LMFDB - Embedded newform 35.4.b.a.29.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,4,Mod(29,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, 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("35.29");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	35.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:	$2.06506685020$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 7^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			29.2
Root			$-5.04851i$ of defining polynomial
Character	$\chi$	$=$	35.29
Dual form			35.4.b.a.29.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-4.04851i q^{2} -6.52749i q^{3} -8.39045 q^{4} +(6.15172 + 9.33576i) q^{5} -26.4266 q^{6} +7.00000i q^{7} +1.58074i q^{8} -15.6081 q^{9} +(37.7959 - 24.9053i) q^{10} +6.78210 q^{11} +54.7685i q^{12} -48.9221i q^{13} +28.3396 q^{14} +(60.9390 - 40.1552i) q^{15} -60.7239 q^{16} +92.4381i q^{17} +63.1894i q^{18} +125.574 q^{19} +(-51.6157 - 78.3312i) q^{20} +45.6924 q^{21} -27.4574i q^{22} +32.2681i q^{23} +10.3183 q^{24} +(-49.3128 + 114.862i) q^{25} -198.062 q^{26} -74.3607i q^{27} -58.7332i q^{28} -282.778 q^{29} +(-162.569 - 246.712i) q^{30} +205.434 q^{31} +258.488i q^{32} -44.2701i q^{33} +374.237 q^{34} +(-65.3503 + 43.0620i) q^{35} +130.959 q^{36} +190.627i q^{37} -508.388i q^{38} -319.338 q^{39} +(-14.7574 + 9.72429i) q^{40} +123.269 q^{41} -184.986i q^{42} -35.0202i q^{43} -56.9049 q^{44} +(-96.0164 - 145.713i) q^{45} +130.638 q^{46} +419.030i q^{47} +396.375i q^{48} -49.0000 q^{49} +(465.020 + 199.643i) q^{50} +603.388 q^{51} +410.478i q^{52} +0.365379i q^{53} -301.050 q^{54} +(41.7215 + 63.3160i) q^{55} -11.0652 q^{56} -819.683i q^{57} +1144.83i q^{58} -328.317 q^{59} +(-511.306 + 336.921i) q^{60} -515.707 q^{61} -831.704i q^{62} -109.256i q^{63} +560.699 q^{64} +(456.725 - 300.955i) q^{65} -179.228 q^{66} -828.957i q^{67} -775.597i q^{68} +210.630 q^{69} +(174.337 + 264.572i) q^{70} -496.231 q^{71} -24.6723i q^{72} -701.132i q^{73} +771.757 q^{74} +(749.759 + 321.888i) q^{75} -1053.62 q^{76} +47.4747i q^{77} +1292.84i q^{78} -199.388 q^{79} +(-373.556 - 566.904i) q^{80} -906.806 q^{81} -499.056i q^{82} +194.923i q^{83} -383.380 q^{84} +(-862.980 + 568.653i) q^{85} -141.780 q^{86} +1845.83i q^{87} +10.7208i q^{88} -137.406 q^{89} +(-589.921 + 388.723i) q^{90} +342.454 q^{91} -270.744i q^{92} -1340.97i q^{93} +1696.45 q^{94} +(772.496 + 1172.33i) q^{95} +1687.27 q^{96} +220.440i q^{97} +198.377i q^{98} -105.855 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 36 q^{4} + 6 q^{5} + 12 q^{6} - 46 q^{9} - 16 q^{10} + 84 q^{11} - 56 q^{14} + 8 q^{15} + 148 q^{16} + 72 q^{19} - 68 q^{20} + 140 q^{21} + 72 q^{24} - 362 q^{25} - 620 q^{26} + 88 q^{29} + 52 q^{30}+ \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 - 56 * q^14 + 8 * q^15 + 148 * q^16 + 72 * q^19 - 68 * q^20 + 140 * q^21 + 72 * q^24 - 362 * q^25 - 620 * q^26 + 88 * q^29 + 52 * q^30 + 120 * q^31 + 964 * q^34 - 28 * q^35 - 420 * q^36 + 212 * q^39 + 1396 * q^40 - 852 * q^41 - 1424 * q^44 - 510 * q^45 + 176 * q^46 - 490 * q^49 + 1644 * q^50 + 1276 * q^51 - 996 * q^54 - 1136 * q^55 + 588 * q^56 + 864 * q^59 - 1692 * q^60 - 884 * q^61 - 2724 * q^64 + 520 * q^65 + 1148 * q^66 + 4808 * q^69 + 756 * q^70 + 880 * q^71 + 3024 * q^74 + 720 * q^75 - 2672 * q^76 - 3580 * q^79 - 2316 * q^80 - 302 * q^81 - 1904 * q^84 + 1572 * q^85 + 2432 * q^86 - 1492 * q^89 - 7748 * q^90 + 476 * q^91 + 1652 * q^94 - 1628 * q^95 + 4080 * q^96 - 5304 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	4.04851i		−	1.43137i	−0.698426	−	0.715683i	$-0.746116\pi$
$2$		−	4.04851i		−	1.43137i	0.698426	−	0.715683i	$-0.253884\pi$
$3$		−	6.52749i		−	1.25622i	−0.778127	−	0.628108i	$-0.783830\pi$
$3$		−	6.52749i		−	1.25622i	0.778127	−	0.628108i	$-0.216170\pi$
$4$	−8.39045			−1.04881
$5$	6.15172	+	9.33576i	0.550226	+	0.835016i
$5$	6.15172	+	9.33576i	0.550226	+	0.835016i
$6$	−26.4266			−1.79810
$7$			7.00000i			0.377964i
$7$			7.00000i			0.377964i
$8$			1.58074i			0.0698597i
$9$	−15.6081			−0.578076
$10$	37.7959	−	24.9053i	1.19521	−	0.787575i
$11$	6.78210			0.185898			0.0929491	−	0.995671i	$-0.470371\pi$
$11$	6.78210			0.185898			0.0929491	+	0.995671i	$0.470371\pi$
$12$			54.7685i			1.31753i
$13$		−	48.9221i		−	1.04373i	−0.853027	−	0.521867i	$-0.825236\pi$
$13$		−	48.9221i		−	1.04373i	0.853027	−	0.521867i	$-0.174764\pi$
$14$	28.3396			0.541005
$15$	60.9390	−	40.1552i	1.04896	−	0.691202i
$16$	−60.7239			−0.948812
$17$			92.4381i			1.31880i	0.751794	+	0.659398i	$0.229189\pi$
$17$			92.4381i			1.31880i	−0.751794	+	0.659398i	$0.770811\pi$
$18$			63.1894i			0.827438i
$19$	125.574			1.51625			0.758123	−	0.652112i	$-0.226117\pi$
$19$	125.574			1.51625			0.758123	+	0.652112i	$0.226117\pi$
$20$	−51.6157	−	78.3312i	−0.577081	−	0.875770i
$21$	45.6924			0.474805
$22$		−	27.4574i		−	0.266088i
$23$			32.2681i			0.292538i	0.989245	+	0.146269i	$0.0467265\pi$
$23$			32.2681i			0.292538i	−0.989245	+	0.146269i	$0.953274\pi$
$24$	10.3183			0.0877588
$25$	−49.3128	+	114.862i	−0.394502	+	0.918895i
$26$	−198.062			−1.49396
$27$		−	74.3607i		−	0.530027i
$28$		−	58.7332i		−	0.396412i
$29$	−282.778			−1.81071			−0.905354	−	0.424659i	$-0.860394\pi$
$29$	−282.778			−1.81071			−0.905354	+	0.424659i	$0.860394\pi$
$30$	−162.569	−	246.712i	−0.989363	−	1.50144i
$31$	205.434			1.19023			0.595115	−	0.803641i	$-0.297107\pi$
$31$	205.434			1.19023			0.595115	+	0.803641i	$0.297107\pi$
$32$			258.488i			1.42796i
$33$		−	44.2701i		−	0.233528i
$34$	374.237			1.88768
$35$	−65.3503	+	43.0620i	−0.315606	+	0.207966i
$36$	130.959			0.606290
$37$			190.627i			0.846998i	0.905897	+	0.423499i	$0.139198\pi$
$37$			190.627i			0.846998i	−0.905897	+	0.423499i	$0.860802\pi$
$38$		−	508.388i		−	2.17030i
$39$	−319.338			−1.31115
$40$	−14.7574	+	9.72429i	−0.0583339	+	0.0384386i
$41$	123.269			0.469546			0.234773	−	0.972050i	$-0.424565\pi$
$41$	123.269			0.469546			0.234773	+	0.972050i	$0.424565\pi$
$42$		−	184.986i		−	0.679619i
$43$		−	35.0202i		−	0.124198i	−0.998070	−	0.0620991i	$-0.980221\pi$
$43$		−	35.0202i		−	0.124198i	0.998070	−	0.0620991i	$-0.0197795\pi$
$44$	−56.9049			−0.194971
$45$	−96.0164	−	145.713i	−0.318073	−	0.482703i
$46$	130.638			0.418728
$47$			419.030i			1.30046i	0.759736	+	0.650231i	$0.225328\pi$
$47$			419.030i			1.30046i	−0.759736	+	0.650231i	$0.774672\pi$
$48$			396.375i			1.19191i
$49$	−49.0000			−0.142857
$50$	465.020	+	199.643i	1.31527	+	0.564677i
$51$	603.388			1.65669
$52$			410.478i			1.09467i
$53$			0.365379i			0.000946956i	1.00000		0.000473478i	$0.000150713\pi$
$53$			0.365379i			0.000946956i	−1.00000		0.000473478i	$0.999849\pi$
$54$	−301.050			−0.758662
$55$	41.7215	+	63.3160i	0.102286	+	0.155228i
$56$	−11.0652			−0.0264045
$57$		−	819.683i		−	1.90473i
$58$			1144.83i			2.59178i
$59$	−328.317			−0.724461			−0.362231	−	0.932088i	$-0.617985\pi$
$59$	−328.317			−0.724461			−0.362231	+	0.932088i	$0.617985\pi$
$60$	−511.306	+	336.921i	−1.10016	+	0.724938i
$61$	−515.707			−1.08245			−0.541226	−	0.840877i	$-0.682040\pi$
$61$	−515.707			−1.08245			−0.541226	+	0.840877i	$0.682040\pi$
$62$		−	831.704i		−	1.70365i
$63$		−	109.256i		−	0.218492i
$64$	560.699			1.09511
$65$	456.725	−	300.955i	0.871534	−	0.574290i
$66$	−179.228			−0.334264
$67$		−	828.957i		−	1.51154i	−0.654837	−	0.755770i	$-0.727263\pi$
$67$		−	828.957i		−	1.51154i	0.654837	−	0.755770i	$-0.272737\pi$
$68$		−	775.597i		−	1.38316i
$69$	210.630			0.367490
$70$	174.337	+	264.572i	0.297675	+	0.451748i
$71$	−496.231			−0.829462			−0.414731	−	0.909944i	$-0.636124\pi$
$71$	−496.231			−0.829462			−0.414731	+	0.909944i	$0.636124\pi$
$72$		−	24.6723i		−	0.0403842i
$73$		−	701.132i		−	1.12413i	−0.827094	−	0.562064i	$-0.810008\pi$
$73$		−	701.132i		−	1.12413i	0.827094	−	0.562064i	$-0.189992\pi$
$74$	771.757			1.21236
$75$	749.759	+	321.888i	1.15433	+	0.495580i
$76$	−1053.62			−1.59025
$77$			47.4747i			0.0702629i
$78$			1292.84i			1.87674i
$79$	−199.388			−0.283961			−0.141981	−	0.989869i	$-0.545347\pi$
$79$	−199.388			−0.283961			−0.141981	+	0.989869i	$0.545347\pi$
$80$	−373.556	−	566.904i	−0.522061	−	0.792273i
$81$	−906.806			−1.24390
$82$		−	499.056i		−	0.672092i
$83$			194.923i			0.257778i	0.991659	+	0.128889i	$0.0411411\pi$
$83$			194.923i			0.257778i	−0.991659	+	0.128889i	$0.958859\pi$
$84$	−383.380			−0.497978
$85$	−862.980	+	568.653i	−1.10122	+	0.725636i
$86$	−141.780			−0.177773
$87$			1845.83i			2.27464i
$88$			10.7208i			0.0129868i
$89$	−137.406			−0.163651			−0.0818257	−	0.996647i	$-0.526075\pi$
$89$	−137.406			−0.163651			−0.0818257	+	0.996647i	$0.526075\pi$
$90$	−589.921	+	388.723i	−0.690924	+	0.455278i
$91$	342.454			0.394494
$92$		−	270.744i		−	0.306815i
$93$		−	1340.97i		−	1.49518i
$94$	1696.45			1.86144
$95$	772.496	+	1172.33i	0.834278	+	1.26609i
$96$	1687.27			1.79382
$97$			220.440i			0.230745i	0.993322	+	0.115372i	$0.0368062\pi$
$97$			220.440i			0.230745i	−0.993322	+	0.115372i	$0.963194\pi$
$98$			198.377i			0.204481i
$99$	−105.855			−0.107463
$100$	413.756	−	963.743i	0.413756	−	0.963743i
$101$	−591.358			−0.582597			−0.291298	−	0.956632i	$-0.594087\pi$
$101$	−591.358			−0.582597			−0.291298	+	0.956632i	$0.594087\pi$
$102$		−	2442.83i		−	2.37133i
$103$			476.494i			0.455829i	0.973681	+	0.227914i	$0.0731906\pi$
$103$			476.494i			0.455829i	−0.973681	+	0.227914i	$0.926809\pi$
$104$	77.3332			0.0729149
$105$	281.087	+	426.573i	0.261250	+	0.396469i
$106$	1.47924			0.00135544
$107$		−	225.584i		−	0.203813i	−0.994794	−	0.101907i	$-0.967506\pi$
$107$		−	225.584i		−	0.203813i	0.994794	−	0.101907i	$-0.0324943\pi$
$108$			623.920i			0.555895i
$109$	1627.65			1.43028			0.715142	−	0.698979i	$-0.246362\pi$
$109$	1627.65			1.43028			0.715142	+	0.698979i	$0.246362\pi$
$110$	256.336	−	168.910i	0.222188	−	0.146409i
$111$	1244.32			1.06401
$112$		−	425.068i		−	0.358617i
$113$		−	357.040i		−	0.297235i	−0.988895	−	0.148617i	$-0.952518\pi$
$113$		−	357.040i		−	0.297235i	0.988895	−	0.148617i	$-0.0474823\pi$
$114$	−3318.50			−2.72636
$115$	−301.247	+	198.504i	−0.244274	+	0.160962i
$116$	2372.63			1.89908
$117$			763.579i			0.603358i
$118$			1329.19i			1.03697i
$119$	−647.067			−0.498458
$120$	63.4751	+	96.3290i	0.0482872	+	0.0732799i
$121$	−1285.00			−0.965442
$122$			2087.85i			1.54938i
$123$		−	804.637i		−	0.589851i
$124$	−1723.69			−1.24832
$125$	−1375.68	+	246.225i	−0.984357	+	0.176185i
$126$	−442.326			−0.312742
$127$		−	1728.25i		−	1.20754i	−0.797158	−	0.603771i	$-0.793664\pi$
$127$		−	1728.25i		−	1.20754i	0.797158	−	0.603771i	$-0.206336\pi$
$128$		−	202.094i		−	0.139553i
$129$	−228.594			−0.156020
$130$	−1218.42	−	1849.06i	−0.822018	−	1.24748i
$131$	1461.19			0.974543			0.487272	−	0.873250i	$-0.337992\pi$
$131$	1461.19			0.974543			0.487272	+	0.873250i	$0.337992\pi$
$132$			371.446i			0.244926i
$133$			879.018i			0.573087i
$134$	−3356.04			−2.16357
$135$	694.214	−	457.446i	0.442581	−	0.291635i
$136$	−146.121			−0.0921306
$137$			1892.96i			1.18049i	0.807226	+	0.590243i	$0.200968\pi$
$137$			1892.96i			1.18049i	−0.807226	+	0.590243i	$0.799032\pi$
$138$		−	852.737i		−	0.526013i
$139$	1715.03			1.04652			0.523262	−	0.852172i	$-0.324715\pi$
$139$	1715.03			1.04652			0.523262	+	0.852172i	$0.324715\pi$
$140$	548.319	−	361.310i	0.331010	−	0.218116i
$141$	2735.21			1.63366
$142$			2009.00i			1.18726i
$143$		−	331.794i		−	0.194028i
$144$	947.783			0.548486
$145$	−1739.57	−	2639.94i	−0.996299	−	1.51197i
$146$	−2838.54			−1.60904
$147$			319.847i			0.179459i
$148$		−	1599.45i		−	0.888337i
$149$	2798.32			1.53857			0.769286	−	0.638904i	$-0.220612\pi$
$149$	2798.32			1.53857			0.769286	+	0.638904i	$0.220612\pi$
$150$	1303.17	−	3035.41i	0.709355	−	1.65227i
$151$	−2867.49			−1.54538			−0.772692	−	0.634781i	$-0.781090\pi$
$151$	−2867.49			−1.54538			−0.772692	+	0.634781i	$0.781090\pi$
$152$			198.500i			0.105924i
$153$		−	1442.78i		−	0.762365i
$154$	192.202			0.100572
$155$	1263.77	+	1917.89i	0.654896	+	0.993860i
$156$	2679.39			1.37515
$157$		−	783.696i		−	0.398381i	−0.979961	−	0.199190i	$-0.936169\pi$
$157$		−	783.696i		−	0.398381i	0.979961	−	0.199190i	$-0.0638312\pi$
$158$			807.226i			0.406452i
$159$	2.38501			0.00118958
$160$	−2413.18	+	1590.14i	−1.19237	+	0.785699i
$161$	−225.877			−0.110569
$162$			3671.22i			1.78048i
$163$		−	2416.93i		−	1.16140i	−0.814116	−	0.580702i	$-0.802778\pi$
$163$		−	2416.93i		−	1.16140i	0.814116	−	0.580702i	$-0.197222\pi$
$164$	−1034.28			−0.492463
$165$	413.295	−	272.337i	0.195000	−	0.128493i
$166$	789.149			0.368975
$167$		−	704.424i		−	0.326407i	−0.986592	−	0.163204i	$-0.947817\pi$
$167$		−	704.424i		−	0.326407i	0.986592	−	0.163204i	$-0.0521827\pi$
$168$			72.2280i			0.0331697i
$169$	−196.369			−0.0893803
$170$	2302.20	+	3493.78i	1.03865	+	1.57624i
$171$	−1959.97			−0.876506
$172$			293.835i			0.130260i
$173$			1398.49i			0.614598i	0.951613	+	0.307299i	$0.0994252\pi$
$173$			1398.49i			0.614598i	−0.951613	+	0.307299i	$0.900575\pi$
$174$	7472.85			3.25584
$175$	−804.033	−	345.189i	−0.347310	−	0.149108i
$176$	−411.836			−0.176382
$177$			2143.08i			0.910079i
$178$			556.289i			0.234245i
$179$	−368.688			−0.153950			−0.0769749	−	0.997033i	$-0.524526\pi$
$179$	−368.688			−0.153950			−0.0769749	+	0.997033i	$0.524526\pi$
$180$	805.621	+	1222.60i	0.333597	+	0.506262i
$181$	−315.621			−0.129613			−0.0648064	−	0.997898i	$-0.520643\pi$
$181$	−315.621			−0.129613			−0.0648064	+	0.997898i	$0.520643\pi$
$182$		−	1386.43i		−	0.564665i
$183$			3366.27i			1.35979i
$184$	−51.0076			−0.0204366
$185$	−1779.65	+	1172.69i	−0.707257	+	0.466041i
$186$	−5428.94			−2.14016
$187$			626.924i			0.245162i
$188$		−	3515.85i		−	1.36393i
$189$	520.525			0.200331
$190$	4746.19	−	3127.46i	1.81224	−	1.19416i
$191$	−151.629			−0.0574424			−0.0287212	−	0.999587i	$-0.509143\pi$
$191$	−151.629			−0.0574424			−0.0287212	+	0.999587i	$0.509143\pi$
$192$		−	3659.95i		−	1.37570i
$193$			690.689i			0.257600i	0.991671	+	0.128800i	$0.0411126\pi$
$193$			690.689i			0.257600i	−0.991671	+	0.128800i	$0.958887\pi$
$194$	892.453			0.330280
$195$	−1964.48	−	2981.26i	−0.721431	−	1.09483i
$196$	411.132			0.149829
$197$		−	834.136i		−	0.301674i	−0.988559	−	0.150837i	$-0.951803\pi$
$197$		−	834.136i		−	0.301674i	0.988559	−	0.150837i	$-0.0481968\pi$
$198$			428.557i			0.153819i
$199$	−387.269			−0.137954			−0.0689769	−	0.997618i	$-0.521973\pi$
$199$	−387.269			−0.137954			−0.0689769	+	0.997618i	$0.521973\pi$
$200$	−181.567	−	77.9509i	−0.0641937	−	0.0275598i
$201$	−5411.00			−1.89882
$202$			2394.12i			0.833909i
$203$		−	1979.44i		−	0.684383i
$204$	−5062.70			−1.73755
$205$	758.316	+	1150.81i	0.258357	+	0.392078i
$206$	1929.09			0.652457
$207$		−	503.643i		−	0.169109i
$208$			2970.74i			0.990307i
$209$	851.656			0.281867
$210$	1726.99	−	1137.98i	0.567492	−	0.373944i
$211$	3070.54			1.00182			0.500912	−	0.865498i	$-0.332998\pi$
$211$	3070.54			1.00182			0.500912	+	0.865498i	$0.332998\pi$
$212$		−	3.06570i		−	0.000993174i
$213$			3239.14i			1.04198i
$214$	−913.278			−0.291731
$215$	326.940	−	215.434i	0.103707	−	0.0683371i
$216$	117.545			0.0370275
$217$			1438.04i			0.449865i
$218$		−	6589.58i		−	2.04726i
$219$	−4576.63			−1.41215
$220$	−350.063	−	531.250i	−0.107278	−	0.162804i
$221$	4522.26			1.37647
$222$		−	5037.63i		−	1.52299i
$223$		−	1004.46i		−	0.301631i	−0.988562	−	0.150816i	$-0.951810\pi$
$223$		−	1004.46i		−	0.301631i	0.988562	−	0.150816i	$-0.0481900\pi$
$224$	−1809.41			−0.539716
$225$	769.677	−	1792.77i	0.228052	−	0.531192i
$226$	−1445.48			−0.425451
$227$		−	5374.22i		−	1.57136i	−0.618631	−	0.785681i	$-0.712313\pi$
$227$		−	5374.22i		−	1.57136i	0.618631	−	0.785681i	$-0.287687\pi$
$228$			6877.51i			1.99769i
$229$	−3650.97			−1.05355			−0.526775	−	0.850005i	$-0.676599\pi$
$229$	−3650.97			−1.05355			−0.526775	+	0.850005i	$0.676599\pi$
$230$	803.647	+	1219.60i	0.230395	+	0.349645i
$231$	309.890			0.0882653
$232$		−	446.999i		−	0.126495i
$233$		−	4582.88i		−	1.28856i	−0.764789	−	0.644280i	$-0.777157\pi$
$233$		−	4582.88i		−	1.28856i	0.764789	−	0.644280i	$-0.222843\pi$
$234$	3091.36			0.863625
$235$	−3911.96	+	2577.75i	−1.08591	+	0.715549i
$236$	2754.73			0.759820
$237$			1301.50i			0.356716i
$238$			2619.66i			0.713476i
$239$	−696.769			−0.188578			−0.0942892	−	0.995545i	$-0.530058\pi$
$239$	−696.769			−0.188578			−0.0942892	+	0.995545i	$0.530058\pi$
$240$	−3700.46	+	2438.38i	−0.995265	+	0.655821i
$241$	5082.82			1.35856			0.679281	−	0.733878i	$-0.262292\pi$
$241$	5082.82			1.35856			0.679281	+	0.733878i	$0.262292\pi$
$242$			5202.35i			1.38190i
$243$			3911.42i			1.03258i
$244$	4327.02			1.13528
$245$	−301.434	−	457.452i	−0.0786037	−	0.119288i
$246$	−3257.58			−0.844292
$247$		−	6143.34i		−	1.58256i
$248$			324.739i			0.0831490i
$249$	1272.36			0.323825
$250$	996.847	+	5569.46i	0.252185	+	1.40897i
$251$	−1207.32			−0.303606			−0.151803	−	0.988411i	$-0.548508\pi$
$251$	−1207.32			−0.303606			−0.151803	+	0.988411i	$0.548508\pi$
$252$			916.711i			0.229156i
$253$			218.846i			0.0543822i
$254$	−6996.86			−1.72843
$255$	3711.87	+	5633.09i	0.911555	+	1.38336i
$256$	3667.41			0.895363
$257$			510.936i			0.124013i	0.998076	+	0.0620064i	$0.0197499\pi$
$257$			510.936i			0.124013i	−0.998076	+	0.0620064i	$0.980250\pi$
$258$			925.464i			0.223321i
$259$	−1334.39			−0.320135
$260$	−3832.13	+	2525.15i	−0.914070	+	0.602319i
$261$	4413.61			1.04673
$262$		−	5915.67i		−	1.39493i
$263$		−	2269.04i		−	0.531997i	−0.963974	−	0.265998i	$-0.914298\pi$
$263$		−	2269.04i		−	0.531997i	0.963974	−	0.265998i	$-0.0857015\pi$
$264$	69.9796			0.0163142
$265$	−3.41109	+	2.24771i	−0.000790723	+	0.000521040i
$266$	3558.72			0.820297
$267$			896.913i			0.205581i
$268$			6955.32i			1.58531i
$269$	7836.10			1.77612			0.888058	−	0.459731i	$-0.152054\pi$
$269$	7836.10			1.77612			0.888058	+	0.459731i	$0.152054\pi$
$270$	−1851.98	−	2810.53i	−0.417436	−	0.633495i
$271$	1466.28			0.328673			0.164336	−	0.986404i	$-0.447452\pi$
$271$	1466.28			0.328673			0.164336	+	0.986404i	$0.447452\pi$
$272$		−	5613.21i		−	1.25129i
$273$		−	2235.37i		−	0.495570i
$274$	7663.67			1.68971
$275$	−334.444	+	779.005i	−0.0733372	+	0.170821i
$276$	−1767.28			−0.385426
$277$			4154.17i			0.901083i	0.892755	+	0.450542i	$0.148769\pi$
$277$			4154.17i			0.901083i	−0.892755	+	0.450542i	$0.851231\pi$
$278$		−	6943.32i		−	1.49796i
$279$	−3206.43			−0.688044
$280$	−68.0700	−	103.302i	−0.0145284	−	0.0220481i
$281$	−3490.40			−0.740996			−0.370498	−	0.928833i	$-0.620813\pi$
$281$	−3490.40			−0.740996			−0.370498	+	0.928833i	$0.620813\pi$
$282$		−	11073.5i		−	2.33837i
$283$			3125.29i			0.656464i	0.944597	+	0.328232i	$0.106453\pi$
$283$			3125.29i			0.656464i	−0.944597	+	0.328232i	$0.893547\pi$
$284$	4163.60			0.869945
$285$	7652.36	−	5042.46i	1.59048	−	1.04803i
$286$	−1343.27			−0.277725
$287$			862.883i			0.177472i
$288$		−	4034.49i		−	0.825467i
$289$	−3631.80			−0.739223
$290$	−10687.8	+	7042.66i	−2.16418	+	1.42607i
$291$	1438.92			0.289865
$292$			5882.81i			1.17899i
$293$			1447.69i			0.288652i	0.989530	+	0.144326i	$0.0461014\pi$
$293$			1447.69i			0.288652i	−0.989530	+	0.144326i	$0.953899\pi$
$294$	1294.90			0.256872
$295$	−2019.71	−	3065.09i	−0.398618	−	0.604936i
$296$	−301.333			−0.0591710
$297$		−	504.322i		−	0.0985310i
$298$		−	11329.0i		−	2.20226i
$299$	1578.62			0.305332
$300$	−6290.82	−	2700.79i	−1.21067	−	0.519767i
$301$	245.141			0.0469425
$302$			11609.1i			2.21201i
$303$			3860.08i			0.731867i
$304$	−7625.35			−1.43863
$305$	−3172.48	−	4814.52i	−0.595593	−	0.903864i
$306$	−5841.11			−1.09122
$307$			1591.43i			0.295856i	0.988998	+	0.147928i	$0.0472603\pi$
$307$			1591.43i			0.295856i	−0.988998	+	0.147928i	$0.952740\pi$
$308$		−	398.334i		−	0.0736922i
$309$	3110.31			0.572619
$310$	7764.59	−	5116.41i	1.42258	−	0.937395i
$311$	−8584.92			−1.56529			−0.782647	−	0.622466i	$-0.786131\pi$
$311$	−8584.92			−1.56529			−0.782647	+	0.622466i	$0.786131\pi$
$312$		−	504.792i		−	0.0915968i
$313$			7210.05i			1.30203i	0.759064	+	0.651016i	$0.225657\pi$
$313$			7210.05i			1.30203i	−0.759064	+	0.651016i	$0.774343\pi$
$314$	−3172.80			−0.570228
$315$	1019.99	−	672.115i	0.182445	−	0.120220i
$316$	1672.96			0.297820
$317$			7787.24i			1.37973i	0.723938	+	0.689865i	$0.242330\pi$
$317$			7787.24i			1.37973i	−0.723938	+	0.689865i	$0.757670\pi$
$318$		−	9.65573i		−	0.00170272i
$319$	−1917.83			−0.336607
$320$	3449.26	+	5234.55i	0.602561	+	0.914438i
$321$	−1472.49			−0.256033
$322$			914.465i			0.158264i
$323$			11607.8i			1.99962i
$324$	7608.51			1.30461
$325$	5619.28	+	2412.48i	0.959082	+	0.411755i
$326$	−9784.98			−1.66239
$327$		−	10624.5i		−	1.79674i
$328$			194.857i			0.0328023i
$329$	−2933.21			−0.491529
$330$	−1102.56	−	1673.23i	−0.183921	−	0.279116i
$331$	−1729.78			−0.287243			−0.143621	−	0.989633i	$-0.545875\pi$
$331$	−1729.78			−0.287243			−0.143621	+	0.989633i	$0.545875\pi$
$332$		−	1635.49i		−	0.270359i
$333$		−	2975.32i		−	0.489630i
$334$	−2851.87			−0.467208
$335$	7738.94	−	5099.51i	1.26216	−	0.831689i
$336$	−2774.62			−0.450500
$337$		−	7815.06i		−	1.26325i	−0.775276	−	0.631623i	$-0.782389\pi$
$337$		−	7815.06i		−	1.26325i	0.775276	−	0.631623i	$-0.217611\pi$
$338$			795.000i			0.127936i
$339$	−2330.57			−0.373391
$340$	7240.79	−	4771.26i	1.15496	−	0.761052i
$341$	1393.28			0.221262
$342$			7934.95i			1.25460i
$343$		−	343.000i		−	0.0539949i
$344$	55.3579			0.00867645
$345$	1295.73	+	1966.39i	0.202203	+	0.306860i
$346$	5661.82			0.879714
$347$		−	2359.77i		−	0.365070i	−0.983199	−	0.182535i	$-0.941570\pi$
$347$		−	2359.77i		−	0.365070i	0.983199	−	0.182535i	$-0.0584303\pi$
$348$		−	15487.3i		−	2.38565i
$349$	−3212.73			−0.492761			−0.246380	−	0.969173i	$-0.579241\pi$
$349$	−3212.73			−0.492761			−0.246380	+	0.969173i	$0.579241\pi$
$350$	−1397.50	+	3255.14i	−0.213428	+	0.497127i
$351$	−3637.88			−0.553207
$352$			1753.09i			0.265454i
$353$		−	5582.04i		−	0.841649i	−0.907142	−	0.420824i	$-0.861741\pi$
$353$		−	5582.04i		−	0.841649i	0.907142	−	0.420824i	$-0.138259\pi$
$354$	8676.30			1.30266
$355$	−3052.67	−	4632.69i	−0.456392	−	0.692614i
$356$	1152.90			0.171639
$357$			4223.72i			0.626171i
$358$			1492.64i			0.220358i
$359$	10630.6			1.56285			0.781425	−	0.623999i	$-0.214493\pi$
$359$	10630.6			1.56285			0.781425	+	0.623999i	$0.214493\pi$
$360$	230.335	−	151.777i	0.0337215	−	0.0222205i
$361$	8909.84			1.29900
$362$			1277.80i			0.185523i
$363$			8387.84i			1.21280i
$364$	−2873.35			−0.413748
$365$	6545.60	−	4313.17i	0.938664	−	0.618524i
$366$	13628.4			1.94636
$367$		−	4514.69i		−	0.642139i	−0.947056	−	0.321070i	$-0.895958\pi$
$367$		−	4514.69i		−	0.642139i	0.947056	−	0.321070i	$-0.104042\pi$
$368$		−	1959.45i		−	0.277563i
$369$	−1923.99			−0.271434
$370$	4747.63	+	7204.94i	0.667074	+	1.01234i
$371$	−2.55765			−0.000357916
$372$			11251.3i			1.56816i
$373$			11445.8i			1.58885i	0.607361	+	0.794426i	$0.292228\pi$
$373$			11445.8i			1.58885i	−0.607361	+	0.794426i	$0.707772\pi$
$374$	2538.11			0.350916
$375$	1607.23	+	8979.74i	0.221326	+	1.23656i
$376$	−662.378			−0.0908499
$377$			13834.1i			1.88990i
$378$		−	2107.35i		−	0.286747i
$379$	−8146.48			−1.10411			−0.552054	−	0.833809i	$-0.686156\pi$
$379$	−8146.48			−1.10411			−0.552054	+	0.833809i	$0.686156\pi$
$380$	−6481.59	−	9836.37i	−0.874996	−	1.32788i
$381$	−11281.2			−1.51693
$382$			613.872i			0.0822210i
$383$		−	5261.56i		−	0.701967i	−0.936382	−	0.350983i	$-0.885847\pi$
$383$		−	5261.56i		−	0.701967i	0.936382	−	0.350983i	$-0.114153\pi$
$384$	−1319.17			−0.175308
$385$	−443.212	+	292.051i	−0.0586706	+	0.0386605i
$386$	2796.26			0.368720
$387$			546.597i			0.0717961i
$388$		−	1849.59i		−	0.242007i
$389$	−13207.1			−1.72141			−0.860706	−	0.509103i	$-0.829977\pi$
$389$	−13207.1			−1.72141			−0.860706	+	0.509103i	$0.829977\pi$
$390$	−12069.7	+	7953.21i	−1.56711	+	1.03263i
$391$	−2982.80			−0.385798
$392$		−	77.4564i		−	0.00997995i
$393$		−	9537.93i		−	1.22424i
$394$	−3377.01			−0.431805
$395$	−1226.58	−	1861.44i	−0.156243	−	0.237112i
$396$	888.175			0.112708
$397$			5663.15i			0.715933i	0.933734	+	0.357967i	$0.116530\pi$
$397$			5663.15i			0.715933i	−0.933734	+	0.357967i	$0.883470\pi$
$398$			1567.86i			0.197462i
$399$	5737.78			0.719920
$400$	2994.47	−	6974.87i	0.374308	−	0.871858i
$401$	−11989.0			−1.49302			−0.746512	−	0.665372i	$-0.768273\pi$
$401$	−11989.0			−1.49302			−0.746512	+	0.665372i	$0.768273\pi$
$402$			21906.5i			2.71790i
$403$		−	10050.3i		−	1.24228i
$404$	4961.76			0.611031
$405$	−5578.41	−	8465.72i	−0.684429	−	1.03868i
$406$	−8013.80			−0.979602
$407$			1292.85i			0.157455i
$408$			953.802i			0.115736i
$409$	−5249.67			−0.634669			−0.317334	−	0.948314i	$-0.602788\pi$
$409$	−5249.67			−0.634669			−0.317334	+	0.948314i	$0.602788\pi$
$410$	4659.07	−	3070.05i	0.561207	−	0.369803i
$411$	12356.3			1.48294
$412$		−	3998.00i		−	0.478076i
$413$		−	2298.22i		−	0.273821i
$414$	−2039.00			−0.242057
$415$	−1819.76	+	1199.11i	−0.215249	+	0.141836i
$416$	12645.7			1.49041
$417$		−	11194.8i		−	1.31466i
$418$		−	3447.94i		−	0.403455i
$419$	14948.9			1.74297			0.871484	−	0.490424i	$-0.163158\pi$
$419$	14948.9			1.74297			0.871484	+	0.490424i	$0.163158\pi$
$420$	−2358.44	−	3579.14i	−0.274001	−	0.415820i
$421$	5840.31			0.676103			0.338051	−	0.941128i	$-0.390232\pi$
$421$	5840.31			0.676103			0.338051	+	0.941128i	$0.390232\pi$
$422$		−	12431.1i		−	1.43398i
$423$		−	6540.24i		−	0.751767i
$424$	−0.577571			−6.61540e−5
$425$	−10617.6	−	4558.38i	−1.21184	−	0.520268i
$426$	13113.7			1.49146
$427$		−	3609.95i		−	0.409128i
$428$			1892.75i			0.213760i
$429$	−2165.78			−0.243741
$430$	−872.188	−	1323.62i	−0.0978154	−	0.148443i
$431$	7439.21			0.831402			0.415701	−	0.909501i	$-0.363536\pi$
$431$	7439.21			0.831402			0.415701	+	0.909501i	$0.363536\pi$
$432$			4515.48i			0.502896i
$433$		−	877.657i		−	0.0974077i	−0.998813	−	0.0487038i	$-0.984491\pi$
$433$		−	877.657i		−	0.0974077i	0.998813	−	0.0487038i	$-0.0155090\pi$
$434$	5821.93			0.643920
$435$	−17232.2	+	11355.0i	−1.89936	+	1.25157i
$436$	−13656.8			−1.50009
$437$			4052.04i			0.443559i
$438$			18528.5i			2.02130i
$439$	10855.8			1.18023			0.590114	−	0.807320i	$-0.299083\pi$
$439$	10855.8			1.18023			0.590114	+	0.807320i	$0.299083\pi$
$440$	−100.086	+	65.9511i	−0.0108442	+	0.00714567i
$441$	764.795			0.0825823
$442$		−	18308.4i		−	1.97023i
$443$		−	10797.0i		−	1.15798i	−0.815336	−	0.578988i	$-0.803448\pi$
$443$		−	10797.0i		−	1.15798i	0.815336	−	0.578988i	$-0.196552\pi$
$444$	−10440.4			−1.11594
$445$	−845.281	−	1282.79i	−0.0900453	−	0.136651i
$446$	−4066.58			−0.431745
$447$		−	18266.0i		−	1.93278i
$448$			3924.89i			0.413914i
$449$	−8621.70			−0.906198			−0.453099	−	0.891460i	$-0.649682\pi$
$449$	−8621.70			−0.906198			−0.453099	+	0.891460i	$0.649682\pi$
$450$	−7258.06	−	3116.05i	−0.760329	−	0.326426i
$451$	836.023			0.0872878
$452$			2995.73i			0.311742i
$453$			18717.5i			1.94134i
$454$	−21757.6			−2.24919
$455$	2106.68	+	3197.07i	0.217061	+	0.329409i
$456$	1295.71			0.133064
$457$			3785.90i			0.387520i	0.981049	+	0.193760i	$0.0620684\pi$
$457$			3785.90i			0.387520i	−0.981049	+	0.193760i	$0.937932\pi$
$458$			14781.0i			1.50801i
$459$	6873.76			0.698997
$460$	2527.60	−	1665.54i	0.256196	−	0.168818i
$461$	5760.18			0.581948			0.290974	−	0.956731i	$-0.406021\pi$
$461$	5760.18			0.581948			0.290974	+	0.956731i	$0.406021\pi$
$462$		−	1254.59i		−	0.126340i
$463$			10760.9i			1.08014i	0.841621	+	0.540068i	$0.181602\pi$
$463$			10760.9i			1.08014i	−0.841621	+	0.540068i	$0.818398\pi$
$464$	17171.4			1.71802
$465$	12519.0	−	8249.27i	1.24850	−	0.822690i
$466$	−18553.9			−1.84440
$467$		−	2153.58i		−	0.213395i	−0.994292	−	0.106698i	$-0.965972\pi$
$467$		−	2153.58i		−	0.213395i	0.994292	−	0.106698i	$-0.0340277\pi$
$468$		−	6406.77i		−	0.632806i
$469$	5802.70			0.571309
$470$	10436.1	+	15837.6i	1.02421	+	1.55433i
$471$	−5115.57			−0.500452
$472$		−	518.985i		−	0.0506106i
$473$		−	237.510i		−	0.0230882i
$474$	5269.15			0.510591
$475$	−6192.40	+	14423.7i	−0.598162	+	1.39327i
$476$	5429.18			0.522786
$477$		−	5.70286i		−	0.000547413i
$478$			2820.88i			0.269924i
$479$	6890.26			0.657253			0.328626	−	0.944460i	$-0.393414\pi$
$479$	6890.26			0.657253			0.328626	+	0.944460i	$0.393414\pi$
$480$	10379.6	+	15752.0i	0.987006	+	1.49787i
$481$	9325.88			0.884041
$482$		−	20577.9i		−	1.94460i
$483$			1474.41i			0.138898i
$484$	10781.8			1.01256
$485$	−2057.97	+	1356.08i	−0.192676	+	0.126962i
$486$	15835.4			1.47801
$487$			19006.4i			1.76850i	0.467011	+	0.884251i	$0.345331\pi$
$487$			19006.4i			1.76850i	−0.467011	+	0.884251i	$0.654669\pi$
$488$		−	815.201i		−	0.0756197i
$489$	−15776.5			−1.45897
$490$	−1852.00	+	1220.36i	−0.170745	+	0.112511i
$491$	4530.05			0.416371			0.208186	−	0.978089i	$-0.433244\pi$
$491$	4530.05			0.416371			0.208186	+	0.978089i	$0.433244\pi$
$492$			6751.27i			0.618639i
$493$		−	26139.4i		−	2.38795i
$494$	−24871.4			−2.26522
$495$	−651.193	−	988.241i	−0.0591292	−	0.0897336i
$496$	−12474.8			−1.12930
$497$		−	3473.62i		−	0.313507i
$498$		−	5151.16i		−	0.463512i
$499$	−3620.18			−0.324773			−0.162386	−	0.986727i	$-0.551919\pi$
$499$	−3620.18			−0.324773			−0.162386	+	0.986727i	$0.551919\pi$
$500$	11542.6	−	2065.94i	1.03240	−	0.184784i
$501$	−4598.12			−0.410038
$502$			4887.84i			0.434571i
$503$			11761.8i			1.04261i	0.853372	+	0.521303i	$0.174554\pi$
$503$			11761.8i			1.04261i	−0.853372	+	0.521303i	$0.825446\pi$
$504$	172.706			0.0152638
$505$	−3637.86	−	5520.77i	−0.320560	−	0.486478i
$506$	885.999			0.0778408
$507$			1281.79i			0.112281i
$508$			14500.8i			1.26648i
$509$	5254.47			0.457564			0.228782	−	0.973478i	$-0.426526\pi$
$509$	5254.47			0.457564			0.228782	+	0.973478i	$0.426526\pi$
$510$	22805.6	−	15027.6i	1.98010	−	1.30477i
$511$	4907.92			0.424880
$512$		−	16464.3i		−	1.42114i
$513$		−	9337.77i		−	0.803651i
$514$	2068.53			0.177508
$515$	−4448.43	+	2931.26i	−0.380624	+	0.250809i
$516$	1918.00			0.163634
$517$			2841.90i			0.241754i
$518$			5402.30i			0.458230i
$519$	9128.64			0.772067
$520$	475.732	+	721.964i	0.0401197	+	0.0608851i
$521$	−15511.8			−1.30439			−0.652193	−	0.758053i	$-0.726151\pi$
$521$	−15511.8			−1.30439			−0.652193	+	0.758053i	$0.726151\pi$
$522$		−	17868.6i		−	1.49825i
$523$			3814.73i			0.318942i	0.987203	+	0.159471i	$0.0509788\pi$
$523$			3814.73i			0.318942i	−0.987203	+	0.159471i	$0.949021\pi$
$524$	−12260.1			−1.02211
$525$	−2253.22	+	5248.31i	−0.187311	+	0.436296i
$526$	−9186.24			−0.761481
$527$			18990.0i			1.56967i
$528$			2688.25i			0.221574i
$529$	11125.8			0.914422
$530$	9.09988	+	13.8098i	0.000745799	+	0.00113181i
$531$	5124.39			0.418794
$532$		−	7375.36i		−	0.601057i
$533$		−	6030.58i		−	0.490081i
$534$	3631.17			0.294262
$535$	2106.00	−	1387.73i	0.170187	−	0.112143i
$536$	1310.37			0.105596
$537$			2406.60i			0.193394i
$538$		−	31724.5i		−	2.54227i
$539$	−332.323			−0.0265569
$540$	−5824.76	+	3838.18i	−0.464181	+	0.305868i
$541$	−4573.77			−0.363478			−0.181739	−	0.983347i	$-0.558173\pi$
$541$	−4573.77			−0.363478			−0.181739	+	0.983347i	$0.558173\pi$
$542$		−	5936.26i		−	0.470451i
$543$			2060.21i			0.162822i
$544$	−23894.1			−1.88318
$545$	10012.9	+	15195.4i	0.786980	+	1.19431i
$546$	−9049.91			−0.709341
$547$		−	13327.6i		−	1.04177i	−0.853627	−	0.520885i	$-0.825602\pi$
$547$		−	13327.6i		−	1.04177i	0.853627	−	0.520885i	$-0.174398\pi$
$548$		−	15882.8i		−	1.23810i
$549$	8049.19			0.625740
$550$	3153.81	+	1354.00i	0.244507	+	0.104972i
$551$	−35509.5			−2.74548
$552$			332.952i			0.0256728i
$553$		−	1395.72i		−	0.107327i
$554$	16818.2			1.28978
$555$	7654.68	+	11616.6i	0.585447	+	0.888467i
$556$	−14389.9			−1.09760
$557$		−	12096.1i		−	0.920155i	−0.887879	−	0.460077i	$-0.847822\pi$
$557$		−	12096.1i		−	0.920155i	0.887879	−	0.460077i	$-0.152178\pi$
$558$			12981.3i			0.984842i
$559$	−1713.26			−0.129630
$560$	3968.33	−	2614.90i	0.299451	−	0.197321i
$561$	4092.24			0.307976
$562$			14130.9i			1.06064i
$563$			22943.6i			1.71751i	0.512387	+	0.858755i	$0.328761\pi$
$563$			22943.6i			1.71751i	−0.512387	+	0.858755i	$0.671239\pi$
$564$	−22949.6			−1.71339
$565$	3333.24	−	2196.41i	0.248196	−	0.163546i
$566$	12652.8			0.939639
$567$		−	6347.64i		−	0.470152i
$568$		−	784.414i		−	0.0579459i
$569$	−485.307			−0.0357560			−0.0178780	−	0.999840i	$-0.505691\pi$
$569$	−485.307			−0.0357560			−0.0178780	+	0.999840i	$0.505691\pi$
$570$	−20414.4	−	30980.7i	−1.50012	−	2.27656i
$571$	12271.8			0.899401			0.449701	−	0.893179i	$-0.351531\pi$
$571$	12271.8			0.899401			0.449701	+	0.893179i	$0.351531\pi$
$572$			2783.90i			0.203498i
$573$			989.756i			0.0721600i
$574$	3493.39			0.254027
$575$	−3706.38	−	1591.23i	−0.268811	−	0.115407i
$576$	−8751.42			−0.633060
$577$			14122.8i			1.01896i	0.860484	+	0.509478i	$0.170162\pi$
$577$			14122.8i			1.01896i	−0.860484	+	0.509478i	$0.829838\pi$
$578$			14703.4i			1.05810i
$579$	4508.46			0.323601
$580$	14595.8	+	22150.3i	1.04492	+	1.58576i
$581$	−1364.46			−0.0974310
$582$		−	5825.47i		−	0.414903i
$583$			2.47804i			0.000176037i
$584$	1108.31			0.0785312
$585$	−7128.59	+	4697.32i	−0.503813	+	0.331983i
$586$	5861.00			0.413167
$587$		−	11005.3i		−	0.773826i	−0.922116	−	0.386913i	$-0.873541\pi$
$587$		−	11005.3i		−	0.773826i	0.922116	−	0.386913i	$-0.126459\pi$
$588$		−	2683.66i		−	0.188218i
$589$	25797.2			1.80468
$590$	−12409.0	+	8176.83i	−0.865885	+	0.570567i
$591$	−5444.81			−0.378967
$592$		−	11575.6i		−	0.803642i
$593$		−	11233.1i		−	0.777889i	−0.921261	−	0.388944i	$-0.872840\pi$
$593$		−	11233.1i		−	0.777889i	0.921261	−	0.388944i	$-0.127160\pi$
$594$	−2041.75			−0.141034
$595$	−3980.57	−	6040.86i	−0.274265	−	0.416220i
$596$	−23479.2			−1.61366
$597$			2527.89i			0.173300i
$598$		−	6391.08i		−	0.437041i
$599$	−14855.4			−1.01331			−0.506656	−	0.862149i	$-0.669118\pi$
$599$	−14855.4			−1.01331			−0.506656	+	0.862149i	$0.669118\pi$
$600$	−508.823	+	1185.18i	−0.0346210	+	0.0806411i
$601$	25358.8			1.72115			0.860573	−	0.509327i	$-0.170106\pi$
$601$	25358.8			1.72115			0.860573	+	0.509327i	$0.170106\pi$
$602$		−	992.457i		−	0.0671919i
$603$			12938.4i			0.873786i
$604$	24059.5			1.62081
$605$	−7904.97	−	11996.5i	−0.531211	−	0.806159i
$606$	15627.6			1.04757
$607$		−	14393.9i		−	0.962487i	−0.876587	−	0.481243i	$-0.840185\pi$
$607$		−	14393.9i		−	0.962487i	0.876587	−	0.481243i	$-0.159815\pi$
$608$			32459.3i			2.16513i
$609$	−12920.8			−0.859732
$610$	−19491.6	+	12843.8i	−1.29376	+	0.852511i
$611$	20499.8			1.35734
$612$			12105.6i			0.799573i
$613$			4769.94i			0.314284i	0.987576	+	0.157142i	$0.0502280\pi$
$613$			4769.94i			0.314284i	−0.987576	+	0.157142i	$0.949772\pi$
$614$	6442.92			0.423477
$615$	7511.90	−	4949.90i	0.492535	−	0.324551i
$616$	−75.0453			−0.00490854
$617$			7769.86i			0.506974i	0.967339	+	0.253487i	$0.0815775\pi$
$617$			7769.86i			0.506974i	−0.967339	+	0.253487i	$0.918423\pi$
$618$		−	12592.1i		−	0.819627i
$619$	5680.75			0.368867			0.184433	−	0.982845i	$-0.440955\pi$
$619$	5680.75			0.368867			0.184433	+	0.982845i	$0.440955\pi$
$620$	−10603.6	−	16091.9i	−0.686859	−	1.04237i
$621$	2399.48			0.155053
$622$			34756.2i			2.24051i
$623$		−	961.840i		−	0.0618544i
$624$	19391.5			1.24404
$625$	−10761.5	−	11328.3i	−0.688736	−	0.725012i
$626$	29190.0			1.86368
$627$		−	5559.17i		−	0.354086i
$628$			6575.56i			0.417824i
$629$	−17621.2			−1.11702
$630$	−2721.06	−	4129.45i	−0.172079	−	0.261145i
$631$	−10395.8			−0.655864			−0.327932	−	0.944701i	$-0.606352\pi$
$631$	−10395.8			−0.655864			−0.327932	+	0.944701i	$0.606352\pi$
$632$		−	315.182i		−	0.0198374i
$633$		−	20042.9i		−	1.25851i
$634$	31526.7			1.97490
$635$	16134.6	−	10631.7i	1.00832	−	0.664421i
$636$	−20.0113			−0.00124764
$637$			2397.18i			0.149105i
$638$			7764.34i			0.481808i
$639$	7745.21			0.479492
$640$	1886.70	−	1243.23i	0.116529	−	0.0767857i
$641$	−8194.28			−0.504921			−0.252461	−	0.967607i	$-0.581240\pi$
$641$	−8194.28			−0.504921			−0.252461	+	0.967607i	$0.581240\pi$
$642$			5961.41i			0.366477i
$643$		−	32118.2i		−	1.96985i	−0.172970	−	0.984927i	$-0.555336\pi$
$643$		−	32118.2i		−	1.96985i	0.172970	−	0.984927i	$-0.444664\pi$
$644$	1895.21			0.115965
$645$	−1406.24	−	2134.09i	−0.0858461	−	0.130279i
$646$	46994.4			2.86218
$647$			22299.0i			1.35496i	0.735539	+	0.677482i	$0.236929\pi$
$647$			22299.0i			1.35496i	−0.735539	+	0.677482i	$0.763071\pi$
$648$		−	1433.43i		−	0.0868987i
$649$	−2226.68			−0.134676
$650$	9766.97	−	22749.7i	0.589372	−	1.37280i
$651$	9386.79			0.565127
$652$			20279.1i			1.21809i
$653$			920.410i			0.0551584i	0.999620	+	0.0275792i	$0.00877984\pi$
$653$			920.410i			0.0551584i	−0.999620	+	0.0275792i	$0.991220\pi$
$654$	−43013.4			−2.57180
$655$	8988.86	+	13641.4i	0.536219	+	0.813759i
$656$	−7485.38			−0.445511
$657$			10943.3i			0.649832i
$658$			11875.1i			0.703557i
$659$	−17824.3			−1.05362			−0.526812	−	0.849982i	$-0.676613\pi$
$659$	−17824.3			−1.05362			−0.526812	+	0.849982i	$0.676613\pi$
$660$	−3467.73	+	2285.03i	−0.204517	+	0.134765i
$661$	11343.8			0.667510			0.333755	−	0.942660i	$-0.391684\pi$
$661$	11343.8			0.667510			0.333755	+	0.942660i	$0.391684\pi$
$662$			7003.03i			0.411149i
$663$		−	29519.0i		−	1.72915i
$664$	−308.123			−0.0180083
$665$	−8206.30	+	5407.47i	−0.478536	+	0.315327i
$666$	−12045.6			−0.700839
$667$		−	9124.71i		−	0.529700i
$668$			5910.44i			0.342338i
$669$	−6556.61			−0.378914
$670$	−20645.4	−	31331.2i	−1.19045	−	1.80661i
$671$	−3497.58			−0.201226
$672$			11810.9i			0.678000i
$673$		−	13422.9i		−	0.768816i	−0.923163	−	0.384408i	$-0.874406\pi$
$673$		−	13422.9i		−	0.768816i	0.923163	−	0.384408i	$-0.125594\pi$
$674$	−31639.4			−1.80817
$675$	8541.21	+	3666.93i	0.487039	+	0.209097i
$676$	1647.62			0.0937426
$677$			1066.77i			0.0605602i	0.999541	+	0.0302801i	$0.00963993\pi$
$677$			1066.77i			0.0605602i	−0.999541	+	0.0302801i	$0.990360\pi$
$678$			9435.36i			0.534458i
$679$	−1543.08			−0.0872134
$680$	−898.895	−	1364.15i	−0.0506927	−	0.0769305i
$681$	−35080.1			−1.97397
$682$		−	5640.70i		−	0.316706i
$683$		−	19090.6i		−	1.06952i	−0.845005	−	0.534759i	$-0.820402\pi$
$683$		−	19090.6i		−	1.06952i	0.845005	−	0.534759i	$-0.179598\pi$
$684$	16445.0			0.919285
$685$	−17672.2	+	11645.0i	−0.985724	+	0.649534i
$686$	−1388.64			−0.0772865
$687$			23831.6i			1.32348i
$688$			2126.56i			0.117841i
$689$	17.8751			0.000988370
$690$	7960.95	−	5245.80i	0.439229	−	0.289426i
$691$	−16878.4			−0.929208			−0.464604	−	0.885518i	$-0.653803\pi$
$691$	−16878.4			−0.929208			−0.464604	+	0.885518i	$0.653803\pi$
$692$		−	11734.0i		−	0.644594i
$693$		−	740.988i		−	0.0406173i
$694$	−9553.57			−0.522549
$695$	10550.4	+	16011.1i	0.575825	+	0.873864i
$696$	−2917.78			−0.158905
$697$			11394.8i			0.619236i
$698$			13006.8i			0.705321i
$699$	−29914.7			−1.61871
$700$	6746.20	+	2896.29i	0.364261	+	0.156385i
$701$	30272.6			1.63107			0.815535	−	0.578707i	$-0.196443\pi$
$701$	30272.6			1.63107			0.815535	+	0.578707i	$0.196443\pi$
$702$			14728.0i			0.791841i
$703$			23937.8i			1.28426i
$704$	3802.71			0.203580
$705$	16826.2	+	25535.3i	0.898883	+	1.36413i
$706$	−22599.0			−1.20471
$707$		−	4139.50i		−	0.220201i
$708$		−	17981.4i		−	0.954497i
$709$	6593.32			0.349248			0.174624	−	0.984635i	$-0.444129\pi$
$709$	6593.32			0.349248			0.174624	+	0.984635i	$0.444129\pi$
$710$	−18755.5	+	12358.8i	−0.991383	+	0.653263i
$711$	3112.06			0.164151
$712$		−	217.203i		−	0.0114326i
$713$			6628.99i			0.348187i
$714$	17099.8			0.896279
$715$	3097.55	−	2041.10i	0.162017	−	0.106759i
$716$	3093.46			0.161464
$717$			4548.15i			0.236895i
$718$		−	43038.2i		−	2.23701i
$719$	−3293.72			−0.170842			−0.0854208	−	0.996345i	$-0.527223\pi$
$719$	−3293.72			−0.170842			−0.0854208	+	0.996345i	$0.527223\pi$
$720$	5830.49	+	8848.27i	0.301791	+	0.457994i
$721$	−3335.46			−0.172287
$722$		−	36071.6i		−	1.85934i
$723$		−	33178.1i		−	1.70665i
$724$	2648.20			0.135939
$725$	13944.6	−	32480.4i	0.714328	−	1.66385i
$726$	33958.3			1.73596
$727$		−	27757.8i		−	1.41606i	−0.706181	−	0.708032i	$-0.749583\pi$
$727$		−	27757.8i		−	1.41606i	0.706181	−	0.708032i	$-0.250417\pi$
$728$			541.333i			0.0275592i
$729$	1048.00			0.0532439
$730$	−17461.9	−	26499.9i	−0.885334	−	1.34357i
$731$	3237.20			0.163792
$732$		−	28244.5i		−	1.42616i
$733$			38324.6i			1.93117i	0.260080	+	0.965587i	$0.416251\pi$
$733$			38324.6i			1.93117i	−0.260080	+	0.965587i	$0.583749\pi$
$734$	−18277.8			−0.919136
$735$	−2986.01	+	1967.61i	−0.149851	+	0.0987432i
$736$	−8340.91			−0.417731
$737$		−	5622.07i		−	0.280993i
$738$			7789.30i			0.388521i
$739$	−21957.3			−1.09298			−0.546490	−	0.837466i	$-0.684036\pi$
$739$	−21957.3			−1.09298			−0.546490	+	0.837466i	$0.684036\pi$
$740$	14932.1	−	9839.36i	0.741775	−	0.488786i
$741$	−40100.6			−1.98803
$742$			10.3547i			0.000512308i
$743$		−	14695.0i		−	0.725580i	−0.931871	−	0.362790i	$-0.881824\pi$
$743$		−	14695.0i		−	0.725580i	0.931871	−	0.362790i	$-0.118176\pi$
$744$	2119.73			0.104453
$745$	17214.5	+	26124.4i	0.846563	+	1.28473i
$746$	46338.5			2.27423
$747$		−	3042.37i		−	0.149016i
$748$		−	5260.18i		−	0.257127i
$749$	1579.09			0.0770341
$750$	36354.6	−	6506.90i	1.76998	−	0.316798i
$751$	−21439.1			−1.04171			−0.520855	−	0.853645i	$-0.674387\pi$
$751$	−21439.1			−1.04171			−0.520855	+	0.853645i	$0.674387\pi$
$752$		−	25445.1i		−	1.23389i
$753$			7880.74i			0.381395i
$754$	56007.4			2.70513
$755$	−17640.0	−	26770.2i	−0.850311	−	1.29042i
$756$	−4367.44			−0.210109
$757$			23896.8i			1.14735i	0.819083	+	0.573675i	$0.194483\pi$
$757$			23896.8i			1.14735i	−0.819083	+	0.573675i	$0.805517\pi$
$758$			32981.1i			1.58038i
$759$	1428.51			0.0683158
$760$	−1853.15	+	1221.12i	−0.0884485	+	0.0582824i
$761$	−24436.9			−1.16404			−0.582022	−	0.813173i	$-0.697738\pi$
$761$	−24436.9			−1.16404			−0.582022	+	0.813173i	$0.697738\pi$
$762$			45671.9i			2.17128i
$763$			11393.6i			0.540597i
$764$	1272.24			0.0602459
$765$	13469.4	−	8875.57i	0.636587	−	0.419473i
$766$	−21301.5			−1.00477
$767$			16061.9i			0.756145i
$768$		−	23938.9i		−	1.12477i
$769$	30689.3			1.43912			0.719560	−	0.694430i	$-0.244343\pi$
$769$	30689.3			1.43912			0.719560	+	0.694430i	$0.244343\pi$
$770$	1182.37	+	1794.35i	0.0553373	+	0.0839791i
$771$	3335.13			0.155787
$772$		−	5795.19i		−	0.270173i
$773$		−	5110.74i		−	0.237801i	−0.992906	−	0.118901i	$-0.962063\pi$
$773$		−	5110.74i		−	0.237801i	0.992906	−	0.118901i	$-0.0379370\pi$
$774$	2212.90			0.102766
$775$	−10130.5	+	23596.6i	−0.469548	+	1.09370i
$776$	−348.459			−0.0161198
$777$			8710.22i			0.402159i
$778$			53469.3i			2.46397i
$779$	15479.4			0.711947
$780$	16482.8	+	25014.1i	0.756642	+	1.14827i
$781$	−3365.49			−0.154195
$782$			12075.9i			0.552217i
$783$			21027.6i			0.959723i
$784$	2975.47			0.135545
$785$	7316.40	−	4821.08i	0.332654	−	0.219199i
$786$	−38614.4			−1.75233
$787$		−	6991.30i		−	0.316662i	−0.987386	−	0.158331i	$-0.949389\pi$
$787$		−	6991.30i		−	0.316662i	0.987386	−	0.158331i	$-0.0506113\pi$
$788$			6998.78i			0.316397i
$789$	−14811.1			−0.668302
$790$	−7536.06	+	4965.82i	−0.339394	+	0.223641i
$791$	2499.28			0.112344
$792$		−	167.330i		−	0.00750735i
$793$			25229.5i			1.12979i
$794$	22927.3			1.02476
$795$	14.6719	+	22.2658i	0.000654539	+	0.000993319i
$796$	3249.36			0.144687
$797$		−	4020.31i		−	0.178678i	−0.996001	−	0.0893392i	$-0.971524\pi$
$797$		−	4020.31i		−	0.178678i	0.996001	−	0.0893392i	$-0.0284755\pi$
$798$		−	23229.5i		−	1.03047i
$799$	−38734.3			−1.71505
$800$	−29690.4	−	12746.7i	−1.31214	−	0.563332i
$801$	2144.64			0.0946030
$802$			48537.7i			2.13706i
$803$		−	4755.15i		−	0.208973i
$804$	45400.8			1.99149
$805$	−1389.53	−	2108.73i	−0.0608379	−	0.0923267i
$806$	−40688.7			−1.77816
$807$		−	51150.0i		−	2.23118i
$808$		−	934.785i		−	0.0407000i
$809$	41608.1			1.80824			0.904119	−	0.427281i	$-0.140528\pi$
$809$	41608.1			1.80824			0.904119	+	0.427281i	$0.140528\pi$
$810$	−34273.6	+	22584.3i	−1.48673	+	0.979667i
$811$	42271.3			1.83027			0.915133	−	0.403152i	$-0.132086\pi$
$811$	42271.3			1.83027			0.915133	+	0.403152i	$0.132086\pi$
$812$			16608.4i			0.717785i
$813$		−	9571.13i		−	0.412884i
$814$	5234.13			0.225376
$815$	22563.9	−	14868.3i	0.969790	−	0.639035i
$816$	−36640.1			−1.57189
$817$		−	4397.62i		−	0.188315i
$818$			21253.4i			0.908443i
$819$	−5345.05			−0.228048
$820$	−6362.62	−	9655.82i	−0.270966	−	0.411214i
$821$	27184.7			1.15561			0.577804	−	0.816176i	$-0.303910\pi$
$821$	27184.7			1.15561			0.577804	+	0.816176i	$0.303910\pi$
$822$		−	50024.5i		−	2.12263i
$823$		−	12967.9i		−	0.549250i	−0.961551	−	0.274625i	$-0.911446\pi$
$823$		−	12967.9i		−	0.549250i	0.961551	−	0.274625i	$-0.0885538\pi$
$824$	−753.215			−0.0318440
$825$	5084.94	+	2183.08i	0.214588	+	0.0921273i
$826$	−9304.36			−0.391937
$827$			33111.2i			1.39225i	0.717921	+	0.696124i	$0.245094\pi$
$827$			33111.2i			1.39225i	−0.717921	+	0.696124i	$0.754906\pi$
$828$			4225.79i			0.177363i
$829$	−3715.75			−0.155673			−0.0778367	−	0.996966i	$-0.524801\pi$
$829$	−3715.75			−0.155673			−0.0778367	+	0.996966i	$0.524801\pi$
$830$	4854.62	+	7367.30i	0.203020	+	0.308100i
$831$	27116.3			1.13195
$832$		−	27430.5i		−	1.14301i
$833$		−	4529.47i		−	0.188399i
$834$	−45322.4			−1.88176
$835$	6576.33	−	4333.42i	0.272555	−	0.179598i
$836$	−7145.77			−0.295624
$837$		−	15276.3i		−	0.630854i
$838$		−	60521.0i		−	2.49482i
$839$	1460.56			0.0601005			0.0300502	−	0.999548i	$-0.490433\pi$
$839$	1460.56			0.0601005			0.0300502	+	0.999548i	$0.490433\pi$
$840$	−674.303	+	444.326i	−0.0276972	+	0.0182508i
$841$	55574.2			2.27866
$842$		−	23644.6i		−	0.967750i
$843$			22783.6i			0.930851i
$844$	−25763.2			−1.05072
$845$	−1208.00	−	1833.25i	−0.0491794	−	0.0746339i
$846$	−26478.2			−1.07605
$847$		−	8995.02i		−	0.364903i
$848$		−	22.1873i		−	0.000898483i
$849$	20400.3			0.824660
$850$	−18454.7	+	42985.5i	−0.744694	+	1.73458i
$851$	−6151.19			−0.247779
$852$		−	27177.9i		−	1.09284i
$853$		−	36027.4i		−	1.44613i	−0.690777	−	0.723067i	$-0.742732\pi$
$853$		−	36027.4i		−	1.44613i	0.690777	−	0.723067i	$-0.257268\pi$
$854$	−14614.9			−0.585612
$855$	−12057.2	−	18297.8i	−0.482276	−	0.731896i
$856$	356.590			0.0142383
$857$		−	23500.7i		−	0.936719i	−0.883538	−	0.468359i	$-0.844845\pi$
$857$		−	23500.7i		−	0.936719i	0.883538	−	0.468359i	$-0.155155\pi$
$858$			8768.20i			0.348883i
$859$	−5551.11			−0.220491			−0.110245	−	0.993904i	$-0.535164\pi$
$859$	−5551.11			−0.220491			−0.110245	+	0.993904i	$0.535164\pi$
$860$	−2743.17	+	1807.59i	−0.108769	+	0.0716724i
$861$	5632.46			0.222943
$862$		−	30117.7i		−	1.19004i
$863$			27721.4i			1.09345i	0.837312	+	0.546725i	$0.184126\pi$
$863$			27721.4i			1.09345i	−0.837312	+	0.546725i	$0.815874\pi$
$864$	19221.3			0.756855
$865$	−13056.0	+	8603.13i	−0.513199	+	0.338168i
$866$	−3553.21			−0.139426
$867$			23706.6i			0.928624i
$868$		−	12065.8i		−	0.471821i
$869$	−1352.27			−0.0527878
$870$	45970.9	+	69764.8i	1.79145	+	2.71867i
$871$	−40554.3			−1.57765
$872$			2572.90i			0.0999192i
$873$		−	3440.64i		−	0.133388i
$874$	16404.7			0.634895
$875$	−1723.58	−	9629.77i	−0.0665915	−	0.372052i
$876$	38400.0			1.48107
$877$		−	47255.6i		−	1.81951i	−0.415149	−	0.909754i	$-0.636270\pi$
$877$		−	47255.6i		−	1.81951i	0.415149	−	0.909754i	$-0.363730\pi$
$878$		−	43950.0i		−	1.68934i
$879$	9449.79			0.362609
$880$	−2533.50	−	3844.80i	−0.0970502	−	0.147282i
$881$	32267.0			1.23394			0.616972	−	0.786985i	$-0.288359\pi$
$881$	32267.0			1.23394			0.616972	+	0.786985i	$0.288359\pi$
$882$		−	3096.28i		−	0.118205i
$883$			5062.08i			0.192925i	0.995337	+	0.0964623i	$0.0307527\pi$
$883$			5062.08i			0.192925i	−0.995337	+	0.0964623i	$0.969247\pi$
$884$	−37943.8			−1.44365
$885$	−20007.3	+	13183.6i	−0.759930	+	0.500749i
$886$	−43712.0			−1.65749
$887$		−	7626.08i		−	0.288679i	−0.989528	−	0.144340i	$-0.953894\pi$
$887$		−	7626.08i		−	0.288679i	0.989528	−	0.144340i	$-0.0461058\pi$
$888$			1966.95i			0.0743315i
$889$	12097.8			0.456408
$890$	−5193.38	+	3422.13i	−0.195598	+	0.128888i
$891$	−6150.05			−0.231239
$892$			8427.89i			0.316353i
$893$			52619.2i			1.97182i
$894$	−73950.1			−2.76651
$895$	−2268.06	−	3441.98i	−0.0847072	−	0.128550i
$896$	1414.66			0.0527460
$897$		−	10304.4i		−	0.383562i
$898$			34905.0i			1.29710i
$899$	−58092.3			−2.15516
$900$	−6457.94	+	15042.2i	−0.239183	+	0.557117i
$901$	−33.7750			−0.00124884
$902$		−	3384.65i		−	0.124941i
$903$		−	1600.16i		−	0.0589699i
$904$	564.389			0.0207647
$905$	−1941.61	−	2946.56i	−0.0713164	−	0.108229i
$906$	75778.0			2.77876
$907$			8546.31i			0.312873i	0.987688	+	0.156436i	$0.0500006\pi$
$907$			8546.31i			0.312873i	−0.987688	+	0.156436i	$0.949999\pi$
$908$			45092.1i			1.64806i
$909$	9229.95			0.336786
$910$	12943.4	−	8528.93i	0.471504	−	0.310694i
$911$	8778.92			0.319274			0.159637	−	0.987176i	$-0.448968\pi$
$911$	8778.92			0.319274			0.159637	+	0.987176i	$0.448968\pi$
$912$			49774.4i			1.80723i
$913$			1321.99i			0.0479205i
$914$	15327.3			0.554683
$915$	−31426.7	+	20708.3i	−1.13545	+	0.748193i
$916$	30633.3			1.10497
$917$			10228.4i			0.368343i
$918$		−	27828.5i		−	1.00052i
$919$	−21626.0			−0.776253			−0.388126	−	0.921606i	$-0.626878\pi$
$919$	−21626.0			−0.776253			−0.388126	+	0.921606i	$0.626878\pi$
$920$	−313.784	−	476.195i	−0.0112447	−	0.0170649i
$921$	10388.0			0.371658
$922$		−	23320.1i		−	0.832981i
$923$			24276.7i			0.865738i
$924$	−2600.12			−0.0925732
$925$	−21895.8	−	9400.36i	−0.778302	−	0.334143i
$926$	43565.8			1.54607
$927$		−	7437.15i		−	0.263504i
$928$		−	73094.5i		−	2.58561i
$929$	−12262.6			−0.433073			−0.216536	−	0.976275i	$-0.569476\pi$
$929$	−12262.6			−0.433073			−0.216536	+	0.976275i	$0.569476\pi$
$930$	−33397.3	−	50683.2i	−1.17757	−	1.78706i
$931$	−6153.13			−0.216606
$932$			38452.5i			1.35145i
$933$			56037.9i			1.96634i
$934$	−8718.78			−0.305447
$935$	−5852.82	+	3856.66i	−0.204714	+	0.134894i
$936$	−1207.02			−0.0421504
$937$			13362.6i			0.465889i	0.972490	+	0.232945i	$0.0748361\pi$
$937$			13362.6i			0.465889i	−0.972490	+	0.232945i	$0.925164\pi$
$938$		−	23492.3i		−	0.817751i
$939$	47063.5			1.63563
$940$	32823.1	−	21628.5i	1.13891	−	0.750472i
$941$	−46330.1			−1.60501			−0.802506	−	0.596643i	$-0.796501\pi$
$941$	−46330.1			−1.60501			−0.802506	+	0.596643i	$0.796501\pi$
$942$			20710.4i			0.716329i
$943$			3977.66i			0.137360i
$944$	19936.7			0.687377
$945$	3202.12	+	4859.49i	0.110228	+	0.167280i
$946$	−961.563			−0.0330477
$947$			17387.6i			0.596643i	0.954465	+	0.298321i	$0.0964267\pi$
$947$			17387.6i			0.596643i	−0.954465	+	0.298321i	$0.903573\pi$
$948$		−	10920.2i		−	0.374126i
$949$	−34300.8			−1.17329
$950$	58394.4	+	25070.0i	1.99428	+	0.856188i
$951$	50831.1			1.73324
$952$		−	1022.85i		−	0.0348221i
$953$		−	42384.6i		−	1.44068i	−0.693619	−	0.720342i	$-0.743985\pi$
$953$		−	42384.6i		−	1.44068i	0.693619	−	0.720342i	$-0.256015\pi$
$954$	−23.0881			−0.000783548
$955$	−932.779	−	1415.57i	−0.0316063	−	0.0479653i
$956$	5846.20			0.197782
$957$			12518.6i			0.422851i
$958$		−	27895.3i		−	0.940769i
$959$	−13250.7			−0.446182
$960$	34168.4	−	22515.0i	1.14873	−	0.756946i
$961$	12412.3			0.416647
$962$		−	37755.9i		−	1.26539i
$963$			3520.92i			0.117820i
$964$	−42647.2			−1.42487
$965$	−6448.10	+	4248.92i	−0.215100	+	0.141738i
$966$	5969.16			0.198814
$967$			15771.6i			0.524489i	0.965001	+	0.262245i	$0.0844627\pi$
$967$			15771.6i			0.524489i	−0.965001	+	0.262245i	$0.915537\pi$
$968$		−	2031.26i		−	0.0674454i
$969$	75769.9			2.51195
$970$	5490.12	+	8331.72i	0.181729	+	0.275789i
$971$	36370.5			1.20204			0.601022	−	0.799232i	$-0.294760\pi$
$971$	36370.5			1.20204			0.601022	+	0.799232i	$0.294760\pi$
$972$		−	32818.6i		−	1.08298i
$973$			12005.2i			0.395549i
$974$	76947.5			2.53137
$975$	15747.4	−	36679.8i	0.517253	−	1.20481i
$976$	31315.8			1.02704
$977$			35122.8i			1.15013i	0.818108	+	0.575065i	$0.195023\pi$
$977$			35122.8i			1.15013i	−0.818108	+	0.575065i	$0.804977\pi$
$978$			63871.3i			2.08832i
$979$	−931.899			−0.0304225
$980$	2529.17	+	3838.23i	0.0824401	+	0.125110i
$981$	−25404.5			−0.826814
$982$		−	18340.0i		−	0.595979i
$983$		−	12798.9i		−	0.415282i	−0.978205	−	0.207641i	$-0.933421\pi$
$983$		−	12798.9i		−	0.415282i	0.978205	−	0.207641i	$-0.0665785\pi$
$984$	1271.92			0.0412068
$985$	7787.30	−	5131.37i	0.251902	−	0.165989i
$986$	−105826.			−3.41803
$987$			19146.5i			0.617466i
$988$			51545.4i			1.65980i
$989$	1130.03			0.0363327
$990$	−4000.90	+	2636.36i	−0.128442	+	0.0846354i
$991$	−46594.9			−1.49358			−0.746789	−	0.665061i	$-0.768406\pi$
$991$	−46594.9			−1.49358			−0.746789	+	0.665061i	$0.768406\pi$
$992$			53102.3i			1.69960i
$993$			11291.1i			0.360838i
$994$	−14063.0			−0.448743
$995$	−2382.37	−	3615.45i	−0.0759058	−	0.115194i
$996$	−10675.7			−0.339630
$997$		−	47534.1i		−	1.50995i	−0.655753	−	0.754975i	$-0.727649\pi$
$997$		−	47534.1i		−	1.50995i	0.655753	−	0.754975i	$-0.272351\pi$
$998$			14656.4i			0.464869i
$999$	14175.2			0.448932

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.4.b.a.29.2	✓	10
3.2	odd	2		315.4.d.c.64.9		10
4.3	odd	2		560.4.g.f.449.9		10
5.2	odd	4		175.4.a.i.1.5		5
5.3	odd	4		175.4.a.j.1.1		5
5.4	even	2	inner	35.4.b.a.29.9	yes	10
7.2	even	3		245.4.j.e.214.2		20
7.3	odd	6		245.4.j.f.79.9		20
7.4	even	3		245.4.j.e.79.9		20
7.5	odd	6		245.4.j.f.214.2		20
7.6	odd	2		245.4.b.d.99.2		10
15.2	even	4		1575.4.a.bq.1.1		5
15.8	even	4		1575.4.a.bn.1.5		5
15.14	odd	2		315.4.d.c.64.2		10
20.19	odd	2		560.4.g.f.449.2		10
35.4	even	6		245.4.j.e.79.2		20
35.9	even	6		245.4.j.e.214.9		20
35.13	even	4		1225.4.a.bh.1.1		5
35.19	odd	6		245.4.j.f.214.9		20
35.24	odd	6		245.4.j.f.79.2		20
35.27	even	4		1225.4.a.be.1.5		5
35.34	odd	2		245.4.b.d.99.9		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.b.a.29.2	✓	10	1.1	even	1	trivial
35.4.b.a.29.9	yes	10	5.4	even	2	inner
175.4.a.i.1.5		5	5.2	odd	4
175.4.a.j.1.1		5	5.3	odd	4
245.4.b.d.99.2		10	7.6	odd	2
245.4.b.d.99.9		10	35.34	odd	2
245.4.j.e.79.2		20	35.4	even	6
245.4.j.e.79.9		20	7.4	even	3
245.4.j.e.214.2		20	7.2	even	3
245.4.j.e.214.9		20	35.9	even	6
245.4.j.f.79.2		20	35.24	odd	6
245.4.j.f.79.9		20	7.3	odd	6
245.4.j.f.214.2		20	7.5	odd	6
245.4.j.f.214.9		20	35.19	odd	6
315.4.d.c.64.2		10	15.14	odd	2
315.4.d.c.64.9		10	3.2	odd	2
560.4.g.f.449.2		10	20.19	odd	2
560.4.g.f.449.9		10	4.3	odd	2
1225.4.a.be.1.5		5	35.27	even	4
1225.4.a.bh.1.1		5	35.13	even	4
1575.4.a.bn.1.5		5	15.8	even	4
1575.4.a.bq.1.1		5	15.2	even	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:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	35.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4.04851i q^{2} -6.52749i q^{3} -8.39045 q^{4} +(6.15172 + 9.33576i) q^{5} -26.4266 q^{6} +7.00000i q^{7} +1.58074i q^{8} -15.6081 q^{9} +(37.7959 - 24.9053i) q^{10} +6.78210 q^{11} +54.7685i q^{12} -48.9221i q^{13} +28.3396 q^{14} +(60.9390 - 40.1552i) q^{15} -60.7239 q^{16} +92.4381i q^{17} +63.1894i q^{18} +125.574 q^{19} +(-51.6157 - 78.3312i) q^{20} +45.6924 q^{21} -27.4574i q^{22} +32.2681i q^{23} +10.3183 q^{24} +(-49.3128 + 114.862i) q^{25} -198.062 q^{26} -74.3607i q^{27} -58.7332i q^{28} -282.778 q^{29} +(-162.569 - 246.712i) q^{30} +205.434 q^{31} +258.488i q^{32} -44.2701i q^{33} +374.237 q^{34} +(-65.3503 + 43.0620i) q^{35} +130.959 q^{36} +190.627i q^{37} -508.388i q^{38} -319.338 q^{39} +(-14.7574 + 9.72429i) q^{40} +123.269 q^{41} -184.986i q^{42} -35.0202i q^{43} -56.9049 q^{44} +(-96.0164 - 145.713i) q^{45} +130.638 q^{46} +419.030i q^{47} +396.375i q^{48} -49.0000 q^{49} +(465.020 + 199.643i) q^{50} +603.388 q^{51} +410.478i q^{52} +0.365379i q^{53} -301.050 q^{54} +(41.7215 + 63.3160i) q^{55} -11.0652 q^{56} -819.683i q^{57} +1144.83i q^{58} -328.317 q^{59} +(-511.306 + 336.921i) q^{60} -515.707 q^{61} -831.704i q^{62} -109.256i q^{63} +560.699 q^{64} +(456.725 - 300.955i) q^{65} -179.228 q^{66} -828.957i q^{67} -775.597i q^{68} +210.630 q^{69} +(174.337 + 264.572i) q^{70} -496.231 q^{71} -24.6723i q^{72} -701.132i q^{73} +771.757 q^{74} +(749.759 + 321.888i) q^{75} -1053.62 q^{76} +47.4747i q^{77} +1292.84i q^{78} -199.388 q^{79} +(-373.556 - 566.904i) q^{80} -906.806 q^{81} -499.056i q^{82} +194.923i q^{83} -383.380 q^{84} +(-862.980 + 568.653i) q^{85} -141.780 q^{86} +1845.83i q^{87} +10.7208i q^{88} -137.406 q^{89} +(-589.921 + 388.723i) q^{90} +342.454 q^{91} -270.744i q^{92} -1340.97i q^{93} +1696.45 q^{94} +(772.496 + 1172.33i) q^{95} +1687.27 q^{96} +220.440i q^{97} +198.377i q^{98} -105.855 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 36 q^{4} + 6 q^{5} + 12 q^{6} - 46 q^{9} - 16 q^{10} + 84 q^{11} - 56 q^{14} + 8 q^{15} + 148 q^{16} + 72 q^{19} - 68 q^{20} + 140 q^{21} + 72 q^{24} - 362 q^{25} - 620 q^{26} + 88 q^{29} + 52 q^{30}+ \cdots - 5304 q^{99}+O(q^{100}) \) 10 * q - 36 * q^4 + 6 * q^5 + 12 * q^6 - 46 * q^9 - 16 * q^10 + 84 * q^11 - 56 * q^14 + 8 * q^15 + 148 * q^16 + 72 * q^19 - 68 * q^20 + 140 * q^21 + 72 * q^24 - 362 * q^25 - 620 * q^26 + 88 * q^29 + 52 * q^30 + 120 * q^31 + 964 * q^34 - 28 * q^35 - 420 * q^36 + 212 * q^39 + 1396 * q^40 - 852 * q^41 - 1424 * q^44 - 510 * q^45 + 176 * q^46 - 490 * q^49 + 1644 * q^50 + 1276 * q^51 - 996 * q^54 - 1136 * q^55 + 588 * q^56 + 864 * q^59 - 1692 * q^60 - 884 * q^61 - 2724 * q^64 + 520 * q^65 + 1148 * q^66 + 4808 * q^69 + 756 * q^70 + 880 * q^71 + 3024 * q^74 + 720 * q^75 - 2672 * q^76 - 3580 * q^79 - 2316 * q^80 - 302 * q^81 - 1904 * q^84 + 1572 * q^85 + 2432 * q^86 - 1492 * q^89 - 7748 * q^90 + 476 * q^91 + 1652 * q^94 - 1628 * q^95 + 4080 * q^96 - 5304 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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