LMFDB - Embedded newform 240.4.v.e.113.12

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			113.12
Character	$\chi$	$=$	240.113
Dual form			240.4.v.e.17.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.52818 + 4.96635i) q^{3} +(1.11114 - 11.1250i) q^{5} +(-9.09927 + 9.09927i) q^{7} +(-22.3293 + 15.1790i) q^{9} +O(q^{10})$	\(q+(1.52818 + 4.96635i) q^{3} +(1.11114 - 11.1250i) q^{5} +(-9.09927 + 9.09927i) q^{7} +(-22.3293 + 15.1790i) q^{9} -42.8278i q^{11} +(-65.7996 - 65.7996i) q^{13} +(56.9486 - 11.4827i) q^{15} +(3.23965 + 3.23965i) q^{17} +67.5802i q^{19} +(-59.0955 - 31.2849i) q^{21} +(42.8262 - 42.8262i) q^{23} +(-122.531 - 24.7228i) q^{25} +(-109.507 - 87.6992i) q^{27} -108.528 q^{29} -100.165 q^{31} +(212.698 - 65.4486i) q^{33} +(91.1188 + 111.340i) q^{35} +(284.046 - 284.046i) q^{37} +(226.230 - 427.338i) q^{39} -215.535i q^{41} +(114.525 + 114.525i) q^{43} +(144.055 + 265.280i) q^{45} +(-384.531 - 384.531i) q^{47} +177.406i q^{49} +(-11.1385 + 21.0400i) q^{51} +(368.409 - 368.409i) q^{53} +(-476.459 - 47.5876i) q^{55} +(-335.627 + 103.275i) q^{57} -244.049 q^{59} -158.686 q^{61} +(65.0633 - 341.298i) q^{63} +(-805.132 + 658.907i) q^{65} +(-99.3488 + 99.3488i) q^{67} +(278.136 + 147.244i) q^{69} +669.159i q^{71} +(48.1561 + 48.1561i) q^{73} +(-64.4669 - 646.312i) q^{75} +(389.702 + 389.702i) q^{77} +785.118i q^{79} +(268.199 - 677.872i) q^{81} +(-749.766 + 749.766i) q^{83} +(39.6407 - 32.4413i) q^{85} +(-165.850 - 538.989i) q^{87} -675.915 q^{89} +1197.46 q^{91} +(-153.069 - 497.452i) q^{93} +(751.828 + 75.0908i) q^{95} +(730.220 - 730.220i) q^{97} +(650.082 + 956.317i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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
$3$	1.52818	+	4.96635i	0.294098	+	0.955775i
$3$	1.52818	+	4.96635i	0.294098	+	0.955775i
$4$		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	−0.908720	−	0.417406i	$-0.862939\pi$
$7$	−9.09927	+	9.09927i	−0.491315	+	0.491315i	0.417406	+	0.908720i	$0.362939\pi$
$8$		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
$15$	56.9486	−	11.4827i	0.980272	−	0.197654i
$16$		0			0
$17$	3.23965	+	3.23965i	0.0462194	+	0.0462194i	0.729839	−	0.683619i	$-0.239595\pi$
$17$	3.23965	+	3.23965i	0.0462194	+	0.0462194i	−0.683619	+	0.729839i	$0.739595\pi$
$18$		0			0
$19$			67.5802i			0.815997i	0.912983	+	0.407999i	$0.133773\pi$
$19$			67.5802i			0.815997i	−0.912983	+	0.407999i	$0.866227\pi$
$20$		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
$27$	−109.507	−	87.6992i	−0.780544	−	0.625101i
$28$		0			0
$29$	−108.528			−0.694937			−0.347469	−	0.937692i	$-0.612959\pi$
$29$	−108.528			−0.694937			−0.347469	+	0.937692i	$0.612959\pi$
$30$		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
$33$	212.698	−	65.4486i	1.12200	−	0.345247i
$34$		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	$-0.865355\pi$
$41$		−	215.535i		−	0.820998i	0.911861	−	0.410499i	$-0.134645\pi$
$42$		0			0
$43$	114.525	+	114.525i	0.406160	+	0.406160i	0.880397	−	0.474237i	$-0.157276\pi$
$43$	114.525	+	114.525i	0.406160	+	0.406160i	−0.474237	+	0.880397i	$0.657276\pi$
$44$		0			0
$45$	144.055	+	265.280i	0.477209	+	0.878790i
$46$		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	−0.0442129	−	0.999022i	$-0.514078\pi$
$53$	368.409	−	368.409i	0.954809	−	0.954809i	0.999022	+	0.0442129i	$0.0140780\pi$
$54$		0			0
$55$	−476.459	−	47.5876i	−1.16810	−	0.116667i
$56$		0			0
$57$	−335.627	+	103.275i	−0.779910	+	0.239983i
$58$		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
$63$	65.0633	−	341.298i	0.130114	−	0.682532i
$64$		0			0
$65$	−805.132	+	658.907i	−1.53637	+	1.25734i
$66$		0			0
$67$	−99.3488	+	99.3488i	−0.181155	+	0.181155i	−0.791859	−	0.610704i	$-0.790887\pi$
$67$	−99.3488	+	99.3488i	−0.181155	+	0.181155i	0.610704	+	0.791859i	$0.290887\pi$
$68$		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
$75$	−64.4669	−	646.312i	−0.0992534	−	0.995062i
$76$		0			0
$77$	389.702	+	389.702i	0.576762	+	0.576762i
$78$		0			0
$79$			785.118i			1.11814i	0.829122	+	0.559068i	$0.188841\pi$
$79$			785.118i			1.11814i	−0.829122	+	0.559068i	$0.811159\pi$
$80$		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
$87$	−165.850	−	538.989i	−0.204380	−	0.664204i
$88$		0			0
$89$	−675.915			−0.805021			−0.402510	−	0.915415i	$-0.631862\pi$
$89$	−675.915			−0.805021			−0.402510	+	0.915415i	$0.631862\pi$
$90$		0			0
$91$	1197.46			1.37942
$92$		0			0
$93$	−153.069	−	497.452i	−0.170673	−	0.554660i
$94$		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	$0.134364\pi$
$101$			831.708i			0.819386i	−0.912223	+	0.409693i	$0.865636\pi$
$102$		0			0
$103$	507.205	+	507.205i	0.485208	+	0.485208i	0.906790	−	0.421582i	$-0.138525\pi$
$103$	507.205	+	507.205i	0.485208	+	0.485208i	−0.421582	+	0.906790i	$0.638525\pi$
$104$		0			0
$105$	−413.707	+	622.675i	−0.384511	+	0.578732i
$106$		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	−0.998558	−	0.0536921i	$-0.982901\pi$
$113$	−1134.98	+	1134.98i	−0.944865	+	0.944865i	0.0536921	+	0.998558i	$0.482901\pi$
$114$		0			0
$115$	−428.856	−	524.027i	−0.347748	−	0.424920i
$116$		0			0
$117$	2468.03	+	470.492i	1.95017	+	0.371770i
$118$		0			0
$119$	−58.9568			−0.0454165
$120$		0			0
$121$	−503.224			−0.378079
$122$		0			0
$123$	1070.42	−	329.376i	0.784689	−	0.241454i
$124$		0			0
$125$	−411.189	+	1335.68i	−0.294223	+	0.955737i
$126$		0			0
$127$	1153.77	−	1153.77i	0.806143	−	0.806143i	−0.177905	−	0.984048i	$-0.556932\pi$
$127$	1153.77	−	1153.77i	0.806143	−	0.806143i	0.984048	+	0.177905i	$0.0569320\pi$
$128$		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
$135$	−1097.33	+	1120.82i	−0.699579	+	0.714555i
$136$		0			0
$137$	−1044.67	−	1044.67i	−0.651476	−	0.651476i	0.301872	−	0.953348i	$-0.402388\pi$
$137$	−1044.67	−	1044.67i	−0.651476	−	0.651476i	−0.953348	+	0.301872i	$0.902388\pi$
$138$		0			0
$139$		−	757.509i		−	0.462238i	−0.972926	−	0.231119i	$-0.925761\pi$
$139$		−	757.509i		−	0.462238i	0.972926	−	0.231119i	$-0.0742386\pi$
$140$		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
$147$	−881.063	+	271.109i	−0.494346	+	0.152113i
$148$		0			0
$149$	2007.45			1.10374			0.551869	−	0.833931i	$-0.313915\pi$
$149$	2007.45			1.10374			0.551869	+	0.833931i	$0.313915\pi$
$150$		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
$153$	−121.514	−	23.1647i	−0.0642078	−	0.0122402i
$154$		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	$-0.893604\pi$
$163$	−2648.59	−	2648.59i	−1.27272	−	1.27272i	−0.328064	−	0.944655i	$-0.606396\pi$
$164$		0			0
$165$	−491.778	−	2438.99i	−0.232030	−	1.15076i
$166$		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	−0.449569	−	0.893246i	$-0.648422\pi$
$173$	1009.57	−	1009.57i	0.443677	−	0.443677i	0.893246	+	0.449569i	$0.148422\pi$
$174$		0			0
$175$	1339.90	−	889.982i	0.578782	−	0.384436i
$176$		0			0
$177$	−372.950	−	1212.03i	−0.158376	−	0.514700i
$178$		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
$183$	−242.500	−	788.090i	−0.0979570	−	0.318346i
$184$		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
$195$	−4502.75	−	2991.64i	−1.65358	−	1.09865i
$196$		0			0
$197$	−375.613	−	375.613i	−0.135844	−	0.135844i	0.635915	−	0.771759i	$-0.280623\pi$
$197$	−375.613	−	375.613i	−0.135844	−	0.135844i	−0.771759	+	0.635915i	$0.780623\pi$
$198$		0			0
$199$			2795.60i			0.995854i	0.867219	+	0.497927i	$0.165905\pi$
$199$			2795.60i			0.995854i	−0.867219	+	0.497927i	$0.834095\pi$
$200$		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
$207$	−306.224	+	1606.34i	−0.102822	+	0.539364i
$208$		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
$213$	−3323.28	+	1022.59i	−1.06905	+	0.328953i
$214$		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	0.209990	−	0.977703i	$-0.432657\pi$
$223$	−2556.56	−	2556.56i	−0.767713	−	0.767713i	−0.977703	+	0.209990i	$0.932657\pi$
$224$		0			0
$225$	3111.30	−	1307.85i	0.921866	−	0.387510i
$226$		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	−0.683847	−	0.729626i	$-0.739694\pi$
$233$	162.816	−	162.816i	0.0457787	−	0.0457787i	0.729626	+	0.683847i	$0.239694\pi$
$234$		0			0
$235$	−4705.17	+	3850.64i	−1.30609	+	1.06888i
$236$		0			0
$237$	−3899.18	+	1199.80i	−1.06869	+	0.328842i
$238$		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
$243$	3776.41	+	296.060i	0.996941	+	0.0781576i
$244$		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
$255$	221.693	+	147.294i	0.0544430	+	0.0361721i
$256$		0			0
$257$	−2744.76	−	2744.76i	−0.666201	−	0.666201i	0.290633	−	0.956834i	$-0.406134\pi$
$257$	−2744.76	−	2744.76i	−0.666201	−	0.666201i	−0.956834	+	0.290633i	$0.906134\pi$
$258$		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
$267$	−1032.92	−	3356.83i	−0.236755	−	0.769419i
$268$		0			0
$269$	4110.94			0.931779			0.465890	−	0.884843i	$-0.345734\pi$
$269$	4110.94			0.931779			0.465890	+	0.884843i	$0.345734\pi$
$270$		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
$273$	1829.93	+	5946.99i	0.405686	+	1.31842i
$274$		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	$0.139353\pi$
$281$			3993.85i			0.847876i	−0.905691	+	0.423938i	$0.860647\pi$
$282$		0			0
$283$	2889.04	+	2889.04i	0.606839	+	0.606839i	0.942119	−	0.335280i	$-0.108831\pi$
$283$	2889.04	+	2889.04i	0.606839	+	0.606839i	−0.335280	+	0.942119i	$0.608831\pi$
$284$		0			0
$285$	776.001	+	3848.60i	0.161285	+	0.799899i
$286$		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	$-0.769888\pi$
$293$	−442.864	+	442.864i	−0.0883016	+	0.0883016i	0.661576	+	0.749878i	$0.269888\pi$
$294$		0			0
$295$	−271.171	+	2715.04i	−0.0535193	+	0.535849i
$296$		0			0
$297$	−3755.97	+	4689.96i	−0.733816	+	0.916293i
$298$		0			0
$299$	−5635.90			−1.09007
$300$		0			0
$301$	−2084.19			−0.399105
$302$		0			0
$303$	−4130.56	+	1271.00i	−0.783149	+	0.240980i
$304$		0			0
$305$	−176.322	+	1765.38i	−0.0331021	+	0.331427i
$306$		0			0
$307$	959.192	−	959.192i	0.178319	−	0.178319i	−0.612304	−	0.790623i	$-0.709757\pi$
$307$	959.192	−	959.192i	0.178319	−	0.178319i	0.790623	+	0.612304i	$0.209757\pi$
$308$		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
$315$	−3724.64	−	1103.06i	−0.666222	−	0.197302i
$316$		0			0
$317$	−6204.00	−	6204.00i	−1.09922	−	1.09922i	−0.994502	−	0.104713i	$-0.966608\pi$
$317$	−6204.00	−	6204.00i	−1.09922	−	1.09922i	−0.104713	−	0.994502i	$-0.533392\pi$
$318$		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
$327$	670.556	−	206.334i	0.113400	−	0.0348940i
$328$		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
$333$	−2031.04	+	10654.1i	−0.334235	+	1.75327i
$334$		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
$345$	1947.14	−	2930.66i	0.303856	−	0.457337i
$346$		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	$-0.413891\pi$
$353$	8163.42	−	8163.42i	1.23086	−	1.23086i	0.963632	−	0.267232i	$-0.0861091\pi$
$354$		0			0
$355$	7444.38	+	743.526i	1.11298	+	0.111161i
$356$		0			0
$357$	−90.0966	−	292.800i	−0.0133569	−	0.0434080i
$358$		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
$363$	−769.016	−	2499.19i	−0.111192	−	0.361359i
$364$		0			0
$365$	589.245	−	482.228i	0.0844999	−	0.0691534i
$366$		0			0
$367$	1284.90	−	1284.90i	0.182756	−	0.182756i	−0.609800	−	0.792555i	$-0.708750\pi$
$367$	1284.90	−	1284.90i	0.182756	−	0.182756i	0.792555	+	0.609800i	$0.208750\pi$
$368$		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
$375$	−7261.84	−	0.946411i	−1.00000	−	0.000130327i
$376$		0			0
$377$	7141.11	+	7141.11i	0.975559	+	0.975559i
$378$		0			0
$379$		−	8370.64i		−	1.13449i	−0.823550	−	0.567244i	$-0.808010\pi$
$379$		−	8370.64i		−	1.13449i	0.823550	−	0.567244i	$-0.191990\pi$
$380$		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
$387$	−4295.63	−	818.897i	−0.564236	−	0.107563i
$388$		0			0
$389$	−11659.2			−1.51965			−0.759827	−	0.650125i	$-0.774717\pi$
$389$	−11659.2			−1.51965			−0.759827	+	0.650125i	$0.774717\pi$
$390$		0			0
$391$	277.484			0.0358899
$392$		0			0
$393$	535.557	−	164.794i	0.0687411	−	0.0211521i
$394$		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	$0.185535\pi$
$401$			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
$405$	−7243.31	−	3736.92i	−0.888699	−	0.458491i
$406$		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
$417$	3762.06	−	1157.61i	0.441795	−	0.135943i
$418$		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
$423$	14423.1	+	2749.55i	1.65786	+	0.316046i
$424$		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
$435$	−6180.53	+	1246.19i	−0.681227	+	0.137357i
$436$		0			0
$437$	2894.20	+	2894.20i	0.316816	+	0.316816i
$438$		0			0
$439$		−	5948.82i		−	0.646747i	−0.946271	−	0.323373i	$-0.895183\pi$
$439$		−	5948.82i		−	0.646747i	0.946271	−	0.323373i	$-0.104817\pi$
$440$		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
$447$	3067.75	+	9969.72i	0.324607	+	1.05492i
$448$		0			0
$449$	3494.32			0.367276			0.183638	−	0.982994i	$-0.441213\pi$
$449$	3494.32			0.367276			0.183638	+	0.982994i	$0.441213\pi$
$450$		0			0
$451$	−9230.90			−0.963783
$452$		0			0
$453$	−2837.56	−	9221.64i	−0.294305	−	0.956447i
$454$		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	$-0.806451\pi$
$461$		−	11309.0i		−	1.14254i	0.820762	−	0.571271i	$-0.193549\pi$
$462$		0			0
$463$	5218.15	+	5218.15i	0.523775	+	0.523775i	0.918709	−	0.394934i	$-0.129233\pi$
$463$	5218.15	+	5218.15i	0.523775	+	0.523775i	−0.394934	+	0.918709i	$0.629233\pi$
$464$		0			0
$465$	−5704.23	+	1150.16i	−0.568876	+	0.114704i
$466$		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
$477$	−2634.27	+	13818.4i	−0.252861	+	1.32642i
$478$		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
$483$	−3870.65	+	1191.02i	−0.364639	+	0.112202i
$484$		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	$0.583432\pi$
$487$	−13164.9	+	13164.9i	−1.22496	+	1.22496i	−0.965846	+	0.259118i	$0.916568\pi$
$488$		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
$495$	11361.3	−	6169.55i	1.03163	−	0.560204i
$496$		0			0
$497$	−6088.86	−	6088.86i	−0.549542	−	0.549542i
$498$		0			0
$499$		−	1957.24i		−	0.175588i	−0.996139	−	0.0877938i	$-0.972018\pi$
$499$		−	1957.24i		−	0.175588i	0.996139	−	0.0877938i	$-0.0279817\pi$
$500$		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
$507$	−32093.4	+	9875.35i	−2.81128	+	0.865049i
$508$		0			0
$509$	−14133.8			−1.23079			−0.615394	−	0.788220i	$-0.711003\pi$
$509$	−14133.8			−1.23079			−0.615394	+	0.788220i	$0.711003\pi$
$510$		0			0
$511$	−876.372			−0.0758677
$512$		0			0
$513$	5926.73	−	7400.52i	0.510081	−	0.636922i
$514$		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	−0.999587	−	0.0287419i	$-0.990850\pi$
$523$	−12299.4	−	12299.4i	−1.02833	−	1.02833i	−0.0287419	−	0.999587i	$-0.509150\pi$
$524$		0			0
$525$	6467.57	+	5294.37i	0.537653	+	0.440124i
$526$		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
$537$	2783.64	+	9046.41i	0.223692	+	0.726967i
$538$		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
$543$	4792.67	+	15575.5i	0.378772	+	1.23095i
$544$		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	$-0.438971\pi$
$547$	14996.7	−	14996.7i	1.17223	−	1.17223i	0.981677	−	0.190555i	$-0.0610286\pi$
$548$		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
$555$	12914.4	−	19437.7i	0.987725	−	1.48664i
$556$		0			0
$557$	16945.4	+	16945.4i	1.28905	+	1.28905i	0.935364	+	0.353688i	$0.115072\pi$
$557$	16945.4	+	16945.4i	1.28905	+	1.28905i	0.353688	+	0.935364i	$0.384928\pi$
$558$		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
$567$	3727.73	+	8608.56i	0.276102	+	0.637611i
$568$		0			0
$569$	8434.10			0.621399			0.310699	−	0.950508i	$-0.399437\pi$
$569$	8434.10			0.621399			0.310699	+	0.950508i	$0.399437\pi$
$570$		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
$573$	21019.3	−	6467.77i	1.53245	−	0.471545i
$574$		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
$585$	7976.54	−	26934.0i	0.563742	−	1.90356i
$586$		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	−0.726412	−	0.687260i	$-0.758814\pi$
$593$	−565.381	+	565.381i	−0.0391525	+	0.0391525i	0.687260	+	0.726412i	$0.258814\pi$
$594$		0			0
$595$	−65.5091	+	655.894i	−0.00451363	+	0.0451917i
$596$		0			0
$597$	−13883.9	+	4272.18i	−0.951812	+	0.292879i
$598$		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
$603$	710.383	−	3726.41i	0.0479751	−	0.251660i
$604$		0			0
$605$	−559.150	+	5598.36i	−0.0375747	+	0.376208i
$606$		0			0
$607$	5119.25	−	5119.25i	0.342313	−	0.342313i	−0.514923	−	0.857236i	$-0.672180\pi$
$607$	5119.25	−	5119.25i	0.342313	−	0.342313i	0.857236	+	0.514923i	$0.172180\pi$
$608$		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
$615$	−2474.92	−	12274.4i	−0.162274	−	0.804801i
$616$		0			0
$617$	4575.66	+	4575.66i	0.298556	+	0.298556i	0.840448	−	0.541892i	$-0.182292\pi$
$617$	4575.66	+	4575.66i	0.298556	+	0.298556i	−0.541892	+	0.840448i	$0.682292\pi$
$618$		0			0
$619$			15541.6i			1.00916i	0.863365	+	0.504579i	$0.168352\pi$
$619$			15541.6i			1.00916i	−0.863365	+	0.504579i	$0.831648\pi$
$620$		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
$627$	4423.03	+	14374.2i	0.281720	+	0.915549i
$628$		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
$633$	6355.19	+	20653.4i	0.399046	+	1.29684i
$634$		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	0.938863	−	0.344291i	$-0.111881\pi$
$643$	9694.41	+	9694.41i	0.594573	+	0.594573i	−0.344291	+	0.938863i	$0.611881\pi$
$644$		0			0
$645$	7837.09	+	5206.98i	0.478426	+	0.317868i
$646$		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	−0.747286	−	0.664502i	$-0.768644\pi$
$653$	−1381.38	+	1381.38i	−0.0827836	+	0.0827836i	0.664502	+	0.747286i	$0.268644\pi$
$654$		0			0
$655$	−1199.69	−	119.822i	−0.0715658	−	0.00714781i
$656$		0			0
$657$	−1806.25	−	344.335i	−0.107258	−	0.0204472i
$658$		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
$663$	2117.33	−	651.515i	0.124027	−	0.0381640i
$664$		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
$675$	11249.8	+	13453.2i	0.641491	+	0.767130i
$676$		0			0
$677$	3849.05	+	3849.05i	0.218510	+	0.218510i	0.807870	−	0.589360i	$-0.200620\pi$
$677$	3849.05	+	3849.05i	0.218510	+	0.218510i	−0.589360	+	0.807870i	$0.700620\pi$
$678$		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
$687$	3022.02	−	929.894i	0.167827	−	0.0516414i
$688$		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
$693$	−14617.1	−	2786.52i	−0.801236	−	0.152743i
$694$		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
$705$	−26314.0	−	17483.1i	−1.40573	−	0.933973i
$706$		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
$717$	−3497.30	−	11365.7i	−0.182161	−	0.591995i
$718$		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
$723$	−351.470	−	1142.22i	−0.0180792	−	0.0587549i
$724$		0			0
$725$	13298.0	+	2683.12i	0.681209	+	0.137446i
$726$		0			0
$727$	−4336.73	+	4336.73i	−0.221239	+	0.221239i	−0.809020	−	0.587781i	$-0.800002\pi$
$727$	−4336.73	+	4336.73i	−0.221239	+	0.221239i	0.587781	+	0.809020i	$0.300002\pi$
$728$		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
$735$	2037.10	+	10103.1i	0.102231	+	0.507016i
$736$		0			0
$737$	4254.90	+	4254.90i	0.212661	+	0.212661i
$738$		0			0
$739$		−	1811.38i		−	0.0901659i	−0.998983	−	0.0450829i	$-0.985645\pi$
$739$		−	1811.38i		−	0.0901659i	0.998983	−	0.0450829i	$-0.0143552\pi$
$740$		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
$747$	5361.11	−	28122.4i	0.262588	−	1.37744i
$748$		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
$753$	30825.8	−	9485.28i	1.49184	−	0.459048i
$754$		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	$0.0238637\pi$
$761$			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
$765$	−392.725	+	1326.10i	−0.0185608	+	0.0626734i
$766$		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	$0.538945\pi$
$773$	−23953.9	+	23953.9i	−1.11457	+	1.11457i	−0.992525	+	0.122044i	$0.961055\pi$
$774$		0			0
$775$	12273.2	+	2476.34i	0.568861	+	0.114778i
$776$		0			0
$777$	−25672.2	+	7899.50i	−1.18531	+	0.364727i
$778$		0			0
$779$	14565.9			0.669932
$780$		0			0
$781$	28658.6			1.31304
$782$		0			0
$783$	11884.6	+	9517.84i	0.542429	+	0.434406i
$784$		0			0
$785$	1860.50	+	2273.38i	0.0845910	+	0.103363i
$786$		0			0
$787$	−3118.12	+	3118.12i	−0.141231	+	0.141231i	−0.774188	−	0.632956i	$-0.781841\pi$
$787$	−3118.12	+	3118.12i	−0.141231	+	0.141231i	0.632956	+	0.774188i	$0.281841\pi$
$788$		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
$795$	16750.1	−	25210.7i	0.747250	−	1.12469i
$796$		0			0
$797$	−8988.82	−	8988.82i	−0.399499	−	0.399499i	0.478558	−	0.878056i	$-0.341160\pi$
$797$	−8988.82	−	8988.82i	−0.399499	−	0.399499i	−0.878056	+	0.478558i	$0.841160\pi$
$798$		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
$807$	6282.25	+	20416.4i	0.274034	+	0.890571i
$808$		0			0
$809$	2250.23			0.0977921			0.0488960	−	0.998804i	$-0.484430\pi$
$809$	2250.23			0.0977921			0.0488960	+	0.998804i	$0.484430\pi$
$810$		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
$813$	−929.612	−	3021.10i	−0.0401020	−	0.130325i
$814$		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	0.104563	−	0.994518i	$-0.466656\pi$
$823$	−21012.0	−	21012.0i	−0.889955	−	0.889955i	−0.994518	+	0.104563i	$0.966656\pi$
$824$		0			0
$825$	−27680.1	+	2760.98i	−1.16812	+	0.116515i
$826$		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
$837$	10968.7	+	8784.35i	0.452969	+	0.362762i
$838$		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
$843$	−19834.9	+	6103.32i	−0.810379	+	0.249359i
$844$		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
$855$	−17927.6	+	9735.24i	−0.717090	+	0.389401i
$856$		0			0
$857$	−31532.4	−	31532.4i	−1.25686	−	1.25686i	−0.952585	−	0.304271i	$-0.901587\pi$
$857$	−31532.4	−	31532.4i	−1.25686	−	1.25686i	−0.304271	−	0.952585i	$-0.598413\pi$
$858$		0			0
$859$		−	36128.6i		−	1.43503i	−0.696543	−	0.717515i	$-0.745279\pi$
$859$		−	36128.6i		−	1.43503i	0.696543	−	0.717515i	$-0.254721\pi$
$860$		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
$867$	24295.4	−	7475.86i	0.951692	−	0.292842i
$868$		0			0
$869$	33624.9			1.31260
$870$		0			0
$871$	13074.2			0.508614
$872$		0			0
$873$	−5221.35	+	27389.3i	−0.202424	+	1.06184i
$874$		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	$0.214497\pi$
$881$			32635.1i			1.24802i	−0.781417	+	0.624009i	$0.785503\pi$
$882$		0			0
$883$	−8157.06	−	8157.06i	−0.310880	−	0.310880i	0.534370	−	0.845250i	$-0.320549\pi$
$883$	−8157.06	−	8157.06i	−0.310880	−	0.310880i	−0.845250	+	0.534370i	$0.820549\pi$
$884$		0			0
$885$	−13898.2	+	2802.33i	−0.527891	+	0.106440i
$886$		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
$897$	−8612.66	−	27989.9i	−0.320589	−	1.04187i
$898$		0			0
$899$	10870.7			0.403289
$900$		0			0
$901$	2387.03			0.0882614
$902$		0			0
$903$	−3185.01	−	10350.8i	−0.117376	−	0.381454i
$904$		0			0
$905$	3484.75	−	34890.2i	0.127997	−	1.28154i
$906$		0			0
$907$	14722.4	−	14722.4i	0.538975	−	0.538975i	−0.384253	−	0.923228i	$-0.625541\pi$
$907$	14722.4	−	14722.4i	0.538975	−	0.538975i	0.923228	+	0.384253i	$0.125541\pi$
$908$		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
$915$	−9036.94	+	1822.14i	−0.326505	+	0.0658339i
$916$		0			0
$917$	981.238	+	981.238i	0.0353362	+	0.0353362i
$918$		0			0
$919$			37285.5i			1.33834i	0.743109	+	0.669170i	$0.233350\pi$
$919$			37285.5i			1.33834i	−0.743109	+	0.669170i	$0.766650\pi$
$920$		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
$927$	−19024.4	−	3626.71i	−0.674049	−	0.128497i
$928$		0			0
$929$	3873.96			0.136814			0.0684072	−	0.997657i	$-0.478208\pi$
$929$	3873.96			0.136814			0.0684072	+	0.997657i	$0.478208\pi$
$930$		0			0
$931$	−11989.2			−0.422050
$932$		0			0
$933$	31964.1	−	9835.57i	1.12161	−	0.345125i
$934$		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	$-0.815701\pi$
$941$		−	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
$945$	−213.749	−	20183.6i	−0.00735794	−	0.694785i
$946$		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	−0.737827	−	0.674990i	$-0.764148\pi$
$953$	−1848.64	+	1848.64i	−0.0628367	+	0.0628367i	0.674990	+	0.737827i	$0.264148\pi$
$954$		0			0
$955$	−47084.8	−	4702.71i	−1.59542	−	0.159347i
$956$		0			0
$957$	−23083.8	+	7103.02i	−0.779720	+	0.239925i
$958$		0			0
$959$	19011.5			0.640160
$960$		0			0
$961$	−19758.1			−0.663223
$962$		0			0
$963$	−7197.53	−	1372.10i	−0.240849	−	0.0459141i
$964$		0			0
$965$	−14878.2	+	12176.1i	−0.496316	+	0.406178i
$966$		0			0
$967$	22516.8	−	22516.8i	0.748800	−	0.748800i	−0.225454	−	0.974254i	$-0.572386\pi$
$967$	22516.8	−	22516.8i	0.748800	−	0.748800i	0.974254	+	0.225454i	$0.0723864\pi$
$968$		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
$975$	−38285.2	+	46768.9i	−1.25754	+	1.53621i
$976$		0			0
$977$	−20875.3	−	20875.3i	−0.683584	−	0.683584i	0.277222	−	0.960806i	$-0.410586\pi$
$977$	−20875.3	−	20875.3i	−0.683584	−	0.683584i	−0.960806	+	0.277222i	$0.910586\pi$
$978$		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
$987$	10694.1	+	34754.1i	0.344879	+	1.12081i
$988$		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
$993$	−15256.1	−	49580.0i	−0.487550	−	1.58446i
$994$		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	240.4.v.e.113.12		36
3.2	odd	2	inner	240.4.v.e.113.17		36
4.3	odd	2		120.4.r.a.113.7	yes	36
5.2	odd	4	inner	240.4.v.e.17.17		36
12.11	even	2		120.4.r.a.113.2	yes	36
15.2	even	4	inner	240.4.v.e.17.12		36
20.7	even	4		120.4.r.a.17.2	✓	36
60.47	odd	4		120.4.r.a.17.7	yes	36

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

\(f(q)\)	\(=\)	\(q+(1.52818 + 4.96635i) q^{3} +(1.11114 - 11.1250i) q^{5} +(-9.09927 + 9.09927i) q^{7} +(-22.3293 + 15.1790i) q^{9} +O(q^{10})\)	\(q+(1.52818 + 4.96635i) q^{3} +(1.11114 - 11.1250i) q^{5} +(-9.09927 + 9.09927i) q^{7} +(-22.3293 + 15.1790i) q^{9} -42.8278i q^{11} +(-65.7996 - 65.7996i) q^{13} +(56.9486 - 11.4827i) q^{15} +(3.23965 + 3.23965i) q^{17} +67.5802i q^{19} +(-59.0955 - 31.2849i) q^{21} +(42.8262 - 42.8262i) q^{23} +(-122.531 - 24.7228i) q^{25} +(-109.507 - 87.6992i) q^{27} -108.528 q^{29} -100.165 q^{31} +(212.698 - 65.4486i) q^{33} +(91.1188 + 111.340i) q^{35} +(284.046 - 284.046i) q^{37} +(226.230 - 427.338i) q^{39} -215.535i q^{41} +(114.525 + 114.525i) q^{43} +(144.055 + 265.280i) q^{45} +(-384.531 - 384.531i) q^{47} +177.406i q^{49} +(-11.1385 + 21.0400i) q^{51} +(368.409 - 368.409i) q^{53} +(-476.459 - 47.5876i) q^{55} +(-335.627 + 103.275i) q^{57} -244.049 q^{59} -158.686 q^{61} +(65.0633 - 341.298i) q^{63} +(-805.132 + 658.907i) q^{65} +(-99.3488 + 99.3488i) q^{67} +(278.136 + 147.244i) q^{69} +669.159i q^{71} +(48.1561 + 48.1561i) q^{73} +(-64.4669 - 646.312i) q^{75} +(389.702 + 389.702i) q^{77} +785.118i q^{79} +(268.199 - 677.872i) q^{81} +(-749.766 + 749.766i) q^{83} +(39.6407 - 32.4413i) q^{85} +(-165.850 - 538.989i) q^{87} -675.915 q^{89} +1197.46 q^{91} +(-153.069 - 497.452i) q^{93} +(751.828 + 75.0908i) q^{95} +(730.220 - 730.220i) q^{97} +(650.082 + 956.317i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 12 q^{7}+O(q^{10}) \) 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

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