LMFDB - Embedded newform 120.4.r.a.113.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [120,4,Mod(17,120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(120, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 2, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("120.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 120 = 2^{3} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	120.r (of order $4$, degree $2$, 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:	$7.08022920069$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			113.2
Character	$\chi$	$=$	120.113
Dual form			120.4.r.a.17.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.96635 - 1.52818i) q^{3} +(-1.11114 + 11.1250i) q^{5} +(9.09927 - 9.09927i) q^{7} +(22.3293 + 15.1790i) q^{9} +O(q^{10})$	\(q+(-4.96635 - 1.52818i) q^{3} +(-1.11114 + 11.1250i) q^{5} +(9.09927 - 9.09927i) q^{7} +(22.3293 + 15.1790i) q^{9} -42.8278i q^{11} +(-65.7996 - 65.7996i) q^{13} +(22.5193 - 53.5526i) q^{15} +(-3.23965 - 3.23965i) q^{17} -67.5802i q^{19} +(-59.0955 + 31.2849i) q^{21} +(42.8262 - 42.8262i) q^{23} +(-122.531 - 24.7228i) q^{25} +(-87.6992 - 109.507i) q^{27} +108.528 q^{29} +100.165 q^{31} +(-65.4486 + 212.698i) q^{33} +(91.1188 + 111.340i) q^{35} +(284.046 - 284.046i) q^{37} +(226.230 + 427.338i) q^{39} +215.535i q^{41} +(-114.525 - 114.525i) q^{43} +(-193.677 + 231.548i) q^{45} +(-384.531 - 384.531i) q^{47} +177.406i q^{49} +(11.1385 + 21.0400i) q^{51} +(-368.409 + 368.409i) q^{53} +(476.459 + 47.5876i) q^{55} +(-103.275 + 335.627i) q^{57} -244.049 q^{59} -158.686 q^{61} +(341.298 - 65.0633i) q^{63} +(805.132 - 658.907i) q^{65} +(99.3488 - 99.3488i) q^{67} +(-278.136 + 147.244i) q^{69} +669.159i q^{71} +(48.1561 + 48.1561i) q^{73} +(570.750 + 310.031i) q^{75} +(-389.702 - 389.702i) q^{77} -785.118i q^{79} +(268.199 + 677.872i) q^{81} +(-749.766 + 749.766i) q^{83} +(39.6407 - 32.4413i) q^{85} +(-538.989 - 165.850i) q^{87} +675.915 q^{89} -1197.46 q^{91} +(-497.452 - 153.069i) q^{93} +(751.828 + 75.0908i) q^{95} +(730.220 - 730.220i) q^{97} +(650.082 - 956.317i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 12 q^{7}+O(q^{10}) $ 36 * q - 12 * q^7	$ 36 q - 12 q^{7} + 24 q^{13} - 12 q^{15} + 32 q^{21} + 72 q^{25} - 168 q^{27} + 216 q^{31} + 204 q^{33} + 576 q^{37} - 464 q^{45} - 816 q^{51} - 372 q^{55} - 1160 q^{57} + 72 q^{61} - 628 q^{63} - 1080 q^{67} - 900 q^{73} + 720 q^{75} + 1196 q^{81} + 912 q^{85} + 1660 q^{87} + 4080 q^{91} + 2568 q^{93} + 2172 q^{97}+O(q^{100}) $ 36 * q - 12 * q^7 + 24 * q^13 - 12 * q^15 + 32 * q^21 + 72 * q^25 - 168 * q^27 + 216 * q^31 + 204 * q^33 + 576 * q^37 - 464 * q^45 - 816 * q^51 - 372 * q^55 - 1160 * q^57 + 72 * q^61 - 628 * q^63 - 1080 * q^67 - 900 * q^73 + 720 * q^75 + 1196 * q^81 + 912 * q^85 + 1660 * q^87 + 4080 * q^91 + 2568 * q^93 + 2172 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$.

$n$	$31$	$41$	$61$	$97$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	−4.96635	−	1.52818i	−0.955775	−	0.294098i
$3$	−4.96635	−	1.52818i	−0.955775	−	0.294098i
$4$		0			0
$5$	−1.11114	+	11.1250i	−0.0993830	+	0.995049i
$5$	−1.11114	+	11.1250i	−0.0993830	+	0.995049i
$6$		0			0
$7$	9.09927	−	9.09927i	0.491315	−	0.491315i	−0.417406	−	0.908720i	$-0.637061\pi$
$7$	9.09927	−	9.09927i	0.491315	−	0.491315i	0.908720	+	0.417406i	$0.137061\pi$
$8$		0			0
$9$	22.3293	+	15.1790i	0.827013	+	0.562183i
$10$		0			0
$11$		−	42.8278i		−	1.17392i	−0.809617	−	0.586958i	$-0.800325\pi$
$11$		−	42.8278i		−	1.17392i	0.809617	−	0.586958i	$-0.199675\pi$
$12$		0			0
$13$	−65.7996	−	65.7996i	−1.40381	−	1.40381i	−0.787519	−	0.616290i	$-0.788635\pi$
$13$	−65.7996	−	65.7996i	−1.40381	−	1.40381i	−0.616290	−	0.787519i	$-0.711365\pi$
$14$		0			0
$15$	22.5193	−	53.5526i	0.387630	−	0.921815i
$16$		0			0
$17$	−3.23965	−	3.23965i	−0.0462194	−	0.0462194i	0.683619	−	0.729839i	$-0.260405\pi$
$17$	−3.23965	−	3.23965i	−0.0462194	−	0.0462194i	−0.729839	+	0.683619i	$0.760405\pi$
$18$		0			0
$19$		−	67.5802i		−	0.815997i	−0.912983	−	0.407999i	$-0.866227\pi$
$19$		−	67.5802i		−	0.815997i	0.912983	−	0.407999i	$-0.133773\pi$
$20$		0			0
$21$	−59.0955	+	31.2849i	−0.614081	+	0.325092i
$22$		0			0
$23$	42.8262	−	42.8262i	0.388256	−	0.388256i	−0.485809	−	0.874065i	$-0.661475\pi$
$23$	42.8262	−	42.8262i	0.388256	−	0.388256i	0.874065	+	0.485809i	$0.161475\pi$
$24$		0			0
$25$	−122.531	−	24.7228i	−0.980246	−	0.197782i
$26$		0			0
$27$	−87.6992	−	109.507i	−0.625101	−	0.780544i
$28$		0			0
$29$	108.528			0.694937			0.347469	−	0.937692i	$-0.387041\pi$
$29$	108.528			0.694937			0.347469	+	0.937692i	$0.387041\pi$
$30$		0			0
$31$	100.165			0.580325			0.290163	−	0.956977i	$-0.406291\pi$
$31$	100.165			0.580325			0.290163	+	0.956977i	$0.406291\pi$
$32$		0			0
$33$	−65.4486	+	212.698i	−0.345247	+	1.12200i
$34$		0			0
$35$	91.1188	+	111.340i	0.440054	+	0.537710i
$36$		0			0
$37$	284.046	−	284.046i	1.26208	−	1.26208i	0.311995	−	0.950084i	$-0.399003\pi$
$37$	284.046	−	284.046i	1.26208	−	1.26208i	0.950084	−	0.311995i	$-0.100997\pi$
$38$		0			0
$39$	226.230	+	427.338i	0.928868	+	1.75458i
$40$		0			0
$41$			215.535i			0.820998i	0.911861	+	0.410499i	$0.134645\pi$
$41$			215.535i			0.820998i	−0.911861	+	0.410499i	$0.865355\pi$
$42$		0			0
$43$	−114.525	−	114.525i	−0.406160	−	0.406160i	0.474237	−	0.880397i	$-0.342724\pi$
$43$	−114.525	−	114.525i	−0.406160	−	0.406160i	−0.880397	+	0.474237i	$0.842724\pi$
$44$		0			0
$45$	−193.677	+	231.548i	−0.641591	+	0.767047i
$46$		0			0
$47$	−384.531	−	384.531i	−1.19340	−	1.19340i	−0.976107	−	0.217289i	$-0.930279\pi$
$47$	−384.531	−	384.531i	−1.19340	−	1.19340i	−0.217289	−	0.976107i	$-0.569721\pi$
$48$		0			0
$49$			177.406i			0.517220i
$50$		0			0
$51$	11.1385	+	21.0400i	0.0305823	+	0.0577684i
$52$		0			0
$53$	−368.409	+	368.409i	−0.954809	+	0.954809i	−0.999022	−	0.0442129i	$-0.985922\pi$
$53$	−368.409	+	368.409i	−0.954809	+	0.954809i	0.0442129	+	0.999022i	$0.485922\pi$
$54$		0			0
$55$	476.459	+	47.5876i	1.16810	+	0.116667i
$56$		0			0
$57$	−103.275	+	335.627i	−0.239983	+	0.779910i
$58$		0			0
$59$	−244.049			−0.538515			−0.269258	−	0.963068i	$-0.586778\pi$
$59$	−244.049			−0.538515			−0.269258	+	0.963068i	$0.586778\pi$
$60$		0			0
$61$	−158.686			−0.333076			−0.166538	−	0.986035i	$-0.553259\pi$
$61$	−158.686			−0.333076			−0.166538	+	0.986035i	$0.553259\pi$
$62$		0			0
$63$	341.298	−	65.0633i	0.682532	−	0.130114i
$64$		0			0
$65$	805.132	−	658.907i	1.53637	−	1.25734i
$66$		0			0
$67$	99.3488	−	99.3488i	0.181155	−	0.181155i	−0.610704	−	0.791859i	$-0.709113\pi$
$67$	99.3488	−	99.3488i	0.181155	−	0.181155i	0.791859	+	0.610704i	$0.209113\pi$
$68$		0			0
$69$	−278.136	+	147.244i	−0.485271	+	0.256900i
$70$		0			0
$71$			669.159i			1.11851i	0.828994	+	0.559257i	$0.188914\pi$
$71$			669.159i			1.11851i	−0.828994	+	0.559257i	$0.811086\pi$
$72$		0			0
$73$	48.1561	+	48.1561i	0.0772089	+	0.0772089i	0.744657	−	0.667448i	$-0.232613\pi$
$73$	48.1561	+	48.1561i	0.0772089	+	0.0772089i	−0.667448	+	0.744657i	$0.732613\pi$
$74$		0			0
$75$	570.750	+	310.031i	0.878728	+	0.477324i
$76$		0			0
$77$	−389.702	−	389.702i	−0.576762	−	0.576762i
$78$		0			0
$79$		−	785.118i		−	1.11814i	−0.829122	−	0.559068i	$-0.811159\pi$
$79$		−	785.118i		−	1.11814i	0.829122	−	0.559068i	$-0.188841\pi$
$80$		0			0
$81$	268.199	+	677.872i	0.367900	+	0.929866i
$82$		0			0
$83$	−749.766	+	749.766i	−0.991536	+	0.991536i	−0.999964	−	0.00842859i	$-0.997317\pi$
$83$	−749.766	+	749.766i	−0.991536	+	0.991536i	0.00842859	+	0.999964i	$0.497317\pi$
$84$		0			0
$85$	39.6407	−	32.4413i	0.0505840	−	0.0413971i
$86$		0			0
$87$	−538.989	−	165.850i	−0.664204	−	0.204380i
$88$		0			0
$89$	675.915			0.805021			0.402510	−	0.915415i	$-0.368138\pi$
$89$	675.915			0.805021			0.402510	+	0.915415i	$0.368138\pi$
$90$		0			0
$91$	−1197.46			−1.37942
$92$		0			0
$93$	−497.452	−	153.069i	−0.554660	−	0.170673i
$94$		0			0
$95$	751.828	+	75.0908i	0.811958	+	0.0810963i
$96$		0			0
$97$	730.220	−	730.220i	0.764357	−	0.764357i	−0.212750	−	0.977107i	$-0.568242\pi$
$97$	730.220	−	730.220i	0.764357	−	0.764357i	0.977107	+	0.212750i	$0.0682420\pi$
$98$		0			0
$99$	650.082	−	956.317i	0.659956	−	0.970843i
$100$		0			0
$101$		−	831.708i		−	0.819386i	−0.912223	−	0.409693i	$-0.865636\pi$
$101$		−	831.708i		−	0.819386i	0.912223	−	0.409693i	$-0.134364\pi$
$102$		0			0
$103$	−507.205	−	507.205i	−0.485208	−	0.485208i	0.421582	−	0.906790i	$-0.361475\pi$
$103$	−507.205	−	507.205i	−0.485208	−	0.485208i	−0.906790	+	0.421582i	$0.861475\pi$
$104$		0			0
$105$	−282.381	−	692.199i	−0.262453	−	0.643349i
$106$		0			0
$107$	191.892	+	191.892i	0.173373	+	0.173373i	0.788459	−	0.615087i	$-0.210879\pi$
$107$	191.892	+	191.892i	0.173373	+	0.173373i	−0.615087	+	0.788459i	$0.710879\pi$
$108$		0			0
$109$		−	135.020i		−	0.118647i	−0.998239	−	0.0593237i	$-0.981106\pi$
$109$		−	135.020i		−	0.118647i	0.998239	−	0.0593237i	$-0.0188944\pi$
$110$		0			0
$111$	−1844.75	+	976.600i	−1.57744	+	0.835088i
$112$		0			0
$113$	1134.98	−	1134.98i	0.944865	−	0.944865i	−0.0536921	−	0.998558i	$-0.517099\pi$
$113$	1134.98	−	1134.98i	0.944865	−	0.944865i	0.998558	+	0.0536921i	$0.0170990\pi$
$114$		0			0
$115$	428.856	+	524.027i	0.347748	+	0.424920i
$116$		0			0
$117$	−470.492	−	2468.03i	−0.371770	−	1.95017i
$118$		0			0
$119$	−58.9568			−0.0454165
$120$		0			0
$121$	−503.224			−0.378079
$122$		0			0
$123$	329.376	−	1070.42i	0.241454	−	0.784689i
$124$		0			0
$125$	411.189	−	1335.68i	0.294223	−	0.955737i
$126$		0			0
$127$	−1153.77	+	1153.77i	−0.806143	+	0.806143i	−0.984048	−	0.177905i	$-0.943068\pi$
$127$	−1153.77	+	1153.77i	−0.806143	+	0.806143i	0.177905	+	0.984048i	$0.443068\pi$
$128$		0			0
$129$	393.757	+	743.785i	0.268747	+	0.507648i
$130$		0			0
$131$		−	107.837i		−	0.0719218i	−0.999353	−	0.0359609i	$-0.988551\pi$
$131$		−	107.837i		−	0.0719218i	0.999353	−	0.0359609i	$-0.0114492\pi$
$132$		0			0
$133$	−614.930	−	614.930i	−0.400911	−	0.400911i
$134$		0			0
$135$	1315.71	−	853.976i	0.838804	−	0.544433i
$136$		0			0
$137$	1044.67	+	1044.67i	0.651476	+	0.651476i	0.953348	−	0.301872i	$-0.0976116\pi$
$137$	1044.67	+	1044.67i	0.651476	+	0.651476i	−0.301872	+	0.953348i	$0.597612\pi$
$138$		0			0
$139$			757.509i			0.462238i	0.972926	+	0.231119i	$0.0742386\pi$
$139$			757.509i			0.462238i	−0.972926	+	0.231119i	$0.925761\pi$
$140$		0			0
$141$	1322.09	+	2497.35i	0.789643	+	1.49159i
$142$		0			0
$143$	−2818.05	+	2818.05i	−1.64795	+	1.64795i
$144$		0			0
$145$	−120.590	+	1207.37i	−0.0690650	+	0.691497i
$146$		0			0
$147$	271.109	−	881.063i	0.152113	−	0.494346i
$148$		0			0
$149$	−2007.45			−1.10374			−0.551869	−	0.833931i	$-0.686085\pi$
$149$	−2007.45			−1.10374			−0.551869	+	0.833931i	$0.686085\pi$
$150$		0			0
$151$	1856.82			1.00070			0.500351	−	0.865822i	$-0.333204\pi$
$151$	1856.82			1.00070			0.500351	+	0.865822i	$0.333204\pi$
$152$		0			0
$153$	−23.1647	−	121.514i	−0.0122402	−	0.0642078i
$154$		0			0
$155$	−111.296	+	1114.33i	−0.0576745	+	0.577452i
$156$		0			0
$157$	−185.792	+	185.792i	−0.0944448	+	0.0944448i	−0.752751	−	0.658306i	$-0.771273\pi$
$157$	−185.792	+	185.792i	−0.0944448	+	0.0944448i	0.658306	+	0.752751i	$0.271273\pi$
$158$		0			0
$159$	2392.65	−	1266.66i	1.19339	−	0.631775i
$160$		0			0
$161$		−	779.375i		−	0.381512i
$162$		0			0
$163$	2648.59	+	2648.59i	1.27272	+	1.27272i	0.944655	+	0.328064i	$0.106396\pi$
$163$	2648.59	+	2648.59i	1.27272	+	1.27272i	0.328064	+	0.944655i	$0.393604\pi$
$164$		0			0
$165$	−2293.54	−	964.452i	−1.08213	−	0.455045i
$166$		0			0
$167$	−2049.86	−	2049.86i	−0.949840	−	0.949840i	0.0489607	−	0.998801i	$-0.484409\pi$
$167$	−2049.86	−	2049.86i	−0.949840	−	0.949840i	−0.998801	+	0.0489607i	$0.984409\pi$
$168$		0			0
$169$			6462.17i			2.94136i
$170$		0			0
$171$	1025.80	−	1509.02i	0.458740	−	0.674840i
$172$		0			0
$173$	−1009.57	+	1009.57i	−0.443677	+	0.443677i	−0.893246	−	0.449569i	$-0.851578\pi$
$173$	−1009.57	+	1009.57i	−0.443677	+	0.443677i	0.449569	+	0.893246i	$0.351578\pi$
$174$		0			0
$175$	−1339.90	+	889.982i	−0.578782	+	0.384436i
$176$		0			0
$177$	1212.03	+	372.950i	0.514700	+	0.158376i
$178$		0			0
$179$	1821.54			0.760604			0.380302	−	0.924862i	$-0.375820\pi$
$179$	1821.54			0.760604			0.380302	+	0.924862i	$0.375820\pi$
$180$		0			0
$181$	3136.20			1.28791			0.643956	−	0.765063i	$-0.277292\pi$
$181$	3136.20			1.28791			0.643956	+	0.765063i	$0.277292\pi$
$182$		0			0
$183$	788.090	+	242.500i	0.318346	+	0.0979570i
$184$		0			0
$185$	2844.40	+	3475.62i	1.13040	+	1.38126i
$186$		0			0
$187$	−138.747	+	138.747i	−0.0542577	+	0.0542577i
$188$		0			0
$189$	−1794.44	−	198.437i	−0.690614	−	0.0763713i
$190$		0			0
$191$		−	4232.34i		−	1.60336i	−0.597754	−	0.801679i	$-0.703940\pi$
$191$		−	4232.34i		−	1.60336i	0.597754	−	0.801679i	$-0.296060\pi$
$192$		0			0
$193$	−1215.92	−	1215.92i	−0.453492	−	0.453492i	0.443020	−	0.896512i	$-0.353907\pi$
$193$	−1215.92	−	1215.92i	−0.453492	−	0.453492i	−0.896512	+	0.443020i	$0.853907\pi$
$194$		0			0
$195$	−5005.50	+	2041.98i	−1.83821	+	0.749894i
$196$		0			0
$197$	375.613	+	375.613i	0.135844	+	0.135844i	0.771759	−	0.635915i	$-0.219377\pi$
$197$	375.613	+	375.613i	0.135844	+	0.135844i	−0.635915	+	0.771759i	$0.719377\pi$
$198$		0			0
$199$		−	2795.60i		−	0.995854i	−0.867219	−	0.497927i	$-0.834095\pi$
$199$		−	2795.60i		−	0.995854i	0.867219	−	0.497927i	$-0.165905\pi$
$200$		0			0
$201$	−645.224	+	341.579i	−0.226421	+	0.119866i
$202$		0			0
$203$	987.528	−	987.528i	0.341433	−	0.341433i
$204$		0			0
$205$	−2397.82	−	239.489i	−0.816933	−	0.0815933i
$206$		0			0
$207$	1606.34	−	306.224i	0.539364	−	0.102822i
$208$		0			0
$209$	−2894.31			−0.957913
$210$		0			0
$211$	−4158.67			−1.35685			−0.678423	−	0.734672i	$-0.737336\pi$
$211$	−4158.67			−1.35685			−0.678423	+	0.734672i	$0.737336\pi$
$212$		0			0
$213$	1022.59	−	3323.28i	0.328953	−	1.06905i
$214$		0			0
$215$	1401.34	−	1146.84i	0.444515	−	0.363784i
$216$		0			0
$217$	911.424	−	911.424i	0.285122	−	0.285122i
$218$		0			0
$219$	−165.569	−	312.752i	−0.0510874	−	0.0965013i
$220$		0			0
$221$			426.335i			0.129766i
$222$		0			0
$223$	2556.56	+	2556.56i	0.767713	+	0.767713i	0.977703	−	0.209990i	$-0.0673432\pi$
$223$	2556.56	+	2556.56i	0.767713	+	0.767713i	−0.209990	+	0.977703i	$0.567343\pi$
$224$		0			0
$225$	−2360.77	−	2411.93i	−0.699486	−	0.714646i
$226$		0			0
$227$	4355.96	+	4355.96i	1.27364	+	1.27364i	0.944166	+	0.329471i	$0.106870\pi$
$227$	4355.96	+	4355.96i	1.27364	+	1.27364i	0.329471	+	0.944166i	$0.393130\pi$
$228$		0			0
$229$		−	608.498i		−	0.175593i	−0.996138	−	0.0877963i	$-0.972018\pi$
$229$		−	608.498i		−	0.175593i	0.996138	−	0.0877963i	$-0.0279825\pi$
$230$		0			0
$231$	1339.86	+	2530.93i	0.381630	+	0.720880i
$232$		0			0
$233$	−162.816	+	162.816i	−0.0457787	+	0.0457787i	−0.729626	−	0.683847i	$-0.760306\pi$
$233$	−162.816	+	162.816i	−0.0457787	+	0.0457787i	0.683847	+	0.729626i	$0.260306\pi$
$234$		0			0
$235$	4705.17	−	3850.64i	1.30609	−	1.06888i
$236$		0			0
$237$	−1199.80	+	3899.18i	−0.328842	+	1.06869i
$238$		0			0
$239$	−2288.54			−0.619387			−0.309694	−	0.950836i	$-0.600227\pi$
$239$	−2288.54			−0.619387			−0.309694	+	0.950836i	$0.600227\pi$
$240$		0			0
$241$	−229.992			−0.0614735			−0.0307368	−	0.999528i	$-0.509785\pi$
$241$	−229.992			−0.0614735			−0.0307368	+	0.999528i	$0.509785\pi$
$242$		0			0
$243$	−296.060	−	3776.41i	−0.0781576	−	0.996941i
$244$		0			0
$245$	−1973.65	−	197.123i	−0.514659	−	0.0514029i
$246$		0			0
$247$	−4446.75	+	4446.75i	−1.14550	+	1.14550i
$248$		0			0
$249$	4869.38	−	2577.83i	1.23929	−	0.656077i
$250$		0			0
$251$		−	6206.92i		−	1.56087i	−0.625240	−	0.780433i	$-0.714999\pi$
$251$		−	6206.92i		−	1.56087i	0.625240	−	0.780433i	$-0.285001\pi$
$252$		0			0
$253$	−1834.16	−	1834.16i	−0.455780	−	0.455780i
$254$		0			0
$255$	−246.446	+	100.537i	−0.0605217	+	0.0246897i
$256$		0			0
$257$	2744.76	+	2744.76i	0.666201	+	0.666201i	0.956834	−	0.290633i	$-0.0938660\pi$
$257$	2744.76	+	2744.76i	0.666201	+	0.666201i	−0.290633	+	0.956834i	$0.593866\pi$
$258$		0			0
$259$		−	5169.23i		−	1.24016i
$260$		0			0
$261$	2423.36	+	1647.34i	0.574722	+	0.390682i
$262$		0			0
$263$	3519.23	−	3519.23i	0.825114	−	0.825114i	−0.161722	−	0.986836i	$-0.551705\pi$
$263$	3519.23	−	3519.23i	0.825114	−	0.825114i	0.986836	+	0.161722i	$0.0517049\pi$
$264$		0			0
$265$	−3689.19	−	4507.90i	−0.855190	−	1.04497i
$266$		0			0
$267$	−3356.83	−	1032.92i	−0.769419	−	0.236755i
$268$		0			0
$269$	−4110.94			−0.931779			−0.465890	−	0.884843i	$-0.654266\pi$
$269$	−4110.94			−0.931779			−0.465890	+	0.884843i	$0.654266\pi$
$270$		0			0
$271$	608.313			0.136356			0.0681779	−	0.997673i	$-0.478281\pi$
$271$	608.313			0.136356			0.0681779	+	0.997673i	$0.478281\pi$
$272$		0			0
$273$	5946.99	+	1829.93i	1.31842	+	0.405686i
$274$		0			0
$275$	−1058.82	+	5247.73i	−0.232180	+	1.15073i
$276$		0			0
$277$	2034.67	−	2034.67i	0.441341	−	0.441341i	−0.451122	−	0.892463i	$-0.648976\pi$
$277$	2034.67	−	2034.67i	0.441341	−	0.441341i	0.892463	+	0.451122i	$0.148976\pi$
$278$		0			0
$279$	2236.61	+	1520.39i	0.479936	+	0.326249i
$280$		0			0
$281$		−	3993.85i		−	0.847876i	−0.905691	−	0.423938i	$-0.860647\pi$
$281$		−	3993.85i		−	0.847876i	0.905691	−	0.423938i	$-0.139353\pi$
$282$		0			0
$283$	−2889.04	−	2889.04i	−0.606839	−	0.606839i	0.335280	−	0.942119i	$-0.391169\pi$
$283$	−2889.04	−	2889.04i	−0.606839	−	0.606839i	−0.942119	+	0.335280i	$0.891169\pi$
$284$		0			0
$285$	−3619.09	−	1521.86i	−0.752199	−	0.316305i
$286$		0			0
$287$	1961.21	+	1961.21i	0.403368	+	0.403368i
$288$		0			0
$289$		−	4892.01i		−	0.995728i
$290$		0			0
$291$	−4742.44	+	2510.62i	−0.955349	+	0.505757i
$292$		0			0
$293$	442.864	−	442.864i	0.0883016	−	0.0883016i	−0.661576	−	0.749878i	$-0.730112\pi$
$293$	442.864	−	442.864i	0.0883016	−	0.0883016i	0.749878	+	0.661576i	$0.230112\pi$
$294$		0			0
$295$	271.171	−	2715.04i	0.0535193	−	0.535849i
$296$		0			0
$297$	−4689.96	+	3755.97i	−0.916293	+	0.733816i
$298$		0			0
$299$	−5635.90			−1.09007
$300$		0			0
$301$	−2084.19			−0.399105
$302$		0			0
$303$	−1271.00	+	4130.56i	−0.240980	+	0.783149i
$304$		0			0
$305$	176.322	−	1765.38i	0.0331021	−	0.331427i
$306$		0			0
$307$	−959.192	+	959.192i	−0.178319	+	0.178319i	−0.790623	−	0.612304i	$-0.790243\pi$
$307$	−959.192	+	959.192i	−0.178319	+	0.178319i	0.612304	+	0.790623i	$0.290243\pi$
$308$		0			0
$309$	1743.86	+	3294.06i	0.321051	+	0.606448i
$310$		0			0
$311$		−	6436.14i		−	1.17350i	−0.809767	−	0.586752i	$-0.800406\pi$
$311$		−	6436.14i		−	1.17350i	0.809767	−	0.586752i	$-0.199594\pi$
$312$		0			0
$313$	2368.48	+	2368.48i	0.427713	+	0.427713i	0.887849	−	0.460135i	$-0.152199\pi$
$313$	2368.48	+	2368.48i	0.427713	+	0.427713i	−0.460135	+	0.887849i	$0.652199\pi$
$314$		0			0
$315$	344.600	+	3869.23i	0.0616381	+	0.692084i
$316$		0			0
$317$	6204.00	+	6204.00i	1.09922	+	1.09922i	0.994502	+	0.104713i	$0.0333925\pi$
$317$	6204.00	+	6204.00i	1.09922	+	1.09922i	0.104713	+	0.994502i	$0.466608\pi$
$318$		0			0
$319$		−	4648.03i		−	0.815798i
$320$		0			0
$321$	−659.758	−	1246.25i	−0.114717	−	0.216694i
$322$		0			0
$323$	−218.936	+	218.936i	−0.0377149	+	0.0377149i
$324$		0			0
$325$	6435.73	+	9689.22i	1.09843	+	1.65373i
$326$		0			0
$327$	−206.334	+	670.556i	−0.0348940	+	0.113400i
$328$		0			0
$329$	−6997.91			−1.17267
$330$		0			0
$331$	9983.17			1.65778			0.828889	−	0.559413i	$-0.188973\pi$
$331$	9983.17			1.65778			0.828889	+	0.559413i	$0.188973\pi$
$332$		0			0
$333$	10654.1	−	2031.04i	1.75327	−	0.334235i
$334$		0			0
$335$	994.865	+	1215.64i	0.162255	+	0.198262i
$336$		0			0
$337$	2744.78	−	2744.78i	0.443673	−	0.443673i	−0.449571	−	0.893244i	$-0.648423\pi$
$337$	2744.78	−	2744.78i	0.443673	−	0.443673i	0.893244	+	0.449571i	$0.148423\pi$
$338$		0			0
$339$	−7371.15	+	3902.25i	−1.18096	+	0.625196i
$340$		0			0
$341$		−	4289.83i		−	0.681253i
$342$		0			0
$343$	4735.32	+	4735.32i	0.745432	+	0.745432i
$344$		0			0
$345$	−1329.04	−	3257.87i	−0.207401	−	0.508400i
$346$		0			0
$347$	6783.85	+	6783.85i	1.04950	+	1.04950i	0.998709	+	0.0507896i	$0.0161738\pi$
$347$	6783.85	+	6783.85i	1.04950	+	1.04950i	0.0507896	+	0.998709i	$0.483826\pi$
$348$		0			0
$349$		−	2413.67i		−	0.370202i	−0.982719	−	0.185101i	$-0.940739\pi$
$349$		−	2413.67i		−	0.370202i	0.982719	−	0.185101i	$-0.0592613\pi$
$350$		0			0
$351$	−1434.96	+	12976.1i	−0.218212	+	1.97326i
$352$		0			0
$353$	−8163.42	+	8163.42i	−1.23086	+	1.23086i	−0.267232	+	0.963632i	$0.586109\pi$
$353$	−8163.42	+	8163.42i	−1.23086	+	1.23086i	−0.963632	+	0.267232i	$0.913891\pi$
$354$		0			0
$355$	−7444.38	−	743.526i	−1.11298	−	0.111161i
$356$		0			0
$357$	292.800	+	90.0966i	0.0434080	+	0.0133569i
$358$		0			0
$359$	2471.05			0.363278			0.181639	−	0.983365i	$-0.441860\pi$
$359$	2471.05			0.363278			0.181639	+	0.983365i	$0.441860\pi$
$360$		0			0
$361$	2291.92			0.334148
$362$		0			0
$363$	2499.19	+	769.016i	0.361359	+	0.111192i
$364$		0			0
$365$	−589.245	+	482.228i	−0.0844999	+	0.0691534i
$366$		0			0
$367$	−1284.90	+	1284.90i	−0.182756	+	0.182756i	−0.792555	−	0.609800i	$-0.791250\pi$
$367$	−1284.90	+	1284.90i	−0.182756	+	0.182756i	0.609800	+	0.792555i	$0.291250\pi$
$368$		0			0
$369$	−3271.60	+	4812.75i	−0.461551	+	0.678976i
$370$		0			0
$371$			6704.51i			0.938223i
$372$		0			0
$373$	−2991.14	−	2991.14i	−0.415215	−	0.415215i	0.468335	−	0.883551i	$-0.344854\pi$
$373$	−2991.14	−	2991.14i	−0.415215	−	0.415215i	−0.883551	+	0.468335i	$0.844854\pi$
$374$		0			0
$375$	−4083.27	+	6005.10i	−0.562291	+	0.826939i
$376$		0			0
$377$	−7141.11	−	7141.11i	−0.975559	−	0.975559i
$378$		0			0
$379$			8370.64i			1.13449i	0.823550	+	0.567244i	$0.191990\pi$
$379$			8370.64i			1.13449i	−0.823550	+	0.567244i	$0.808010\pi$
$380$		0			0
$381$	7493.17	−	3966.85i	1.00758	−	0.533406i
$382$		0			0
$383$	−3642.07	+	3642.07i	−0.485904	+	0.485904i	−0.907011	−	0.421107i	$-0.861642\pi$
$383$	−3642.07	+	3642.07i	−0.485904	+	0.485904i	0.421107	+	0.907011i	$0.361642\pi$
$384$		0			0
$385$	4768.44	−	3902.42i	0.631227	−	0.516586i
$386$		0			0
$387$	−818.897	−	4295.63i	−0.107563	−	0.564236i
$388$		0			0
$389$	11659.2			1.51965			0.759827	−	0.650125i	$-0.225283\pi$
$389$	11659.2			1.51965			0.759827	+	0.650125i	$0.225283\pi$
$390$		0			0
$391$	−277.484			−0.0358899
$392$		0			0
$393$	−164.794	+	535.557i	−0.0211521	+	0.0687411i
$394$		0			0
$395$	8734.43	+	872.373i	1.11260	+	0.111124i
$396$		0			0
$397$	−231.789	+	231.789i	−0.0293027	+	0.0293027i	−0.721606	−	0.692304i	$-0.756596\pi$
$397$	−231.789	+	231.789i	−0.0293027	+	0.0293027i	0.692304	+	0.721606i	$0.256596\pi$
$398$		0			0
$399$	2114.24	+	3993.68i	0.265274	+	0.501088i
$400$		0			0
$401$		−	8839.88i		−	1.10085i	−0.834883	−	0.550427i	$-0.814465\pi$
$401$		−	8839.88i		−	1.10085i	0.834883	−	0.550427i	$-0.185535\pi$
$402$		0			0
$403$	−6590.78	−	6590.78i	−0.814666	−	0.814666i
$404$		0			0
$405$	−7839.32	+	2230.50i	−0.961825	+	0.273665i
$406$		0			0
$407$	−12165.1	−	12165.1i	−1.48157	−	1.48157i
$408$		0			0
$409$			4982.46i			0.602364i	0.953567	+	0.301182i	$0.0973811\pi$
$409$			4982.46i			0.602364i	−0.953567	+	0.301182i	$0.902619\pi$
$410$		0			0
$411$	−3591.76	−	6784.65i	−0.431067	−	0.814263i
$412$		0			0
$413$	−2220.66	+	2220.66i	−0.264580	+	0.264580i
$414$		0			0
$415$	−7508.04	−	9174.23i	−0.888085	−	1.08517i
$416$		0			0
$417$	1157.61	−	3762.06i	0.135943	−	0.441795i
$418$		0			0
$419$	7454.99			0.869212			0.434606	−	0.900621i	$-0.356888\pi$
$419$	7454.99			0.869212			0.434606	+	0.900621i	$0.356888\pi$
$420$		0			0
$421$	−4152.82			−0.480750			−0.240375	−	0.970680i	$-0.577270\pi$
$421$	−4152.82			−0.480750			−0.240375	+	0.970680i	$0.577270\pi$
$422$		0			0
$423$	−2749.55	−	14423.1i	−0.316046	−	1.65786i
$424$		0			0
$425$	316.863	+	477.049i	0.0361650	+	0.0544477i
$426$		0			0
$427$	−1443.93	+	1443.93i	−0.163645	+	0.163645i
$428$		0			0
$429$	18301.9	−	9688.96i	2.05973	−	1.09041i
$430$		0			0
$431$			4760.61i			0.532043i	0.963967	+	0.266021i	$0.0857092\pi$
$431$			4760.61i			0.532043i	−0.963967	+	0.266021i	$0.914291\pi$
$432$		0			0
$433$	3075.11	+	3075.11i	0.341294	+	0.341294i	0.856854	−	0.515560i	$-0.172416\pi$
$433$	3075.11	+	3075.11i	0.341294	+	0.341294i	−0.515560	+	0.856854i	$0.672416\pi$
$434$		0			0
$435$	2443.98	−	5811.97i	0.269379	−	0.640604i
$436$		0			0
$437$	−2894.20	−	2894.20i	−0.316816	−	0.316816i
$438$		0			0
$439$			5948.82i			0.646747i	0.946271	+	0.323373i	$0.104817\pi$
$439$			5948.82i			0.646747i	−0.946271	+	0.323373i	$0.895183\pi$
$440$		0			0
$441$	−2692.84	+	3961.37i	−0.290773	+	0.427747i
$442$		0			0
$443$	4236.57	−	4236.57i	0.454369	−	0.454369i	−0.442433	−	0.896802i	$-0.645884\pi$
$443$	4236.57	−	4236.57i	0.454369	−	0.454369i	0.896802	+	0.442433i	$0.145884\pi$
$444$		0			0
$445$	−751.034	+	7519.55i	−0.0800054	+	0.801035i
$446$		0			0
$447$	9969.72	+	3067.75i	1.05492	+	0.324607i
$448$		0			0
$449$	−3494.32			−0.367276			−0.183638	−	0.982994i	$-0.558787\pi$
$449$	−3494.32			−0.367276			−0.183638	+	0.982994i	$0.558787\pi$
$450$		0			0
$451$	9230.90			0.963783
$452$		0			0
$453$	−9221.64	−	2837.56i	−0.956447	−	0.294305i
$454$		0			0
$455$	1330.54	−	13321.7i	0.137091	−	1.37259i
$456$		0			0
$457$	9375.14	−	9375.14i	0.959630	−	0.959630i	−0.0395865	−	0.999216i	$-0.512604\pi$
$457$	9375.14	−	9375.14i	0.959630	−	0.959630i	0.999216	+	0.0395865i	$0.0126041\pi$
$458$		0			0
$459$	−70.6503	+	638.879i	−0.00718447	+	0.0649680i
$460$		0			0
$461$			11309.0i			1.14254i	0.820762	+	0.571271i	$0.193549\pi$
$461$			11309.0i			1.14254i	−0.820762	+	0.571271i	$0.806451\pi$
$462$		0			0
$463$	−5218.15	−	5218.15i	−0.523775	−	0.523775i	0.394934	−	0.918709i	$-0.370767\pi$
$463$	−5218.15	−	5218.15i	−0.523775	−	0.523775i	−0.918709	+	0.394934i	$0.870767\pi$
$464$		0			0
$465$	2255.63	−	5364.07i	0.224951	−	0.534952i
$466$		0			0
$467$	873.432	+	873.432i	0.0865473	+	0.0865473i	0.749055	−	0.662508i	$-0.230508\pi$
$467$	873.432	+	873.432i	0.0865473	+	0.0865473i	−0.662508	+	0.749055i	$0.730508\pi$
$468$		0			0
$469$		−	1808.00i		−	0.178008i
$470$		0			0
$471$	1206.63	−	638.786i	0.118044	−	0.0624919i
$472$		0			0
$473$	−4904.85	+	4904.85i	−0.476798	+	0.476798i
$474$		0			0
$475$	−1670.77	+	8280.65i	−0.161390	+	0.799878i
$476$		0			0
$477$	−13818.4	+	2634.27i	−1.32642	+	0.252861i
$478$		0			0
$479$	−13677.3			−1.30466			−0.652328	−	0.757937i	$-0.726208\pi$
$479$	−13677.3			−1.30466			−0.652328	+	0.757937i	$0.726208\pi$
$480$		0			0
$481$	−37380.2			−3.54343
$482$		0			0
$483$	−1191.02	+	3870.65i	−0.112202	+	0.364639i
$484$		0			0
$485$	7312.31	+	8935.06i	0.684608	+	0.836537i
$486$		0			0
$487$	13164.9	−	13164.9i	1.22496	−	1.22496i	0.259118	−	0.965846i	$-0.416568\pi$
$487$	13164.9	−	13164.9i	1.22496	−	1.22496i	0.965846	−	0.259118i	$-0.0834319\pi$
$488$		0			0
$489$	−9106.30	−	17201.3i	−0.842130	−	1.59074i
$490$		0			0
$491$		−	5318.45i		−	0.488836i	−0.969670	−	0.244418i	$-0.921403\pi$
$491$		−	5318.45i		−	0.488836i	0.969670	−	0.244418i	$-0.0785968\pi$
$492$		0			0
$493$	−351.593	−	351.593i	−0.0321196	−	0.0321196i
$494$		0			0
$495$	9916.69	+	8294.75i	0.900449	+	0.753174i
$496$		0			0
$497$	6088.86	+	6088.86i	0.549542	+	0.549542i
$498$		0			0
$499$			1957.24i			0.175588i	0.996139	+	0.0877938i	$0.0279817\pi$
$499$			1957.24i			0.175588i	−0.996139	+	0.0877938i	$0.972018\pi$
$500$		0			0
$501$	7047.79	+	13312.9i	0.628487	+	1.18718i
$502$		0			0
$503$	−897.828	+	897.828i	−0.0795868	+	0.0795868i	−0.745780	−	0.666193i	$-0.767923\pi$
$503$	−897.828	+	897.828i	−0.0795868	+	0.0795868i	0.666193	+	0.745780i	$0.267923\pi$
$504$		0			0
$505$	9252.74	+	924.141i	0.815330	+	0.0814331i
$506$		0			0
$507$	9875.35	−	32093.4i	0.865049	−	2.81128i
$508$		0			0
$509$	14133.8			1.23079			0.615394	−	0.788220i	$-0.288997\pi$
$509$	14133.8			1.23079			0.615394	+	0.788220i	$0.288997\pi$
$510$		0			0
$511$	876.372			0.0758677
$512$		0			0
$513$	−7400.52	+	5926.73i	−0.636922	+	0.510081i
$514$		0			0
$515$	6206.23	−	5079.08i	0.531027	−	0.434584i
$516$		0			0
$517$	−16468.6	+	16468.6i	−1.40095	+	1.40095i
$518$		0			0
$519$	6556.68	−	3471.07i	0.554540	−	0.293571i
$520$		0			0
$521$			6045.03i			0.508326i	0.967161	+	0.254163i	$0.0817999\pi$
$521$			6045.03i			0.508326i	−0.967161	+	0.254163i	$0.918200\pi$
$522$		0			0
$523$	12299.4	+	12299.4i	1.02833	+	1.02833i	0.999587	+	0.0287419i	$0.00915009\pi$
$523$	12299.4	+	12299.4i	1.02833	+	1.02833i	0.0287419	+	0.999587i	$0.490850\pi$
$524$		0			0
$525$	8014.47	−	2372.36i	0.666248	−	0.197216i
$526$		0			0
$527$	−324.497	−	324.497i	−0.0268223	−	0.0268223i
$528$		0			0
$529$			8498.83i			0.698515i
$530$		0			0
$531$	−5449.44	−	3704.40i	−0.445359	−	0.302744i
$532$		0			0
$533$	14182.1	−	14182.1i	1.15252	−	1.15252i
$534$		0			0
$535$	−2348.01	+	1921.58i	−0.189745	+	0.155284i
$536$		0			0
$537$	−9046.41	−	2783.64i	−0.726967	−	0.223692i
$538$		0			0
$539$	7597.94			0.607173
$540$		0			0
$541$	15041.4			1.19534			0.597672	−	0.801741i	$-0.296092\pi$
$541$	15041.4			1.19534			0.597672	+	0.801741i	$0.296092\pi$
$542$		0			0
$543$	−15575.5	−	4792.67i	−1.23095	−	0.378772i
$544$		0			0
$545$	1502.09	+	150.025i	0.118060	+	0.0117915i
$546$		0			0
$547$	−14996.7	+	14996.7i	−1.17223	+	1.17223i	−0.190555	+	0.981677i	$0.561029\pi$
$547$	−14996.7	+	14996.7i	−1.17223	+	1.17223i	−0.981677	+	0.190555i	$0.938971\pi$
$548$		0			0
$549$	−3543.35	−	2408.68i	−0.275458	−	0.187250i
$550$		0			0
$551$		−	7334.35i		−	0.567067i
$552$		0			0
$553$	−7144.01	−	7144.01i	−0.549356	−	0.549356i
$554$		0			0
$555$	−8814.90	−	21607.9i	−0.674183	−	1.65262i
$556$		0			0
$557$	−16945.4	−	16945.4i	−1.28905	−	1.28905i	−0.935364	−	0.353688i	$-0.884928\pi$
$557$	−16945.4	−	16945.4i	−1.28905	−	1.28905i	−0.353688	−	0.935364i	$-0.615072\pi$
$558$		0			0
$559$			15071.4i			1.14034i
$560$		0			0
$561$	901.097	−	477.036i	0.0678152	−	0.0359011i
$562$		0			0
$563$	−15295.6	+	15295.6i	−1.14500	+	1.14500i	−0.157476	+	0.987523i	$0.550336\pi$
$563$	−15295.6	+	15295.6i	−1.14500	+	1.14500i	−0.987523	+	0.157476i	$0.949664\pi$
$564$		0			0
$565$	11365.5	+	13887.7i	0.846284	+	1.03409i
$566$		0			0
$567$	8608.56	+	3727.73i	0.637611	+	0.276102i
$568$		0			0
$569$	−8434.10			−0.621399			−0.310699	−	0.950508i	$-0.600563\pi$
$569$	−8434.10			−0.621399			−0.310699	+	0.950508i	$0.600563\pi$
$570$		0			0
$571$	2074.02			0.152006			0.0760028	−	0.997108i	$-0.475784\pi$
$571$	2074.02			0.152006			0.0760028	+	0.997108i	$0.475784\pi$
$572$		0			0
$573$	−6467.77	+	21019.3i	−0.471545	+	1.53245i
$574$		0			0
$575$	−6306.31	+	4188.75i	−0.457377	+	0.303796i
$576$		0			0
$577$	6290.98	−	6290.98i	0.453894	−	0.453894i	−0.442751	−	0.896645i	$-0.645997\pi$
$577$	6290.98	−	6290.98i	0.453894	−	0.453894i	0.896645	+	0.442751i	$0.145997\pi$
$578$		0			0
$579$	4180.55	+	7896.84i	0.300065	+	0.566808i
$580$		0			0
$581$			13644.6i			0.974312i
$582$		0			0
$583$	15778.2	+	15778.2i	1.12087	+	1.12087i
$584$		0			0
$585$	27979.6	−	2491.91i	1.97746	−	0.176116i
$586$		0			0
$587$	−5305.40	−	5305.40i	−0.373045	−	0.373045i	0.495540	−	0.868585i	$-0.334970\pi$
$587$	−5305.40	−	5305.40i	−0.373045	−	0.373045i	−0.868585	+	0.495540i	$0.834970\pi$
$588$		0			0
$589$		−	6769.13i		−	0.473544i
$590$		0			0
$591$	−1291.42	−	2439.43i	−0.0898851	−	0.169788i
$592$		0			0
$593$	565.381	−	565.381i	0.0391525	−	0.0391525i	−0.687260	−	0.726412i	$-0.741186\pi$
$593$	565.381	−	565.381i	0.0391525	−	0.0391525i	0.726412	+	0.687260i	$0.241186\pi$
$594$		0			0
$595$	65.5091	−	655.894i	0.00451363	−	0.0451917i
$596$		0			0
$597$	−4272.18	+	13883.9i	−0.292879	+	0.951812i
$598$		0			0
$599$	−4867.36			−0.332011			−0.166006	−	0.986125i	$-0.553087\pi$
$599$	−4867.36			−0.332011			−0.166006	+	0.986125i	$0.553087\pi$
$600$		0			0
$601$	−3873.53			−0.262903			−0.131451	−	0.991323i	$-0.541964\pi$
$601$	−3873.53			−0.262903			−0.131451	+	0.991323i	$0.541964\pi$
$602$		0			0
$603$	3726.41	−	710.383i	0.251660	−	0.0479751i
$604$		0			0
$605$	559.150	−	5598.36i	0.0375747	−	0.376208i
$606$		0			0
$607$	−5119.25	+	5119.25i	−0.342313	+	0.342313i	−0.857236	−	0.514923i	$-0.827820\pi$
$607$	−5119.25	+	5119.25i	−0.342313	+	0.342313i	0.514923	+	0.857236i	$0.327820\pi$
$608$		0			0
$609$	−6413.53	+	3395.29i	−0.426748	+	0.225918i
$610$		0			0
$611$			50604.0i			3.35060i
$612$		0			0
$613$	−4804.53	−	4804.53i	−0.316563	−	0.316563i	0.530882	−	0.847446i	$-0.321861\pi$
$613$	−4804.53	−	4804.53i	−0.316563	−	0.316563i	−0.847446	+	0.530882i	$0.821861\pi$
$614$		0			0
$615$	11542.5	+	4853.69i	0.756808	+	0.318243i
$616$		0			0
$617$	−4575.66	−	4575.66i	−0.298556	−	0.298556i	0.541892	−	0.840448i	$-0.317708\pi$
$617$	−4575.66	−	4575.66i	−0.298556	−	0.298556i	−0.840448	+	0.541892i	$0.817708\pi$
$618$		0			0
$619$		−	15541.6i		−	1.00916i	−0.863365	−	0.504579i	$-0.831648\pi$
$619$		−	15541.6i		−	1.00916i	0.863365	−	0.504579i	$-0.168352\pi$
$620$		0			0
$621$	−8445.61	−	933.956i	−0.545750	−	0.0603516i
$622$		0			0
$623$	6150.33	−	6150.33i	0.395518	−	0.395518i
$624$		0			0
$625$	14402.6	+	6058.60i	0.921765	+	0.387750i
$626$		0			0
$627$	14374.2	+	4423.03i	0.915549	+	0.281720i
$628$		0			0
$629$	−1840.42			−0.116665
$630$		0			0
$631$	4294.54			0.270940			0.135470	−	0.990781i	$-0.456746\pi$
$631$	4294.54			0.270940			0.135470	+	0.990781i	$0.456746\pi$
$632$		0			0
$633$	20653.4	+	6355.19i	1.29684	+	0.399046i
$634$		0			0
$635$	−11553.6	−	14117.6i	−0.722035	−	0.882269i
$636$		0			0
$637$	11673.3	−	11673.3i	0.726078	−	0.726078i
$638$		0			0
$639$	−10157.1	+	14941.9i	−0.628810	+	0.925026i
$640$		0			0
$641$		−	8325.71i		−	0.513020i	−0.966542	−	0.256510i	$-0.917427\pi$
$641$		−	8325.71i		−	0.513020i	0.966542	−	0.256510i	$-0.0825726\pi$
$642$		0			0
$643$	−9694.41	−	9694.41i	−0.594573	−	0.594573i	0.344291	−	0.938863i	$-0.388119\pi$
$643$	−9694.41	−	9694.41i	−0.594573	−	0.594573i	−0.938863	+	0.344291i	$0.888119\pi$
$644$		0			0
$645$	−8712.12	+	3554.09i	−0.531844	+	0.216965i
$646$		0			0
$647$	6915.00	+	6915.00i	0.420180	+	0.420180i	0.885266	−	0.465085i	$-0.153976\pi$
$647$	6915.00	+	6915.00i	0.420180	+	0.420180i	−0.465085	+	0.885266i	$0.653976\pi$
$648$		0			0
$649$			10452.1i			0.632172i
$650$		0			0
$651$	−5919.27	+	3133.64i	−0.356367	+	0.188659i
$652$		0			0
$653$	1381.38	−	1381.38i	0.0827836	−	0.0827836i	−0.664502	−	0.747286i	$-0.731356\pi$
$653$	1381.38	−	1381.38i	0.0827836	−	0.0827836i	0.747286	+	0.664502i	$0.231356\pi$
$654$		0			0
$655$	1199.69	+	119.822i	0.0715658	+	0.00714781i
$656$		0			0
$657$	344.335	+	1806.25i	0.0204472	+	0.107258i
$658$		0			0
$659$	−6196.14			−0.366263			−0.183132	−	0.983088i	$-0.558623\pi$
$659$	−6196.14			−0.366263			−0.183132	+	0.983088i	$0.558623\pi$
$660$		0			0
$661$	−3415.14			−0.200958			−0.100479	−	0.994939i	$-0.532038\pi$
$661$	−3415.14			−0.200958			−0.100479	+	0.994939i	$0.532038\pi$
$662$		0			0
$663$	651.515	−	2117.33i	0.0381640	−	0.124027i
$664$		0			0
$665$	7524.36	−	6157.82i	0.438770	−	0.359083i
$666$		0			0
$667$	4647.85	−	4647.85i	0.269814	−	0.269814i
$668$		0			0
$669$	−8789.91	−	16603.7i	−0.507978	−	0.959544i
$670$		0			0
$671$			6796.17i			0.391003i
$672$		0			0
$673$	11018.2	+	11018.2i	0.631083	+	0.631083i	0.948340	−	0.317257i	$-0.102762\pi$
$673$	11018.2	+	11018.2i	0.631083	+	0.631083i	−0.317257	+	0.948340i	$0.602762\pi$
$674$		0			0
$675$	8038.53	+	15586.2i	0.458375	+	0.888759i
$676$		0			0
$677$	−3849.05	−	3849.05i	−0.218510	−	0.218510i	0.589360	−	0.807870i	$-0.299380\pi$
$677$	−3849.05	−	3849.05i	−0.218510	−	0.218510i	−0.807870	+	0.589360i	$0.799380\pi$
$678$		0			0
$679$		−	13288.9i		−	0.751079i
$680$		0			0
$681$	−14976.6	−	28290.0i	−0.842736	−	1.59188i
$682$		0			0
$683$	−1507.97	+	1507.97i	−0.0844816	+	0.0844816i	−0.748085	−	0.663603i	$-0.769026\pi$
$683$	−1507.97	+	1507.97i	−0.0844816	+	0.0844816i	0.663603	+	0.748085i	$0.269026\pi$
$684$		0			0
$685$	−12782.7	+	10461.2i	−0.712997	+	0.583505i
$686$		0			0
$687$	−929.894	+	3022.02i	−0.0516414	+	0.167827i
$688$		0			0
$689$	48482.3			2.68074
$690$		0			0
$691$	1020.29			0.0561703			0.0280852	−	0.999606i	$-0.491059\pi$
$691$	1020.29			0.0561703			0.0280852	+	0.999606i	$0.491059\pi$
$692$		0			0
$693$	−2786.52	−	14617.1i	−0.152743	−	0.801236i
$694$		0			0
$695$	−8427.28	−	841.695i	−0.459949	−	0.0459386i
$696$		0			0
$697$	698.257	−	698.257i	0.0379460	−	0.0379460i
$698$		0			0
$699$	1057.41	−	559.790i	0.0572176	−	0.0302907i
$700$		0			0
$701$		−	18815.1i		−	1.01375i	−0.862020	−	0.506874i	$-0.830801\pi$
$701$		−	18815.1i		−	1.01375i	0.862020	−	0.506874i	$-0.169199\pi$
$702$		0			0
$703$	−19195.9	−	19195.9i	−1.02985	−	1.02985i
$704$		0			0
$705$	−29252.0	+	11933.3i	−1.56269	+	0.637495i
$706$		0			0
$707$	−7567.94	−	7567.94i	−0.402576	−	0.402576i
$708$		0			0
$709$		−	19930.8i		−	1.05574i	−0.849326	−	0.527868i	$-0.822992\pi$
$709$		−	19930.8i		−	1.05574i	0.849326	−	0.527868i	$-0.177008\pi$
$710$		0			0
$711$	11917.3	−	17531.2i	0.628597	−	0.924712i
$712$		0			0
$713$	4289.67	−	4289.67i	0.225315	−	0.225315i
$714$		0			0
$715$	−28219.6	−	34482.1i	−1.47602	−	1.80357i
$716$		0			0
$717$	11365.7	+	3497.30i	0.591995	+	0.182161i
$718$		0			0
$719$	1847.05			0.0958044			0.0479022	−	0.998852i	$-0.484746\pi$
$719$	1847.05			0.0958044			0.0479022	+	0.998852i	$0.484746\pi$
$720$		0			0
$721$	−9230.40			−0.476779
$722$		0			0
$723$	1142.22	+	351.470i	0.0587549	+	0.0180792i
$724$		0			0
$725$	−13298.0	−	2683.12i	−0.681209	−	0.137446i
$726$		0			0
$727$	4336.73	−	4336.73i	0.221239	−	0.221239i	−0.587781	−	0.809020i	$-0.699998\pi$
$727$	4336.73	−	4336.73i	0.221239	−	0.221239i	0.809020	+	0.587781i	$0.199998\pi$
$728$		0			0
$729$	−4300.69	+	19207.4i	−0.218497	+	0.975838i
$730$		0			0
$731$			742.040i			0.0375449i
$732$		0			0
$733$	−20726.6	−	20726.6i	−1.04441	−	1.04441i	−0.998967	−	0.0454458i	$-0.985529\pi$
$733$	−20726.6	−	20726.6i	−1.04441	−	1.04441i	−0.0454458	−	0.998967i	$-0.514471\pi$
$734$		0			0
$735$	9500.58	+	3995.06i	0.476781	+	0.200490i
$736$		0			0
$737$	−4254.90	−	4254.90i	−0.212661	−	0.212661i
$738$		0			0
$739$			1811.38i			0.0901659i	0.998983	+	0.0450829i	$0.0143552\pi$
$739$			1811.38i			0.0901659i	−0.998983	+	0.0450829i	$0.985645\pi$
$740$		0			0
$741$	28879.5	−	15288.7i	1.43174	−	0.757954i
$742$		0			0
$743$	3890.85	−	3890.85i	0.192115	−	0.192115i	−0.604494	−	0.796609i	$-0.706625\pi$
$743$	3890.85	−	3890.85i	0.192115	−	0.192115i	0.796609	+	0.604494i	$0.206625\pi$
$744$		0			0
$745$	2230.55	−	22332.9i	0.109693	−	1.09827i
$746$		0			0
$747$	−28122.4	+	5361.11i	−1.37744	+	0.262588i
$748$		0			0
$749$	3492.15			0.170361
$750$		0			0
$751$	−5633.24			−0.273715			−0.136857	−	0.990591i	$-0.543700\pi$
$751$	−5633.24			−0.273715			−0.136857	+	0.990591i	$0.543700\pi$
$752$		0			0
$753$	−9485.28	+	30825.8i	−0.459048	+	1.49184i
$754$		0			0
$755$	−2063.18	+	20657.1i	−0.0994529	+	0.995749i
$756$		0			0
$757$	8481.33	−	8481.33i	0.407211	−	0.407211i	−0.473554	−	0.880765i	$-0.657029\pi$
$757$	8481.33	−	8481.33i	0.407211	−	0.407211i	0.880765	+	0.473554i	$0.157029\pi$
$758$		0			0
$759$	6306.15	+	11912.0i	0.301579	+	0.569667i
$760$		0			0
$761$		−	3144.76i		−	0.149800i	−0.997191	−	0.0748998i	$-0.976136\pi$
$761$		−	3144.76i		−	0.149800i	0.997191	−	0.0748998i	$-0.0238637\pi$
$762$		0			0
$763$	−1228.58	−	1228.58i	−0.0582932	−	0.0582932i
$764$		0			0
$765$	1377.58	−	122.689i	0.0651064	−	0.00579847i
$766$		0			0
$767$	16058.3	+	16058.3i	0.755973	+	0.755973i
$768$		0			0
$769$		−	14340.0i		−	0.672449i	−0.941782	−	0.336225i	$-0.890850\pi$
$769$		−	14340.0i		−	0.672449i	0.941782	−	0.336225i	$-0.109150\pi$
$770$		0			0
$771$	−9436.98	−	17826.0i	−0.440810	−	0.832667i
$772$		0			0
$773$	23953.9	−	23953.9i	1.11457	−	1.11457i	0.122044	−	0.992525i	$-0.461055\pi$
$773$	23953.9	−	23953.9i	1.11457	−	1.11457i	0.992525	−	0.122044i	$-0.0389450\pi$
$774$		0			0
$775$	−12273.2	−	2476.34i	−0.568861	−	0.114778i
$776$		0			0
$777$	−7899.50	+	25672.2i	−0.364727	+	1.18531i
$778$		0			0
$779$	14565.9			0.669932
$780$		0			0
$781$	28658.6			1.31304
$782$		0			0
$783$	−9517.84	−	11884.6i	−0.434406	−	0.542429i
$784$		0			0
$785$	−1860.50	−	2273.38i	−0.0845910	−	0.103363i
$786$		0			0
$787$	3118.12	−	3118.12i	0.141231	−	0.141231i	−0.632956	−	0.774188i	$-0.718159\pi$
$787$	3118.12	−	3118.12i	0.141231	−	0.141231i	0.774188	+	0.632956i	$0.218159\pi$
$788$		0			0
$789$	−22855.7	+	12099.7i	−1.03129	+	0.545959i
$790$		0			0
$791$		−	20655.0i		−	0.928452i
$792$		0			0
$793$	10441.5	+	10441.5i	0.467575	+	0.467575i
$794$		0			0
$795$	11433.0	+	28025.6i	0.510045	+	1.25027i
$796$		0			0
$797$	8988.82	+	8988.82i	0.399499	+	0.399499i	0.878056	−	0.478558i	$-0.158840\pi$
$797$	8988.82	+	8988.82i	0.399499	+	0.399499i	−0.478558	+	0.878056i	$0.658840\pi$
$798$		0			0
$799$			2491.49i			0.110316i
$800$		0			0
$801$	15092.7	+	10259.7i	0.665762	+	0.452569i
$802$		0			0
$803$	2062.42	−	2062.42i	0.0906368	−	0.0906368i
$804$		0			0
$805$	8670.54	+	865.992i	0.379623	+	0.0379158i
$806$		0			0
$807$	20416.4	+	6282.25i	0.890571	+	0.274034i
$808$		0			0
$809$	−2250.23			−0.0977921			−0.0488960	−	0.998804i	$-0.515570\pi$
$809$	−2250.23			−0.0977921			−0.0488960	+	0.998804i	$0.515570\pi$
$810$		0			0
$811$	30640.2			1.32666			0.663330	−	0.748327i	$-0.269143\pi$
$811$	30640.2			1.32666			0.663330	+	0.748327i	$0.269143\pi$
$812$		0			0
$813$	−3021.10	−	929.612i	−0.130325	−	0.0401020i
$814$		0			0
$815$	−32408.4	+	26522.6i	−1.39291	+	1.13993i
$816$		0			0
$817$	−7739.61	+	7739.61i	−0.331425	+	0.331425i
$818$		0			0
$819$	−26738.4	−	18176.1i	−1.14080	−	0.775489i
$820$		0			0
$821$			42088.7i			1.78917i	0.446900	+	0.894584i	$0.352528\pi$
$821$			42088.7i			1.78917i	−0.446900	+	0.894584i	$0.647472\pi$
$822$		0			0
$823$	21012.0	+	21012.0i	0.889955	+	0.889955i	0.994518	−	0.104563i	$-0.0333445\pi$
$823$	21012.0	+	21012.0i	0.889955	+	0.889955i	−0.104563	+	0.994518i	$0.533344\pi$
$824$		0			0
$825$	13278.0	−	24444.0i	0.560338	−	1.03155i
$826$		0			0
$827$	11663.6	+	11663.6i	0.490428	+	0.490428i	0.908441	−	0.418013i	$-0.137273\pi$
$827$	11663.6	+	11663.6i	0.490428	+	0.490428i	−0.418013	+	0.908441i	$0.637273\pi$
$828$		0			0
$829$		−	3655.87i		−	0.153165i	−0.997063	−	0.0765823i	$-0.975599\pi$
$829$		−	3655.87i		−	0.153165i	0.997063	−	0.0765823i	$-0.0244008\pi$
$830$		0			0
$831$	−13214.2	+	6995.55i	−0.551620	+	0.292025i
$832$		0			0
$833$	574.734	−	574.734i	0.0239056	−	0.0239056i
$834$		0			0
$835$	25082.4	−	20527.0i	1.03954	−	0.850740i
$836$		0			0
$837$	−8784.35	−	10968.7i	−0.362762	−	0.452969i
$838$		0			0
$839$	−15080.1			−0.620527			−0.310263	−	0.950651i	$-0.600417\pi$
$839$	−15080.1			−0.620527			−0.310263	+	0.950651i	$0.600417\pi$
$840$		0			0
$841$	−12610.6			−0.517062
$842$		0			0
$843$	−6103.32	+	19834.9i	−0.249359	+	0.810379i
$844$		0			0
$845$	−71891.6	−	7180.35i	−2.92680	−	0.292321i
$846$		0			0
$847$	−4578.97	+	4578.97i	−0.185756	+	0.185756i
$848$		0			0
$849$	9933.01	+	18762.9i	0.401531	+	0.758472i
$850$		0			0
$851$		−	24329.3i		−	0.980019i
$852$		0			0
$853$	−13603.0	−	13603.0i	−0.546023	−	0.546023i	0.379265	−	0.925288i	$-0.376177\pi$
$853$	−13603.0	−	13603.0i	−0.546023	−	0.546023i	−0.925288	+	0.379265i	$0.876177\pi$
$854$		0			0
$855$	15648.0	+	13088.7i	0.625908	+	0.523537i
$856$		0			0
$857$	31532.4	+	31532.4i	1.25686	+	1.25686i	0.952585	+	0.304271i	$0.0984130\pi$
$857$	31532.4	+	31532.4i	1.25686	+	1.25686i	0.304271	+	0.952585i	$0.401587\pi$
$858$		0			0
$859$			36128.6i			1.43503i	0.696543	+	0.717515i	$0.254721\pi$
$859$			36128.6i			1.43503i	−0.696543	+	0.717515i	$0.745279\pi$
$860$		0			0
$861$	−6742.99	−	12737.2i	−0.266899	−	0.504159i
$862$		0			0
$863$	24247.2	−	24247.2i	0.956413	−	0.956413i	−0.0426762	−	0.999089i	$-0.513588\pi$
$863$	24247.2	−	24247.2i	0.956413	−	0.956413i	0.999089	+	0.0426762i	$0.0135884\pi$
$864$		0			0
$865$	−10109.7	−	12353.2i	−0.397386	−	0.485574i
$866$		0			0
$867$	−7475.86	+	24295.4i	−0.292842	+	0.951692i
$868$		0			0
$869$	−33624.9			−1.31260
$870$		0			0
$871$	−13074.2			−0.508614
$872$		0			0
$873$	27389.3	−	5221.35i	1.06184	−	0.202424i
$874$		0			0
$875$	−8412.22	−	15895.3i	−0.325012	−	0.614123i
$876$		0			0
$877$	3656.81	−	3656.81i	0.140800	−	0.140800i	−0.633193	−	0.773994i	$-0.718256\pi$
$877$	3656.81	−	3656.81i	0.140800	−	0.140800i	0.773994	+	0.633193i	$0.218256\pi$
$878$		0			0
$879$	−2876.19	+	1522.64i	−0.110366	+	0.0584271i
$880$		0			0
$881$		−	32635.1i		−	1.24802i	−0.781417	−	0.624009i	$-0.785503\pi$
$881$		−	32635.1i		−	1.24802i	0.781417	−	0.624009i	$-0.214497\pi$
$882$		0			0
$883$	8157.06	+	8157.06i	0.310880	+	0.310880i	0.845250	−	0.534370i	$-0.179451\pi$
$883$	8157.06	+	8157.06i	0.310880	+	0.310880i	−0.534370	+	0.845250i	$0.679451\pi$
$884$		0			0
$885$	−5495.79	+	13069.4i	−0.208745	+	0.496412i
$886$		0			0
$887$	−22438.3	−	22438.3i	−0.849384	−	0.849384i	0.140673	−	0.990056i	$-0.455074\pi$
$887$	−22438.3	−	22438.3i	−0.849384	−	0.849384i	−0.990056	+	0.140673i	$0.955074\pi$
$888$		0			0
$889$			20996.9i			0.792139i
$890$		0			0
$891$	29031.8	−	11486.4i	1.09158	−	0.431883i
$892$		0			0
$893$	−25986.7	+	25986.7i	−0.973808	+	0.973808i
$894$		0			0
$895$	−2023.98	+	20264.6i	−0.0755912	+	0.756839i
$896$		0			0
$897$	27989.9	+	8612.66i	1.04187	+	0.320589i
$898$		0			0
$899$	10870.7			0.403289
$900$		0			0
$901$	2387.03			0.0882614
$902$		0			0
$903$	10350.8	+	3185.01i	0.381454	+	0.117376i
$904$		0			0
$905$	−3484.75	+	34890.2i	−0.127997	+	1.28154i
$906$		0			0
$907$	−14722.4	+	14722.4i	−0.538975	+	0.538975i	−0.923228	−	0.384253i	$-0.874459\pi$
$907$	−14722.4	+	14722.4i	−0.538975	+	0.538975i	0.384253	+	0.923228i	$0.374459\pi$
$908$		0			0
$909$	12624.5	−	18571.5i	0.460645	−	0.677643i
$910$		0			0
$911$			29099.5i			1.05830i	0.848529	+	0.529148i	$0.177489\pi$
$911$			29099.5i			1.05830i	−0.848529	+	0.529148i	$0.822511\pi$
$912$		0			0
$913$	32110.8	+	32110.8i	1.16398	+	1.16398i
$914$		0			0
$915$	−3573.49	+	8498.04i	−0.129110	+	0.307035i
$916$		0			0
$917$	−981.238	−	981.238i	−0.0353362	−	0.0353362i
$918$		0			0
$919$		−	37285.5i		−	1.33834i	−0.743109	−	0.669170i	$-0.766650\pi$
$919$		−	37285.5i		−	1.33834i	0.743109	−	0.669170i	$-0.233350\pi$
$920$		0			0
$921$	6229.50	−	3297.87i	0.222876	−	0.117990i
$922$		0			0
$923$	44030.4	−	44030.4i	1.57018	−	1.57018i
$924$		0			0
$925$	−41826.8	+	27782.0i	−1.48676	+	0.987531i
$926$		0			0
$927$	−3626.71	−	19024.4i	−0.128497	−	0.674049i
$928$		0			0
$929$	−3873.96			−0.136814			−0.0684072	−	0.997657i	$-0.521792\pi$
$929$	−3873.96			−0.136814			−0.0684072	+	0.997657i	$0.521792\pi$
$930$		0			0
$931$	11989.2			0.422050
$932$		0			0
$933$	−9835.57	+	31964.1i	−0.345125	+	1.12161i
$934$		0			0
$935$	−1389.39	−	1697.73i	−0.0485968	−	0.0593813i
$936$		0			0
$937$	457.817	−	457.817i	0.0159618	−	0.0159618i	−0.699081	−	0.715043i	$-0.746407\pi$
$937$	457.817	−	457.817i	0.0159618	−	0.0159618i	0.715043	+	0.699081i	$0.246407\pi$
$938$		0			0
$939$	−8143.24	−	15382.2i	−0.283008	−	0.534588i
$940$		0			0
$941$			31589.7i			1.09436i	0.837014	+	0.547181i	$0.184299\pi$
$941$			31589.7i			1.09436i	−0.837014	+	0.547181i	$0.815701\pi$
$942$		0			0
$943$	9230.55	+	9230.55i	0.318757	+	0.318757i
$944$		0			0
$945$	4201.47	−	19742.6i	0.144629	−	0.679605i
$946$		0			0
$947$	−24458.4	−	24458.4i	−0.839273	−	0.839273i	0.149490	−	0.988763i	$-0.452237\pi$
$947$	−24458.4	−	24458.4i	−0.839273	−	0.839273i	−0.988763	+	0.149490i	$0.952237\pi$
$948$		0			0
$949$		−	6337.31i		−	0.216773i
$950$		0			0
$951$	−21330.4	−	40292.1i	−0.727326	−	1.37388i
$952$		0			0
$953$	1848.64	−	1848.64i	0.0628367	−	0.0628367i	−0.674990	−	0.737827i	$-0.735852\pi$
$953$	1848.64	−	1848.64i	0.0628367	−	0.0628367i	0.737827	+	0.674990i	$0.235852\pi$
$954$		0			0
$955$	47084.8	+	4702.71i	1.59542	+	0.159347i
$956$		0			0
$957$	−7103.02	+	23083.8i	−0.239925	+	0.779720i
$958$		0			0
$959$	19011.5			0.640160
$960$		0			0
$961$	−19758.1			−0.663223
$962$		0			0
$963$	1372.10	+	7197.53i	0.0459141	+	0.240849i
$964$		0			0
$965$	14878.2	−	12176.1i	0.496316	−	0.406178i
$966$		0			0
$967$	−22516.8	+	22516.8i	−0.748800	+	0.748800i	−0.974254	−	0.225454i	$-0.927614\pi$
$967$	−22516.8	+	22516.8i	−0.748800	+	0.748800i	0.225454	+	0.974254i	$0.427614\pi$
$968$		0			0
$969$	1421.89	−	752.739i	0.0471388	−	0.0249551i
$970$		0			0
$971$		−	108.007i		−	0.00356964i	−0.999998	−	0.00178482i	$-0.999432\pi$
$971$		−	108.007i		−	0.00356964i	0.999998	−	0.00178482i	$-0.000568127\pi$
$972$		0			0
$973$	6892.78	+	6892.78i	0.227104	+	0.227104i
$974$		0			0
$975$	−17155.2	−	57955.0i	−0.563494	−	1.90364i
$976$		0			0
$977$	20875.3	+	20875.3i	0.683584	+	0.683584i	0.960806	−	0.277222i	$-0.0894138\pi$
$977$	20875.3	+	20875.3i	0.683584	+	0.683584i	−0.277222	+	0.960806i	$0.589414\pi$
$978$		0			0
$979$		−	28948.0i		−	0.945027i
$980$		0			0
$981$	2049.46	−	3014.90i	0.0667016	−	0.0981228i
$982$		0			0
$983$	7028.60	−	7028.60i	0.228054	−	0.228054i	−0.583825	−	0.811879i	$-0.698445\pi$
$983$	7028.60	−	7028.60i	0.228054	−	0.228054i	0.811879	+	0.583825i	$0.198445\pi$
$984$		0			0
$985$	−4596.05	+	3761.34i	−0.148672	+	0.121671i
$986$		0			0
$987$	34754.1	+	10694.1i	1.12081	+	0.344879i
$988$		0			0
$989$	−9809.34			−0.315388
$990$		0			0
$991$	18505.0			0.593171			0.296585	−	0.955006i	$-0.404152\pi$
$991$	18505.0			0.593171			0.296585	+	0.955006i	$0.404152\pi$
$992$		0			0
$993$	−49580.0	−	15256.1i	−1.58446	−	0.487550i
$994$		0			0
$995$	31101.0	+	3106.29i	0.990924	+	0.0989710i
$996$		0			0
$997$	−13470.8	+	13470.8i	−0.427907	+	0.427907i	−0.887915	−	0.460008i	$-0.847847\pi$
$997$	−13470.8	+	13470.8i	−0.427907	+	0.427907i	0.460008	+	0.887915i	$0.347847\pi$
$998$		0			0
$999$	−56015.8	−	6194.49i	−1.77403	−	0.196181i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	120.4.r.a.113.2	yes	36
3.2	odd	2	inner	120.4.r.a.113.7	yes	36
4.3	odd	2		240.4.v.e.113.17		36
5.2	odd	4	inner	120.4.r.a.17.7	yes	36
12.11	even	2		240.4.v.e.113.12		36
15.2	even	4	inner	120.4.r.a.17.2	✓	36
20.7	even	4		240.4.v.e.17.12		36
60.47	odd	4		240.4.v.e.17.17		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.4.r.a.17.2	✓	36	15.2	even	4	inner
120.4.r.a.17.7	yes	36	5.2	odd	4	inner
120.4.r.a.113.2	yes	36	1.1	even	1	trivial
120.4.r.a.113.7	yes	36	3.2	odd	2	inner
240.4.v.e.17.12		36	20.7	even	4
240.4.v.e.17.17		36	60.47	odd	4
240.4.v.e.113.12		36	12.11	even	2
240.4.v.e.113.17		36	4.3	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:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	120.r (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.96635 - 1.52818i) q^{3} +(-1.11114 + 11.1250i) q^{5} +(9.09927 - 9.09927i) q^{7} +(22.3293 + 15.1790i) q^{9} +O(q^{10})\)	\(q+(-4.96635 - 1.52818i) q^{3} +(-1.11114 + 11.1250i) q^{5} +(9.09927 - 9.09927i) q^{7} +(22.3293 + 15.1790i) q^{9} -42.8278i q^{11} +(-65.7996 - 65.7996i) q^{13} +(22.5193 - 53.5526i) q^{15} +(-3.23965 - 3.23965i) q^{17} -67.5802i q^{19} +(-59.0955 + 31.2849i) q^{21} +(42.8262 - 42.8262i) q^{23} +(-122.531 - 24.7228i) q^{25} +(-87.6992 - 109.507i) q^{27} +108.528 q^{29} +100.165 q^{31} +(-65.4486 + 212.698i) q^{33} +(91.1188 + 111.340i) q^{35} +(284.046 - 284.046i) q^{37} +(226.230 + 427.338i) q^{39} +215.535i q^{41} +(-114.525 - 114.525i) q^{43} +(-193.677 + 231.548i) q^{45} +(-384.531 - 384.531i) q^{47} +177.406i q^{49} +(11.1385 + 21.0400i) q^{51} +(-368.409 + 368.409i) q^{53} +(476.459 + 47.5876i) q^{55} +(-103.275 + 335.627i) q^{57} -244.049 q^{59} -158.686 q^{61} +(341.298 - 65.0633i) q^{63} +(805.132 - 658.907i) q^{65} +(99.3488 - 99.3488i) q^{67} +(-278.136 + 147.244i) q^{69} +669.159i q^{71} +(48.1561 + 48.1561i) q^{73} +(570.750 + 310.031i) q^{75} +(-389.702 - 389.702i) q^{77} -785.118i q^{79} +(268.199 + 677.872i) q^{81} +(-749.766 + 749.766i) q^{83} +(39.6407 - 32.4413i) q^{85} +(-538.989 - 165.850i) q^{87} +675.915 q^{89} -1197.46 q^{91} +(-497.452 - 153.069i) q^{93} +(751.828 + 75.0908i) q^{95} +(730.220 - 730.220i) q^{97} +(650.082 - 956.317i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 12 q^{7}+O(q^{10}) \) 36 * q - 12 * q^7	\( 36 q - 12 q^{7} + 24 q^{13} - 12 q^{15} + 32 q^{21} + 72 q^{25} - 168 q^{27} + 216 q^{31} + 204 q^{33} + 576 q^{37} - 464 q^{45} - 816 q^{51} - 372 q^{55} - 1160 q^{57} + 72 q^{61} - 628 q^{63} - 1080 q^{67} - 900 q^{73} + 720 q^{75} + 1196 q^{81} + 912 q^{85} + 1660 q^{87} + 4080 q^{91} + 2568 q^{93} + 2172 q^{97}+O(q^{100}) \) 36 * q - 12 * q^7 + 24 * q^13 - 12 * q^15 + 32 * q^21 + 72 * q^25 - 168 * q^27 + 216 * q^31 + 204 * q^33 + 576 * q^37 - 464 * q^45 - 816 * q^51 - 372 * q^55 - 1160 * q^57 + 72 * q^61 - 628 * q^63 - 1080 * q^67 - 900 * q^73 + 720 * q^75 + 1196 * q^81 + 912 * q^85 + 1660 * q^87 + 4080 * q^91 + 2568 * q^93 + 2172 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more