LMFDB - Embedded newform 245.4.b.d.99.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,4,Mod(99,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("245.99");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	245.b (of order $2$, degree $1$, 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:	$14.4554679514$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 55x^{8} + 983x^{6} + 6409x^{4} + 13560x^{2} + 3600 $ x^10 + 55x^8 + 983x^6 + 6409x^4 + 13560x^2 + 3600
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3}\cdot 7^{4} $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.4
Root			$-2.67516i$ of defining polynomial
Character	$\chi$	$=$	245.99
Dual form			245.4.b.d.99.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.67516i q^{2} -2.49396i q^{3} +5.19383 q^{4} +(-6.35505 + 9.19855i) q^{5} -4.17779 q^{6} -22.1018i q^{8} +20.7802 q^{9} +(15.4091 + 10.6457i) q^{10} -57.5880 q^{11} -12.9532i q^{12} -45.5159i q^{13} +(22.9408 + 15.8492i) q^{15} +4.52655 q^{16} -92.0051i q^{17} -34.8101i q^{18} +125.177 q^{19} +(-33.0070 + 47.7757i) q^{20} +96.4692i q^{22} -158.496i q^{23} -55.1211 q^{24} +(-44.2268 - 116.914i) q^{25} -76.2466 q^{26} -119.162i q^{27} +40.1708 q^{29} +(26.5500 - 38.4296i) q^{30} -49.5590 q^{31} -184.397i q^{32} +143.622i q^{33} -154.123 q^{34} +107.929 q^{36} +231.307i q^{37} -209.692i q^{38} -113.515 q^{39} +(203.305 + 140.458i) q^{40} -169.556 q^{41} +147.428i q^{43} -299.102 q^{44} +(-132.059 + 191.147i) q^{45} -265.507 q^{46} +67.0327i q^{47} -11.2890i q^{48} +(-195.851 + 74.0870i) q^{50} -229.457 q^{51} -236.402i q^{52} -268.647i q^{53} -199.615 q^{54} +(365.974 - 529.726i) q^{55} -312.187i q^{57} -67.2926i q^{58} -240.843 q^{59} +(119.151 + 82.3183i) q^{60} -90.4579 q^{61} +83.0194i q^{62} -272.683 q^{64} +(418.681 + 289.256i) q^{65} +240.591 q^{66} -406.498i q^{67} -477.859i q^{68} -395.283 q^{69} +330.782 q^{71} -459.279i q^{72} +546.255i q^{73} +387.477 q^{74} +(-291.580 + 110.300i) q^{75} +650.149 q^{76} +190.156i q^{78} +25.3087 q^{79} +(-28.7664 + 41.6377i) q^{80} +263.879 q^{81} +284.034i q^{82} +376.255i q^{83} +(846.314 + 584.697i) q^{85} +246.965 q^{86} -100.184i q^{87} +1272.80i q^{88} +1026.44 q^{89} +(320.203 + 221.220i) q^{90} -823.203i q^{92} +123.598i q^{93} +112.291 q^{94} +(-795.506 + 1151.45i) q^{95} -459.879 q^{96} +942.660i q^{97} -1196.69 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 36 q^{4} - 6 q^{5} - 12 q^{6} - 46 q^{9} + 16 q^{10} + 84 q^{11} + 8 q^{15} + 148 q^{16} - 72 q^{19} + 68 q^{20} - 72 q^{24} - 362 q^{25} + 620 q^{26} + 88 q^{29} + 52 q^{30} - 120 q^{31} - 964 q^{34}+ \cdots - 5304 q^{99}+O(q^{100}) $ 10 * q - 36 * q^4 - 6 * q^5 - 12 * q^6 - 46 * q^9 + 16 * q^10 + 84 * q^11 + 8 * q^15 + 148 * q^16 - 72 * q^19 + 68 * q^20 - 72 * q^24 - 362 * q^25 + 620 * q^26 + 88 * q^29 + 52 * q^30 - 120 * q^31 - 964 * q^34 - 420 * q^36 + 212 * q^39 - 1396 * q^40 + 852 * q^41 - 1424 * q^44 + 510 * q^45 + 176 * q^46 + 1644 * q^50 + 1276 * q^51 + 996 * q^54 + 1136 * q^55 - 864 * q^59 - 1692 * q^60 + 884 * q^61 - 2724 * q^64 + 520 * q^65 - 1148 * q^66 - 4808 * q^69 + 880 * q^71 + 3024 * q^74 - 720 * q^75 + 2672 * q^76 - 3580 * q^79 + 2316 * q^80 - 302 * q^81 + 1572 * q^85 + 2432 * q^86 + 1492 * q^89 + 7748 * q^90 - 1652 * q^94 - 1628 * q^95 - 4080 * q^96 - 5304 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	1.67516i		−	0.592259i	−0.955148	−	0.296130i	$-0.904304\pi$
$2$		−	1.67516i		−	0.592259i	0.955148	−	0.296130i	$-0.0956960\pi$
$3$		−	2.49396i		−	0.479963i	−0.970777	−	0.239982i	$-0.922859\pi$
$3$		−	2.49396i		−	0.479963i	0.970777	−	0.239982i	$-0.0771414\pi$
$4$	5.19383			0.649229
$5$	−6.35505	+	9.19855i	−0.568413	+	0.822744i
$5$	−6.35505	+	9.19855i	−0.568413	+	0.822744i
$6$	−4.17779			−0.284263
$7$		0			0
$7$		0			0
$8$		−	22.1018i		−	0.976771i
$9$	20.7802			0.769635
$10$	15.4091	+	10.6457i	0.487278	+	0.336648i
$11$	−57.5880			−1.57849			−0.789247	−	0.614076i	$-0.789529\pi$
$11$	−57.5880			−1.57849			−0.789247	+	0.614076i	$0.789529\pi$
$12$		−	12.9532i		−	0.311606i
$13$		−	45.5159i		−	0.971066i	−0.874218	−	0.485533i	$-0.838626\pi$
$13$		−	45.5159i		−	0.971066i	0.874218	−	0.485533i	$-0.161374\pi$
$14$		0			0
$15$	22.9408	+	15.8492i	0.394887	+	0.272817i
$16$	4.52655			0.0707273
$17$		−	92.0051i		−	1.31262i	−0.754492	−	0.656309i	$-0.772117\pi$
$17$		−	92.0051i		−	1.31262i	0.754492	−	0.656309i	$-0.227883\pi$
$18$		−	34.8101i		−	0.455824i
$19$	125.177			1.51145			0.755726	−	0.654888i	$-0.227284\pi$
$19$	125.177			1.51145			0.755726	+	0.654888i	$0.227284\pi$
$20$	−33.0070	+	47.7757i	−0.369030	+	0.534149i
$21$		0			0
$22$			96.4692i			0.934878i
$23$		−	158.496i		−	1.43690i	−0.695578	−	0.718451i	$-0.744851\pi$
$23$		−	158.496i		−	1.43690i	0.695578	−	0.718451i	$-0.255149\pi$
$24$	−55.1211			−0.468814
$25$	−44.2268	−	116.914i	−0.353814	−	0.935316i
$26$	−76.2466			−0.575123
$27$		−	119.162i		−	0.849360i
$28$		0			0
$29$	40.1708			0.257225			0.128613	−	0.991695i	$-0.458948\pi$
$29$	40.1708			0.257225			0.128613	+	0.991695i	$0.458948\pi$
$30$	26.5500	−	38.4296i	0.161578	−	0.233875i
$31$	−49.5590			−0.287131			−0.143566	−	0.989641i	$-0.545857\pi$
$31$	−49.5590			−0.287131			−0.143566	+	0.989641i	$0.545857\pi$
$32$		−	184.397i		−	1.01866i
$33$			143.622i			0.757619i
$34$	−154.123			−0.777410
$35$		0			0
$36$	107.929			0.499670
$37$			231.307i			1.02775i	0.857866	+	0.513874i	$0.171790\pi$
$37$			231.307i			1.02775i	−0.857866	+	0.513874i	$0.828210\pi$
$38$		−	209.692i		−	0.895171i
$39$	−113.515			−0.466076
$40$	203.305	+	140.458i	0.803632	+	0.555209i
$41$	−169.556			−0.645859			−0.322929	−	0.946423i	$-0.604668\pi$
$41$	−169.556			−0.645859			−0.322929	+	0.946423i	$0.604668\pi$
$42$		0			0
$43$			147.428i			0.522849i	0.965224	+	0.261425i	$0.0841923\pi$
$43$			147.428i			0.522849i	−0.965224	+	0.261425i	$0.915808\pi$
$44$	−299.102			−1.02480
$45$	−132.059	+	191.147i	−0.437470	+	0.633213i
$46$	−265.507			−0.851018
$47$			67.0327i			0.208037i	0.994575	+	0.104018i	$0.0331701\pi$
$47$			67.0327i			0.208037i	−0.994575	+	0.104018i	$0.966830\pi$
$48$		−	11.2890i		−	0.0339465i
$49$		0			0
$50$	−195.851	+	74.0870i	−0.553949	+	0.209550i
$51$	−229.457			−0.630008
$52$		−	236.402i		−	0.630444i
$53$		−	268.647i		−	0.696254i	−0.937447	−	0.348127i	$-0.886818\pi$
$53$		−	268.647i		−	0.696254i	0.937447	−	0.348127i	$-0.113182\pi$
$54$	−199.615			−0.503041
$55$	365.974	−	529.726i	0.897236	−	1.29870i
$56$		0			0
$57$		−	312.187i		−	0.725441i
$58$		−	67.2926i		−	0.152344i
$59$	−240.843			−0.531442			−0.265721	−	0.964050i	$-0.585610\pi$
$59$	−240.843			−0.531442			−0.265721	+	0.964050i	$0.585610\pi$
$60$	119.151	+	82.3183i	0.256372	+	0.177121i
$61$	−90.4579			−0.189868			−0.0949340	−	0.995484i	$-0.530264\pi$
$61$	−90.4579			−0.189868			−0.0949340	+	0.995484i	$0.530264\pi$
$62$			83.0194i			0.170056i
$63$		0			0
$64$	−272.683			−0.532583
$65$	418.681	+	289.256i	0.798938	+	0.551966i
$66$	240.591			0.448707
$67$		−	406.498i		−	0.741218i	−0.928789	−	0.370609i	$-0.879149\pi$
$67$		−	406.498i		−	0.741218i	0.928789	−	0.370609i	$-0.120851\pi$
$68$		−	477.859i		−	0.852190i
$69$	−395.283			−0.689660
$70$		0			0
$71$	330.782			0.552910			0.276455	−	0.961027i	$-0.410840\pi$
$71$	330.782			0.552910			0.276455	+	0.961027i	$0.410840\pi$
$72$		−	459.279i		−	0.751758i
$73$			546.255i			0.875812i	0.899021	+	0.437906i	$0.144280\pi$
$73$			546.255i			0.875812i	−0.899021	+	0.437906i	$0.855720\pi$
$74$	387.477			0.608693
$75$	−291.580	+	110.300i	−0.448917	+	0.169818i
$76$	650.149			0.981279
$77$		0			0
$78$			190.156i			0.276038i
$79$	25.3087			0.0360436			0.0180218	−	0.999838i	$-0.494263\pi$
$79$	25.3087			0.0360436			0.0180218	+	0.999838i	$0.494263\pi$
$80$	−28.7664	+	41.6377i	−0.0402023	+	0.0581905i
$81$	263.879			0.361974
$82$			284.034i			0.382516i
$83$			376.255i			0.497582i	0.968557	+	0.248791i	$0.0800333\pi$
$83$			376.255i			0.497582i	−0.968557	+	0.248791i	$0.919967\pi$
$84$		0			0
$85$	846.314	+	584.697i	1.07995	+	0.746109i
$86$	246.965			0.309662
$87$		−	100.184i		−	0.123459i
$88$			1272.80i			1.54183i
$89$	1026.44			1.22250			0.611248	−	0.791439i	$-0.290668\pi$
$89$	1026.44			1.22250			0.611248	+	0.791439i	$0.290668\pi$
$90$	320.203	+	221.220i	0.375026	+	0.259096i
$91$		0			0
$92$		−	823.203i		−	0.932878i
$93$			123.598i			0.137812i
$94$	112.291			0.123212
$95$	−795.506	+	1151.45i	−0.859128	+	1.24354i
$96$	−459.879			−0.488919
$97$			942.660i			0.986728i	0.869823	+	0.493364i	$0.164233\pi$
$97$			942.660i			0.986728i	−0.869823	+	0.493364i	$0.835767\pi$
$98$		0			0
$99$	−1196.69			−1.21487
$100$	−229.706	−	607.234i	−0.229706	−	0.607234i
$101$	604.617			0.595659			0.297830	−	0.954619i	$-0.403737\pi$
$101$	604.617			0.595659			0.297830	+	0.954619i	$0.403737\pi$
$102$			384.378i			0.373128i
$103$		−	300.967i		−	0.287914i	−0.989584	−	0.143957i	$-0.954017\pi$
$103$		−	300.967i		−	0.287914i	0.989584	−	0.143957i	$-0.0459828\pi$
$104$	−1005.98			−0.948509
$105$		0			0
$106$	−450.027			−0.412363
$107$			1511.66i			1.36577i	0.730525	+	0.682886i	$0.239276\pi$
$107$			1511.66i			1.36577i	−0.730525	+	0.682886i	$0.760724\pi$
$108$		−	618.907i		−	0.551429i
$109$	1767.09			1.55281			0.776406	−	0.630233i	$-0.217041\pi$
$109$	1767.09			1.55281			0.776406	+	0.630233i	$0.217041\pi$
$110$	−887.377	−	613.066i	−0.769165	−	0.531396i
$111$	576.871			0.493281
$112$		0			0
$113$		−	1045.27i		−	0.870182i	−0.900387	−	0.435091i	$-0.856716\pi$
$113$		−	1045.27i		−	0.870182i	0.900387	−	0.435091i	$-0.143284\pi$
$114$	−522.963			−0.429649
$115$	1457.94	+	1007.25i	1.18220	+	0.816753i
$116$	208.640			0.166998
$117$		−	945.828i		−	0.747366i
$118$			403.451i			0.314751i
$119$		0			0
$120$	350.297	−	507.034i	0.266480	−	0.385714i
$121$	1985.38			1.49164
$122$			151.532i			0.112451i
$123$			422.866i			0.309988i
$124$	−257.401			−0.186414
$125$	1356.51	+	336.174i	0.970638	+	0.240547i
$126$		0			0
$127$			260.727i			0.182171i	0.995843	+	0.0910857i	$0.0290337\pi$
$127$			260.727i			0.182171i	−0.995843	+	0.0910857i	$0.970966\pi$
$128$		−	1018.39i		−	0.703233i
$129$	367.679			0.250948
$130$	484.551	−	701.358i	0.326907	−	0.473178i
$131$	723.522			0.482553			0.241276	−	0.970456i	$-0.422434\pi$
$131$	723.522			0.482553			0.241276	+	0.970456i	$0.422434\pi$
$132$			745.950i			0.491868i
$133$		0			0
$134$	−680.950			−0.438993
$135$	1096.12	+	757.279i	0.698805	+	0.482787i
$136$	−2033.48			−1.28213
$137$			773.693i			0.482490i	0.970464	+	0.241245i	$0.0775557\pi$
$137$			773.693i			0.482490i	−0.970464	+	0.241245i	$0.922444\pi$
$138$			662.164i			0.408457i
$139$	−2952.97			−1.80192			−0.900961	−	0.433899i	$-0.857137\pi$
$139$	−2952.97			−1.80192			−0.900961	+	0.433899i	$0.857137\pi$
$140$		0			0
$141$	167.177			0.0998499
$142$		−	554.114i		−	0.327466i
$143$			2621.17i			1.53282i
$144$	94.0624			0.0544343
$145$	−255.287	+	369.513i	−0.146210	+	0.211630i
$146$	915.066			0.518708
$147$		0			0
$148$			1201.37i			0.667244i
$149$	−2514.00			−1.38225			−0.691124	−	0.722736i	$-0.742884\pi$
$149$	−2514.00			−1.38225			−0.691124	+	0.722736i	$0.742884\pi$
$150$	184.770	+	488.444i	0.100576	+	0.265875i
$151$	101.052			0.0544605			0.0272302	−	0.999629i	$-0.491331\pi$
$151$	101.052			0.0544605			0.0272302	+	0.999629i	$0.491331\pi$
$152$		−	2766.64i		−	1.47634i
$153$		−	1911.88i		−	1.01024i
$154$		0			0
$155$	314.950	−	455.872i	0.163209	−	0.236235i
$156$	−589.578			−0.302590
$157$		−	2338.35i		−	1.18867i	−0.804219	−	0.594333i	$-0.797416\pi$
$157$		−	2338.35i		−	1.18867i	0.804219	−	0.594333i	$-0.202584\pi$
$158$		−	42.3961i		−	0.0213472i
$159$	−669.995			−0.334176
$160$	1696.19	+	1171.85i	0.838096	+	0.579019i
$161$		0			0
$162$		−	442.040i		−	0.214383i
$163$			1325.20i			0.636798i	0.947957	+	0.318399i	$0.103145\pi$
$163$			1325.20i			0.636798i	−0.947957	+	0.318399i	$0.896855\pi$
$164$	−880.646			−0.419310
$165$	−1321.12	−	912.726i	−0.623326	−	0.430640i
$166$	630.288			0.294698
$167$		−	2086.20i		−	0.966675i	−0.875434	−	0.483338i	$-0.839424\pi$
$167$		−	2086.20i		−	0.966675i	0.875434	−	0.483338i	$-0.160576\pi$
$168$		0			0
$169$	125.299			0.0570317
$170$	979.462	−	1417.71i	0.441890	−	0.639609i
$171$	2601.20			1.16327
$172$			765.715i			0.339449i
$173$			1918.19i			0.842990i	0.906831	+	0.421495i	$0.138495\pi$
$173$			1918.19i			0.842990i	−0.906831	+	0.421495i	$0.861505\pi$
$174$	−167.825			−0.0731195
$175$		0			0
$176$	−260.675			−0.111643
$177$			600.652i			0.255072i
$178$		−	1719.45i		−	0.724035i
$179$	−629.046			−0.262665			−0.131333	−	0.991338i	$-0.541926\pi$
$179$	−629.046			−0.262665			−0.131333	+	0.991338i	$0.541926\pi$
$180$	−685.891	+	992.787i	−0.284019	+	0.411100i
$181$	2800.85			1.15020			0.575099	−	0.818084i	$-0.304964\pi$
$181$	2800.85			1.15020			0.575099	+	0.818084i	$0.304964\pi$
$182$		0			0
$183$			225.599i			0.0911296i
$184$	−3503.05			−1.40352
$185$	−2127.69	−	1469.97i	−0.845573	−	0.584185i
$186$	207.047			0.0816207
$187$			5298.39i			2.07196i
$188$			348.157i			0.135063i
$189$		0			0
$190$	1928.86	+	1332.60i	0.736497	+	0.508827i
$191$	740.255			0.280434			0.140217	−	0.990121i	$-0.455220\pi$
$191$	740.255			0.280434			0.140217	+	0.990121i	$0.455220\pi$
$192$			680.060i			0.255620i
$193$		−	4082.57i		−	1.52264i	−0.648375	−	0.761321i	$-0.724551\pi$
$193$		−	4082.57i		−	1.52264i	0.648375	−	0.761321i	$-0.275449\pi$
$194$	1579.11			0.584399
$195$	721.393	−	1044.17i	0.264923	−	0.383461i
$196$		0			0
$197$			3414.89i			1.23503i	0.786559	+	0.617515i	$0.211860\pi$
$197$			3414.89i			1.23503i	−0.786559	+	0.617515i	$0.788140\pi$
$198$			2004.65i			0.719515i
$199$	−3392.44			−1.20846			−0.604231	−	0.796809i	$-0.706520\pi$
$199$	−3392.44			−1.20846			−0.604231	+	0.796809i	$0.706520\pi$
$200$	−2584.02	+	977.492i	−0.913589	+	0.345596i
$201$	−1013.79			−0.355757
$202$		−	1012.83i		−	0.352785i
$203$		0			0
$204$	−1191.76			−0.409020
$205$	1077.54	−	1559.67i	0.367114	−	0.531376i
$206$	−504.169			−0.170520
$207$		−	3293.58i		−	1.10589i
$208$		−	206.030i		−	0.0686809i
$209$	−7208.70			−2.38582
$210$		0			0
$211$	3398.04			1.10867			0.554337	−	0.832292i	$-0.312972\pi$
$211$	3398.04			1.10867			0.554337	+	0.832292i	$0.312972\pi$
$212$		−	1395.31i		−	0.452029i
$213$		−	824.958i		−	0.265376i
$214$	2532.28			0.808892
$215$	−1356.12	−	936.910i	−0.430171	−	0.297194i
$216$	−2633.69			−0.829630
$217$		0			0
$218$		−	2960.16i		−	0.919667i
$219$	1362.34			0.420358
$220$	1900.81	−	2751.31i	0.582512	−	0.843151i
$221$	−4187.70			−1.27464
$222$		−	966.353i		−	0.292150i
$223$			182.611i			0.0548365i	0.999624	+	0.0274183i	$0.00872860\pi$
$223$			182.611i			0.0548365i	−0.999624	+	0.0274183i	$0.991271\pi$
$224$		0			0
$225$	−919.040	−	2429.50i	−0.272308	−	0.719852i
$226$	−1750.99			−0.515373
$227$			3152.33i			0.921707i	0.887476	+	0.460854i	$0.152457\pi$
$227$			3152.33i			0.921707i	−0.887476	+	0.460854i	$0.847543\pi$
$228$		−	1621.45i		−	0.470977i
$229$	6012.35			1.73497			0.867483	−	0.497466i	$-0.165736\pi$
$229$	6012.35			1.73497			0.867483	+	0.497466i	$0.165736\pi$
$230$	1687.31	−	2442.28i	0.483730	−	0.700170i
$231$		0			0
$232$		−	887.848i		−	0.251250i
$233$			940.660i			0.264484i	0.991217	+	0.132242i	$0.0422175\pi$
$233$			940.660i			0.264484i	−0.991217	+	0.132242i	$0.957782\pi$
$234$	−1584.42			−0.442635
$235$	−616.604	−	425.996i	−0.171161	−	0.118251i
$236$	−1250.90			−0.345027
$237$		−	63.1188i		−	0.0172996i
$238$		0			0
$239$	−5158.82			−1.39622			−0.698109	−	0.715991i	$-0.745975\pi$
$239$	−5158.82			−1.39622			−0.698109	+	0.715991i	$0.745975\pi$
$240$	103.843	+	71.7423i	0.0279293	+	0.0192956i
$241$	463.836			0.123976			0.0619882	−	0.998077i	$-0.480256\pi$
$241$	463.836			0.123976			0.0619882	+	0.998077i	$0.480256\pi$
$242$		−	3325.83i		−	0.883440i
$243$		−	3875.47i		−	1.02309i
$244$	−469.823			−0.123268
$245$		0			0
$246$	708.370			0.183594
$247$		−	5697.55i		−	1.46772i
$248$			1095.34i			0.280461i
$249$	938.365			0.238821
$250$	563.146	−	2272.37i	0.142466	−	0.574869i
$251$	−2290.25			−0.575934			−0.287967	−	0.957640i	$-0.592979\pi$
$251$	−2290.25			−0.575934			−0.287967	+	0.957640i	$0.592979\pi$
$252$		0			0
$253$			9127.48i			2.26814i
$254$	436.760			0.107893
$255$	1458.21	−	2110.67i	0.358105	−	0.518335i
$256$	−3887.43			−0.949079
$257$			802.202i			0.194708i	0.995250	+	0.0973541i	$0.0310379\pi$
$257$			802.202i			0.194708i	−0.995250	+	0.0973541i	$0.968962\pi$
$258$		−	615.922i		−	0.148627i
$259$		0			0
$260$	2174.56	+	1502.35i	0.518694	+	0.358352i
$261$	834.756			0.197970
$262$		−	1212.02i		−	0.285796i
$263$			286.978i			0.0672845i	0.999434	+	0.0336423i	$0.0107107\pi$
$263$			286.978i			0.0672845i	−0.999434	+	0.0336423i	$0.989289\pi$
$264$	3174.31			0.740020
$265$	2471.16	+	1707.26i	0.572839	+	0.395760i
$266$		0			0
$267$		−	2559.90i		−	0.586753i
$268$		−	2111.28i		−	0.481221i
$269$	3561.22			0.807180			0.403590	−	0.914940i	$-0.367762\pi$
$269$	3561.22			0.807180			0.403590	+	0.914940i	$0.367762\pi$
$270$	1268.57	−	1836.17i	0.285935	−	0.413874i
$271$	−1928.81			−0.432349			−0.216175	−	0.976355i	$-0.569358\pi$
$271$	−1928.81			−0.432349			−0.216175	+	0.976355i	$0.569358\pi$
$272$		−	416.466i		−	0.0928380i
$273$		0			0
$274$	1296.06			0.285759
$275$	2546.93	+	6732.87i	0.558494	+	1.47639i
$276$	−2053.04			−0.447747
$277$			6588.69i			1.42916i	0.699556	+	0.714578i	$0.253381\pi$
$277$			6588.69i			1.42916i	−0.699556	+	0.714578i	$0.746619\pi$
$278$			4946.70i			1.06721i
$279$	−1029.84			−0.220986
$280$		0			0
$281$	815.552			0.173138			0.0865689	−	0.996246i	$-0.472410\pi$
$281$	815.552			0.173138			0.0865689	+	0.996246i	$0.472410\pi$
$282$		−	280.049i		−	0.0591371i
$283$		−	6513.49i		−	1.36815i	−0.729411	−	0.684076i	$-0.760206\pi$
$283$		−	6513.49i		−	1.36815i	0.729411	−	0.684076i	$-0.239794\pi$
$284$	1718.03			0.358965
$285$	2871.67	+	1983.96i	0.596852	+	0.412350i
$286$	4390.89			0.907828
$287$		0			0
$288$		−	3831.80i		−	0.783997i
$289$	−3551.94			−0.722967
$290$	618.995	+	427.648i	0.125340	+	0.0865943i
$291$	2350.96			0.473593
$292$			2837.16i			0.568603i
$293$			435.520i			0.0868373i	0.999057	+	0.0434186i	$0.0138249\pi$
$293$			435.520i			0.0868373i	−0.999057	+	0.0434186i	$0.986175\pi$
$294$		0			0
$295$	1530.57	−	2215.40i	0.302078	−	0.437240i
$296$	5112.31			1.00387
$297$			6862.29i			1.34071i
$298$			4211.36i			0.818650i
$299$	−7214.10			−1.39533
$300$	−1514.42	+	572.879i	−0.291450	+	0.110251i
$301$		0			0
$302$		−	169.279i		−	0.0322547i
$303$		−	1507.89i		−	0.285895i
$304$	566.620			0.106901
$305$	574.864	−	832.082i	0.107923	−	0.156213i
$306$	−3202.71			−0.598323
$307$			4915.99i			0.913910i	0.889490	+	0.456955i	$0.151060\pi$
$307$			4915.99i			0.913910i	−0.889490	+	0.456955i	$0.848940\pi$
$308$		0			0
$309$	−750.601			−0.138188
$310$	−763.659	−	527.592i	−0.139913	−	0.0966620i
$311$	1831.11			0.333868			0.166934	−	0.985968i	$-0.446613\pi$
$311$	1831.11			0.333868			0.166934	+	0.985968i	$0.446613\pi$
$312$			2508.89i			0.455249i
$313$		−	2442.96i		−	0.441163i	−0.975369	−	0.220582i	$-0.929204\pi$
$313$		−	2442.96i		−	0.441163i	0.975369	−	0.220582i	$-0.0707955\pi$
$314$	−3917.11			−0.703998
$315$		0			0
$316$	131.449			0.0234006
$317$			1666.19i			0.295214i	0.989046	+	0.147607i	$0.0471570\pi$
$317$			1666.19i			0.295214i	−0.989046	+	0.147607i	$0.952843\pi$
$318$			1122.35i			0.197919i
$319$	−2313.36			−0.406029
$320$	1732.91	−	2508.29i	0.302727	−	0.438180i
$321$	3770.02			0.655521
$322$		0			0
$323$		−	11516.9i		−	1.98396i
$324$	1370.54			0.235004
$325$	−5321.47	+	2013.02i	−0.908253	+	0.343577i
$326$	2219.93			0.377149
$327$		−	4407.05i		−	0.745292i
$328$			3747.50i			0.630856i
$329$		0			0
$330$	−1528.96	+	2213.09i	−0.255051	+	0.369171i
$331$	−5466.38			−0.907732			−0.453866	−	0.891070i	$-0.649956\pi$
$331$	−5466.38			−0.907732			−0.453866	+	0.891070i	$0.649956\pi$
$332$			1954.20i			0.323045i
$333$			4806.60i			0.790991i
$334$	−3494.72			−0.572522
$335$	3739.19	+	2583.31i	0.609833	+	0.421318i
$336$		0			0
$337$			10650.5i			1.72157i	0.508970	+	0.860784i	$0.330027\pi$
$337$			10650.5i			1.72157i	−0.508970	+	0.860784i	$0.669973\pi$
$338$		−	209.896i		−	0.0337776i
$339$	−2606.86			−0.417655
$340$	4395.61	+	3036.82i	0.701134	+	0.484395i
$341$	2854.01			0.453235
$342$		−	4357.43i		−	0.688956i
$343$		0			0
$344$	3258.42			0.510704
$345$	2512.04	−	3636.04i	0.392011	−	0.567413i
$346$	3213.28			0.499269
$347$			4019.13i			0.621782i	0.950446	+	0.310891i	$0.100627\pi$
$347$			4019.13i			0.621782i	−0.950446	+	0.310891i	$0.899373\pi$
$348$		−	520.341i		−	0.0801529i
$349$	10544.9			1.61735			0.808674	−	0.588256i	$-0.200185\pi$
$349$	10544.9			1.61735			0.808674	+	0.588256i	$0.200185\pi$
$350$		0			0
$351$	−5423.76			−0.824784
$352$			10619.1i			1.60795i
$353$			2959.98i			0.446300i	0.974784	+	0.223150i	$0.0716340\pi$
$353$			2959.98i			0.446300i	−0.974784	+	0.223150i	$0.928366\pi$
$354$	1006.19			0.151069
$355$	−2102.14	+	3042.72i	−0.314281	+	0.454903i
$356$	5331.14			0.793680
$357$		0			0
$358$			1053.75i			0.155566i
$359$	−2170.17			−0.319045			−0.159523	−	0.987194i	$-0.550995\pi$
$359$	−2170.17			−0.319045			−0.159523	+	0.987194i	$0.550995\pi$
$360$	4224.70	+	2918.74i	0.618504	+	0.427309i
$361$	8810.30			1.28449
$362$		−	4691.88i		−	0.681215i
$363$		−	4951.46i		−	0.715934i
$364$		0			0
$365$	−5024.76	−	3471.48i	−0.720569	−	0.497823i
$366$	377.914			0.0539724
$367$			1252.20i			0.178105i	0.996027	+	0.0890523i	$0.0283838\pi$
$367$			1252.20i			0.178105i	−0.996027	+	0.0890523i	$0.971616\pi$
$368$		−	717.441i		−	0.101628i
$369$	−3523.40			−0.497076
$370$	−2462.43	+	3564.23i	−0.345989	+	0.500798i
$371$		0			0
$372$			641.949i			0.0894718i
$373$		−	4646.02i		−	0.644938i	−0.946580	−	0.322469i	$-0.895487\pi$
$373$		−	4646.02i		−	0.644938i	0.946580	−	0.322469i	$-0.104513\pi$
$374$	8875.66			1.22714
$375$	838.406	−	3383.08i	0.115454	−	0.465870i
$376$	1481.54			0.203204
$377$		−	1828.41i		−	0.249783i
$378$		0			0
$379$	−1434.84			−0.194466			−0.0972331	−	0.995262i	$-0.530999\pi$
$379$	−1434.84			−0.194466			−0.0972331	+	0.995262i	$0.530999\pi$
$380$	−4131.72	+	5980.43i	−0.557771	+	0.807341i
$381$	650.242			0.0874355
$382$		−	1240.05i		−	0.166090i
$383$		−	13216.7i		−	1.76330i	−0.471905	−	0.881649i	$-0.656434\pi$
$383$		−	13216.7i		−	1.76330i	0.471905	−	0.881649i	$-0.343566\pi$
$384$	−2539.82			−0.337526
$385$		0			0
$386$	−6838.97			−0.901799
$387$			3063.57i			0.402403i
$388$			4896.02i			0.640612i
$389$	7755.01			1.01078			0.505391	−	0.862890i	$-0.331348\pi$
$389$	7755.01			1.01078			0.505391	+	0.862890i	$0.331348\pi$
$390$	−1749.16	−	1208.45i	−0.227108	−	0.156903i
$391$	−14582.5			−1.88610
$392$		0			0
$393$		−	1804.44i		−	0.231607i
$394$	5720.49			0.731457
$395$	−160.838	+	232.803i	−0.0204876	+	0.0296547i
$396$	−6215.40			−0.788726
$397$			3560.83i			0.450158i	0.974341	+	0.225079i	$0.0722640\pi$
$397$			3560.83i			0.450158i	−0.974341	+	0.225079i	$0.927736\pi$
$398$			5682.89i			0.715723i
$399$		0			0
$400$	−200.195	−	529.219i	−0.0250243	−	0.0661524i
$401$	−5430.61			−0.676288			−0.338144	−	0.941094i	$-0.609799\pi$
$401$	−5430.61			−0.676288			−0.338144	+	0.941094i	$0.609799\pi$
$402$			1698.26i			0.210701i
$403$			2255.73i			0.278823i
$404$	3140.28			0.386719
$405$	−1676.96	+	2427.31i	−0.205751	+	0.297812i
$406$		0			0
$407$		−	13320.5i		−	1.62229i
$408$			5071.42i			0.615374i
$409$	−9698.79			−1.17255			−0.586277	−	0.810111i	$-0.699407\pi$
$409$	−9698.79			−1.17255			−0.586277	+	0.810111i	$0.699407\pi$
$410$	−2612.70	−	1805.05i	−0.314713	−	0.217427i
$411$	1929.56			0.231577
$412$		−	1563.17i		−	0.186922i
$413$		0			0
$414$	−5517.27			−0.654974
$415$	−3461.00	−	2391.12i	−0.409383	−	0.282832i
$416$	−8393.01			−0.989186
$417$			7364.58i			0.864856i
$418$			12075.7i			1.41302i
$419$	13830.9			1.61261			0.806307	−	0.591498i	$-0.201463\pi$
$419$	13830.9			1.61261			0.806307	+	0.591498i	$0.201463\pi$
$420$		0			0
$421$	16703.0			1.93362			0.966810	−	0.255498i	$-0.0822393\pi$
$421$	16703.0			1.93362			0.966810	+	0.255498i	$0.0822393\pi$
$422$		−	5692.26i		−	0.656623i
$423$			1392.95i			0.160112i
$424$	−5937.58			−0.680081
$425$	−10756.7	+	4069.09i	−1.22771	+	0.464423i
$426$	−1381.94			−0.157172
$427$		0			0
$428$			7851.31i			0.886699i
$429$	6537.10			0.735698
$430$	−1569.48	+	2271.72i	−0.176016	+	0.254773i
$431$	8174.07			0.913530			0.456765	−	0.889588i	$-0.349008\pi$
$431$	8174.07			0.913530			0.456765	+	0.889588i	$0.349008\pi$
$432$		−	539.392i		−	0.0600729i
$433$			14222.8i			1.57853i	0.614051	+	0.789267i	$0.289539\pi$
$433$			14222.8i			1.57853i	−0.614051	+	0.789267i	$0.710461\pi$
$434$		0			0
$435$	921.552	+	636.677i	0.101575	+	0.0701755i
$436$	9177.96			1.00813
$437$		−	19840.1i		−	2.17181i
$438$		−	2282.14i		−	0.248961i
$439$	5537.38			0.602016			0.301008	−	0.953622i	$-0.402677\pi$
$439$	5537.38			0.602016			0.301008	+	0.953622i	$0.402677\pi$
$440$	−11707.9	−	8088.70i	−1.26853	−	0.876394i
$441$		0			0
$442$			7015.07i			0.754916i
$443$		−	3974.09i		−	0.426218i	−0.977028	−	0.213109i	$-0.931641\pi$
$443$		−	3974.09i		−	0.426218i	0.977028	−	0.213109i	$-0.0683589\pi$
$444$	2996.17			0.320252
$445$	−6523.06	+	9441.74i	−0.694882	+	1.00580i
$446$	305.903			0.0324774
$447$			6269.82i			0.663428i
$448$		0			0
$449$	15243.1			1.60216			0.801078	−	0.598559i	$-0.204260\pi$
$449$	15243.1			1.60216			0.801078	+	0.598559i	$0.204260\pi$
$450$	−4069.81	+	1539.54i	−0.426339	+	0.161277i
$451$	9764.40			1.01948
$452$		−	5428.95i		−	0.564947i
$453$		−	252.021i		−	0.0261390i
$454$	5280.67			0.545890
$455$		0			0
$456$	−6899.89			−0.708590
$457$		−	10768.9i		−	1.10229i	−0.834410	−	0.551145i	$-0.814191\pi$
$457$		−	10768.9i		−	1.10229i	0.834410	−	0.551145i	$-0.185809\pi$
$458$		−	10071.7i		−	1.02755i
$459$	−10963.5			−1.11489
$460$	7572.27	+	5231.49i	0.767520	+	0.530260i
$461$	332.605			0.0336029			0.0168015	−	0.999859i	$-0.494652\pi$
$461$	332.605			0.0336029			0.0168015	+	0.999859i	$0.494652\pi$
$462$		0			0
$463$			8205.35i			0.823618i	0.911270	+	0.411809i	$0.135103\pi$
$463$			8205.35i			0.823618i	−0.911270	+	0.411809i	$0.864897\pi$
$464$	181.835			0.0181929
$465$	−1136.93	−	785.473i	−0.113384	−	0.0783343i
$466$	1575.76			0.156643
$467$			167.628i			0.0166100i	0.999966	+	0.00830501i	$0.00264360\pi$
$467$			167.628i			0.0166100i	−0.999966	+	0.00830501i	$0.997356\pi$
$468$		−	4912.47i		−	0.485212i
$469$		0			0
$470$	−713.612	+	1032.91i	−0.0700351	+	0.101372i
$471$	−5831.75			−0.570515
$472$			5323.06i			0.519097i
$473$		−	8490.07i		−	0.825315i
$474$	−105.734			−0.0102459
$475$	−5536.18	−	14635.0i	−0.534773	−	1.41368i
$476$		0			0
$477$		−	5582.52i		−	0.535862i
$478$			8641.86i			0.826924i
$479$	6628.58			0.632292			0.316146	−	0.948711i	$-0.397611\pi$
$479$	6628.58			0.632292			0.316146	+	0.948711i	$0.397611\pi$
$480$	2922.55	−	4230.23i	0.277908	−	0.402255i
$481$	10528.2			0.998010
$482$		−	777.001i		−	0.0734262i
$483$		0			0
$484$	10311.7			0.968419
$485$	−8671.11	−	5990.65i	−0.811824	−	0.560868i
$486$	−6492.05			−0.605937
$487$		−	20641.6i		−	1.92065i	−0.278875	−	0.960327i	$-0.589961\pi$
$487$		−	20641.6i		−	1.92065i	0.278875	−	0.960327i	$-0.410039\pi$
$488$			1999.28i			0.185458i
$489$	3305.01			0.305640
$490$		0			0
$491$	−16710.8			−1.53594			−0.767972	−	0.640484i	$-0.778734\pi$
$491$	−16710.8			−1.53594			−0.767972	+	0.640484i	$0.778734\pi$
$492$			2196.30i			0.201253i
$493$		−	3695.92i		−	0.337639i
$494$	−9544.32			−0.869270
$495$	7605.01	−	11007.8i	0.690545	−	0.999523i
$496$	−224.331			−0.0203080
$497$		0			0
$498$		−	1571.91i		−	0.141444i
$499$	13728.7			1.23162			0.615812	−	0.787893i	$-0.288828\pi$
$499$	13728.7			1.23162			0.615812	+	0.787893i	$0.288828\pi$
$500$	7045.47	+	1746.03i	0.630166	+	0.156170i
$501$	−5202.90			−0.463969
$502$			3836.54i			0.341102i
$503$		−	19523.7i		−	1.73065i	−0.501209	−	0.865326i	$-0.667111\pi$
$503$		−	19523.7i		−	1.73065i	0.501209	−	0.865326i	$-0.332889\pi$
$504$		0			0
$505$	−3842.37	+	5561.60i	−0.338580	+	0.490075i
$506$	15290.0			1.34333
$507$		−	312.490i		−	0.0273731i
$508$			1354.17i			0.118271i
$509$	−8688.17			−0.756574			−0.378287	−	0.925688i	$-0.623487\pi$
$509$	−8688.17			−0.756574			−0.378287	+	0.925688i	$0.623487\pi$
$510$	−3535.72	−	2442.74i	−0.306989	−	0.212091i
$511$		0			0
$512$		−	1635.04i		−	0.141131i
$513$		−	14916.3i		−	1.28377i
$514$	1343.82			0.115318
$515$	2768.46	+	1912.66i	0.236880	+	0.163654i
$516$	1909.66			0.162923
$517$		−	3860.28i		−	0.328385i
$518$		0			0
$519$	4783.89			0.404604
$520$	6393.08	−	9253.60i	0.539144	−	0.780380i
$521$	−6771.36			−0.569402			−0.284701	−	0.958616i	$-0.591894\pi$
$521$	−6771.36			−0.569402			−0.284701	+	0.958616i	$0.591894\pi$
$522$		−	1398.35i		−	0.117249i
$523$		−	1365.89i		−	0.114200i	−0.998368	−	0.0570998i	$-0.981815\pi$
$523$		−	1365.89i		−	0.114200i	0.998368	−	0.0570998i	$-0.0181853\pi$
$524$	3757.85			0.313287
$525$		0			0
$526$	480.735			0.0398499
$527$			4559.68i			0.376894i
$528$			650.113i			0.0535844i
$529$	−12954.0			−1.06469
$530$	2859.94	−	4139.60i	0.234392	−	0.339269i
$531$	−5004.75			−0.409016
$532$		0			0
$533$			7717.51i			0.627171i
$534$	−4288.24			−0.347510
$535$	−13905.1	−	9606.67i	−1.12368	−	0.776322i
$536$	−8984.34			−0.724001
$537$			1568.82i			0.126070i
$538$		−	5965.62i		−	0.478060i
$539$		0			0
$540$	5693.05	+	3933.18i	0.453685	+	0.313439i
$541$	−23250.1			−1.84769			−0.923844	−	0.382770i	$-0.874970\pi$
$541$	−23250.1			−1.84769			−0.923844	+	0.382770i	$0.874970\pi$
$542$			3231.06i			0.256063i
$543$		−	6985.22i		−	0.552052i
$544$	−16965.5			−1.33711
$545$	−11229.9	+	16254.7i	−0.882638	+	1.27757i
$546$		0			0
$547$		−	11552.7i		−	0.903033i	−0.892263	−	0.451516i	$-0.850883\pi$
$547$		−	11552.7i		−	0.903033i	0.892263	−	0.451516i	$-0.149117\pi$
$548$			4018.43i			0.313246i
$549$	−1879.73			−0.146129
$550$	11278.6	−	4266.52i	0.874406	−	0.330773i
$551$	5028.47			0.388784
$552$			8736.48i			0.673640i
$553$		0			0
$554$	11037.1			0.846430
$555$	−3666.04	+	5306.38i	−0.280387	+	0.405844i
$556$	−15337.2			−1.16986
$557$		−	16406.2i		−	1.24803i	−0.781413	−	0.624014i	$-0.785501\pi$
$557$		−	16406.2i		−	1.24803i	0.781413	−	0.624014i	$-0.214499\pi$
$558$			1725.16i			0.130881i
$559$	6710.31			0.507721
$560$		0			0
$561$	13214.0			0.994465
$562$		−	1366.18i		−	0.102542i
$563$			13631.9i			1.02045i	0.860040	+	0.510227i	$0.170439\pi$
$563$			13631.9i			1.02045i	−0.860040	+	0.510227i	$0.829561\pi$
$564$	868.289			0.0648255
$565$	9614.95	+	6642.72i	0.715936	+	0.494622i
$566$	−10911.2			−0.810300
$567$		0			0
$568$		−	7310.88i		−	0.540067i
$569$	3086.83			0.227428			0.113714	−	0.993514i	$-0.463725\pi$
$569$	3086.83			0.227428			0.113714	+	0.993514i	$0.463725\pi$
$570$	3323.46	−	4810.51i	0.244218	−	0.353491i
$571$	−3258.06			−0.238784			−0.119392	−	0.992847i	$-0.538095\pi$
$571$	−3258.06			−0.238784			−0.119392	+	0.992847i	$0.538095\pi$
$572$			13613.9i			0.995152i
$573$		−	1846.17i		−	0.134598i
$574$		0			0
$575$	−18530.5	+	7009.78i	−1.34396	+	0.508396i
$576$	−5666.39			−0.409895
$577$		−	23758.4i		−	1.71417i	−0.515178	−	0.857083i	$-0.672274\pi$
$577$		−	23758.4i		−	1.71417i	0.515178	−	0.857083i	$-0.327726\pi$
$578$			5950.07i			0.428184i
$579$	−10181.8			−0.730812
$580$	−1325.92	+	1919.19i	−0.0949238	+	0.137397i
$581$		0			0
$582$		−	3938.23i		−	0.280490i
$583$			15470.8i			1.09903i
$584$	12073.2			0.855468
$585$	8700.25	+	6010.78i	0.614891	+	0.424812i
$586$	729.566			0.0514302
$587$		−	596.893i		−	0.0419701i	−0.999780	−	0.0209850i	$-0.993320\pi$
$587$		−	596.893i		−	0.0419701i	0.999780	−	0.0209850i	$-0.00668023\pi$
$588$		0			0
$589$	−6203.66			−0.433985
$590$	−3711.16	−	2563.95i	−0.258960	−	0.178909i
$591$	8516.60			0.592768
$592$			1047.02i			0.0726898i
$593$			19496.3i			1.35012i	0.737765	+	0.675058i	$0.235881\pi$
$593$			19496.3i			1.35012i	−0.737765	+	0.675058i	$0.764119\pi$
$594$	11495.5			0.794047
$595$		0			0
$596$	−13057.3			−0.897396
$597$			8460.62i			0.580017i
$598$			12084.8i			0.826395i
$599$	−3797.02			−0.259001			−0.129501	−	0.991579i	$-0.541337\pi$
$599$	−3797.02			−0.259001			−0.129501	+	0.991579i	$0.541337\pi$
$600$	2437.83	+	6444.45i	0.165873	+	0.438489i
$601$	−5789.33			−0.392931			−0.196466	−	0.980511i	$-0.562946\pi$
$601$	−5789.33			−0.392931			−0.196466	+	0.980511i	$0.562946\pi$
$602$		0			0
$603$		−	8447.09i		−	0.570468i
$604$	524.850			0.0353573
$605$	−12617.2	+	18262.6i	−0.847869	+	1.22724i
$606$	−2525.96			−0.169324
$607$		−	18536.4i		−	1.23949i	−0.784803	−	0.619745i	$-0.787236\pi$
$607$		−	18536.4i		−	1.23949i	0.784803	−	0.619745i	$-0.212764\pi$
$608$		−	23082.3i		−	1.53966i
$609$		0			0
$610$	−1393.87	−	962.991i	−0.0925184	−	0.0639186i
$611$	3051.06			0.202017
$612$		−	9929.98i		−	0.655876i
$613$		−	2163.47i		−	0.142548i	−0.997457	−	0.0712738i	$-0.977294\pi$
$613$		−	2163.47i		−	0.142548i	0.997457	−	0.0712738i	$-0.0227064\pi$
$614$	8235.08			0.541272
$615$	−3889.76	−	2687.34i	−0.255041	−	0.176201i
$616$		0			0
$617$			22964.9i			1.49843i	0.662327	+	0.749215i	$0.269569\pi$
$617$			22964.9i			1.49843i	−0.662327	+	0.749215i	$0.730431\pi$
$618$			1257.38i			0.0818433i
$619$	−1386.67			−0.0900401			−0.0450200	−	0.998986i	$-0.514335\pi$
$619$	−1386.67			−0.0900401			−0.0450200	+	0.998986i	$0.514335\pi$
$620$	1635.80	−	2367.72i	0.105960	−	0.153371i
$621$	−18886.7			−1.22045
$622$		−	3067.41i		−	0.197736i
$623$		0			0
$624$	−513.831			−0.0329643
$625$	−11713.0	+	10341.5i	−0.749631	+	0.661856i
$626$	−4092.35			−0.261283
$627$			17978.2i			1.14510i
$628$		−	12145.0i		−	0.771716i
$629$	21281.4			1.34904
$630$		0			0
$631$	5969.39			0.376605			0.188303	−	0.982111i	$-0.439701\pi$
$631$	5969.39			0.376605			0.188303	+	0.982111i	$0.439701\pi$
$632$		−	559.367i		−	0.0352064i
$633$		−	8474.57i		−	0.532123i
$634$	2791.14			0.174843
$635$	−2398.31	−	1656.93i	−0.149880	−	0.103548i
$636$	−3479.84			−0.216957
$637$		0			0
$638$			3875.25i			0.240474i
$639$	6873.70			0.425539
$640$	9367.71	+	6471.91i	0.578580	+	0.399726i
$641$	30367.1			1.87118			0.935592	−	0.353084i	$-0.114867\pi$
$641$	30367.1			1.87118			0.935592	+	0.353084i	$0.114867\pi$
$642$		−	6315.40i		−	0.388238i
$643$			28592.2i			1.75360i	0.480851	+	0.876802i	$0.340328\pi$
$643$			28592.2i			1.75360i	−0.480851	+	0.876802i	$0.659672\pi$
$644$		0			0
$645$	−2336.62	+	3382.12i	−0.142642	+	0.206466i
$646$	−19292.7			−1.17502
$647$			14507.9i			0.881555i	0.897616	+	0.440778i	$0.145297\pi$
$647$			14507.9i			0.881555i	−0.897616	+	0.440778i	$0.854703\pi$
$648$		−	5832.21i		−	0.353566i
$649$	13869.7			0.838877
$650$	3372.14	+	8914.33i	0.203487	+	0.537921i
$651$		0			0
$652$			6882.89i			0.413428i
$653$		−	6999.85i		−	0.419488i	−0.977756	−	0.209744i	$-0.932737\pi$
$653$		−	6999.85i		−	0.419488i	0.977756	−	0.209744i	$-0.0672630\pi$
$654$	−7382.53			−0.441406
$655$	−4598.01	+	6655.35i	−0.274289	+	0.397017i
$656$	−767.504			−0.0456799
$657$			11351.3i			0.674056i
$658$		0			0
$659$	−7308.92			−0.432041			−0.216020	−	0.976389i	$-0.569308\pi$
$659$	−7308.92			−0.432041			−0.216020	+	0.976389i	$0.569308\pi$
$660$	−6861.66	−	4740.55i	−0.404681	−	0.279584i
$661$	30097.2			1.77102			0.885512	−	0.464617i	$-0.153808\pi$
$661$	30097.2			1.77102			0.885512	+	0.464617i	$0.153808\pi$
$662$			9157.07i			0.537613i
$663$			10444.0i			0.611779i
$664$	8315.91			0.486024
$665$		0			0
$666$	8051.83			0.468472
$667$		−	6366.92i		−	0.369608i
$668$		−	10835.4i		−	0.627594i
$669$	455.425			0.0263195
$670$	4327.47	−	6263.76i	0.249529	−	0.361179i
$671$	5209.29			0.299706
$672$		0			0
$673$			5400.26i			0.309309i	0.987969	+	0.154654i	$0.0494264\pi$
$673$			5400.26i			0.309309i	−0.987969	+	0.154654i	$0.950574\pi$
$674$	17841.3			1.01962
$675$	−13931.7	+	5270.15i	−0.794419	+	0.300516i
$676$	650.781			0.0370267
$677$		−	6431.09i		−	0.365091i	−0.983197	−	0.182546i	$-0.941566\pi$
$677$		−	6431.09i		−	0.365091i	0.983197	−	0.182546i	$-0.0584338\pi$
$678$			4366.91i			0.247360i
$679$		0			0
$680$	12922.9	−	18705.1i	0.728778	−	1.05486i
$681$	7861.79			0.442385
$682$		−	4780.92i		−	0.268433i
$683$			20865.8i			1.16897i	0.811404	+	0.584486i	$0.198704\pi$
$683$			20865.8i			1.16897i	−0.811404	+	0.584486i	$0.801296\pi$
$684$	13510.2			0.755227
$685$	−7116.86	−	4916.86i	−0.396965	−	0.274253i
$686$		0			0
$687$		−	14994.6i		−	0.832720i
$688$			667.339i			0.0369797i
$689$	−12227.7			−0.676109
$690$	−6090.95	−	4208.08i	−0.336056	−	0.232172i
$691$	−18450.3			−1.01575			−0.507873	−	0.861432i	$-0.669568\pi$
$691$	−18450.3			−1.01575			−0.507873	+	0.861432i	$0.669568\pi$
$692$			9962.76i			0.547294i
$693$		0			0
$694$	6732.70			0.368256
$695$	18766.2	−	27163.0i	1.02424	−	1.48252i
$696$	−2214.26			−0.120591
$697$			15600.0i			0.847766i
$698$		−	17664.4i		−	0.957890i
$699$	2345.97			0.126942
$700$		0			0
$701$	12639.3			0.680996			0.340498	−	0.940245i	$-0.389404\pi$
$701$	12639.3			0.680996			0.340498	+	0.940245i	$0.389404\pi$
$702$			9085.69i			0.488486i
$703$			28954.4i			1.55339i
$704$	15703.3			0.840680
$705$	−1062.42	+	1537.79i	−0.0567560	+	0.0821509i
$706$	4958.45			0.264325
$707$		0			0
$708$			3119.69i			0.165600i
$709$	23126.8			1.22503			0.612514	−	0.790460i	$-0.290158\pi$
$709$	23126.8			1.22503			0.612514	+	0.790460i	$0.290158\pi$
$710$	5097.04	+	3521.42i	0.269421	+	0.186136i
$711$	525.918			0.0277404
$712$		−	22686.1i		−	1.19410i
$713$			7854.92i			0.412579i
$714$		0			0
$715$	−24111.0	−	16657.7i	−1.26112	−	0.871275i
$716$	−3267.16			−0.170530
$717$			12865.9i			0.670134i
$718$			3635.39i			0.188957i
$719$	−24093.1			−1.24968			−0.624841	−	0.780752i	$-0.714836\pi$
$719$	−24093.1			−1.24968			−0.624841	+	0.780752i	$0.714836\pi$
$720$	−597.771	+	865.238i	−0.0309411	+	0.0447854i
$721$		0			0
$722$		−	14758.7i		−	0.760750i
$723$		−	1156.79i		−	0.0595041i
$724$	14547.2			0.746741
$725$	−1776.63	−	4696.55i	−0.0910100	−	0.240587i
$726$	−8294.49			−0.424019
$727$		−	35983.4i		−	1.83570i	−0.396931	−	0.917849i	$-0.629925\pi$
$727$		−	35983.4i		−	1.83570i	0.396931	−	0.917849i	$-0.370075\pi$
$728$		0			0
$729$	−2540.55			−0.129073
$730$	−5815.28	+	8417.28i	−0.294840	+	0.426764i
$731$	13564.1			0.686302
$732$			1171.72i			0.0591640i
$733$		−	1451.50i		−	0.0731413i	−0.999331	−	0.0365706i	$-0.988357\pi$
$733$		−	1451.50i		−	0.0731413i	0.999331	−	0.0365706i	$-0.0116434\pi$
$734$	2097.64			0.105484
$735$		0			0
$736$	−29226.3			−1.46371
$737$			23409.4i			1.17001i
$738$			5902.27i			0.294398i
$739$	5891.67			0.293273			0.146636	−	0.989190i	$-0.453155\pi$
$739$	5891.67			0.293273			0.146636	+	0.989190i	$0.453155\pi$
$740$	−11050.9	−	7634.77i	−0.548970	−	0.379270i
$741$	−14209.5			−0.704451
$742$		0			0
$743$		−	7438.65i		−	0.367292i	−0.982992	−	0.183646i	$-0.941210\pi$
$743$		−	7438.65i		−	0.367292i	0.982992	−	0.183646i	$-0.0587900\pi$
$744$	2731.75			0.134611
$745$	15976.6	−	23125.2i	0.785688	−	1.13724i
$746$	−7782.84			−0.381970
$747$			7818.64i			0.382957i
$748$			27518.9i			1.34518i
$749$		0			0
$750$	−5667.20	−	1404.47i	−0.275916	−	0.0683784i
$751$	20272.4			0.985018			0.492509	−	0.870307i	$-0.336080\pi$
$751$	20272.4			0.985018			0.492509	+	0.870307i	$0.336080\pi$
$752$			303.427i			0.0147139i
$753$			5711.80i			0.276427i
$754$	−3062.89			−0.147936
$755$	−642.193	+	929.537i	−0.0309560	+	0.0448070i
$756$		0			0
$757$		−	10193.8i		−	0.489432i	−0.969595	−	0.244716i	$-0.921305\pi$
$757$		−	10193.8i		−	0.489432i	0.969595	−	0.244716i	$-0.0786947\pi$
$758$			2403.59i			0.115174i
$759$	22763.6			1.08862
$760$	25449.1	+	17582.1i	1.21465	+	0.839172i
$761$	41117.6			1.95862			0.979311	−	0.202362i	$-0.0648618\pi$
$761$	41117.6			1.95862			0.979311	+	0.202362i	$0.0648618\pi$
$762$		−	1089.26i		−	0.0517845i
$763$		0			0
$764$	3844.76			0.182066
$765$	17586.5	+	12150.1i	0.831167	+	0.574232i
$766$	−22140.2			−1.04433
$767$			10962.2i			0.516065i
$768$			9695.10i			0.455523i
$769$	11486.6			0.538642			0.269321	−	0.963050i	$-0.413201\pi$
$769$	11486.6			0.538642			0.269321	+	0.963050i	$0.413201\pi$
$770$		0			0
$771$	2000.66			0.0934527
$772$		−	21204.2i		−	0.988544i
$773$		−	21799.2i		−	1.01431i	−0.861854	−	0.507156i	$-0.830697\pi$
$773$		−	21799.2i		−	1.01431i	0.861854	−	0.507156i	$-0.169303\pi$
$774$	5131.98			0.238327
$775$	2191.84	+	5794.17i	0.101591	+	0.268558i
$776$	20834.5			0.963807
$777$		0			0
$778$		−	12990.9i		−	0.598645i
$779$	−21224.5			−0.976185
$780$	3746.79	−	5423.26i	0.171996	−	0.248954i
$781$	−19049.1			−0.872765
$782$			24428.0i			1.11706i
$783$		−	4786.83i		−	0.218477i
$784$		0			0
$785$	21509.4	+	14860.3i	0.977967	+	0.675652i
$786$	−3022.72			−0.137172
$787$			24080.3i			1.09068i	0.838214	+	0.545342i	$0.183600\pi$
$787$			24080.3i			1.09068i	−0.838214	+	0.545342i	$0.816400\pi$
$788$			17736.4i			0.801817i
$789$	715.712			0.0322941
$790$	389.983	+	269.429i	0.0175632	+	0.0121340i
$791$		0			0
$792$			26449.0i			1.18665i
$793$			4117.28i			0.184374i
$794$	5964.96			0.266610
$795$	4257.85	−	6162.98i	0.189950	−	0.274941i
$796$	−17619.8			−0.784569
$797$			17194.3i			0.764184i	0.924124	+	0.382092i	$0.124796\pi$
$797$			17194.3i			0.764184i	−0.924124	+	0.382092i	$0.875204\pi$
$798$		0			0
$799$	6167.35			0.273073
$800$	−21558.7	+	8155.29i	−0.952769	+	0.360416i
$801$	21329.5			0.940876
$802$			9097.15i			0.400538i
$803$		−	31457.7i		−	1.38246i
$804$	−5265.46			−0.230968
$805$		0			0
$806$	3778.71			0.165136
$807$		−	8881.55i		−	0.387417i
$808$		−	13363.1i		−	0.581823i
$809$	−33349.1			−1.44931			−0.724656	−	0.689111i	$-0.758001\pi$
$809$	−33349.1			−1.44931			−0.724656	+	0.689111i	$0.758001\pi$
$810$	4066.13	+	2809.19i	0.176382	+	0.121858i
$811$	−4577.87			−0.198213			−0.0991066	−	0.995077i	$-0.531598\pi$
$811$	−4577.87			−0.198213			−0.0991066	+	0.995077i	$0.531598\pi$
$812$		0			0
$813$			4810.37i			0.207512i
$814$	−22314.0			−0.960819
$815$	−12190.0	−	8421.74i	−0.523921	−	0.361964i
$816$	−1038.65			−0.0445588
$817$			18454.6i			0.790262i
$818$			16247.0i			0.694455i
$819$		0			0
$820$	5596.55	−	8100.67i	0.238341	−	0.344985i
$821$	−5832.52			−0.247937			−0.123969	−	0.992286i	$-0.539562\pi$
$821$	−5832.52			−0.247937			−0.123969	+	0.992286i	$0.539562\pi$
$822$		−	3232.33i		−	0.137154i
$823$		−	37974.3i		−	1.60838i	−0.594369	−	0.804192i	$-0.702598\pi$
$823$		−	37974.3i		−	1.60838i	0.594369	−	0.804192i	$-0.297402\pi$
$824$	−6651.92			−0.281226
$825$	16791.5	−	6351.95i	0.708613	−	0.268056i
$826$		0			0
$827$			15796.2i			0.664193i	0.943245	+	0.332096i	$0.107756\pi$
$827$			15796.2i			0.664193i	−0.943245	+	0.332096i	$0.892244\pi$
$828$		−	17106.3i		−	0.717976i
$829$	−12714.1			−0.532666			−0.266333	−	0.963881i	$-0.585812\pi$
$829$	−12714.1			−0.532666			−0.266333	+	0.963881i	$0.585812\pi$
$830$	−4005.51	+	5797.74i	−0.167510	+	0.242461i
$831$	16431.9			0.685942
$832$			12411.4i			0.517173i
$833$		0			0
$834$	12336.9			0.512219
$835$	19190.0	+	13257.9i	0.795326	+	0.549470i
$836$	−37440.8			−1.54894
$837$			5905.55i			0.243878i
$838$		−	23169.0i		−	0.955085i
$839$	−42924.2			−1.76628			−0.883140	−	0.469109i	$-0.844575\pi$
$839$	−42924.2			−1.76628			−0.883140	+	0.469109i	$0.844575\pi$
$840$		0			0
$841$	−22775.3			−0.933835
$842$		−	27980.2i		−	1.14520i
$843$		−	2033.95i		−	0.0830998i
$844$	17648.8			0.719784
$845$	−796.279	+	1152.57i	−0.0324176	+	0.0469225i
$846$	2333.42			0.0948281
$847$		0			0
$848$		−	1216.04i		−	0.0492442i
$849$	−16244.4			−0.656662
$850$	6816.38	+	18019.3i	0.275059	+	0.727124i
$851$	36661.3			1.47677
$852$		−	4284.69i		−	0.172290i
$853$		−	36172.5i		−	1.45196i	−0.687716	−	0.725980i	$-0.741387\pi$
$853$		−	36172.5i		−	1.45196i	0.687716	−	0.725980i	$-0.258613\pi$
$854$		0			0
$855$	−16530.7	+	23927.3i	−0.661216	+	0.957071i
$856$	33410.4			1.33405
$857$			32039.9i			1.27709i	0.769586	+	0.638544i	$0.220463\pi$
$857$			32039.9i			1.27709i	−0.769586	+	0.638544i	$0.779537\pi$
$858$		−	10950.7i		−	0.435724i
$859$	−6798.07			−0.270020			−0.135010	−	0.990844i	$-0.543107\pi$
$859$	−6798.07			−0.270020			−0.135010	+	0.990844i	$0.543107\pi$
$860$	−7043.47	−	4866.15i	−0.279280	−	0.192947i
$861$		0			0
$862$		−	13692.9i		−	0.541046i
$863$			30179.3i			1.19040i	0.803577	+	0.595200i	$0.202927\pi$
$863$			30179.3i			1.19040i	−0.803577	+	0.595200i	$0.797073\pi$
$864$	−21973.1			−0.865209
$865$	−17644.6	−	12190.2i	−0.693565	−	0.479166i
$866$	23825.5			0.934901
$867$			8858.39i			0.346997i
$868$		0			0
$869$	−1457.47			−0.0568946
$870$	1066.54	−	1543.75i	0.0415621	−	0.0601586i
$871$	−18502.1			−0.719772
$872$		−	39055.9i		−	1.51674i
$873$			19588.6i			0.759421i
$874$	−33235.4			−1.28627
$875$		0			0
$876$	7075.76			0.272908
$877$		−	1700.51i		−	0.0654758i	−0.999464	−	0.0327379i	$-0.989577\pi$
$877$		−	1700.51i		−	0.0654758i	0.999464	−	0.0327379i	$-0.0104227\pi$
$878$		−	9276.02i		−	0.356549i
$879$	1086.17			0.0416787
$880$	1656.60	−	2397.83i	0.0634591	−	0.0918533i
$881$	−1678.46			−0.0641869			−0.0320935	−	0.999485i	$-0.510217\pi$
$881$	−1678.46			−0.0641869			−0.0320935	+	0.999485i	$0.510217\pi$
$882$		0			0
$883$		−	10285.8i		−	0.392009i	−0.980603	−	0.196005i	$-0.937203\pi$
$883$		−	10285.8i		−	0.392009i	0.980603	−	0.196005i	$-0.0627968\pi$
$884$	−21750.2			−0.827532
$885$	−5525.13	−	3817.17i	−0.209859	−	0.144986i
$886$	−6657.24			−0.252432
$887$			12167.5i			0.460593i	0.973121	+	0.230296i	$0.0739696\pi$
$887$			12167.5i			0.460593i	−0.973121	+	0.230296i	$0.926030\pi$
$888$		−	12749.9i		−	0.481823i
$889$		0			0
$890$	15816.4	+	10927.2i	0.595695	+	0.411550i
$891$	−15196.3			−0.571374
$892$			948.452i			0.0356015i
$893$			8390.96i			0.314438i
$894$	10503.0			0.392922
$895$	3997.62	−	5786.31i	0.149302	−	0.216106i
$896$		0			0
$897$			17991.7i			0.669705i
$898$		−	25534.7i		−	0.948892i
$899$	−1990.83			−0.0738574
$900$	−4773.34	−	12618.4i	−0.176790	−	0.467349i
$901$	−24716.9			−0.913916
$902$		−	16356.9i		−	0.603799i
$903$		0			0
$904$	−23102.3			−0.849968
$905$	−17799.5	+	25763.8i	−0.653787	+	0.946317i
$906$	−422.176			−0.0154811
$907$		−	50766.0i		−	1.85850i	−0.369452	−	0.929250i	$-0.620455\pi$
$907$		−	50766.0i		−	1.85850i	0.369452	−	0.929250i	$-0.379545\pi$
$908$			16372.7i			0.598399i
$909$	12564.0			0.458441
$910$		0			0
$911$	18451.1			0.671033			0.335517	−	0.942034i	$-0.391089\pi$
$911$	18451.1			0.671033			0.335517	+	0.942034i	$0.391089\pi$
$912$		−	1413.13i		−	0.0513085i
$913$		−	21667.8i		−	0.785431i
$914$	−18039.6			−0.652841
$915$	−2075.18	−	1433.69i	−0.0749763	−	0.0517992i
$916$	31227.1			1.12639
$917$		0			0
$918$			18365.6i			0.660301i
$919$	−393.861			−0.0141374			−0.00706870	−	0.999975i	$-0.502250\pi$
$919$	−393.861			−0.0141374			−0.00706870	+	0.999975i	$0.502250\pi$
$920$	22262.1	−	32223.0i	0.797781	−	1.15474i
$921$	12260.3			0.438643
$922$		−	557.167i		−	0.0199016i
$923$		−	15055.9i		−	0.536912i
$924$		0			0
$925$	27043.2	−	10230.0i	0.961269	−	0.363632i
$926$	13745.3			0.487795
$927$		−	6254.15i		−	0.221589i
$928$		−	7407.39i		−	0.262025i
$929$	27452.3			0.969517			0.484759	−	0.874648i	$-0.338907\pi$
$929$	27452.3			0.969517			0.484759	+	0.874648i	$0.338907\pi$
$930$	−1315.79	+	1904.54i	−0.0463942	+	0.0671529i
$931$		0			0
$932$			4885.63i			0.171710i
$933$		−	4566.72i		−	0.160244i
$934$	280.803			0.00983744
$935$	−48737.5	−	33671.5i	−1.70469	−	1.17773i
$936$	−20904.5			−0.730006
$937$		−	21608.3i		−	0.753375i	−0.926340	−	0.376688i	$-0.877063\pi$
$937$		−	21608.3i		−	0.753375i	0.926340	−	0.376688i	$-0.122937\pi$
$938$		0			0
$939$	−6092.64			−0.211742
$940$	−3202.54	−	2212.55i	−0.111123	−	0.0767718i
$941$	16708.5			0.578832			0.289416	−	0.957203i	$-0.406539\pi$
$941$	16708.5			0.578832			0.289416	+	0.957203i	$0.406539\pi$
$942$			9769.12i			0.337893i
$943$			26874.0i			0.928036i
$944$	−1090.19			−0.0375874
$945$		0			0
$946$	−14222.2			−0.488800
$947$			13972.8i			0.479466i	0.970839	+	0.239733i	$0.0770599\pi$
$947$			13972.8i			0.479466i	−0.970839	+	0.239733i	$0.922940\pi$
$948$		−	327.828i		−	0.0112314i
$949$	24863.3			0.850471
$950$	−24516.0	+	9274.00i	−0.837268	+	0.316724i
$951$	4155.42			0.141692
$952$		0			0
$953$			11155.9i			0.379197i	0.981862	+	0.189598i	$0.0607186\pi$
$953$			11155.9i			0.379197i	−0.981862	+	0.189598i	$0.939281\pi$
$954$	−9351.63			−0.317369
$955$	−4704.35	+	6809.27i	−0.159402	+	0.230726i
$956$	−26794.0			−0.906466
$957$			5769.42i			0.194879i
$958$		−	11104.0i		−	0.374481i
$959$		0			0
$960$	−6255.57	−	4321.81i	−0.210310	−	0.145298i
$961$	−27334.9			−0.917556
$962$		−	17636.4i		−	0.591081i
$963$			31412.5i			1.05115i
$964$	2409.09			0.0804891
$965$	37553.8	+	25944.9i	1.25274	+	0.865489i
$966$		0			0
$967$		−	1212.55i		−	0.0403238i	−0.999797	−	0.0201619i	$-0.993582\pi$
$967$		−	1212.55i		−	0.0403238i	0.999797	−	0.0201619i	$-0.00641816\pi$
$968$		−	43880.4i		−	1.45699i
$969$	−28722.8			−0.952227
$970$	−10035.3	+	14525.5i	−0.332180	+	0.480810i
$971$	48832.2			1.61390			0.806952	−	0.590617i	$-0.201115\pi$
$971$	48832.2			1.61390			0.806952	+	0.590617i	$0.201115\pi$
$972$		−	20128.6i		−	0.664222i
$973$		0			0
$974$	−34578.0			−1.13753
$975$	5020.40	+	13271.5i	0.164904	+	0.435928i
$976$	−409.462			−0.0134289
$977$			5939.19i			0.194485i	0.995261	+	0.0972424i	$0.0310022\pi$
$977$			5939.19i			0.194485i	−0.995261	+	0.0972424i	$0.968998\pi$
$978$		−	5536.43i		−	0.181018i
$979$	−59110.5			−1.92970
$980$		0			0
$981$	36720.4			1.19510
$982$			27993.3i			0.909677i
$983$		−	21863.5i		−	0.709398i	−0.934980	−	0.354699i	$-0.884583\pi$
$983$		−	21863.5i		−	0.709398i	0.934980	−	0.354699i	$-0.115417\pi$
$984$	9346.11			0.302788
$985$	−31412.0	−	21701.8i	−1.01611	−	0.702006i
$986$	−6191.26			−0.199970
$987$		0			0
$988$		−	29592.1i		−	0.952886i
$989$	23366.7			0.751283
$990$	−18439.8	−	12739.6i	−0.591976	−	0.408981i
$991$	−44618.5			−1.43023			−0.715113	−	0.699009i	$-0.753625\pi$
$991$	−44618.5			−1.43023			−0.715113	+	0.699009i	$0.753625\pi$
$992$			9138.55i			0.292489i
$993$			13632.9i			0.435678i
$994$		0			0
$995$	21559.1	−	31205.6i	0.686905	−	0.994255i
$996$	4873.71			0.155050
$997$			37923.9i			1.20468i	0.798241	+	0.602338i	$0.205764\pi$
$997$			37923.9i			1.20468i	−0.798241	+	0.602338i	$0.794236\pi$
$998$		−	22997.8i		−	0.729441i
$999$	27563.0			0.872928

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.4.b.d.99.4		10
5.2	odd	4		1225.4.a.be.1.4		5
5.3	odd	4		1225.4.a.bh.1.2		5
5.4	even	2	inner	245.4.b.d.99.7		10
7.2	even	3		245.4.j.f.214.4		20
7.3	odd	6		245.4.j.e.79.7		20
7.4	even	3		245.4.j.f.79.7		20
7.5	odd	6		245.4.j.e.214.4		20
7.6	odd	2		35.4.b.a.29.4	✓	10
21.20	even	2		315.4.d.c.64.7		10
28.27	even	2		560.4.g.f.449.4		10
35.4	even	6		245.4.j.f.79.4		20
35.9	even	6		245.4.j.f.214.7		20
35.13	even	4		175.4.a.j.1.2		5
35.19	odd	6		245.4.j.e.214.7		20
35.24	odd	6		245.4.j.e.79.4		20
35.27	even	4		175.4.a.i.1.4		5
35.34	odd	2		35.4.b.a.29.7	yes	10
105.62	odd	4		1575.4.a.bq.1.2		5
105.83	odd	4		1575.4.a.bn.1.4		5
105.104	even	2		315.4.d.c.64.4		10
140.139	even	2		560.4.g.f.449.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.b.a.29.4	✓	10	7.6	odd	2
35.4.b.a.29.7	yes	10	35.34	odd	2
175.4.a.i.1.4		5	35.27	even	4
175.4.a.j.1.2		5	35.13	even	4
245.4.b.d.99.4		10	1.1	even	1	trivial
245.4.b.d.99.7		10	5.4	even	2	inner
245.4.j.e.79.4		20	35.24	odd	6
245.4.j.e.79.7		20	7.3	odd	6
245.4.j.e.214.4		20	7.5	odd	6
245.4.j.e.214.7		20	35.19	odd	6
245.4.j.f.79.4		20	35.4	even	6
245.4.j.f.79.7		20	7.4	even	3
245.4.j.f.214.4		20	7.2	even	3
245.4.j.f.214.7		20	35.9	even	6
315.4.d.c.64.4		10	105.104	even	2
315.4.d.c.64.7		10	21.20	even	2
560.4.g.f.449.4		10	28.27	even	2
560.4.g.f.449.7		10	140.139	even	2
1225.4.a.be.1.4		5	5.2	odd	4
1225.4.a.bh.1.2		5	5.3	odd	4
1575.4.a.bn.1.4		5	105.83	odd	4
1575.4.a.bq.1.2		5	105.62	odd	4

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:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	245.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.67516i q^{2} -2.49396i q^{3} +5.19383 q^{4} +(-6.35505 + 9.19855i) q^{5} -4.17779 q^{6} -22.1018i q^{8} +20.7802 q^{9} +(15.4091 + 10.6457i) q^{10} -57.5880 q^{11} -12.9532i q^{12} -45.5159i q^{13} +(22.9408 + 15.8492i) q^{15} +4.52655 q^{16} -92.0051i q^{17} -34.8101i q^{18} +125.177 q^{19} +(-33.0070 + 47.7757i) q^{20} +96.4692i q^{22} -158.496i q^{23} -55.1211 q^{24} +(-44.2268 - 116.914i) q^{25} -76.2466 q^{26} -119.162i q^{27} +40.1708 q^{29} +(26.5500 - 38.4296i) q^{30} -49.5590 q^{31} -184.397i q^{32} +143.622i q^{33} -154.123 q^{34} +107.929 q^{36} +231.307i q^{37} -209.692i q^{38} -113.515 q^{39} +(203.305 + 140.458i) q^{40} -169.556 q^{41} +147.428i q^{43} -299.102 q^{44} +(-132.059 + 191.147i) q^{45} -265.507 q^{46} +67.0327i q^{47} -11.2890i q^{48} +(-195.851 + 74.0870i) q^{50} -229.457 q^{51} -236.402i q^{52} -268.647i q^{53} -199.615 q^{54} +(365.974 - 529.726i) q^{55} -312.187i q^{57} -67.2926i q^{58} -240.843 q^{59} +(119.151 + 82.3183i) q^{60} -90.4579 q^{61} +83.0194i q^{62} -272.683 q^{64} +(418.681 + 289.256i) q^{65} +240.591 q^{66} -406.498i q^{67} -477.859i q^{68} -395.283 q^{69} +330.782 q^{71} -459.279i q^{72} +546.255i q^{73} +387.477 q^{74} +(-291.580 + 110.300i) q^{75} +650.149 q^{76} +190.156i q^{78} +25.3087 q^{79} +(-28.7664 + 41.6377i) q^{80} +263.879 q^{81} +284.034i q^{82} +376.255i q^{83} +(846.314 + 584.697i) q^{85} +246.965 q^{86} -100.184i q^{87} +1272.80i q^{88} +1026.44 q^{89} +(320.203 + 221.220i) q^{90} -823.203i q^{92} +123.598i q^{93} +112.291 q^{94} +(-795.506 + 1151.45i) q^{95} -459.879 q^{96} +942.660i q^{97} -1196.69 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 36 q^{4} - 6 q^{5} - 12 q^{6} - 46 q^{9} + 16 q^{10} + 84 q^{11} + 8 q^{15} + 148 q^{16} - 72 q^{19} + 68 q^{20} - 72 q^{24} - 362 q^{25} + 620 q^{26} + 88 q^{29} + 52 q^{30} - 120 q^{31} - 964 q^{34}+ \cdots - 5304 q^{99}+O(q^{100}) \) 10 * q - 36 * q^4 - 6 * q^5 - 12 * q^6 - 46 * q^9 + 16 * q^10 + 84 * q^11 + 8 * q^15 + 148 * q^16 - 72 * q^19 + 68 * q^20 - 72 * q^24 - 362 * q^25 + 620 * q^26 + 88 * q^29 + 52 * q^30 - 120 * q^31 - 964 * q^34 - 420 * q^36 + 212 * q^39 - 1396 * q^40 + 852 * q^41 - 1424 * q^44 + 510 * q^45 + 176 * q^46 + 1644 * q^50 + 1276 * q^51 + 996 * q^54 + 1136 * q^55 - 864 * q^59 - 1692 * q^60 + 884 * q^61 - 2724 * q^64 + 520 * q^65 - 1148 * q^66 - 4808 * q^69 + 880 * q^71 + 3024 * q^74 - 720 * q^75 + 2672 * q^76 - 3580 * q^79 + 2316 * q^80 - 302 * q^81 + 1572 * q^85 + 2432 * q^86 + 1492 * q^89 + 7748 * q^90 - 1652 * q^94 - 1628 * q^95 - 4080 * q^96 - 5304 * q^99

Introduction

L-functions

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