LMFDB - Embedded newform 11.5.b.b.10.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [11,5,Mod(10,11)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(11, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("11.10");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 11 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	11.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:	$1.13706959392$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-30}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 30 $ x^2 + 30
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			10.2
Root			$5.47723i$ of defining polynomial
Character	$\chi$	$=$	11.10
Dual form			11.5.b.b.10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.47723i q^{2} -3.00000 q^{3} -14.0000 q^{4} +31.0000 q^{5} -16.4317i q^{6} -54.7723i q^{7} +10.9545i q^{8} -72.0000 q^{9} +O(q^{10})$	\(q+5.47723i q^{2} -3.00000 q^{3} -14.0000 q^{4} +31.0000 q^{5} -16.4317i q^{6} -54.7723i q^{7} +10.9545i q^{8} -72.0000 q^{9} +169.794i q^{10} +(11.0000 - 120.499i) q^{11} +42.0000 q^{12} +186.226i q^{13} +300.000 q^{14} -93.0000 q^{15} -284.000 q^{16} -230.043i q^{17} -394.360i q^{18} +98.5901i q^{19} -434.000 q^{20} +164.317i q^{21} +(660.000 + 60.2495i) q^{22} +277.000 q^{23} -32.8634i q^{24} +336.000 q^{25} -1020.00 q^{26} +459.000 q^{27} +766.812i q^{28} +1270.72i q^{29} -509.382i q^{30} -1363.00 q^{31} -1380.26i q^{32} +(-33.0000 + 361.497i) q^{33} +1260.00 q^{34} -1697.94i q^{35} +1008.00 q^{36} +167.000 q^{37} -540.000 q^{38} -558.677i q^{39} +339.588i q^{40} +1062.58i q^{41} -900.000 q^{42} -1204.99i q^{43} +(-154.000 + 1686.99i) q^{44} -2232.00 q^{45} +1517.19i q^{46} +1702.00 q^{47} +852.000 q^{48} -599.000 q^{49} +1840.35i q^{50} +690.130i q^{51} -2607.16i q^{52} +4522.00 q^{53} +2514.05i q^{54} +(341.000 - 3735.47i) q^{55} +600.000 q^{56} -295.770i q^{57} -6960.00 q^{58} -2363.00 q^{59} +1302.00 q^{60} -3965.51i q^{61} -7465.46i q^{62} +3943.60i q^{63} +3016.00 q^{64} +5773.00i q^{65} +(-1980.00 - 180.748i) q^{66} -2803.00 q^{67} +3220.61i q^{68} -831.000 q^{69} +9300.00 q^{70} +3397.00 q^{71} -788.720i q^{72} +3319.20i q^{73} +914.697i q^{74} -1008.00 q^{75} -1380.26i q^{76} +(-6600.00 - 602.495i) q^{77} +3060.00 q^{78} +6090.67i q^{79} -8804.00 q^{80} +4455.00 q^{81} -5820.00 q^{82} -832.538i q^{83} -2300.43i q^{84} -7131.35i q^{85} +6600.00 q^{86} -3812.15i q^{87} +(1320.00 + 120.499i) q^{88} -4673.00 q^{89} -12225.2i q^{90} +10200.0 q^{91} -3878.00 q^{92} +4089.00 q^{93} +9322.24i q^{94} +3056.29i q^{95} +4140.78i q^{96} +4247.00 q^{97} -3280.86i q^{98} +(-792.000 + 8675.93i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 6 q^{3} - 28 q^{4} + 62 q^{5} - 144 q^{9}+O(q^{10}) $ 2 * q - 6 * q^3 - 28 * q^4 + 62 * q^5 - 144 * q^9	$ 2 q - 6 q^{3} - 28 q^{4} + 62 q^{5} - 144 q^{9} + 22 q^{11} + 84 q^{12} + 600 q^{14} - 186 q^{15} - 568 q^{16} - 868 q^{20} + 1320 q^{22} + 554 q^{23} + 672 q^{25} - 2040 q^{26} + 918 q^{27} - 2726 q^{31} - 66 q^{33} + 2520 q^{34} + 2016 q^{36} + 334 q^{37} - 1080 q^{38} - 1800 q^{42} - 308 q^{44} - 4464 q^{45} + 3404 q^{47} + 1704 q^{48} - 1198 q^{49} + 9044 q^{53} + 682 q^{55} + 1200 q^{56} - 13920 q^{58} - 4726 q^{59} + 2604 q^{60} + 6032 q^{64} - 3960 q^{66} - 5606 q^{67} - 1662 q^{69} + 18600 q^{70} + 6794 q^{71} - 2016 q^{75} - 13200 q^{77} + 6120 q^{78} - 17608 q^{80} + 8910 q^{81} - 11640 q^{82} + 13200 q^{86} + 2640 q^{88} - 9346 q^{89} + 20400 q^{91} - 7756 q^{92} + 8178 q^{93} + 8494 q^{97} - 1584 q^{99}+O(q^{100}) $ 2 * q - 6 * q^3 - 28 * q^4 + 62 * q^5 - 144 * q^9 + 22 * q^11 + 84 * q^12 + 600 * q^14 - 186 * q^15 - 568 * q^16 - 868 * q^20 + 1320 * q^22 + 554 * q^23 + 672 * q^25 - 2040 * q^26 + 918 * q^27 - 2726 * q^31 - 66 * q^33 + 2520 * q^34 + 2016 * q^36 + 334 * q^37 - 1080 * q^38 - 1800 * q^42 - 308 * q^44 - 4464 * q^45 + 3404 * q^47 + 1704 * q^48 - 1198 * q^49 + 9044 * q^53 + 682 * q^55 + 1200 * q^56 - 13920 * q^58 - 4726 * q^59 + 2604 * q^60 + 6032 * q^64 - 3960 * q^66 - 5606 * q^67 - 1662 * q^69 + 18600 * q^70 + 6794 * q^71 - 2016 * q^75 - 13200 * q^77 + 6120 * q^78 - 17608 * q^80 + 8910 * q^81 - 11640 * q^82 + 13200 * q^86 + 2640 * q^88 - 9346 * q^89 + 20400 * q^91 - 7756 * q^92 + 8178 * q^93 + 8494 * q^97 - 1584 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/11\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$			5.47723i			1.36931i	0.728869	+	0.684653i	$0.240046\pi$
$2$			5.47723i			1.36931i	−0.728869	+	0.684653i	$0.759954\pi$
$3$	−3.00000			−0.333333			−0.166667	−	0.986013i	$-0.553300\pi$
$3$	−3.00000			−0.333333			−0.166667	+	0.986013i	$0.553300\pi$
$4$	−14.0000			−0.875000
$5$	31.0000			1.24000			0.620000	−	0.784602i	$-0.287133\pi$
$5$	31.0000			1.24000			0.620000	+	0.784602i	$0.287133\pi$
$6$		−	16.4317i		−	0.456435i
$7$		−	54.7723i		−	1.11780i	−0.829235	−	0.558901i	$-0.811223\pi$
$7$		−	54.7723i		−	1.11780i	0.829235	−	0.558901i	$-0.188777\pi$
$8$			10.9545i			0.171163i
$9$	−72.0000			−0.888889
$10$			169.794i			1.69794i
$11$	11.0000	−	120.499i	0.0909091	−	0.995859i
$11$	11.0000	−	120.499i	0.0909091	−	0.995859i
$12$	42.0000			0.291667
$13$			186.226i			1.10193i	0.834529	+	0.550964i	$0.185740\pi$
$13$			186.226i			1.10193i	−0.834529	+	0.550964i	$0.814260\pi$
$14$	300.000			1.53061
$15$	−93.0000			−0.413333
$16$	−284.000			−1.10938
$17$		−	230.043i		−	0.795998i	−0.917386	−	0.397999i	$-0.869705\pi$
$17$		−	230.043i		−	0.795998i	0.917386	−	0.397999i	$-0.130295\pi$
$18$		−	394.360i		−	1.21716i
$19$			98.5901i			0.273103i	0.990633	+	0.136551i	$0.0436019\pi$
$19$			98.5901i			0.273103i	−0.990633	+	0.136551i	$0.956398\pi$
$20$	−434.000			−1.08500
$21$			164.317i			0.372600i
$22$	660.000	+	60.2495i	1.36364	+	0.124482i
$23$	277.000			0.523629			0.261815	−	0.965118i	$-0.415679\pi$
$23$	277.000			0.523629			0.261815	+	0.965118i	$0.415679\pi$
$24$		−	32.8634i		−	0.0570544i
$25$	336.000			0.537600
$26$	−1020.00			−1.50888
$27$	459.000			0.629630
$28$			766.812i			0.978076i
$29$			1270.72i			1.51096i	0.655172	+	0.755479i	$0.272596\pi$
$29$			1270.72i			1.51096i	−0.655172	+	0.755479i	$0.727404\pi$
$30$		−	509.382i		−	0.565980i
$31$	−1363.00			−1.41831			−0.709157	−	0.705050i	$-0.750924\pi$
$31$	−1363.00			−1.41831			−0.709157	+	0.705050i	$0.750924\pi$
$32$		−	1380.26i		−	1.34791i
$33$	−33.0000	+	361.497i	−0.0303030	+	0.331953i
$34$	1260.00			1.08997
$35$		−	1697.94i		−	1.38607i
$36$	1008.00			0.777778
$37$	167.000			0.121987			0.0609934	−	0.998138i	$-0.480573\pi$
$37$	167.000			0.121987			0.0609934	+	0.998138i	$0.480573\pi$
$38$	−540.000			−0.373961
$39$		−	558.677i		−	0.367309i
$40$			339.588i			0.212242i
$41$			1062.58i			0.632113i	0.948740	+	0.316056i	$0.102359\pi$
$41$			1062.58i			0.632113i	−0.948740	+	0.316056i	$0.897641\pi$
$42$	−900.000			−0.510204
$43$		−	1204.99i		−	0.651698i	−0.945422	−	0.325849i	$-0.894350\pi$
$43$		−	1204.99i		−	0.651698i	0.945422	−	0.325849i	$-0.105650\pi$
$44$	−154.000	+	1686.99i	−0.0795455	+	0.871377i
$45$	−2232.00			−1.10222
$46$			1517.19i			0.717009i
$47$	1702.00			0.770484			0.385242	−	0.922816i	$-0.374118\pi$
$47$	1702.00			0.770484			0.385242	+	0.922816i	$0.374118\pi$
$48$	852.000			0.369792
$49$	−599.000			−0.249479
$50$			1840.35i			0.736139i
$51$			690.130i			0.265333i
$52$		−	2607.16i		−	0.964186i
$53$	4522.00			1.60983			0.804913	−	0.593393i	$-0.202212\pi$
$53$	4522.00			1.60983			0.804913	+	0.593393i	$0.202212\pi$
$54$			2514.05i			0.862156i
$55$	341.000	−	3735.47i	0.112727	−	1.23487i
$56$	600.000			0.191327
$57$		−	295.770i		−	0.0910342i
$58$	−6960.00			−2.06897
$59$	−2363.00			−0.678828			−0.339414	−	0.940637i	$-0.610229\pi$
$59$	−2363.00			−0.678828			−0.339414	+	0.940637i	$0.610229\pi$
$60$	1302.00			0.361667
$61$		−	3965.51i		−	1.06571i	−0.846206	−	0.532856i	$-0.821119\pi$
$61$		−	3965.51i		−	1.06571i	0.846206	−	0.532856i	$-0.178881\pi$
$62$		−	7465.46i		−	1.94211i
$63$			3943.60i			0.993601i
$64$	3016.00			0.736328
$65$			5773.00i			1.36639i
$66$	−1980.00	−	180.748i	−0.454545	−	0.0414941i
$67$	−2803.00			−0.624415			−0.312208	−	0.950014i	$-0.601068\pi$
$67$	−2803.00			−0.624415			−0.312208	+	0.950014i	$0.601068\pi$
$68$			3220.61i			0.696498i
$69$	−831.000			−0.174543
$70$	9300.00			1.89796
$71$	3397.00			0.673874			0.336937	−	0.941527i	$-0.390609\pi$
$71$	3397.00			0.673874			0.336937	+	0.941527i	$0.390609\pi$
$72$		−	788.720i		−	0.152145i
$73$			3319.20i			0.622856i	0.950270	+	0.311428i	$0.100807\pi$
$73$			3319.20i			0.622856i	−0.950270	+	0.311428i	$0.899193\pi$
$74$			914.697i			0.167037i
$75$	−1008.00			−0.179200
$76$		−	1380.26i		−	0.238965i
$77$	−6600.00	−	602.495i	−1.11317	−	0.101618i
$78$	3060.00			0.502959
$79$			6090.67i			0.975913i	0.872868	+	0.487957i	$0.162258\pi$
$79$			6090.67i			0.975913i	−0.872868	+	0.487957i	$0.837742\pi$
$80$	−8804.00			−1.37563
$81$	4455.00			0.679012
$82$	−5820.00			−0.865556
$83$		−	832.538i		−	0.120850i	−0.998173	−	0.0604252i	$-0.980754\pi$
$83$		−	832.538i		−	0.120850i	0.998173	−	0.0604252i	$-0.0192457\pi$
$84$		−	2300.43i		−	0.326025i
$85$		−	7131.35i		−	0.987038i
$86$	6600.00			0.892374
$87$		−	3812.15i		−	0.503653i
$88$	1320.00	+	120.499i	0.170455	+	0.0155603i
$89$	−4673.00			−0.589951			−0.294975	−	0.955505i	$-0.595311\pi$
$89$	−4673.00			−0.589951			−0.294975	+	0.955505i	$0.595311\pi$
$90$		−	12225.2i		−	1.50928i
$91$	10200.0			1.23174
$92$	−3878.00			−0.458176
$93$	4089.00			0.472771
$94$			9322.24i			1.05503i
$95$			3056.29i			0.338647i
$96$			4140.78i			0.449304i
$97$	4247.00			0.451376			0.225688	−	0.974200i	$-0.427537\pi$
$97$	4247.00			0.451376			0.225688	+	0.974200i	$0.427537\pi$
$98$		−	3280.86i		−	0.341614i
$99$	−792.000	+	8675.93i	−0.0808081	+	0.885208i
$100$	−4704.00			−0.470400
$101$		−	12104.7i		−	1.18662i	−0.804976	−	0.593308i	$-0.797822\pi$
$101$		−	12104.7i		−	1.18662i	0.804976	−	0.593308i	$-0.202178\pi$
$102$	−3780.00			−0.363322
$103$	−11218.0			−1.05740			−0.528702	−	0.848807i	$-0.677321\pi$
$103$	−11218.0			−1.05740			−0.528702	+	0.848807i	$0.677321\pi$
$104$	−2040.00			−0.188609
$105$			5093.82i			0.462024i
$106$			24768.0i			2.20434i
$107$			4436.55i			0.387506i	0.981050	+	0.193753i	$0.0620660\pi$
$107$			4436.55i			0.387506i	−0.981050	+	0.193753i	$0.937934\pi$
$108$	−6426.00			−0.550926
$109$		−	16628.9i		−	1.39962i	−0.714330	−	0.699809i	$-0.753269\pi$
$109$		−	16628.9i		−	1.39962i	0.714330	−	0.699809i	$-0.246731\pi$
$110$	20460.0	+	1867.73i	1.69091	+	0.154358i
$111$	−501.000			−0.0406623
$112$			15555.3i			1.24006i
$113$	3847.00			0.301277			0.150638	−	0.988589i	$-0.451867\pi$
$113$	3847.00			0.301277			0.150638	+	0.988589i	$0.451867\pi$
$114$	1620.00			0.124654
$115$	8587.00			0.649301
$116$		−	17790.0i		−	1.32209i
$117$		−	13408.2i		−	0.979491i
$118$		−	12942.7i		−	0.929523i
$119$	−12600.0			−0.889768
$120$		−	1018.76i		−	0.0707475i
$121$	−14399.0	−	2650.98i	−0.983471	−	0.181065i
$122$	21720.0			1.45929
$123$		−	3187.75i		−	0.210704i
$124$	19082.0			1.24102
$125$	−8959.00			−0.573376
$126$	−21600.0			−1.36054
$127$			13506.8i			0.837426i	0.908119	+	0.418713i	$0.137519\pi$
$127$			13506.8i			0.837426i	−0.908119	+	0.418713i	$0.862481\pi$
$128$		−	5564.86i		−	0.339652i
$129$			3614.97i			0.217233i
$130$	−31620.0			−1.87101
$131$			21569.3i			1.25688i	0.777858	+	0.628440i	$0.216306\pi$
$131$			21569.3i			1.25688i	−0.777858	+	0.628440i	$0.783694\pi$
$132$	462.000	−	5060.96i	0.0265152	−	0.290459i
$133$	5400.00			0.305274
$134$		−	15352.7i		−	0.855016i
$135$	14229.0			0.780741
$136$	2520.00			0.136246
$137$	11647.0			0.620545			0.310272	−	0.950648i	$-0.399580\pi$
$137$	11647.0			0.620545			0.310272	+	0.950648i	$0.399580\pi$
$138$		−	4551.57i		−	0.239003i
$139$		−	17165.6i		−	0.888444i	−0.895917	−	0.444222i	$-0.853480\pi$
$139$		−	17165.6i		−	0.888444i	0.895917	−	0.444222i	$-0.146520\pi$
$140$			23771.2i			1.21281i
$141$	−5106.00			−0.256828
$142$			18606.1i			0.922740i
$143$	22440.0	+	2048.48i	1.09736	+	0.100175i
$144$	20448.0			0.986111
$145$			39392.2i			1.87359i
$146$	−18180.0			−0.852880
$147$	1797.00			0.0831598
$148$	−2338.00			−0.106738
$149$			6517.90i			0.293586i	0.989167	+	0.146793i	$0.0468951\pi$
$149$			6517.90i			0.293586i	−0.989167	+	0.146793i	$0.953105\pi$
$150$		−	5521.04i		−	0.245380i
$151$		−	34725.6i		−	1.52299i	−0.648173	−	0.761493i	$-0.724467\pi$
$151$		−	34725.6i		−	1.52299i	0.648173	−	0.761493i	$-0.275533\pi$
$152$	−1080.00			−0.0467452
$153$			16563.1i			0.707554i
$154$	3300.00	−	36149.7i	0.139147	−	1.52427i
$155$	−42253.0			−1.75871
$156$			7821.48i			0.321395i
$157$	23207.0			0.941499			0.470749	−	0.882267i	$-0.343984\pi$
$157$	23207.0			0.941499			0.470749	+	0.882267i	$0.343984\pi$
$158$	−33360.0			−1.33632
$159$	−13566.0			−0.536609
$160$		−	42788.1i		−	1.67141i
$161$		−	15171.9i		−	0.585314i
$162$			24401.0i			0.929776i
$163$	25862.0			0.973390			0.486695	−	0.873572i	$-0.338202\pi$
$163$	25862.0			0.973390			0.486695	+	0.873572i	$0.338202\pi$
$164$		−	14876.1i		−	0.553099i
$165$	−1023.00	+	11206.4i	−0.0375758	+	0.411622i
$166$	4560.00			0.165481
$167$		−	777.766i		−	0.0278879i	−0.999903	−	0.0139440i	$-0.995561\pi$
$167$		−	777.766i		−	0.0278879i	0.999903	−	0.0139440i	$-0.00443864\pi$
$168$	−1800.00			−0.0637755
$169$	−6119.00			−0.214243
$170$	39060.0			1.35156
$171$		−	7098.48i		−	0.242758i
$172$			16869.9i			0.570236i
$173$			2388.07i			0.0797912i	0.999204	+	0.0398956i	$0.0127025\pi$
$173$			2388.07i			0.0797912i	−0.999204	+	0.0398956i	$0.987297\pi$
$174$	20880.0			0.689655
$175$		−	18403.5i		−	0.600930i
$176$	−3124.00	+	34221.7i	−0.100852	+	1.10478i
$177$	7089.00			0.226276
$178$		−	25595.1i		−	0.807823i
$179$	−26843.0			−0.837770			−0.418885	−	0.908039i	$-0.637579\pi$
$179$	−26843.0			−0.837770			−0.418885	+	0.908039i	$0.637579\pi$
$180$	31248.0			0.964444
$181$	−37633.0			−1.14871			−0.574357	−	0.818605i	$-0.694748\pi$
$181$	−37633.0			−1.14871			−0.574357	+	0.818605i	$0.694748\pi$
$182$			55867.7i			1.68662i
$183$			11896.5i			0.355237i
$184$			3034.38i			0.0896262i
$185$	5177.00			0.151264
$186$			22396.4i			0.647369i
$187$	−27720.0	−	2530.48i	−0.792702	−	0.0723635i
$188$	−23828.0			−0.674174
$189$		−	25140.5i		−	0.703801i
$190$	−16740.0			−0.463712
$191$	34597.0			0.948357			0.474178	−	0.880429i	$-0.342745\pi$
$191$	34597.0			0.948357			0.474178	+	0.880429i	$0.342745\pi$
$192$	−9048.00			−0.245443
$193$			28810.2i			0.773449i	0.922195	+	0.386725i	$0.126394\pi$
$193$			28810.2i			0.773449i	−0.922195	+	0.386725i	$0.873606\pi$
$194$			23261.8i			0.618073i
$195$		−	17319.0i		−	0.455463i
$196$	8386.00			0.218294
$197$		−	53501.5i		−	1.37859i	−0.724483	−	0.689293i	$-0.757921\pi$
$197$		−	53501.5i		−	1.37859i	0.724483	−	0.689293i	$-0.242079\pi$
$198$	−47520.0	−	4337.96i	−1.21212	−	0.110651i
$199$	8582.00			0.216712			0.108356	−	0.994112i	$-0.465441\pi$
$199$	8582.00			0.216712			0.108356	+	0.994112i	$0.465441\pi$
$200$			3680.70i			0.0920174i
$201$	8409.00			0.208138
$202$	66300.0			1.62484
$203$	69600.0			1.68895
$204$		−	9661.83i		−	0.232166i
$205$			32940.0i			0.783820i
$206$		−	61443.5i		−	1.44791i
$207$	−19944.0			−0.465448
$208$		−	52888.1i		−	1.22245i
$209$	11880.0	+	1084.49i	0.271972	+	0.0248275i
$210$	−27900.0			−0.632653
$211$		−	22588.1i		−	0.507358i	−0.967288	−	0.253679i	$-0.918359\pi$
$211$		−	22588.1i		−	0.507358i	0.967288	−	0.253679i	$-0.0816407\pi$
$212$	−63308.0			−1.40860
$213$	−10191.0			−0.224625
$214$	−24300.0			−0.530614
$215$		−	37354.7i		−	0.808106i
$216$			5028.09i			0.107769i
$217$			74654.6i			1.58539i
$218$	91080.0			1.91651
$219$		−	9957.60i		−	0.207619i
$220$	−4774.00	+	52296.5i	−0.0986364	+	1.08051i
$221$	42840.0			0.877132
$222$		−	2744.09i		−	0.0556791i
$223$	−86683.0			−1.74311			−0.871554	−	0.490300i	$-0.836887\pi$
$223$	−86683.0			−1.74311			−0.871554	+	0.490300i	$0.836887\pi$
$224$	−75600.0			−1.50670
$225$	−24192.0			−0.477867
$226$			21070.9i			0.412540i
$227$			8139.16i			0.157953i	0.996876	+	0.0789765i	$0.0251652\pi$
$227$			8139.16i			0.157953i	−0.996876	+	0.0789765i	$0.974835\pi$
$228$			4140.78i			0.0796549i
$229$	14807.0			0.282355			0.141178	−	0.989984i	$-0.454911\pi$
$229$	14807.0			0.282355			0.141178	+	0.989984i	$0.454911\pi$
$230$			47032.9i			0.889091i
$231$	19800.0	+	1807.48i	0.371058	+	0.0338728i
$232$	−13920.0			−0.258621
$233$			9464.65i			0.174338i	0.996194	+	0.0871691i	$0.0277820\pi$
$233$			9464.65i			0.174338i	−0.996194	+	0.0871691i	$0.972218\pi$
$234$	73440.0			1.34122
$235$	52762.0			0.955401
$236$	33082.0			0.593974
$237$		−	18272.0i		−	0.325304i
$238$		−	69013.0i		−	1.21836i
$239$			36127.8i			0.632478i	0.948680	+	0.316239i	$0.102420\pi$
$239$			36127.8i			0.632478i	−0.948680	+	0.316239i	$0.897580\pi$
$240$	26412.0			0.458542
$241$			101460.i			1.74687i	0.486938	+	0.873436i	$0.338114\pi$
$241$			101460.i			1.74687i	−0.486938	+	0.873436i	$0.661886\pi$
$242$	14520.0	−	78866.6i	0.247934	−	1.34667i
$243$	−50544.0			−0.855967
$244$			55517.2i			0.932497i
$245$	−18569.0			−0.309354
$246$	17460.0			0.288519
$247$	−18360.0			−0.300939
$248$		−	14930.9i		−	0.242763i
$249$			2497.61i			0.0402835i
$250$		−	49070.5i		−	0.785127i
$251$	−6203.00			−0.0984588			−0.0492294	−	0.998787i	$-0.515677\pi$
$251$	−6203.00			−0.0984588			−0.0492294	+	0.998787i	$0.515677\pi$
$252$		−	55210.4i		−	0.869401i
$253$	3047.00	−	33378.2i	0.0476027	−	0.521461i
$254$	−73980.0			−1.14669
$255$			21394.0i			0.329013i
$256$	78736.0			1.20142
$257$	−89318.0			−1.35230			−0.676150	−	0.736764i	$-0.736353\pi$
$257$	−89318.0			−1.35230			−0.676150	+	0.736764i	$0.736353\pi$
$258$	−19800.0			−0.297458
$259$		−	9146.97i		−	0.136357i
$260$		−	80821.9i		−	1.19559i
$261$		−	91491.6i		−	1.34307i
$262$	−118140.			−1.72105
$263$			62298.0i			0.900663i	0.892861	+	0.450332i	$0.148694\pi$
$263$			62298.0i			0.900663i	−0.892861	+	0.450332i	$0.851306\pi$
$264$	−3960.00	−	361.497i	−0.0568182	−	0.00518677i
$265$	140182.			1.99618
$266$			29577.0i			0.418014i
$267$	14019.0			0.196650
$268$	39242.0			0.546363
$269$	−38678.0			−0.534514			−0.267257	−	0.963625i	$-0.586117\pi$
$269$	−38678.0			−0.534514			−0.267257	+	0.963625i	$0.586117\pi$
$270$			77935.4i			1.06907i
$271$		−	16201.6i		−	0.220607i	−0.993898	−	0.110304i	$-0.964818\pi$
$271$		−	16201.6i		−	0.220607i	0.993898	−	0.110304i	$-0.0351824\pi$
$272$			65332.3i			0.883060i
$273$	−30600.0			−0.410578
$274$			63793.2i			0.849716i
$275$	3696.00	−	40487.7i	0.0488727	−	0.535374i
$276$	11634.0			0.152725
$277$		−	68377.7i		−	0.891158i	−0.895243	−	0.445579i	$-0.852998\pi$
$277$		−	68377.7i		−	0.891158i	0.895243	−	0.445579i	$-0.147002\pi$
$278$	94020.0			1.21655
$279$	98136.0			1.26072
$280$	18600.0			0.237245
$281$		−	123741.i		−	1.56712i	−0.621315	−	0.783561i	$-0.713401\pi$
$281$		−	123741.i		−	1.56712i	0.621315	−	0.783561i	$-0.286599\pi$
$282$		−	27966.7i		−	0.351676i
$283$			126020.i			1.57350i	0.617272	+	0.786750i	$0.288238\pi$
$283$			126020.i			1.57350i	−0.617272	+	0.786750i	$0.711762\pi$
$284$	−47558.0			−0.589640
$285$		−	9168.88i		−	0.112882i
$286$	−11220.0	+	122909.i	−0.137171	+	1.50263i
$287$	58200.0			0.706577
$288$			99378.8i			1.19814i
$289$	30601.0			0.366387
$290$	−215760.			−2.56552
$291$	−12741.0			−0.150459
$292$		−	46468.8i		−	0.544999i
$293$			90319.4i			1.05207i	0.850462	+	0.526037i	$0.176323\pi$
$293$			90319.4i			1.05207i	−0.850462	+	0.526037i	$0.823677\pi$
$294$			9842.57i			0.113871i
$295$	−73253.0			−0.841747
$296$			1829.39i			0.0208797i
$297$	5049.00	−	55309.0i	0.0572391	−	0.627022i
$298$	−35700.0			−0.402009
$299$			51584.5i			0.577001i
$300$	14112.0			0.156800
$301$	−66000.0			−0.728469
$302$	190200.			2.08543
$303$			36314.0i			0.395539i
$304$		−	27999.6i		−	0.302973i
$305$		−	122931.i		−	1.32148i
$306$	−90720.0			−0.968858
$307$		−	153636.i		−	1.63011i	−0.579384	−	0.815055i	$-0.696707\pi$
$307$		−	153636.i		−	1.63011i	0.579384	−	0.815055i	$-0.303293\pi$
$308$	92400.0	+	8434.93i	0.974026	+	0.0889160i
$309$	33654.0			0.352468
$310$		−	231429.i		−	2.40821i
$311$	−90698.0			−0.937728			−0.468864	−	0.883270i	$-0.655337\pi$
$311$	−90698.0			−0.937728			−0.468864	+	0.883270i	$0.655337\pi$
$312$	6120.00			0.0628698
$313$	−104953.			−1.07129			−0.535644	−	0.844444i	$-0.679931\pi$
$313$	−104953.			−1.07129			−0.535644	+	0.844444i	$0.679931\pi$
$314$			127110.i			1.28920i
$315$			122252.i			1.23207i
$316$		−	85269.4i		−	0.853924i
$317$	77287.0			0.769109			0.384555	−	0.923102i	$-0.374355\pi$
$317$	77287.0			0.769109			0.384555	+	0.923102i	$0.374355\pi$
$318$		−	74304.0i		−	0.734781i
$319$	153120.	+	13977.9i	1.50470	+	0.137360i
$320$	93496.0			0.913047
$321$		−	13309.7i		−	0.129169i
$322$	83100.0			0.801474
$323$	22680.0			0.217389
$324$	−62370.0			−0.594136
$325$			62571.8i			0.592396i
$326$			141652.i			1.33287i
$327$			49886.6i			0.466539i
$328$	−11640.0			−0.108195
$329$		−	93222.4i		−	0.861248i
$330$	−61380.0	−	5603.20i	−0.563636	−	0.0514527i
$331$	−174403.			−1.59183			−0.795917	−	0.605405i	$-0.793011\pi$
$331$	−174403.			−1.59183			−0.795917	+	0.605405i	$0.793011\pi$
$332$			11655.5i			0.105744i
$333$	−12024.0			−0.108433
$334$	4260.00			0.0381871
$335$	−86893.0			−0.774275
$336$		−	46666.0i		−	0.413354i
$337$		−	115493.i		−	1.01694i	−0.861080	−	0.508470i	$-0.830211\pi$
$337$		−	115493.i		−	1.01694i	0.861080	−	0.508470i	$-0.169789\pi$
$338$		−	33515.1i		−	0.293365i
$339$	−11541.0			−0.100426
$340$			99838.9i			0.863658i
$341$	−14993.0	+	164240.i	−0.128938	+	1.41244i
$342$	38880.0			0.332410
$343$		−	98699.6i		−	0.838933i
$344$	13200.0			0.111547
$345$	−25761.0			−0.216434
$346$	−13080.0			−0.109259
$347$			137380.i			1.14094i	0.821317	+	0.570471i	$0.193239\pi$
$347$			137380.i			1.14094i	−0.821317	+	0.570471i	$0.806761\pi$
$348$			53370.1i			0.440696i
$349$			180365.i			1.48082i	0.672157	+	0.740409i	$0.265368\pi$
$349$			180365.i			1.48082i	−0.672157	+	0.740409i	$0.734632\pi$
$350$	100800.			0.822857
$351$			85477.6i			0.693806i
$352$	−166320.	−	15182.9i	−1.34233	−	0.122537i
$353$	107527.			0.862915			0.431458	−	0.902133i	$-0.357999\pi$
$353$	107527.			0.862915			0.431458	+	0.902133i	$0.357999\pi$
$354$			38828.1i			0.309841i
$355$	105307.			0.835604
$356$	65422.0			0.516207
$357$	37800.0			0.296589
$358$		−	147025.i		−	1.14716i
$359$		−	62473.2i		−	0.484736i	−0.970184	−	0.242368i	$-0.922076\pi$
$359$		−	62473.2i		−	0.484736i	0.970184	−	0.242368i	$-0.0779241\pi$
$360$		−	24450.3i		−	0.188660i
$361$	120601.			0.925415
$362$		−	206124.i		−	1.57294i
$363$	43197.0	+	7952.93i	0.327824	+	0.0603551i
$364$	−142800.			−1.07777
$365$			102895.i			0.772341i
$366$	−65160.0			−0.486428
$367$	142397.			1.05723			0.528614	−	0.848862i	$-0.322712\pi$
$367$	142397.			1.05723			0.528614	+	0.848862i	$0.322712\pi$
$368$	−78668.0			−0.580901
$369$		−	76505.9i		−	0.561878i
$370$			28355.6i			0.207126i
$371$		−	247680.i		−	1.79946i
$372$	−57246.0			−0.413675
$373$			59406.0i			0.426985i	0.976945	+	0.213492i	$0.0684839\pi$
$373$			59406.0i			0.426985i	−0.976945	+	0.213492i	$0.931516\pi$
$374$	13860.0	−	151829.i	0.0990878	−	1.08545i
$375$	26877.0			0.191125
$376$			18644.5i			0.131879i
$377$	−236640.			−1.66497
$378$	137700.			0.963719
$379$	123077.			0.856838			0.428419	−	0.903580i	$-0.359071\pi$
$379$	123077.			0.856838			0.428419	+	0.903580i	$0.359071\pi$
$380$		−	42788.1i		−	0.296316i
$381$		−	40520.5i		−	0.279142i
$382$			189496.i			1.29859i
$383$	−155363.			−1.05913			−0.529566	−	0.848269i	$-0.677645\pi$
$383$	−155363.			−1.05913			−0.529566	+	0.848269i	$0.677645\pi$
$384$			16694.6i			0.113217i
$385$	−204600.	−	18677.3i	−1.38033	−	0.126007i
$386$	−157800.			−1.05909
$387$			86759.3i			0.579287i
$388$	−59458.0			−0.394954
$389$	−41633.0			−0.275130			−0.137565	−	0.990493i	$-0.543928\pi$
$389$	−41633.0			−0.275130			−0.137565	+	0.990493i	$0.543928\pi$
$390$	94860.0			0.623669
$391$		−	63722.0i		−	0.416808i
$392$		−	6561.72i		−	0.0427017i
$393$		−	64707.9i		−	0.418960i
$394$	293040.			1.88771
$395$			188811.i			1.21013i
$396$	11088.0	−	121463.i	0.0707071	−	0.774557i
$397$	77882.0			0.494147			0.247073	−	0.968997i	$-0.420531\pi$
$397$	77882.0			0.494147			0.247073	+	0.968997i	$0.420531\pi$
$398$			47005.5i			0.296745i
$399$	−16200.0			−0.101758
$400$	−95424.0			−0.596400
$401$	198922.			1.23707			0.618535	−	0.785757i	$-0.287727\pi$
$401$	198922.			1.23707			0.618535	+	0.785757i	$0.287727\pi$
$402$			46058.0i			0.285005i
$403$		−	253826.i		−	1.56288i
$404$			169465.i			1.03829i
$405$	138105.			0.841975
$406$			381215.i			2.31269i
$407$	1837.00	−	20123.3i	0.0110897	−	0.121482i
$408$	−7560.00			−0.0454152
$409$			30913.5i			0.184800i	0.995722	+	0.0923998i	$0.0294538\pi$
$409$			30913.5i			0.184800i	−0.995722	+	0.0923998i	$0.970546\pi$
$410$	−180420.			−1.07329
$411$	−34941.0			−0.206848
$412$	157052.			0.925229
$413$			129427.i			0.758795i
$414$		−	109238.i		−	0.637342i
$415$		−	25808.7i		−	0.149854i
$416$	257040.			1.48530
$417$			51496.9i			0.296148i
$418$	−5940.00	+	65069.4i	−0.0339965	+	0.372413i
$419$	−232538.			−1.32454			−0.662271	−	0.749264i	$-0.730407\pi$
$419$	−232538.			−1.32454			−0.662271	+	0.749264i	$0.730407\pi$
$420$		−	71313.5i		−	0.404271i
$421$	−46918.0			−0.264713			−0.132357	−	0.991202i	$-0.542254\pi$
$421$	−46918.0			−0.264713			−0.132357	+	0.991202i	$0.542254\pi$
$422$	123720.			0.694728
$423$	−122544.			−0.684875
$424$			49536.0i			0.275543i
$425$		−	77294.6i		−	0.427929i
$426$		−	55818.4i		−	0.307580i
$427$	−217200.			−1.19125
$428$		−	62111.7i		−	0.339067i
$429$	−67320.0	−	6145.45i	−0.365788	−	0.0333917i
$430$	204600.			1.10654
$431$		−	57412.3i		−	0.309065i	−0.987988	−	0.154533i	$-0.950613\pi$
$431$		−	57412.3i		−	0.309065i	0.987988	−	0.154533i	$-0.0493872\pi$
$432$	−130356.			−0.698495
$433$	33167.0			0.176901			0.0884505	−	0.996081i	$-0.471808\pi$
$433$	33167.0			0.176901			0.0884505	+	0.996081i	$0.471808\pi$
$434$	−408900.			−2.17089
$435$		−	118177.i		−	0.624530i
$436$			232804.i			1.22467i
$437$			27309.4i			0.143005i
$438$	54540.0			0.284293
$439$		−	353303.i		−	1.83324i	−0.399765	−	0.916618i	$-0.630908\pi$
$439$		−	353303.i		−	1.83324i	0.399765	−	0.916618i	$-0.369092\pi$
$440$	40920.0	+	3735.47i	0.211364	+	0.0192948i
$441$	43128.0			0.221759
$442$			234644.i			1.20106i
$443$	279397.			1.42369			0.711843	−	0.702339i	$-0.247861\pi$
$443$	279397.			1.42369			0.711843	+	0.702339i	$0.247861\pi$
$444$	7014.00			0.0355795
$445$	−144863.			−0.731539
$446$		−	474782.i		−	2.38685i
$447$		−	19553.7i		−	0.0978619i
$448$		−	165193.i		−	0.823068i
$449$	144607.			0.717293			0.358647	−	0.933473i	$-0.383238\pi$
$449$	144607.			0.717293			0.358647	+	0.933473i	$0.383238\pi$
$450$		−	132505.i		−	0.654346i
$451$	128040.	+	11688.4i	0.629495	+	0.0574648i
$452$	−53858.0			−0.263617
$453$			104177.i			0.507662i
$454$	−44580.0			−0.216286
$455$	316200.			1.52735
$456$	3240.00			0.0155817
$457$			384282.i			1.84000i	0.391918	+	0.920000i	$0.371812\pi$
$457$			384282.i			1.84000i	−0.391918	+	0.920000i	$0.628188\pi$
$458$			81101.3i			0.386631i
$459$		−	105590.i		−	0.501184i
$460$	−120218.			−0.568138
$461$			6988.94i			0.0328859i	0.999865	+	0.0164429i	$0.00523419\pi$
$461$			6988.94i			0.0328859i	−0.999865	+	0.0164429i	$0.994766\pi$
$462$	−9900.00	+	108449.i	−0.0463822	+	0.508091i
$463$	−227203.			−1.05987			−0.529934	−	0.848039i	$-0.677783\pi$
$463$	−227203.			−1.05987			−0.529934	+	0.848039i	$0.677783\pi$
$464$		−	360883.i		−	1.67622i
$465$	126759.			0.586237
$466$	−51840.0			−0.238722
$467$	328117.			1.50451			0.752255	−	0.658872i	$-0.228966\pi$
$467$	328117.			1.50451			0.752255	+	0.658872i	$0.228966\pi$
$468$			187715.i			0.857054i
$469$			153527.i			0.697972i
$470$			288989.i			1.30824i
$471$	−69621.0			−0.313833
$472$		−	25885.4i		−	0.116190i
$473$	−145200.	−	13254.9i	−0.648999	−	0.0592453i
$474$	100080.			0.445441
$475$			33126.3i			0.146820i
$476$	176400.			0.778547
$477$	−325584.			−1.43096
$478$	−197880.			−0.866056
$479$			132560.i			0.577751i	0.957367	+	0.288876i	$0.0932814\pi$
$479$			132560.i			0.577751i	−0.957367	+	0.288876i	$0.906719\pi$
$480$			128364.i			0.557137i
$481$			31099.7i			0.134421i
$482$	−555720.			−2.39200
$483$			45515.7i			0.195105i
$484$	201586.	+	37113.7i	0.860537	+	0.158432i
$485$	131657.			0.559707
$486$		−	276841.i		−	1.17208i
$487$	−106483.			−0.448975			−0.224488	−	0.974477i	$-0.572071\pi$
$487$	−106483.			−0.448975			−0.224488	+	0.974477i	$0.572071\pi$
$488$	43440.0			0.182411
$489$	−77586.0			−0.324463
$490$		−	101707.i		−	0.423601i
$491$			234557.i			0.972937i	0.873698	+	0.486469i	$0.161715\pi$
$491$			234557.i			0.972937i	−0.873698	+	0.486469i	$0.838285\pi$
$492$			44628.4i			0.184366i
$493$	292320.			1.20272
$494$		−	100562.i		−	0.412078i
$495$	−24552.0	+	268954.i	−0.100202	+	1.09766i
$496$	387092.			1.57344
$497$		−	186061.i		−	0.753257i
$498$	−13680.0			−0.0551604
$499$	−292378.			−1.17420			−0.587102	−	0.809513i	$-0.699731\pi$
$499$	−292378.			−1.17420			−0.587102	+	0.809513i	$0.699731\pi$
$500$	125426.			0.501704
$501$			2333.30i			0.00929597i
$502$		−	33975.2i		−	0.134820i
$503$		−	25567.7i		−	0.101054i	−0.998723	−	0.0505272i	$-0.983910\pi$
$503$		−	25567.7i		−	0.101054i	0.998723	−	0.0505272i	$-0.0160902\pi$
$504$	−43200.0			−0.170068
$505$		−	375245.i		−	1.47140i
$506$	182820.	+	16689.1i	0.714040	+	0.0651827i
$507$	18357.0			0.0714144
$508$		−	189096.i		−	0.732747i
$509$	307447.			1.18668			0.593341	−	0.804951i	$-0.297808\pi$
$509$	307447.			1.18668			0.593341	+	0.804951i	$0.297808\pi$
$510$	−117180.			−0.450519
$511$	181800.			0.696229
$512$			342217.i			1.30545i
$513$			45252.8i			0.171954i
$514$		−	489215.i		−	1.85171i
$515$	−347758.			−1.31118
$516$		−	50609.6i		−	0.190079i
$517$	18722.0	−	205089.i	0.0700440	−	0.767294i
$518$	50100.0			0.186715
$519$		−	7164.21i		−	0.0265971i
$520$	−63240.0			−0.233876
$521$	−375593.			−1.38370			−0.691850	−	0.722041i	$-0.743204\pi$
$521$	−375593.			−1.38370			−0.691850	+	0.722041i	$0.743204\pi$
$522$	501120.			1.83908
$523$		−	272076.i		−	0.994687i	−0.867554	−	0.497343i	$-0.834309\pi$
$523$		−	272076.i		−	0.994687i	0.867554	−	0.497343i	$-0.165691\pi$
$524$		−	301970.i		−	1.09977i
$525$			55210.4i			0.200310i
$526$	−341220.			−1.23328
$527$			313549.i			1.12898i
$528$	9372.00	−	102665.i	0.0336174	−	0.368260i
$529$	−203112.			−0.725812
$530$			767808.i			2.73339i
$531$	170136.			0.603403
$532$	−75600.0			−0.267115
$533$	−197880.			−0.696542
$534$			76785.2i			0.269274i
$535$			137533.i			0.480507i
$536$		−	30705.3i		−	0.106877i
$537$	80529.0			0.279257
$538$		−	211848.i		−	0.731914i
$539$	−6589.00	+	72178.9i	−0.0226799	+	0.248446i
$540$	−199206.			−0.683148
$541$			150810.i			0.515271i	0.966242	+	0.257635i	$0.0829433\pi$
$541$			150810.i			0.515271i	−0.966242	+	0.257635i	$0.917057\pi$
$542$	88740.0			0.302079
$543$	112899.			0.382904
$544$	−317520.			−1.07293
$545$		−	515495.i		−	1.73553i
$546$		−	167603.i		−	0.562208i
$547$			215430.i			0.719999i	0.932952	+	0.360000i	$0.117223\pi$
$547$			215430.i			0.719999i	−0.932952	+	0.360000i	$0.882777\pi$
$548$	−163058.			−0.542976
$549$			285517.i			0.947299i
$550$	221760.	+	20243.8i	0.733091	+	0.0669217i
$551$	−125280.			−0.412647
$552$		−	9103.15i		−	0.0298754i
$553$	333600.			1.09088
$554$	374520.			1.22027
$555$	−15531.0			−0.0504212
$556$			240319.i			0.777388i
$557$		−	298892.i		−	0.963395i	−0.876338	−	0.481697i	$-0.840020\pi$
$557$		−	298892.i		−	0.963395i	0.876338	−	0.481697i	$-0.159980\pi$
$558$			537513.i			1.72632i
$559$	224400.			0.718124
$560$			482215.i			1.53768i
$561$	83160.0	+	7591.43i	0.264234	+	0.0241212i
$562$	677760.			2.14587
$563$		−	257079.i		−	0.811054i	−0.914083	−	0.405527i	$-0.867088\pi$
$563$		−	257079.i		−	0.811054i	0.914083	−	0.405527i	$-0.132912\pi$
$564$	71484.0			0.224725
$565$	119257.			0.373583
$566$	−690240.			−2.15460
$567$		−	244010.i		−	0.759001i
$568$			37212.3i			0.115343i
$569$			133250.i			0.411569i	0.978597	+	0.205784i	$0.0659746\pi$
$569$			133250.i			0.411569i	−0.978597	+	0.205784i	$0.934025\pi$
$570$	50220.0			0.154571
$571$			171832.i			0.527024i	0.964656	+	0.263512i	$0.0848809\pi$
$571$			171832.i			0.527024i	−0.964656	+	0.263512i	$0.915119\pi$
$572$	−314160.	−	28678.8i	−0.960194	−	0.0876533i
$573$	−103791.			−0.316119
$574$			318775.i			0.967520i
$575$	93072.0			0.281503
$576$	−217152.			−0.654514
$577$	41567.0			0.124852			0.0624262	−	0.998050i	$-0.480116\pi$
$577$	41567.0			0.124852			0.0624262	+	0.998050i	$0.480116\pi$
$578$			167609.i			0.501696i
$579$		−	86430.6i		−	0.257816i
$580$		−	551491.i		−	1.63939i
$581$	−45600.0			−0.135087
$582$		−	69785.3i		−	0.206024i
$583$	49742.0	−	544896.i	0.146348	−	1.60316i
$584$	−36360.0			−0.106610
$585$		−	415656.i		−	1.21457i
$586$	−494700.			−1.44061
$587$	236062.			0.685094			0.342547	−	0.939501i	$-0.388710\pi$
$587$	236062.			0.685094			0.342547	+	0.939501i	$0.388710\pi$
$588$	−25158.0			−0.0727648
$589$		−	134378.i		−	0.387345i
$590$		−	401223.i		−	1.15261i
$591$			160505.i			0.459529i
$592$	−47428.0			−0.135329
$593$			39764.7i			0.113081i	0.998400	+	0.0565403i	$0.0180069\pi$
$593$			39764.7i			0.113081i	−0.998400	+	0.0565403i	$0.981993\pi$
$594$	302940.	+	27654.5i	0.858586	+	0.0783778i
$595$	−390600.			−1.10331
$596$		−	91250.6i		−	0.256888i
$597$	−25746.0			−0.0722372
$598$	−282540.			−0.790092
$599$	−2378.00			−0.00662763			−0.00331381	−	0.999995i	$-0.501055\pi$
$599$	−2378.00			−0.00662763			−0.00331381	+	0.999995i	$0.501055\pi$
$600$		−	11042.1i		−	0.0306725i
$601$			184309.i			0.510266i	0.966906	+	0.255133i	$0.0821193\pi$
$601$			184309.i			0.510266i	−0.966906	+	0.255133i	$0.917881\pi$
$602$		−	361497.i		−	0.997497i
$603$	201816.			0.555036
$604$			486159.i			1.33261i
$605$	−446369.	−	82180.3i	−1.21950	−	0.224521i
$606$	−198900.			−0.541614
$607$			640397.i			1.73809i	0.494734	+	0.869045i	$0.335266\pi$
$607$			640397.i			1.73809i	−0.494734	+	0.869045i	$0.664734\pi$
$608$	136080.			0.368118
$609$	−208800.			−0.562984
$610$	673320.			1.80951
$611$			316956.i			0.849018i
$612$		−	231884.i		−	0.619110i
$613$		−	144139.i		−	0.383583i	−0.981436	−	0.191792i	$-0.938570\pi$
$613$		−	144139.i		−	0.383583i	0.981436	−	0.191792i	$-0.0614298\pi$
$614$	841500.			2.23212
$615$		−	98820.1i		−	0.261273i
$616$	6600.00	−	72299.4i	0.0173933	−	0.190534i
$617$	707962.			1.85969			0.929843	−	0.367957i	$-0.119942\pi$
$617$	707962.			1.85969			0.929843	+	0.367957i	$0.119942\pi$
$618$			184331.i			0.482637i
$619$	−487963.			−1.27352			−0.636760	−	0.771062i	$-0.719726\pi$
$619$	−487963.			−1.27352			−0.636760	+	0.771062i	$0.719726\pi$
$620$	591542.			1.53887
$621$	127143.			0.329693
$622$		−	496773.i		−	1.28404i
$623$			255951.i			0.659448i
$624$			158664.i			0.407483i
$625$	−487729.			−1.24859
$626$		−	574851.i		−	1.46692i
$627$	−35640.0	−	3253.47i	−0.0906573	−	0.00827584i
$628$	−324898.			−0.823811
$629$		−	38417.3i		−	0.0971013i
$630$	−669600.			−1.68707
$631$	274397.			0.689161			0.344580	−	0.938757i	$-0.388021\pi$
$631$	274397.			0.689161			0.344580	+	0.938757i	$0.388021\pi$
$632$	−66720.0			−0.167041
$633$			67764.2i			0.169119i
$634$			423318.i			1.05315i
$635$			418712.i			1.03841i
$636$	189924.			0.469532
$637$		−	111549.i		−	0.274908i
$638$	−76560.0	+	838673.i	−0.188088	+	2.06040i
$639$	−244584.			−0.598999
$640$		−	172511.i		−	0.421169i
$641$	−99113.0			−0.241221			−0.120610	−	0.992700i	$-0.538485\pi$
$641$	−99113.0			−0.241221			−0.120610	+	0.992700i	$0.538485\pi$
$642$	72900.0			0.176871
$643$	526997.			1.27464			0.637318	−	0.770601i	$-0.280044\pi$
$643$	526997.			1.27464			0.637318	+	0.770601i	$0.280044\pi$
$644$			212407.i			0.512149i
$645$			112064.i			0.269369i
$646$			124223.i			0.297672i
$647$	−140843.			−0.336455			−0.168227	−	0.985748i	$-0.553804\pi$
$647$	−140843.			−0.336455			−0.168227	+	0.985748i	$0.553804\pi$
$648$			48802.1i			0.116222i
$649$	−25993.0	+	284739.i	−0.0617116	+	0.676017i
$650$	−342720.			−0.811172
$651$		−	223964.i		−	0.528464i
$652$	−362068.			−0.851716
$653$	−240953.			−0.565075			−0.282537	−	0.959256i	$-0.591176\pi$
$653$	−240953.			−0.565075			−0.282537	+	0.959256i	$0.591176\pi$
$654$	−273240.			−0.638835
$655$			668649.i			1.55853i
$656$		−	301773.i		−	0.701250i
$657$		−	238982.i		−	0.553650i
$658$	510600.			1.17931
$659$		−	499830.i		−	1.15094i	−0.817824	−	0.575468i	$-0.804820\pi$
$659$		−	499830.i		−	1.15094i	0.817824	−	0.575468i	$-0.195180\pi$
$660$	14322.0	−	156890.i	0.0328788	−	0.360169i
$661$	122927.			0.281348			0.140674	−	0.990056i	$-0.455073\pi$
$661$	122927.			0.281348			0.140674	+	0.990056i	$0.455073\pi$
$662$		−	955245.i		−	2.17971i
$663$	−128520.			−0.292377
$664$	9120.00			0.0206852
$665$	167400.			0.378540
$666$		−	65858.2i		−	0.148478i
$667$			351988.i			0.791183i
$668$			10888.7i			0.0244019i
$669$	260049.			0.581036
$670$		−	475933.i		−	1.06022i
$671$	−477840.	−	43620.6i	−1.06130	−	0.0968828i
$672$	226800.			0.502232
$673$			202745.i			0.447631i	0.974632	+	0.223815i	$0.0718513\pi$
$673$			202745.i			0.447631i	−0.974632	+	0.223815i	$0.928149\pi$
$674$	632580.			1.39250
$675$	154224.			0.338489
$676$	85666.0			0.187463
$677$		−	776966.i		−	1.69522i	−0.530623	−	0.847608i	$-0.678042\pi$
$677$		−	776966.i		−	1.69522i	0.530623	−	0.847608i	$-0.321958\pi$
$678$		−	63212.7i		−	0.137513i
$679$		−	232618.i		−	0.504549i
$680$	78120.0			0.168945
$681$		−	24417.5i		−	0.0526510i
$682$	−899580.	−	82120.0i	−1.93406	−	0.176555i
$683$	68422.0			0.146674			0.0733372	−	0.997307i	$-0.476635\pi$
$683$	68422.0			0.146674			0.0733372	+	0.997307i	$0.476635\pi$
$684$			99378.8i			0.212413i
$685$	361057.			0.769475
$686$	540600.			1.14876
$687$	−44421.0			−0.0941185
$688$			342217.i			0.722977i
$689$			842112.i			1.77391i
$690$		−	141099.i		−	0.296364i
$691$	662597.			1.38769			0.693846	−	0.720123i	$-0.255915\pi$
$691$	662597.			1.38769			0.693846	+	0.720123i	$0.255915\pi$
$692$		−	33433.0i		−	0.0698173i
$693$	475200.	+	43379.6i	0.989487	+	0.0903274i
$694$	−752460.			−1.56230
$695$		−	532134.i		−	1.10167i
$696$	41760.0			0.0862069
$697$	244440.			0.503161
$698$	−987900.			−2.02769
$699$		−	28393.9i		−	0.0581127i
$700$			257649.i			0.525814i
$701$		−	64247.9i		−	0.130744i	−0.997861	−	0.0653721i	$-0.979177\pi$
$701$		−	64247.9i		−	0.130744i	0.997861	−	0.0653721i	$-0.0208234\pi$
$702$	−468180.			−0.950033
$703$			16464.5i			0.0333149i
$704$	33176.0	−	363425.i	0.0669389	−	0.733279i
$705$	−158286.			−0.318467
$706$			588950.i			1.18160i
$707$	−663000.			−1.32640
$708$	−99246.0			−0.197991
$709$	−656713.			−1.30642			−0.653210	−	0.757176i	$-0.726578\pi$
$709$	−656713.			−1.30642			−0.653210	+	0.757176i	$0.726578\pi$
$710$			576790.i			1.14420i
$711$		−	438529.i		−	0.867478i
$712$		−	51190.2i		−	0.100978i
$713$	−377551.			−0.742671
$714$			207039.i			0.406122i
$715$	695640.	+	63503.0i	1.36073	+	0.124217i
$716$	375802.			0.733049
$717$		−	108383.i		−	0.210826i
$718$	342180.			0.663752
$719$	278797.			0.539300			0.269650	−	0.962958i	$-0.413092\pi$
$719$	278797.			0.539300			0.269650	+	0.962958i	$0.413092\pi$
$720$	633888.			1.22278
$721$			614435.i			1.18197i
$722$			660559.i			1.26718i
$723$		−	304380.i		−	0.582291i
$724$	526862.			1.00512
$725$			426961.i			0.812291i
$726$	−43560.0	+	236600.i	−0.0826446	+	0.448891i
$727$	−384283.			−0.727080			−0.363540	−	0.931579i	$-0.618432\pi$
$727$	−384283.			−0.727080			−0.363540	+	0.931579i	$0.618432\pi$
$728$			111735.i			0.210828i
$729$	−209223.			−0.393690
$730$	−563580.			−1.05757
$731$	−277200.			−0.518750
$732$		−	166551.i		−	0.310832i
$733$		−	900303.i		−	1.67564i	−0.545947	−	0.837820i	$-0.683830\pi$
$733$		−	900303.i		−	1.67564i	0.545947	−	0.837820i	$-0.316170\pi$
$734$			779940.i			1.44767i
$735$	55707.0			0.103118
$736$		−	382332.i		−	0.705806i
$737$	−30833.0	+	337759.i	−0.0567650	+	0.621830i
$738$	419040.			0.769383
$739$		−	179237.i		−	0.328200i	−0.986444	−	0.164100i	$-0.947528\pi$
$739$		−	179237.i		−	0.328200i	0.986444	−	0.164100i	$-0.0524719\pi$
$740$	−72478.0			−0.132356
$741$	55080.0			0.100313
$742$	1.35660e6			2.46402
$743$		−	815888.i		−	1.47793i	−0.673746	−	0.738963i	$-0.735316\pi$
$743$		−	815888.i		−	1.47793i	0.673746	−	0.738963i	$-0.264684\pi$
$744$			44792.8i			0.0809211i
$745$			202055.i			0.364046i
$746$	−325380.			−0.584673
$747$			59942.8i			0.107423i
$748$	388080.	+	35426.7i	0.693614	+	0.0633180i
$749$	243000.			0.433154
$750$			147211.i			0.261709i
$751$	463757.			0.822263			0.411131	−	0.911576i	$-0.365134\pi$
$751$	463757.			0.822263			0.411131	+	0.911576i	$0.365134\pi$
$752$	−483368.			−0.854756
$753$	18609.0			0.0328196
$754$		−	1.29613e6i		−	2.27985i
$755$		−	1.07649e6i		−	1.88850i
$756$			351967.i			0.615826i
$757$	−593878.			−1.03635			−0.518174	−	0.855275i	$-0.673388\pi$
$757$	−593878.			−1.03635			−0.518174	+	0.855275i	$0.673388\pi$
$758$			674120.i			1.17327i
$759$	−9141.00	+	100135.i	−0.0158676	+	0.173820i
$760$	−33480.0			−0.0579640
$761$			1.06130e6i			1.83261i	0.400487	+	0.916303i	$0.368841\pi$
$761$			1.06130e6i			1.83261i	−0.400487	+	0.916303i	$0.631159\pi$
$762$	221940.			0.382231
$763$	−910800.			−1.56449
$764$	−484358.			−0.829812
$765$			513457.i			0.877367i
$766$		−	850958.i		−	1.45028i
$767$		−	440051.i		−	0.748019i
$768$	−236208.			−0.400472
$769$			219188.i			0.370649i	0.982677	+	0.185325i	$0.0593337\pi$
$769$			219188.i			0.370649i	−0.982677	+	0.185325i	$0.940666\pi$
$770$	102300.	−	1.12064e6i	0.172542	−	1.89010i
$771$	267954.			0.450766
$772$		−	403343.i		−	0.676768i
$773$	−315758.			−0.528440			−0.264220	−	0.964462i	$-0.585114\pi$
$773$	−315758.			−0.528440			−0.264220	+	0.964462i	$0.585114\pi$
$774$	−475200.			−0.793222
$775$	−457968.			−0.762486
$776$			46523.6i			0.0772591i
$777$			27440.9i			0.0454523i
$778$		−	228033.i		−	0.376738i
$779$	−104760.			−0.172632
$780$			242466.i			0.398530i
$781$	37367.0	−	409335.i	0.0612613	−	0.671084i
$782$	349020.			0.570738
$783$			583259.i			0.951344i
$784$	170116.			0.276766
$785$	719417.			1.16746
$786$	354420.			0.573685
$787$			15796.3i			0.0255039i	0.999919	+	0.0127519i	$0.00405918\pi$
$787$			15796.3i			0.0255039i	−0.999919	+	0.0127519i	$0.995941\pi$
$788$			749022.i			1.20626i
$789$		−	186894.i		−	0.300221i
$790$	−1.03416e6			−1.65704
$791$		−	210709.i		−	0.336767i
$792$	−95040.0	−	8675.93i	−0.151515	−	0.0138314i
$793$	738480.			1.17434
$794$			426577.i			0.676639i
$795$	−420546.			−0.665395
$796$	−120148.			−0.189623
$797$	378607.			0.596035			0.298018	−	0.954560i	$-0.403675\pi$
$797$	378607.			0.596035			0.298018	+	0.954560i	$0.403675\pi$
$798$		−	88731.1i		−	0.139338i
$799$		−	391534.i		−	0.613304i
$800$		−	463768.i		−	0.724637i
$801$	336456.			0.524401
$802$			1.08954e6i			1.69393i
$803$	399960.	+	36511.2i	0.620277	+	0.0566233i
$804$	−117726.			−0.182121
$805$		−	470329.i		−	0.725789i
$806$	1.39026e6			2.14006
$807$	116034.			0.178171
$808$	132600.			0.203105
$809$			891221.i			1.36172i	0.732413	+	0.680861i	$0.238394\pi$
$809$			891221.i			1.36172i	−0.732413	+	0.680861i	$0.761606\pi$
$810$			756432.i			1.15292i
$811$			944690.i			1.43631i	0.695884	+	0.718154i	$0.255013\pi$
$811$			944690.i			1.43631i	−0.695884	+	0.718154i	$0.744987\pi$
$812$	−974400.			−1.47783
$813$			48604.9i			0.0735358i
$814$	110220.	+	10061.7i	0.166346	+	0.0151852i
$815$	801722.			1.20700
$816$		−	195997.i		−	0.294353i
$817$	118800.			0.177980
$818$	−169320.			−0.253047
$819$	−734400.			−1.09488
$820$		−	461160.i		−	0.685842i
$821$		−	551820.i		−	0.818674i	−0.912383	−	0.409337i	$-0.865760\pi$
$821$		−	551820.i		−	0.818674i	0.912383	−	0.409337i	$-0.134240\pi$
$822$		−	191380.i		−	0.283239i
$823$	−55483.0			−0.0819144			−0.0409572	−	0.999161i	$-0.513041\pi$
$823$	−55483.0			−0.0819144			−0.0409572	+	0.999161i	$0.513041\pi$
$824$		−	122887.i		−	0.180989i
$825$	−11088.0	+	121463.i	−0.0162909	+	0.178458i
$826$	−708900.			−1.03902
$827$			581714.i			0.850548i	0.905065	+	0.425274i	$0.139822\pi$
$827$			581714.i			0.850548i	−0.905065	+	0.425274i	$0.860178\pi$
$828$	279216.			0.407267
$829$	−86953.0			−0.126525			−0.0632624	−	0.997997i	$-0.520150\pi$
$829$	−86953.0			−0.126525			−0.0632624	+	0.997997i	$0.520150\pi$
$830$	141360.			0.205197
$831$			205133.i			0.297053i
$832$			561657.i			0.811380i
$833$			137796.i			0.198585i
$834$	−282060.			−0.405517
$835$		−	24110.7i		−	0.0345810i
$836$	−166320.	−	15182.9i	−0.237975	−	0.0217241i
$837$	−625617.			−0.893013
$838$		−	1.27366e6i		−	1.81370i
$839$	1.03048e6			1.46391			0.731955	−	0.681353i	$-0.238608\pi$
$839$	1.03048e6			1.46391			0.731955	+	0.681353i	$0.238608\pi$
$840$	−55800.0			−0.0790816
$841$	−907439.			−1.28300
$842$		−	256980.i		−	0.362473i
$843$			371224.i			0.522374i
$844$			316233.i			0.443938i
$845$	−189689.			−0.265662
$846$		−	671201.i		−	0.937804i
$847$	−145200.	+	788666.i	−0.202395	+	1.09933i
$848$	−1.28425e6			−1.78590
$849$		−	378060.i		−	0.524500i
$850$	423360.			0.585965
$851$	46259.0			0.0638759
$852$	142674.			0.196547
$853$		−	225925.i		−	0.310503i	−0.987875	−	0.155251i	$-0.950381\pi$
$853$		−	225925.i		−	0.310503i	0.987875	−	0.155251i	$-0.0496188\pi$
$854$		−	1.18965e6i		−	1.63119i
$855$		−	220053.i		−	0.301020i
$856$	−48600.0			−0.0663268
$857$		−	49404.6i		−	0.0672675i	−0.999434	−	0.0336338i	$-0.989292\pi$
$857$		−	49404.6i		−	0.0672675i	0.999434	−	0.0336338i	$-0.0107080\pi$
$858$	33660.0	−	368727.i	0.0457235	−	0.500876i
$859$	1.08224e6			1.46668			0.733341	−	0.679861i	$-0.237960\pi$
$859$	1.08224e6			1.46668			0.733341	+	0.679861i	$0.237960\pi$
$860$			522965.i			0.707092i
$861$	−174600.			−0.235526
$862$	314460.			0.423205
$863$	132262.			0.177588			0.0887940	−	0.996050i	$-0.471699\pi$
$863$	132262.			0.177588			0.0887940	+	0.996050i	$0.471699\pi$
$864$		−	633540.i		−	0.848685i
$865$			74030.2i			0.0989411i
$866$			181663.i			0.242232i
$867$	−91803.0			−0.122129
$868$		−	1.04516e6i		−	1.38722i
$869$	733920.	+	66997.4i	0.971872	+	0.0887194i
$870$	647280.			0.855172
$871$		−	521991.i		−	0.688060i
$872$	182160.			0.239563
$873$	−305784.			−0.401223
$874$	−149580.			−0.195817
$875$			490705.i			0.640920i
$876$			139406.i			0.181666i
$877$		−	679034.i		−	0.882860i	−0.897296	−	0.441430i	$-0.854471\pi$
$877$		−	679034.i		−	0.882860i	0.897296	−	0.441430i	$-0.145529\pi$
$878$	1.93512e6			2.51026
$879$		−	270958.i		−	0.350691i
$880$	−96844.0	+	1.06087e6i	−0.125057	+	1.36993i
$881$	−1.01711e6			−1.31044			−0.655220	−	0.755438i	$-0.727424\pi$
$881$	−1.01711e6			−1.31044			−0.655220	+	0.755438i	$0.727424\pi$
$882$			236222.i			0.303657i
$883$	−1.51674e6			−1.94531			−0.972656	−	0.232252i	$-0.925391\pi$
$883$	−1.51674e6			−1.94531			−0.972656	+	0.232252i	$0.925391\pi$
$884$	−599760.			−0.767490
$885$	219759.			0.280582
$886$			1.53032e6i			1.94946i
$887$			1.30820e6i			1.66275i	0.555710	+	0.831376i	$0.312447\pi$
$887$			1.30820e6i			1.66275i	−0.555710	+	0.831376i	$0.687553\pi$
$888$		−	5488.18i		−	0.00695989i
$889$	739800.			0.936075
$890$		−	793447.i		−	1.00170i
$891$	49005.0	−	536823.i	0.0617284	−	0.676201i
$892$	1.21356e6			1.52522
$893$			167800.i			0.210421i
$894$	107100.			0.134003
$895$	−832133.			−1.03884
$896$	−304800.			−0.379664
$897$		−	154754.i		−	0.192334i
$898$			792045.i			0.982194i
$899$		−	1.73199e6i		−	2.14301i
$900$	338688.			0.418133
$901$		−	1.04026e6i		−	1.28142i
$902$	−64020.0	+	701304.i	−0.0786869	+	0.861972i
$903$	198000.			0.242823
$904$			42141.8i			0.0515675i
$905$	−1.16662e6			−1.42440
$906$	−570600.			−0.695145
$907$	711302.			0.864648			0.432324	−	0.901718i	$-0.357694\pi$
$907$	711302.			0.864648			0.432324	+	0.901718i	$0.357694\pi$
$908$		−	113948.i		−	0.138209i
$909$			871536.i			1.05477i
$910$			1.73190e6i			2.09141i
$911$	−1.48510e6			−1.78945			−0.894723	−	0.446622i	$-0.852627\pi$
$911$	−1.48510e6			−1.78945			−0.894723	+	0.446622i	$0.852627\pi$
$912$			83998.7i			0.100991i
$913$	−100320.	−	9157.92i	−0.120350	−	0.0109864i
$914$	−2.10480e6			−2.51952
$915$			368793.i			0.440494i
$916$	−207298.			−0.247061
$917$	1.18140e6			1.40494
$918$	578340.			0.686275
$919$		−	143021.i		−	0.169344i	−0.996409	−	0.0846720i	$-0.973016\pi$
$919$		−	143021.i		−	0.169344i	0.996409	−	0.0846720i	$-0.0269842\pi$
$920$			94065.9i			0.111136i
$921$			460909.i			0.543370i
$922$	−38280.0			−0.0450308
$923$			632609.i			0.742560i
$924$	−277200.	−	25304.8i	−0.324675	−	0.0296387i
$925$	56112.0			0.0655801
$926$		−	1.24444e6i		−	1.45129i
$927$	807696.			0.939915
$928$	1.75392e6			2.03664
$929$	1.18628e6			1.37454			0.687269	−	0.726403i	$-0.258810\pi$
$929$	1.18628e6			1.37454			0.687269	+	0.726403i	$0.258810\pi$
$930$			694288.i			0.802737i
$931$		−	59055.4i		−	0.0681335i
$932$		−	132505.i		−	0.152546i
$933$	272094.			0.312576
$934$			1.79717e6i			2.06013i
$935$	−859320.	−	78444.8i	−0.982951	−	0.0897307i
$936$	146880.			0.167653
$937$		−	1.16865e6i		−	1.33109i	−0.746359	−	0.665544i	$-0.768200\pi$
$937$		−	1.16865e6i		−	1.33109i	0.746359	−	0.665544i	$-0.231800\pi$
$938$	−840900.			−0.955738
$939$	314859.			0.357096
$940$	−738668.			−0.835976
$941$		−	40838.2i		−	0.0461198i	−0.999734	−	0.0230599i	$-0.992659\pi$
$941$		−	40838.2i		−	0.0461198i	0.999734	−	0.0230599i	$-0.00734084\pi$
$942$		−	381330.i		−	0.429733i
$943$			294335.i			0.330993i
$944$	671092.			0.753075
$945$		−	779354.i		−	0.872713i
$946$	72600.0	−	795293.i	0.0811249	−	0.888679i
$947$	1.40080e6			1.56198			0.780990	−	0.624544i	$-0.214715\pi$
$947$	1.40080e6			1.56198			0.780990	+	0.624544i	$0.214715\pi$
$948$			255808.i			0.284641i
$949$	−618120.			−0.686342
$950$	−181440.			−0.201042
$951$	−231861.			−0.256370
$952$		−	138026.i		−	0.152296i
$953$		−	1.12238e6i		−	1.23582i	−0.786249	−	0.617910i	$-0.787980\pi$
$953$		−	1.12238e6i		−	1.23582i	0.786249	−	0.617910i	$-0.212020\pi$
$954$		−	1.78330e6i		−	1.95942i
$955$	1.07251e6			1.17596
$956$		−	505789.i		−	0.553418i
$957$	−459360.	−	41933.6i	−0.501567	−	0.0457866i
$958$	−726060.			−0.791118
$959$		−	637932.i		−	0.693645i
$960$	−280488.			−0.304349
$961$	934248.			1.01162
$962$	−170340.			−0.184063
$963$		−	319432.i		−	0.344450i
$964$		−	1.42044e6i		−	1.52851i
$965$			893116.i			0.959077i
$966$	−249300.			−0.267158
$967$			1.64168e6i			1.75564i	0.478992	+	0.877819i	$0.341002\pi$
$967$			1.64168e6i			1.75564i	−0.478992	+	0.877819i	$0.658998\pi$
$968$	29040.0	−	157733.i	0.0309917	−	0.168334i
$969$	−68040.0			−0.0724631
$970$			721115.i			0.766410i
$971$	−677603.			−0.718682			−0.359341	−	0.933206i	$-0.616999\pi$
$971$	−677603.			−0.718682			−0.359341	+	0.933206i	$0.616999\pi$
$972$	707616.			0.748971
$973$	−940200.			−0.993104
$974$		−	583231.i		−	0.614785i
$975$		−	187715.i		−	0.197465i
$976$			1.12621e6i			1.18227i
$977$	−486353.			−0.509521			−0.254761	−	0.967004i	$-0.581997\pi$
$977$	−486353.			−0.509521			−0.254761	+	0.967004i	$0.581997\pi$
$978$		−	424956.i		−	0.444290i
$979$	−51403.0	+	563092.i	−0.0536319	+	0.587508i
$980$	259966.			0.270685
$981$			1.19728e6i			1.24410i
$982$	−1.28472e6			−1.33225
$983$	−618803.			−0.640391			−0.320196	−	0.947351i	$-0.603749\pi$
$983$	−618803.			−0.640391			−0.320196	+	0.947351i	$0.603749\pi$
$984$	34920.0			0.0360648
$985$		−	1.65855e6i		−	1.70945i
$986$			1.60110e6i			1.64689i
$987$			279667.i			0.287083i
$988$	257040.			0.263322
$989$		−	333782.i		−	0.341248i
$990$	−1.47312e6	−	134477.i	−1.50303	−	0.137207i
$991$	53462.0			0.0544375			0.0272187	−	0.999630i	$-0.491335\pi$
$991$	53462.0			0.0544375			0.0272187	+	0.999630i	$0.491335\pi$
$992$			1.88130e6i			1.91176i
$993$	523209.			0.530612
$994$	1.01910e6			1.03144
$995$	266042.			0.268723
$996$		−	34966.6i		−	0.0352480i
$997$		−	393363.i		−	0.395734i	−0.980229	−	0.197867i	$-0.936599\pi$
$997$		−	393363.i		−	0.395734i	0.980229	−	0.197867i	$-0.0634015\pi$
$998$		−	1.60142e6i		−	1.60785i
$999$	76653.0			0.0768065

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.5.b.b.10.2	yes	2
3.2	odd	2		99.5.c.b.10.1		2
4.3	odd	2		176.5.h.c.65.2		2
5.2	odd	4		275.5.d.b.274.2		4
5.3	odd	4		275.5.d.b.274.3		4
5.4	even	2		275.5.c.e.76.1		2
8.3	odd	2		704.5.h.d.65.2		2
8.5	even	2		704.5.h.f.65.1		2
11.2	odd	10		121.5.d.b.40.1		8
11.3	even	5		121.5.d.b.112.2		8
11.4	even	5		121.5.d.b.94.1		8
11.5	even	5		121.5.d.b.118.1		8
11.6	odd	10		121.5.d.b.118.2		8
11.7	odd	10		121.5.d.b.94.2		8
11.8	odd	10		121.5.d.b.112.1		8
11.9	even	5		121.5.d.b.40.2		8
11.10	odd	2	inner	11.5.b.b.10.1	✓	2
33.32	even	2		99.5.c.b.10.2		2
44.43	even	2		176.5.h.c.65.1		2
55.32	even	4		275.5.d.b.274.4		4
55.43	even	4		275.5.d.b.274.1		4
55.54	odd	2		275.5.c.e.76.2		2
88.21	odd	2		704.5.h.f.65.2		2
88.43	even	2		704.5.h.d.65.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.5.b.b.10.1	✓	2	11.10	odd	2	inner
11.5.b.b.10.2	yes	2	1.1	even	1	trivial
99.5.c.b.10.1		2	3.2	odd	2
99.5.c.b.10.2		2	33.32	even	2
121.5.d.b.40.1		8	11.2	odd	10
121.5.d.b.40.2		8	11.9	even	5
121.5.d.b.94.1		8	11.4	even	5
121.5.d.b.94.2		8	11.7	odd	10
121.5.d.b.112.1		8	11.8	odd	10
121.5.d.b.112.2		8	11.3	even	5
121.5.d.b.118.1		8	11.5	even	5
121.5.d.b.118.2		8	11.6	odd	10
176.5.h.c.65.1		2	44.43	even	2
176.5.h.c.65.2		2	4.3	odd	2
275.5.c.e.76.1		2	5.4	even	2
275.5.c.e.76.2		2	55.54	odd	2
275.5.d.b.274.1		4	55.43	even	4
275.5.d.b.274.2		4	5.2	odd	4
275.5.d.b.274.3		4	5.3	odd	4
275.5.d.b.274.4		4	55.32	even	4
704.5.h.d.65.1		2	88.43	even	2
704.5.h.d.65.2		2	8.3	odd	2
704.5.h.f.65.1		2	8.5	even	2
704.5.h.f.65.2		2	88.21	odd	2

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:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	11.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+5.47723i q^{2} -3.00000 q^{3} -14.0000 q^{4} +31.0000 q^{5} -16.4317i q^{6} -54.7723i q^{7} +10.9545i q^{8} -72.0000 q^{9} +O(q^{10})\)	\(q+5.47723i q^{2} -3.00000 q^{3} -14.0000 q^{4} +31.0000 q^{5} -16.4317i q^{6} -54.7723i q^{7} +10.9545i q^{8} -72.0000 q^{9} +169.794i q^{10} +(11.0000 - 120.499i) q^{11} +42.0000 q^{12} +186.226i q^{13} +300.000 q^{14} -93.0000 q^{15} -284.000 q^{16} -230.043i q^{17} -394.360i q^{18} +98.5901i q^{19} -434.000 q^{20} +164.317i q^{21} +(660.000 + 60.2495i) q^{22} +277.000 q^{23} -32.8634i q^{24} +336.000 q^{25} -1020.00 q^{26} +459.000 q^{27} +766.812i q^{28} +1270.72i q^{29} -509.382i q^{30} -1363.00 q^{31} -1380.26i q^{32} +(-33.0000 + 361.497i) q^{33} +1260.00 q^{34} -1697.94i q^{35} +1008.00 q^{36} +167.000 q^{37} -540.000 q^{38} -558.677i q^{39} +339.588i q^{40} +1062.58i q^{41} -900.000 q^{42} -1204.99i q^{43} +(-154.000 + 1686.99i) q^{44} -2232.00 q^{45} +1517.19i q^{46} +1702.00 q^{47} +852.000 q^{48} -599.000 q^{49} +1840.35i q^{50} +690.130i q^{51} -2607.16i q^{52} +4522.00 q^{53} +2514.05i q^{54} +(341.000 - 3735.47i) q^{55} +600.000 q^{56} -295.770i q^{57} -6960.00 q^{58} -2363.00 q^{59} +1302.00 q^{60} -3965.51i q^{61} -7465.46i q^{62} +3943.60i q^{63} +3016.00 q^{64} +5773.00i q^{65} +(-1980.00 - 180.748i) q^{66} -2803.00 q^{67} +3220.61i q^{68} -831.000 q^{69} +9300.00 q^{70} +3397.00 q^{71} -788.720i q^{72} +3319.20i q^{73} +914.697i q^{74} -1008.00 q^{75} -1380.26i q^{76} +(-6600.00 - 602.495i) q^{77} +3060.00 q^{78} +6090.67i q^{79} -8804.00 q^{80} +4455.00 q^{81} -5820.00 q^{82} -832.538i q^{83} -2300.43i q^{84} -7131.35i q^{85} +6600.00 q^{86} -3812.15i q^{87} +(1320.00 + 120.499i) q^{88} -4673.00 q^{89} -12225.2i q^{90} +10200.0 q^{91} -3878.00 q^{92} +4089.00 q^{93} +9322.24i q^{94} +3056.29i q^{95} +4140.78i q^{96} +4247.00 q^{97} -3280.86i q^{98} +(-792.000 + 8675.93i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 6 q^{3} - 28 q^{4} + 62 q^{5} - 144 q^{9}+O(q^{10}) \) 2 * q - 6 * q^3 - 28 * q^4 + 62 * q^5 - 144 * q^9	\( 2 q - 6 q^{3} - 28 q^{4} + 62 q^{5} - 144 q^{9} + 22 q^{11} + 84 q^{12} + 600 q^{14} - 186 q^{15} - 568 q^{16} - 868 q^{20} + 1320 q^{22} + 554 q^{23} + 672 q^{25} - 2040 q^{26} + 918 q^{27} - 2726 q^{31} - 66 q^{33} + 2520 q^{34} + 2016 q^{36} + 334 q^{37} - 1080 q^{38} - 1800 q^{42} - 308 q^{44} - 4464 q^{45} + 3404 q^{47} + 1704 q^{48} - 1198 q^{49} + 9044 q^{53} + 682 q^{55} + 1200 q^{56} - 13920 q^{58} - 4726 q^{59} + 2604 q^{60} + 6032 q^{64} - 3960 q^{66} - 5606 q^{67} - 1662 q^{69} + 18600 q^{70} + 6794 q^{71} - 2016 q^{75} - 13200 q^{77} + 6120 q^{78} - 17608 q^{80} + 8910 q^{81} - 11640 q^{82} + 13200 q^{86} + 2640 q^{88} - 9346 q^{89} + 20400 q^{91} - 7756 q^{92} + 8178 q^{93} + 8494 q^{97} - 1584 q^{99}+O(q^{100}) \) 2 * q - 6 * q^3 - 28 * q^4 + 62 * q^5 - 144 * q^9 + 22 * q^11 + 84 * q^12 + 600 * q^14 - 186 * q^15 - 568 * q^16 - 868 * q^20 + 1320 * q^22 + 554 * q^23 + 672 * q^25 - 2040 * q^26 + 918 * q^27 - 2726 * q^31 - 66 * q^33 + 2520 * q^34 + 2016 * q^36 + 334 * q^37 - 1080 * q^38 - 1800 * q^42 - 308 * q^44 - 4464 * q^45 + 3404 * q^47 + 1704 * q^48 - 1198 * q^49 + 9044 * q^53 + 682 * q^55 + 1200 * q^56 - 13920 * q^58 - 4726 * q^59 + 2604 * q^60 + 6032 * q^64 - 3960 * q^66 - 5606 * q^67 - 1662 * q^69 + 18600 * q^70 + 6794 * q^71 - 2016 * q^75 - 13200 * q^77 + 6120 * q^78 - 17608 * q^80 + 8910 * q^81 - 11640 * q^82 + 13200 * q^86 + 2640 * q^88 - 9346 * q^89 + 20400 * q^91 - 7756 * q^92 + 8178 * q^93 + 8494 * q^97 - 1584 * q^99

Introduction

L-functions

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