LMFDB - Embedded newform 240.4.v.e.17.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,4,Mod(17,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, 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("240.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	240.v (of order $4$, degree $2$, not 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:	$14.1604584014$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			17.17
Character	$\chi$	$=$	240.17
Dual form			240.4.v.e.113.17

$q$-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 $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$		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	$-0.362939\pi$
$7$	−9.09927	−	9.09927i	−0.491315	−	0.491315i	−0.908720	+	0.417406i	$0.862939\pi$
$8$		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	−0.616290	+	0.787519i	$0.711365\pi$
$13$	−65.7996	+	65.7996i	−1.40381	+	1.40381i	−0.787519	+	0.616290i	$0.788635\pi$
$14$		0			0
$15$	−22.5193	−	53.5526i	−0.387630	−	0.921815i
$16$		0			0
$17$	−3.23965	+	3.23965i	−0.0462194	+	0.0462194i	−0.729839	−	0.683619i	$-0.760405\pi$
$17$	−3.23965	+	3.23965i	−0.0462194	+	0.0462194i	0.683619	+	0.729839i	$0.260405\pi$
$18$		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	$-0.338525\pi$
$23$	−42.8262	−	42.8262i	−0.388256	−	0.388256i	−0.874065	+	0.485809i	$0.838525\pi$
$24$		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	$-0.593709\pi$
$31$	−100.165			−0.580325			−0.290163	+	0.956977i	$0.593709\pi$
$32$		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	0.950084	+	0.311995i	$0.100997\pi$
$37$	284.046	+	284.046i	1.26208	+	1.26208i	0.311995	+	0.950084i	$0.399003\pi$
$38$		0			0
$39$	−226.230	+	427.338i	−0.928868	+	1.75458i
$40$		0			0
$41$		−	215.535i		−	0.820998i	−0.911861	−	0.410499i	$-0.865355\pi$
$41$		−	215.535i		−	0.820998i	0.911861	−	0.410499i	$-0.134645\pi$
$42$		0			0
$43$	114.525	−	114.525i	0.406160	−	0.406160i	−0.474237	−	0.880397i	$-0.657276\pi$
$43$	114.525	−	114.525i	0.406160	−	0.406160i	0.880397	+	0.474237i	$0.157276\pi$
$44$		0			0
$45$	−193.677	−	231.548i	−0.641591	−	0.767047i
$46$		0			0
$47$	384.531	−	384.531i	1.19340	−	1.19340i	0.217289	−	0.976107i	$-0.430279\pi$
$47$	384.531	−	384.531i	1.19340	−	1.19340i	0.976107	−	0.217289i	$-0.0697215\pi$
$48$		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	0.0442129	−	0.999022i	$-0.485922\pi$
$53$	−368.409	−	368.409i	−0.954809	−	0.954809i	−0.999022	+	0.0442129i	$0.985922\pi$
$54$		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	$-0.413222\pi$
$59$	244.049			0.538515			0.269258	+	0.963068i	$0.413222\pi$
$60$		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	$-0.290887\pi$
$67$	−99.3488	−	99.3488i	−0.181155	−	0.181155i	−0.791859	+	0.610704i	$0.790887\pi$
$68$		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	−0.667448	−	0.744657i	$-0.732613\pi$
$73$	48.1561	−	48.1561i	0.0772089	−	0.0772089i	0.744657	+	0.667448i	$0.232613\pi$
$74$		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	$-0.00268293\pi$
$83$	749.766	+	749.766i	0.991536	+	0.991536i	−0.00842859	+	0.999964i	$0.502683\pi$
$84$		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	0.977107	−	0.212750i	$-0.0682420\pi$
$97$	730.220	+	730.220i	0.764357	+	0.764357i	−0.212750	+	0.977107i	$0.568242\pi$
$98$		0			0
$99$	−650.082	−	956.317i	−0.659956	−	0.970843i
$100$		0			0
$101$			831.708i			0.819386i	0.912223	+	0.409693i	$0.134364\pi$
$101$			831.708i			0.819386i	−0.912223	+	0.409693i	$0.865636\pi$
$102$		0			0
$103$	507.205	−	507.205i	0.485208	−	0.485208i	−0.421582	−	0.906790i	$-0.638525\pi$
$103$	507.205	−	507.205i	0.485208	−	0.485208i	0.906790	+	0.421582i	$0.138525\pi$
$104$		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	$-0.789121\pi$
$107$	−191.892	+	191.892i	−0.173373	+	0.173373i	0.615087	+	0.788459i	$0.289121\pi$
$108$		0			0
$109$			135.020i			0.118647i	0.998239	+	0.0593237i	$0.0188944\pi$
$109$			135.020i			0.118647i	−0.998239	+	0.0593237i	$0.981106\pi$
$110$		0			0
$111$	1844.75	+	976.600i	1.57744	+	0.835088i
$112$		0			0
$113$	1134.98	+	1134.98i	0.944865	+	0.944865i	0.998558	−	0.0536921i	$-0.0170990\pi$
$113$	1134.98	+	1134.98i	0.944865	+	0.944865i	−0.0536921	+	0.998558i	$0.517099\pi$
$114$		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	$-0.0569320\pi$
$127$	1153.77	+	1153.77i	0.806143	+	0.806143i	−0.177905	+	0.984048i	$0.556932\pi$
$128$		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	−0.301872	−	0.953348i	$-0.597612\pi$
$137$	1044.67	−	1044.67i	0.651476	−	0.651476i	0.953348	+	0.301872i	$0.0976116\pi$
$138$		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	$-0.666796\pi$
$151$	−1856.82			−1.00070			−0.500351	+	0.865822i	$0.666796\pi$
$152$		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	0.658306	−	0.752751i	$-0.271273\pi$
$157$	−185.792	−	185.792i	−0.0944448	−	0.0944448i	−0.752751	+	0.658306i	$0.771273\pi$
$158$		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	−0.328064	+	0.944655i	$0.606396\pi$
$163$	−2648.59	+	2648.59i	−1.27272	+	1.27272i	−0.944655	+	0.328064i	$0.893604\pi$
$164$		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	$-0.515591\pi$
$167$	2049.86	−	2049.86i	0.949840	−	0.949840i	0.998801	+	0.0489607i	$0.0155909\pi$
$168$		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	0.449569	−	0.893246i	$-0.351578\pi$
$173$	−1009.57	−	1009.57i	−0.443677	−	0.443677i	−0.893246	+	0.449569i	$0.851578\pi$
$174$		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	$-0.624180\pi$
$179$	−1821.54			−0.760604			−0.380302	+	0.924862i	$0.624180\pi$
$180$		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	−0.896512	−	0.443020i	$-0.853907\pi$
$193$	−1215.92	+	1215.92i	−0.453492	+	0.453492i	0.443020	+	0.896512i	$0.353907\pi$
$194$		0			0
$195$	5005.50	+	2041.98i	1.83821	+	0.749894i
$196$		0			0
$197$	375.613	−	375.613i	0.135844	−	0.135844i	−0.635915	−	0.771759i	$-0.719377\pi$
$197$	375.613	−	375.613i	0.135844	−	0.135844i	0.771759	+	0.635915i	$0.219377\pi$
$198$		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	$-0.262664\pi$
$211$	4158.67			1.35685			0.678423	+	0.734672i	$0.262664\pi$
$212$		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	$-0.932657\pi$
$223$	−2556.56	+	2556.56i	−0.767713	+	0.767713i	0.209990	+	0.977703i	$0.432657\pi$
$224$		0			0
$225$	−2360.77	+	2411.93i	−0.699486	+	0.714646i
$226$		0			0
$227$	−4355.96	+	4355.96i	−1.27364	+	1.27364i	−0.329471	+	0.944166i	$0.606870\pi$
$227$	−4355.96	+	4355.96i	−1.27364	+	1.27364i	−0.944166	+	0.329471i	$0.893130\pi$
$228$		0			0
$229$			608.498i			0.175593i	0.996138	+	0.0877963i	$0.0279825\pi$
$229$			608.498i			0.175593i	−0.996138	+	0.0877963i	$0.972018\pi$
$230$		0			0
$231$	−1339.86	+	2530.93i	−0.381630	+	0.720880i
$232$		0			0
$233$	−162.816	−	162.816i	−0.0457787	−	0.0457787i	0.683847	−	0.729626i	$-0.260306\pi$
$233$	−162.816	−	162.816i	−0.0457787	−	0.0457787i	−0.729626	+	0.683847i	$0.760306\pi$
$234$		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	$-0.399773\pi$
$239$	2288.54			0.619387			0.309694	+	0.950836i	$0.399773\pi$
$240$		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	−0.290633	−	0.956834i	$-0.593866\pi$
$257$	2744.76	−	2744.76i	0.666201	−	0.666201i	0.956834	+	0.290633i	$0.0938660\pi$
$258$		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	$-0.448295\pi$
$263$	−3519.23	−	3519.23i	−0.825114	−	0.825114i	−0.986836	+	0.161722i	$0.948295\pi$
$264$		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	$-0.521719\pi$
$271$	−608.313			−0.136356			−0.0681779	+	0.997673i	$0.521719\pi$
$272$		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	0.892463	−	0.451122i	$-0.148976\pi$
$277$	2034.67	+	2034.67i	0.441341	+	0.441341i	−0.451122	+	0.892463i	$0.648976\pi$
$278$		0			0
$279$	−2236.61	+	1520.39i	−0.479936	+	0.326249i
$280$		0			0
$281$			3993.85i			0.847876i	0.905691	+	0.423938i	$0.139353\pi$
$281$			3993.85i			0.847876i	−0.905691	+	0.423938i	$0.860647\pi$
$282$		0			0
$283$	2889.04	−	2889.04i	0.606839	−	0.606839i	−0.335280	−	0.942119i	$-0.608831\pi$
$283$	2889.04	−	2889.04i	0.606839	−	0.606839i	0.942119	+	0.335280i	$0.108831\pi$
$284$		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	0.749878	−	0.661576i	$-0.230112\pi$
$293$	442.864	+	442.864i	0.0883016	+	0.0883016i	−0.661576	+	0.749878i	$0.730112\pi$
$294$		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	$-0.209757\pi$
$307$	959.192	+	959.192i	0.178319	+	0.178319i	−0.612304	+	0.790623i	$0.709757\pi$
$308$		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	−0.460135	−	0.887849i	$-0.652199\pi$
$313$	2368.48	−	2368.48i	0.427713	−	0.427713i	0.887849	+	0.460135i	$0.152199\pi$
$314$		0			0
$315$	−344.600	+	3869.23i	−0.0616381	+	0.692084i
$316$		0			0
$317$	6204.00	−	6204.00i	1.09922	−	1.09922i	0.104713	−	0.994502i	$-0.466608\pi$
$317$	6204.00	−	6204.00i	1.09922	−	1.09922i	0.994502	−	0.104713i	$-0.0333925\pi$
$318$		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	$-0.811027\pi$
$331$	−9983.17			−1.65778			−0.828889	+	0.559413i	$0.811027\pi$
$332$		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	0.893244	−	0.449571i	$-0.148423\pi$
$337$	2744.78	+	2744.78i	0.443673	+	0.443673i	−0.449571	+	0.893244i	$0.648423\pi$
$338$		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	−0.0507896	+	0.998709i	$0.516174\pi$
$347$	−6783.85	+	6783.85i	−1.04950	+	1.04950i	−0.998709	+	0.0507896i	$0.983826\pi$
$348$		0			0
$349$			2413.67i			0.370202i	0.982719	+	0.185101i	$0.0592613\pi$
$349$			2413.67i			0.370202i	−0.982719	+	0.185101i	$0.940739\pi$
$350$		0			0
$351$	1434.96	+	12976.1i	0.218212	+	1.97326i
$352$		0			0
$353$	−8163.42	−	8163.42i	−1.23086	−	1.23086i	−0.963632	−	0.267232i	$-0.913891\pi$
$353$	−8163.42	−	8163.42i	−1.23086	−	1.23086i	−0.267232	−	0.963632i	$-0.586109\pi$
$354$		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	$-0.558140\pi$
$359$	−2471.05			−0.363278			−0.181639	+	0.983365i	$0.558140\pi$
$360$		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	$-0.208750\pi$
$367$	1284.90	+	1284.90i	0.182756	+	0.182756i	−0.609800	+	0.792555i	$0.708750\pi$
$368$		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	−0.883551	−	0.468335i	$-0.844854\pi$
$373$	−2991.14	+	2991.14i	−0.415215	+	0.415215i	0.468335	+	0.883551i	$0.344854\pi$
$374$		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	$-0.138358\pi$
$383$	3642.07	+	3642.07i	0.485904	+	0.485904i	−0.421107	+	0.907011i	$0.638358\pi$
$384$		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	0.692304	−	0.721606i	$-0.256596\pi$
$397$	−231.789	−	231.789i	−0.0293027	−	0.0293027i	−0.721606	+	0.692304i	$0.756596\pi$
$398$		0			0
$399$	−2114.24	+	3993.68i	−0.265274	+	0.501088i
$400$		0			0
$401$			8839.88i			1.10085i	0.834883	+	0.550427i	$0.185535\pi$
$401$			8839.88i			1.10085i	−0.834883	+	0.550427i	$0.814465\pi$
$402$		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	$-0.902619\pi$
$409$		−	4982.46i		−	0.602364i	0.953567	−	0.301182i	$-0.0973811\pi$
$410$		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	$-0.643112\pi$
$419$	−7454.99			−0.869212			−0.434606	+	0.900621i	$0.643112\pi$
$420$		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	−0.515560	−	0.856854i	$-0.672416\pi$
$433$	3075.11	−	3075.11i	0.341294	−	0.341294i	0.856854	+	0.515560i	$0.172416\pi$
$434$		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	$-0.354116\pi$
$443$	−4236.57	−	4236.57i	−0.454369	−	0.454369i	−0.896802	+	0.442433i	$0.854116\pi$
$444$		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	0.999216	−	0.0395865i	$-0.0126041\pi$
$457$	9375.14	+	9375.14i	0.959630	+	0.959630i	−0.0395865	+	0.999216i	$0.512604\pi$
$458$		0			0
$459$	70.6503	+	638.879i	0.00718447	+	0.0649680i
$460$		0			0
$461$		−	11309.0i		−	1.14254i	−0.820762	−	0.571271i	$-0.806451\pi$
$461$		−	11309.0i		−	1.14254i	0.820762	−	0.571271i	$-0.193549\pi$
$462$		0			0
$463$	5218.15	−	5218.15i	0.523775	−	0.523775i	−0.394934	−	0.918709i	$-0.629233\pi$
$463$	5218.15	−	5218.15i	0.523775	−	0.523775i	0.918709	+	0.394934i	$0.129233\pi$
$464$		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	$-0.769492\pi$
$467$	−873.432	+	873.432i	−0.0865473	+	0.0865473i	0.662508	+	0.749055i	$0.269492\pi$
$468$		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	$-0.273792\pi$
$479$	13677.3			1.30466			0.652328	+	0.757937i	$0.273792\pi$
$480$		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	−0.965846	−	0.259118i	$-0.916568\pi$
$487$	−13164.9	−	13164.9i	−1.22496	−	1.22496i	−0.259118	−	0.965846i	$-0.583432\pi$
$488$		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	$-0.232077\pi$
$503$	897.828	+	897.828i	0.0795868	+	0.0795868i	−0.666193	+	0.745780i	$0.732077\pi$
$504$		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	$-0.918200\pi$
$521$		−	6045.03i		−	0.508326i	0.967161	−	0.254163i	$-0.0817999\pi$
$522$		0			0
$523$	−12299.4	+	12299.4i	−1.02833	+	1.02833i	−0.0287419	+	0.999587i	$0.509150\pi$
$523$	−12299.4	+	12299.4i	−1.02833	+	1.02833i	−0.999587	+	0.0287419i	$0.990850\pi$
$524$		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	0.981677	+	0.190555i	$0.0610286\pi$
$547$	14996.7	+	14996.7i	1.17223	+	1.17223i	0.190555	+	0.981677i	$0.438971\pi$
$548$		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	−0.353688	+	0.935364i	$0.615072\pi$
$557$	−16945.4	+	16945.4i	−1.28905	+	1.28905i	−0.935364	+	0.353688i	$0.884928\pi$
$558$		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	0.987523	+	0.157476i	$0.0503356\pi$
$563$	15295.6	+	15295.6i	1.14500	+	1.14500i	0.157476	+	0.987523i	$0.449664\pi$
$564$		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	$-0.524216\pi$
$571$	−2074.02			−0.152006			−0.0760028	+	0.997108i	$0.524216\pi$
$572$		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	0.896645	−	0.442751i	$-0.145997\pi$
$577$	6290.98	+	6290.98i	0.453894	+	0.453894i	−0.442751	+	0.896645i	$0.645997\pi$
$578$		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	$-0.665030\pi$
$587$	5305.40	−	5305.40i	0.373045	−	0.373045i	0.868585	+	0.495540i	$0.165030\pi$
$588$		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	0.726412	−	0.687260i	$-0.241186\pi$
$593$	565.381	+	565.381i	0.0391525	+	0.0391525i	−0.687260	+	0.726412i	$0.741186\pi$
$594$		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	$-0.446913\pi$
$599$	4867.36			0.332011			0.166006	+	0.986125i	$0.446913\pi$
$600$		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	$-0.172180\pi$
$607$	5119.25	+	5119.25i	0.342313	+	0.342313i	−0.514923	+	0.857236i	$0.672180\pi$
$608$		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	−0.847446	−	0.530882i	$-0.821861\pi$
$613$	−4804.53	+	4804.53i	−0.316563	+	0.316563i	0.530882	+	0.847446i	$0.321861\pi$
$614$		0			0
$615$	−11542.5	+	4853.69i	−0.756808	+	0.318243i
$616$		0			0
$617$	−4575.66	+	4575.66i	−0.298556	+	0.298556i	−0.840448	−	0.541892i	$-0.817708\pi$
$617$	−4575.66	+	4575.66i	−0.298556	+	0.298556i	0.541892	+	0.840448i	$0.317708\pi$
$618$		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	$-0.543254\pi$
$631$	−4294.54			−0.270940			−0.135470	+	0.990781i	$0.543254\pi$
$632$		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	$0.0825726\pi$
$641$			8325.71i			0.513020i	−0.966542	+	0.256510i	$0.917427\pi$
$642$		0			0
$643$	9694.41	−	9694.41i	0.594573	−	0.594573i	−0.344291	−	0.938863i	$-0.611881\pi$
$643$	9694.41	−	9694.41i	0.594573	−	0.594573i	0.938863	+	0.344291i	$0.111881\pi$
$644$		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	$-0.846024\pi$
$647$	−6915.00	+	6915.00i	−0.420180	+	0.420180i	0.465085	+	0.885266i	$0.346024\pi$
$648$		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	0.747286	−	0.664502i	$-0.231356\pi$
$653$	1381.38	+	1381.38i	0.0827836	+	0.0827836i	−0.664502	+	0.747286i	$0.731356\pi$
$654$		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	$-0.441377\pi$
$659$	6196.14			0.366263			0.183132	+	0.983088i	$0.441377\pi$
$660$		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	−0.317257	−	0.948340i	$-0.602762\pi$
$673$	11018.2	−	11018.2i	0.631083	−	0.631083i	0.948340	+	0.317257i	$0.102762\pi$
$674$		0			0
$675$	−8038.53	+	15586.2i	−0.458375	+	0.888759i
$676$		0			0
$677$	−3849.05	+	3849.05i	−0.218510	+	0.218510i	−0.807870	−	0.589360i	$-0.799380\pi$
$677$	−3849.05	+	3849.05i	−0.218510	+	0.218510i	0.589360	+	0.807870i	$0.299380\pi$
$678$		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	$-0.230974\pi$
$683$	1507.97	+	1507.97i	0.0844816	+	0.0844816i	−0.663603	+	0.748085i	$0.730974\pi$
$684$		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	$-0.508941\pi$
$691$	−1020.29			−0.0561703			−0.0280852	+	0.999606i	$0.508941\pi$
$692$		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	$0.169199\pi$
$701$			18815.1i			1.01375i	−0.862020	+	0.506874i	$0.830801\pi$
$702$		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	$0.177008\pi$
$709$			19930.8i			1.05574i	−0.849326	+	0.527868i	$0.822992\pi$
$710$		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	$-0.515254\pi$
$719$	−1847.05			−0.0958044			−0.0479022	+	0.998852i	$0.515254\pi$
$720$		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	$-0.300002\pi$
$727$	−4336.73	−	4336.73i	−0.221239	−	0.221239i	−0.809020	+	0.587781i	$0.800002\pi$
$728$		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	−0.0454458	+	0.998967i	$0.514471\pi$
$733$	−20726.6	+	20726.6i	−1.04441	+	1.04441i	−0.998967	+	0.0454458i	$0.985529\pi$
$734$		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	$-0.293375\pi$
$743$	−3890.85	−	3890.85i	−0.192115	−	0.192115i	−0.796609	+	0.604494i	$0.793375\pi$
$744$		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	$-0.456300\pi$
$751$	5633.24			0.273715			0.136857	+	0.990591i	$0.456300\pi$
$752$		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	0.880765	−	0.473554i	$-0.157029\pi$
$757$	8481.33	+	8481.33i	0.407211	+	0.407211i	−0.473554	+	0.880765i	$0.657029\pi$
$758$		0			0
$759$	−6306.15	+	11912.0i	−0.301579	+	0.569667i
$760$		0			0
$761$			3144.76i			0.149800i	0.997191	+	0.0748998i	$0.0238637\pi$
$761$			3144.76i			0.149800i	−0.997191	+	0.0748998i	$0.976136\pi$
$762$		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	$0.109150\pi$
$769$			14340.0i			0.672449i	−0.941782	+	0.336225i	$0.890850\pi$
$770$		0			0
$771$	9436.98	−	17826.0i	0.440810	−	0.832667i
$772$		0			0
$773$	23953.9	+	23953.9i	1.11457	+	1.11457i	0.992525	+	0.122044i	$0.0389450\pi$
$773$	23953.9	+	23953.9i	1.11457	+	1.11457i	0.122044	+	0.992525i	$0.461055\pi$
$774$		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	$-0.281841\pi$
$787$	−3118.12	−	3118.12i	−0.141231	−	0.141231i	−0.774188	+	0.632956i	$0.781841\pi$
$788$		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	−0.478558	−	0.878056i	$-0.658840\pi$
$797$	8988.82	−	8988.82i	0.399499	−	0.399499i	0.878056	+	0.478558i	$0.158840\pi$
$798$		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	$-0.730857\pi$
$811$	−30640.2			−1.32666			−0.663330	+	0.748327i	$0.730857\pi$
$812$		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	$-0.647472\pi$
$821$		−	42088.7i		−	1.78917i	0.446900	−	0.894584i	$-0.352528\pi$
$822$		0			0
$823$	−21012.0	+	21012.0i	−0.889955	+	0.889955i	−0.994518	−	0.104563i	$-0.966656\pi$
$823$	−21012.0	+	21012.0i	−0.889955	+	0.889955i	0.104563	+	0.994518i	$0.466656\pi$
$824$		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	$-0.862727\pi$
$827$	−11663.6	+	11663.6i	−0.490428	+	0.490428i	0.418013	+	0.908441i	$0.362727\pi$
$828$		0			0
$829$			3655.87i			0.153165i	0.997063	+	0.0765823i	$0.0244008\pi$
$829$			3655.87i			0.153165i	−0.997063	+	0.0765823i	$0.975599\pi$
$830$		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	$-0.399583\pi$
$839$	15080.1			0.620527			0.310263	+	0.950651i	$0.399583\pi$
$840$		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	−0.925288	−	0.379265i	$-0.876177\pi$
$853$	−13603.0	+	13603.0i	−0.546023	+	0.546023i	0.379265	+	0.925288i	$0.376177\pi$
$854$		0			0
$855$	−15648.0	+	13088.7i	−0.625908	+	0.523537i
$856$		0			0
$857$	31532.4	−	31532.4i	1.25686	−	1.25686i	0.304271	−	0.952585i	$-0.401587\pi$
$857$	31532.4	−	31532.4i	1.25686	−	1.25686i	0.952585	−	0.304271i	$-0.0984130\pi$
$858$		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	$-0.486412\pi$
$863$	−24247.2	−	24247.2i	−0.956413	−	0.956413i	−0.999089	+	0.0426762i	$0.986412\pi$
$864$		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	0.773994	−	0.633193i	$-0.218256\pi$
$877$	3656.81	+	3656.81i	0.140800	+	0.140800i	−0.633193	+	0.773994i	$0.718256\pi$
$878$		0			0
$879$	2876.19	+	1522.64i	0.110366	+	0.0584271i
$880$		0			0
$881$			32635.1i			1.24802i	0.781417	+	0.624009i	$0.214497\pi$
$881$			32635.1i			1.24802i	−0.781417	+	0.624009i	$0.785503\pi$
$882$		0			0
$883$	−8157.06	+	8157.06i	−0.310880	+	0.310880i	−0.845250	−	0.534370i	$-0.820549\pi$
$883$	−8157.06	+	8157.06i	−0.310880	+	0.310880i	0.534370	+	0.845250i	$0.320549\pi$
$884$		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	$-0.544926\pi$
$887$	22438.3	−	22438.3i	0.849384	−	0.849384i	0.990056	+	0.140673i	$0.0449265\pi$
$888$		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	$-0.125541\pi$
$907$	14722.4	+	14722.4i	0.538975	+	0.538975i	−0.384253	+	0.923228i	$0.625541\pi$
$908$		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	0.715043	−	0.699081i	$-0.246407\pi$
$937$	457.817	+	457.817i	0.0159618	+	0.0159618i	−0.699081	+	0.715043i	$0.746407\pi$
$938$		0			0
$939$	8143.24	−	15382.2i	0.283008	−	0.534588i
$940$		0			0
$941$		−	31589.7i		−	1.09436i	−0.837014	−	0.547181i	$-0.815701\pi$
$941$		−	31589.7i		−	1.09436i	0.837014	−	0.547181i	$-0.184299\pi$
$942$		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	$-0.547763\pi$
$947$	24458.4	−	24458.4i	0.839273	−	0.839273i	0.988763	+	0.149490i	$0.0477633\pi$
$948$		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	0.737827	−	0.674990i	$-0.235852\pi$
$953$	1848.64	+	1848.64i	0.0628367	+	0.0628367i	−0.674990	+	0.737827i	$0.735852\pi$
$954$		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	$-0.0723864\pi$
$967$	22516.8	+	22516.8i	0.748800	+	0.748800i	−0.225454	+	0.974254i	$0.572386\pi$
$968$		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	−0.277222	−	0.960806i	$-0.589414\pi$
$977$	20875.3	−	20875.3i	0.683584	−	0.683584i	0.960806	+	0.277222i	$0.0894138\pi$
$978$		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	$-0.301555\pi$
$983$	−7028.60	−	7028.60i	−0.228054	−	0.228054i	−0.811879	+	0.583825i	$0.801555\pi$
$984$		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	$-0.595848\pi$
$991$	−18505.0			−0.593171			−0.296585	+	0.955006i	$0.595848\pi$
$992$		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	0.460008	−	0.887915i	$-0.347847\pi$
$997$	−13470.8	−	13470.8i	−0.427907	−	0.427907i	−0.887915	+	0.460008i	$0.847847\pi$
$998$		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	240.4.v.e.17.17		36
3.2	odd	2	inner	240.4.v.e.17.12		36
4.3	odd	2		120.4.r.a.17.2	✓	36
5.3	odd	4	inner	240.4.v.e.113.12		36
12.11	even	2		120.4.r.a.17.7	yes	36
15.8	even	4	inner	240.4.v.e.113.17		36
20.3	even	4		120.4.r.a.113.7	yes	36
60.23	odd	4		120.4.r.a.113.2	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.4.r.a.17.2	✓	36	4.3	odd	2
120.4.r.a.17.7	yes	36	12.11	even	2
120.4.r.a.113.2	yes	36	60.23	odd	4
120.4.r.a.113.7	yes	36	20.3	even	4
240.4.v.e.17.12		36	3.2	odd	2	inner
240.4.v.e.17.17		36	1.1	even	1	trivial
240.4.v.e.113.12		36	5.3	odd	4	inner
240.4.v.e.113.17		36	15.8	even	4	inner

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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	240.v (of order \(4\), degree \(2\), not 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

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