LMFDB - Embedded newform 175.4.f.g.118.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [175,4,Mod(118,175)] 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("175.118"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(175, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([3, 2])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	175.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,-4,0,0,0,0,-32,-176,0,0,-152] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$10.3253342510$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 10654x^{12} + 22102125x^{8} + 5700572500x^{4} + 44626562500 $ x^16 + 10654x^12 + 22102125x^8 + 5700572500*x^4 + 44626562500
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			118.8
Root			$-4.94129 - 4.94129i$ of defining polynomial
Character	$\chi$	$=$	175.118
Dual form			175.4.f.g.132.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.57033 - 3.57033i) q^{2} +(4.94129 - 4.94129i) q^{3} -17.4944i q^{4} -35.2840i q^{6} +(-0.826888 + 18.5018i) q^{7} +(-33.8983 - 33.8983i) q^{8} -21.8328i q^{9} -30.6825 q^{11} +(-86.4452 - 86.4452i) q^{12} +(38.4644 - 38.4644i) q^{13} +(63.1052 + 69.0097i) q^{14} -102.100 q^{16} +(34.5683 + 34.5683i) q^{17} +(-77.9500 - 77.9500i) q^{18} +22.1767 q^{19} +(87.3369 + 95.5087i) q^{21} +(-109.546 + 109.546i) q^{22} +(3.20638 + 3.20638i) q^{23} -335.002 q^{24} -274.661i q^{26} +(25.5329 + 25.5329i) q^{27} +(323.679 + 14.4660i) q^{28} +179.259i q^{29} -37.6201i q^{31} +(-93.3444 + 93.3444i) q^{32} +(-151.611 + 151.611i) q^{33} +246.840 q^{34} -381.952 q^{36} +(135.426 - 135.426i) q^{37} +(79.1782 - 79.1782i) q^{38} -380.128i q^{39} +326.823i q^{41} +(652.818 + 29.1760i) q^{42} +(-193.381 - 193.381i) q^{43} +536.773i q^{44} +22.8956 q^{46} +(91.5534 + 91.5534i) q^{47} +(-504.506 + 504.506i) q^{48} +(-341.633 - 30.5978i) q^{49} +341.624 q^{51} +(-672.914 - 672.914i) q^{52} +(-210.622 - 210.622i) q^{53} +182.321 q^{54} +(655.209 - 599.149i) q^{56} +(109.582 - 109.582i) q^{57} +(640.012 + 640.012i) q^{58} -230.155 q^{59} -37.1467i q^{61} +(-134.316 - 134.316i) q^{62} +(403.945 + 18.0532i) q^{63} -150.261i q^{64} +1082.60i q^{66} +(-325.340 + 325.340i) q^{67} +(604.753 - 604.753i) q^{68} +31.6873 q^{69} -474.107 q^{71} +(-740.092 + 740.092i) q^{72} +(-642.183 + 642.183i) q^{73} -967.032i q^{74} -387.970i q^{76} +(25.3710 - 567.681i) q^{77} +(-1357.18 - 1357.18i) q^{78} +636.110i q^{79} +841.815 q^{81} +(1166.87 + 1166.87i) q^{82} +(993.219 - 993.219i) q^{83} +(1670.87 - 1527.91i) q^{84} -1380.87 q^{86} +(885.770 + 885.770i) q^{87} +(1040.08 + 1040.08i) q^{88} +1205.77 q^{89} +(679.855 + 743.467i) q^{91} +(56.0938 - 56.0938i) q^{92} +(-185.892 - 185.892i) q^{93} +653.751 q^{94} +922.484i q^{96} +(-917.344 - 917.344i) q^{97} +(-1328.98 + 1110.50i) q^{98} +669.883i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 32 q^{7} - 176 q^{8} - 152 q^{11} - 504 q^{16} - 288 q^{18} + 328 q^{21} - 348 q^{22} + 72 q^{23} + 528 q^{28} - 432 q^{32} + 344 q^{36} + 256 q^{37} + 1300 q^{42} + 312 q^{43} - 1856 q^{46}+ \cdots - 3308 q^{98}+O(q^{100}) $ 16 * q - 4 * q^2 - 32 * q^7 - 176 * q^8 - 152 * q^11 - 504 * q^16 - 288 * q^18 + 328 * q^21 - 348 * q^22 + 72 * q^23 + 528 * q^28 - 432 * q^32 + 344 * q^36 + 256 * q^37 + 1300 * q^42 + 312 * q^43 - 1856 * q^46 + 696 * q^51 - 1768 * q^53 + 1304 * q^56 + 3920 * q^57 + 4764 * q^58 - 2544 * q^63 - 4504 * q^67 + 6368 * q^71 - 7848 * q^72 + 3016 * q^77 - 5340 * q^78 - 3088 * q^81 - 9336 * q^86 + 2048 * q^88 + 1608 * q^91 + 6328 * q^92 + 3960 * q^93 - 3308 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	3.57033	−	3.57033i	1.26230	−	1.26230i	0.312325	−	0.949975i	$-0.398892\pi$
$2$	3.57033	−	3.57033i	1.26230	−	1.26230i	0.949975	−	0.312325i	$-0.101108\pi$
$3$	4.94129	−	4.94129i	0.950952	−	0.950952i	−0.0478999	−	0.998852i	$-0.515253\pi$
$3$	4.94129	−	4.94129i	0.950952	−	0.950952i	0.998852	+	0.0478999i	$0.0152528\pi$
$4$		−	17.4944i		−	2.18681i
$5$		0			0
$5$		0			0
$6$		−	35.2840i		−	2.40078i
$7$	−0.826888	+	18.5018i	−0.0446478	+	0.999003i
$7$	−0.826888	+	18.5018i	−0.0446478	+	0.999003i
$8$	−33.8983	−	33.8983i	−1.49811	−	1.49811i
$9$		−	21.8328i		−	0.808620i
$10$		0			0
$11$	−30.6825			−0.841010			−0.420505	−	0.907290i	$-0.638147\pi$
$11$	−30.6825			−0.841010			−0.420505	+	0.907290i	$0.638147\pi$
$12$	−86.4452	−	86.4452i	−2.07955	−	2.07955i
$13$	38.4644	−	38.4644i	0.820624	−	0.820624i	−0.165573	−	0.986198i	$-0.552947\pi$
$13$	38.4644	−	38.4644i	0.820624	−	0.820624i	0.986198	+	0.165573i	$0.0529474\pi$
$14$	63.1052	+	69.0097i	1.20468	+	1.31740i
$15$		0			0
$16$	−102.100			−1.59531
$17$	34.5683	+	34.5683i	0.493179	+	0.493179i	0.909306	−	0.416127i	$-0.136613\pi$
$17$	34.5683	+	34.5683i	0.493179	+	0.493179i	−0.416127	+	0.909306i	$0.636613\pi$
$18$	−77.9500	−	77.9500i	−1.02072	−	1.02072i
$19$	22.1767			0.267773			0.133887	−	0.990997i	$-0.457254\pi$
$19$	22.1767			0.267773			0.133887	+	0.990997i	$0.457254\pi$
$20$		0			0
$21$	87.3369	+	95.5087i	0.907546	+	0.992462i
$22$	−109.546	+	109.546i	−1.06161	+	1.06161i
$23$	3.20638	+	3.20638i	0.0290685	+	0.0290685i	0.721492	−	0.692423i	$-0.243457\pi$
$23$	3.20638	+	3.20638i	0.0290685	+	0.0290685i	−0.692423	+	0.721492i	$0.743457\pi$
$24$	−335.002			−2.84925
$25$		0			0
$26$		−	274.661i		−	2.07175i
$27$	25.5329	+	25.5329i	0.181993	+	0.181993i
$28$	323.679	+	14.4660i	2.18463	+	0.0976360i
$29$			179.259i			1.14785i	0.818910	+	0.573923i	$0.194579\pi$
$29$			179.259i			1.14785i	−0.818910	+	0.573923i	$0.805421\pi$
$30$		0			0
$31$		−	37.6201i		−	0.217960i	−0.994044	−	0.108980i	$-0.965242\pi$
$31$		−	37.6201i		−	0.217960i	0.994044	−	0.108980i	$-0.0347585\pi$
$32$	−93.3444	+	93.3444i	−0.515660	+	0.515660i
$33$	−151.611	+	151.611i	−0.799761	+	0.799761i
$34$	246.840			1.24508
$35$		0			0
$36$	−381.952			−1.76830
$37$	135.426	−	135.426i	0.601728	−	0.601728i	−0.339043	−	0.940771i	$-0.610103\pi$
$37$	135.426	−	135.426i	0.601728	−	0.601728i	0.940771	+	0.339043i	$0.110103\pi$
$38$	79.1782	−	79.1782i	0.338010	−	0.338010i
$39$		−	380.128i		−	1.56075i
$40$		0			0
$41$			326.823i			1.24491i	0.782656	+	0.622454i	$0.213864\pi$
$41$			326.823i			1.24491i	−0.782656	+	0.622454i	$0.786136\pi$
$42$	652.818	+	29.1760i	2.39838	+	0.107189i
$43$	−193.381	−	193.381i	−0.685823	−	0.685823i	0.275483	−	0.961306i	$-0.411162\pi$
$43$	−193.381	−	193.381i	−0.685823	−	0.685823i	−0.961306	+	0.275483i	$0.911162\pi$
$44$			536.773i			1.83913i
$45$		0			0
$46$	22.8956			0.0733864
$47$	91.5534	+	91.5534i	0.284137	+	0.284137i	0.834756	−	0.550620i	$-0.185608\pi$
$47$	91.5534	+	91.5534i	0.284137	+	0.284137i	−0.550620	+	0.834756i	$0.685608\pi$
$48$	−504.506	+	504.506i	−1.51707	+	1.51707i
$49$	−341.633	−	30.5978i	−0.996013	−	0.0892065i
$50$		0			0
$51$	341.624			0.937979
$52$	−672.914	−	672.914i	−1.79455	−	1.79455i
$53$	−210.622	−	210.622i	−0.545871	−	0.545871i	0.379373	−	0.925244i	$-0.376140\pi$
$53$	−210.622	−	210.622i	−0.545871	−	0.545871i	−0.925244	+	0.379373i	$0.876140\pi$
$54$	182.321			0.459459
$55$		0			0
$56$	655.209	−	599.149i	1.56350	−	1.42972i
$57$	109.582	−	109.582i	0.254640	−	0.254640i
$58$	640.012	+	640.012i	1.44893	+	1.44893i
$59$	−230.155			−0.507858			−0.253929	−	0.967223i	$-0.581723\pi$
$59$	−230.155			−0.507858			−0.253929	+	0.967223i	$0.581723\pi$
$60$		0			0
$61$		−	37.1467i		−	0.0779696i	−0.999240	−	0.0389848i	$-0.987588\pi$
$61$		−	37.1467i		−	0.0779696i	0.999240	−	0.0389848i	$-0.0124124\pi$
$62$	−134.316	−	134.316i	−0.275131	−	0.275131i
$63$	403.945	+	18.0532i	0.807814	+	0.0361031i
$64$		−	150.261i		−	0.293478i
$65$		0			0
$66$			1082.60i			2.01908i
$67$	−325.340	+	325.340i	−0.593232	+	0.593232i	−0.938503	−	0.345271i	$-0.887787\pi$
$67$	−325.340	+	325.340i	−0.593232	+	0.593232i	0.345271	+	0.938503i	$0.387787\pi$
$68$	604.753	−	604.753i	1.07849	−	1.07849i
$69$	31.6873			0.0552855
$70$		0			0
$71$	−474.107			−0.792481			−0.396240	−	0.918147i	$-0.629685\pi$
$71$	−474.107			−0.792481			−0.396240	+	0.918147i	$0.629685\pi$
$72$	−740.092	+	740.092i	−1.21140	+	1.21140i
$73$	−642.183	+	642.183i	−1.02961	+	1.02961i	−0.0300668	+	0.999548i	$0.509572\pi$
$73$	−642.183	+	642.183i	−1.02961	+	1.02961i	−0.999548	+	0.0300668i	$0.990428\pi$
$74$		−	967.032i		−	1.51912i
$75$		0			0
$76$		−	387.970i		−	0.585568i
$77$	25.3710	−	567.681i	0.0375492	−	0.840172i
$78$	−1357.18	−	1357.18i	−1.97013	−	1.97013i
$79$			636.110i			0.905923i	0.891530	+	0.452962i	$0.149633\pi$
$79$			636.110i			0.905923i	−0.891530	+	0.452962i	$0.850367\pi$
$80$		0			0
$81$	841.815			1.15475
$82$	1166.87	+	1166.87i	1.57145	+	1.57145i
$83$	993.219	−	993.219i	1.31349	−	1.31349i	0.394670	−	0.918823i	$-0.370859\pi$
$83$	993.219	−	993.219i	1.31349	−	1.31349i	0.918823	−	0.394670i	$-0.129141\pi$
$84$	1670.87	−	1527.91i	2.17032	−	1.98463i
$85$		0			0
$86$	−1380.87			−1.73143
$87$	885.770	+	885.770i	1.09155	+	1.09155i
$88$	1040.08	+	1040.08i	1.25992	+	1.25992i
$89$	1205.77			1.43608			0.718041	−	0.696001i	$-0.245039\pi$
$89$	1205.77			1.43608			0.718041	+	0.696001i	$0.245039\pi$
$90$		0			0
$91$	679.855	+	743.467i	0.783167	+	0.856445i
$92$	56.0938	−	56.0938i	0.0635672	−	0.0635672i
$93$	−185.892	−	185.892i	−0.207270	−	0.207270i
$94$	653.751			0.717332
$95$		0			0
$96$			922.484i			0.980736i
$97$	−917.344	−	917.344i	−0.960229	−	0.960229i	0.0390103	−	0.999239i	$-0.487579\pi$
$97$	−917.344	−	917.344i	−0.960229	−	0.960229i	−0.999239	+	0.0390103i	$0.987579\pi$
$98$	−1328.98	+	1110.50i	−1.36987	+	1.14466i
$99$			669.883i			0.680058i
$100$		0			0
$101$		−	295.537i		−	0.291159i	−0.989347	−	0.145580i	$-0.953495\pi$
$101$		−	295.537i		−	0.291159i	0.989347	−	0.145580i	$-0.0465047\pi$
$102$	1219.71	−	1219.71i	1.18401	−	1.18401i
$103$	−59.7442	+	59.7442i	−0.0571531	+	0.0571531i	−0.735106	−	0.677953i	$-0.762867\pi$
$103$	−59.7442	+	59.7442i	−0.0571531	+	0.0571531i	0.677953	+	0.735106i	$0.262867\pi$
$104$	−2607.76			−2.45876
$105$		0			0
$106$	−1503.98			−1.37811
$107$	−697.268	+	697.268i	−0.629976	+	0.629976i	−0.948062	−	0.318086i	$-0.896960\pi$
$107$	−697.268	+	697.268i	−0.629976	+	0.629976i	0.318086	+	0.948062i	$0.396960\pi$
$108$	446.684	−	446.684i	0.397983	−	0.397983i
$109$			869.901i			0.764417i	0.924076	+	0.382208i	$0.124836\pi$
$109$			869.901i			0.764417i	−0.924076	+	0.382208i	$0.875164\pi$
$110$		0			0
$111$		−	1338.36i		−	1.14443i
$112$	84.4254	−	1889.03i	0.0712272	−	1.59372i
$113$	787.832	+	787.832i	0.655867	+	0.655867i	0.954400	−	0.298532i	$-0.0964970\pi$
$113$	787.832	+	787.832i	0.655867	+	0.655867i	−0.298532	+	0.954400i	$0.596497\pi$
$114$		−	782.485i		−	0.642864i
$115$		0			0
$116$	3136.03			2.51011
$117$	−839.785	−	839.785i	−0.663574	−	0.663574i
$118$	−821.728	+	821.728i	−0.641070	+	0.641070i
$119$	−668.159	+	610.991i	−0.514706	+	0.470668i
$120$		0			0
$121$	−389.586			−0.292702
$122$	−132.626	−	132.626i	−0.0984210	−	0.0984210i
$123$	1614.93	+	1614.93i	1.18385	+	1.18385i
$124$	−658.142			−0.476636
$125$		0			0
$126$	1506.67	−	1377.76i	1.06528	−	0.974131i
$127$	−691.381	+	691.381i	−0.483072	+	0.483072i	−0.906111	−	0.423039i	$-0.860963\pi$
$127$	−691.381	+	691.381i	−0.483072	+	0.483072i	0.423039	+	0.906111i	$0.360963\pi$
$128$	−1283.24	−	1283.24i	−0.886117	−	0.886117i
$129$	−1911.11			−1.30437
$130$		0			0
$131$			1847.22i			1.23200i	0.787746	+	0.616000i	$0.211248\pi$
$131$			1847.22i			1.23200i	−0.787746	+	0.616000i	$0.788752\pi$
$132$	2652.35	+	2652.35i	1.74892	+	1.74892i
$133$	−18.3377	+	410.309i	−0.0119555	+	0.267506i
$134$			2323.14i			1.49767i
$135$		0			0
$136$		−	2343.61i		−	1.47767i
$137$	1532.08	−	1532.08i	0.955432	−	0.955432i	−0.0436159	−	0.999048i	$-0.513888\pi$
$137$	1532.08	−	1532.08i	0.955432	−	0.955432i	0.999048	+	0.0436159i	$0.0138878\pi$
$138$	113.134	−	113.134i	0.0697870	−	0.0697870i
$139$	160.189			0.0977488			0.0488744	−	0.998805i	$-0.484437\pi$
$139$	160.189			0.0977488			0.0488744	+	0.998805i	$0.484437\pi$
$140$		0			0
$141$	904.784			0.540401
$142$	−1692.72	+	1692.72i	−1.00035	+	1.00035i
$143$	−1180.18	+	1180.18i	−0.690154	+	0.690154i
$144$			2229.13i			1.29000i
$145$		0			0
$146$			4585.61i			2.59937i
$147$	−1839.30	+	1536.91i	−1.03199	+	0.862330i
$148$	−2369.21	−	2369.21i	−1.31586	−	1.31586i
$149$		−	398.652i		−	0.219187i	−0.993976	−	0.109594i	$-0.965045\pi$
$149$		−	398.652i		−	0.219187i	0.993976	−	0.109594i	$-0.0349549\pi$
$150$		0			0
$151$	−3472.49			−1.87144			−0.935718	−	0.352748i	$-0.885247\pi$
$151$	−3472.49			−1.87144			−0.935718	+	0.352748i	$0.885247\pi$
$152$	−751.753	−	751.753i	−0.401153	−	0.401153i
$153$	754.721	−	754.721i	0.398795	−	0.398795i
$154$	−1936.22	−	2117.39i	−1.01315	−	1.10795i
$155$		0			0
$156$	−6650.13			−3.41306
$157$	−515.983	−	515.983i	−0.262292	−	0.262292i	0.563692	−	0.825985i	$-0.309380\pi$
$157$	−515.983	−	515.983i	−0.262292	−	0.262292i	−0.825985	+	0.563692i	$0.809380\pi$
$158$	2271.12	+	2271.12i	1.14355	+	1.14355i
$159$	−2081.49			−1.03819
$160$		0			0
$161$	−61.9750	+	56.6724i	−0.0303374	+	0.0277417i
$162$	3005.55	−	3005.55i	1.45765	−	1.45765i
$163$	70.5300	+	70.5300i	0.0338916	+	0.0338916i	0.723850	−	0.689958i	$-0.242371\pi$
$163$	70.5300	+	70.5300i	0.0338916	+	0.0338916i	−0.689958	+	0.723850i	$0.742371\pi$
$164$	5717.59			2.72237
$165$		0			0
$166$		−	7092.23i		−	3.31605i
$167$	−1207.85	−	1207.85i	−0.559676	−	0.559676i	0.369539	−	0.929215i	$-0.379516\pi$
$167$	−1207.85	−	1207.85i	−0.559676	−	0.559676i	−0.929215	+	0.369539i	$0.879516\pi$
$168$	277.010	−	6198.15i	0.127213	−	2.84641i
$169$		−	762.027i		−	0.346849i
$170$		0			0
$171$		−	484.179i		−	0.216527i
$172$	−3383.10	+	3383.10i	−1.49976	+	1.49976i
$173$	−800.716	+	800.716i	−0.351892	+	0.351892i	−0.860813	−	0.508921i	$-0.830044\pi$
$173$	−800.716	+	800.716i	−0.351892	+	0.351892i	0.508921	+	0.860813i	$0.330044\pi$
$174$	6324.97			2.75572
$175$		0			0
$176$	3132.68			1.34168
$177$	−1137.26	+	1137.26i	−0.482949	+	0.482949i
$178$	4304.99	−	4304.99i	1.81277	−	1.81277i
$179$		−	1435.34i		−	0.599343i	−0.954042	−	0.299672i	$-0.903123\pi$
$179$		−	1435.34i		−	0.599343i	0.954042	−	0.299672i	$-0.0968771\pi$
$180$		0			0
$181$		−	3536.87i		−	1.45245i	−0.687458	−	0.726224i	$-0.741273\pi$
$181$		−	3536.87i		−	1.45245i	0.687458	−	0.726224i	$-0.258727\pi$
$182$	5081.72	+	227.114i	2.06968	+	0.0924990i
$183$	−183.553	−	183.553i	−0.0741453	−	0.0741453i
$184$		−	217.381i		−	0.0870954i
$185$		0			0
$186$	−1327.39			−0.523273
$187$	−1060.64	−	1060.64i	−0.414769	−	0.414769i
$188$	1601.68	−	1601.68i	0.621352	−	0.621352i
$189$	−493.517	+	451.291i	−0.189937	+	0.173686i
$190$		0			0
$191$	1402.92			0.531474			0.265737	−	0.964046i	$-0.414385\pi$
$191$	1402.92			0.531474			0.265737	+	0.964046i	$0.414385\pi$
$192$	−742.482	−	742.482i	−0.279084	−	0.279084i
$193$	−3290.28	−	3290.28i	−1.22715	−	1.22715i	−0.965038	−	0.262110i	$-0.915582\pi$
$193$	−3290.28	−	3290.28i	−1.22715	−	1.22715i	−0.262110	−	0.965038i	$-0.584418\pi$
$194$	−6550.43			−2.42419
$195$		0			0
$196$	−535.292	+	5976.67i	−0.195077	+	2.17809i
$197$	−1207.31	+	1207.31i	−0.436636	+	0.436636i	−0.890878	−	0.454242i	$-0.849910\pi$
$197$	−1207.31	+	1207.31i	−0.436636	+	0.436636i	0.454242	+	0.890878i	$0.349910\pi$
$198$	2391.70	+	2391.70i	0.858438	+	0.858438i
$199$	1348.10			0.480221			0.240111	−	0.970746i	$-0.422816\pi$
$199$	1348.10			0.480221			0.240111	+	0.970746i	$0.422816\pi$
$200$		0			0
$201$			3215.20i			1.12827i
$202$	−1055.16	−	1055.16i	−0.367530	−	0.367530i
$203$	−3316.61	−	148.227i	−1.14670	−	0.0512487i
$204$		−	5976.52i		−	2.05118i
$205$		0			0
$206$			426.612i			0.144289i
$207$	70.0040	−	70.0040i	0.0235054	−	0.0235054i
$208$	−3927.22	+	3927.22i	−1.30915	+	1.30915i
$209$	−680.437			−0.225200
$210$		0			0
$211$	−1242.22			−0.405298			−0.202649	−	0.979251i	$-0.564955\pi$
$211$	−1242.22			−0.405298			−0.202649	+	0.979251i	$0.564955\pi$
$212$	−3684.71	+	3684.71i	−1.19371	+	1.19371i
$213$	−2342.70	+	2342.70i	−0.753611	+	0.753611i
$214$			4978.95i			1.59044i
$215$		0			0
$216$		−	1731.04i		−	0.545289i
$217$	696.038	+	31.1076i	0.217743	+	0.00973143i
$218$	3105.83	+	3105.83i	0.964924	+	0.964924i
$219$			6346.43i			1.95823i
$220$		0			0
$221$	2659.30			0.809429
$222$	−4778.39	−	4778.39i	−1.44461	−	1.44461i
$223$	−803.061	+	803.061i	−0.241152	+	0.241152i	−0.817327	−	0.576174i	$-0.804545\pi$
$223$	−803.061	+	803.061i	−0.241152	+	0.241152i	0.576174	+	0.817327i	$0.304545\pi$
$224$	−1649.85	−	1804.22i	−0.492123	−	0.538169i
$225$		0			0
$226$	5625.63			1.65580
$227$	3190.90	+	3190.90i	0.932986	+	0.932986i	0.997891	−	0.0649056i	$-0.0206746\pi$
$227$	3190.90	+	3190.90i	0.932986	+	0.932986i	−0.0649056	+	0.997891i	$0.520675\pi$
$228$	−1917.07	−	1917.07i	−0.556847	−	0.556847i
$229$	4312.63			1.24448			0.622242	−	0.782825i	$-0.286222\pi$
$229$	4312.63			1.24448			0.622242	+	0.782825i	$0.286222\pi$
$230$		0			0
$231$	−2679.71	−	2930.44i	−0.763256	−	0.834671i
$232$	6076.56	−	6076.56i	1.71959	−	1.71959i
$233$	4511.59	+	4511.59i	1.26852	+	1.26852i	0.946855	+	0.321661i	$0.104241\pi$
$233$	4511.59	+	4511.59i	1.26852	+	1.26852i	0.321661	+	0.946855i	$0.395759\pi$
$234$	−5996.61			−1.67526
$235$		0			0
$236$			4026.43i			1.11059i
$237$	3143.21	+	3143.21i	0.861490	+	0.861490i
$238$	−204.109	+	4566.98i	−0.0555900	+	1.24384i
$239$		−	1219.08i		−	0.329941i	−0.986298	−	0.164971i	$-0.947247\pi$
$239$		−	1219.08i		−	0.329941i	0.986298	−	0.164971i	$-0.0527529\pi$
$240$		0			0
$241$			2266.52i			0.605807i	0.953021	+	0.302904i	$0.0979560\pi$
$241$			2266.52i			0.605807i	−0.953021	+	0.302904i	$0.902044\pi$
$242$	−1390.95	+	1390.95i	−0.369477	+	0.369477i
$243$	3470.27	−	3470.27i	0.916123	−	0.916123i
$244$	−649.860			−0.170504
$245$		0			0
$246$	11531.6			2.98874
$247$	853.016	−	853.016i	0.219741	−	0.219741i
$248$	−1275.25	+	1275.25i	−0.326527	+	0.326527i
$249$		−	9815.57i		−	2.49814i
$250$		0			0
$251$		−	2913.88i		−	0.732758i	−0.930466	−	0.366379i	$-0.880597\pi$
$251$		−	2913.88i		−	0.732758i	0.930466	−	0.366379i	$-0.119403\pi$
$252$	315.832	−	7066.79i	0.0789505	−	1.76653i
$253$	−98.3796	−	98.3796i	−0.0244469	−	0.0244469i
$254$			4936.91i			1.21956i
$255$		0			0
$256$	−7961.05			−1.94362
$257$	2533.26	+	2533.26i	0.614866	+	0.614866i	0.944210	−	0.329344i	$-0.106828\pi$
$257$	2533.26	+	2533.26i	0.614866	+	0.614866i	−0.329344	+	0.944210i	$0.606828\pi$
$258$	−6823.28	+	6823.28i	−1.64651	+	1.64651i
$259$	2393.65	+	2617.61i	0.574262	+	0.627994i
$260$		0			0
$261$	3913.71			0.928171
$262$	6595.16	+	6595.16i	1.55515	+	1.55515i
$263$	−4347.32	−	4347.32i	−1.01927	−	1.01927i	−0.999811	−	0.0194552i	$-0.993807\pi$
$263$	−4347.32	−	4347.32i	−1.01927	−	1.01927i	−0.0194552	−	0.999811i	$-0.506193\pi$
$264$	10278.7			2.39625
$265$		0			0
$266$	1399.47	+	1530.41i	0.322582	+	0.352765i
$267$	5958.06	−	5958.06i	1.36565	−	1.36565i
$268$	5691.64	+	5691.64i	1.29728	+	1.29728i
$269$	−719.233			−0.163020			−0.0815100	−	0.996673i	$-0.525974\pi$
$269$	−719.233			−0.163020			−0.0815100	+	0.996673i	$0.525974\pi$
$270$		0			0
$271$			5060.37i			1.13430i	0.823614	+	0.567151i	$0.191954\pi$
$271$			5060.37i			1.13430i	−0.823614	+	0.567151i	$0.808046\pi$
$272$	−3529.43	−	3529.43i	−0.786775	−	0.786775i
$273$	7033.05	+	314.324i	1.55919	+	0.0696840i
$274$		−	10940.0i		−	2.41209i
$275$		0			0
$276$		−	554.352i		−	0.120899i
$277$	−365.718	+	365.718i	−0.0793281	+	0.0793281i	−0.745658	−	0.666329i	$-0.767864\pi$
$277$	−365.718	+	365.718i	−0.0793281	+	0.0793281i	0.666329	+	0.745658i	$0.267864\pi$
$278$	571.928	−	571.928i	0.123388	−	0.123388i
$279$	−821.349			−0.176247
$280$		0			0
$281$	914.357			0.194114			0.0970569	−	0.995279i	$-0.469057\pi$
$281$	914.357			0.194114			0.0970569	+	0.995279i	$0.469057\pi$
$282$	3230.37	−	3230.37i	0.682149	−	0.682149i
$283$	6608.81	−	6608.81i	1.38817	−	1.38817i	0.559019	−	0.829155i	$-0.311178\pi$
$283$	6608.81	−	6608.81i	1.38817	−	1.38817i	0.829155	−	0.559019i	$-0.188822\pi$
$284$			8294.24i			1.73300i
$285$		0			0
$286$			8427.28i			1.74236i
$287$	−6046.82	−	270.246i	−1.24367	−	0.0555824i
$288$	2037.97	+	2037.97i	0.416973	+	0.416973i
$289$		−	2523.07i		−	0.513549i
$290$		0			0
$291$	−9065.73			−1.82626
$292$	11234.6	+	11234.6i	2.25157	+	2.25157i
$293$	−1637.54	+	1637.54i	−0.326505	+	0.326505i	−0.851256	−	0.524751i	$-0.824159\pi$
$293$	−1637.54	+	1637.54i	−0.326505	+	0.326505i	0.524751	+	0.851256i	$0.324159\pi$
$294$	−1079.62	+	12054.2i	−0.214165	+	2.39120i
$295$		0			0
$296$	−9181.43			−1.80290
$297$	−783.412	−	783.412i	−0.153058	−	0.153058i
$298$	−1423.32	−	1423.32i	−0.276680	−	0.276680i
$299$	246.663			0.0477087
$300$		0			0
$301$	3737.81	−	3418.00i	0.715760	−	0.654519i
$302$	−12397.9	+	12397.9i	−2.36232	+	2.36232i
$303$	−1460.34	−	1460.34i	−0.276878	−	0.276878i
$304$	−2264.25			−0.427182
$305$		0			0
$306$		−	5389.20i		−	1.00680i
$307$	−2309.09	−	2309.09i	−0.429273	−	0.429273i	0.459108	−	0.888380i	$-0.348169\pi$
$307$	−2309.09	−	2309.09i	−0.429273	−	0.429273i	−0.888380	+	0.459108i	$0.848169\pi$
$308$	−9931.26	−	443.851i	−1.83729	−	0.0821129i
$309$			590.427i			0.108700i
$310$		0			0
$311$		−	4040.25i		−	0.736661i	−0.929695	−	0.368331i	$-0.879929\pi$
$311$		−	4040.25i		−	0.736661i	0.929695	−	0.368331i	$-0.120071\pi$
$312$	−12885.7	+	12885.7i	−2.33817	+	2.33817i
$313$	−2531.50	+	2531.50i	−0.457153	+	0.457153i	−0.897720	−	0.440566i	$-0.854778\pi$
$313$	−2531.50	+	2531.50i	−0.457153	+	0.457153i	0.440566	+	0.897720i	$0.354778\pi$
$314$	−3684.45			−0.662184
$315$		0			0
$316$	11128.4			1.98108
$317$	2394.74	−	2394.74i	0.424297	−	0.424297i	−0.462383	−	0.886680i	$-0.653006\pi$
$317$	2394.74	−	2394.74i	0.424297	−	0.424297i	0.886680	+	0.462383i	$0.153006\pi$
$318$	−7431.60	+	7431.60i	−1.31051	+	1.31051i
$319$		−	5500.10i		−	0.965350i
$320$		0			0
$321$			6890.81i			1.19815i
$322$	−18.9321	+	423.610i	−0.00327654	+	0.0733132i
$323$	766.612	+	766.612i	0.132060	+	0.132060i
$324$		−	14727.1i		−	2.52522i
$325$		0			0
$326$	503.630			0.0855629
$327$	4298.44	+	4298.44i	0.726924	+	0.726924i
$328$	11078.7	−	11078.7i	1.86500	−	1.86500i
$329$	−1769.61	+	1618.20i	−0.296540	+	0.271167i
$330$		0			0
$331$	1609.07			0.267198			0.133599	−	0.991036i	$-0.457347\pi$
$331$	1609.07			0.267198			0.133599	+	0.991036i	$0.457347\pi$
$332$	−17375.8	−	17375.8i	−2.87235	−	2.87235i
$333$	−2956.73	−	2956.73i	−0.486570	−	0.486570i
$334$	−8624.80			−1.41296
$335$		0			0
$336$	−8917.10	−	9751.44i	−1.44782	−	1.58329i
$337$	7839.49	−	7839.49i	1.26719	−	1.26719i	0.319663	−	0.947531i	$-0.396430\pi$
$337$	7839.49	−	7839.49i	1.26719	−	1.26719i	0.947531	−	0.319663i	$-0.103570\pi$
$338$	−2720.69	−	2720.69i	−0.437828	−	0.437828i
$339$	7785.82			1.24740
$340$		0			0
$341$			1154.28i			0.183307i
$342$	−1728.68	−	1728.68i	−0.273322	−	0.273322i
$343$	848.606	−	6295.51i	0.133587	−	0.991037i
$344$			13110.6i			2.05487i
$345$		0			0
$346$			5717.63i			0.888387i
$347$	8391.62	−	8391.62i	1.29823	−	1.29823i	0.368668	−	0.929561i	$-0.379814\pi$
$347$	8391.62	−	8391.62i	1.29823	−	1.29823i	0.929561	−	0.368668i	$-0.120186\pi$
$348$	15496.1	−	15496.1i	2.38700	−	2.38700i
$349$	−504.762			−0.0774192			−0.0387096	−	0.999251i	$-0.512325\pi$
$349$	−504.762			−0.0774192			−0.0387096	+	0.999251i	$0.512325\pi$
$350$		0			0
$351$	1964.22			0.298696
$352$	2864.04	−	2864.04i	0.433675	−	0.433675i
$353$	2910.85	−	2910.85i	0.438892	−	0.438892i	−0.452747	−	0.891639i	$-0.649556\pi$
$353$	2910.85	−	2910.85i	0.438892	−	0.438892i	0.891639	+	0.452747i	$0.149556\pi$
$354$			8120.80i			1.21925i
$355$		0			0
$356$		−	21094.3i		−	3.14043i
$357$	−282.485	+	6320.66i	−0.0418787	+	0.937044i
$358$	−5124.64	−	5124.64i	−0.756552	−	0.756552i
$359$			122.174i			0.0179612i	0.999960	+	0.00898060i	$0.00285865\pi$
$359$			122.174i			0.0179612i	−0.999960	+	0.00898060i	$0.997141\pi$
$360$		0			0
$361$	−6367.19			−0.928297
$362$	−12627.8	−	12627.8i	−1.83343	−	1.83343i
$363$	−1925.06	+	1925.06i	−0.278345	+	0.278345i
$364$	13006.5	−	11893.7i	1.87288	−	1.71263i
$365$		0			0
$366$	−1310.68			−0.187187
$367$	−7525.98	−	7525.98i	−1.07044	−	1.07044i	−0.997323	−	0.0731207i	$-0.976704\pi$
$367$	−7525.98	−	7525.98i	−1.07044	−	1.07044i	−0.0731207	−	0.997323i	$-0.523296\pi$
$368$	−327.371	−	327.371i	−0.0463734	−	0.0463734i
$369$	7135.45			1.00666
$370$		0			0
$371$	4071.04	−	3722.72i	0.569698	−	0.520955i
$372$	−3252.07	+	3252.07i	−0.453258	+	0.453258i
$373$	−3824.72	−	3824.72i	−0.530929	−	0.530929i	0.389920	−	0.920849i	$-0.372503\pi$
$373$	−3824.72	−	3824.72i	−0.530929	−	0.530929i	−0.920849	+	0.389920i	$0.872503\pi$
$374$	−7573.66			−1.04713
$375$		0			0
$376$		−	6207.00i		−	0.851334i
$377$	6895.09	+	6895.09i	0.941950	+	0.941950i
$378$	−150.759	+	3373.27i	−0.0205138	+	0.459001i
$379$		−	6001.43i		−	0.813385i	−0.913565	−	0.406692i	$-0.866682\pi$
$379$		−	6001.43i		−	0.813385i	0.913565	−	0.406692i	$-0.133318\pi$
$380$		0			0
$381$			6832.64i			0.918757i
$382$	5008.87	−	5008.87i	0.670880	−	0.670880i
$383$	−5683.84	+	5683.84i	−0.758305	+	0.758305i	−0.976014	−	0.217709i	$-0.930142\pi$
$383$	−5683.84	+	5683.84i	−0.758305	+	0.758305i	0.217709	+	0.976014i	$0.430142\pi$
$384$	−12681.7			−1.68531
$385$		0			0
$386$	−23494.7			−3.09806
$387$	−4222.05	+	4222.05i	−0.554571	+	0.554571i
$388$	−16048.4	+	16048.4i	−2.09983	+	2.09983i
$389$		−	5540.42i		−	0.722134i	−0.932540	−	0.361067i	$-0.882413\pi$
$389$		−	5540.42i		−	0.722134i	0.932540	−	0.361067i	$-0.117587\pi$
$390$		0			0
$391$			221.678i			0.0286719i
$392$	10543.5	+	12618.0i	1.35849	+	1.62577i
$393$	9127.64	+	9127.64i	1.17157	+	1.17157i
$394$			8620.98i			1.10233i
$395$		0			0
$396$	11719.2			1.48716
$397$	3568.08	+	3568.08i	0.451076	+	0.451076i	0.895711	−	0.444636i	$-0.146667\pi$
$397$	3568.08	+	3568.08i	0.451076	+	0.451076i	−0.444636	+	0.895711i	$0.646667\pi$
$398$	4813.14	−	4813.14i	0.606184	−	0.606184i
$399$	1936.85	+	2118.07i	0.243017	+	0.265755i
$400$		0			0
$401$	−304.302			−0.0378956			−0.0189478	−	0.999820i	$-0.506032\pi$
$401$	−304.302			−0.0378956			−0.0189478	+	0.999820i	$0.506032\pi$
$402$	11479.3	+	11479.3i	1.42422	+	1.42422i
$403$	−1447.03	−	1447.03i	−0.178863	−	0.178863i
$404$	−5170.26			−0.636708
$405$		0			0
$406$	−12370.6	+	11312.1i	−1.51217	+	1.38279i
$407$	−4155.21	+	4155.21i	−0.506060	+	0.506060i
$408$	−11580.5	−	11580.5i	−1.40519	−	1.40519i
$409$	11817.3			1.42867			0.714334	−	0.699805i	$-0.246730\pi$
$409$	11817.3			1.42867			0.714334	+	0.699805i	$0.246730\pi$
$410$		0			0
$411$		−	15140.9i		−	1.81714i
$412$	1045.19	+	1045.19i	0.124983	+	0.124983i
$413$	190.312	−	4258.28i	0.0226747	−	0.507352i
$414$		−	499.874i		−	0.0593417i
$415$		0			0
$416$			7180.88i			0.846326i
$417$	791.543	−	791.543i	0.0929545	−	0.0929545i
$418$	−2429.38	+	2429.38i	−0.284270	+	0.284270i
$419$	−6280.26			−0.732246			−0.366123	−	0.930567i	$-0.619315\pi$
$419$	−6280.26			−0.732246			−0.366123	+	0.930567i	$0.619315\pi$
$420$		0			0
$421$	5592.95			0.647467			0.323734	−	0.946148i	$-0.395062\pi$
$421$	5592.95			0.647467			0.323734	+	0.946148i	$0.395062\pi$
$422$	−4435.13	+	4435.13i	−0.511608	+	0.511608i
$423$	1998.86	−	1998.86i	0.229759	−	0.229759i
$424$			14279.4i			1.63554i
$425$		0			0
$426$			16728.4i			1.90257i
$427$	687.280	+	30.7161i	0.0778918	+	0.00348117i
$428$	12198.3	+	12198.3i	1.37764	+	1.37764i
$429$			11663.3i			1.31261i
$430$		0			0
$431$	3211.63			0.358930			0.179465	−	0.983764i	$-0.442563\pi$
$431$	3211.63			0.358930			0.179465	+	0.983764i	$0.442563\pi$
$432$	−2606.91	−	2606.91i	−0.290336	−	0.290336i
$433$	8998.00	−	8998.00i	0.998652	−	0.998652i	−0.00134740	−	0.999999i	$-0.500429\pi$
$433$	8998.00	−	8998.00i	0.998652	−	0.998652i	0.999999	+	0.00134740i	$0.000428890\pi$
$434$	2596.15	−	2374.02i	0.287141	−	0.262573i
$435$		0			0
$436$	15218.4			1.67163
$437$	71.1070	+	71.1070i	0.00778377	+	0.00778377i
$438$	22658.8	+	22658.8i	2.47187	+	2.47187i
$439$	−15391.3			−1.67332			−0.836658	−	0.547725i	$-0.815494\pi$
$439$	−15391.3			−1.67332			−0.836658	+	0.547725i	$0.815494\pi$
$440$		0			0
$441$	−668.035	+	7458.78i	−0.0721342	+	0.805397i
$442$	9494.57	−	9494.57i	1.02174	−	1.02174i
$443$	5980.38	+	5980.38i	0.641391	+	0.641391i	0.950897	−	0.309506i	$-0.100164\pi$
$443$	5980.38	+	5980.38i	0.641391	+	0.641391i	−0.309506	+	0.950897i	$0.600164\pi$
$444$	−23413.9			−2.50265
$445$		0			0
$446$			5734.38i			0.608813i
$447$	−1969.86	−	1969.86i	−0.208436	−	0.208436i
$448$	2780.09	+	124.249i	0.293185	+	0.0131031i
$449$			9630.65i			1.01225i	0.862461	+	0.506123i	$0.168922\pi$
$449$			9630.65i			1.01225i	−0.862461	+	0.506123i	$0.831078\pi$
$450$		0			0
$451$		−	10027.7i		−	1.04698i
$452$	13782.7	−	13782.7i	1.43425	−	1.43425i
$453$	−17158.6	+	17158.6i	−1.77965	+	1.77965i
$454$	22785.1			2.35542
$455$		0			0
$456$	−7429.26			−0.762954
$457$	−10749.0	+	10749.0i	−1.10025	+	1.10025i	−0.105873	+	0.994380i	$0.533764\pi$
$457$	−10749.0	+	10749.0i	−1.10025	+	1.10025i	−0.994380	+	0.105873i	$0.966236\pi$
$458$	15397.5	−	15397.5i	1.57091	−	1.57091i
$459$			1765.26i			0.179510i
$460$		0			0
$461$			7419.80i			0.749620i	0.927102	+	0.374810i	$0.122292\pi$
$461$			7419.80i			0.749620i	−0.927102	+	0.374810i	$0.877708\pi$
$462$	−20030.1	−	895.191i	−2.01706	−	0.0901473i
$463$	−7829.44	−	7829.44i	−0.785886	−	0.785886i	0.194931	−	0.980817i	$-0.437552\pi$
$463$	−7829.44	−	7829.44i	−0.785886	−	0.785886i	−0.980817	+	0.194931i	$0.937552\pi$
$464$		−	18302.3i		−	1.83117i
$465$		0			0
$466$	32215.7			3.20250
$467$	−2236.87	−	2236.87i	−0.221649	−	0.221649i	0.587543	−	0.809193i	$-0.300095\pi$
$467$	−2236.87	−	2236.87i	−0.221649	−	0.221649i	−0.809193	+	0.587543i	$0.800095\pi$
$468$	−14691.6	+	14691.6i	−1.45111	+	1.45111i
$469$	−5750.35	−	6288.39i	−0.566154	−	0.619127i
$470$		0			0
$471$	−5099.24			−0.498855
$472$	7801.85	+	7801.85i	0.760825	+	0.760825i
$473$	5933.42	+	5933.42i	0.576784	+	0.576784i
$474$	22444.5			2.17492
$475$		0			0
$476$	10689.0	+	11689.1i	1.02926	+	1.12556i
$477$	−4598.46	+	4598.46i	−0.441402	+	0.441402i
$478$	−4352.52	−	4352.52i	−0.416485	−	0.416485i
$479$	−16127.0			−1.53833			−0.769167	−	0.639047i	$-0.779329\pi$
$479$	−16127.0			−1.53833			−0.769167	+	0.639047i	$0.779329\pi$
$480$		0			0
$481$		−	10418.2i		−	0.987586i
$482$	8092.22	+	8092.22i	0.764711	+	0.764711i
$483$	−26.2018	+	586.272i	−0.00246838	+	0.0552304i
$484$			6815.59i			0.640081i
$485$		0			0
$486$		−	24780.0i		−	2.31284i
$487$	−7934.50	+	7934.50i	−0.738288	+	0.738288i	−0.972247	−	0.233958i	$-0.924832\pi$
$487$	−7934.50	+	7934.50i	−0.738288	+	0.738288i	0.233958	+	0.972247i	$0.424832\pi$
$488$	−1259.21	+	1259.21i	−0.116807	+	0.116807i
$489$	697.019			0.0644587
$490$		0			0
$491$	−4160.37			−0.382393			−0.191196	−	0.981552i	$-0.561237\pi$
$491$	−4160.37			−0.382393			−0.191196	+	0.981552i	$0.561237\pi$
$492$	28252.3	−	28252.3i	2.58885	−	2.58885i
$493$	−6196.67	+	6196.67i	−0.566093	+	0.566093i
$494$		−	6091.09i		−	0.554759i
$495$		0			0
$496$			3841.01i			0.347715i
$497$	392.033	−	8771.83i	0.0353825	−	0.791691i
$498$	−35044.8	−	35044.8i	−3.15340	−	3.15340i
$499$			5858.81i			0.525603i	0.964850	+	0.262802i	$0.0846465\pi$
$499$			5858.81i			0.525603i	−0.964850	+	0.262802i	$0.915353\pi$
$500$		0			0
$501$	−11936.6			−1.06445
$502$	−10403.5	−	10403.5i	−0.924961	−	0.924961i
$503$	−13951.3	+	13951.3i	−1.23669	+	1.23669i	−0.275347	+	0.961345i	$0.588793\pi$
$503$	−13951.3	+	13951.3i	−1.23669	+	1.23669i	−0.961345	+	0.275347i	$0.911207\pi$
$504$	−13081.1	−	14305.0i	−1.15610	−	1.26428i
$505$		0			0
$506$	−702.494			−0.0617187
$507$	−3765.40	−	3765.40i	−0.329837	−	0.329837i
$508$	12095.3	+	12095.3i	1.05639	+	1.05639i
$509$	18246.3			1.58891			0.794454	−	0.607324i	$-0.207757\pi$
$509$	18246.3			1.58891			0.794454	+	0.607324i	$0.207757\pi$
$510$		0			0
$511$	−11350.5	−	12412.6i	−0.982618	−	1.07456i
$512$	−18157.7	+	18157.7i	−1.56731	+	1.56731i
$513$	566.236	+	566.236i	0.0487328	+	0.0487328i
$514$	18089.1			1.55229
$515$		0			0
$516$			33433.8i			2.85240i
$517$	−2809.08	−	2809.08i	−0.238962	−	0.238962i
$518$	17891.8	+	799.627i	1.51761	+	0.0678255i
$519$			7913.14i			0.669265i
$520$		0			0
$521$			14936.8i			1.25603i	0.778200	+	0.628016i	$0.216133\pi$
$521$			14936.8i			1.25603i	−0.778200	+	0.628016i	$0.783867\pi$
$522$	13973.2	−	13973.2i	1.17163	−	1.17163i
$523$	15191.9	−	15191.9i	1.27017	−	1.27017i	0.324165	−	0.946001i	$-0.394917\pi$
$523$	15191.9	−	15191.9i	1.27017	−	1.27017i	0.946001	−	0.324165i	$-0.105083\pi$
$524$	32316.0			2.69415
$525$		0			0
$526$	−31042.7			−2.57324
$527$	1300.46	−	1300.46i	0.107493	−	0.107493i
$528$	15479.5	−	15479.5i	1.27587	−	1.27587i
$529$		−	12146.4i		−	0.998310i
$530$		0			0
$531$			5024.92i			0.410664i
$532$	7178.14	+	320.808i	0.584984	+	0.0261443i
$533$	12571.1	+	12571.1i	1.02160	+	1.02160i
$534$		−	42544.4i		−	3.44771i
$535$		0			0
$536$	22056.9			1.77745
$537$	−7092.44	−	7092.44i	−0.569947	−	0.569947i
$538$	−2567.89	+	2567.89i	−0.205780	+	0.205780i
$539$	10482.1	+	938.817i	0.837657	+	0.0750236i
$540$		0			0
$541$	8027.88			0.637977			0.318988	−	0.947759i	$-0.396657\pi$
$541$	8027.88			0.637977			0.318988	+	0.947759i	$0.396657\pi$
$542$	18067.2	+	18067.2i	1.43183	+	1.43183i
$543$	−17476.7	−	17476.7i	−1.38121	−	1.38121i
$544$	−6453.51			−0.508625
$545$		0			0
$546$	26232.5	−	23988.0i	2.05613	−	1.88021i
$547$	−5287.54	+	5287.54i	−0.413307	+	0.413307i	−0.882889	−	0.469582i	$-0.844405\pi$
$547$	−5287.54	+	5287.54i	−0.413307	+	0.413307i	0.469582	+	0.882889i	$0.344405\pi$
$548$	−26802.9	−	26802.9i	−2.08935	−	2.08935i
$549$	−811.014			−0.0630478
$550$		0			0
$551$			3975.37i			0.307362i
$552$	−1074.14	−	1074.14i	−0.0828236	−	0.0828236i
$553$	−11769.2	−	525.992i	−0.905020	−	0.0404475i
$554$			2611.47i			0.200272i
$555$		0			0
$556$		−	2802.43i		−	0.213758i
$557$	4891.64	−	4891.64i	0.372111	−	0.372111i	−0.496135	−	0.868245i	$-0.665248\pi$
$557$	4891.64	−	4891.64i	0.372111	−	0.372111i	0.868245	+	0.496135i	$0.165248\pi$
$558$	−2932.48	+	2932.48i	−0.222477	+	0.222477i
$559$	−14876.6			−1.12561
$560$		0			0
$561$	−10481.9			−0.788850
$562$	3264.55	−	3264.55i	0.245030	−	0.245030i
$563$	1138.04	−	1138.04i	0.0851916	−	0.0851916i	−0.663227	−	0.748418i	$-0.730814\pi$
$563$	1138.04	−	1138.04i	0.0851916	−	0.0851916i	0.748418	+	0.663227i	$0.230814\pi$
$564$		−	15828.7i		−	1.18175i
$565$		0			0
$566$		−	47191.2i		−	3.50459i
$567$	−696.087	+	15575.1i	−0.0515572	+	1.15360i
$568$	16071.4	+	16071.4i	1.18722	+	1.18722i
$569$		−	7200.63i		−	0.530521i	−0.964177	−	0.265260i	$-0.914542\pi$
$569$		−	7200.63i		−	0.530521i	0.964177	−	0.265260i	$-0.0854579\pi$
$570$		0			0
$571$	2089.22			0.153119			0.0765597	−	0.997065i	$-0.475606\pi$
$571$	2089.22			0.153119			0.0765597	+	0.997065i	$0.475606\pi$
$572$	20646.7	+	20646.7i	1.50923	+	1.50923i
$573$	6932.22	−	6932.22i	0.505406	−	0.505406i
$574$	−22554.0	+	20624.2i	−1.64004	+	1.49972i
$575$		0			0
$576$	−3280.61			−0.237312
$577$	−7943.75	−	7943.75i	−0.573141	−	0.573141i	0.359864	−	0.933005i	$-0.382823\pi$
$577$	−7943.75	−	7943.75i	−0.573141	−	0.573141i	−0.933005	+	0.359864i	$0.882823\pi$
$578$	−9008.17	−	9008.17i	−0.648253	−	0.648253i
$579$	−32516.5			−2.33392
$580$		0			0
$581$	17555.0	+	19197.6i	1.25354	+	1.37083i
$582$	−32367.6	+	32367.6i	−2.30529	+	2.30529i
$583$	6462.40	+	6462.40i	0.459083	+	0.459083i
$584$	43537.8			3.08494
$585$		0			0
$586$			11693.1i			0.824295i
$587$	−18688.9	−	18688.9i	−1.31410	−	1.31410i	−0.918368	−	0.395727i	$-0.870493\pi$
$587$	−18688.9	−	18688.9i	−1.31410	−	1.31410i	−0.395727	−	0.918368i	$-0.629507\pi$
$588$	26887.5	+	32177.5i	1.88575	+	2.25677i
$589$		−	834.290i		−	0.0583639i
$590$		0			0
$591$			11931.4i			0.830440i
$592$	−13827.0	+	13827.0i	−0.959945	+	0.959945i
$593$	5453.19	−	5453.19i	0.377632	−	0.377632i	−0.492615	−	0.870247i	$-0.663959\pi$
$593$	5453.19	−	5453.19i	0.377632	−	0.377632i	0.870247	+	0.492615i	$0.163959\pi$
$594$	−5594.07			−0.386410
$595$		0			0
$596$	−6974.20			−0.479320
$597$	6661.34	−	6661.34i	0.456668	−	0.456668i
$598$	880.667	−	880.667i	0.0602227	−	0.0602227i
$599$		−	13401.4i		−	0.914136i	−0.889432	−	0.457068i	$-0.848900\pi$
$599$		−	13401.4i		−	0.914136i	0.889432	−	0.457068i	$-0.151100\pi$
$600$		0			0
$601$		−	15689.8i		−	1.06489i	−0.846464	−	0.532446i	$-0.821273\pi$
$601$		−	15689.8i		−	1.06489i	0.846464	−	0.532446i	$-0.178727\pi$
$602$	1141.82	−	25548.6i	0.0773045	−	1.72970i
$603$	7103.06	+	7103.06i	0.479700	+	0.479700i
$604$			60749.2i			4.09247i
$605$		0			0
$606$	−10427.8			−0.699008
$607$	9429.70	+	9429.70i	0.630543	+	0.630543i	0.948204	−	0.317661i	$-0.102897\pi$
$607$	9429.70	+	9429.70i	0.630543	+	0.630543i	−0.317661	+	0.948204i	$0.602897\pi$
$608$	−2070.08	+	2070.08i	−0.138080	+	0.138080i
$609$	−17120.8	+	15655.9i	−1.13919	+	1.04172i
$610$		0			0
$611$	7043.10			0.466339
$612$	−13203.4	−	13203.4i	−0.872086	−	0.872086i
$613$	13138.6	+	13138.6i	0.865681	+	0.865681i	0.991991	−	0.126310i	$-0.0403133\pi$
$613$	13138.6	+	13138.6i	0.865681	+	0.865681i	−0.126310	+	0.991991i	$0.540313\pi$
$614$	−16488.4			−1.08374
$615$		0			0
$616$	−20103.4	+	18383.4i	−1.31492	+	1.20241i
$617$	10622.2	−	10622.2i	0.693088	−	0.693088i	−0.269822	−	0.962910i	$-0.586965\pi$
$617$	10622.2	−	10622.2i	0.693088	−	0.693088i	0.962910	+	0.269822i	$0.0869648\pi$
$618$	2108.02	+	2108.02i	0.137212	+	0.137212i
$619$	1244.71			0.0808224			0.0404112	−	0.999183i	$-0.487133\pi$
$619$	1244.71			0.0808224			0.0404112	+	0.999183i	$0.487133\pi$
$620$		0			0
$621$			163.736i			0.0105805i
$622$	−14425.0	−	14425.0i	−0.929888	−	0.929888i
$623$	−997.036	+	22308.9i	−0.0641178	+	1.43465i
$624$			38811.1i			2.48989i
$625$		0			0
$626$			18076.6i			1.15413i
$627$	−3362.24	+	3362.24i	−0.214155	+	0.214155i
$628$	−9026.83	+	9026.83i	−0.573582	+	0.573582i
$629$	9362.91			0.593519
$630$		0			0
$631$	−7532.27			−0.475206			−0.237603	−	0.971362i	$-0.576362\pi$
$631$	−7532.27			−0.475206			−0.237603	+	0.971362i	$0.576362\pi$
$632$	21563.0	−	21563.0i	1.35717	−	1.35717i
$633$	−6138.17	+	6138.17i	−0.385419	+	0.385419i
$634$		−	17100.0i		−	1.07118i
$635$		0			0
$636$			36414.5i			2.27033i
$637$	−14317.6	+	11963.8i	−0.890558	+	0.744148i
$638$	−19637.1	−	19637.1i	−1.21856	−	1.21856i
$639$			10351.1i			0.640816i
$640$		0			0
$641$	−6109.53			−0.376462			−0.188231	−	0.982125i	$-0.560275\pi$
$641$	−6109.53			−0.376462			−0.188231	+	0.982125i	$0.560275\pi$
$642$	24602.4	+	24602.4i	1.51243	+	1.51243i
$643$	1890.33	−	1890.33i	0.115937	−	0.115937i	−0.646758	−	0.762695i	$-0.723876\pi$
$643$	1890.33	−	1890.33i	0.115937	−	0.115937i	0.762695	+	0.646758i	$0.223876\pi$
$644$	991.452	+	1084.22i	0.0606657	+	0.0663419i
$645$		0			0
$646$	5474.11			0.333399
$647$	18918.1	+	18918.1i	1.14953	+	1.14953i	0.986644	+	0.162889i	$0.0520811\pi$
$647$	18918.1	+	18918.1i	1.14953	+	1.14953i	0.162889	+	0.986644i	$0.447919\pi$
$648$	−28536.1	−	28536.1i	−1.72994	−	1.72994i
$649$	7061.72			0.427114
$650$		0			0
$651$	3593.04	−	3285.62i	0.216317	−	0.197809i
$652$	1233.88	−	1233.88i	0.0741144	−	0.0741144i
$653$	3650.44	+	3650.44i	0.218764	+	0.218764i	0.807977	−	0.589214i	$-0.200562\pi$
$653$	3650.44	+	3650.44i	0.218764	+	0.218764i	−0.589214	+	0.807977i	$0.700562\pi$
$654$	30693.6			1.83519
$655$		0			0
$656$		−	33368.7i		−	1.98602i
$657$	14020.6	+	14020.6i	0.832567	+	0.832567i
$658$	−540.579	+	12095.6i	−0.0320273	+	0.716617i
$659$			30832.1i			1.82253i	0.411817	+	0.911267i	$0.364894\pi$
$659$			30832.1i			1.82253i	−0.411817	+	0.911267i	$0.635106\pi$
$660$		0			0
$661$		−	4032.29i		−	0.237274i	−0.992938	−	0.118637i	$-0.962148\pi$
$661$		−	4032.29i		−	0.237274i	0.992938	−	0.118637i	$-0.0378524\pi$
$662$	5744.90	−	5744.90i	0.337284	−	0.337284i
$663$	13140.4	−	13140.4i	0.769729	−	0.769729i
$664$	−67336.8			−3.93550
$665$		0			0
$666$	−21113.0			−1.22839
$667$	−574.771	+	574.771i	−0.0333661	+	0.0333661i
$668$	−21130.6	+	21130.6i	−1.22390	+	1.22390i
$669$			7936.32i			0.458649i
$670$		0			0
$671$			1139.75i			0.0655732i
$672$	−17067.6	−	762.791i	−0.979758	−	0.0437877i
$673$	−17723.3	−	17723.3i	−1.01513	−	1.01513i	−0.999884	−	0.0152461i	$-0.995147\pi$
$673$	−17723.3	−	17723.3i	−1.01513	−	1.01513i	−0.0152461	−	0.999884i	$-0.504853\pi$
$674$		−	55979.1i		−	3.19916i
$675$		0			0
$676$	−13331.2			−0.758491
$677$	−9377.64	−	9377.64i	−0.532366	−	0.532366i	0.388910	−	0.921276i	$-0.372852\pi$
$677$	−9377.64	−	9377.64i	−0.532366	−	0.532366i	−0.921276	+	0.388910i	$0.872852\pi$
$678$	27797.9	−	27797.9i	1.57459	−	1.57459i
$679$	17731.0	−	16214.0i	1.00214	−	0.916399i
$680$		0			0
$681$	31534.4			1.77445
$682$	4121.14	+	4121.14i	0.231388	+	0.231388i
$683$	−11971.7	−	11971.7i	−0.670693	−	0.670693i	0.287183	−	0.957876i	$-0.407281\pi$
$683$	−11971.7	−	11971.7i	−0.670693	−	0.670693i	−0.957876	+	0.287183i	$0.907281\pi$
$684$	−8470.45			−0.473502
$685$		0			0
$686$	−19447.2	−	25506.8i	−1.08236	−	1.41961i
$687$	21310.0	−	21310.0i	1.18344	−	1.18344i
$688$	19744.3	+	19744.3i	1.09410	+	1.09410i
$689$	−16202.9			−0.895910
$690$		0			0
$691$			4704.44i			0.258995i	0.991580	+	0.129497i	$0.0413364\pi$
$691$			4704.44i			0.258995i	−0.991580	+	0.129497i	$0.958664\pi$
$692$	14008.1	+	14008.1i	0.769519	+	0.769519i
$693$	−12394.0	−	553.918i	−0.679380	−	0.0303631i
$694$		−	59921.6i		−	3.27751i
$695$		0			0
$696$		−	60052.1i		−	3.27050i
$697$	−11297.7	+	11297.7i	−0.613962	+	0.613962i
$698$	−1802.16	+	1802.16i	−0.0977263	+	0.0977263i
$699$	44586.2			2.41260
$700$		0			0
$701$	29583.6			1.59395			0.796974	−	0.604014i	$-0.206433\pi$
$701$	29583.6			1.59395			0.796974	+	0.604014i	$0.206433\pi$
$702$	7012.89	−	7012.89i	0.377044	−	0.377044i
$703$	3003.31	−	3003.31i	0.161127	−	0.161127i
$704$			4610.37i			0.246818i
$705$		0			0
$706$		−	20785.4i		−	1.10803i
$707$	5467.97	+	244.376i	0.290869	+	0.0129996i
$708$	19895.8	+	19895.8i	1.05612	+	1.05612i
$709$			29637.0i			1.56988i	0.619574	+	0.784938i	$0.287305\pi$
$709$			29637.0i			1.56988i	−0.619574	+	0.784938i	$0.712695\pi$
$710$		0			0
$711$	13888.0			0.732548
$712$	−40873.5	−	40873.5i	−2.15140	−	2.15140i
$713$	120.624	−	120.624i	0.00633577	−	0.00633577i
$714$	21558.2	+	23575.4i	1.12997	+	1.23569i
$715$		0			0
$716$	−25110.5			−1.31065
$717$	−6023.85	−	6023.85i	−0.313758	−	0.313758i
$718$	436.199	+	436.199i	0.0226724	+	0.0226724i
$719$	19761.2			1.02499			0.512496	−	0.858690i	$-0.328721\pi$
$719$	19761.2			1.02499			0.512496	+	0.858690i	$0.328721\pi$
$720$		0			0
$721$	−1055.97	−	1154.78i	−0.0545444	−	0.0596479i
$722$	−22732.9	+	22732.9i	−1.17179	+	1.17179i
$723$	11199.5	+	11199.5i	0.576094	+	0.576094i
$724$	−61875.5			−3.17622
$725$		0			0
$726$			13746.2i			0.702711i
$727$	2991.47	+	2991.47i	0.152610	+	0.152610i	0.779283	−	0.626673i	$-0.215584\pi$
$727$	2991.47	+	2991.47i	0.152610	+	0.152610i	−0.626673	+	0.779283i	$0.715584\pi$
$728$	2156.32	−	48248.2i	0.109778	−	2.45631i
$729$		−	11566.2i		−	0.587624i
$730$		0			0
$731$		−	13369.7i		−	0.676467i
$732$	−3211.15	+	3211.15i	−0.162141	+	0.162141i
$733$	14061.2	−	14061.2i	0.708542	−	0.708542i	−0.257687	−	0.966229i	$-0.582960\pi$
$733$	14061.2	−	14061.2i	0.708542	−	0.708542i	0.966229	+	0.257687i	$0.0829602\pi$
$734$	−53740.4			−2.70244
$735$		0			0
$736$	−598.595			−0.0299789
$737$	9982.22	−	9982.22i	0.498914	−	0.498914i
$738$	25475.9	−	25475.9i	1.27071	−	1.27071i
$739$		−	3186.25i		−	0.158604i	−0.996851	−	0.0793018i	$-0.974731\pi$
$739$		−	3186.25i		−	0.158604i	0.996851	−	0.0793018i	$-0.0252691\pi$
$740$		0			0
$741$		−	8430.00i		−	0.417927i
$742$	1243.62	−	27826.3i	0.0615294	−	1.37673i
$743$	8149.04	+	8149.04i	0.402368	+	0.402368i	0.879067	−	0.476699i	$-0.158167\pi$
$743$	8149.04	+	8149.04i	0.402368	+	0.402368i	−0.476699	+	0.879067i	$0.658167\pi$
$744$			12602.8i			0.621024i
$745$		0			0
$746$	−27311.0			−1.34038
$747$	−21684.7	−	21684.7i	−1.06212	−	1.06212i
$748$	−18555.3	+	18555.3i	−0.907018	+	0.907018i
$749$	−12324.1	−	13477.3i	−0.601221	−	0.657475i
$750$		0			0
$751$	−33944.9			−1.64936			−0.824679	−	0.565601i	$-0.808644\pi$
$751$	−33944.9			−1.64936			−0.824679	+	0.565601i	$0.808644\pi$
$752$	−9347.61	−	9347.61i	−0.453287	−	0.453287i
$753$	−14398.3	−	14398.3i	−0.696818	−	0.696818i
$754$	49235.4			2.37805
$755$		0			0
$756$	7895.09	+	8633.81i	0.379817	+	0.415355i
$757$	1632.37	−	1632.37i	0.0783743	−	0.0783743i	−0.666833	−	0.745207i	$-0.732351\pi$
$757$	1632.37	−	1632.37i	0.0783743	−	0.0783743i	0.745207	+	0.666833i	$0.232351\pi$
$758$	−21427.1	−	21427.1i	−1.02674	−	1.02674i
$759$	−972.244			−0.0464957
$760$		0			0
$761$			8358.98i			0.398177i	0.979981	+	0.199089i	$0.0637982\pi$
$761$			8358.98i			0.398177i	−0.979981	+	0.199089i	$0.936202\pi$
$762$	24394.7	+	24394.7i	1.15975	+	1.15975i
$763$	−16094.7	−	719.311i	−0.763654	−	0.0341295i
$764$		−	24543.3i		−	1.16223i
$765$		0			0
$766$			40586.3i			1.91442i
$767$	−8852.78	+	8852.78i	−0.416761	+	0.416761i
$768$	−39337.9	+	39337.9i	−1.84829	+	1.84829i
$769$	26741.8			1.25401			0.627006	−	0.779014i	$-0.284280\pi$
$769$	26741.8			1.25401			0.627006	+	0.779014i	$0.284280\pi$
$770$		0			0
$771$	25035.2			1.16942
$772$	−57561.6	+	57561.6i	−2.68353	+	2.68353i
$773$	−842.330	+	842.330i	−0.0391934	+	0.0391934i	−0.726432	−	0.687238i	$-0.758823\pi$
$773$	−842.330	+	842.330i	−0.0391934	+	0.0391934i	0.687238	+	0.726432i	$0.258823\pi$
$774$			30148.2i			1.40007i
$775$		0			0
$776$			62192.7i			2.87705i
$777$	24762.1	+	1106.68i	1.14329	+	0.0510962i
$778$	−19781.1	−	19781.1i	−0.911551	−	0.911551i
$779$			7247.88i			0.333353i
$780$		0			0
$781$	14546.8			0.666485
$782$	791.462	+	791.462i	0.0361926	+	0.0361926i
$783$	−4576.99	+	4576.99i	−0.208900	+	0.208900i
$784$	34880.7	+	3124.04i	1.58895	+	0.142312i
$785$		0			0
$786$	65177.3			2.95776
$787$	5939.92	+	5939.92i	0.269041	+	0.269041i	0.828714	−	0.559673i	$-0.189073\pi$
$787$	5939.92	+	5939.92i	0.269041	+	0.269041i	−0.559673	+	0.828714i	$0.689073\pi$
$788$	21121.2	+	21121.2i	0.954838	+	0.954838i
$789$	−42962.7			−1.93855
$790$		0			0
$791$	−15227.8	+	13924.9i	−0.684496	+	0.625930i
$792$	22707.9	−	22707.9i	1.01880	−	1.01880i
$793$	−1428.83	−	1428.83i	−0.0639837	−	0.0639837i
$794$	25478.4			1.13879
$795$		0			0
$796$		−	23584.2i		−	1.05015i
$797$	11178.2	+	11178.2i	0.496803	+	0.496803i	0.910441	−	0.413639i	$-0.135742\pi$
$797$	11178.2	+	11178.2i	0.496803	+	0.496803i	−0.413639	+	0.910441i	$0.635742\pi$
$798$	14477.4	+	647.028i	0.642222	+	0.0287024i
$799$			6329.69i			0.280261i
$800$		0			0
$801$		−	26325.3i		−	1.16125i
$802$	−1086.46	+	1086.46i	−0.0478356	+	0.0478356i
$803$	19703.8	−	19703.8i	0.865917	−	0.865917i
$804$	56248.1			2.46731
$805$		0			0
$806$	−10332.8			−0.451559
$807$	−3553.94	+	3553.94i	−0.155024	+	0.155024i
$808$	−10018.2	+	10018.2i	−0.436187	+	0.436187i
$809$		−	8276.48i		−	0.359685i	−0.983695	−	0.179843i	$-0.942441\pi$
$809$		−	8276.48i		−	0.359685i	0.983695	−	0.179843i	$-0.0575589\pi$
$810$		0			0
$811$			38978.8i			1.68771i	0.536572	+	0.843854i	$0.319719\pi$
$811$			38978.8i			1.68771i	−0.536572	+	0.843854i	$0.680281\pi$
$812$	−2593.15	+	58022.2i	−0.112071	+	2.50761i
$813$	25004.8	+	25004.8i	1.07867	+	1.07867i
$814$			29670.9i			1.27760i
$815$		0			0
$816$	−34879.8			−1.49637
$817$	−4288.57	−	4288.57i	−0.183645	−	0.183645i
$818$	42191.4	−	42191.4i	1.80341	−	1.80341i
$819$	16231.9	−	14843.1i	0.692539	−	0.633285i
$820$		0			0
$821$	−23105.0			−0.982180			−0.491090	−	0.871109i	$-0.663401\pi$
$821$	−23105.0			−0.982180			−0.491090	+	0.871109i	$0.663401\pi$
$822$	−54057.9	−	54057.9i	−2.29378	−	2.29378i
$823$	−3288.90	−	3288.90i	−0.139300	−	0.139300i	0.634018	−	0.773318i	$-0.281404\pi$
$823$	−3288.90	−	3288.90i	−0.139300	−	0.139300i	−0.773318	+	0.634018i	$0.781404\pi$
$824$	4050.45			0.171243
$825$		0			0
$826$	−14524.0	−	15882.9i	−0.611808	−	0.669053i
$827$	−786.261	+	786.261i	−0.0330604	+	0.0330604i	−0.723444	−	0.690383i	$-0.757442\pi$
$827$	−786.261	+	786.261i	−0.0330604	+	0.0330604i	0.690383	+	0.723444i	$0.257442\pi$
$828$	−1224.68	−	1224.68i	−0.0514017	−	0.0514017i
$829$	−24870.0			−1.04194			−0.520971	−	0.853575i	$-0.674430\pi$
$829$	−24870.0			−1.04194			−0.520971	+	0.853575i	$0.674430\pi$
$830$		0			0
$831$			3614.24i			0.150874i
$832$	−5779.70	−	5779.70i	−0.240835	−	0.240835i
$833$	−10751.9	−	12867.4i	−0.447218	−	0.535207i
$834$		−	5652.13i		−	0.234673i
$835$		0			0
$836$			11903.9i			0.492469i
$837$	960.549	−	960.549i	0.0396672	−	0.0396672i
$838$	−22422.6	+	22422.6i	−0.924314	+	0.924314i
$839$	−22765.1			−0.936755			−0.468378	−	0.883528i	$-0.655161\pi$
$839$	−22765.1			−0.936755			−0.468378	+	0.883528i	$0.655161\pi$
$840$		0			0
$841$	−7744.68			−0.317548
$842$	19968.7	−	19968.7i	0.817299	−	0.817299i
$843$	4518.11	−	4518.11i	0.184593	−	0.184593i
$844$			21731.9i			0.886309i
$845$		0			0
$846$		−	14273.2i		−	0.580049i
$847$	322.144	−	7208.03i	0.0130685	−	0.292410i
$848$	21504.5	+	21504.5i	0.870835	+	0.870835i
$849$		−	65312.2i		−	2.64017i
$850$		0			0
$851$	868.455			0.0349827
$852$	40984.3	+	40984.3i	1.64800	+	1.64800i
$853$	11703.5	−	11703.5i	0.469777	−	0.469777i	−0.432065	−	0.901842i	$-0.642215\pi$
$853$	11703.5	−	11703.5i	0.469777	−	0.469777i	0.901842	+	0.432065i	$0.142215\pi$
$854$	2563.48	−	2344.15i	0.102717	−	0.0939286i
$855$		0			0
$856$	47272.3			1.88754
$857$	25881.3	+	25881.3i	1.03161	+	1.03161i	0.999484	+	0.0321229i	$0.0102268\pi$
$857$	25881.3	+	25881.3i	1.03161	+	1.03161i	0.0321229	+	0.999484i	$0.489773\pi$
$858$	41641.7	+	41641.7i	1.65690	+	1.65690i
$859$	−11267.9			−0.447563			−0.223782	−	0.974639i	$-0.571840\pi$
$859$	−11267.9			−0.447563			−0.223782	+	0.974639i	$0.571840\pi$
$860$		0			0
$861$	−31214.5	+	28543.7i	−1.23552	+	1.12981i
$862$	11466.6	−	11466.6i	0.453077	−	0.453077i
$863$	−21760.8	−	21760.8i	−0.858338	−	0.858338i	0.132804	−	0.991142i	$-0.457602\pi$
$863$	−21760.8	−	21760.8i	−0.858338	−	0.858338i	−0.991142	+	0.132804i	$0.957602\pi$
$864$	−4766.71			−0.187693
$865$		0			0
$866$		−	64251.6i		−	2.52120i
$867$	−12467.2	−	12467.2i	−0.488361	−	0.488361i
$868$	544.210	−	12176.8i	0.0212807	−	0.476161i
$869$		−	19517.4i		−	0.761891i
$870$		0			0
$871$			25028.0i			0.973642i
$872$	29488.1	−	29488.1i	1.14518	−	1.14518i
$873$	−20028.1	+	20028.1i	−0.776460	+	0.776460i
$874$	507.750			0.0196509
$875$		0			0
$876$	111027.			4.28227
$877$	10089.3	−	10089.3i	0.388473	−	0.388473i	−0.485669	−	0.874143i	$-0.661424\pi$
$877$	10089.3	−	10089.3i	0.388473	−	0.388473i	0.874143	+	0.485669i	$0.161424\pi$
$878$	−54951.9	+	54951.9i	−2.11223	+	2.11223i
$879$			16183.1i			0.620982i
$880$		0			0
$881$		−	12811.2i		−	0.489920i	−0.969533	−	0.244960i	$-0.921225\pi$
$881$		−	12811.2i		−	0.489920i	0.969533	−	0.244960i	$-0.0787748\pi$
$882$	24245.2	+	29015.4i	0.925598	+	1.10771i
$883$	30984.3	+	30984.3i	1.18086	+	1.18086i	0.979521	+	0.201344i	$0.0645310\pi$
$883$	30984.3	+	30984.3i	1.18086	+	1.18086i	0.201344	+	0.979521i	$0.435469\pi$
$884$		−	46523.0i		−	1.77006i
$885$		0			0
$886$	42703.8			1.61926
$887$	15820.5	+	15820.5i	0.598871	+	0.598871i	0.940012	−	0.341141i	$-0.110813\pi$
$887$	15820.5	+	15820.5i	0.598871	+	0.598871i	−0.341141	+	0.940012i	$0.610813\pi$
$888$	−45368.1	+	45368.1i	−1.71448	+	1.71448i
$889$	−12220.1	−	13363.5i	−0.461022	−	0.504159i
$890$		0			0
$891$	−25829.0			−0.971160
$892$	14049.1	+	14049.1i	0.527353	+	0.527353i
$893$	2030.36	+	2030.36i	0.0760843	+	0.0760843i
$894$	−14066.1			−0.526219
$895$		0			0
$896$	24803.2	−	22681.1i	0.924797	−	0.845671i
$897$	1218.83	−	1218.83i	0.0453687	−	0.0453687i
$898$	34384.6	+	34384.6i	1.27776	+	1.27776i
$899$	6743.72			0.250184
$900$		0			0
$901$		−	14561.7i		−	0.538424i
$902$	−35802.3	−	35802.3i	−1.32160	−	1.32160i
$903$	1580.27	−	35358.9i	0.0582372	−	1.30307i
$904$		−	53412.3i		−	1.96512i
$905$		0			0
$906$			122523.i			4.49290i
$907$	24731.1	−	24731.1i	0.905384	−	0.905384i	−0.0905113	−	0.995895i	$-0.528850\pi$
$907$	24731.1	−	24731.1i	0.905384	−	0.905384i	0.995895	+	0.0905113i	$0.0288501\pi$
$908$	55823.1	−	55823.1i	2.04026	−	2.04026i
$909$	−6452.39			−0.235437
$910$		0			0
$911$	24805.3			0.902127			0.451063	−	0.892492i	$-0.351045\pi$
$911$	24805.3			0.902127			0.451063	+	0.892492i	$0.351045\pi$
$912$	−11188.3	+	11188.3i	−0.406230	+	0.406230i
$913$	−30474.4	+	30474.4i	−1.10466	+	1.10466i
$914$			76754.6i			2.77770i
$915$		0			0
$916$		−	75447.1i		−	2.72144i
$917$	−34176.8	−	1527.44i	−1.23077	−	0.0550061i
$918$	6302.54	+	6302.54i	0.226596	+	0.226596i
$919$		−	33228.1i		−	1.19270i	−0.802724	−	0.596351i	$-0.796617\pi$
$919$		−	33228.1i		−	1.19270i	0.802724	−	0.596351i	$-0.203383\pi$
$920$		0			0
$921$	−22819.8			−0.816435
$922$	26491.1	+	26491.1i	0.946245	+	0.946245i
$923$	−18236.3	+	18236.3i	−0.650329	+	0.650329i
$924$	−51266.5	+	46880.1i	−1.82526	+	1.66909i
$925$		0			0
$926$	−55907.3			−1.98405
$927$	1304.38	+	1304.38i	0.0462152	+	0.0462152i
$928$	−16732.8	−	16732.8i	−0.591898	−	0.591898i
$929$	41777.1			1.47542			0.737708	−	0.675120i	$-0.235908\pi$
$929$	41777.1			1.47542			0.737708	+	0.675120i	$0.235908\pi$
$930$		0			0
$931$	−7576.29	−	678.560i	−0.266706	−	0.0238871i
$932$	78927.8	−	78927.8i	2.77400	−	2.77400i
$933$	−19964.1	−	19964.1i	−0.700530	−	0.700530i
$934$	−15972.7			−0.559576
$935$		0			0
$936$			56934.5i			1.98821i
$937$	12969.5	+	12969.5i	0.452183	+	0.452183i	0.896078	−	0.443896i	$-0.146404\pi$
$937$	12969.5	+	12969.5i	0.452183	+	0.452183i	−0.443896	+	0.896078i	$0.646404\pi$
$938$	−42982.2	−	1920.97i	−1.49618	−	0.0668678i
$939$			25017.8i			0.869462i
$940$		0			0
$941$		−	6982.50i		−	0.241895i	−0.992659	−	0.120947i	$-0.961407\pi$
$941$		−	6982.50i		−	0.241895i	0.992659	−	0.120947i	$-0.0385932\pi$
$942$	−18206.0	+	18206.0i	−0.629705	+	0.629705i
$943$	−1047.92	+	1047.92i	−0.0361876	+	0.0361876i
$944$	23498.8			0.810193
$945$		0			0
$946$	42368.5			1.45615
$947$	−12625.2	+	12625.2i	−0.433226	+	0.433226i	−0.889724	−	0.456498i	$-0.849103\pi$
$947$	−12625.2	+	12625.2i	−0.433226	+	0.433226i	0.456498	+	0.889724i	$0.349103\pi$
$948$	54988.6	−	54988.6i	1.88391	−	1.88391i
$949$			49402.5i			1.68985i
$950$		0			0
$951$		−	23666.2i		−	0.806972i
$952$	43361.0	+	1937.90i	1.47619	+	0.0659746i
$953$	−77.2788	−	77.2788i	−0.00262676	−	0.00262676i	0.705792	−	0.708419i	$-0.250591\pi$
$953$	−77.2788	−	77.2788i	−0.00262676	−	0.00262676i	−0.708419	+	0.705792i	$0.750591\pi$
$954$			32836.0i			1.11436i
$955$		0			0
$956$	−21327.2			−0.721517
$957$	−27177.6	−	27177.6i	−0.918001	−	0.918001i
$958$	−57578.7	+	57578.7i	−1.94184	+	1.94184i
$959$	27079.3	+	29613.0i	0.911822	+	0.997138i
$960$		0			0
$961$	28375.7			0.952493
$962$	−37196.3	−	37196.3i	−1.24663	−	1.24663i
$963$	15223.3	+	15223.3i	0.509411	+	0.509411i
$964$	39651.5			1.32478
$965$		0			0
$966$	1999.63	+	2186.73i	0.0666015	+	0.0728332i
$967$	−9581.76	+	9581.76i	−0.318644	+	0.318644i	−0.848246	−	0.529602i	$-0.822341\pi$
$967$	−9581.76	+	9581.76i	−0.318644	+	0.318644i	0.529602	+	0.848246i	$0.322341\pi$
$968$	13206.3	+	13206.3i	0.438498	+	0.438498i
$969$	7576.11			0.251166
$970$		0			0
$971$			8228.52i			0.271952i	0.990712	+	0.135976i	$0.0434171\pi$
$971$			8228.52i			0.271952i	−0.990712	+	0.135976i	$0.956583\pi$
$972$	−60710.4	−	60710.4i	−2.00338	−	2.00338i
$973$	−132.459	+	2963.79i	−0.00436427	+	0.0976514i
$974$			56657.5i			1.86388i
$975$		0			0
$976$			3792.68i			0.124386i
$977$	−37618.1	+	37618.1i	−1.23184	+	1.23184i	−0.268587	+	0.963256i	$0.586557\pi$
$977$	−37618.1	+	37618.1i	−1.23184	+	1.23184i	−0.963256	+	0.268587i	$0.913443\pi$
$978$	2488.58	−	2488.58i	0.0813662	−	0.0813662i
$979$	−36996.0			−1.20776
$980$		0			0
$981$	18992.3			0.618123
$982$	−14853.9	+	14853.9i	−0.482695	+	0.482695i
$983$	−6732.17	+	6732.17i	−0.218436	+	0.218436i	−0.807839	−	0.589403i	$-0.799363\pi$
$983$	−6732.17	+	6732.17i	−0.218436	+	0.218436i	0.589403	+	0.807839i	$0.299363\pi$
$984$		−	109487.i		−	3.54706i
$985$		0			0
$986$			44248.2i			1.42916i
$987$	−748.155	+	16740.1i	−0.0241277	+	0.539862i
$988$	−14923.0	−	14923.0i	−0.480532	−	0.480532i
$989$		−	1240.11i		−	0.0398717i
$990$		0			0
$991$	−26503.0			−0.849543			−0.424771	−	0.905301i	$-0.639646\pi$
$991$	−26503.0			−0.849543			−0.424771	+	0.905301i	$0.639646\pi$
$992$	3511.62	+	3511.62i	0.112393	+	0.112393i
$993$	7950.88	−	7950.88i	0.254092	−	0.254092i
$994$	−29918.6	−	32718.0i	−0.954688	−	1.04401i
$995$		0			0
$996$	−171718.			−5.46294
$997$	−20316.7	−	20316.7i	−0.645372	−	0.645372i	0.306499	−	0.951871i	$-0.400842\pi$
$997$	−20316.7	−	20316.7i	−0.645372	−	0.645372i	−0.951871	+	0.306499i	$0.900842\pi$
$998$	20917.8	+	20917.8i	0.663470	+	0.663470i
$999$	6915.65			0.219020

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.4.f.g.118.8		16
5.2	odd	4	inner	175.4.f.g.132.7		16
5.3	odd	4		35.4.f.b.27.2	yes	16
5.4	even	2		35.4.f.b.13.1	✓	16
7.6	odd	2	inner	175.4.f.g.118.7		16
35.3	even	12		245.4.l.b.117.7		32
35.4	even	6		245.4.l.b.68.2		32
35.9	even	6		245.4.l.b.178.7		32
35.13	even	4		35.4.f.b.27.1	yes	16
35.18	odd	12		245.4.l.b.117.8		32
35.19	odd	6		245.4.l.b.178.8		32
35.23	odd	12		245.4.l.b.227.1		32
35.24	odd	6		245.4.l.b.68.1		32
35.27	even	4	inner	175.4.f.g.132.8		16
35.33	even	12		245.4.l.b.227.2		32
35.34	odd	2		35.4.f.b.13.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.f.b.13.1	✓	16	5.4	even	2
35.4.f.b.13.2	yes	16	35.34	odd	2
35.4.f.b.27.1	yes	16	35.13	even	4
35.4.f.b.27.2	yes	16	5.3	odd	4
175.4.f.g.118.7		16	7.6	odd	2	inner
175.4.f.g.118.8		16	1.1	even	1	trivial
175.4.f.g.132.7		16	5.2	odd	4	inner
175.4.f.g.132.8		16	35.27	even	4	inner
245.4.l.b.68.1		32	35.24	odd	6
245.4.l.b.68.2		32	35.4	even	6
245.4.l.b.117.7		32	35.3	even	12
245.4.l.b.117.8		32	35.18	odd	12
245.4.l.b.178.7		32	35.9	even	6
245.4.l.b.178.8		32	35.19	odd	6
245.4.l.b.227.1		32	35.23	odd	12
245.4.l.b.227.2		32	35.33	even	12

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	175.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.57033 - 3.57033i) q^{2} +(4.94129 - 4.94129i) q^{3} -17.4944i q^{4} -35.2840i q^{6} +(-0.826888 + 18.5018i) q^{7} +(-33.8983 - 33.8983i) q^{8} -21.8328i q^{9} -30.6825 q^{11} +(-86.4452 - 86.4452i) q^{12} +(38.4644 - 38.4644i) q^{13} +(63.1052 + 69.0097i) q^{14} -102.100 q^{16} +(34.5683 + 34.5683i) q^{17} +(-77.9500 - 77.9500i) q^{18} +22.1767 q^{19} +(87.3369 + 95.5087i) q^{21} +(-109.546 + 109.546i) q^{22} +(3.20638 + 3.20638i) q^{23} -335.002 q^{24} -274.661i q^{26} +(25.5329 + 25.5329i) q^{27} +(323.679 + 14.4660i) q^{28} +179.259i q^{29} -37.6201i q^{31} +(-93.3444 + 93.3444i) q^{32} +(-151.611 + 151.611i) q^{33} +246.840 q^{34} -381.952 q^{36} +(135.426 - 135.426i) q^{37} +(79.1782 - 79.1782i) q^{38} -380.128i q^{39} +326.823i q^{41} +(652.818 + 29.1760i) q^{42} +(-193.381 - 193.381i) q^{43} +536.773i q^{44} +22.8956 q^{46} +(91.5534 + 91.5534i) q^{47} +(-504.506 + 504.506i) q^{48} +(-341.633 - 30.5978i) q^{49} +341.624 q^{51} +(-672.914 - 672.914i) q^{52} +(-210.622 - 210.622i) q^{53} +182.321 q^{54} +(655.209 - 599.149i) q^{56} +(109.582 - 109.582i) q^{57} +(640.012 + 640.012i) q^{58} -230.155 q^{59} -37.1467i q^{61} +(-134.316 - 134.316i) q^{62} +(403.945 + 18.0532i) q^{63} -150.261i q^{64} +1082.60i q^{66} +(-325.340 + 325.340i) q^{67} +(604.753 - 604.753i) q^{68} +31.6873 q^{69} -474.107 q^{71} +(-740.092 + 740.092i) q^{72} +(-642.183 + 642.183i) q^{73} -967.032i q^{74} -387.970i q^{76} +(25.3710 - 567.681i) q^{77} +(-1357.18 - 1357.18i) q^{78} +636.110i q^{79} +841.815 q^{81} +(1166.87 + 1166.87i) q^{82} +(993.219 - 993.219i) q^{83} +(1670.87 - 1527.91i) q^{84} -1380.87 q^{86} +(885.770 + 885.770i) q^{87} +(1040.08 + 1040.08i) q^{88} +1205.77 q^{89} +(679.855 + 743.467i) q^{91} +(56.0938 - 56.0938i) q^{92} +(-185.892 - 185.892i) q^{93} +653.751 q^{94} +922.484i q^{96} +(-917.344 - 917.344i) q^{97} +(-1328.98 + 1110.50i) q^{98} +669.883i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 32 q^{7} - 176 q^{8} - 152 q^{11} - 504 q^{16} - 288 q^{18} + 328 q^{21} - 348 q^{22} + 72 q^{23} + 528 q^{28} - 432 q^{32} + 344 q^{36} + 256 q^{37} + 1300 q^{42} + 312 q^{43} - 1856 q^{46}+ \cdots - 3308 q^{98}+O(q^{100}) \) 16 * q - 4 * q^2 - 32 * q^7 - 176 * q^8 - 152 * q^11 - 504 * q^16 - 288 * q^18 + 328 * q^21 - 348 * q^22 + 72 * q^23 + 528 * q^28 - 432 * q^32 + 344 * q^36 + 256 * q^37 + 1300 * q^42 + 312 * q^43 - 1856 * q^46 + 696 * q^51 - 1768 * q^53 + 1304 * q^56 + 3920 * q^57 + 4764 * q^58 - 2544 * q^63 - 4504 * q^67 + 6368 * q^71 - 7848 * q^72 + 3016 * q^77 - 5340 * q^78 - 3088 * q^81 - 9336 * q^86 + 2048 * q^88 + 1608 * q^91 + 6328 * q^92 + 3960 * q^93 - 3308 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more