228			0.122649
$757$			45.4891i			1.65333i	0.562694	+	0.826665i	$0.309765\pi$
$757$			45.4891i			1.65333i	−0.562694	+	0.826665i	$0.690235\pi$
$758$		−	28.0000i		−	1.01701i
$759$		−	1.72281i		−	0.0625342i
$760$			6.00000i			0.217643i
$761$	28.1168			1.01923			0.509617	−	0.860401i	$-0.329787\pi$
$761$	28.1168			1.01923			0.509617	+	0.860401i	$0.329787\pi$
$762$			13.4891i			0.488659i
$763$		−	47.6060i		−	1.72345i
$764$		−	10.1168i		−	0.366015i
$765$	−5.37228			−0.194235
$766$	−21.7228			−0.784877
$767$	53.9565			1.94826
$768$	−1.00000			−0.0360844
$769$			32.0000i			1.15395i	0.816762	+	0.576975i	$0.195767\pi$
$769$			32.0000i			1.15395i	−0.816762	+	0.576975i	$0.804233\pi$
$770$	−2.11684			−0.0762858
$771$			0.510875i			0.0183987i
$772$			16.2337i			0.584263i
$773$	−16.3505			−0.588088			−0.294044	−	0.955792i	$-0.595001\pi$
$773$	−16.3505			−0.588088			−0.294044	+	0.955792i	$0.595001\pi$
$774$	1.37228			0.0493256
$775$			2.62772i			0.0943904i
$776$	−10.1168			−0.363174
$777$	−19.3723	−	6.74456i	−0.694977	−	0.241960i
$778$	22.8614			0.819621
$779$			48.7011i			1.74490i
$780$	6.74456			0.241494
$781$	1.72281			0.0616471
$782$		−	14.7446i		−	0.527264i
$783$		−	9.37228i		−	0.334938i
$784$	4.37228			0.156153
$785$			10.6277i			0.379320i
$786$	−13.4891			−0.481141
$787$	35.2119			1.25517			0.627585	−	0.778548i	$-0.284043\pi$
$787$	35.2119			1.25517			0.627585	+	0.778548i	$0.284043\pi$
$788$	7.48913			0.266789
$789$	23.6060			0.840395
$790$		−	4.74456i		−	0.168804i
$791$		−	63.6060i		−	2.26157i
$792$			0.627719i			0.0223050i
$793$	76.7011			2.72373
$794$			14.0000i			0.496841i
$795$		−	2.62772i		−	0.0931956i
$796$		−	0.744563i		−	0.0263903i
$797$		−	0.744563i		−	0.0263738i	−0.999913	−	0.0131869i	$-0.995802\pi$
$797$		−	0.744563i		−	0.0263738i	0.999913	−	0.0131869i	$-0.00419764\pi$
$798$	−20.2337			−0.716265
$799$		0			0
$800$			1.00000i			0.0353553i
$801$		−	8.74456i		−	0.308974i
$802$	−16.9783			−0.599523
$803$	8.78806			0.310124
$804$	−2.74456			−0.0967933
$805$	9.25544			0.326211
$806$		−	17.7228i		−	0.624259i
$807$	−6.23369			−0.219436
$808$		−	16.7446i		−	0.589072i
$809$		−	6.00000i		−	0.210949i	−0.994422	−	0.105474i	$-0.966364\pi$
$809$		−	6.00000i		−	0.210949i	0.994422	−	0.105474i	$-0.0336361\pi$
$810$	−1.00000			−0.0351364
$811$	−9.48913			−0.333208			−0.166604	−	0.986024i	$-0.553280\pi$
$811$	−9.48913			−0.333208			−0.166604	+	0.986024i	$0.553280\pi$
$812$		−	31.6060i		−	1.10915i
$813$	21.4891			0.753657
$814$	1.25544	−	3.60597i	0.0440031	−	0.126389i
$815$	8.11684			0.284321
$816$			5.37228i			0.188067i
$817$	−8.23369			−0.288060
$818$	1.48913			0.0520660
$819$			22.7446i			0.794759i
$820$			8.11684i			0.283452i
$821$	−43.7228			−1.52594			−0.762968	−	0.646436i	$-0.776259\pi$
$821$	−43.7228			−1.52594			−0.762968	+	0.646436i	$0.776259\pi$
$822$			8.74456i			0.305002i
$823$	−2.97825			−0.103815			−0.0519076	−	0.998652i	$-0.516530\pi$
$823$	−2.97825			−0.103815			−0.0519076	+	0.998652i	$0.516530\pi$
$824$	−15.4891			−0.539589
$825$	0.627719			0.0218544
$826$	−26.9783			−0.938693
$827$			24.8614i			0.864516i	0.901750	+	0.432258i	$0.142283\pi$
$827$			24.8614i			0.864516i	−0.901750	+	0.432258i	$0.857717\pi$
$828$		−	2.74456i		−	0.0953801i
$829$		−	4.86141i		−	0.168844i	−0.996430	−	0.0844218i	$-0.973096\pi$
$829$		−	4.86141i		−	0.168844i	0.996430	−	0.0844218i	$-0.0269043\pi$
$830$	−17.4891			−0.607056
$831$			13.4891i			0.467933i
$832$		−	6.74456i		−	0.233826i
$833$		−	23.4891i		−	0.813850i
$834$		−	7.37228i		−	0.255281i
$835$	14.7446			0.510257
$836$		−	3.76631i		−	0.130261i
$837$			2.62772i			0.0908272i
$838$			8.00000i			0.276355i
$839$	13.7228			0.473764			0.236882	−	0.971538i	$-0.423875\pi$
$839$	13.7228			0.473764			0.236882	+	0.971538i	$0.423875\pi$
$840$	−3.37228			−0.116355
$841$	−58.8397			−2.02895
$842$	2.74456			0.0945839
$843$			24.9783i			0.860297i
$844$	4.86141			0.167337
$845$			32.4891i			1.11766i
$846$		0			0
$847$	−35.7663			−1.22895
$848$	−2.62772			−0.0902362
$849$		−	19.2554i		−	0.660845i
$850$	5.37228			0.184268
$851$	−5.48913	+	15.7663i	−0.188165	+	0.540462i
$852$	2.74456			0.0940272
$853$		−	21.2554i		−	0.727772i	−0.931443	−	0.363886i	$-0.881450\pi$
$853$		−	21.2554i		−	0.727772i	0.931443	−	0.363886i	$-0.118550\pi$
$854$	−38.3505			−1.31233
$855$	6.00000			0.205196
$856$			14.7446i			0.503959i
$857$		−	21.6060i		−	0.738046i	−0.929420	−	0.369023i	$-0.879692\pi$
$857$		−	21.6060i		−	0.738046i	0.929420	−	0.369023i	$-0.120308\pi$
$858$	−4.23369			−0.144536
$859$		−	30.0000i		−	1.02359i	−0.859109	−	0.511793i	$-0.828981\pi$
$859$		−	30.0000i		−	1.02359i	0.859109	−	0.511793i	$-0.171019\pi$
$860$	−1.37228			−0.0467944
$861$	−27.3723			−0.932845
$862$	19.3723			0.659823
$863$	−38.5842			−1.31342			−0.656711	−	0.754142i	$-0.728053\pi$
$863$	−38.5842			−1.31342			−0.656711	+	0.754142i	$0.728053\pi$
$864$			1.00000i			0.0340207i
$865$			13.3723i			0.454671i
$866$		−	11.4891i		−	0.390416i
$867$	11.8614			0.402834
$868$			8.86141i			0.300776i
$869$			2.97825i			0.101030i
$870$			9.37228i			0.317750i
$871$		−	18.5109i		−	0.627217i
$872$	14.1168			0.478057
$873$			10.1168i			0.342403i
$874$			16.4674i			0.557017i
$875$			3.37228i			0.114004i
$876$	14.0000			0.473016
$877$	23.8832			0.806477			0.403238	−	0.915095i	$-0.367885\pi$
$877$	23.8832			0.806477			0.403238	+	0.915095i	$0.367885\pi$
$878$	6.62772			0.223675
$879$	−4.11684			−0.138858
$880$		−	0.627719i		−	0.0211604i
$881$	−49.3723			−1.66339			−0.831697	−	0.555229i	$-0.812630\pi$
$881$	−49.3723			−1.66339			−0.831697	+	0.555229i	$0.812630\pi$
$882$		−	4.37228i		−	0.147222i
$883$		−	5.13859i		−	0.172927i	−0.996255	−	0.0864637i	$-0.972443\pi$
$883$		−	5.13859i		−	0.172927i	0.996255	−	0.0864637i	$-0.0275567\pi$
$884$	−36.2337			−1.21867
$885$	8.00000			0.268917
$886$		−	4.00000i		−	0.134383i
$887$	−4.62772			−0.155384			−0.0776918	−	0.996977i	$-0.524755\pi$
$887$	−4.62772			−0.155384			−0.0776918	+	0.996977i	$0.524755\pi$
$888$	2.00000	−	5.74456i	0.0671156	−	0.192775i
$889$	45.4891			1.52566
$890$			8.74456i			0.293118i
$891$	0.627719			0.0210294
$892$	−12.6277			−0.422807
$893$		0			0
$894$		−	11.4891i		−	0.384254i
$895$	−2.74456			−0.0917406
$896$			3.37228i			0.112660i
$897$	18.5109			0.618060
$898$	−8.97825			−0.299608
$899$	24.6277			0.821380
$900$	1.00000			0.0333333
$901$			14.1168i			0.470300i
$902$		−	5.09509i		−	0.169648i
$903$		−	4.62772i		−	0.154001i
$904$	18.8614			0.627321
$905$		−	11.2554i		−	0.374143i
$906$		−	22.7446i		−	0.755637i
$907$		−	27.7228i		−	0.920521i	−0.887784	−	0.460260i	$-0.847756\pi$
$907$		−	27.7228i		−	0.920521i	0.887784	−	0.460260i	$-0.152244\pi$
$908$			0.627719i			0.0208316i
$909$	−16.7446			−0.555382
$910$		−	22.7446i		−	0.753975i
$911$			30.5109i			1.01087i	0.862865	+	0.505435i	$0.168668\pi$
$911$			30.5109i			1.01087i	−0.862865	+	0.505435i	$0.831332\pi$
$912$		−	6.00000i		−	0.198680i
$913$	10.9783			0.363327
$914$	−11.3723			−0.376162
$915$	11.3723			0.375956
$916$	−27.4891			−0.908266
$917$			45.4891i			1.50218i
$918$	5.37228			0.177312
$919$			23.7228i			0.782543i	0.920275	+	0.391272i	$0.127965\pi$
$919$			23.7228i			0.782543i	−0.920275	+	0.391272i	$0.872035\pi$
$920$			2.74456i			0.0904856i
$921$	−25.4891			−0.839895
$922$	−25.6060			−0.843288
$923$			18.5109i			0.609293i
$924$	2.11684			0.0696391
$925$	−5.74456	−	2.00000i	−0.188880	−	0.0657596i
$926$	−22.2337			−0.730644
$927$			15.4891i			0.508730i
$928$	9.37228			0.307660
$929$	−17.6060			−0.577633			−0.288817	−	0.957384i	$-0.593262\pi$
$929$	−17.6060			−0.577633			−0.288817	+	0.957384i	$0.593262\pi$
$930$		−	2.62772i		−	0.0861663i
$931$			26.2337i			0.859774i
$932$	−3.25544			−0.106635
$933$		−	8.86141i		−	0.290109i
$934$	20.6277			0.674960
$935$	−3.37228			−0.110285
$936$	−6.74456			−0.220453
$937$	16.7446			0.547021			0.273511	−	0.961869i	$-0.411815\pi$
$937$	16.7446			0.547021			0.273511	+	0.961869i	$0.411815\pi$
$938$			9.25544i			0.302201i
$939$		−	16.2337i		−	0.529766i
$940$		0			0
$941$	−43.7228			−1.42532			−0.712661	−	0.701508i	$-0.752510\pi$
$941$	−43.7228			−1.42532			−0.712661	+	0.701508i	$0.752510\pi$
$942$		−	10.6277i		−	0.346270i
$943$			22.2772i			0.725445i
$944$		−	8.00000i		−	0.260378i
$945$			3.37228i			0.109700i
$946$	0.861407			0.0280067
$947$		−	23.1386i		−	0.751903i	−0.926639	−	0.375952i	$-0.877316\pi$
$947$		−	23.1386i		−	0.751903i	0.926639	−	0.375952i	$-0.122684\pi$
$948$			4.74456i			0.154096i
$949$			94.4239i			3.06513i
$950$	−6.00000			−0.194666
$951$	−10.6277			−0.344627
$952$	18.1168			0.587170
$953$	−47.9565			−1.55346			−0.776732	−	0.629832i	$-0.783124\pi$
$953$	−47.9565			−1.55346			−0.776732	+	0.629832i	$0.783124\pi$
$954$			2.62772i			0.0850755i
$955$	10.1168			0.327373
$956$			20.8614i			0.674706i
$957$		−	5.88316i		−	0.190175i
$958$	−34.9783			−1.13010
$959$	29.4891			0.952254
$960$		−	1.00000i		−	0.0322749i
$961$	24.0951			0.777261
$962$	38.7446	+	13.4891i	1.24917	+	0.434907i
$963$	14.7446			0.475137
$964$		−	1.48913i		−	0.0479615i
$965$	−16.2337			−0.522581
$966$	−9.25544			−0.297789
$967$			3.48913i			0.112203i	0.998425	+	0.0561014i	$0.0178670\pi$
$967$			3.48913i			0.112203i	−0.998425	+	0.0561014i	$0.982133\pi$
$968$		−	10.6060i		−	0.340889i
$969$	−32.2337			−1.03550
$970$		−	10.1168i		−	0.324832i
$971$	−46.3505			−1.48746			−0.743730	−	0.668480i	$-0.766945\pi$
$971$	−46.3505			−1.48746			−0.743730	+	0.668480i	$0.766945\pi$
$972$	1.00000			0.0320750
$973$	−24.8614			−0.797020
$974$	−7.25544			−0.232479
$975$			6.74456i			0.215999i
$976$		−	11.3723i		−	0.364018i
$977$			2.39403i			0.0765918i	0.999266	+	0.0382959i	$0.0121929\pi$
$977$			2.39403i			0.0765918i	−0.999266	+	0.0382959i	$0.987807\pi$
$978$	−8.11684			−0.259548
$979$		−	5.48913i		−	0.175433i
$980$			4.37228i			0.139667i
$981$		−	14.1168i		−	0.450716i
$982$			32.4674i			1.03608i
$983$	39.6060			1.26323			0.631617	−	0.775280i	$-0.282391\pi$
$983$	39.6060			1.26323			0.631617	+	0.775280i	$0.282391\pi$
$984$		−	8.11684i		−	0.258756i
$985$			7.48913i			0.238623i
$986$		−	50.3505i		−	1.60349i
$987$		0			0
$988$	40.4674			1.28744
$989$	−3.76631			−0.119762
$990$	−0.627719			−0.0199502
$991$			1.13859i			0.0361686i	0.999836	+	0.0180843i	$0.00575673\pi$
$991$			1.13859i			0.0361686i	−0.999836	+	0.0180843i	$0.994243\pi$
$992$	−2.62772			−0.0834302
$993$		−	19.4891i		−	0.618469i
$994$		−	9.25544i		−	0.293565i
$995$	0.744563			0.0236042
$996$	17.4891			0.554164
$997$			20.4674i			0.648208i	0.946021	+	0.324104i	$0.105063\pi$
$997$			20.4674i			0.648208i	−0.946021	+	0.324104i	$0.894937\pi$
$998$	20.9783			0.664055
$999$	−5.74456	−	2.00000i	−0.181750	−	0.0632772i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.h.e.961.2	✓	4
3.2	odd	2		3330.2.h.k.2071.4		4
37.36	even	2	inner	1110.2.h.e.961.4	yes	4
111.110	odd	2		3330.2.h.k.2071.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.h.e.961.2	✓	4	1.1	even	1	trivial
1110.2.h.e.961.4	yes	4	37.36	even	2	inner
3330.2.h.k.2071.2		4	111.110	odd	2
3330.2.h.k.2071.4		4	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} -1.00000i q^{5} +1.00000i q^{6} +3.37228 q^{7} +1.00000i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} -1.00000i q^{5} +1.00000i q^{6} +3.37228 q^{7} +1.00000i q^{8} +1.00000 q^{9} -1.00000 q^{10} +0.627719 q^{11} +1.00000 q^{12} +6.74456i q^{13} -3.37228i q^{14} +1.00000i q^{15} +1.00000 q^{16} -5.37228i q^{17} -1.00000i q^{18} +6.00000i q^{19} +1.00000i q^{20} -3.37228 q^{21} -0.627719i q^{22} +2.74456i q^{23} -1.00000i q^{24} -1.00000 q^{25} +6.74456 q^{26} -1.00000 q^{27} -3.37228 q^{28} +9.37228i q^{29} +1.00000 q^{30} -2.62772i q^{31} -1.00000i q^{32} -0.627719 q^{33} -5.37228 q^{34} -3.37228i q^{35} -1.00000 q^{36} +(5.74456 + 2.00000i) q^{37} +6.00000 q^{38} -6.74456i q^{39} +1.00000 q^{40} +8.11684 q^{41} +3.37228i q^{42} +1.37228i q^{43} -0.627719 q^{44} -1.00000i q^{45} +2.74456 q^{46} -1.00000 q^{48} +4.37228 q^{49} +1.00000i q^{50} +5.37228i q^{51} -6.74456i q^{52} -2.62772 q^{53} +1.00000i q^{54} -0.627719i q^{55} +3.37228i q^{56} -6.00000i q^{57} +9.37228 q^{58} -8.00000i q^{59} -1.00000i q^{60} -11.3723i q^{61} -2.62772 q^{62} +3.37228 q^{63} -1.00000 q^{64} +6.74456 q^{65} +0.627719i q^{66} -2.74456 q^{67} +5.37228i q^{68} -2.74456i q^{69} -3.37228 q^{70} +2.74456 q^{71} +1.00000i q^{72} +14.0000 q^{73} +(2.00000 - 5.74456i) q^{74} +1.00000 q^{75} -6.00000i q^{76} +2.11684 q^{77} -6.74456 q^{78} +4.74456i q^{79} -1.00000i q^{80} +1.00000 q^{81} -8.11684i q^{82} +17.4891 q^{83} +3.37228 q^{84} -5.37228 q^{85} +1.37228 q^{86} -9.37228i q^{87} +0.627719i q^{88} -8.74456i q^{89} -1.00000 q^{90} +22.7446i q^{91} -2.74456i q^{92} +2.62772i q^{93} +6.00000 q^{95} +1.00000i q^{96} +10.1168i q^{97} -4.37228i q^{98} +0.627719 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} - 4 q^{4} + 2 q^{7} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^3 - 4 * q^4 + 2 * q^7 + 4 * q^9	\( 4 q - 4 q^{3} - 4 q^{4} + 2 q^{7} + 4 q^{9} - 4 q^{10} + 14 q^{11} + 4 q^{12} + 4 q^{16} - 2 q^{21} - 4 q^{25} + 4 q^{26} - 4 q^{27} - 2 q^{28} + 4 q^{30} - 14 q^{33} - 10 q^{34} - 4 q^{36} + 24 q^{38} + 4 q^{40} - 2 q^{41} - 14 q^{44} - 12 q^{46} - 4 q^{48} + 6 q^{49} - 22 q^{53} + 26 q^{58} - 22 q^{62} + 2 q^{63} - 4 q^{64} + 4 q^{65} + 12 q^{67} - 2 q^{70} - 12 q^{71} + 56 q^{73} + 8 q^{74} + 4 q^{75} - 26 q^{77} - 4 q^{78} + 4 q^{81} + 24 q^{83} + 2 q^{84} - 10 q^{85} - 6 q^{86} - 4 q^{90} + 24 q^{95} + 14 q^{99}+O(q^{100}) \) 4 * q - 4 * q^3 - 4 * q^4 + 2 * q^7 + 4 * q^9 - 4 * q^10 + 14 * q^11 + 4 * q^12 + 4 * q^16 - 2 * q^21 - 4 * q^25 + 4 * q^26 - 4 * q^27 - 2 * q^28 + 4 * q^30 - 14 * q^33 - 10 * q^34 - 4 * q^36 + 24 * q^38 + 4 * q^40 - 2 * q^41 - 14 * q^44 - 12 * q^46 - 4 * q^48 + 6 * q^49 - 22 * q^53 + 26 * q^58 - 22 * q^62 + 2 * q^63 - 4 * q^64 + 4 * q^65 + 12 * q^67 - 2 * q^70 - 12 * q^71 + 56 * q^73 + 8 * q^74 + 4 * q^75 - 26 * q^77 - 4 * q^78 + 4 * q^81 + 24 * q^83 + 2 * q^84 - 10 * q^85 - 6 * q^86 - 4 * q^90 + 24 * q^95 + 14 * q^99

Introduction

L-functions

Modular forms

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Database

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