LMFDB - Embedded newform 240.4.v.e.17.12

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			17.12
Character	$\chi$	$=$	240.17
Dual form			240.4.v.e.113.12

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

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

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
$3$	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	0.417406	−	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	$0.199675\pi$
$11$			42.8278i			1.17392i	−0.809617	+	0.586958i	$0.800325\pi$
$12$		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
$15$	56.9486	+	11.4827i	0.980272	+	0.197654i
$16$		0			0
$17$	3.23965	−	3.23965i	0.0462194	−	0.0462194i	−0.683619	−	0.729839i	$-0.739595\pi$
$17$	3.23965	−	3.23965i	0.0462194	−	0.0462194i	0.729839	+	0.683619i	$0.239595\pi$
$18$		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	0.874065	−	0.485809i	$-0.161475\pi$
$23$	42.8262	+	42.8262i	0.388256	+	0.388256i	−0.485809	+	0.874065i	$0.661475\pi$
$24$		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	0.950084	+	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	$0.134645\pi$
$41$			215.535i			0.820998i	−0.911861	+	0.410499i	$0.865355\pi$
$42$		0			0
$43$	114.525	−	114.525i	0.406160	−	0.406160i	−0.474237	−	0.880397i	$-0.657276\pi$
$43$	114.525	−	114.525i	0.406160	−	0.406160i	0.880397	+	0.474237i	$0.157276\pi$
$44$		0			0
$45$	144.055	−	265.280i	0.477209	−	0.878790i
$46$		0			0
$47$	−384.531	+	384.531i	−1.19340	+	1.19340i	−0.217289	+	0.976107i	$0.569721\pi$
$47$	−384.531	+	384.531i	−1.19340	+	1.19340i	−0.976107	+	0.217289i	$0.930279\pi$
$48$		0			0
$49$		−	177.406i		−	0.517220i
$50$		0			0
$51$	−11.1385	−	21.0400i	−0.0305823	−	0.0577684i
$52$		0			0
$53$	368.409	+	368.409i	0.954809	+	0.954809i	0.999022	−	0.0442129i	$-0.0140780\pi$
$53$	368.409	+	368.409i	0.954809	+	0.954809i	−0.0442129	+	0.999022i	$0.514078\pi$
$54$		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	0.610704	−	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	$-0.811086\pi$
$71$		−	669.159i		−	1.11851i	0.828994	−	0.559257i	$-0.188914\pi$
$72$		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
$75$	−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	$-0.811159\pi$
$79$		−	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	0.00842859	−	0.999964i	$-0.497317\pi$
$83$	−749.766	−	749.766i	−0.991536	−	0.991536i	−0.999964	+	0.00842859i	$0.997317\pi$
$84$		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	0.977107	−	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	$-0.865636\pi$
$101$		−	831.708i		−	0.819386i	0.912223	−	0.409693i	$-0.134364\pi$
$102$		0			0
$103$	507.205	−	507.205i	0.485208	−	0.485208i	−0.421582	−	0.906790i	$-0.638525\pi$
$103$	507.205	−	507.205i	0.485208	−	0.485208i	0.906790	+	0.421582i	$0.138525\pi$
$104$		0			0
$105$	−413.707	−	622.675i	−0.384511	−	0.578732i
$106$		0			0
$107$	191.892	−	191.892i	0.173373	−	0.173373i	−0.615087	−	0.788459i	$-0.710879\pi$
$107$	191.892	−	191.892i	0.173373	−	0.173373i	0.788459	+	0.615087i	$0.210879\pi$
$108$		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	0.0536921	−	0.998558i	$-0.482901\pi$
$113$	−1134.98	−	1134.98i	−0.944865	−	0.944865i	−0.998558	+	0.0536921i	$0.982901\pi$
$114$		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	0.984048	−	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	$0.0114492\pi$
$131$			107.837i			0.0719218i	−0.999353	+	0.0359609i	$0.988551\pi$
$132$		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	−0.953348	−	0.301872i	$-0.902388\pi$
$137$	−1044.67	+	1044.67i	−0.651476	+	0.651476i	0.301872	+	0.953348i	$0.402388\pi$
$138$		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
$147$	−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	0.658306	−	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
$165$	−491.778	+	2438.99i	−0.232030	+	1.15076i
$166$		0			0
$167$	−2049.86	+	2049.86i	−0.949840	+	0.949840i	−0.998801	−	0.0489607i	$-0.984409\pi$
$167$	−2049.86	+	2049.86i	−0.949840	+	0.949840i	0.0489607	+	0.998801i	$0.484409\pi$
$168$		0			0
$169$		−	6462.17i		−	2.94136i
$170$		0			0
$171$	−1025.80	+	1509.02i	−0.458740	+	0.674840i
$172$		0			0
$173$	1009.57	+	1009.57i	0.443677	+	0.443677i	0.893246	−	0.449569i	$-0.148422\pi$
$173$	1009.57	+	1009.57i	0.443677	+	0.443677i	−0.449569	+	0.893246i	$0.648422\pi$
$174$		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	$0.296060\pi$
$191$			4232.34i			1.60336i	−0.597754	+	0.801679i	$0.703940\pi$
$192$		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
$195$	−4502.75	+	2991.64i	−1.65358	+	1.09865i
$196$		0			0
$197$	−375.613	+	375.613i	−0.135844	+	0.135844i	−0.771759	−	0.635915i	$-0.780623\pi$
$197$	−375.613	+	375.613i	−0.135844	+	0.135844i	0.635915	+	0.771759i	$0.280623\pi$
$198$		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
$207$	−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	−0.977703	−	0.209990i	$-0.932657\pi$
$223$	−2556.56	+	2556.56i	−0.767713	+	0.767713i	0.209990	+	0.977703i	$0.432657\pi$
$224$		0			0
$225$	3111.30	+	1307.85i	0.921866	+	0.387510i
$226$		0			0
$227$	4355.96	−	4355.96i	1.27364	−	1.27364i	0.329471	−	0.944166i	$-0.393130\pi$
$227$	4355.96	−	4355.96i	1.27364	−	1.27364i	0.944166	−	0.329471i	$-0.106870\pi$
$228$		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	0.729626	−	0.683847i	$-0.239694\pi$
$233$	162.816	+	162.816i	0.0457787	+	0.0457787i	−0.683847	+	0.729626i	$0.739694\pi$
$234$		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	$0.285001\pi$
$251$			6206.92i			1.56087i	−0.625240	+	0.780433i	$0.714999\pi$
$252$		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	−0.956834	−	0.290633i	$-0.906134\pi$
$257$	−2744.76	+	2744.76i	−0.666201	+	0.666201i	0.290633	+	0.956834i	$0.406134\pi$
$258$		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	0.986836	−	0.161722i	$-0.0517049\pi$
$263$	3519.23	+	3519.23i	0.825114	+	0.825114i	−0.161722	+	0.986836i	$0.551705\pi$
$264$		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	0.892463	−	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	$-0.860647\pi$
$281$		−	3993.85i		−	0.847876i	0.905691	−	0.423938i	$-0.139353\pi$
$282$		0			0
$283$	2889.04	−	2889.04i	0.606839	−	0.606839i	−0.335280	−	0.942119i	$-0.608831\pi$
$283$	2889.04	−	2889.04i	0.606839	−	0.606839i	0.942119	+	0.335280i	$0.108831\pi$
$284$		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	0.661576	−	0.749878i	$-0.269888\pi$
$293$	−442.864	−	442.864i	−0.0883016	−	0.0883016i	−0.749878	+	0.661576i	$0.769888\pi$
$294$		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	0.790623	−	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	$0.199594\pi$
$311$			6436.14i			1.17350i	−0.809767	+	0.586752i	$0.800406\pi$
$312$		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
$315$	−3724.64	+	1103.06i	−0.666222	+	0.197302i
$316$		0			0
$317$	−6204.00	+	6204.00i	−1.09922	+	1.09922i	−0.104713	+	0.994502i	$0.533392\pi$
$317$	−6204.00	+	6204.00i	−1.09922	+	1.09922i	−0.994502	+	0.104713i	$0.966608\pi$
$318$		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	0.893244	−	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
$345$	1947.14	+	2930.66i	0.303856	+	0.457337i
$346$		0			0
$347$	6783.85	−	6783.85i	1.04950	−	1.04950i	0.0507896	−	0.998709i	$-0.483826\pi$
$347$	6783.85	−	6783.85i	1.04950	−	1.04950i	0.998709	−	0.0507896i	$-0.0161738\pi$
$348$		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	$0.0861091\pi$
$353$	8163.42	+	8163.42i	1.23086	+	1.23086i	0.267232	+	0.963632i	$0.413891\pi$
$354$		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	0.792555	−	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
$375$	−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	$0.191990\pi$
$379$			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	0.421107	−	0.907011i	$-0.361642\pi$
$383$	−3642.07	−	3642.07i	−0.485904	−	0.485904i	−0.907011	+	0.421107i	$0.861642\pi$
$384$		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	0.692304	−	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	$-0.814465\pi$
$401$		−	8839.88i		−	1.10085i	0.834883	−	0.550427i	$-0.185535\pi$
$402$		0			0
$403$	6590.78	−	6590.78i	0.814666	−	0.814666i
$404$		0			0
$405$	−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	$-0.902619\pi$
$409$		−	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
$417$	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	$-0.914291\pi$
$431$		−	4760.61i		−	0.532043i	0.963967	−	0.266021i	$-0.0857092\pi$
$432$		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
$435$	−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	$0.104817\pi$
$439$			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	0.896802	−	0.442433i	$-0.145884\pi$
$443$	4236.57	+	4236.57i	0.454369	+	0.454369i	−0.442433	+	0.896802i	$0.645884\pi$
$444$		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	0.999216	−	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	$0.193549\pi$
$461$			11309.0i			1.14254i	−0.820762	+	0.571271i	$0.806451\pi$
$462$		0			0
$463$	5218.15	−	5218.15i	0.523775	−	0.523775i	−0.394934	−	0.918709i	$-0.629233\pi$
$463$	5218.15	−	5218.15i	0.523775	−	0.523775i	0.918709	+	0.394934i	$0.129233\pi$
$464$		0			0
$465$	−5704.23	−	1150.16i	−0.568876	−	0.114704i
$466$		0			0
$467$	873.432	−	873.432i	0.0865473	−	0.0865473i	−0.662508	−	0.749055i	$-0.730508\pi$
$467$	873.432	−	873.432i	0.0865473	−	0.0865473i	0.749055	+	0.662508i	$0.230508\pi$
$468$		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	−0.965846	−	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	$0.0785968\pi$
$491$			5318.45i			0.488836i	−0.969670	+	0.244418i	$0.921403\pi$
$492$		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	$0.0279817\pi$
$499$			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	0.666193	−	0.745780i	$-0.267923\pi$
$503$	−897.828	−	897.828i	−0.0795868	−	0.0795868i	−0.745780	+	0.666193i	$0.767923\pi$
$504$		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	$0.0817999\pi$
$521$			6045.03i			0.508326i	−0.967161	+	0.254163i	$0.918200\pi$
$522$		0			0
$523$	−12299.4	+	12299.4i	−1.02833	+	1.02833i	−0.0287419	+	0.999587i	$0.509150\pi$
$523$	−12299.4	+	12299.4i	−1.02833	+	1.02833i	−0.999587	+	0.0287419i	$0.990850\pi$
$524$		0			0
$525$	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	0.981677	+	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
$555$	12914.4	+	19437.7i	0.987725	+	1.48664i
$556$		0			0
$557$	16945.4	−	16945.4i	1.28905	−	1.28905i	0.353688	−	0.935364i	$-0.384928\pi$
$557$	16945.4	−	16945.4i	1.28905	−	1.28905i	0.935364	−	0.353688i	$-0.115072\pi$
$558$		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	$-0.949664\pi$
$563$	−15295.6	−	15295.6i	−1.14500	−	1.14500i	−0.157476	−	0.987523i	$-0.550336\pi$
$564$		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	0.896645	−	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
$585$	7976.54	+	26934.0i	0.563742	+	1.90356i
$586$		0			0
$587$	−5305.40	+	5305.40i	−0.373045	+	0.373045i	−0.868585	−	0.495540i	$-0.834970\pi$
$587$	−5305.40	+	5305.40i	−0.373045	+	0.373045i	0.495540	+	0.868585i	$0.334970\pi$
$588$		0			0
$589$			6769.13i			0.473544i
$590$		0			0
$591$	1291.42	+	2439.43i	0.0898851	+	0.169788i
$592$		0			0
$593$	−565.381	−	565.381i	−0.0391525	−	0.0391525i	0.687260	−	0.726412i	$-0.258814\pi$
$593$	−565.381	−	565.381i	−0.0391525	−	0.0391525i	−0.726412	+	0.687260i	$0.758814\pi$
$594$		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	0.857236	−	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
$615$	−2474.92	+	12274.4i	−0.162274	+	0.804801i
$616$		0			0
$617$	4575.66	−	4575.66i	0.298556	−	0.298556i	−0.541892	−	0.840448i	$-0.682292\pi$
$617$	4575.66	−	4575.66i	0.298556	−	0.298556i	0.840448	+	0.541892i	$0.182292\pi$
$618$		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
$627$	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	$-0.917427\pi$
$641$		−	8325.71i		−	0.513020i	0.966542	−	0.256510i	$-0.0825726\pi$
$642$		0			0
$643$	9694.41	−	9694.41i	0.594573	−	0.594573i	−0.344291	−	0.938863i	$-0.611881\pi$
$643$	9694.41	−	9694.41i	0.594573	−	0.594573i	0.938863	+	0.344291i	$0.111881\pi$
$644$		0			0
$645$	7837.09	−	5206.98i	0.478426	−	0.317868i
$646$		0			0
$647$	6915.00	−	6915.00i	0.420180	−	0.420180i	−0.465085	−	0.885266i	$-0.653976\pi$
$647$	6915.00	−	6915.00i	0.420180	−	0.420180i	0.885266	+	0.465085i	$0.153976\pi$
$648$		0			0
$649$		−	10452.1i		−	0.632172i
$650$		0			0
$651$	5919.27	−	3133.64i	0.356367	−	0.188659i
$652$		0			0
$653$	−1381.38	−	1381.38i	−0.0827836	−	0.0827836i	0.664502	−	0.747286i	$-0.268644\pi$
$653$	−1381.38	−	1381.38i	−0.0827836	−	0.0827836i	−0.747286	+	0.664502i	$0.768644\pi$
$654$		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	−0.317257	−	0.948340i	$-0.602762\pi$
$673$	11018.2	−	11018.2i	0.631083	−	0.631083i	0.948340	+	0.317257i	$0.102762\pi$
$674$		0			0
$675$	11249.8	−	13453.2i	0.641491	−	0.767130i
$676$		0			0
$677$	3849.05	−	3849.05i	0.218510	−	0.218510i	−0.589360	−	0.807870i	$-0.700620\pi$
$677$	3849.05	−	3849.05i	0.218510	−	0.218510i	0.807870	+	0.589360i	$0.200620\pi$
$678$		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	0.663603	−	0.748085i	$-0.269026\pi$
$683$	−1507.97	−	1507.97i	−0.0844816	−	0.0844816i	−0.748085	+	0.663603i	$0.769026\pi$
$684$		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	$-0.830801\pi$
$701$		−	18815.1i		−	1.01375i	0.862020	−	0.506874i	$-0.169199\pi$
$702$		0			0
$703$	19195.9	−	19195.9i	1.02985	−	1.02985i
$704$		0			0
$705$	−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	$0.177008\pi$
$709$			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
$717$	−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	0.587781	−	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
$735$	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	$0.0143552\pi$
$739$			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	0.796609	−	0.604494i	$-0.206625\pi$
$743$	3890.85	+	3890.85i	0.192115	+	0.192115i	−0.604494	+	0.796609i	$0.706625\pi$
$744$		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	0.880765	−	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	$-0.976136\pi$
$761$		−	3144.76i		−	0.149800i	0.997191	−	0.0748998i	$-0.0238637\pi$
$762$		0			0
$763$	1228.58	−	1228.58i	0.0582932	−	0.0582932i
$764$		0			0
$765$	−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	$0.109150\pi$
$769$			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	$-0.961055\pi$
$773$	−23953.9	−	23953.9i	−1.11457	−	1.11457i	−0.122044	−	0.992525i	$-0.538945\pi$
$774$		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	0.632956	−	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
$795$	16750.1	+	25210.7i	0.747250	+	1.12469i
$796$		0			0
$797$	−8988.82	+	8988.82i	−0.399499	+	0.399499i	−0.878056	−	0.478558i	$-0.841160\pi$
$797$	−8988.82	+	8988.82i	−0.399499	+	0.399499i	0.478558	+	0.878056i	$0.341160\pi$
$798$		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	$0.352528\pi$
$821$			42088.7i			1.78917i	−0.446900	+	0.894584i	$0.647472\pi$
$822$		0			0
$823$	−21012.0	+	21012.0i	−0.889955	+	0.889955i	−0.994518	−	0.104563i	$-0.966656\pi$
$823$	−21012.0	+	21012.0i	−0.889955	+	0.889955i	0.104563	+	0.994518i	$0.466656\pi$
$824$		0			0
$825$	−27680.1	−	2760.98i	−1.16812	−	0.116515i
$826$		0			0
$827$	11663.6	−	11663.6i	0.490428	−	0.490428i	−0.418013	−	0.908441i	$-0.637273\pi$
$827$	11663.6	−	11663.6i	0.490428	−	0.490428i	0.908441	+	0.418013i	$0.137273\pi$
$828$		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
$837$	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	−0.925288	−	0.379265i	$-0.876177\pi$
$853$	−13603.0	+	13603.0i	−0.546023	+	0.546023i	0.379265	+	0.925288i	$0.376177\pi$
$854$		0			0
$855$	−17927.6	−	9735.24i	−0.717090	−	0.389401i
$856$		0			0
$857$	−31532.4	+	31532.4i	−1.25686	+	1.25686i	−0.304271	+	0.952585i	$0.598413\pi$
$857$	−31532.4	+	31532.4i	−1.25686	+	1.25686i	−0.952585	+	0.304271i	$0.901587\pi$
$858$		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	0.999089	−	0.0426762i	$-0.0135884\pi$
$863$	24247.2	+	24247.2i	0.956413	+	0.956413i	−0.0426762	+	0.999089i	$0.513588\pi$
$864$		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	0.773994	−	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	$-0.785503\pi$
$881$		−	32635.1i		−	1.24802i	0.781417	−	0.624009i	$-0.214497\pi$
$882$		0			0
$883$	−8157.06	+	8157.06i	−0.310880	+	0.310880i	−0.845250	−	0.534370i	$-0.820549\pi$
$883$	−8157.06	+	8157.06i	−0.310880	+	0.310880i	0.534370	+	0.845250i	$0.320549\pi$
$884$		0			0
$885$	−13898.2	−	2802.33i	−0.527891	−	0.106440i
$886$		0			0
$887$	−22438.3	+	22438.3i	−0.849384	+	0.849384i	−0.990056	−	0.140673i	$-0.955074\pi$
$887$	−22438.3	+	22438.3i	−0.849384	+	0.849384i	0.140673	+	0.990056i	$0.455074\pi$
$888$		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	0.923228	−	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	$-0.822511\pi$
$911$		−	29099.5i		−	1.05830i	0.848529	−	0.529148i	$-0.177489\pi$
$912$		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	$-0.766650\pi$
$919$		−	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
$927$	−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	0.715043	−	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	$0.184299\pi$
$941$			31589.7i			1.09436i	−0.837014	+	0.547181i	$0.815701\pi$
$942$		0			0
$943$	−9230.55	+	9230.55i	−0.318757	+	0.318757i
$944$		0			0
$945$	−213.749	+	20183.6i	−0.00735794	+	0.694785i
$946$		0			0
$947$	−24458.4	+	24458.4i	−0.839273	+	0.839273i	−0.988763	−	0.149490i	$-0.952237\pi$
$947$	−24458.4	+	24458.4i	−0.839273	+	0.839273i	0.149490	+	0.988763i	$0.452237\pi$
$948$		0			0
$949$			6337.31i			0.216773i
$950$		0			0
$951$	21330.4	+	40292.1i	0.727326	+	1.37388i
$952$		0			0
$953$	−1848.64	−	1848.64i	−0.0628367	−	0.0628367i	0.674990	−	0.737827i	$-0.264148\pi$
$953$	−1848.64	−	1848.64i	−0.0628367	−	0.0628367i	−0.737827	+	0.674990i	$0.764148\pi$
$954$		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	0.974254	−	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	$0.000568127\pi$
$971$			108.007i			0.00356964i	−0.999998	+	0.00178482i	$0.999432\pi$
$972$		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	−0.960806	−	0.277222i	$-0.910586\pi$
$977$	−20875.3	+	20875.3i	−0.683584	+	0.683584i	0.277222	+	0.960806i	$0.410586\pi$
$978$		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	0.811879	−	0.583825i	$-0.198445\pi$
$983$	7028.60	+	7028.60i	0.228054	+	0.228054i	−0.583825	+	0.811879i	$0.698445\pi$
$984$		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	0.460008	−	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.17.12		36
3.2	odd	2	inner	240.4.v.e.17.17		36
4.3	odd	2		120.4.r.a.17.7	yes	36
5.3	odd	4	inner	240.4.v.e.113.17		36
12.11	even	2		120.4.r.a.17.2	✓	36
15.8	even	4	inner	240.4.v.e.113.12		36
20.3	even	4		120.4.r.a.113.2	yes	36
60.23	odd	4		120.4.r.a.113.7	yes	36

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

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