LMFDB - Embedded newform 115.2.b.b.24.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(24,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, 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("115.24");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.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:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.527896576.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 2x^{6} + 2x^{5} + 7x^{4} - 10x^{3} + 8x^{2} + 4x + 1 $ x^8 - 2x^7 + 2x^6 + 2x^5 + 7x^4 - 10x^3 + 8x^2 + 4*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			24.1
Root			$1.47984 + 1.47984i$ of defining polynomial
Character	$\chi$	$=$	115.24
Dual form			115.2.b.b.24.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.37988i q^{2} -1.95969i q^{3} -3.66382 q^{4} +(0.479844 + 2.18398i) q^{5} -4.66382 q^{6} -2.28394i q^{7} +3.95969i q^{8} -0.840379 q^{9} +O(q^{10})$	\(q-2.37988i q^{2} -1.95969i q^{3} -3.66382 q^{4} +(0.479844 + 2.18398i) q^{5} -4.66382 q^{6} -2.28394i q^{7} +3.95969i q^{8} -0.840379 q^{9} +(5.19760 - 1.14197i) q^{10} +1.12432 q^{11} +7.17995i q^{12} +5.95969i q^{13} -5.43550 q^{14} +(4.27991 - 0.940345i) q^{15} +2.09594 q^{16} -5.80007i q^{17} +2.00000i q^{18} +4.08401 q^{19} +(-1.75806 - 8.00169i) q^{20} -4.47581 q^{21} -2.67575i q^{22} -1.00000i q^{23} +7.75976 q^{24} +(-4.53950 + 2.09594i) q^{25} +14.1833 q^{26} -4.23218i q^{27} +8.36795i q^{28} +0.408263 q^{29} +(-2.23791 - 10.1857i) q^{30} -3.19187 q^{31} +2.93130i q^{32} -2.20332i q^{33} -13.8035 q^{34} +(4.98807 - 1.09594i) q^{35} +3.07900 q^{36} +9.80345i q^{37} -9.71944i q^{38} +11.6791 q^{39} +(-8.64786 + 1.90003i) q^{40} +6.27087 q^{41} +10.6519i q^{42} +7.75474i q^{43} -4.11931 q^{44} +(-0.403251 - 1.83537i) q^{45} -2.37988 q^{46} +6.40020i q^{47} -4.10738i q^{48} +1.78361 q^{49} +(4.98807 + 10.8035i) q^{50} -11.3663 q^{51} -21.8352i q^{52} -6.73590i q^{53} -10.0721 q^{54} +(0.539499 + 2.45549i) q^{55} +9.04370 q^{56} -8.00339i q^{57} -0.971615i q^{58} +4.75976 q^{59} +(-15.6808 + 3.44526i) q^{60} -6.33265 q^{61} +7.59627i q^{62} +1.91938i q^{63} +11.1680 q^{64} +(-13.0158 + 2.85972i) q^{65} -5.24363 q^{66} -0.283942i q^{67} +21.2504i q^{68} -1.95969 q^{69} +(-2.60819 - 11.8710i) q^{70} -13.9516 q^{71} -3.32764i q^{72} +9.61659i q^{73} +23.3310 q^{74} +(4.10738 + 8.89600i) q^{75} -14.9631 q^{76} -2.56788i q^{77} -27.7949i q^{78} -4.48387 q^{79} +(1.00572 + 4.57747i) q^{80} -10.8149 q^{81} -14.9239i q^{82} -10.8223i q^{83} +16.3986 q^{84} +(12.6672 - 2.78313i) q^{85} +18.4553 q^{86} -0.800068i q^{87} +4.45196i q^{88} -5.68414 q^{89} +(-4.36795 + 0.959689i) q^{90} +13.6116 q^{91} +3.66382i q^{92} +6.25508i q^{93} +15.2317 q^{94} +(1.95969 + 8.91938i) q^{95} +5.74444 q^{96} -11.0676i q^{97} -4.24477i q^{98} -0.944856 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{4} - 6 q^{5} - 12 q^{6} - 8 q^{9}+O(q^{10}) $ 8 * q - 4 * q^4 - 6 * q^5 - 12 * q^6 - 8 * q^9	$ 8 q - 4 q^{4} - 6 q^{5} - 12 q^{6} - 8 q^{9} + 6 q^{10} + 4 q^{11} + 8 q^{14} + 6 q^{15} + 4 q^{16} + 8 q^{19} - 8 q^{20} - 4 q^{21} + 24 q^{24} - 16 q^{25} + 12 q^{26} - 8 q^{29} - 2 q^{30} - 28 q^{34} + 28 q^{35} - 16 q^{36} + 16 q^{39} - 10 q^{40} - 16 q^{41} - 12 q^{44} + 24 q^{45} + 28 q^{50} + 20 q^{51} - 44 q^{54} - 16 q^{55} + 28 q^{56} - 16 q^{60} - 16 q^{61} + 40 q^{64} - 14 q^{65} - 16 q^{66} + 4 q^{69} - 28 q^{70} - 48 q^{71} + 72 q^{74} - 36 q^{76} - 48 q^{79} - 2 q^{80} + 16 q^{81} - 4 q^{84} + 12 q^{85} + 28 q^{86} + 16 q^{89} - 4 q^{90} + 52 q^{91} + 84 q^{94} - 4 q^{95} + 60 q^{96} - 72 q^{99}+O(q^{100}) $ 8 * q - 4 * q^4 - 6 * q^5 - 12 * q^6 - 8 * q^9 + 6 * q^10 + 4 * q^11 + 8 * q^14 + 6 * q^15 + 4 * q^16 + 8 * q^19 - 8 * q^20 - 4 * q^21 + 24 * q^24 - 16 * q^25 + 12 * q^26 - 8 * q^29 - 2 * q^30 - 28 * q^34 + 28 * q^35 - 16 * q^36 + 16 * q^39 - 10 * q^40 - 16 * q^41 - 12 * q^44 + 24 * q^45 + 28 * q^50 + 20 * q^51 - 44 * q^54 - 16 * q^55 + 28 * q^56 - 16 * q^60 - 16 * q^61 + 40 * q^64 - 14 * q^65 - 16 * q^66 + 4 * q^69 - 28 * q^70 - 48 * q^71 + 72 * q^74 - 36 * q^76 - 48 * q^79 - 2 * q^80 + 16 * q^81 - 4 * q^84 + 12 * q^85 + 28 * q^86 + 16 * q^89 - 4 * q^90 + 52 * q^91 + 84 * q^94 - 4 * q^95 + 60 * q^96 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	2.37988i		−	1.68283i	−0.540391	−	0.841414i	$-0.681724\pi$
$2$		−	2.37988i		−	1.68283i	0.540391	−	0.841414i	$-0.318276\pi$
$3$		−	1.95969i		−	1.13143i	−0.824602	−	0.565713i	$-0.808601\pi$
$3$		−	1.95969i		−	1.13143i	0.824602	−	0.565713i	$-0.191399\pi$
$4$	−3.66382			−1.83191
$5$	0.479844	+	2.18398i	0.214593	+	0.976704i
$5$	0.479844	+	2.18398i	0.214593	+	0.976704i
$6$	−4.66382			−1.90400
$7$		−	2.28394i		−	0.863249i	−0.902053	−	0.431624i	$-0.857941\pi$
$7$		−	2.28394i		−	0.863249i	0.902053	−	0.431624i	$-0.142059\pi$
$8$			3.95969i			1.39996i
$9$	−0.840379			−0.280126
$10$	5.19760	−	1.14197i	1.64362	−	0.361123i
$11$	1.12432			0.338996			0.169498	−	0.985531i	$-0.445785\pi$
$11$	1.12432			0.338996			0.169498	+	0.985531i	$0.445785\pi$
$12$			7.17995i			2.07267i
$13$			5.95969i			1.65292i	0.562995	+	0.826460i	$0.309649\pi$
$13$			5.95969i			1.65292i	−0.562995	+	0.826460i	$0.690351\pi$
$14$	−5.43550			−1.45270
$15$	4.27991	−	0.940345i	1.10507	−	0.242796i
$16$	2.09594			0.523984
$17$		−	5.80007i		−	1.40672i	−0.710832	−	0.703362i	$-0.751682\pi$
$17$		−	5.80007i		−	1.40672i	0.710832	−	0.703362i	$-0.248318\pi$
$18$			2.00000i			0.471405i
$19$	4.08401			0.936936			0.468468	−	0.883480i	$-0.344806\pi$
$19$	4.08401			0.936936			0.468468	+	0.883480i	$0.344806\pi$
$20$	−1.75806	−	8.00169i	−0.393115	−	1.78923i
$21$	−4.47581			−0.976703
$22$		−	2.67575i		−	0.570471i
$23$		−	1.00000i		−	0.208514i
$23$		−	1.00000i		−	0.208514i
$24$	7.75976			1.58395
$25$	−4.53950	+	2.09594i	−0.907900	+	0.419187i
$26$	14.1833			2.78158
$27$		−	4.23218i		−	0.814484i
$28$			8.36795i			1.58139i
$29$	0.408263			0.0758125			0.0379062	−	0.999281i	$-0.487931\pi$
$29$	0.408263			0.0758125			0.0379062	+	0.999281i	$0.487931\pi$
$30$	−2.23791	−	10.1857i	−0.408584	−	1.85964i
$31$	−3.19187			−0.573277			−0.286639	−	0.958039i	$-0.592538\pi$
$31$	−3.19187			−0.573277			−0.286639	+	0.958039i	$0.592538\pi$
$32$			2.93130i			0.518186i
$33$		−	2.20332i		−	0.383549i
$34$	−13.8035			−2.36727
$35$	4.98807	−	1.09594i	0.843138	−	0.185247i
$36$	3.07900			0.513166
$37$			9.80345i			1.61168i	0.592135	+	0.805839i	$0.298285\pi$
$37$			9.80345i			1.61168i	−0.592135	+	0.805839i	$0.701715\pi$
$38$		−	9.71944i		−	1.57670i
$39$	11.6791			1.87016
$40$	−8.64786	+	1.90003i	−1.36735	+	0.300422i
$41$	6.27087			0.979345			0.489673	−	0.871906i	$-0.337116\pi$
$41$	6.27087			0.979345			0.489673	+	0.871906i	$0.337116\pi$
$42$			10.6519i			1.64362i
$43$			7.75474i			1.18259i	0.806456	+	0.591294i	$0.201383\pi$
$43$			7.75474i			1.18259i	−0.806456	+	0.591294i	$0.798617\pi$
$44$	−4.11931			−0.621009
$45$	−0.403251	−	1.83537i	−0.0601131	−	0.273600i
$46$	−2.37988			−0.350894
$47$			6.40020i			0.933566i	0.884372	+	0.466783i	$0.154587\pi$
$47$			6.40020i			0.933566i	−0.884372	+	0.466783i	$0.845413\pi$
$48$		−	4.10738i		−	0.592850i
$49$	1.78361			0.254801
$50$	4.98807	+	10.8035i	0.705420	+	1.52784i
$51$	−11.3663			−1.59160
$52$		−	21.8352i		−	3.02800i
$53$		−	6.73590i		−	0.925247i	−0.886555	−	0.462624i	$-0.846908\pi$
$53$		−	6.73590i		−	0.925247i	0.886555	−	0.462624i	$-0.153092\pi$
$54$	−10.0721			−1.37064
$55$	0.539499	+	2.45549i	0.0727460	+	0.331098i
$56$	9.04370			1.20851
$57$		−	8.00339i		−	1.06007i
$58$		−	0.971615i		−	0.127579i
$59$	4.75976			0.619667			0.309834	−	0.950791i	$-0.399727\pi$
$59$	4.75976			0.619667			0.309834	+	0.950791i	$0.399727\pi$
$60$	−15.6808	+	3.44526i	−2.02439	+	0.444781i
$61$	−6.33265			−0.810813			−0.405406	−	0.914137i	$-0.632870\pi$
$61$	−6.33265			−0.810813			−0.405406	+	0.914137i	$0.632870\pi$
$62$			7.59627i			0.964727i
$63$			1.91938i			0.241819i
$64$	11.1680			1.39600
$65$	−13.0158	+	2.85972i	−1.61441	+	0.354705i
$66$	−5.24363			−0.645446
$67$		−	0.283942i		−	0.0346890i	−0.999850	−	0.0173445i	$-0.994479\pi$
$67$		−	0.283942i		−	0.0346890i	0.999850	−	0.0173445i	$-0.00552120\pi$
$68$			21.2504i			2.57699i
$69$	−1.95969			−0.235919
$70$	−2.60819	−	11.8710i	−0.311739	−	1.41886i
$71$	−13.9516			−1.65575			−0.827877	−	0.560910i	$-0.810451\pi$
$71$	−13.9516			−1.65575			−0.827877	+	0.560910i	$0.810451\pi$
$72$		−	3.32764i		−	0.392166i
$73$			9.61659i			1.12554i	0.826615	+	0.562769i	$0.190264\pi$
$73$			9.61659i			1.12554i	−0.826615	+	0.562769i	$0.809736\pi$
$74$	23.3310			2.71218
$75$	4.10738	+	8.89600i	0.474280	+	1.02722i
$76$	−14.9631			−1.71638
$77$		−	2.56788i		−	0.292637i
$78$		−	27.7949i		−	3.14715i
$79$	−4.48387			−0.504475			−0.252238	−	0.967665i	$-0.581166\pi$
$79$	−4.48387			−0.504475			−0.252238	+	0.967665i	$0.581166\pi$
$80$	1.00572	+	4.57747i	0.112443	+	0.511777i
$81$	−10.8149			−1.20166
$82$		−	14.9239i		−	1.64807i
$83$		−	10.8223i		−	1.18790i	−0.804501	−	0.593951i	$-0.797567\pi$
$83$		−	10.8223i		−	1.18790i	0.804501	−	0.593951i	$-0.202433\pi$
$84$	16.3986			1.78923
$85$	12.6672	−	2.78313i	1.37395	−	0.301873i
$86$	18.4553			1.99009
$87$		−	0.800068i		−	0.0857763i
$88$			4.45196i			0.474581i
$89$	−5.68414			−0.602518			−0.301259	−	0.953542i	$-0.597407\pi$
$89$	−5.68414			−0.602518			−0.301259	+	0.953542i	$0.597407\pi$
$90$	−4.36795	+	0.959689i	−0.460422	+	0.101160i
$91$	13.6116			1.42688
$92$			3.66382i			0.381980i
$93$			6.25508i			0.648621i
$94$	15.2317			1.57103
$95$	1.95969	+	8.91938i	0.201060	+	0.915109i
$96$	5.74444			0.586290
$97$		−	11.0676i		−	1.12374i	−0.827226	−	0.561870i	$-0.810082\pi$
$97$		−	11.0676i		−	1.12374i	0.827226	−	0.561870i	$-0.189918\pi$
$98$		−	4.24477i		−	0.428787i
$99$	−0.944856			−0.0949616
$100$	16.6319	−	7.67913i	1.66319	−	0.767913i
$101$	1.60014			0.159219			0.0796097	−	0.996826i	$-0.474633\pi$
$101$	1.60014			0.159219			0.0796097	+	0.996826i	$0.474633\pi$
$102$			27.0505i			2.67840i
$103$			1.23218i			0.121411i	0.998156	+	0.0607054i	$0.0193350\pi$
$103$			1.23218i			0.121411i	−0.998156	+	0.0607054i	$0.980665\pi$
$104$	−23.5985			−2.31402
$105$	−2.14769	−	9.77507i	−0.209593	−	0.953949i
$106$	−16.0306			−1.55703
$107$			0.235232i			0.0227408i	0.999935	+	0.0113704i	$0.00361938\pi$
$107$			0.235232i			0.0227408i	−0.999935	+	0.0113704i	$0.996381\pi$
$108$			15.5060i			1.49206i
$109$	−7.43550			−0.712192			−0.356096	−	0.934449i	$-0.615892\pi$
$109$	−7.43550			−0.712192			−0.356096	+	0.934449i	$0.615892\pi$
$110$	5.84377	−	1.28394i	0.557181	−	0.122419i
$111$	19.2117			1.82350
$112$		−	4.78700i		−	0.452329i
$113$		−	2.28394i		−	0.214855i	−0.994213	−	0.107428i	$-0.965739\pi$
$113$		−	2.28394i		−	0.214855i	0.994213	−	0.107428i	$-0.0342614\pi$
$114$	−19.0471			−1.78392
$115$	2.18398	−	0.479844i	0.203657	−	0.0447457i
$116$	−1.49580			−0.138882
$117$		−	5.00840i		−	0.463027i
$118$		−	11.3276i		−	1.04279i
$119$	−13.2470			−1.21435
$120$	3.72347	+	16.9471i	0.339905	+	1.54705i
$121$	−9.73590			−0.885082
$122$			15.0709i			1.36446i
$123$		−	12.2890i		−	1.10806i
$124$	11.6944			1.05019
$125$	−6.75573	−	8.90843i	−0.604251	−	0.796794i
$126$	4.56788			0.406939
$127$			10.2151i			0.906444i	0.891398	+	0.453222i	$0.149725\pi$
$127$			10.2151i			0.906444i	−0.891398	+	0.453222i	$0.850275\pi$
$128$		−	20.7159i		−	1.83105i
$129$	15.1969			1.33801
$130$	6.80579	+	30.9761i	0.596907	+	2.71678i
$131$	−16.2232			−1.41742			−0.708712	−	0.705498i	$-0.750724\pi$
$131$	−16.2232			−1.41742			−0.708712	+	0.705498i	$0.750724\pi$
$132$			8.07256i			0.702626i
$133$		−	9.32764i		−	0.808809i
$134$	−0.675747			−0.0583756
$135$	9.24299	−	2.03079i	0.795510	−	0.174783i
$136$	22.9665			1.96936
$137$			4.89715i			0.418392i	0.977874	+	0.209196i	$0.0670846\pi$
$137$			4.89715i			0.418392i	−0.977874	+	0.209196i	$0.932915\pi$
$138$			4.66382i			0.397011i
$139$	−4.43889			−0.376502			−0.188251	−	0.982121i	$-0.560282\pi$
$139$	−4.43889			−0.376502			−0.188251	+	0.982121i	$0.560282\pi$
$140$	−18.2754	+	4.01531i	−1.54455	+	0.339356i
$141$	12.5424			1.05626
$142$			33.2032i			2.78635i
$143$			6.70060i			0.560333i
$144$	−1.76138			−0.146782
$145$	0.195903	+	0.891636i	0.0162688	+	0.0740463i
$146$	22.8863			1.89409
$147$		−	3.49532i		−	0.288289i
$148$		−	35.9181i		−	2.95245i
$149$	2.78361			0.228042			0.114021	−	0.993478i	$-0.463627\pi$
$149$	2.78361			0.228042			0.114021	+	0.993478i	$0.463627\pi$
$150$	21.1714	−	9.77507i	1.72864	−	0.798131i
$151$	11.9278			0.970669			0.485334	−	0.874329i	$-0.338698\pi$
$151$	11.9278			0.970669			0.485334	+	0.874329i	$0.338698\pi$
$152$			16.1714i			1.31167i
$153$			4.87426i			0.394060i
$154$	−6.11125			−0.492459
$155$	−1.53160	−	6.97097i	−0.123021	−	0.559922i
$156$	−42.7902			−3.42596
$157$		−	22.9550i		−	1.83201i	−0.401167	−	0.916005i	$-0.631395\pi$
$157$		−	22.9550i		−	1.83201i	0.401167	−	0.916005i	$-0.368605\pi$
$158$			10.6711i			0.848945i
$159$	−13.2003			−1.04685
$160$	−6.40190	+	1.40657i	−0.506114	+	0.111199i
$161$	−2.28394			−0.180000
$162$			25.7381i			2.02218i
$163$		−	10.2083i		−	0.799578i	−0.916607	−	0.399789i	$-0.869083\pi$
$163$		−	10.2083i		−	0.799578i	0.916607	−	0.399789i	$-0.130917\pi$
$164$	−22.9753			−1.79407
$165$	4.81199	−	1.05725i	0.374613	−	0.0823068i
$166$	−25.7557			−1.99903
$167$		−	6.84715i		−	0.529849i	−0.964269	−	0.264924i	$-0.914653\pi$
$167$		−	6.84715i		−	0.529849i	0.964269	−	0.264924i	$-0.0853470\pi$
$168$		−	17.7228i		−	1.36735i
$169$	−22.5179			−1.73215
$170$	−6.62351	−	30.1464i	−0.508000	−	2.31212i
$171$	−3.43212			−0.262461
$172$		−	28.4120i		−	2.16639i
$173$			4.29539i			0.326572i	0.986579	+	0.163286i	$0.0522094\pi$
$173$			4.29539i			0.326572i	−0.986579	+	0.163286i	$0.947791\pi$
$174$	−1.90406			−0.144347
$175$	4.78700	+	10.3680i	0.361863	+	0.783743i
$176$	2.35651			0.177628
$177$		−	9.32764i		−	0.701108i
$178$			13.5276i			1.01393i
$179$	14.8626			1.11088			0.555442	−	0.831555i	$-0.312549\pi$
$179$	14.8626			1.11088			0.555442	+	0.831555i	$0.312549\pi$
$180$	1.47744	+	6.72446i	0.110122	+	0.501211i
$181$	13.1311			0.976027			0.488013	−	0.872836i	$-0.337722\pi$
$181$	13.1311			0.976027			0.488013	+	0.872836i	$0.337722\pi$
$182$		−	32.3939i		−	2.40120i
$183$			12.4100i			0.917375i
$184$	3.95969			0.291912
$185$	−21.4105	+	4.70413i	−1.57413	+	0.345855i
$186$	14.8863			1.09152
$187$		−	6.52114i		−	0.476873i
$188$		−	23.4492i		−	1.71021i
$189$	−9.66606			−0.703103
$190$	21.2270	−	4.66382i	1.53997	−	0.338349i
$191$	13.9819			1.01170			0.505848	−	0.862623i	$-0.331180\pi$
$191$	13.9819			1.01170			0.505848	+	0.862623i	$0.331180\pi$
$192$		−	21.8858i		−	1.57947i
$193$			8.71267i			0.627152i	0.949563	+	0.313576i	$0.101527\pi$
$193$			8.71267i			0.627152i	−0.949563	+	0.313576i	$0.898473\pi$
$194$	−26.3394			−1.89106
$195$	5.60417	+	25.5069i	0.401323	+	1.82659i
$196$	−6.53483			−0.466773
$197$			22.4876i			1.60218i	0.598547	+	0.801088i	$0.295745\pi$
$197$			22.4876i			1.60218i	−0.598547	+	0.801088i	$0.704255\pi$
$198$			2.24864i			0.159804i
$199$	−9.01078			−0.638757			−0.319379	−	0.947627i	$-0.603474\pi$
$199$	−9.01078			−0.638757			−0.319379	+	0.947627i	$0.603474\pi$
$200$	−8.29926	−	17.9750i	−0.586846	−	1.27102i
$201$	−0.556437			−0.0392481
$202$		−	3.80813i		−	0.267939i
$203$		−	0.932448i		−	0.0654450i
$204$	41.6442			2.91568
$205$	3.00904	+	13.6954i	0.210161	+	0.956530i
$206$	2.93245			0.204313
$207$			0.840379i			0.0584104i
$208$			12.4911i			0.866104i
$209$	4.59174			0.317617
$210$	−23.2635	+	5.11125i	−1.60533	+	0.352710i
$211$	5.60014			0.385529			0.192765	−	0.981245i	$-0.438255\pi$
$211$	5.60014			0.385529			0.192765	+	0.981245i	$0.438255\pi$
$212$			24.6791i			1.69497i
$213$			27.3408i			1.87336i
$214$	0.559824			0.0382688
$215$	−16.9362	+	3.72107i	−1.15504	+	0.253775i
$216$	16.7581			1.14025
$217$			7.29005i			0.494881i
$218$			17.6956i			1.19850i
$219$	18.8455			1.27346
$220$	−1.97663	−	8.99647i	−0.133264	−	0.606542i
$221$	34.5666			2.32520
$222$		−	45.7215i		−	3.06863i
$223$		−	7.06517i		−	0.473119i	−0.971617	−	0.236559i	$-0.923980\pi$
$223$		−	7.06517i		−	0.473119i	0.971617	−	0.236559i	$-0.0760198\pi$
$224$	6.69493			0.447324
$225$	3.81490	−	1.76138i	0.254327	−	0.117425i
$226$	−5.43550			−0.361564
$227$		−	25.1072i		−	1.66643i	−0.552952	−	0.833213i	$-0.686499\pi$
$227$		−	25.1072i		−	1.66643i	0.552952	−	0.833213i	$-0.313501\pi$
$228$			29.3230i			1.94196i
$229$	3.20366			0.211704			0.105852	−	0.994382i	$-0.466243\pi$
$229$	3.20366			0.211704			0.105852	+	0.994382i	$0.466243\pi$
$230$	−1.14197	−	5.19760i	−0.0752993	−	0.342719i
$231$	−5.03225			−0.331098
$232$			1.61659i			0.106135i
$233$			18.6388i			1.22107i	0.791989	+	0.610535i	$0.209046\pi$
$233$			18.6388i			1.22107i	−0.791989	+	0.610535i	$0.790954\pi$
$234$	−11.9194			−0.779194
$235$	−13.9779	+	3.07110i	−0.911817	+	0.200337i
$236$	−17.4389			−1.13518
$237$			8.78700i			0.570777i
$238$			31.5263i			2.04355i
$239$	−3.18185			−0.205817			−0.102908	−	0.994691i	$-0.532815\pi$
$239$	−3.18185			−0.205817			−0.102908	+	0.994691i	$0.532815\pi$
$240$	8.97042	−	1.97090i	0.579038	−	0.127221i
$241$	4.79844			0.309095			0.154547	−	0.987985i	$-0.450608\pi$
$241$	4.79844			0.309095			0.154547	+	0.987985i	$0.450608\pi$
$242$			23.1703i			1.48944i
$243$			8.49728i			0.545101i
$244$	23.2017			1.48534
$245$	0.855855	+	3.89536i	0.0546786	+	0.248865i
$246$	−29.2462			−1.86467
$247$			24.3394i			1.54868i
$248$		−	12.6388i		−	0.802566i
$249$	−21.2083			−1.34402
$250$	−21.2010	+	16.0778i	−1.34087	+	1.01685i
$251$	−2.24668			−0.141809			−0.0709045	−	0.997483i	$-0.522589\pi$
$251$	−2.24668			−0.141809			−0.0709045	+	0.997483i	$0.522589\pi$
$252$		−	7.03225i		−	0.442990i
$253$		−	1.12432i		−	0.0706855i
$254$	24.3107			1.52539
$255$	−5.45407	−	24.8238i	−0.341547	−	1.55453i
$256$	−26.9653			−1.68533
$257$		−	11.0148i		−	0.687086i	−0.939137	−	0.343543i	$-0.888373\pi$
$257$		−	11.0148i		−	0.687086i	0.939137	−	0.343543i	$-0.111627\pi$
$258$		−	36.1667i		−	2.25164i
$259$	22.3905			1.39128
$260$	47.6876	−	10.4775i	2.95746	−	0.649787i
$261$	−0.343095			−0.0212371
$262$			38.6092i			2.38528i
$263$		−	11.0585i		−	0.681898i	−0.940082	−	0.340949i	$-0.889252\pi$
$263$		−	11.0585i		−	0.681898i	0.940082	−	0.340949i	$-0.110748\pi$
$264$	8.72446			0.536953
$265$	14.7110	−	3.23218i	0.903692	−	0.198551i
$266$	−22.1986			−1.36109
$267$			11.1392i			0.681705i
$268$			1.04031i			0.0635471i
$269$	9.90392			0.603853			0.301926	−	0.953331i	$-0.402370\pi$
$269$	9.90392			0.603853			0.301926	+	0.953331i	$0.402370\pi$
$270$	−4.83303	−	21.9972i	−0.294129	−	1.33871i
$271$	4.82655			0.293192			0.146596	−	0.989196i	$-0.453168\pi$
$271$	4.82655			0.293192			0.146596	+	0.989196i	$0.453168\pi$
$272$		−	12.1566i		−	0.737100i
$273$		−	26.6745i		−	1.61441i
$274$	11.6546			0.704081
$275$	−5.10385	+	2.35651i	−0.307774	+	0.142103i
$276$	7.17995			0.432182
$277$		−	7.54303i		−	0.453217i	−0.973986	−	0.226608i	$-0.927236\pi$
$277$		−	7.54303i		−	0.453217i	0.973986	−	0.226608i	$-0.0727637\pi$
$278$			10.5640i			0.633588i
$279$	2.68238			0.160590
$280$	4.33957	+	19.7512i	0.259339	+	1.18036i
$281$	6.01145			0.358613			0.179306	−	0.983793i	$-0.442615\pi$
$281$	6.01145			0.358613			0.179306	+	0.983793i	$0.442615\pi$
$282$		−	29.8494i		−	1.77751i
$283$		−	15.6388i		−	0.929631i	−0.885407	−	0.464816i	$-0.846121\pi$
$283$		−	15.6388i		−	0.929631i	0.885407	−	0.464816i	$-0.153879\pi$
$284$	51.1163			3.03319
$285$	17.4792	−	3.84038i	1.03538	−	0.227484i
$286$	15.9466			0.942943
$287$		−	14.3223i		−	0.845419i
$288$		−	2.46341i		−	0.145158i
$289$	−16.6408			−0.978870
$290$	2.12198	−	0.466224i	0.124607	−	0.0273776i
$291$	−21.6890			−1.27143
$292$		−	35.2335i		−	2.06188i
$293$		−	3.21639i		−	0.187904i	−0.995577	−	0.0939518i	$-0.970050\pi$
$293$		−	3.21639i		−	0.187904i	0.995577	−	0.0939518i	$-0.0299499\pi$
$294$	−8.31844			−0.485141
$295$	2.28394	+	10.3952i	0.132976	+	0.605231i
$296$	−38.8186			−2.25629
$297$		−	4.75833i		−	0.276106i
$298$		−	6.62465i		−	0.383756i
$299$	5.95969			0.344658
$300$	−15.0487	−	32.5934i	−0.868838	−	1.88178i
$301$	17.7114			1.02087
$302$		−	28.3867i		−	1.63347i
$303$		−	3.13577i		−	0.180145i
$304$	8.55982			0.490940
$305$	−3.03869	−	13.8304i	−0.173995	−	0.791924i
$306$	11.6001			0.663136
$307$			34.4702i			1.96732i	0.180044	+	0.983659i	$0.442376\pi$
$307$			34.4702i			1.96732i	−0.180044	+	0.983659i	$0.557624\pi$
$308$			9.40826i			0.536086i
$309$	2.41470			0.137367
$310$	−16.5901	+	3.64503i	−0.942252	+	0.207024i
$311$	−18.7443			−1.06289			−0.531446	−	0.847092i	$-0.678351\pi$
$311$	−18.7443			−1.06289			−0.531446	+	0.847092i	$0.678351\pi$
$312$			46.2457i			2.61815i
$313$			9.91260i			0.560294i	0.959957	+	0.280147i	$0.0903831\pi$
$313$			9.91260i			0.560294i	−0.959957	+	0.280147i	$0.909617\pi$
$314$	−54.6301			−3.08296
$315$	−4.19187	+	0.921002i	−0.236185	+	0.0518926i
$316$	16.4281			0.924153
$317$			9.24024i			0.518984i	0.965745	+	0.259492i	$0.0835551\pi$
$317$			9.24024i			0.518984i	−0.965745	+	0.259492i	$0.916445\pi$
$318$			31.4150i			1.76167i
$319$	0.459018			0.0257001
$320$	5.35891	+	24.3907i	0.299572	+	1.36348i
$321$	0.460982			0.0257295
$322$			5.43550i			0.302909i
$323$		−	23.6875i		−	1.31801i
$324$	39.6238			2.20132
$325$	−12.4911	−	27.0540i	−0.692883	−	1.50069i
$326$	−24.2946			−1.34555
$327$			14.5713i			0.805793i
$328$			24.8307i			1.37105i
$329$	14.6177			0.805899
$330$	−2.51613	−	11.4520i	−0.138508	−	0.630410i
$331$	−23.9684			−1.31742			−0.658712	−	0.752395i	$-0.728898\pi$
$331$	−23.9684			−1.31742			−0.658712	+	0.752395i	$0.728898\pi$
$332$			39.6509i			2.17613i
$333$		−	8.23862i		−	0.451474i
$334$	−16.2954			−0.891644
$335$	0.620122	−	0.136248i	0.0338809	−	0.00744401i
$336$	−9.38102			−0.511777
$337$		−	9.76477i		−	0.531921i	−0.963984	−	0.265960i	$-0.914311\pi$
$337$		−	9.76477i		−	0.531921i	0.963984	−	0.265960i	$-0.0856890\pi$
$338$			53.5898i			2.91490i
$339$	−4.47581			−0.243093
$340$	−46.4104	+	10.1969i	−2.51696	+	0.553004i
$341$	−3.58869			−0.194338
$342$			8.16802i			0.441676i
$343$		−	20.0613i		−	1.08321i
$344$	−30.7064			−1.65558
$345$	−0.940345	−	4.27991i	−0.0506265	−	0.230423i
$346$	10.2225			0.549565
$347$		−	1.38441i		−	0.0743190i	−0.999309	−	0.0371595i	$-0.988169\pi$
$347$		−	1.38441i		−	0.0743190i	0.999309	−	0.0371595i	$-0.0118310\pi$
$348$			2.93130i			0.157134i
$349$	32.3106			1.72954			0.864772	−	0.502164i	$-0.167463\pi$
$349$	32.3106			1.72954			0.864772	+	0.502164i	$0.167463\pi$
$350$	24.6745	−	11.3925i	1.31891	−	0.608953i
$351$	25.2225			1.34628
$352$			3.29573i			0.175663i
$353$			11.4386i			0.608813i	0.952542	+	0.304406i	$0.0984581\pi$
$353$			11.4386i			0.608813i	−0.952542	+	0.304406i	$0.901542\pi$
$354$	−22.1986			−1.17984
$355$	−6.69461	−	30.4700i	−0.355313	−	1.61718i
$356$	20.8257			1.10376
$357$			25.9600i			1.37395i
$358$		−	35.3712i		−	1.86943i
$359$	−9.95568			−0.525441			−0.262720	−	0.964872i	$-0.584620\pi$
$359$	−9.95568			−0.525441			−0.262720	+	0.964872i	$0.584620\pi$
$360$	7.26748	−	1.59675i	0.383030	−	0.0841561i
$361$	−2.32087			−0.122151
$362$		−	31.2504i		−	1.64248i
$363$			19.0793i			1.00141i
$364$	−49.8704			−2.61392
$365$	−21.0024	+	4.61447i	−1.09932	+	0.241532i
$366$	29.5343			1.54378
$367$		−	27.6785i		−	1.44481i	−0.691472	−	0.722403i	$-0.743037\pi$
$367$		−	27.6785i		−	1.44481i	0.691472	−	0.722403i	$-0.256963\pi$
$368$		−	2.09594i		−	0.109258i
$369$	−5.26991			−0.274341
$370$	11.1953	+	50.9544i	0.582014	+	2.64899i
$371$	−15.3844			−0.798719
$372$		−	22.9175i		−	1.18822i
$373$			28.7356i			1.48787i	0.668251	+	0.743936i	$0.267043\pi$
$373$			28.7356i			1.48787i	−0.668251	+	0.743936i	$0.732957\pi$
$374$	−15.5195			−0.802495
$375$	−17.4578	+	13.2391i	−0.901514	+	0.683665i
$376$	−25.3428			−1.30696
$377$			2.43312i			0.125312i
$378$			23.0040i			1.18320i
$379$	18.2715			0.938546			0.469273	−	0.883053i	$-0.344516\pi$
$379$	18.2715			0.938546			0.469273	+	0.883053i	$0.344516\pi$
$380$	−7.17995	−	32.6790i	−0.368323	−	1.67640i
$381$	20.0184			1.02557
$382$		−	33.2753i		−	1.70251i
$383$		−	29.0356i		−	1.48365i	−0.670593	−	0.741826i	$-0.733960\pi$
$383$		−	29.0356i		−	1.48365i	0.670593	−	0.741826i	$-0.266040\pi$
$384$	−40.5967			−2.07169
$385$	5.60819	−	1.23218i	0.285820	−	0.0627979i
$386$	20.7351			1.05539
$387$		−	6.51693i		−	0.331274i
$388$			40.5495i			2.05859i
$389$	−2.86423			−0.145222			−0.0726112	−	0.997360i	$-0.523133\pi$
$389$	−2.86423			−0.145222			−0.0726112	+	0.997360i	$0.523133\pi$
$390$	60.7034	−	13.3372i	3.07384	−	0.675357i
$391$	−5.80007			−0.293322
$392$			7.06254i			0.356712i
$393$			31.7923i			1.60371i
$394$	53.5177			2.69619
$395$	−2.15156	−	9.79267i	−0.108257	−	0.492723i
$396$	3.46178			0.173961
$397$		−	16.5592i		−	0.831080i	−0.909575	−	0.415540i	$-0.863593\pi$
$397$		−	16.5592i		−	0.831080i	0.909575	−	0.415540i	$-0.136407\pi$
$398$			21.4446i			1.07492i
$399$	−18.2793			−0.915108
$400$	−9.51450	+	4.39295i	−0.475725	+	0.219647i
$401$	−3.09479			−0.154547			−0.0772733	−	0.997010i	$-0.524621\pi$
$401$	−3.09479			−0.154547			−0.0772733	+	0.997010i	$0.524621\pi$
$402$			1.32425i			0.0660477i
$403$		−	19.0226i		−	0.947582i
$404$	−5.86261			−0.291676
$405$	−5.18947	−	23.6195i	−0.257867	−	1.17366i
$406$	−2.21911			−0.110133
$407$			11.0222i			0.546352i
$408$		−	45.0071i		−	2.22818i
$409$	−8.93617			−0.441865			−0.220933	−	0.975289i	$-0.570910\pi$
$409$	−8.93617			−0.441865			−0.220933	+	0.975289i	$0.570910\pi$
$410$	32.5935	−	7.16115i	1.60968	−	0.353664i
$411$	9.59689			0.473379
$412$		−	4.51450i		−	0.222413i
$413$		−	10.8710i		−	0.534927i
$414$	2.00000			0.0982946
$415$	23.6356	−	5.19302i	1.16023	−	0.254915i
$416$	−17.4697			−0.856520
$417$			8.69884i			0.425984i
$418$		−	10.9278i		−	0.534495i
$419$	−24.1237			−1.17852			−0.589260	−	0.807944i	$-0.700581\pi$
$419$	−24.1237			−1.17852			−0.589260	+	0.807944i	$0.700581\pi$
$420$	7.86876	+	35.8141i	0.383956	+	1.74755i
$421$	23.8602			1.16288			0.581438	−	0.813591i	$-0.302490\pi$
$421$	23.8602			1.16288			0.581438	+	0.813591i	$0.302490\pi$
$422$		−	13.3276i		−	0.648779i
$423$		−	5.37860i		−	0.261516i
$424$	26.6721			1.29531
$425$	12.1566	+	26.3294i	0.589680	+	1.27716i
$426$	65.0679			3.15255
$427$			14.4634i			0.699933i
$428$		−	0.861848i		−	0.0416590i
$429$	13.1311			0.633975
$430$	8.85569	+	40.3060i	0.427059	+	1.94373i
$431$	4.45096			0.214395			0.107198	−	0.994238i	$-0.465812\pi$
$431$	4.45096			0.214395			0.107198	+	0.994238i	$0.465812\pi$
$432$		−	8.87039i		−	0.426777i
$433$			8.10929i			0.389707i	0.980832	+	0.194854i	$0.0624232\pi$
$433$			8.10929i			0.389707i	−0.980832	+	0.194854i	$0.937577\pi$
$434$	17.3494			0.832799
$435$	1.74733	−	0.383908i	0.0837780	−	0.0184070i
$436$	27.2423			1.30467
$437$		−	4.08401i		−	0.195365i
$438$		−	44.8501i		−	2.14302i
$439$	−4.47180			−0.213428			−0.106714	−	0.994290i	$-0.534033\pi$
$439$	−4.47180			−0.213428			−0.106714	+	0.994290i	$0.534033\pi$
$440$	−9.72297	+	2.13625i	−0.463525	+	0.101842i
$441$	−1.49891			−0.0713766
$442$		−	82.2643i		−	3.91291i
$443$			9.60047i			0.456132i	0.973646	+	0.228066i	$0.0732402\pi$
$443$			9.60047i			0.456132i	−0.973646	+	0.228066i	$0.926760\pi$
$444$	−70.3883			−3.34048
$445$	−2.72750	−	12.4140i	−0.129296	−	0.588482i
$446$	−16.8142			−0.796177
$447$		−	5.45501i		−	0.258013i
$448$		−	25.5071i		−	1.20510i
$449$	6.79944			0.320886			0.160443	−	0.987045i	$-0.448708\pi$
$449$	6.79944			0.320886			0.160443	+	0.987045i	$0.448708\pi$
$450$	−4.19187	−	9.07900i	−0.197607	−	0.427988i
$451$	7.05047			0.331994
$452$			8.36795i			0.393595i
$453$		−	23.3747i		−	1.09824i
$454$	−59.7522			−2.80431
$455$	6.53144	+	29.7274i	0.306199	+	1.39364i
$456$	31.6909			1.48406
$457$			19.5582i			0.914894i	0.889237	+	0.457447i	$0.151236\pi$
$457$			19.5582i			0.914894i	−0.889237	+	0.457447i	$0.848764\pi$
$458$		−	7.62431i		−	0.356261i
$459$	−24.5470			−1.14575
$460$	−8.00169	+	1.75806i	−0.373081	+	0.0819701i
$461$	−42.7081			−1.98912			−0.994558	−	0.104184i	$-0.966777\pi$
$461$	−42.7081			−1.98912			−0.994558	+	0.104184i	$0.966777\pi$
$462$			11.9761i			0.557181i
$463$		−	7.42209i		−	0.344934i	−0.985015	−	0.172467i	$-0.944826\pi$
$463$		−	7.42209i		−	0.344934i	0.985015	−	0.172467i	$-0.0551738\pi$
$464$	0.855693			0.0397245
$465$	−13.6609	+	3.00146i	−0.633511	+	0.139189i
$466$	44.3581			2.05485
$467$			22.5041i			1.04136i	0.853751	+	0.520682i	$0.174322\pi$
$467$			22.5041i			1.04136i	−0.853751	+	0.520682i	$0.825678\pi$
$468$			18.3499i			0.848223i
$469$	−0.648506			−0.0299452
$470$	7.30885	+	33.2657i	0.337132	+	1.53443i
$471$	−44.9847			−2.07278
$472$			18.8472i			0.867510i
$473$			8.71882i			0.400892i
$474$	20.9120			0.960519
$475$	−18.5394	+	8.55982i	−0.850644	+	0.392752i
$476$	48.5347			2.22458
$477$			5.66071i			0.259186i
$478$			7.57241i			0.346354i
$479$	10.1667			0.464530			0.232265	−	0.972653i	$-0.425386\pi$
$479$	10.1667			0.464530			0.232265	+	0.972653i	$0.425386\pi$
$480$	2.75644	+	12.5457i	0.125814	+	0.572631i
$481$	−58.4255			−2.66398
$482$		−	11.4197i		−	0.520153i
$483$			4.47581i			0.203657i
$484$	35.6706			1.62139
$485$	24.1713	−	5.31070i	1.09756	−	0.241147i
$486$	20.2225			0.917311
$487$		−	34.9917i		−	1.58562i	−0.609467	−	0.792812i	$-0.708616\pi$
$487$		−	34.9917i		−	1.58562i	0.609467	−	0.792812i	$-0.291384\pi$
$488$		−	25.0753i		−	1.13511i
$489$	−20.0051			−0.904664
$490$	9.27048	−	2.03683i	0.418798	−	0.0920146i
$491$	−2.27087			−0.102483			−0.0512415	−	0.998686i	$-0.516318\pi$
$491$	−2.27087			−0.102483			−0.0512415	+	0.998686i	$0.516318\pi$
$492$			45.0245i			2.02986i
$493$		−	2.36795i		−	0.106647i
$494$	57.9249			2.60616
$495$	−0.453384	−	2.06354i	−0.0203781	−	0.0927493i
$496$	−6.68996			−0.300388
$497$			31.8647i			1.42933i
$498$			50.4732i			2.26176i
$499$	−20.9929			−0.939773			−0.469887	−	0.882727i	$-0.655705\pi$
$499$	−20.9929			−0.939773			−0.469887	+	0.882727i	$0.655705\pi$
$500$	24.7518	+	32.6389i	1.10693	+	1.45966i
$501$	−13.4183			−0.599485
$502$			5.34682i			0.238640i
$503$		−	18.5041i		−	0.825055i	−0.910945	−	0.412528i	$-0.864646\pi$
$503$		−	18.5041i		−	0.825055i	0.910945	−	0.412528i	$-0.135354\pi$
$504$	−7.60014			−0.338537
$505$	0.767816	+	3.49466i	0.0341674	+	0.155510i
$506$	−2.67575			−0.118951
$507$			44.1280i			1.95980i
$508$		−	37.4263i		−	1.66052i
$509$	41.8472			1.85484			0.927421	−	0.374019i	$-0.122020\pi$
$509$	41.8472			1.85484			0.927421	+	0.374019i	$0.122020\pi$
$510$	−59.0776	+	12.9800i	−2.61600	+	0.574765i
$511$	21.9637			0.971619
$512$			22.7423i			1.00508i
$513$		−	17.2843i		−	0.763120i
$514$	−26.2140			−1.15625
$515$	−2.69106	+	0.591257i	−0.118582	+	0.0260539i
$516$	−55.6786			−2.45112
$517$			7.19588i			0.316475i
$518$		−	53.2867i		−	2.34128i
$519$	8.41762			0.369493
$520$	−11.3236	−	51.5386i	−0.496573	−	2.26012i
$521$	34.1103			1.49440			0.747199	−	0.664600i	$-0.231398\pi$
$521$	34.1103			1.49440			0.747199	+	0.664600i	$0.231398\pi$
$522$			0.816525i			0.0357383i
$523$			36.4755i			1.59496i	0.603343	+	0.797482i	$0.293835\pi$
$523$			36.4755i			1.59496i	−0.603343	+	0.797482i	$0.706165\pi$
$524$	59.4387			2.59659
$525$	20.3180	−	9.38102i	0.886748	−	0.409421i
$526$	−26.3180			−1.14752
$527$			18.5131i			0.806442i
$528$		−	4.61802i		−	0.200973i
$529$	−1.00000			−0.0434783
$530$	−7.69220	−	35.0105i	−0.334128	−	1.52076i
$531$	−4.00000			−0.173585
$532$			34.1748i			1.48167i
$533$			37.3724i			1.61878i
$534$	26.5098			1.14719
$535$	−0.513741	+	0.112875i	−0.0222110	+	0.00488000i
$536$	1.12432			0.0485633
$537$		−	29.1261i		−	1.25688i
$538$		−	23.5701i		−	1.01618i
$539$	2.00535			0.0863765
$540$	−33.8646	+	7.44045i	−1.45730	+	0.320186i
$541$	28.2171			1.21315			0.606573	−	0.795028i	$-0.292544\pi$
$541$	28.2171			1.21315			0.606573	+	0.795028i	$0.292544\pi$
$542$		−	11.4866i		−	0.493392i
$543$		−	25.7329i		−	1.10430i
$544$	17.0018			0.728945
$545$	−3.56788	−	16.2390i	−0.152831	−	0.695601i
$546$	−63.4820			−2.71678
$547$		−	15.1638i		−	0.648356i	−0.945996	−	0.324178i	$-0.894912\pi$
$547$		−	15.1638i		−	0.648356i	0.945996	−	0.324178i	$-0.105088\pi$
$548$		−	17.9423i		−	0.766456i
$549$	5.32183			0.227130
$550$	5.60819	+	12.1465i	0.239134	+	0.517931i
$551$	1.66735			0.0710314
$552$		−	7.75976i		−	0.330277i
$553$			10.2409i			0.435488i
$554$	−17.9515			−0.762686
$555$	9.21863	+	41.9579i	0.391309	+	1.78101i
$556$	16.2633			0.689717
$557$			9.52222i			0.403469i	0.979440	+	0.201735i	$0.0646579\pi$
$557$			9.52222i			0.403469i	−0.979440	+	0.201735i	$0.935342\pi$
$558$		−	6.38375i		−	0.270245i
$559$	−46.2159			−1.95472
$560$	10.4547	−	2.29701i	0.441791	−	0.0970665i
$561$	−12.7794			−0.539547
$562$		−	14.3065i		−	0.603484i
$563$			32.7494i			1.38022i	0.723702	+	0.690112i	$0.242439\pi$
$563$			32.7494i			1.38022i	−0.723702	+	0.690112i	$0.757561\pi$
$564$	−45.9531			−1.93498
$565$	4.98807	−	1.09594i	0.209850	−	0.0461064i
$566$	−37.2185			−1.56441
$567$			24.7006i			1.03733i
$568$		−	55.2441i		−	2.31799i
$569$	26.8926			1.12740			0.563698	−	0.825981i	$-0.309378\pi$
$569$	26.8926			1.12740			0.563698	+	0.825981i	$0.309378\pi$
$570$	−9.13963	−	41.5984i	−0.382817	−	1.74236i
$571$	0.920000			0.0385008			0.0192504	−	0.999815i	$-0.493872\pi$
$571$	0.920000			0.0385008			0.0192504	+	0.999815i	$0.493872\pi$
$572$		−	24.5498i		−	1.02648i
$573$		−	27.4002i		−	1.14466i
$574$	−34.0853			−1.42269
$575$	2.09594	+	4.53950i	0.0874066	+	0.189310i
$576$	−9.38537			−0.391057
$577$		−	42.5888i		−	1.77300i	−0.462732	−	0.886498i	$-0.653131\pi$
$577$		−	42.5888i		−	1.77300i	0.462732	−	0.886498i	$-0.346869\pi$
$578$			39.6030i			1.64727i
$579$	17.0741			0.709576
$580$	−0.717752	−	3.26679i	−0.0298030	−	0.135646i
$581$	−24.7175			−1.02545
$582$			51.6171i			2.13960i
$583$		−	7.57332i		−	0.313655i
$584$	−38.0787			−1.57571
$585$	10.9382	−	2.40325i	0.452240	−	0.0993622i
$586$	−7.65462			−0.316209
$587$		−	9.51212i		−	0.392607i	−0.980543	−	0.196304i	$-0.937106\pi$
$587$		−	9.51212i		−	0.392607i	0.980543	−	0.196304i	$-0.0628938\pi$
$588$			12.8062i			0.528120i
$589$	−13.0356			−0.537124
$590$	24.7393	−	5.43550i	1.01850	−	0.223776i
$591$	44.0687			1.81274
$592$			20.5474i			0.844494i
$593$		−	31.0719i		−	1.27597i	−0.770048	−	0.637986i	$-0.779768\pi$
$593$		−	31.0719i		−	1.27597i	0.770048	−	0.637986i	$-0.220232\pi$
$594$	−11.3243			−0.464640
$595$	−6.35651	−	28.9312i	−0.260591	−	1.18606i
$596$	−10.1986			−0.417753
$597$			17.6583i			0.722707i
$598$		−	14.1833i		−	0.580000i
$599$	−2.04065			−0.0833787			−0.0416893	−	0.999131i	$-0.513274\pi$
$599$	−2.04065			−0.0833787			−0.0416893	+	0.999131i	$0.513274\pi$
$600$	−35.2254	+	16.2640i	−1.43807	+	0.663973i
$601$	−25.2377			−1.02947			−0.514733	−	0.857351i	$-0.672109\pi$
$601$	−25.2377			−1.02947			−0.514733	+	0.857351i	$0.672109\pi$
$602$		−	42.1509i		−	1.71794i
$603$			0.238619i			0.00971731i
$604$	−43.7012			−1.77818
$605$	−4.67172	−	21.2630i	−0.189932	−	0.864463i
$606$	−7.46274			−0.303153
$607$		−	10.4305i		−	0.423361i	−0.977339	−	0.211680i	$-0.932106\pi$
$607$		−	10.4305i		−	0.423361i	0.977339	−	0.211680i	$-0.0678936\pi$
$608$			11.9715i			0.485507i
$609$	−1.82731			−0.0740463
$610$	−32.9146	+	7.23170i	−1.33267	+	0.292803i
$611$	−38.1432			−1.54311
$612$		−	17.8584i		−	0.721883i
$613$		−	4.97745i		−	0.201037i	−0.994935	−	0.100519i	$-0.967950\pi$
$613$		−	4.97745i		−	0.201037i	0.994935	−	0.100519i	$-0.0320502\pi$
$614$	82.0348			3.31066
$615$	26.8388	−	5.89678i	1.08224	−	0.237781i
$616$	10.1680			0.409681
$617$		−	30.5881i		−	1.23143i	−0.787969	−	0.615715i	$-0.788867\pi$
$617$		−	30.5881i		−	1.23143i	0.787969	−	0.615715i	$-0.211133\pi$
$618$		−	5.74669i		−	0.231166i
$619$	48.0404			1.93091			0.965453	−	0.260579i	$-0.0839133\pi$
$619$	48.0404			1.93091			0.965453	+	0.260579i	$0.0839133\pi$
$620$	5.61151	+	25.5404i	0.225364	+	1.02573i
$621$	−4.23218			−0.169832
$622$			44.6092i			1.78866i
$623$			12.9823i			0.520123i
$624$	24.4787			0.979933
$625$	16.2141	−	19.0290i	0.648564	−	0.761160i
$626$	23.5908			0.942878
$627$		−	8.99837i		−	0.359360i
$628$			84.1030i			3.35608i
$629$	56.8607			2.26718
$630$	2.19187	+	9.97615i	0.0873263	+	0.397459i
$631$	10.6157			0.422605			0.211303	−	0.977421i	$-0.432229\pi$
$631$	10.6157			0.422605			0.211303	+	0.977421i	$0.432229\pi$
$632$		−	17.7547i		−	0.706246i
$633$		−	10.9745i		−	0.436198i
$634$	21.9907			0.873360
$635$	−22.3095	+	4.90166i	−0.885327	+	0.194516i
$636$	48.3634			1.91773
$637$			10.6298i			0.421166i
$638$		−	1.09241i		−	0.0432488i
$639$	11.7247			0.463820
$640$	45.2431	−	9.94041i	1.78839	−	0.392929i
$641$	3.47844			0.137390			0.0686951	−	0.997638i	$-0.478116\pi$
$641$	3.47844			0.137390			0.0686951	+	0.997638i	$0.478116\pi$
$642$		−	1.09708i		−	0.0432983i
$643$			2.05348i			0.0809813i	0.999180	+	0.0404906i	$0.0128921\pi$
$643$			2.05348i			0.0809813i	−0.999180	+	0.0404906i	$0.987108\pi$
$644$	8.36795			0.329743
$645$	7.29214	+	33.1896i	0.287128	+	1.30684i
$646$	−56.3734			−2.21798
$647$			19.3408i			0.760367i	0.924911	+	0.380184i	$0.124139\pi$
$647$			19.3408i			0.760367i	−0.924911	+	0.380184i	$0.875861\pi$
$648$		−	42.8236i		−	1.68227i
$649$	5.35149			0.210064
$650$	−64.3852	+	29.7274i	−2.52540	+	1.16600i
$651$	14.2862			0.559922
$652$			37.4015i			1.46476i
$653$			21.9288i			0.858139i	0.903271	+	0.429070i	$0.141159\pi$
$653$			21.9288i			0.858139i	−0.903271	+	0.429070i	$0.858841\pi$
$654$	34.6778			1.35601
$655$	−7.78459	−	35.4310i	−0.304169	−	1.38440i
$656$	13.1433			0.513161
$657$		−	8.08158i		−	0.315293i
$658$		−	34.7883i		−	1.35619i
$659$	−38.1351			−1.48553			−0.742767	−	0.669550i	$-0.766487\pi$
$659$	−38.1351			−1.48553			−0.742767	+	0.669550i	$0.766487\pi$
$660$	−17.6303	+	3.87357i	−0.686258	+	0.150779i
$661$	−28.9007			−1.12411			−0.562053	−	0.827101i	$-0.689988\pi$
$661$	−28.9007			−1.12411			−0.562053	+	0.827101i	$0.689988\pi$
$662$			57.0419i			2.21700i
$663$		−	67.7398i		−	2.63079i
$664$	42.8529			1.66302
$665$	20.3713	−	4.47581i	0.789967	−	0.173565i
$666$	−19.6069			−0.759752
$667$		−	0.408263i		−	0.0158080i
$668$			25.0867i			0.970635i
$669$	−13.8455			−0.535299
$670$	−0.324253	−	1.47581i	−0.0125270	−	0.0570157i
$671$	−7.11993			−0.274862
$672$		−	13.1200i		−	0.506114i
$673$			49.5051i			1.90828i	0.299361	+	0.954140i	$0.403226\pi$
$673$			49.5051i			1.90828i	−0.299361	+	0.954140i	$0.596774\pi$
$674$	−23.2390			−0.895131
$675$	8.87039	+	19.2120i	0.341421	+	0.739470i
$676$	82.5015			3.17313
$677$		−	6.87426i		−	0.264199i	−0.991236	−	0.132100i	$-0.957828\pi$
$677$		−	6.87426i		−	0.264199i	0.991236	−	0.132100i	$-0.0421719\pi$
$678$			10.6519i			0.409083i
$679$	−25.2776			−0.970067
$680$	11.0203	+	50.1582i	0.422610	+	1.92348i
$681$	−49.2024			−1.88544
$682$			8.54064i			0.327038i
$683$		−	36.9887i		−	1.41533i	−0.706547	−	0.707666i	$-0.749748\pi$
$683$		−	36.9887i		−	1.41533i	0.706547	−	0.707666i	$-0.250252\pi$
$684$	12.5747			0.480804
$685$	−10.6953	+	2.34987i	−0.408645	+	0.0897839i
$686$	−47.7433			−1.82285
$687$		−	6.27817i		−	0.239527i
$688$			16.2535i			0.619657i
$689$	40.1439			1.52936
$690$	−10.1857	+	2.23791i	−0.387762	+	0.0851957i
$691$	38.5485			1.46645			0.733227	−	0.679984i	$-0.238013\pi$
$691$	38.5485			1.46645			0.733227	+	0.679984i	$0.238013\pi$
$692$		−	15.7375i		−	0.598251i
$693$			2.15800i			0.0819755i
$694$	−3.29472			−0.125066
$695$	−2.12998	−	9.69443i	−0.0807946	−	0.367731i
$696$	3.16802			0.120083
$697$		−	36.3715i		−	1.37767i
$698$		−	76.8952i		−	2.91053i
$699$	36.5263			1.38155
$700$	−17.5387	−	37.9863i	−0.662900	−	1.43575i
$701$	−36.3146			−1.37158			−0.685791	−	0.727798i	$-0.740544\pi$
$701$	−36.3146			−1.37158			−0.685791	+	0.727798i	$0.740544\pi$
$702$		−	60.0265i		−	2.26555i
$703$			40.0374i			1.51004i
$704$	12.5564			0.473239
$705$	6.01840	+	27.3923i	0.226666	+	1.03165i
$706$	27.2224			1.02453
$707$		−	3.65462i		−	0.137446i
$708$			34.1748i			1.28437i
$709$	3.24463			0.121855			0.0609274	−	0.998142i	$-0.480594\pi$
$709$	3.24463			0.121855			0.0609274	+	0.998142i	$0.480594\pi$
$710$	−72.5149	+	15.9324i	−2.72144	+	0.597931i
$711$	3.76815			0.141317
$712$		−	22.5074i		−	0.843502i
$713$			3.19187i			0.119537i
$714$	61.7817			2.31212
$715$	−14.6340	+	3.21525i	−0.547279	+	0.120243i
$716$	−54.4539			−2.03504
$717$			6.23543i			0.232867i
$718$			23.6933i			0.884226i
$719$	−10.4214			−0.388654			−0.194327	−	0.980937i	$-0.562252\pi$
$719$	−10.4214			−0.388654			−0.194327	+	0.980937i	$0.562252\pi$
$720$	−0.845189	−	3.84681i	−0.0314983	−	0.143362i
$721$	2.81424			0.104808
$722$			5.52338i			0.205559i
$723$		−	9.40345i		−	0.349718i
$724$	−48.1100			−1.78799
$725$	−1.85331	+	0.855693i	−0.0688301	+	0.0317796i
$726$	45.4065			1.68519
$727$			9.67651i			0.358882i	0.983769	+	0.179441i	$0.0574289\pi$
$727$			9.67651i			0.358882i	−0.983769	+	0.179441i	$0.942571\pi$
$728$			53.8976i			1.99758i
$729$	−15.7927			−0.584914
$730$	10.9819	+	49.9832i	0.406457	+	1.84996i
$731$	44.9780			1.66357
$732$		−	45.4681i		−	1.68055i
$733$			15.5782i			0.575396i	0.957721	+	0.287698i	$0.0928899\pi$
$733$			15.5782i			0.575396i	−0.957721	+	0.287698i	$0.907110\pi$
$734$	−65.8715			−2.43136
$735$	7.63369	−	1.67721i	0.281573	−	0.0618648i
$736$	2.93130			0.108049
$737$		−	0.319242i		−	0.0117594i
$738$			12.5417i			0.461668i
$739$	−14.4328			−0.530919			−0.265459	−	0.964122i	$-0.585524\pi$
$739$	−14.4328			−0.530919			−0.265459	+	0.964122i	$0.585524\pi$
$740$	78.4442	−	17.2351i	2.88367	−	0.633575i
$741$	47.6977			1.75222
$742$			36.6130i			1.34411i
$743$		−	4.50305i		−	0.165201i	−0.996583	−	0.0826005i	$-0.973677\pi$
$743$		−	4.50305i		−	0.165201i	0.996583	−	0.0826005i	$-0.0263226\pi$
$744$	−24.7682			−0.908045
$745$	1.33570	+	6.07934i	0.0489362	+	0.222730i
$746$	68.3872			2.50383
$747$			9.09483i			0.332763i
$748$			23.8923i			0.873588i
$749$	0.537257			0.0196309
$750$	31.5075	+	41.5473i	1.15049	+	1.51709i
$751$	18.5451			0.676721			0.338361	−	0.941017i	$-0.390128\pi$
$751$	18.5451			0.676721			0.338361	+	0.941017i	$0.390128\pi$
$752$			13.4144i			0.489174i
$753$			4.40279i			0.160447i
$754$	5.79053			0.210878
$755$	5.72347	+	26.0500i	0.208299	+	0.948055i
$756$	35.4147			1.28802
$757$			27.0366i			0.982663i	0.870973	+	0.491332i	$0.163490\pi$
$757$			27.0366i			0.982663i	−0.870973	+	0.491332i	$0.836510\pi$
$758$		−	43.4840i		−	1.57941i
$759$	−2.20332			−0.0799754
$760$	−35.3180	+	7.75976i	−1.28112	+	0.281476i
$761$	15.4066			0.558490			0.279245	−	0.960220i	$-0.409916\pi$
$761$	15.4066			0.558490			0.279245	+	0.960220i	$0.409916\pi$
$762$		−	47.6414i		−	1.72587i
$763$			16.9823i			0.614799i
$764$	−51.2272			−1.85334
$765$	−10.6453	+	2.33888i	−0.384880	+	0.0845625i
$766$	−69.1013			−2.49673
$767$			28.3667i			1.02426i
$768$			52.8436i			1.90683i
$769$	−15.1216			−0.545299			−0.272650	−	0.962113i	$-0.587900\pi$
$769$	−15.1216			−0.545299			−0.272650	+	0.962113i	$0.587900\pi$
$770$	−2.93245	−	13.3468i	−0.105678	−	0.480986i
$771$	−21.5856			−0.777388
$772$		−	31.9217i		−	1.14889i
$773$		−	28.7131i		−	1.03274i	−0.856366	−	0.516370i	$-0.827283\pi$
$773$		−	28.7131i		−	1.03274i	0.856366	−	0.516370i	$-0.172717\pi$
$774$	−15.5095			−0.557477
$775$	14.4895	−	6.68996i	0.520478	−	0.240311i
$776$	43.8241			1.57319
$777$		−	43.8784i		−	1.57413i
$778$			6.81653i			0.244384i
$779$	25.6103			0.917584
$780$	−20.5327	−	93.4528i	−0.735187	−	3.34615i
$781$	−15.6861			−0.561293
$782$			13.8035i			0.493611i
$783$		−	1.72784i		−	0.0617481i
$784$	3.73833			0.133512
$785$	50.1332	−	11.0148i	1.78933	−	0.393136i
$786$	75.6619			2.69877
$787$			16.3131i			0.581501i	0.956799	+	0.290750i	$0.0939049\pi$
$787$			16.3131i			0.581501i	−0.956799	+	0.290750i	$0.906095\pi$
$788$		−	82.3905i		−	2.93504i
$789$	−21.6713			−0.771518
$790$	−23.3054	+	5.12045i	−0.829168	+	0.182178i
$791$	−5.21639			−0.185473
$792$		−	3.74134i		−	0.132943i
$793$		−	37.7406i		−	1.34021i
$794$	−39.4088			−1.39857
$795$	−6.33407	−	28.8291i	−0.224646	−	1.02246i
$796$	33.0139			1.17015
$797$		−	2.88374i		−	0.102147i	−0.998695	−	0.0510736i	$-0.983736\pi$
$797$		−	2.88374i		−	0.102147i	0.998695	−	0.0510736i	$-0.0162643\pi$
$798$			43.5024i			1.53997i
$799$	37.1216			1.31327
$800$	−6.14383	−	13.3067i	−0.217217	−	0.470461i
$801$	4.77684			0.168781
$802$			7.36523i			0.260075i
$803$			10.8121i			0.381552i
$804$	2.03869			0.0718989
$805$	−1.09594	−	4.98807i	−0.0386267	−	0.175806i
$806$	−45.2714			−1.59462
$807$		−	19.4086i		−	0.683215i
$808$			6.33604i			0.222901i
$809$	−39.7878			−1.39886			−0.699432	−	0.714699i	$-0.746564\pi$
$809$	−39.7878			−1.39886			−0.699432	+	0.714699i	$0.746564\pi$
$810$	−56.2115	+	12.3503i	−1.97507	+	0.433945i
$811$	38.5454			1.35351			0.676756	−	0.736208i	$-0.263385\pi$
$811$	38.5454			1.35351			0.676756	+	0.736208i	$0.263385\pi$
$812$			3.41632i			0.119889i
$813$		−	9.45853i		−	0.331725i
$814$	26.2316			0.919416
$815$	22.2947	−	4.89841i	0.780951	−	0.171584i
$816$	−23.8231			−0.833975
$817$			31.6705i			1.10801i
$818$			21.2670i			0.743583i
$819$	−11.4389			−0.399707
$820$	−11.0246	−	50.1776i	−0.384995	−	1.75228i
$821$	−16.3428			−0.570368			−0.285184	−	0.958473i	$-0.592055\pi$
$821$	−16.3428			−0.570368			−0.285184	+	0.958473i	$0.592055\pi$
$822$		−	22.8394i		−	0.796616i
$823$			38.6446i			1.34707i	0.739157	+	0.673534i	$0.235224\pi$
$823$			38.6446i			1.34707i	−0.739157	+	0.673534i	$0.764776\pi$
$824$	−4.87907			−0.169970
$825$	4.61802	+	10.0020i	0.160779	+	0.348224i
$826$	−25.8717			−0.900191
$827$		−	21.6969i		−	0.754474i	−0.926117	−	0.377237i	$-0.876874\pi$
$827$		−	21.6969i		−	0.754474i	0.926117	−	0.377237i	$-0.123126\pi$
$828$		−	3.07900i		−	0.107003i
$829$	−13.9429			−0.484259			−0.242129	−	0.970244i	$-0.577846\pi$
$829$	−13.9429			−0.484259			−0.242129	+	0.970244i	$0.577846\pi$
$830$	−12.3587	−	56.2499i	−0.428978	−	1.95246i
$831$	−14.7820			−0.512781
$832$			66.5579i			2.30748i
$833$		−	10.3451i		−	0.358435i
$834$	20.7022			0.716858
$835$	14.9540	−	3.28557i	0.517505	−	0.113702i
$836$	−16.8233			−0.581846
$837$			13.5086i			0.466925i
$838$			57.4115i			1.98325i
$839$	−52.4484			−1.81072			−0.905360	−	0.424644i	$-0.860399\pi$
$839$	−52.4484			−1.81072			−0.905360	+	0.424644i	$0.860399\pi$
$840$	38.7062	−	8.50420i	1.33549	−	0.293423i
$841$	−28.8333			−0.994252
$842$		−	56.7844i		−	1.95692i
$843$		−	11.7806i		−	0.405744i
$844$	−20.5179			−0.706255
$845$	−10.8051	−	49.1785i	−0.371706	−	1.69179i
$846$	−12.8004			−0.440087
$847$			22.2362i			0.764046i
$848$		−	14.1180i		−	0.484815i
$849$	−30.6472			−1.05181
$850$	62.6608	−	28.9312i	2.14925	−	0.992331i
$851$	9.80345			0.336058
$852$		−	100.172i		−	3.43183i
$853$			30.4634i			1.04305i	0.853237	+	0.521524i	$0.174636\pi$
$853$			30.4634i			1.04305i	−0.853237	+	0.521524i	$0.825364\pi$
$854$	34.4211			1.17787
$855$	−1.64688	−	7.49566i	−0.0563222	−	0.256346i
$856$	−0.931446			−0.0318362
$857$			42.4911i			1.45147i	0.687975	+	0.725735i	$0.258500\pi$
$857$			42.4911i			1.45147i	−0.687975	+	0.725735i	$0.741500\pi$
$858$		−	31.2504i		−	1.06687i
$859$	15.5856			0.531775			0.265888	−	0.964004i	$-0.414335\pi$
$859$	15.5856			0.531775			0.265888	+	0.964004i	$0.414335\pi$
$860$	62.0511	−	13.6333i	2.11592	−	0.464893i
$861$	−28.0673			−0.956529
$862$		−	10.5927i		−	0.360790i
$863$			50.8852i			1.73215i	0.499913	+	0.866076i	$0.333365\pi$
$863$			50.8852i			1.73215i	−0.499913	+	0.866076i	$0.666635\pi$
$864$	12.4058			0.422055
$865$	−9.38102	+	2.06112i	−0.318964	+	0.0700801i
$866$	19.2991			0.655811
$867$			32.6108i			1.10752i
$868$		−	26.7094i		−	0.906577i
$869$	−5.04131			−0.171015
$870$	−0.913654	−	4.15843i	−0.0309758	−	0.140984i
$871$	1.69220			0.0573382
$872$		−	29.4423i		−	0.997041i
$873$			9.30094i			0.314789i
$874$	−9.71944			−0.328765
$875$	−20.3463	+	15.4297i	−0.687832	+	0.521619i
$876$	−69.0466			−2.33287
$877$			30.1080i			1.01667i	0.861158	+	0.508337i	$0.169740\pi$
$877$			30.1080i			1.01667i	−0.861158	+	0.508337i	$0.830260\pi$
$878$			10.6424i			0.359162i
$879$	−6.30312			−0.212599
$880$	1.13076	+	5.14655i	0.0381178	+	0.173490i
$881$	20.2245			0.681379			0.340690	−	0.940176i	$-0.389339\pi$
$881$	20.2245			0.681379			0.340690	+	0.940176i	$0.389339\pi$
$882$			3.56722i			0.120115i
$883$		−	30.6482i		−	1.03139i	−0.856771	−	0.515697i	$-0.827533\pi$
$883$		−	30.6482i		−	1.03139i	0.856771	−	0.515697i	$-0.172467\pi$
$884$	−126.646			−4.25956
$885$	20.3713	−	4.47581i	0.684775	−	0.150453i
$886$	22.8480			0.767592
$887$		−	14.0064i		−	0.470290i	−0.971960	−	0.235145i	$-0.924443\pi$
$887$		−	14.0064i		−	0.470290i	0.971960	−	0.235145i	$-0.0755565\pi$
$888$			76.0724i			2.55282i
$889$	23.3307			0.782487
$890$	−29.5439	+	6.49113i	−0.990313	+	0.217583i
$891$	−12.1594			−0.407356
$892$			25.8855i			0.866711i
$893$			26.1385i			0.874691i
$894$	−12.9823			−0.434192
$895$	7.13174	+	32.4596i	0.238388	+	1.08500i
$896$	−47.3139			−1.58065
$897$		−	11.6791i		−	0.389955i
$898$		−	16.1818i		−	0.539995i
$899$	−1.30312			−0.0434616
$900$	−13.9771	+	6.45338i	−0.465904	+	0.215113i
$901$	−39.0687			−1.30157
$902$		−	16.7793i		−	0.558688i
$903$		−	34.7088i		−	1.15504i
$904$	9.04370			0.300789
$905$	6.30088	+	28.6780i	0.209448	+	0.953289i
$906$	−55.6290			−1.84815
$907$			36.4739i			1.21109i	0.795809	+	0.605547i	$0.207046\pi$
$907$			36.4739i			1.21109i	−0.795809	+	0.605547i	$0.792954\pi$
$908$			91.9884i			3.05274i
$909$	−1.34472			−0.0446016
$910$	70.7475	−	15.5440i	2.34526	−	0.515280i
$911$	−14.2327			−0.471549			−0.235775	−	0.971808i	$-0.575763\pi$
$911$	−14.2327			−0.471549			−0.235775	+	0.971808i	$0.575763\pi$
$912$		−	16.7746i		−	0.555462i
$913$		−	12.1677i		−	0.402693i
$914$	46.5461			1.53961
$915$	−27.1032	+	5.95488i	−0.896004	+	0.196862i
$916$	−11.7376			−0.387822
$917$			37.0528i			1.22359i
$918$			58.4188i			1.92811i
$919$	−34.3246			−1.13226			−0.566132	−	0.824315i	$-0.691561\pi$
$919$	−34.3246			−1.13226			−0.566132	+	0.824315i	$0.691561\pi$
$920$	1.90003	+	8.64786i	0.0626423	+	0.285112i
$921$	67.5508			2.22588
$922$			101.640i			3.34734i
$923$		−	83.1474i		−	2.73683i
$924$	18.4373			0.606541
$925$	−20.5474	−	44.5028i	−0.675595	−	1.46324i
$926$	−17.6637			−0.580464
$927$		−	1.03550i		−	0.0340103i
$928$			1.19674i			0.0392850i
$929$	−6.14579			−0.201637			−0.100818	−	0.994905i	$-0.532146\pi$
$929$	−6.14579			−0.201637			−0.100818	+	0.994905i	$0.532146\pi$
$930$	7.14312	+	32.5114i	0.234232	+	1.06609i
$931$	7.28428			0.238733
$932$		−	68.2893i		−	2.23689i
$933$			36.7330i			1.20258i
$934$	53.5569			1.75244
$935$	14.2420	−	3.12913i	0.465763	−	0.102334i
$936$	19.8317			0.648219
$937$		−	18.4581i		−	0.602998i	−0.953466	−	0.301499i	$-0.902513\pi$
$937$		−	18.4581i		−	0.602998i	0.953466	−	0.301499i	$-0.0974871\pi$
$938$			1.54337i			0.0503927i
$939$	19.4256			0.633931
$940$	51.2125	−	11.2520i	1.67037	−	0.366998i
$941$	30.7623			1.00282			0.501411	−	0.865209i	$-0.332815\pi$
$941$	30.7623			1.00282			0.501411	+	0.865209i	$0.332815\pi$
$942$			107.058i			3.48814i
$943$		−	6.27087i		−	0.204208i
$944$	9.97615			0.324696
$945$	−4.63820	−	21.1104i	−0.150881	−	0.686723i
$946$	20.7497			0.674632
$947$		−	11.4692i		−	0.372698i	−0.982484	−	0.186349i	$-0.940334\pi$
$947$		−	11.4692i		−	0.372698i	0.982484	−	0.186349i	$-0.0596655\pi$
$948$		−	32.1940i		−	1.04561i
$949$	−57.3119			−1.86042
$950$	20.3713	+	44.1214i	0.660933	+	1.43149i
$951$	18.1080			0.587192
$952$		−	52.4541i		−	1.70005i
$953$			2.40664i			0.0779586i	0.999240	+	0.0389793i	$0.0124106\pi$
$953$			2.40664i			0.0779586i	−0.999240	+	0.0389793i	$0.987589\pi$
$954$	13.4718			0.436166
$955$	6.70914	+	30.5362i	0.217103	+	0.988127i
$956$	11.6577			0.377038
$957$		−	0.899533i		−	0.0290778i
$958$		−	24.1956i		−	0.781724i
$959$	11.1848			0.361176
$960$	47.7981	−	10.5018i	1.54268	−	0.338944i
$961$	−20.8119			−0.671353
$962$			139.046i			4.48301i
$963$		−	0.197684i		−	0.00637029i
$964$	−17.5806			−0.566234
$965$	−19.0283	+	4.18073i	−0.612541	+	0.134582i
$966$	10.6519			0.342719
$967$		−	57.4766i		−	1.84832i	−0.382001	−	0.924162i	$-0.624765\pi$
$967$		−	57.4766i		−	1.84832i	0.382001	−	0.924162i	$-0.375235\pi$
$968$		−	38.5511i		−	1.23908i
$969$	−46.4202			−1.49123
$970$	−12.6388	−	57.5247i	−0.405808	−	1.84701i
$971$	53.1909			1.70698			0.853489	−	0.521111i	$-0.174482\pi$
$971$	53.1909			1.70698			0.853489	+	0.521111i	$0.174482\pi$
$972$		−	31.1325i		−	0.998576i
$973$			10.1382i			0.325015i
$974$	−83.2759			−2.66833
$975$	−53.0174	+	24.4787i	−1.69792	+	0.783946i
$976$	−13.2728			−0.424853
$977$		−	54.4716i		−	1.74270i	−0.490661	−	0.871350i	$-0.663245\pi$
$977$		−	54.4716i		−	1.74270i	0.490661	−	0.871350i	$-0.336755\pi$
$978$			47.6098i			1.52239i
$979$	−6.39080			−0.204251
$980$	−3.13570	−	14.2719i	−0.100166	−	0.455899i
$981$	6.24864			0.199504
$982$			5.40440i			0.172461i
$983$			37.5908i			1.19896i	0.800390	+	0.599480i	$0.204626\pi$
$983$			37.5908i			1.19896i	−0.800390	+	0.599480i	$0.795374\pi$
$984$	48.6604			1.55124
$985$	−49.1124	+	10.7905i	−1.56485	+	0.343815i
$986$	−5.63544			−0.179469
$987$		−	28.6461i		−	0.911816i
$988$		−	89.1753i		−	2.83704i
$989$	7.75474			0.246587
$990$	−4.91098	+	1.07900i	−0.156081	+	0.0342928i
$991$	14.0545			0.446455			0.223228	−	0.974766i	$-0.428341\pi$
$991$	14.0545			0.446455			0.223228	+	0.974766i	$0.428341\pi$
$992$		−	9.35635i		−	0.297064i
$993$			46.9706i			1.49057i
$994$	75.8341			2.40531
$995$	−4.32377	−	19.6793i	−0.137073	−	0.623877i
$996$	77.7035			2.46213
$997$		−	10.9378i		−	0.346404i	−0.984886	−	0.173202i	$-0.944589\pi$
$997$		−	10.9378i		−	0.346404i	0.984886	−	0.173202i	$-0.0554113\pi$
$998$			49.9606i			1.58148i
$999$	41.4900			1.31269

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.b.b.24.1	✓	8
3.2	odd	2		1035.2.b.e.829.8		8
4.3	odd	2		1840.2.e.d.369.7		8
5.2	odd	4		575.2.a.j.1.4		4
5.3	odd	4		575.2.a.i.1.1		4
5.4	even	2	inner	115.2.b.b.24.8	yes	8
15.2	even	4		5175.2.a.bw.1.1		4
15.8	even	4		5175.2.a.bv.1.4		4
15.14	odd	2		1035.2.b.e.829.1		8
20.3	even	4		9200.2.a.cq.1.1		4
20.7	even	4		9200.2.a.ck.1.4		4
20.19	odd	2		1840.2.e.d.369.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.b.b.24.1	✓	8	1.1	even	1	trivial
115.2.b.b.24.8	yes	8	5.4	even	2	inner
575.2.a.i.1.1		4	5.3	odd	4
575.2.a.j.1.4		4	5.2	odd	4
1035.2.b.e.829.1		8	15.14	odd	2
1035.2.b.e.829.8		8	3.2	odd	2
1840.2.e.d.369.2		8	20.19	odd	2
1840.2.e.d.369.7		8	4.3	odd	2
5175.2.a.bv.1.4		4	15.8	even	4
5175.2.a.bw.1.1		4	15.2	even	4
9200.2.a.ck.1.4		4	20.7	even	4
9200.2.a.cq.1.1		4	20.3	even	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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.37988i q^{2} -1.95969i q^{3} -3.66382 q^{4} +(0.479844 + 2.18398i) q^{5} -4.66382 q^{6} -2.28394i q^{7} +3.95969i q^{8} -0.840379 q^{9} +O(q^{10})\)	\(q-2.37988i q^{2} -1.95969i q^{3} -3.66382 q^{4} +(0.479844 + 2.18398i) q^{5} -4.66382 q^{6} -2.28394i q^{7} +3.95969i q^{8} -0.840379 q^{9} +(5.19760 - 1.14197i) q^{10} +1.12432 q^{11} +7.17995i q^{12} +5.95969i q^{13} -5.43550 q^{14} +(4.27991 - 0.940345i) q^{15} +2.09594 q^{16} -5.80007i q^{17} +2.00000i q^{18} +4.08401 q^{19} +(-1.75806 - 8.00169i) q^{20} -4.47581 q^{21} -2.67575i q^{22} -1.00000i q^{23} +7.75976 q^{24} +(-4.53950 + 2.09594i) q^{25} +14.1833 q^{26} -4.23218i q^{27} +8.36795i q^{28} +0.408263 q^{29} +(-2.23791 - 10.1857i) q^{30} -3.19187 q^{31} +2.93130i q^{32} -2.20332i q^{33} -13.8035 q^{34} +(4.98807 - 1.09594i) q^{35} +3.07900 q^{36} +9.80345i q^{37} -9.71944i q^{38} +11.6791 q^{39} +(-8.64786 + 1.90003i) q^{40} +6.27087 q^{41} +10.6519i q^{42} +7.75474i q^{43} -4.11931 q^{44} +(-0.403251 - 1.83537i) q^{45} -2.37988 q^{46} +6.40020i q^{47} -4.10738i q^{48} +1.78361 q^{49} +(4.98807 + 10.8035i) q^{50} -11.3663 q^{51} -21.8352i q^{52} -6.73590i q^{53} -10.0721 q^{54} +(0.539499 + 2.45549i) q^{55} +9.04370 q^{56} -8.00339i q^{57} -0.971615i q^{58} +4.75976 q^{59} +(-15.6808 + 3.44526i) q^{60} -6.33265 q^{61} +7.59627i q^{62} +1.91938i q^{63} +11.1680 q^{64} +(-13.0158 + 2.85972i) q^{65} -5.24363 q^{66} -0.283942i q^{67} +21.2504i q^{68} -1.95969 q^{69} +(-2.60819 - 11.8710i) q^{70} -13.9516 q^{71} -3.32764i q^{72} +9.61659i q^{73} +23.3310 q^{74} +(4.10738 + 8.89600i) q^{75} -14.9631 q^{76} -2.56788i q^{77} -27.7949i q^{78} -4.48387 q^{79} +(1.00572 + 4.57747i) q^{80} -10.8149 q^{81} -14.9239i q^{82} -10.8223i q^{83} +16.3986 q^{84} +(12.6672 - 2.78313i) q^{85} +18.4553 q^{86} -0.800068i q^{87} +4.45196i q^{88} -5.68414 q^{89} +(-4.36795 + 0.959689i) q^{90} +13.6116 q^{91} +3.66382i q^{92} +6.25508i q^{93} +15.2317 q^{94} +(1.95969 + 8.91938i) q^{95} +5.74444 q^{96} -11.0676i q^{97} -4.24477i q^{98} -0.944856 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{4} - 6 q^{5} - 12 q^{6} - 8 q^{9}+O(q^{10}) \) 8 * q - 4 * q^4 - 6 * q^5 - 12 * q^6 - 8 * q^9	\( 8 q - 4 q^{4} - 6 q^{5} - 12 q^{6} - 8 q^{9} + 6 q^{10} + 4 q^{11} + 8 q^{14} + 6 q^{15} + 4 q^{16} + 8 q^{19} - 8 q^{20} - 4 q^{21} + 24 q^{24} - 16 q^{25} + 12 q^{26} - 8 q^{29} - 2 q^{30} - 28 q^{34} + 28 q^{35} - 16 q^{36} + 16 q^{39} - 10 q^{40} - 16 q^{41} - 12 q^{44} + 24 q^{45} + 28 q^{50} + 20 q^{51} - 44 q^{54} - 16 q^{55} + 28 q^{56} - 16 q^{60} - 16 q^{61} + 40 q^{64} - 14 q^{65} - 16 q^{66} + 4 q^{69} - 28 q^{70} - 48 q^{71} + 72 q^{74} - 36 q^{76} - 48 q^{79} - 2 q^{80} + 16 q^{81} - 4 q^{84} + 12 q^{85} + 28 q^{86} + 16 q^{89} - 4 q^{90} + 52 q^{91} + 84 q^{94} - 4 q^{95} + 60 q^{96} - 72 q^{99}+O(q^{100}) \) 8 * q - 4 * q^4 - 6 * q^5 - 12 * q^6 - 8 * q^9 + 6 * q^10 + 4 * q^11 + 8 * q^14 + 6 * q^15 + 4 * q^16 + 8 * q^19 - 8 * q^20 - 4 * q^21 + 24 * q^24 - 16 * q^25 + 12 * q^26 - 8 * q^29 - 2 * q^30 - 28 * q^34 + 28 * q^35 - 16 * q^36 + 16 * q^39 - 10 * q^40 - 16 * q^41 - 12 * q^44 + 24 * q^45 + 28 * q^50 + 20 * q^51 - 44 * q^54 - 16 * q^55 + 28 * q^56 - 16 * q^60 - 16 * q^61 + 40 * q^64 - 14 * q^65 - 16 * q^66 + 4 * q^69 - 28 * q^70 - 48 * q^71 + 72 * q^74 - 36 * q^76 - 48 * q^79 - 2 * q^80 + 16 * q^81 - 4 * q^84 + 12 * q^85 + 28 * q^86 + 16 * q^89 - 4 * q^90 + 52 * q^91 + 84 * q^94 - 4 * q^95 + 60 * q^96 - 72 * q^99

Introduction

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