LMFDB - Embedded newform 416.4.i.h.289.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [416,4,Mod(289,416)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("416.289"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(416, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	416.i (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [22,0,0,0,10,0,26] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$24.5447945624$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.1
Character	$\chi$	$=$	416.289
Dual form			416.4.i.h.321.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-5.10450 - 8.84125i) q^{3} +2.27672 q^{5} +(12.0705 - 20.9067i) q^{7} +(-38.6118 + 66.8776i) q^{9} +(16.8093 + 29.1146i) q^{11} +(46.6898 + 4.13045i) q^{13} +(-11.6215 - 20.1290i) q^{15} +(-47.5050 + 82.2810i) q^{17} +(-47.5062 + 82.2831i) q^{19} -246.455 q^{21} +(65.7077 + 113.809i) q^{23} -119.817 q^{25} +512.732 q^{27} +(134.898 + 233.651i) q^{29} -165.370 q^{31} +(171.606 - 297.231i) q^{33} +(27.4810 - 47.5985i) q^{35} +(7.07469 + 12.2537i) q^{37} +(-201.810 - 433.880i) q^{39} +(-46.5925 - 80.7006i) q^{41} +(-55.3880 + 95.9349i) q^{43} +(-87.9081 + 152.261i) q^{45} -133.152 q^{47} +(-119.892 - 207.660i) q^{49} +969.956 q^{51} +235.653 q^{53} +(38.2700 + 66.2857i) q^{55} +969.980 q^{57} +(307.515 - 532.631i) q^{59} +(-145.173 + 251.447i) q^{61} +(932.125 + 1614.49i) q^{63} +(106.299 + 9.40386i) q^{65} +(201.856 + 349.625i) q^{67} +(670.809 - 1161.88i) q^{69} +(68.6883 - 118.972i) q^{71} -387.353 q^{73} +(611.603 + 1059.33i) q^{75} +811.585 q^{77} -608.582 q^{79} +(-1574.72 - 2727.50i) q^{81} -436.570 q^{83} +(-108.155 + 187.331i) q^{85} +(1377.18 - 2385.34i) q^{87} +(428.464 + 742.121i) q^{89} +(649.922 - 926.272i) q^{91} +(844.132 + 1462.08i) q^{93} +(-108.158 + 187.335i) q^{95} +(-232.079 + 401.972i) q^{97} -2596.15 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 10 q^{5} + 26 q^{7} - 117 q^{9} + 22 q^{11} + 37 q^{13} + 86 q^{15} - 109 q^{17} + 140 q^{19} + 20 q^{21} + 292 q^{23} + 812 q^{25} - 60 q^{27} + 101 q^{29} - 988 q^{31} - 226 q^{33} + 216 q^{35}+ \cdots - 8040 q^{99}+O(q^{100}) $ 22 * q + 10 * q^5 + 26 * q^7 - 117 * q^9 + 22 * q^11 + 37 * q^13 + 86 * q^15 - 109 * q^17 + 140 * q^19 + 20 * q^21 + 292 * q^23 + 812 * q^25 - 60 * q^27 + 101 * q^29 - 988 * q^31 - 226 * q^33 + 216 * q^35 - 223 * q^37 + 452 * q^39 - 117 * q^41 - 110 * q^43 - 453 * q^45 - 2300 * q^47 - 989 * q^49 + 2184 * q^51 + 98 * q^53 - 92 * q^55 - 100 * q^57 + 710 * q^59 + 281 * q^61 + 2008 * q^63 + 1785 * q^65 + 492 * q^67 + 358 * q^69 - 928 * q^71 - 906 * q^73 + 422 * q^75 - 780 * q^77 + 2936 * q^79 - 2971 * q^81 - 520 * q^83 + 1385 * q^85 + 4012 * q^87 + 1088 * q^89 - 662 * q^91 + 1180 * q^93 - 2742 * q^95 - 640 * q^97 - 8040 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−5.10450	−	8.84125i	−0.982361	−	1.70150i	−0.653122	−	0.757253i	$-0.726541\pi$
$3$	−5.10450	−	8.84125i	−0.982361	−	1.70150i	−0.329239	−	0.944247i	$-0.606792\pi$
$4$		0			0
$5$	2.27672			0.203636			0.101818	−	0.994803i	$-0.467534\pi$
$5$	2.27672			0.203636			0.101818	+	0.994803i	$0.467534\pi$
$6$		0			0
$7$	12.0705	−	20.9067i	0.651744	−	1.12885i	−0.330955	−	0.943646i	$-0.607371\pi$
$7$	12.0705	−	20.9067i	0.651744	−	1.12885i	0.982699	−	0.185208i	$-0.0592957\pi$
$8$		0			0
$9$	−38.6118	+	66.8776i	−1.43007	+	2.47695i
$10$		0			0
$11$	16.8093	+	29.1146i	0.460745	+	0.798034i	0.998998	−	0.0447489i	$-0.0142488\pi$
$11$	16.8093	+	29.1146i	0.460745	+	0.798034i	−0.538253	+	0.842783i	$0.680915\pi$
$12$		0			0
$13$	46.6898	+	4.13045i	0.996110	+	0.0881216i
$13$	46.6898	+	4.13045i	0.996110	+	0.0881216i
$14$		0			0
$15$	−11.6215	−	20.1290i	−0.200044	−	0.346486i
$16$		0			0
$17$	−47.5050	+	82.2810i	−0.677744	+	1.17389i	0.297915	+	0.954593i	$0.403709\pi$
$17$	−47.5050	+	82.2810i	−0.677744	+	1.17389i	−0.975659	+	0.219295i	$0.929624\pi$
$18$		0			0
$19$	−47.5062	+	82.2831i	−0.573614	+	0.993528i	0.422577	+	0.906327i	$0.361126\pi$
$19$	−47.5062	+	82.2831i	−0.573614	+	0.993528i	−0.996191	+	0.0872010i	$0.972208\pi$
$20$		0			0
$21$	−246.455			−2.56099
$22$		0			0
$23$	65.7077	+	113.809i	0.595695	+	1.03177i	0.993448	+	0.114282i	$0.0364568\pi$
$23$	65.7077	+	113.809i	0.595695	+	1.03177i	−0.397753	+	0.917493i	$0.630210\pi$
$24$		0			0
$25$	−119.817			−0.958533
$26$		0			0
$27$	512.732			3.65464
$28$		0			0
$29$	134.898	+	233.651i	0.863793	+	1.49613i	0.868241	+	0.496143i	$0.165251\pi$
$29$	134.898	+	233.651i	0.863793	+	1.49613i	−0.00444782	+	0.999990i	$0.501416\pi$
$30$		0			0
$31$	−165.370			−0.958109			−0.479055	−	0.877785i	$-0.659020\pi$
$31$	−165.370			−0.958109			−0.479055	+	0.877785i	$0.659020\pi$
$32$		0			0
$33$	171.606	−	297.231i	0.905237	−	1.56792i
$34$		0			0
$35$	27.4810	−	47.5985i	0.132718	−	0.229875i
$36$		0			0
$37$	7.07469	+	12.2537i	0.0314344	+	0.0544459i	0.881315	−	0.472530i	$-0.156659\pi$
$37$	7.07469	+	12.2537i	0.0314344	+	0.0544459i	−0.849880	+	0.526976i	$0.823326\pi$
$38$		0			0
$39$	−201.810	−	433.880i	−0.828601	−	1.78145i
$40$		0			0
$41$	−46.5925	−	80.7006i	−0.177476	−	0.307398i	0.763539	−	0.645762i	$-0.223460\pi$
$41$	−46.5925	−	80.7006i	−0.177476	−	0.307398i	−0.941015	+	0.338363i	$0.890127\pi$
$42$		0			0
$43$	−55.3880	+	95.9349i	−0.196432	+	0.340231i	−0.947369	−	0.320143i	$-0.896269\pi$
$43$	−55.3880	+	95.9349i	−0.196432	+	0.340231i	0.750937	+	0.660374i	$0.229602\pi$
$44$		0			0
$45$	−87.9081	+	152.261i	−0.291213	+	0.504395i
$46$		0			0
$47$	−133.152			−0.413240			−0.206620	−	0.978421i	$-0.566246\pi$
$47$	−133.152			−0.413240			−0.206620	+	0.978421i	$0.566246\pi$
$48$		0			0
$49$	−119.892	−	207.660i	−0.349541	−	0.605422i
$50$		0			0
$51$	969.956			2.66316
$52$		0			0
$53$	235.653			0.610745			0.305372	−	0.952233i	$-0.401219\pi$
$53$	235.653			0.610745			0.305372	+	0.952233i	$0.401219\pi$
$54$		0			0
$55$	38.2700	+	66.2857i	0.0938242	+	0.162508i
$56$		0			0
$57$	969.980			2.25398
$58$		0			0
$59$	307.515	−	532.631i	0.678560	−	1.17530i	−0.296855	−	0.954923i	$-0.595938\pi$
$59$	307.515	−	532.631i	0.678560	−	1.17530i	0.975415	−	0.220377i	$-0.0707288\pi$
$60$		0			0
$61$	−145.173	+	251.447i	−0.304713	+	0.527779i	−0.977197	−	0.212332i	$-0.931894\pi$
$61$	−145.173	+	251.447i	−0.304713	+	0.527779i	0.672484	+	0.740112i	$0.265227\pi$
$62$		0			0
$63$	932.125	+	1614.49i	1.86407	+	3.22867i
$64$		0			0
$65$	106.299	+	9.40386i	0.202843	+	0.0179447i
$66$		0			0
$67$	201.856	+	349.625i	0.368070	+	0.637515i	0.989264	−	0.146142i	$-0.0466855\pi$
$67$	201.856	+	349.625i	0.368070	+	0.637515i	−0.621194	+	0.783657i	$0.713352\pi$
$68$		0			0
$69$	670.809	−	1161.88i	1.17038	−	2.02715i
$70$		0			0
$71$	68.6883	−	118.972i	0.114814	−	0.198864i	−0.802891	−	0.596125i	$-0.796706\pi$
$71$	68.6883	−	118.972i	0.114814	−	0.198864i	0.917705	+	0.397262i	$0.130039\pi$
$72$		0			0
$73$	−387.353			−0.621044			−0.310522	−	0.950566i	$-0.600504\pi$
$73$	−387.353			−0.621044			−0.310522	+	0.950566i	$0.600504\pi$
$74$		0			0
$75$	611.603	+	1059.33i	0.941625	+	1.63094i
$76$		0			0
$77$	811.585			1.20115
$78$		0			0
$79$	−608.582			−0.866719			−0.433359	−	0.901221i	$-0.642672\pi$
$79$	−608.582			−0.866719			−0.433359	+	0.901221i	$0.642672\pi$
$80$		0			0
$81$	−1574.72	−	2727.50i	−2.16011	−	3.74143i
$82$		0			0
$83$	−436.570			−0.577346			−0.288673	−	0.957428i	$-0.593214\pi$
$83$	−436.570			−0.577346			−0.288673	+	0.957428i	$0.593214\pi$
$84$		0			0
$85$	−108.155	+	187.331i	−0.138013	+	0.239045i
$86$		0			0
$87$	1377.18	−	2385.34i	1.69711	−	2.93949i
$88$		0			0
$89$	428.464	+	742.121i	0.510304	+	0.883872i	0.999929	+	0.0119390i	$0.00380039\pi$
$89$	428.464	+	742.121i	0.510304	+	0.883872i	−0.489625	+	0.871933i	$0.662866\pi$
$90$		0			0
$91$	649.922	−	926.272i	0.748685	−	1.06703i
$92$		0			0
$93$	844.132	+	1462.08i	0.941209	+	1.63022i
$94$		0			0
$95$	−108.158	+	187.335i	−0.116808	+	0.202318i
$96$		0			0
$97$	−232.079	+	401.972i	−0.242928	+	0.420764i	−0.961547	−	0.274640i	$-0.911441\pi$
$97$	−232.079	+	401.972i	−0.242928	+	0.420764i	0.718619	+	0.695404i	$0.244775\pi$
$98$		0			0
$99$	−2596.15			−2.63559
$100$		0			0
$101$	42.6225	+	73.8243i	0.0419910	+	0.0727306i	0.886257	−	0.463194i	$-0.153297\pi$
$101$	42.6225	+	73.8243i	0.0419910	+	0.0727306i	−0.844266	+	0.535924i	$0.819963\pi$
$102$		0			0
$103$	959.374			0.917766			0.458883	−	0.888497i	$-0.348250\pi$
$103$	959.374			0.917766			0.458883	+	0.888497i	$0.348250\pi$
$104$		0			0
$105$	−561.108			−0.521509
$106$		0			0
$107$	−296.956	−	514.343i	−0.268297	−	0.464704i	0.700125	−	0.714020i	$-0.253128\pi$
$107$	−296.956	−	514.343i	−0.268297	−	0.464704i	−0.968422	+	0.249316i	$0.919794\pi$
$108$		0			0
$109$	−1284.37			−1.12863			−0.564313	−	0.825561i	$-0.690859\pi$
$109$	−1284.37			−1.12863			−0.564313	+	0.825561i	$0.690859\pi$
$110$		0			0
$111$	72.2255	−	125.098i	0.0617598	−	0.106971i
$112$		0			0
$113$	−910.240	+	1576.58i	−0.757772	+	1.31250i	0.186213	+	0.982509i	$0.440379\pi$
$113$	−910.240	+	1576.58i	−0.757772	+	1.31250i	−0.943985	+	0.329990i	$0.892955\pi$
$114$		0			0
$115$	149.598	+	259.111i	0.121305	+	0.210106i
$116$		0			0
$117$	−2079.01	+	2963.02i	−1.64278	+	2.34129i
$118$		0			0
$119$	1146.81	+	1986.34i	0.883431	+	1.53015i
$120$		0			0
$121$	100.394	−	173.887i	0.0754273	−	0.130644i
$122$		0			0
$123$	−475.663	+	823.872i	−0.348692	+	0.603952i
$124$		0			0
$125$	−557.378			−0.398827
$126$		0			0
$127$	87.3688	+	151.327i	0.0610451	+	0.105733i	0.894933	−	0.446201i	$-0.147223\pi$
$127$	87.3688	+	151.327i	0.0610451	+	0.105733i	−0.833888	+	0.551934i	$0.813890\pi$
$128$		0			0
$129$	1130.91			0.771870
$130$		0			0
$131$	−1822.67			−1.21563			−0.607814	−	0.794079i	$-0.707953\pi$
$131$	−1822.67			−1.21563			−0.607814	+	0.794079i	$0.707953\pi$
$132$		0			0
$133$	1146.84	+	1986.39i	0.747699	+	1.29505i
$134$		0			0
$135$	1167.35			0.744216
$136$		0			0
$137$	567.436	−	982.829i	0.353864	−	0.612910i	−0.633059	−	0.774104i	$-0.718201\pi$
$137$	567.436	−	982.829i	0.353864	−	0.612910i	0.986923	+	0.161193i	$0.0515343\pi$
$138$		0			0
$139$	637.791	−	1104.69i	0.389185	−	0.674089i	−0.603155	−	0.797624i	$-0.706090\pi$
$139$	637.791	−	1104.69i	0.389185	−	0.674089i	0.992340	+	0.123535i	$0.0394233\pi$
$140$		0			0
$141$	679.676	+	1177.23i	0.405951	+	0.703127i
$142$		0			0
$143$	664.568	+	1428.79i	0.388629	+	0.835532i
$144$		0			0
$145$	307.125	+	531.957i	0.175899	+	0.304666i
$146$		0			0
$147$	−1223.98	+	2120.00i	−0.686751	+	1.18949i
$148$		0			0
$149$	−788.778	+	1366.20i	−0.433686	+	0.751166i	−0.997187	−	0.0749488i	$-0.976121\pi$
$149$	−788.778	+	1366.20i	−0.433686	+	0.751166i	0.563501	+	0.826115i	$0.309454\pi$
$150$		0			0
$151$	−2417.13			−1.30267			−0.651336	−	0.758789i	$-0.725791\pi$
$151$	−2417.13			−1.30267			−0.651336	+	0.758789i	$0.725791\pi$
$152$		0			0
$153$	−3668.50	−	6354.04i	−1.93844	−	3.35747i
$154$		0			0
$155$	−376.501			−0.195105
$156$		0			0
$157$	−1121.21			−0.569951			−0.284976	−	0.958535i	$-0.591986\pi$
$157$	−1121.21			−0.569951			−0.284976	+	0.958535i	$0.591986\pi$
$158$		0			0
$159$	−1202.89	−	2083.47i	−0.599972	−	1.03918i
$160$		0			0
$161$	3172.49			1.55296
$162$		0			0
$163$	−37.6930	+	65.2862i	−0.0181125	+	0.0313718i	−0.874940	−	0.484232i	$-0.839099\pi$
$163$	−37.6930	+	65.2862i	−0.0181125	+	0.0313718i	0.856827	+	0.515604i	$0.172432\pi$
$164$		0			0
$165$	390.699	−	676.710i	0.184339	−	0.319284i
$166$		0			0
$167$	−1731.03	−	2998.24i	−0.802104	−	1.38929i	−0.918229	−	0.396050i	$-0.870381\pi$
$167$	−1731.03	−	2998.24i	−0.802104	−	1.38929i	0.116125	−	0.993235i	$-0.462953\pi$
$168$		0			0
$169$	2162.88	+	385.700i	0.984469	+	0.175557i
$170$		0			0
$171$	−3668.60	−	6354.19i	−1.64061	−	2.84162i
$172$		0			0
$173$	−103.360	+	179.025i	−0.0454237	+	0.0786762i	−0.887843	−	0.460146i	$-0.847797\pi$
$173$	−103.360	+	179.025i	−0.0454237	+	0.0786762i	0.842420	+	0.538822i	$0.181130\pi$
$174$		0			0
$175$	−1446.24	+	2504.97i	−0.624718	+	1.08204i
$176$		0			0
$177$	−6278.83			−2.66636
$178$		0			0
$179$	−176.705	−	306.062i	−0.0737851	−	0.127800i	0.826772	−	0.562537i	$-0.190175\pi$
$179$	−176.705	−	306.062i	−0.0737851	−	0.127800i	−0.900557	+	0.434737i	$0.856841\pi$
$180$		0			0
$181$	3145.99			1.29193			0.645965	−	0.763367i	$-0.276455\pi$
$181$	3145.99			1.29193			0.645965	+	0.763367i	$0.276455\pi$
$182$		0			0
$183$	2964.14			1.19735
$184$		0			0
$185$	16.1071	+	27.8983i	0.00640116	+	0.0110871i
$186$		0			0
$187$	−3194.10			−1.24907
$188$		0			0
$189$	6188.92	−	10719.5i	2.38189	−	4.12556i
$190$		0			0
$191$	−294.787	+	510.587i	−0.111676	+	0.193428i	−0.916446	−	0.400158i	$-0.868955\pi$
$191$	−294.787	+	510.587i	−0.111676	+	0.193428i	0.804770	+	0.593586i	$0.202288\pi$
$192$		0			0
$193$	2498.21	+	4327.03i	0.931738	+	1.61382i	0.780350	+	0.625343i	$0.215041\pi$
$193$	2498.21	+	4327.03i	0.931738	+	1.61382i	0.151387	+	0.988475i	$0.451626\pi$
$194$		0			0
$195$	−459.464	−	987.822i	−0.168733	−	0.362766i
$196$		0			0
$197$	−171.510	−	297.064i	−0.0620284	−	0.107436i	0.833344	−	0.552755i	$-0.186424\pi$
$197$	−171.510	−	297.064i	−0.0620284	−	0.107436i	−0.895372	+	0.445319i	$0.853090\pi$
$198$		0			0
$199$	−506.061	+	876.523i	−0.180270	+	0.312237i	−0.941972	−	0.335690i	$-0.891030\pi$
$199$	−506.061	+	876.523i	−0.180270	+	0.312237i	0.761703	+	0.647927i	$0.224364\pi$
$200$		0			0
$201$	2060.75	−	3569.32i	0.723154	−	1.25254i
$202$		0			0
$203$	6513.15			2.25189
$204$		0			0
$205$	−106.078	−	183.732i	−0.0361405	−	0.0625972i
$206$		0			0
$207$	−10148.4			−3.40754
$208$		0			0
$209$	−3194.18			−1.05716
$210$		0			0
$211$	2377.47	+	4117.90i	0.775696	+	1.34354i	0.934403	+	0.356218i	$0.115934\pi$
$211$	2377.47	+	4117.90i	0.775696	+	1.34354i	−0.158707	+	0.987326i	$0.550733\pi$
$212$		0			0
$213$	−1402.48			−0.451155
$214$		0			0
$215$	−126.103	+	218.416i	−0.0400006	+	0.0692832i
$216$		0			0
$217$	−1996.10	+	3457.34i	−0.624442	+	1.08157i
$218$		0			0
$219$	1977.24	+	3424.68i	0.610090	+	1.05671i
$220$		0			0
$221$	−2557.86	+	3645.47i	−0.778552	+	1.10960i
$222$		0			0
$223$	126.436	+	218.993i	0.0379676	+	0.0657617i	0.884385	−	0.466759i	$-0.154578\pi$
$223$	126.436	+	218.993i	0.0379676	+	0.0657617i	−0.846417	+	0.532520i	$0.821245\pi$
$224$		0			0
$225$	4626.33	−	8013.04i	1.37077	−	2.37423i
$226$		0			0
$227$	2116.97	−	3666.71i	0.618980	−	1.07211i	−0.370692	−	0.928756i	$-0.620879\pi$
$227$	2116.97	−	3666.71i	0.618980	−	1.07211i	0.989672	−	0.143349i	$-0.0457872\pi$
$228$		0			0
$229$	6420.73			1.85281			0.926406	−	0.376527i	$-0.122882\pi$
$229$	6420.73			1.85281			0.926406	+	0.376527i	$0.122882\pi$
$230$		0			0
$231$	−4142.74	−	7175.43i	−1.17997	−	2.04376i
$232$		0			0
$233$	2582.41			0.726092			0.363046	−	0.931771i	$-0.381737\pi$
$233$	2582.41			0.726092			0.363046	+	0.931771i	$0.381737\pi$
$234$		0			0
$235$	−303.150			−0.0841504
$236$		0			0
$237$	3106.50	+	5380.62i	0.851431	+	1.47472i
$238$		0			0
$239$	−1397.21			−0.378149			−0.189075	−	0.981963i	$-0.560549\pi$
$239$	−1397.21			−0.378149			−0.189075	+	0.981963i	$0.560549\pi$
$240$		0			0
$241$	582.050	−	1008.14i	0.155573	−	0.269461i	−0.777694	−	0.628642i	$-0.783611\pi$
$241$	582.050	−	1008.14i	0.155573	−	0.269461i	0.933268	+	0.359182i	$0.116944\pi$
$242$		0			0
$243$	−9154.45	+	15856.0i	−2.41670	+	4.18585i
$244$		0			0
$245$	−272.961	−	472.783i	−0.0711790	−	0.123286i
$246$		0			0
$247$	−2557.92	+	3645.56i	−0.658933	+	0.939115i
$248$		0			0
$249$	2228.47	+	3859.82i	0.567162	+	0.982354i
$250$		0			0
$251$	3427.19	−	5936.06i	0.861841	−	1.49275i	−0.00830936	−	0.999965i	$-0.502645\pi$
$251$	3427.19	−	5936.06i	0.861841	−	1.49275i	0.870150	−	0.492787i	$-0.164022\pi$
$252$		0			0
$253$	−2209.00	+	3826.10i	−0.548928	+	0.950771i
$254$		0			0
$255$	2208.31			0.542314
$256$		0			0
$257$	1545.34	+	2676.62i	0.375082	+	0.649660i	0.990339	−	0.138666i	$-0.0442814\pi$
$257$	1545.34	+	2676.62i	0.375082	+	0.649660i	−0.615258	+	0.788326i	$0.710948\pi$
$258$		0			0
$259$	341.579			0.0819487
$260$		0			0
$261$	−20834.7			−4.94113
$262$		0			0
$263$	3357.89	+	5816.04i	0.787287	+	1.36362i	0.927623	+	0.373518i	$0.121848\pi$
$263$	3357.89	+	5816.04i	0.787287	+	1.36362i	−0.140336	+	0.990104i	$0.544818\pi$
$264$		0			0
$265$	536.516			0.124369
$266$		0			0
$267$	4374.18	−	7576.31i	1.00261	−	1.73656i
$268$		0			0
$269$	549.501	−	951.764i	0.124549	−	0.215725i	−0.797008	−	0.603969i	$-0.793585\pi$
$269$	549.501	−	951.764i	0.124549	−	0.215725i	0.921557	+	0.388244i	$0.126918\pi$
$270$		0			0
$271$	−2300.73	−	3984.98i	−0.515717	−	0.893248i	−0.999834	−	0.0182445i	$-0.994192\pi$
$271$	−2300.73	−	3984.98i	−0.515717	−	0.893248i	0.484117	−	0.875004i	$-0.339141\pi$
$272$		0			0
$273$	−11506.9	−	1017.97i	−2.55103	−	0.225679i
$274$		0			0
$275$	−2014.03	−	3488.41i	−0.441639	−	0.764942i
$276$		0			0
$277$	2790.07	−	4832.54i	0.605195	−	1.04823i	−0.386825	−	0.922153i	$-0.626428\pi$
$277$	2790.07	−	4832.54i	0.605195	−	1.04823i	0.992021	−	0.126076i	$-0.0402383\pi$
$278$		0			0
$279$	6385.24	−	11059.6i	1.37016	−	2.37319i
$280$		0			0
$281$	258.903			0.0549639			0.0274820	−	0.999622i	$-0.491251\pi$
$281$	258.903			0.0549639			0.0274820	+	0.999622i	$0.491251\pi$
$282$		0			0
$283$	−1366.08	−	2366.12i	−0.286943	−	0.497000i	0.686135	−	0.727474i	$-0.259306\pi$
$283$	−1366.08	−	2366.12i	−0.286943	−	0.497000i	−0.973079	+	0.230474i	$0.925972\pi$
$284$		0			0
$285$	2208.37			0.458991
$286$		0			0
$287$	−2249.58			−0.462677
$288$		0			0
$289$	−2056.95	−	3562.73i	−0.418674	−	0.725165i
$290$		0			0
$291$	4738.58			0.954572
$292$		0			0
$293$	−3304.11	+	5722.89i	−0.658799	+	1.14107i	0.322128	+	0.946696i	$0.395602\pi$
$293$	−3304.11	+	5722.89i	−0.658799	+	1.14107i	−0.980927	+	0.194377i	$0.937731\pi$
$294$		0			0
$295$	700.124	−	1212.65i	0.138179	−	0.239333i
$296$		0			0
$297$	8618.68	+	14928.0i	1.68386	+	2.91653i
$298$		0			0
$299$	2597.80	+	5585.12i	0.502456	+	1.08025i
$300$		0			0
$301$	1337.12	+	2315.96i	0.256047	+	0.443487i
$302$		0			0
$303$	435.132	−	753.671i	0.0825007	−	0.142895i
$304$		0			0
$305$	−330.518	+	572.474i	−0.0620505	+	0.107475i
$306$		0			0
$307$	2674.08			0.497127			0.248564	−	0.968616i	$-0.420042\pi$
$307$	2674.08			0.497127			0.248564	+	0.968616i	$0.420042\pi$
$308$		0			0
$309$	−4897.12	−	8482.06i	−0.901578	−	1.56158i
$310$		0			0
$311$	−3325.59			−0.606357			−0.303179	−	0.952934i	$-0.598048\pi$
$311$	−3325.59			−0.606357			−0.303179	+	0.952934i	$0.598048\pi$
$312$		0			0
$313$	−3156.36			−0.569994			−0.284997	−	0.958528i	$-0.591993\pi$
$313$	−3156.36			−0.569994			−0.284997	+	0.958528i	$0.591993\pi$
$314$		0			0
$315$	2122.18	+	3675.73i	0.379592	+	0.657473i
$316$		0			0
$317$	7253.57			1.28518			0.642589	−	0.766211i	$-0.277860\pi$
$317$	7253.57			1.28518			0.642589	+	0.766211i	$0.277860\pi$
$318$		0			0
$319$	−4535.10	+	7855.02i	−0.795977	+	1.37867i
$320$		0			0
$321$	−3031.62	+	5250.92i	−0.527129	+	0.913015i
$322$		0			0
$323$	−4513.56	−	7817.71i	−0.777526	−	1.34672i
$324$		0			0
$325$	−5594.21	−	494.896i	−0.954804	−	0.0844674i
$326$		0			0
$327$	6556.06	+	11355.4i	1.10872	+	1.92036i
$328$		0			0
$329$	−1607.21	+	2783.77i	−0.269327	+	0.466488i
$330$		0			0
$331$	−5793.88	+	10035.3i	−0.962116	+	1.66643i	−0.244944	+	0.969537i	$0.578770\pi$
$331$	−5793.88	+	10035.3i	−0.962116	+	1.66643i	−0.717172	+	0.696896i	$0.754564\pi$
$332$		0			0
$333$	−1092.67			−0.179813
$334$		0			0
$335$	459.569	+	795.997i	0.0749521	+	0.129821i
$336$		0			0
$337$	−3901.81			−0.630698			−0.315349	−	0.948976i	$-0.602122\pi$
$337$	−3901.81			−0.630698			−0.315349	+	0.948976i	$0.602122\pi$
$338$		0			0
$339$	18585.3			2.97762
$340$		0			0
$341$	−2779.76	−	4814.69i	−0.441444	−	0.764604i
$342$		0			0
$343$	2491.71			0.392244
$344$		0			0
$345$	1527.24	−	2645.26i	0.238330	−	0.412800i
$346$		0			0
$347$	−486.340	+	842.366i	−0.0752395	+	0.130319i	−0.901190	−	0.433423i	$-0.857305\pi$
$347$	−486.340	+	842.366i	−0.0752395	+	0.130319i	0.825951	+	0.563742i	$0.190639\pi$
$348$		0			0
$349$	5175.73	+	8964.62i	0.793840	+	1.37497i	0.923573	+	0.383423i	$0.125255\pi$
$349$	5175.73	+	8964.62i	0.793840	+	1.37497i	−0.129733	+	0.991549i	$0.541412\pi$
$350$		0			0
$351$	23939.4	+	2117.81i	3.64043	+	0.322053i
$352$		0			0
$353$	1783.16	+	3088.53i	0.268862	+	0.465682i	0.968568	−	0.248748i	$-0.0800192\pi$
$353$	1783.16	+	3088.53i	0.268862	+	0.465682i	−0.699706	+	0.714430i	$0.746686\pi$
$354$		0			0
$355$	156.384	−	270.865i	0.0233802	−	0.0404958i
$356$		0			0
$357$	11707.8	−	20278.6i	1.73570	−	3.00632i
$358$		0			0
$359$	−3465.53			−0.509481			−0.254740	−	0.967010i	$-0.581990\pi$
$359$	−3465.53			−0.509481			−0.254740	+	0.967010i	$0.581990\pi$
$360$		0			0
$361$	−1084.17	−	1877.84i	−0.158065	−	0.273777i
$362$		0			0
$363$	−2049.84			−0.296387
$364$		0			0
$365$	−881.893			−0.126467
$366$		0			0
$367$	5411.84	+	9373.57i	0.769743	+	1.33323i	0.937702	+	0.347439i	$0.112949\pi$
$367$	5411.84	+	9373.57i	0.769743	+	1.33323i	−0.167960	+	0.985794i	$0.553718\pi$
$368$		0			0
$369$	7196.09			1.01521
$370$		0			0
$371$	2844.45	−	4926.73i	0.398049	−	0.689442i
$372$		0			0
$373$	−239.114	+	414.158i	−0.0331927	+	0.0574914i	−0.882145	−	0.470979i	$-0.843901\pi$
$373$	−239.114	+	414.158i	−0.0331927	+	0.0574914i	0.848952	+	0.528470i	$0.177234\pi$
$374$		0			0
$375$	2845.13	+	4927.92i	0.391792	+	0.678604i
$376$		0			0
$377$	5333.30	+	11466.3i	0.728591	+	1.56643i
$378$		0			0
$379$	−1302.69	−	2256.32i	−0.176556	−	0.305804i	0.764143	−	0.645047i	$-0.223162\pi$
$379$	−1302.69	−	2256.32i	−0.176556	−	0.305804i	−0.940699	+	0.339243i	$0.889829\pi$
$380$		0			0
$381$	891.948	−	1544.90i	0.119937	−	0.207736i
$382$		0			0
$383$	4318.61	−	7480.05i	0.576164	−	0.997945i	−0.419750	−	0.907640i	$-0.637882\pi$
$383$	4318.61	−	7480.05i	0.576164	−	0.997945i	0.995914	−	0.0903053i	$-0.0287843\pi$
$384$		0			0
$385$	1847.75			0.244598
$386$		0			0
$387$	−4277.26	−	7408.43i	−0.561823	−	0.973106i
$388$		0			0
$389$	2326.59			0.303247			0.151623	−	0.988438i	$-0.451550\pi$
$389$	2326.59			0.303247			0.151623	+	0.988438i	$0.451550\pi$
$390$		0			0
$391$	−12485.8			−1.61492
$392$		0			0
$393$	9303.81	+	16114.7i	1.19419	+	2.06839i
$394$		0			0
$395$	−1385.57			−0.176495
$396$		0			0
$397$	6009.32	−	10408.4i	0.759695	−	1.31583i	−0.183311	−	0.983055i	$-0.558682\pi$
$397$	6009.32	−	10408.4i	0.759695	−	1.31583i	0.943006	−	0.332775i	$-0.107985\pi$
$398$		0			0
$399$	11708.1	−	20279.1i	1.46902	−	2.54442i
$400$		0			0
$401$	−3128.67	−	5419.01i	−0.389621	−	0.674844i	0.602777	−	0.797910i	$-0.294061\pi$
$401$	−3128.67	−	5419.01i	−0.389621	−	0.674844i	−0.992399	+	0.123066i	$0.960727\pi$
$402$		0			0
$403$	−7721.11	−	683.054i	−0.954382	−	0.0844301i
$404$		0			0
$405$	−3585.20	−	6209.74i	−0.439876	−	0.761888i
$406$		0			0
$407$	−237.841	+	411.953i	−0.0289665	+	0.0501714i
$408$		0			0
$409$	5387.61	−	9331.62i	0.651346	−	1.12816i	−0.331451	−	0.943472i	$-0.607538\pi$
$409$	5387.61	−	9331.62i	0.651346	−	1.12816i	0.982797	−	0.184691i	$-0.0591285\pi$
$410$		0			0
$411$	−11585.9			−1.39049
$412$		0			0
$413$	−7423.70	−	12858.2i	−0.884494	−	1.53199i
$414$		0			0
$415$	−993.945			−0.117568
$416$		0			0
$417$	−13022.4			−1.52928
$418$		0			0
$419$	−535.922	−	928.245i	−0.0624857	−	0.108228i	0.833090	−	0.553137i	$-0.186569\pi$
$419$	−535.922	−	928.245i	−0.0624857	−	0.108228i	−0.895576	+	0.444909i	$0.853236\pi$
$420$		0			0
$421$	−10966.8			−1.26958			−0.634788	−	0.772687i	$-0.718912\pi$
$421$	−10966.8			−1.26958			−0.634788	+	0.772687i	$0.718912\pi$
$422$		0			0
$423$	5141.25	−	8904.91i	0.590961	−	1.02357i
$424$		0			0
$425$	5691.88	−	9858.63i	0.649640	−	1.12521i
$426$		0			0
$427$	3504.62	+	6070.17i	0.397190	+	0.687954i
$428$		0			0
$429$	9239.96	−	13168.8i	1.03988	−	1.48205i
$430$		0			0
$431$	3693.17	+	6396.76i	0.412747	+	0.714899i	0.995189	−	0.0979736i	$-0.0312361\pi$
$431$	3693.17	+	6396.76i	0.412747	+	0.714899i	−0.582442	+	0.812872i	$0.697903\pi$
$432$		0			0
$433$	−2734.86	+	4736.92i	−0.303532	+	0.525732i	−0.976933	−	0.213545i	$-0.931499\pi$
$433$	−2734.86	+	4736.92i	−0.303532	+	0.525732i	0.673402	+	0.739277i	$0.264832\pi$
$434$		0			0
$435$	3135.44	−	5430.74i	0.345593	−	0.598584i
$436$		0			0
$437$	−12486.1			−1.36680
$438$		0			0
$439$	4579.13	+	7931.28i	0.497836	+	0.862277i	0.999997	−	0.00249744i	$-0.000794961\pi$
$439$	4579.13	+	7931.28i	0.497836	+	0.862277i	−0.502161	+	0.864774i	$0.667462\pi$
$440$		0			0
$441$	18517.1			1.99947
$442$		0			0
$443$	10116.8			1.08502			0.542509	−	0.840050i	$-0.317475\pi$
$443$	10116.8			1.08502			0.542509	+	0.840050i	$0.317475\pi$
$444$		0			0
$445$	975.490	+	1689.60i	0.103916	+	0.179988i
$446$		0			0
$447$	16105.3			1.70415
$448$		0			0
$449$	8526.80	−	14768.9i	0.896224	−	1.55231i	0.0639426	−	0.997954i	$-0.479633\pi$
$449$	8526.80	−	14768.9i	0.896224	−	1.55231i	0.832282	−	0.554353i	$-0.187034\pi$
$450$		0			0
$451$	1566.38	−	2713.05i	0.163543	−	0.283265i
$452$		0			0
$453$	12338.3	+	21370.5i	1.27969	+	2.21650i
$454$		0			0
$455$	1479.69	−	2108.86i	0.152459	−	0.217285i
$456$		0			0
$457$	−8468.80	−	14668.4i	−0.866857	−	1.50144i	−0.865191	−	0.501442i	$-0.832803\pi$
$457$	−8468.80	−	14668.4i	−0.866857	−	1.50144i	−0.00166576	−	0.999999i	$-0.500530\pi$
$458$		0			0
$459$	−24357.3	+	42188.1i	−2.47691	+	4.29014i
$460$		0			0
$461$	3622.02	−	6273.52i	0.365931	−	0.633812i	−0.622994	−	0.782227i	$-0.714084\pi$
$461$	3622.02	−	6273.52i	0.365931	−	0.633812i	0.988925	+	0.148415i	$0.0474172\pi$
$462$		0			0
$463$	−12328.0			−1.23743			−0.618715	−	0.785616i	$-0.712346\pi$
$463$	−12328.0			−1.23743			−0.618715	+	0.785616i	$0.712346\pi$
$464$		0			0
$465$	1921.85	+	3328.74i	0.191664	+	0.331971i
$466$		0			0
$467$	8974.81			0.889303			0.444651	−	0.895704i	$-0.353328\pi$
$467$	8974.81			0.889303			0.444651	+	0.895704i	$0.353328\pi$
$468$		0			0
$469$	9746.00			0.959549
$470$		0			0
$471$	5723.22	+	9912.91i	0.559898	+	0.969772i
$472$		0			0
$473$	−3724.14			−0.362021
$474$		0			0
$475$	5692.02	−	9858.87i	0.549827	−	0.952329i
$476$		0			0
$477$	−9099.00	+	15759.9i	−0.873406	+	1.51278i
$478$		0			0
$479$	−247.933	−	429.433i	−0.0236500	−	0.0409630i	0.853958	−	0.520342i	$-0.174195\pi$
$479$	−247.933	−	429.433i	−0.0236500	−	0.0409630i	−0.877608	+	0.479379i	$0.840862\pi$
$480$		0			0
$481$	279.703	+	601.346i	0.0265142	+	0.0570042i
$482$		0			0
$483$	−16194.0	−	28048.8i	−1.52557	−	2.64237i
$484$		0			0
$485$	−528.377	+	915.176i	−0.0494688	+	0.0856825i
$486$		0			0
$487$	−7644.29	+	13240.3i	−0.711285	+	1.23198i	0.253089	+	0.967443i	$0.418553\pi$
$487$	−7644.29	+	13240.3i	−0.711285	+	1.23198i	−0.964375	+	0.264540i	$0.914780\pi$
$488$		0			0
$489$	769.615			0.0711722
$490$		0			0
$491$	10555.2	+	18282.2i	0.970166	+	1.68038i	0.695044	+	0.718968i	$0.255385\pi$
$491$	10555.2	+	18282.2i	0.970166	+	1.68038i	0.275122	+	0.961409i	$0.411282\pi$
$492$		0			0
$493$	−25633.4			−2.34172
$494$		0			0
$495$	−5910.70			−0.536699
$496$		0			0
$497$	−1658.20	−	2872.09i	−0.149659	−	0.259217i
$498$		0			0
$499$	−10400.6			−0.933059			−0.466530	−	0.884506i	$-0.654496\pi$
$499$	−10400.6			−0.933059			−0.466530	+	0.884506i	$0.654496\pi$
$500$		0			0
$501$	−17672.1	+	30609.0i	−1.57591	+	2.72956i
$502$		0			0
$503$	6210.60	−	10757.1i	0.550531	−	0.953548i	−0.447705	−	0.894181i	$-0.647759\pi$
$503$	6210.60	−	10757.1i	0.550531	−	0.953548i	0.998236	−	0.0593664i	$-0.0189080\pi$
$504$		0			0
$505$	97.0392	+	168.077i	0.00855087	+	0.0148105i
$506$		0			0
$507$	−7630.34	−	21091.4i	−0.668393	−	1.84753i
$508$		0			0
$509$	4054.90	+	7023.29i	0.353105	+	0.611595i	0.986792	−	0.161994i	$-0.0517926\pi$
$509$	4054.90	+	7023.29i	0.353105	+	0.611595i	−0.633687	+	0.773589i	$0.718459\pi$
$510$		0			0
$511$	−4675.53	+	8098.26i	−0.404762	+	0.701068i
$512$		0			0
$513$	−24357.9	+	42189.2i	−2.09635	+	3.63099i
$514$		0			0
$515$	2184.22			0.186890
$516$		0			0
$517$	−2238.20	−	3876.68i	−0.190398	−	0.329780i
$518$		0			0
$519$	2110.40			0.178490
$520$		0			0
$521$	418.325			0.0351769			0.0175885	−	0.999845i	$-0.494401\pi$
$521$	418.325			0.0351769			0.0175885	+	0.999845i	$0.494401\pi$
$522$		0			0
$523$	−2770.12	−	4797.98i	−0.231604	−	0.401149i	0.726676	−	0.686980i	$-0.241064\pi$
$523$	−2770.12	−	4797.98i	−0.231604	−	0.401149i	−0.958280	+	0.285830i	$0.907731\pi$
$524$		0			0
$525$	29529.4			2.45479
$526$		0			0
$527$	7855.91	−	13606.8i	0.649353	−	1.12471i
$528$		0			0
$529$	−2551.49	+	4419.31i	−0.209706	+	0.363221i
$530$		0			0
$531$	23747.4	+	41131.7i	1.94077	+	3.36151i
$532$		0			0
$533$	−1842.07	−	3960.35i	−0.149698	−	0.321842i
$534$		0			0
$535$	−676.084	−	1171.01i	−0.0546349	−	0.0946304i
$536$		0			0
$537$	−1803.98	+	3124.58i	−0.144967	+	0.251091i
$538$		0			0
$539$	4030.62	−	6981.24i	0.322099	−	0.557891i
$540$		0			0
$541$	7129.33			0.566569			0.283285	−	0.959036i	$-0.408576\pi$
$541$	7129.33			0.566569			0.283285	+	0.959036i	$0.408576\pi$
$542$		0			0
$543$	−16058.7	−	27814.5i	−1.26914	−	2.19822i
$544$		0			0
$545$	−2924.14			−0.229829
$546$		0			0
$547$	3794.55			0.296606			0.148303	−	0.988942i	$-0.452619\pi$
$547$	3794.55			0.296606			0.148303	+	0.988942i	$0.452619\pi$
$548$		0			0
$549$	−11210.8	−	19417.7i	−0.871521	−	1.50952i
$550$		0			0
$551$	−25634.0			−1.98193
$552$		0			0
$553$	−7345.87	+	12723.4i	−0.564879	+	0.978399i
$554$		0			0
$555$	164.437	−	284.813i	0.0125765	−	0.0217831i
$556$		0			0
$557$	−8771.59	−	15192.8i	−0.667261	−	1.15573i	−0.978667	−	0.205453i	$-0.934133\pi$
$557$	−8771.59	−	15192.8i	−0.667261	−	1.15573i	0.311406	−	0.950277i	$-0.399200\pi$
$558$		0			0
$559$	−2982.31	+	4250.40i	−0.225650	+	0.321597i
$560$		0			0
$561$	16304.3	+	28239.9i	1.22704	+	2.12529i
$562$		0			0
$563$	2250.08	−	3897.26i	0.168436	−	0.291740i	−0.769434	−	0.638726i	$-0.779462\pi$
$563$	2250.08	−	3897.26i	0.168436	−	0.291740i	0.937870	+	0.346986i	$0.112795\pi$
$564$		0			0
$565$	−2072.36	+	3589.43i	−0.154309	+	0.267272i
$566$		0			0
$567$	−76030.6			−5.63137
$568$		0			0
$569$	1303.74	+	2258.14i	0.0960556	+	0.166373i	0.910049	−	0.414501i	$-0.136044\pi$
$569$	1303.74	+	2258.14i	0.0960556	+	0.166373i	−0.813993	+	0.580875i	$0.802711\pi$
$570$		0			0
$571$	−4409.79			−0.323194			−0.161597	−	0.986857i	$-0.551665\pi$
$571$	−4409.79			−0.323194			−0.161597	+	0.986857i	$0.551665\pi$
$572$		0			0
$573$	6018.96			0.438823
$574$		0			0
$575$	−7872.87	−	13636.2i	−0.570993	−	0.988989i
$576$		0			0
$577$	−21487.8			−1.55034			−0.775172	−	0.631750i	$-0.782337\pi$
$577$	−21487.8			−1.55034			−0.775172	+	0.631750i	$0.782337\pi$
$578$		0			0
$579$	25504.3	−	44174.7i	1.83061	−	3.17070i
$580$		0			0
$581$	−5269.60	+	9127.22i	−0.376282	+	0.651740i
$582$		0			0
$583$	3961.17	+	6860.95i	0.281398	+	0.487396i
$584$		0			0
$585$	−4733.32	+	6745.95i	−0.334528	+	0.476771i
$586$		0			0
$587$	−4040.02	−	6997.52i	−0.284071	−	0.492025i	0.688313	−	0.725414i	$-0.258352\pi$
$587$	−4040.02	−	6997.52i	−0.284071	−	0.492025i	−0.972383	+	0.233389i	$0.925018\pi$
$588$		0			0
$589$	7856.11	−	13607.2i	0.549584	−	0.951908i
$590$		0			0
$591$	−1750.95	+	3032.73i	−0.121868	+	0.211082i
$592$		0			0
$593$	10054.7			0.696283			0.348141	−	0.937442i	$-0.386813\pi$
$593$	10054.7			0.696283			0.348141	+	0.937442i	$0.386813\pi$
$594$		0			0
$595$	2610.97	+	4522.34i	0.179898	+	0.311593i
$596$		0			0
$597$	10332.7			0.708360
$598$		0			0
$599$	−8304.77			−0.566484			−0.283242	−	0.959049i	$-0.591410\pi$
$599$	−8304.77			−0.566484			−0.283242	+	0.959049i	$0.591410\pi$
$600$		0			0
$601$	−7000.68	−	12125.5i	−0.475148	−	0.822980i	0.524447	−	0.851443i	$-0.324272\pi$
$601$	−7000.68	−	12125.5i	−0.475148	−	0.822980i	−0.999595	+	0.0284633i	$0.990939\pi$
$602$		0			0
$603$	−31176.1			−2.10546
$604$		0			0
$605$	228.568	−	395.891i	0.0153597	−	0.0266038i
$606$		0			0
$607$	−10242.9	+	17741.3i	−0.684923	+	1.18632i	0.288538	+	0.957469i	$0.406831\pi$
$607$	−10242.9	+	17741.3i	−0.684923	+	1.18632i	−0.973461	+	0.228853i	$0.926502\pi$
$608$		0			0
$609$	−33246.3	−	57584.3i	−2.21217	−	3.83159i
$610$		0			0
$611$	−6216.86	−	549.979i	−0.411632	−	0.0364154i
$612$		0			0
$613$	−12076.1	−	20916.4i	−0.795676	−	1.37815i	−0.922409	−	0.386215i	$-0.873782\pi$
$613$	−12076.1	−	20916.4i	−0.795676	−	1.37815i	0.126732	−	0.991937i	$-0.459551\pi$
$614$		0			0
$615$	−1082.95	+	1875.72i	−0.0710061	+	0.122986i
$616$		0			0
$617$	−2957.21	+	5122.04i	−0.192954	+	0.334207i	−0.946228	−	0.323501i	$-0.895140\pi$
$617$	−2957.21	+	5122.04i	−0.192954	+	0.334207i	0.753274	+	0.657707i	$0.228474\pi$
$618$		0			0
$619$	−99.7569			−0.00647749			−0.00323875	−	0.999995i	$-0.501031\pi$
$619$	−99.7569			−0.00647749			−0.00323875	+	0.999995i	$0.501031\pi$
$620$		0			0
$621$	33690.4	+	58353.6i	2.17705	+	3.77077i
$622$		0			0
$623$	20687.0			1.33035
$624$		0			0
$625$	13708.1			0.877317
$626$		0			0
$627$	16304.7	+	28240.6i	1.03851	+	1.79876i
$628$		0			0
$629$	−1344.33			−0.0852179
$630$		0			0
$631$	−8138.93	+	14097.0i	−0.513480	+	0.889373i	0.486398	+	0.873737i	$0.338311\pi$
$631$	−8138.93	+	14097.0i	−0.513480	+	0.889373i	−0.999878	+	0.0156356i	$0.995023\pi$
$632$		0			0
$633$	24271.6	−	42039.6i	1.52403	−	2.63969i
$634$		0			0
$635$	198.914	+	344.529i	0.0124310	+	0.0215311i
$636$		0			0
$637$	−4740.03	−	10190.8i	−0.294830	−	0.633869i
$638$		0			0
$639$	5304.36	+	9187.41i	0.328383	+	0.568777i
$640$		0			0
$641$	10167.2	−	17610.0i	0.626488	−	1.08511i	−0.361763	−	0.932270i	$-0.617825\pi$
$641$	10167.2	−	17610.0i	0.626488	−	1.08511i	0.988251	−	0.152839i	$-0.0488416\pi$
$642$		0			0
$643$	2579.29	−	4467.47i	0.158192	−	0.273996i	−0.776025	−	0.630702i	$-0.782767\pi$
$643$	2579.29	−	4467.47i	0.158192	−	0.273996i	0.934217	+	0.356706i	$0.116100\pi$
$644$		0			0
$645$	2574.77			0.157180
$646$		0			0
$647$	3537.96	+	6127.93i	0.214979	+	0.372355i	0.953266	−	0.302132i	$-0.0976983\pi$
$647$	3537.96	+	6127.93i	0.214979	+	0.372355i	−0.738287	+	0.674487i	$0.764365\pi$
$648$		0			0
$649$	20676.5			1.25057
$650$		0			0
$651$	40756.3			2.45371
$652$		0			0
$653$	36.1116	+	62.5470i	0.00216410	+	0.00374832i	0.867105	−	0.498125i	$-0.165978\pi$
$653$	36.1116	+	62.5470i	0.00216410	+	0.00374832i	−0.864941	+	0.501873i	$0.832644\pi$
$654$		0			0
$655$	−4149.70			−0.247545
$656$		0			0
$657$	14956.4	−	25905.2i	0.888135	−	1.53829i
$658$		0			0
$659$	−2328.19	+	4032.53i	−0.137622	+	0.238369i	−0.926596	−	0.376058i	$-0.877279\pi$
$659$	−2328.19	+	4032.53i	−0.137622	+	0.238369i	0.788974	+	0.614427i	$0.210613\pi$
$660$		0			0
$661$	−1786.90	−	3095.00i	−0.105147	−	0.182120i	0.808651	−	0.588289i	$-0.200198\pi$
$661$	−1786.90	−	3095.00i	−0.105147	−	0.182120i	−0.913798	+	0.406168i	$0.866865\pi$
$662$		0			0
$663$	45287.1	+	4006.35i	2.65280	+	0.234682i
$664$		0			0
$665$	2611.04	+	4522.45i	0.152258	+	0.263719i
$666$		0			0
$667$	−17727.7	+	30705.3i	−1.02911	+	1.78248i
$668$		0			0
$669$	1290.78	−	2235.70i	0.0745957	−	0.129204i
$670$		0			0
$671$	−9761.05			−0.561581
$672$		0			0
$673$	1649.16	+	2856.43i	0.0944584	+	0.163607i	0.909382	−	0.415961i	$-0.136555\pi$
$673$	1649.16	+	2856.43i	0.0944584	+	0.163607i	−0.814924	+	0.579568i	$0.803221\pi$
$674$		0			0
$675$	−61433.8			−3.50310
$676$		0			0
$677$	19778.6			1.12283			0.561413	−	0.827536i	$-0.310258\pi$
$677$	19778.6			1.12283			0.561413	+	0.827536i	$0.310258\pi$
$678$		0			0
$679$	5602.60	+	9703.98i	0.316654	+	0.548461i
$680$		0			0
$681$	−43224.4			−2.43225
$682$		0			0
$683$	1145.84	−	1984.65i	0.0641937	−	0.111187i	−0.832142	−	0.554562i	$-0.812886\pi$
$683$	1145.84	−	1984.65i	0.0641937	−	0.111187i	0.896336	+	0.443375i	$0.146219\pi$
$684$		0			0
$685$	1291.89	−	2237.62i	0.0720593	−	0.124810i
$686$		0			0
$687$	−32774.6	−	56767.3i	−1.82013	−	3.15256i
$688$		0			0
$689$	11002.6	+	973.354i	0.608369	+	0.0538198i
$690$		0			0
$691$	4748.27	+	8224.24i	0.261407	+	0.452771i	0.966616	−	0.256229i	$-0.0824801\pi$
$691$	4748.27	+	8224.24i	0.261407	+	0.452771i	−0.705209	+	0.709000i	$0.749147\pi$
$692$		0			0
$693$	−31336.8	+	54276.9i	−1.71773	+	2.97519i
$694$		0			0
$695$	1452.07	−	2515.06i	0.0792520	−	0.137269i
$696$		0			0
$697$	8853.51			0.481134
$698$		0			0
$699$	−13181.9	−	22831.7i	−0.713284	−	1.23544i
$700$		0			0
$701$	−19712.0			−1.06207			−0.531036	−	0.847349i	$-0.678197\pi$
$701$	−19712.0			−1.06207			−0.531036	+	0.847349i	$0.678197\pi$
$702$		0			0
$703$	−1344.37			−0.0721248
$704$		0			0
$705$	1547.43	+	2680.23i	0.0826661	+	0.143182i
$706$		0			0
$707$	2057.89			0.109470
$708$		0			0
$709$	629.703	−	1090.68i	0.0333554	−	0.0577733i	−0.848866	−	0.528608i	$-0.822714\pi$
$709$	629.703	−	1090.68i	0.0333554	−	0.0577733i	0.882221	+	0.470835i	$0.156047\pi$
$710$		0			0
$711$	23498.4	−	40700.5i	1.23947	−	2.14682i
$712$		0			0
$713$	−10866.1	−	18820.6i	−0.570741	−	0.988553i
$714$		0			0
$715$	1513.03	+	3252.94i	0.0791387	+	0.170144i
$716$		0			0
$717$	7132.03	+	12353.0i	0.371479	+	0.643421i
$718$		0			0
$719$	−4287.14	+	7425.55i	−0.222369	+	0.385155i	−0.955527	−	0.294904i	$-0.904712\pi$
$719$	−4287.14	+	7425.55i	−0.222369	+	0.385155i	0.733158	+	0.680059i	$0.238046\pi$
$720$		0			0
$721$	11580.1	−	20057.3i	0.598149	−	1.03602i
$722$		0			0
$723$	−11884.3			−0.611316
$724$		0			0
$725$	−16163.1	−	27995.2i	−0.827974	−	1.43409i
$726$		0			0
$727$	−21535.4			−1.09863			−0.549314	−	0.835616i	$-0.685111\pi$
$727$	−21535.4			−1.09863			−0.549314	+	0.835616i	$0.685111\pi$
$728$		0			0
$729$	101880.			5.17606
$730$		0			0
$731$	−5262.41	−	9114.77i	−0.266262	−	0.461179i
$732$		0			0
$733$	36997.3			1.86429			0.932146	−	0.362083i	$-0.117934\pi$
$733$	36997.3			1.86429			0.932146	+	0.362083i	$0.117934\pi$
$734$		0			0
$735$	−2786.66	+	4826.64i	−0.139847	+	0.242222i
$736$		0			0
$737$	−6786.13	+	11753.9i	−0.339173	+	0.587464i
$738$		0			0
$739$	−2649.09	−	4588.36i	−0.131865	−	0.228397i	0.792530	−	0.609832i	$-0.208763\pi$
$739$	−2649.09	−	4588.36i	−0.131865	−	0.228397i	−0.924396	+	0.381435i	$0.875430\pi$
$740$		0			0
$741$	45288.2	+	4006.45i	2.24521	+	0.198624i
$742$		0			0
$743$	2236.51	+	3873.76i	0.110430	+	0.191271i	0.915944	−	0.401306i	$-0.131444\pi$
$743$	2236.51	+	3873.76i	0.110430	+	0.191271i	−0.805514	+	0.592577i	$0.798110\pi$
$744$		0			0
$745$	−1795.82	+	3110.46i	−0.0883140	+	0.152964i
$746$		0			0
$747$	16856.7	−	29196.7i	0.825643	−	1.43006i
$748$		0			0
$749$	−14337.6			−0.699445
$750$		0			0
$751$	−14118.4	−	24453.8i	−0.686002	−	1.18819i	−0.973121	−	0.230295i	$-0.926031\pi$
$751$	−14118.4	−	24453.8i	−0.686002	−	1.18819i	0.287119	−	0.957895i	$-0.407302\pi$
$752$		0			0
$753$	−69976.2			−3.38656
$754$		0			0
$755$	−5503.13			−0.265271
$756$		0			0
$757$	13715.1	+	23755.3i	0.658500	+	1.14056i	0.981004	+	0.193987i	$0.0621421\pi$
$757$	13715.1	+	23755.3i	0.658500	+	1.14056i	−0.322504	+	0.946568i	$0.604525\pi$
$758$		0			0
$759$	45103.4			2.15698
$760$		0			0
$761$	−11175.7	+	19356.8i	−0.532349	+	0.922056i	0.466937	+	0.884290i	$0.345357\pi$
$761$	−11175.7	+	19356.8i	−0.532349	+	0.922056i	−0.999287	+	0.0377656i	$0.987976\pi$
$762$		0			0
$763$	−15502.9	+	26851.9i	−0.735576	+	1.27405i
$764$		0			0
$765$	−8352.14	−	14466.3i	−0.394735	−	0.683701i
$766$		0			0
$767$	16557.8	−	23598.3i	0.779489	−	1.11093i
$768$		0			0
$769$	−17115.4	−	29644.8i	−0.802598	−	1.39014i	−0.917901	−	0.396811i	$-0.870117\pi$
$769$	−17115.4	−	29644.8i	−0.802598	−	1.39014i	0.115302	−	0.993330i	$-0.463216\pi$
$770$		0			0
$771$	15776.4	−	27325.6i	0.736931	−	1.27640i
$772$		0			0
$773$	−13129.7	+	22741.3i	−0.610921	+	1.05815i	0.380165	+	0.924919i	$0.375867\pi$
$773$	−13129.7	+	22741.3i	−0.610921	+	1.05815i	−0.991086	+	0.133227i	$0.957466\pi$
$774$		0			0
$775$	19814.1			0.918379
$776$		0			0
$777$	−1743.59	−	3019.99i	−0.0805032	−	0.139436i
$778$		0			0
$779$	8853.73			0.407211
$780$		0			0
$781$	4618.41			0.211600
$782$		0			0
$783$	69166.8	+	119800.i	3.15686	+	5.46783i
$784$		0			0
$785$	−2552.68			−0.116062
$786$		0			0
$787$	−4121.33	+	7138.35i	−0.186670	+	0.323322i	−0.944138	−	0.329550i	$-0.893103\pi$
$787$	−4121.33	+	7138.35i	−0.186670	+	0.323322i	0.757468	+	0.652872i	$0.226436\pi$
$788$		0			0
$789$	34280.7	−	59375.9i	1.54680	−	2.67914i
$790$		0			0
$791$	21974.1	+	38060.2i	0.987746	+	1.71083i
$792$		0			0
$793$	−7816.70	+	11140.4i	−0.350037	+	0.498874i
$794$		0			0
$795$	−2738.64	−	4743.47i	−0.122176	−	0.211615i
$796$		0			0
$797$	−8055.27	+	13952.1i	−0.358008	+	0.620088i	−0.987628	−	0.156815i	$-0.949877\pi$
$797$	−8055.27	+	13952.1i	−0.358008	+	0.620088i	0.629620	+	0.776903i	$0.283211\pi$
$798$		0			0
$799$	6325.40	−	10955.9i	0.280071	−	0.485097i
$800$		0			0
$801$	−66175.0			−2.91907
$802$		0			0
$803$	−6511.14	−	11277.6i	−0.286143	−	0.495615i
$804$		0			0
$805$	7222.86			0.316239
$806$		0			0
$807$	−11219.7			−0.489408
$808$		0			0
$809$	−4590.29	−	7950.61i	−0.199488	−	0.345524i	0.748874	−	0.662712i	$-0.230595\pi$
$809$	−4590.29	−	7950.61i	−0.199488	−	0.345524i	−0.948363	+	0.317188i	$0.897261\pi$
$810$		0			0
$811$	−9117.75			−0.394781			−0.197391	−	0.980325i	$-0.563247\pi$
$811$	−9117.75			−0.394781			−0.197391	+	0.980325i	$0.563247\pi$
$812$		0			0
$813$	−23488.1	+	40682.6i	−1.01324	+	1.75498i
$814$		0			0
$815$	−85.8162	+	148.638i	−0.00368836	+	0.00638842i
$816$		0			0
$817$	−5262.54	−	9114.99i	−0.225353	−	0.390322i
$818$		0			0
$819$	36852.2	+	79230.2i	1.57231	+	3.38038i
$820$		0			0
$821$	−11125.0	−	19269.1i	−0.472917	−	0.819117i	0.526602	−	0.850112i	$-0.323466\pi$
$821$	−11125.0	−	19269.1i	−0.472917	−	0.819117i	−0.999520	+	0.0309951i	$0.990132\pi$
$822$		0			0
$823$	17868.3	−	30948.9i	0.756806	−	1.31083i	−0.187666	−	0.982233i	$-0.560092\pi$
$823$	17868.3	−	30948.9i	0.756806	−	1.31083i	0.944472	−	0.328593i	$-0.106574\pi$
$824$		0			0
$825$	−20561.3	+	35613.2i	−0.867699	+	1.50290i
$826$		0			0
$827$	11229.2			0.472162			0.236081	−	0.971733i	$-0.424137\pi$
$827$	11229.2			0.472162			0.236081	+	0.971733i	$0.424137\pi$
$828$		0			0
$829$	20617.7	+	35710.9i	0.863790	+	1.49613i	0.868243	+	0.496139i	$0.165249\pi$
$829$	20617.7	+	35710.9i	0.863790	+	1.49613i	−0.00445289	+	0.999990i	$0.501417\pi$
$830$		0			0
$831$	−56967.6			−2.37808
$832$		0			0
$833$	22782.0			0.947597
$834$		0			0
$835$	−3941.07	−	6826.14i	−0.163337	−	0.282908i
$836$		0			0
$837$	−84790.7			−3.50155
$838$		0			0
$839$	−2921.61	+	5060.37i	−0.120221	+	0.208228i	−0.919855	−	0.392259i	$-0.871694\pi$
$839$	−2921.61	+	5060.37i	−0.120221	+	0.208228i	0.799634	+	0.600488i	$0.205027\pi$
$840$		0			0
$841$	−24200.6	+	41916.7i	−0.992276	+	1.71867i
$842$		0			0
$843$	−1321.57	−	2289.03i	−0.0539944	−	0.0935211i
$844$		0			0
$845$	4924.26	+	878.129i	0.200473	+	0.0357498i
$846$		0			0
$847$	−2423.60	−	4197.80i	−0.0983186	−	0.170293i
$848$		0			0
$849$	−13946.3	+	24155.7i	−0.563763	+	0.976467i
$850$		0			0
$851$	−929.723	+	1610.33i	−0.0374506	+	0.0648664i
$852$		0			0
$853$	43746.6			1.75599			0.877993	−	0.478673i	$-0.158882\pi$
$853$	43746.6			1.75599			0.877993	+	0.478673i	$0.158882\pi$
$854$		0			0
$855$	−8352.35	−	14466.7i	−0.334087	−	0.578656i
$856$		0			0
$857$	33068.9			1.31810			0.659049	−	0.752100i	$-0.270959\pi$
$857$	33068.9			1.31810			0.659049	+	0.752100i	$0.270959\pi$
$858$		0			0
$859$	12332.5			0.489847			0.244924	−	0.969542i	$-0.421237\pi$
$859$	12332.5			0.489847			0.244924	+	0.969542i	$0.421237\pi$
$860$		0			0
$861$	11483.0	+	19889.1i	0.454516	+	0.787244i
$862$		0			0
$863$	35801.1			1.41215			0.706075	−	0.708137i	$-0.250464\pi$
$863$	35801.1			1.41215			0.706075	+	0.708137i	$0.250464\pi$
$864$		0			0
$865$	−235.321	+	407.588i	−0.00924990	+	0.0160213i
$866$		0			0
$867$	−20999.3	+	36371.9i	−0.822578	+	1.42475i
$868$		0			0
$869$	−10229.8	−	17718.6i	−0.399337	−	0.691671i
$870$		0			0
$871$	7980.52	+	17157.7i	0.310459	+	0.667470i
$872$		0			0
$873$	−17922.0	−	31041.7i	−0.694807	−	1.20344i
$874$		0			0
$875$	−6727.81	+	11652.9i	−0.259933	+	0.450218i
$876$		0			0
$877$	−8336.10	+	14438.5i	−0.320969	+	0.555935i	−0.980688	−	0.195577i	$-0.937342\pi$
$877$	−8336.10	+	14438.5i	−0.320969	+	0.555935i	0.659719	+	0.751512i	$0.270675\pi$
$878$		0			0
$879$	67463.3			2.58871
$880$		0			0
$881$	19721.9	+	34159.3i	0.754195	+	1.30630i	0.945773	+	0.324827i	$0.105306\pi$
$881$	19721.9	+	34159.3i	0.754195	+	1.30630i	−0.191578	+	0.981477i	$0.561361\pi$
$882$		0			0
$883$	−20868.8			−0.795347			−0.397673	−	0.917527i	$-0.630182\pi$
$883$	−20868.8			−0.795347			−0.397673	+	0.917527i	$0.630182\pi$
$884$		0			0
$885$	−14295.1			−0.542966
$886$		0			0
$887$	1771.57	+	3068.45i	0.0670614	+	0.116154i	0.897607	−	0.440798i	$-0.145304\pi$
$887$	1771.57	+	3068.45i	0.0670614	+	0.116154i	−0.830545	+	0.556951i	$0.811971\pi$
$888$		0			0
$889$	4218.33			0.159143
$890$		0			0
$891$	52940.0	−	91694.8i	1.99052	−	3.44769i
$892$		0			0
$893$	6325.56	−	10956.2i	0.237040	−	0.410565i
$894$		0			0
$895$	−402.307	−	696.815i	−0.0150253	−	0.0260245i
$896$		0			0
$897$	36119.0	−	51477.0i	1.34446	−	1.91613i
$898$		0			0
$899$	−22308.2	−	38638.9i	−0.827608	−	1.43346i
$900$		0			0
$901$	−11194.7	+	19389.8i	−0.413929	+	0.716946i
$902$		0			0
$903$	13650.6	−	23643.6i	0.503062	−	0.871329i
$904$		0			0
$905$	7162.52			0.263083
$906$		0			0
$907$	−13350.4	−	23123.6i	−0.488747	−	0.846534i	0.511169	−	0.859480i	$-0.329213\pi$
$907$	−13350.4	−	23123.6i	−0.488747	−	0.846534i	−0.999916	+	0.0129456i	$0.995879\pi$
$908$		0			0
$909$	−6582.92			−0.240200
$910$		0			0
$911$	28583.6			1.03953			0.519767	−	0.854308i	$-0.326019\pi$
$911$	28583.6			1.03953			0.519767	+	0.854308i	$0.326019\pi$
$912$		0			0
$913$	−7338.44	−	12710.5i	−0.266010	−	0.460742i
$914$		0			0
$915$	6748.52			0.243824
$916$		0			0
$917$	−22000.5	+	38105.9i	−0.792279	+	1.37227i
$918$		0			0
$919$	−8159.51	+	14132.7i	−0.292881	+	0.507284i	−0.974490	−	0.224432i	$-0.927947\pi$
$919$	−8159.51	+	14132.7i	−0.292881	+	0.507284i	0.681609	+	0.731717i	$0.261281\pi$
$920$		0			0
$921$	−13649.9	−	23642.2i	−0.488358	−	0.845861i
$922$		0			0
$923$	3698.45	−	5271.05i	0.131892	−	0.187973i
$924$		0			0
$925$	−847.665	−	1468.20i	−0.0301309	−	0.0521882i
$926$		0			0
$927$	−37043.1	+	64160.6i	−1.31247	+	2.27326i
$928$		0			0
$929$	−1196.99	+	2073.24i	−0.0422733	+	0.0732195i	−0.886388	−	0.462943i	$-0.846793\pi$
$929$	−1196.99	+	2073.24i	−0.0422733	+	0.0732195i	0.844115	+	0.536163i	$0.180127\pi$
$930$		0			0
$931$	22782.5			0.802005
$932$		0			0
$933$	16975.5	+	29402.4i	0.595662	+	1.03172i
$934$		0			0
$935$	−7272.07			−0.254355
$936$		0			0
$937$	−9538.91			−0.332575			−0.166287	−	0.986077i	$-0.553178\pi$
$937$	−9538.91			−0.332575			−0.166287	+	0.986077i	$0.553178\pi$
$938$		0			0
$939$	16111.6	+	27906.2i	0.559940	+	0.969844i
$940$		0			0
$941$	−25196.8			−0.872893			−0.436447	−	0.899730i	$-0.643763\pi$
$941$	−25196.8			−0.872893			−0.436447	+	0.899730i	$0.643763\pi$
$942$		0			0
$943$	6122.97	−	10605.3i	0.211444	−	0.366231i
$944$		0			0
$945$	14090.4	−	24405.3i	0.485038	−	0.840111i
$946$		0			0
$947$	−12508.8	−	21665.9i	−0.429232	−	0.743452i	0.567573	−	0.823323i	$-0.307882\pi$
$947$	−12508.8	−	21665.9i	−0.429232	−	0.743452i	−0.996805	+	0.0798714i	$0.974549\pi$
$948$		0			0
$949$	−18085.4	−	1599.94i	−0.618628	−	0.0547274i
$950$		0			0
$951$	−37025.8	−	64130.6i	−1.26251	−	2.18673i
$952$		0			0
$953$	25996.9	−	45028.0i	0.883655	−	1.53054i	0.0364071	−	0.999337i	$-0.488409\pi$
$953$	25996.9	−	45028.0i	0.883655	−	1.53054i	0.847248	−	0.531198i	$-0.178258\pi$
$954$		0			0
$955$	−671.147	+	1162.46i	−0.0227412	+	0.0393888i
$956$		0			0
$957$	92597.6			3.12775
$958$		0			0
$959$	−13698.4	−	23726.4i	−0.461257	−	0.798921i
$960$		0			0
$961$	−2443.67			−0.0820270
$962$		0			0
$963$	45864.0			1.53473
$964$		0			0
$965$	5687.72	+	9851.43i	0.189735	+	0.328631i
$966$		0			0
$967$	26140.9			0.869321			0.434661	−	0.900594i	$-0.356868\pi$
$967$	26140.9			0.869321			0.434661	+	0.900594i	$0.356868\pi$
$968$		0			0
$969$	−46078.9	+	79811.0i	−1.52762	+	2.64592i
$970$		0			0
$971$	−7744.13	+	13413.2i	−0.255943	+	0.443307i	−0.965151	−	0.261692i	$-0.915719\pi$
$971$	−7744.13	+	13413.2i	−0.255943	+	0.443307i	0.709208	+	0.704999i	$0.249053\pi$
$972$		0			0
$973$	−15396.9	−	26668.2i	−0.507298	−	0.878667i
$974$		0			0
$975$	24180.2	+	51986.0i	0.794241	+	1.70757i
$976$		0			0
$977$	21996.0	+	38098.3i	0.720282	+	1.24757i	0.960887	+	0.276942i	$0.0893211\pi$
$977$	21996.0	+	38098.3i	0.720282	+	1.24757i	−0.240604	+	0.970623i	$0.577346\pi$
$978$		0			0
$979$	−14404.4	+	24949.1i	−0.470240	+	0.814480i
$980$		0			0
$981$	49591.8	−	85895.5i	1.61401	−	2.79555i
$982$		0			0
$983$	−33273.5			−1.07961			−0.539806	−	0.841789i	$-0.681502\pi$
$983$	−33273.5			−1.07961			−0.539806	+	0.841789i	$0.681502\pi$
$984$		0			0
$985$	−390.480	−	676.331i	−0.0126312	−	0.0218779i
$986$		0			0
$987$	32816.0			1.05830
$988$		0			0
$989$	−14557.7			−0.468055
$990$		0			0
$991$	−22466.1	−	38912.4i	−0.720140	−	1.24732i	−0.960943	−	0.276745i	$-0.910744\pi$
$991$	−22466.1	−	38912.4i	−0.720140	−	1.24732i	0.240804	−	0.970574i	$-0.422589\pi$
$992$		0			0
$993$	118299.			3.78058
$994$		0			0
$995$	−1152.16	+	1995.59i	−0.0367094	+	0.0635825i
$996$		0			0
$997$	−18618.8	+	32248.7i	−0.591438	+	1.02440i	0.402601	+	0.915375i	$0.368106\pi$
$997$	−18618.8	+	32248.7i	−0.591438	+	1.02440i	−0.994039	+	0.109025i	$0.965227\pi$
$998$		0			0
$999$	3627.42	+	6282.88i	0.114881	+	0.198981i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	416.4.i.h.289.1	yes	22
4.3	odd	2		416.4.i.g.289.11	✓	22
13.9	even	3	inner	416.4.i.h.321.1	yes	22
52.35	odd	6		416.4.i.g.321.11	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
416.4.i.g.289.11	✓	22	4.3	odd	2
416.4.i.g.321.11	yes	22	52.35	odd	6
416.4.i.h.289.1	yes	22	1.1	even	1	trivial
416.4.i.h.321.1	yes	22	13.9	even	3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	416.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.10450 - 8.84125i) q^{3} +2.27672 q^{5} +(12.0705 - 20.9067i) q^{7} +(-38.6118 + 66.8776i) q^{9} +(16.8093 + 29.1146i) q^{11} +(46.6898 + 4.13045i) q^{13} +(-11.6215 - 20.1290i) q^{15} +(-47.5050 + 82.2810i) q^{17} +(-47.5062 + 82.2831i) q^{19} -246.455 q^{21} +(65.7077 + 113.809i) q^{23} -119.817 q^{25} +512.732 q^{27} +(134.898 + 233.651i) q^{29} -165.370 q^{31} +(171.606 - 297.231i) q^{33} +(27.4810 - 47.5985i) q^{35} +(7.07469 + 12.2537i) q^{37} +(-201.810 - 433.880i) q^{39} +(-46.5925 - 80.7006i) q^{41} +(-55.3880 + 95.9349i) q^{43} +(-87.9081 + 152.261i) q^{45} -133.152 q^{47} +(-119.892 - 207.660i) q^{49} +969.956 q^{51} +235.653 q^{53} +(38.2700 + 66.2857i) q^{55} +969.980 q^{57} +(307.515 - 532.631i) q^{59} +(-145.173 + 251.447i) q^{61} +(932.125 + 1614.49i) q^{63} +(106.299 + 9.40386i) q^{65} +(201.856 + 349.625i) q^{67} +(670.809 - 1161.88i) q^{69} +(68.6883 - 118.972i) q^{71} -387.353 q^{73} +(611.603 + 1059.33i) q^{75} +811.585 q^{77} -608.582 q^{79} +(-1574.72 - 2727.50i) q^{81} -436.570 q^{83} +(-108.155 + 187.331i) q^{85} +(1377.18 - 2385.34i) q^{87} +(428.464 + 742.121i) q^{89} +(649.922 - 926.272i) q^{91} +(844.132 + 1462.08i) q^{93} +(-108.158 + 187.335i) q^{95} +(-232.079 + 401.972i) q^{97} -2596.15 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 10 q^{5} + 26 q^{7} - 117 q^{9} + 22 q^{11} + 37 q^{13} + 86 q^{15} - 109 q^{17} + 140 q^{19} + 20 q^{21} + 292 q^{23} + 812 q^{25} - 60 q^{27} + 101 q^{29} - 988 q^{31} - 226 q^{33} + 216 q^{35}+ \cdots - 8040 q^{99}+O(q^{100}) \) 22 * q + 10 * q^5 + 26 * q^7 - 117 * q^9 + 22 * q^11 + 37 * q^13 + 86 * q^15 - 109 * q^17 + 140 * q^19 + 20 * q^21 + 292 * q^23 + 812 * q^25 - 60 * q^27 + 101 * q^29 - 988 * q^31 - 226 * q^33 + 216 * q^35 - 223 * q^37 + 452 * q^39 - 117 * q^41 - 110 * q^43 - 453 * q^45 - 2300 * q^47 - 989 * q^49 + 2184 * q^51 + 98 * q^53 - 92 * q^55 - 100 * q^57 + 710 * q^59 + 281 * q^61 + 2008 * q^63 + 1785 * q^65 + 492 * q^67 + 358 * q^69 - 928 * q^71 - 906 * q^73 + 422 * q^75 - 780 * q^77 + 2936 * q^79 - 2971 * q^81 - 520 * q^83 + 1385 * q^85 + 4012 * q^87 + 1088 * q^89 - 662 * q^91 + 1180 * q^93 - 2742 * q^95 - 640 * q^97 - 8040 * q^99

Introduction

L-functions

Modular forms

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