LMFDB - Embedded newform 354.5.b.a.119.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,5,Mod(119,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("354.119");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	354.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:	$36.5929669317$
Analytic rank:	$0$
Dimension:	$76$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			119.1
Character	$\chi$	$=$	354.119
Dual form			354.5.b.a.119.39

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.82843i q^{2} +(-8.93212 + 1.10332i) q^{3} -8.00000 q^{4} +5.83517i q^{5} +(3.12065 + 25.2638i) q^{6} -18.4051 q^{7} +22.6274i q^{8} +(78.5654 - 19.7099i) q^{9} +O(q^{10})$	\(q-2.82843i q^{2} +(-8.93212 + 1.10332i) q^{3} -8.00000 q^{4} +5.83517i q^{5} +(3.12065 + 25.2638i) q^{6} -18.4051 q^{7} +22.6274i q^{8} +(78.5654 - 19.7099i) q^{9} +16.5043 q^{10} +91.9352i q^{11} +(71.4569 - 8.82652i) q^{12} -102.941 q^{13} +52.0576i q^{14} +(-6.43803 - 52.1204i) q^{15} +64.0000 q^{16} +209.308i q^{17} +(-55.7480 - 222.216i) q^{18} +387.804 q^{19} -46.6813i q^{20} +(164.397 - 20.3067i) q^{21} +260.032 q^{22} -516.833i q^{23} +(-24.9652 - 202.111i) q^{24} +590.951 q^{25} +291.160i q^{26} +(-680.009 + 262.733i) q^{27} +147.241 q^{28} +344.653i q^{29} +(-147.419 + 18.2095i) q^{30} +1119.64 q^{31} -181.019i q^{32} +(-101.433 - 821.176i) q^{33} +592.013 q^{34} -107.397i q^{35} +(-628.523 + 157.679i) q^{36} -1955.68 q^{37} -1096.87i q^{38} +(919.477 - 113.576i) q^{39} -132.035 q^{40} -3123.24i q^{41} +(-57.4359 - 464.984i) q^{42} -2865.07 q^{43} -735.481i q^{44} +(115.010 + 458.442i) q^{45} -1461.82 q^{46} +3252.80i q^{47} +(-571.655 + 70.6122i) q^{48} -2062.25 q^{49} -1671.46i q^{50} +(-230.933 - 1869.57i) q^{51} +823.524 q^{52} -0.558046i q^{53} +(743.122 + 1923.36i) q^{54} -536.457 q^{55} -416.461i q^{56} +(-3463.91 + 427.870i) q^{57} +974.826 q^{58} +453.188i q^{59} +(51.5042 + 416.963i) q^{60} +1345.64 q^{61} -3166.82i q^{62} +(-1446.01 + 362.763i) q^{63} -512.000 q^{64} -600.675i q^{65} +(-2322.64 + 286.897i) q^{66} -6584.93 q^{67} -1674.47i q^{68} +(570.230 + 4616.41i) q^{69} -303.765 q^{70} -5275.49i q^{71} +(445.984 + 1777.73i) q^{72} +105.778 q^{73} +5531.49i q^{74} +(-5278.44 + 652.005i) q^{75} -3102.43 q^{76} -1692.08i q^{77} +(-321.241 - 2600.67i) q^{78} -9587.37 q^{79} +373.451i q^{80} +(5784.04 - 3097.03i) q^{81} -8833.85 q^{82} +7888.34i q^{83} +(-1315.17 + 162.453i) q^{84} -1221.35 q^{85} +8103.63i q^{86} +(-380.261 - 3078.48i) q^{87} -2080.26 q^{88} -11840.4i q^{89} +(1296.67 - 325.299i) q^{90} +1894.63 q^{91} +4134.66i q^{92} +(-10000.8 + 1235.32i) q^{93} +9200.32 q^{94} +2262.90i q^{95} +(199.721 + 1616.89i) q^{96} +840.648 q^{97} +5832.93i q^{98} +(1812.03 + 7222.92i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 608 q^{4} - 64 q^{6} - 184 q^{7} + 168 q^{9}+O(q^{10}) $ 76 * q - 608 * q^4 - 64 * q^6 - 184 * q^7 + 168 * q^9	$ 76 q - 608 q^{4} - 64 q^{6} - 184 q^{7} + 168 q^{9} + 256 q^{10} - 200 q^{13} - 26 q^{15} + 4864 q^{16} - 512 q^{18} + 616 q^{19} + 330 q^{21} + 640 q^{22} + 512 q^{24} - 10540 q^{25} - 354 q^{27} + 1472 q^{28} - 832 q^{30} - 3920 q^{31} - 188 q^{33} + 2560 q^{34} - 1344 q^{36} - 1440 q^{37} + 8204 q^{39} - 2048 q^{40} - 5760 q^{42} - 1944 q^{43} + 3886 q^{45} + 4864 q^{46} + 33636 q^{49} - 7544 q^{51} + 1600 q^{52} + 3392 q^{54} - 10536 q^{55} - 12182 q^{57} - 7168 q^{58} + 208 q^{60} + 6360 q^{61} + 10860 q^{63} - 38912 q^{64} + 19712 q^{66} + 30744 q^{67} - 34208 q^{69} - 23808 q^{70} + 4096 q^{72} + 4032 q^{73} + 22324 q^{75} - 4928 q^{76} + 12864 q^{78} - 29824 q^{79} - 22584 q^{81} + 13184 q^{82} - 2640 q^{84} + 9240 q^{85} + 32850 q^{87} - 5120 q^{88} - 16448 q^{90} - 31160 q^{91} - 1780 q^{93} + 5248 q^{94} - 4096 q^{96} + 77504 q^{97} - 15412 q^{99}+O(q^{100}) $ 76 * q - 608 * q^4 - 64 * q^6 - 184 * q^7 + 168 * q^9 + 256 * q^10 - 200 * q^13 - 26 * q^15 + 4864 * q^16 - 512 * q^18 + 616 * q^19 + 330 * q^21 + 640 * q^22 + 512 * q^24 - 10540 * q^25 - 354 * q^27 + 1472 * q^28 - 832 * q^30 - 3920 * q^31 - 188 * q^33 + 2560 * q^34 - 1344 * q^36 - 1440 * q^37 + 8204 * q^39 - 2048 * q^40 - 5760 * q^42 - 1944 * q^43 + 3886 * q^45 + 4864 * q^46 + 33636 * q^49 - 7544 * q^51 + 1600 * q^52 + 3392 * q^54 - 10536 * q^55 - 12182 * q^57 - 7168 * q^58 + 208 * q^60 + 6360 * q^61 + 10860 * q^63 - 38912 * q^64 + 19712 * q^66 + 30744 * q^67 - 34208 * q^69 - 23808 * q^70 + 4096 * q^72 + 4032 * q^73 + 22324 * q^75 - 4928 * q^76 + 12864 * q^78 - 29824 * q^79 - 22584 * q^81 + 13184 * q^82 - 2640 * q^84 + 9240 * q^85 + 32850 * q^87 - 5120 * q^88 - 16448 * q^90 - 31160 * q^91 - 1780 * q^93 + 5248 * q^94 - 4096 * q^96 + 77504 * q^97 - 15412 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	2.82843i		−	0.707107i
$2$		−	2.82843i		−	0.707107i
$3$	−8.93212	+	1.10332i	−0.992457	+	0.122591i
$3$	−8.93212	+	1.10332i	−0.992457	+	0.122591i
$4$	−8.00000			−0.500000
$5$			5.83517i			0.233407i	0.993167	+	0.116703i	$0.0372327\pi$
$5$			5.83517i			0.233407i	−0.993167	+	0.116703i	$0.962767\pi$
$6$	3.12065	+	25.2638i	0.0866846	+	0.701773i
$7$	−18.4051			−0.375615			−0.187807	−	0.982206i	$-0.560138\pi$
$7$	−18.4051			−0.375615			−0.187807	+	0.982206i	$0.560138\pi$
$8$			22.6274i			0.353553i
$9$	78.5654	−	19.7099i	0.969943	−	0.243332i
$10$	16.5043			0.165043
$11$			91.9352i			0.759795i	0.925029	+	0.379897i	$0.124041\pi$
$11$			91.9352i			0.759795i	−0.925029	+	0.379897i	$0.875959\pi$
$12$	71.4569	−	8.82652i	0.496229	−	0.0612953i
$13$	−102.941			−0.609116			−0.304558	−	0.952494i	$-0.598509\pi$
$13$	−102.941			−0.609116			−0.304558	+	0.952494i	$0.598509\pi$
$14$			52.0576i			0.265600i
$15$	−6.43803	−	52.1204i	−0.0286135	−	0.231646i
$16$	64.0000			0.250000
$17$			209.308i			0.724250i	0.932130	+	0.362125i	$0.117949\pi$
$17$			209.308i			0.724250i	−0.932130	+	0.362125i	$0.882051\pi$
$18$	−55.7480	−	222.216i	−0.172062	−	0.685853i
$19$	387.804			1.07425			0.537124	−	0.843503i	$-0.319511\pi$
$19$	387.804			1.07425			0.537124	+	0.843503i	$0.319511\pi$
$20$		−	46.6813i		−	0.116703i
$21$	164.397	−	20.3067i	0.372782	−	0.0460469i
$22$	260.032			0.537256
$23$		−	516.833i		−	0.977000i	−0.872564	−	0.488500i	$-0.837544\pi$
$23$		−	516.833i		−	0.977000i	0.872564	−	0.488500i	$-0.162456\pi$
$24$	−24.9652	−	202.111i	−0.0433423	−	0.350887i
$25$	590.951			0.945521
$26$			291.160i			0.430710i
$27$	−680.009	+	262.733i	−0.932797	+	0.360402i
$28$	147.241			0.187807
$29$			344.653i			0.409813i	0.978782	+	0.204907i	$0.0656891\pi$
$29$			344.653i			0.409813i	−0.978782	+	0.204907i	$0.934311\pi$
$30$	−147.419	+	18.2095i	−0.163799	+	0.0202328i
$31$	1119.64			1.16508			0.582540	−	0.812802i	$-0.302059\pi$
$31$	1119.64			1.16508			0.582540	+	0.812802i	$0.302059\pi$
$32$		−	181.019i		−	0.176777i
$33$	−101.433	−	821.176i	−0.0931437	−	0.754064i
$34$	592.013			0.512122
$35$		−	107.397i		−	0.0876710i
$36$	−628.523	+	157.679i	−0.484972	+	0.121666i
$37$	−1955.68			−1.42854			−0.714272	−	0.699869i	$-0.753242\pi$
$37$	−1955.68			−1.42854			−0.714272	+	0.699869i	$0.753242\pi$
$38$		−	1096.87i		−	0.759608i
$39$	919.477	−	113.576i	0.604521	−	0.0746718i
$40$	−132.035			−0.0825217
$41$		−	3123.24i		−	1.85796i	−0.370124	−	0.928982i	$-0.620685\pi$
$41$		−	3123.24i		−	1.85796i	0.370124	−	0.928982i	$-0.379315\pi$
$42$	−57.4359	−	464.984i	−0.0325600	−	0.263596i
$43$	−2865.07			−1.54952			−0.774761	−	0.632254i	$-0.782130\pi$
$43$	−2865.07			−1.54952			−0.774761	+	0.632254i	$0.782130\pi$
$44$		−	735.481i		−	0.379897i
$45$	115.010	+	458.442i	0.0567953	+	0.226391i
$46$	−1461.82			−0.690843
$47$			3252.80i			1.47252i	0.676697	+	0.736262i	$0.263411\pi$
$47$			3252.80i			1.47252i	−0.676697	+	0.736262i	$0.736589\pi$
$48$	−571.655	+	70.6122i	−0.248114	+	0.0306476i
$49$	−2062.25			−0.858913
$50$		−	1671.46i		−	0.668585i
$51$	−230.933	−	1869.57i	−0.0887862	−	0.718787i
$52$	823.524			0.304558
$53$		−	0.558046i		−	0.000198663i	−1.00000		9.93317e-5i	$-0.999968\pi$
$53$		−	0.558046i		−	0.000198663i	1.00000		9.93317e-5i	$-3.16183e-5\pi$
$54$	743.122	+	1923.36i	0.254843	+	0.659587i
$55$	−536.457			−0.177341
$56$		−	416.461i		−	0.132800i
$57$	−3463.91	+	427.870i	−1.06615	+	0.131693i
$58$	974.826			0.289782
$59$			453.188i			0.130189i
$59$			453.188i			0.130189i
$60$	51.5042	+	416.963i	0.0143067	+	0.115823i
$61$	1345.64			0.361635			0.180818	−	0.983517i	$-0.442126\pi$
$61$	1345.64			0.361635			0.180818	+	0.983517i	$0.442126\pi$
$62$		−	3166.82i		−	0.823836i
$63$	−1446.01	+	362.763i	−0.364325	+	0.0913991i
$64$	−512.000			−0.125000
$65$		−	600.675i		−	0.142172i
$66$	−2322.64	+	286.897i	−0.533204	+	0.0658625i
$67$	−6584.93			−1.46690			−0.733452	−	0.679741i	$-0.762092\pi$
$67$	−6584.93			−1.46690			−0.733452	+	0.679741i	$0.762092\pi$
$68$		−	1674.47i		−	0.362125i
$69$	570.230	+	4616.41i	0.119771	+	0.969630i
$70$	−303.765			−0.0619928
$71$		−	5275.49i		−	1.04652i	−0.852174	−	0.523258i	$-0.824716\pi$
$71$		−	5275.49i		−	1.04652i	0.852174	−	0.523258i	$-0.175284\pi$
$72$	445.984	+	1777.73i	0.0860308	+	0.342927i
$73$	105.778			0.0198495			0.00992474	−	0.999951i	$-0.496841\pi$
$73$	105.778			0.0198495			0.00992474	+	0.999951i	$0.496841\pi$
$74$			5531.49i			1.01013i
$75$	−5278.44	+	652.005i	−0.938390	+	0.115912i
$76$	−3102.43			−0.537124
$77$		−	1692.08i		−	0.285390i
$78$	−321.241	−	2600.67i	−0.0528010	−	0.427461i
$79$	−9587.37			−1.53619			−0.768096	−	0.640335i	$-0.778796\pi$
$79$	−9587.37			−1.53619			−0.768096	+	0.640335i	$0.778796\pi$
$80$			373.451i			0.0583517i
$81$	5784.04	−	3097.03i	0.881579	−	0.472036i
$82$	−8833.85			−1.31378
$83$			7888.34i			1.14506i	0.819883	+	0.572532i	$0.194039\pi$
$83$			7888.34i			1.14506i	−0.819883	+	0.572532i	$0.805961\pi$
$84$	−1315.17	+	162.453i	−0.186391	+	0.0230234i
$85$	−1221.35			−0.169045
$86$			8103.63i			1.09568i
$87$	−380.261	−	3078.48i	−0.0502393	−	0.406722i
$88$	−2080.26			−0.268628
$89$		−	11840.4i		−	1.49481i	−0.664368	−	0.747406i	$-0.731299\pi$
$89$		−	11840.4i		−	1.49481i	0.664368	−	0.747406i	$-0.268701\pi$
$90$	1296.67	−	325.299i	0.160083	−	0.0401603i
$91$	1894.63			0.228793
$92$			4134.66i			0.488500i
$93$	−10000.8	+	1235.32i	−1.15629	+	0.142828i
$94$	9200.32			1.04123
$95$			2262.90i			0.250737i
$96$	199.721	+	1616.89i	0.0216712	+	0.175443i
$97$	840.648			0.0893451			0.0446725	−	0.999002i	$-0.485776\pi$
$97$	840.648			0.0893451			0.0446725	+	0.999002i	$0.485776\pi$
$98$			5832.93i			0.607344i
$99$	1812.03	+	7222.92i	0.184882	+	0.736958i
$100$	−4727.61			−0.472761
$101$		−	18864.0i		−	1.84923i	−0.380898	−	0.924617i	$-0.624385\pi$
$101$		−	18864.0i		−	1.84923i	0.380898	−	0.924617i	$-0.375615\pi$
$102$	−5287.93	+	653.177i	−0.508259	+	0.0627814i
$103$	−10598.0			−0.998967			−0.499484	−	0.866323i	$-0.666477\pi$
$103$	−10598.0			−0.998967			−0.499484	+	0.866323i	$0.666477\pi$
$104$		−	2329.28i		−	0.215355i
$105$	118.493	+	959.283i	0.0107476	+	0.0870098i
$106$	−1.57839			−0.000140476
$107$		−	3956.45i		−	0.345572i	−0.984959	−	0.172786i	$-0.944723\pi$
$107$		−	3956.45i		−	0.345572i	0.984959	−	0.172786i	$-0.0552769\pi$
$108$	5440.07	−	2101.87i	0.466398	−	0.180201i
$109$	−1549.68			−0.130434			−0.0652168	−	0.997871i	$-0.520774\pi$
$109$	−1549.68			−0.130434			−0.0652168	+	0.997871i	$0.520774\pi$
$110$			1517.33i			0.125399i
$111$	17468.3	−	2157.73i	1.41777	−	0.175126i
$112$	−1177.93			−0.0939037
$113$		−	1665.68i		−	0.130447i	−0.997871	−	0.0652236i	$-0.979224\pi$
$113$		−	1665.68i		−	0.130447i	0.997871	−	0.0652236i	$-0.0207761\pi$
$114$	1210.20	+	9797.41i	0.0931208	+	0.753879i
$115$	3015.81			0.228038
$116$		−	2757.22i		−	0.204907i
$117$	−8087.56	+	2028.95i	−0.590807	+	0.148217i
$118$	1281.81			0.0920575
$119$		−	3852.35i		−	0.272039i
$120$	1179.35	−	145.676i	0.0818993	−	0.0101164i
$121$	6188.92			0.422712
$122$		−	3806.06i		−	0.255715i
$123$	3445.92	+	27897.1i	0.227769	+	1.84395i
$124$	−8957.13			−0.582540
$125$			7095.28i			0.454098i
$126$	1026.05	+	4089.92i	0.0646289	+	0.257617i
$127$	20583.5			1.27618			0.638091	−	0.769961i	$-0.279724\pi$
$127$	20583.5			1.27618			0.638091	+	0.769961i	$0.279724\pi$
$128$			1448.15i			0.0883883i
$129$	25591.1	−	3161.07i	1.53783	−	0.189957i
$130$	−1698.97			−0.100531
$131$			13891.9i			0.809504i	0.914427	+	0.404752i	$0.132642\pi$
$131$			13891.9i			0.809504i	−0.914427	+	0.404752i	$0.867358\pi$
$132$	811.468	+	6569.41i	0.0465719	+	0.377032i
$133$	−7137.58			−0.403504
$134$			18625.0i			1.03726i
$135$	−1533.09	−	3967.97i	−0.0841203	−	0.217721i
$136$	−4736.11			−0.256061
$137$		−	3733.15i		−	0.198900i	−0.995043	−	0.0994498i	$-0.968292\pi$
$137$		−	3733.15i		−	0.198900i	0.995043	−	0.0994498i	$-0.0317083\pi$
$138$	13057.2	−	1612.85i	0.685632	−	0.0846909i
$139$	−23166.5			−1.19903			−0.599517	−	0.800362i	$-0.704641\pi$
$139$	−23166.5			−1.19903			−0.599517	+	0.800362i	$0.704641\pi$
$140$			859.176i			0.0438355i
$141$	−3588.87	−	29054.4i	−0.180518	−	1.46142i
$142$	−14921.3			−0.739999
$143$		−	9463.86i		−	0.462803i
$144$	5028.18	−	1261.43i	0.242486	−	0.0608330i
$145$	−2011.11			−0.0956532
$146$		−	299.185i		−	0.0140357i
$147$	18420.3	−	2275.31i	0.852435	−	0.105295i
$148$	15645.4			0.714272
$149$		−	42781.0i		−	1.92698i	−0.267738	−	0.963492i	$-0.586276\pi$
$149$		−	42781.0i		−	1.92698i	0.267738	−	0.963492i	$-0.413724\pi$
$150$	1844.15	+	14929.7i	0.0819622	+	0.663542i
$151$	−25860.3			−1.13417			−0.567086	−	0.823659i	$-0.691929\pi$
$151$	−25860.3			−1.13417			−0.567086	+	0.823659i	$0.691929\pi$
$152$			8774.99i			0.379804i
$153$	4125.44	+	16444.4i	0.176233	+	0.702481i
$154$	−4785.92			−0.201801
$155$			6533.30i			0.271937i
$156$	−7355.81	+	908.607i	−0.302261	+	0.0373359i
$157$	−13806.5			−0.560124			−0.280062	−	0.959982i	$-0.590355\pi$
$157$	−13806.5			−0.560124			−0.280062	+	0.959982i	$0.590355\pi$
$158$			27117.2i			1.08625i
$159$	0.615700	+	4.98453i	2.43543e−5	+	0.000197165i
$160$	1056.28			0.0412609
$161$			9512.37i			0.366976i
$162$	−8759.72	−	16359.7i	−0.333780	−	0.623371i
$163$	34652.1			1.30423			0.652116	−	0.758119i	$-0.273882\pi$
$163$	34652.1			1.30423			0.652116	+	0.758119i	$0.273882\pi$
$164$			24985.9i			0.928982i
$165$	4791.70	−	591.881i	0.176004	−	0.0217404i
$166$	22311.6			0.809682
$167$		−	10070.4i		−	0.361090i	−0.983567	−	0.180545i	$-0.942214\pi$
$167$		−	10070.4i		−	0.361090i	0.983567	−	0.180545i	$-0.0577861\pi$
$168$	459.487	+	3719.87i	0.0162800	+	0.131798i
$169$	−17964.2			−0.628978
$170$			3454.50i			0.119533i
$171$	30467.9	−	7643.56i	1.04196	−	0.261399i
$172$	22920.5			0.774761
$173$		−	51820.9i		−	1.73146i	−0.500510	−	0.865731i	$-0.666854\pi$
$173$		−	51820.9i		−	1.73146i	0.500510	−	0.865731i	$-0.333146\pi$
$174$	−8707.26	+	1075.54i	−0.287596	+	0.0355245i
$175$	−10876.5			−0.355152
$176$			5883.85i			0.189949i
$177$	−500.009	−	4047.92i	−0.0159599	−	0.129207i
$178$	−33489.7			−1.05699
$179$		−	58473.1i		−	1.82495i	−0.409135	−	0.912474i	$-0.634170\pi$
$179$		−	58473.1i		−	1.82495i	0.409135	−	0.912474i	$-0.365830\pi$
$180$	−920.084	−	3667.54i	−0.0283976	−	0.113196i
$181$	−25580.7			−0.780826			−0.390413	−	0.920640i	$-0.627668\pi$
$181$	−25580.7			−0.780826			−0.390413	+	0.920640i	$0.627668\pi$
$182$		−	5358.83i		−	0.161781i
$183$	−12019.5	+	1484.67i	−0.358908	+	0.0443331i
$184$	11694.6			0.345422
$185$		−	11411.7i		−	0.333432i
$186$	3494.01	+	28286.4i	0.100994	+	0.817622i
$187$	−19242.8			−0.550281
$188$		−	26022.4i		−	0.736262i
$189$	12515.7	−	4835.64i	0.350372	−	0.135373i
$190$	6400.45			0.177298
$191$		−	10512.9i		−	0.288175i	−0.989565	−	0.144087i	$-0.953975\pi$
$191$		−	10512.9i		−	0.288175i	0.989565	−	0.144087i	$-0.0460247\pi$
$192$	4573.24	−	564.897i	0.124057	−	0.0153238i
$193$	20740.8			0.556814			0.278407	−	0.960463i	$-0.410194\pi$
$193$	20740.8			0.556814			0.278407	+	0.960463i	$0.410194\pi$
$194$		−	2377.71i		−	0.0631765i
$195$	662.734	+	5365.30i	0.0174289	+	0.141099i
$196$	16498.0			0.429457
$197$			10620.4i			0.273659i	0.990595	+	0.136829i	$0.0436912\pi$
$197$			10620.4i			0.273659i	−0.990595	+	0.136829i	$0.956309\pi$
$198$	20429.5	−	5125.20i	0.521108	−	0.130732i
$199$	44110.8			1.11388			0.556940	−	0.830553i	$-0.311975\pi$
$199$	44110.8			1.11388			0.556940	+	0.830553i	$0.311975\pi$
$200$			13371.7i			0.334292i
$201$	58817.4	−	7265.26i	1.45584	−	0.179829i
$202$	−53355.6			−1.30761
$203$		−	6343.38i		−	0.153932i
$204$	1847.46	+	14956.5i	0.0443931	+	0.359394i
$205$	18224.6			0.433661
$206$			29975.8i			0.706377i
$207$	−10186.7	−	40605.2i	−0.237735	−	0.947634i
$208$	−6588.19			−0.152279
$209$			35652.8i			0.816208i
$210$	2713.26	−	335.148i	0.0615252	−	0.00759973i
$211$	73011.7			1.63994			0.819969	−	0.572408i	$-0.193991\pi$
$211$	73011.7			1.63994			0.819969	+	0.572408i	$0.193991\pi$
$212$			4.46437i			9.93317e-5i
$213$	5820.53	+	47121.3i	0.128293	+	1.03862i
$214$	−11190.5			−0.244356
$215$		−	16718.1i		−	0.361669i
$216$	−5944.98	−	15386.8i	−0.127421	−	0.329794i
$217$	−20607.1			−0.437621
$218$			4383.16i			0.0922305i
$219$	−944.821	+	116.706i	−0.0196998	+	0.00243336i
$220$	4291.66			0.0886706
$221$		−	21546.3i		−	0.441152i
$222$	−6102.97	−	49407.9i	−0.123833	−	1.00251i
$223$	42645.6			0.857559			0.428780	−	0.903409i	$-0.358944\pi$
$223$	42645.6			0.857559			0.428780	+	0.903409i	$0.358944\pi$
$224$			3331.68i			0.0664000i
$225$	46428.3	−	11647.6i	0.917102	−	0.230075i
$226$	−4711.26			−0.0922401
$227$		−	26814.4i		−	0.520375i	−0.965558	−	0.260188i	$-0.916216\pi$
$227$		−	26814.4i		−	0.520375i	0.965558	−	0.260188i	$-0.0837844\pi$
$228$	27711.3	−	3422.96i	0.533073	−	0.0658464i
$229$	−30655.6			−0.584573			−0.292287	−	0.956331i	$-0.594416\pi$
$229$	−30655.6			−0.584573			−0.292287	+	0.956331i	$0.594416\pi$
$230$		−	8529.99i		−	0.161247i
$231$	1866.90	+	15113.8i	0.0349862	+	0.283238i
$232$	−7798.61			−0.144891
$233$			23081.1i			0.425152i	0.977145	+	0.212576i	$0.0681853\pi$
$233$			23081.1i			0.425152i	−0.977145	+	0.212576i	$0.931815\pi$
$234$	5738.73	+	22875.1i	0.104805	+	0.417764i
$235$	−18980.7			−0.343697
$236$		−	3625.50i		−	0.0650945i
$237$	85635.5	−	10577.9i	1.52460	−	0.188323i
$238$	−10896.1			−0.192361
$239$			82684.4i			1.44753i	0.690046	+	0.723766i	$0.257590\pi$
$239$			82684.4i			1.44753i	−0.690046	+	0.723766i	$0.742410\pi$
$240$	−412.034	−	3335.71i	−0.00715337	−	0.0579116i
$241$	−69736.6			−1.20068			−0.600339	−	0.799745i	$-0.704968\pi$
$241$	−69736.6			−1.20068			−0.600339	+	0.799745i	$0.704968\pi$
$242$		−	17504.9i		−	0.298902i
$243$	−48246.7	+	34044.6i	−0.817063	+	0.576549i
$244$	−10765.2			−0.180818
$245$		−	12033.6i		−	0.200476i
$246$	78905.0	−	9746.52i	1.30387	−	0.161057i
$247$	−39920.7			−0.654341
$248$			25334.6i			0.411918i
$249$	−8703.33	−	70459.6i	−0.140374	−	1.13643i
$250$	20068.5			0.321096
$251$			79068.1i			1.25503i	0.778604	+	0.627515i	$0.215928\pi$
$251$			79068.1i			1.25503i	−0.778604	+	0.627515i	$0.784072\pi$
$252$	11568.0	−	2902.10i	0.182163	−	0.0456995i
$253$	47515.1			0.742319
$254$		−	58219.0i		−	0.902397i
$255$	10909.2	−	1347.53i	0.167770	−	0.0207233i
$256$	4096.00			0.0625000
$257$		−	85115.4i		−	1.28867i	−0.764743	−	0.644336i	$-0.777134\pi$
$257$		−	85115.4i		−	1.28867i	0.764743	−	0.644336i	$-0.222866\pi$
$258$	−8940.86	−	72382.6i	−0.134320	−	1.08741i
$259$	35994.5			0.536582
$260$			4805.40i			0.0710858i
$261$	6793.07	+	27077.8i	0.0997207	+	0.397496i
$262$	39292.2			0.572406
$263$			58606.9i			0.847301i	0.905826	+	0.423650i	$0.139251\pi$
$263$			58606.9i			0.847301i	−0.905826	+	0.423650i	$0.860749\pi$
$264$	18581.1	−	2295.18i	0.266602	−	0.0329313i
$265$	3.25629			4.63694e−5
$266$			20188.1i			0.285320i
$267$	13063.7	+	105760.i	0.183250	+	1.48354i
$268$	52679.4			0.733452
$269$		−	49166.6i		−	0.679463i	−0.940522	−	0.339732i	$-0.889664\pi$
$269$		−	49166.6i		−	0.679463i	0.940522	−	0.339732i	$-0.110336\pi$
$270$	−11223.1	+	4336.24i	−0.153952	+	0.0594821i
$271$	−88196.4			−1.20092			−0.600458	−	0.799657i	$-0.705015\pi$
$271$	−88196.4			−1.20092			−0.600458	+	0.799657i	$0.705015\pi$
$272$			13395.7i			0.181063i
$273$	−16923.1	+	2090.38i	−0.227067	+	0.0280479i
$274$	−10558.9			−0.140643
$275$			54329.2i			0.718402i
$276$	−4561.84	−	36931.3i	−0.0598855	−	0.484815i
$277$	49153.9			0.640616			0.320308	−	0.947313i	$-0.396214\pi$
$277$	49153.9			0.640616			0.320308	+	0.947313i	$0.396214\pi$
$278$			65524.8i			0.847845i
$279$	87965.1	−	22068.0i	1.13006	−	0.283501i
$280$	2430.12			0.0309964
$281$			110974.i			1.40543i	0.711473	+	0.702714i	$0.248029\pi$
$281$			110974.i			1.40543i	−0.711473	+	0.702714i	$0.751971\pi$
$282$	−82178.3	+	10150.9i	−1.03338	+	0.127645i
$283$	−149932.			−1.87207			−0.936033	−	0.351913i	$-0.885531\pi$
$283$	−149932.			−1.87207			−0.936033	+	0.351913i	$0.885531\pi$
$284$			42203.9i			0.523258i
$285$	−2496.69	−	20212.5i	−0.0307380	−	0.248846i
$286$	−26767.8			−0.327251
$287$			57483.6i			0.697879i
$288$	−3567.87	−	14221.9i	−0.0430154	−	0.171463i
$289$	39711.0			0.475462
$290$			5688.27i			0.0676370i
$291$	−7508.76	+	927.500i	−0.0886712	+	0.0109529i
$292$	−846.223			−0.00992474
$293$		−	25552.6i		−	0.297645i	−0.988864	−	0.148823i	$-0.952452\pi$
$293$		−	25552.6i		−	0.297645i	0.988864	−	0.148823i	$-0.0475484\pi$
$294$	−6435.56	−	52100.4i	−0.0744546	−	0.602763i
$295$	−2644.43			−0.0303870
$296$		−	44251.9i		−	0.505066i
$297$	−24154.4	−	62516.7i	−0.273832	−	0.708734i
$298$	−121003.			−1.36258
$299$			53203.0i			0.595106i
$300$	42227.5	−	5216.04i	0.469195	−	0.0579560i
$301$	52731.9			0.582024
$302$			73143.8i			0.801981i
$303$	20813.0	+	168496.i	0.226699	+	1.83529i
$304$	24819.4			0.268562
$305$			7852.06i			0.0844081i
$306$	46511.7	−	11668.5i	0.496729	−	0.124616i
$307$	−31951.5			−0.339011			−0.169506	−	0.985529i	$-0.554217\pi$
$307$	−31951.5			−0.339011			−0.169506	+	0.985529i	$0.554217\pi$
$308$			13536.6i			0.142695i
$309$	94663.0	−	11693.0i	0.991433	−	0.122464i
$310$	18479.0			0.192289
$311$		−	157024.i		−	1.62348i	−0.584022	−	0.811738i	$-0.698522\pi$
$311$		−	157024.i		−	1.62348i	0.584022	−	0.811738i	$-0.301478\pi$
$312$	2569.93	+	20805.4i	0.0264005	+	0.213731i
$313$	−17965.9			−0.183383			−0.0916915	−	0.995787i	$-0.529227\pi$
$313$	−17965.9			−0.183383			−0.0916915	+	0.995787i	$0.529227\pi$
$314$			39050.7i			0.396067i
$315$	−2116.78	−	8437.69i	−0.0213332	−	0.0850359i
$316$	76699.0			0.768096
$317$		−	25546.5i		−	0.254222i	−0.991889	−	0.127111i	$-0.959430\pi$
$317$		−	25546.5i		−	0.254222i	0.991889	−	0.127111i	$-0.0405704\pi$
$318$	14.0984	−	1.74146i	0.000139417	−	1.72211e-5i
$319$	−31685.7			−0.311374
$320$		−	2987.61i		−	0.0291758i
$321$	4365.22	+	35339.5i	0.0423639	+	0.342966i
$322$	26905.1			0.259491
$323$			81170.5i			0.778024i
$324$	−46272.3	+	24776.2i	−0.440790	+	0.236018i
$325$	−60832.8			−0.575932
$326$		−	98011.0i		−	0.922231i
$327$	13841.9	−	1709.79i	0.129450	−	0.0159899i
$328$	70670.8			0.656890
$329$		−	59868.3i		−	0.553102i
$330$	−1674.09	−	13553.0i	−0.0153728	−	0.124453i
$331$	−130161.			−1.18803			−0.594013	−	0.804455i	$-0.702457\pi$
$331$	−130161.			−1.18803			−0.594013	+	0.804455i	$0.702457\pi$
$332$		−	63106.7i		−	0.572532i
$333$	−153648.	+	38546.1i	−1.38561	+	0.347610i
$334$	−28483.5			−0.255329
$335$		−	38424.2i		−	0.342385i
$336$	10521.4	−	1299.63i	0.0931954	−	0.0115117i
$337$	136183.			1.19912			0.599561	−	0.800329i	$-0.295342\pi$
$337$	136183.			1.19912			0.599561	+	0.800329i	$0.295342\pi$
$338$			50810.6i			0.444755i
$339$	1837.77	+	14878.1i	0.0159916	+	0.129463i
$340$	9770.79			0.0845224
$341$			102934.i			0.885221i
$342$	−21619.3	−	86176.3i	−0.184837	−	0.736777i
$343$	82146.7			0.698236
$344$		−	64829.0i		−	0.547839i
$345$	−26937.5	+	3327.39i	−0.226318	+	0.0279553i
$346$	−146572.			−1.22433
$347$			150294.i			1.24820i	0.781346	+	0.624098i	$0.214534\pi$
$347$			150294.i			1.24820i	−0.781346	+	0.624098i	$0.785466\pi$
$348$	3042.09	+	24627.8i	0.0251196	+	0.203361i
$349$	65643.1			0.538937			0.269468	−	0.963009i	$-0.413152\pi$
$349$	65643.1			0.538937			0.269468	+	0.963009i	$0.413152\pi$
$350$			30763.5i			0.251130i
$351$	70000.5	−	27045.9i	0.568181	−	0.219527i
$352$	16642.0			0.134314
$353$		−	95511.0i		−	0.766486i	−0.923648	−	0.383243i	$-0.874807\pi$
$353$		−	95511.0i		−	0.766486i	0.923648	−	0.383243i	$-0.125193\pi$
$354$	−11449.3	+	1414.24i	−0.0913631	+	0.0112854i
$355$	30783.4			0.244264
$356$			94723.2i			0.747406i
$357$	4250.35	+	34409.6i	0.0333494	+	0.269987i
$358$	−165387.			−1.29043
$359$		−	229970.i		−	1.78436i	−0.451681	−	0.892179i	$-0.649176\pi$
$359$		−	229970.i		−	1.78436i	0.451681	−	0.892179i	$-0.350824\pi$
$360$	−10373.4	+	2602.39i	−0.0800414	+	0.0200802i
$361$	20070.6			0.154009
$362$			72353.0i			0.552128i
$363$	−55280.2	+	6828.33i	−0.419523	+	0.0518205i
$364$	−15157.1			−0.114396
$365$			617.232i			0.00463300i
$366$	4199.28	+	33996.2i	0.0313482	+	0.253786i
$367$	−64831.4			−0.481341			−0.240671	−	0.970607i	$-0.577367\pi$
$367$	−64831.4			−0.481341			−0.240671	+	0.970607i	$0.577367\pi$
$368$		−	33077.3i		−	0.244250i
$369$	−61558.7	−	245378.i	−0.452102	−	1.80212i
$370$	−32277.2			−0.235772
$371$			10.2709i			7.46210e-5i
$372$	80006.1	−	9882.54i	0.578146	−	0.0714139i
$373$	−254434.			−1.82876			−0.914381	−	0.404854i	$-0.867322\pi$
$373$	−254434.			−1.82876			−0.914381	+	0.404854i	$0.867322\pi$
$374$			54426.8i			0.389108i
$375$	−7828.33	−	63375.8i	−0.0556681	−	0.450673i
$376$	−73602.6			−0.520616
$377$		−	35478.8i		−	0.249624i
$378$	−13677.3	−	35399.6i	−0.0957228	−	0.247751i
$379$	−169347.			−1.17896			−0.589481	−	0.807783i	$-0.700668\pi$
$379$	−169347.			−1.17896			−0.589481	+	0.807783i	$0.700668\pi$
$380$		−	18103.2i		−	0.125368i
$381$	−183854.	+	22710.1i	−1.26656	+	0.156448i
$382$	−29735.0			−0.203770
$383$			158771.i			1.08237i	0.840904	+	0.541184i	$0.182024\pi$
$383$			158771.i			1.08237i	−0.840904	+	0.541184i	$0.817976\pi$
$384$	−1597.77	−	12935.1i	−0.0108356	−	0.0877217i
$385$	9873.56			0.0666120
$386$		−	58663.7i		−	0.393727i
$387$	−225095.	+	56470.1i	−1.50295	+	0.377048i
$388$	−6725.18			−0.0446725
$389$			159932.i			1.05691i	0.848963	+	0.528453i	$0.177228\pi$
$389$			159932.i			1.05691i	−0.848963	+	0.528453i	$0.822772\pi$
$390$	15175.4	−	1874.50i	0.0997723	−	0.0123241i
$391$	108177.			0.707592
$392$		−	46663.4i		−	0.303672i
$393$	−15327.1	−	124084.i	−0.0992376	−	0.803398i
$394$	30039.1			0.193506
$395$		−	55943.9i		−	0.358557i
$396$	−14496.3	−	57783.4i	−0.0924411	−	0.368479i
$397$	−173872.			−1.10318			−0.551592	−	0.834114i	$-0.685979\pi$
$397$	−173872.			−1.10318			−0.551592	+	0.834114i	$0.685979\pi$
$398$		−	124764.i		−	0.787632i
$399$	63753.6	−	7875.00i	0.400460	−	0.0494657i
$400$	37820.9			0.236380
$401$		−	82529.5i		−	0.513240i	−0.966512	−	0.256620i	$-0.917391\pi$
$401$		−	82529.5i		−	0.513240i	0.966512	−	0.256620i	$-0.0826089\pi$
$402$	−20549.2	−	166361.i	−0.127158	−	1.02943i
$403$	−115256.			−0.709668
$404$			150912.i			0.924617i
$405$	18071.7	+	33750.9i	0.110176	+	0.205767i
$406$	−17941.8			−0.108846
$407$		−	179795.i		−	1.08540i
$408$	42303.4	−	5225.42i	0.254130	−	0.0313907i
$409$	−75897.2			−0.453711			−0.226855	−	0.973928i	$-0.572844\pi$
$409$	−75897.2			−0.453711			−0.226855	+	0.973928i	$0.572844\pi$
$410$		−	51547.0i		−	0.306645i
$411$	4118.84	+	33344.9i	0.0243832	+	0.197399i
$412$	84784.4			0.499484
$413$		−	8340.98i		−	0.0489009i
$414$	−114849.	+	28812.4i	−0.670078	+	0.168104i
$415$	−46029.8			−0.267265
$416$			18634.2i			0.107677i
$417$	206926.	−	25560.0i	1.18999	−	0.146990i
$418$	100841.			0.577146
$419$			219259.i			1.24890i	0.781063	+	0.624452i	$0.214678\pi$
$419$			219259.i			1.24890i	−0.781063	+	0.624452i	$0.785322\pi$
$420$	−947.942	−	7674.26i	−0.00537382	−	0.0435049i
$421$	−33161.0			−0.187096			−0.0935478	−	0.995615i	$-0.529821\pi$
$421$	−33161.0			−0.187096			−0.0935478	+	0.995615i	$0.529821\pi$
$422$		−	206508.i		−	1.15961i
$423$	64112.4	+	255558.i	0.358312	+	1.42826i
$424$	12.6271			7.02382e−5
$425$			123691.i			0.684794i
$426$	133279.	−	16462.9i	0.734417	−	0.0907169i
$427$	−24766.8			−0.135836
$428$			31651.6i			0.172786i
$429$	10441.6	+	84532.3i	0.0567353	+	0.459312i
$430$	−47286.0			−0.255738
$431$			131444.i			0.707596i	0.935322	+	0.353798i	$0.115110\pi$
$431$			131444.i			0.707596i	−0.935322	+	0.353798i	$0.884890\pi$
$432$	−43520.6	+	16814.9i	−0.233199	+	0.0901006i
$433$	−56821.0			−0.303063			−0.151532	−	0.988452i	$-0.548421\pi$
$433$	−56821.0			−0.303063			−0.151532	+	0.988452i	$0.548421\pi$
$434$			58285.8i			0.309445i
$435$	17963.5	−	2218.89i	0.0949317	−	0.0117262i
$436$	12397.5			0.0652168
$437$		−	200430.i		−	1.04954i
$438$	330.096	+	2672.36i	0.00172065	+	0.0139298i
$439$	−274702.			−1.42539			−0.712694	−	0.701475i	$-0.752525\pi$
$439$	−274702.			−1.42539			−0.712694	+	0.701475i	$0.752525\pi$
$440$		−	12138.6i		−	0.0626996i
$441$	−162022.	+	40646.7i	−0.833097	+	0.209001i
$442$	−60942.2			−0.311942
$443$			5803.94i			0.0295744i	0.999891	+	0.0147872i	$0.00470708\pi$
$443$			5803.94i			0.0295744i	−0.999891	+	0.0147872i	$0.995293\pi$
$444$	−139747.	+	17261.8i	−0.708884	+	0.0875630i
$445$	69090.7			0.348899
$446$		−	120620.i		−	0.606386i
$447$	47200.9	+	382124.i	0.236230	+	1.91245i
$448$	9423.43			0.0469519
$449$		−	198692.i		−	0.985573i	−0.870150	−	0.492786i	$-0.835978\pi$
$449$		−	198692.i		−	0.985573i	0.870150	−	0.492786i	$-0.164022\pi$
$450$	−32944.3	−	131319.i	−0.162688	−	0.648489i
$451$	287135.			1.41167
$452$			13325.4i			0.0652236i
$453$	230987.	−	28532.0i	1.12562	−	0.139039i
$454$	−75842.6			−0.367961
$455$			11055.5i			0.0534018i
$456$	−9681.58	−	78379.3i	−0.0465604	−	0.376939i
$457$	14736.2			0.0705593			0.0352796	−	0.999377i	$-0.488768\pi$
$457$	14736.2			0.0705593			0.0352796	+	0.999377i	$0.488768\pi$
$458$			86707.2i			0.413356i
$459$	−54992.3	−	142331.i	−0.261021	−	0.675578i
$460$	−24126.4			−0.114019
$461$		−	245531.i		−	1.15533i	−0.816275	−	0.577663i	$-0.803965\pi$
$461$		−	245531.i		−	1.15533i	0.816275	−	0.577663i	$-0.196035\pi$
$462$	42748.4	−	5280.38i	0.200279	−	0.0247390i
$463$	−260276.			−1.21415			−0.607076	−	0.794644i	$-0.707658\pi$
$463$	−260276.			−1.21415			−0.607076	+	0.794644i	$0.707658\pi$
$464$			22057.8i			0.102453i
$465$	−7208.29	−	58356.2i	−0.0333370	−	0.269886i
$466$	65283.1			0.300628
$467$		−	145207.i		−	0.665815i	−0.942959	−	0.332908i	$-0.891970\pi$
$467$		−	145207.i		−	0.665815i	0.942959	−	0.332908i	$-0.108030\pi$
$468$	64700.5	−	16231.6i	0.295404	−	0.0741086i
$469$	121197.			0.550991
$470$			53685.4i			0.243030i
$471$	123321.	−	15232.9i	0.555899	−	0.0686659i
$472$	−10254.5			−0.0460287
$473$		−	263400.i		−	1.17732i
$474$	−29918.8	−	242214.i	−0.133164	−	1.07806i
$475$	229173.			1.01572
$476$			30818.8i			0.136020i
$477$	−10.9990	−	43.8431i	−4.83412e−5	−	0.000192692i
$478$	233867.			1.02356
$479$		−	50569.6i		−	0.220404i	−0.993909	−	0.110202i	$-0.964850\pi$
$479$		−	50569.6i		−	0.220404i	0.993909	−	0.110202i	$-0.0351497\pi$
$480$	−9434.80	+	1165.41i	−0.0409497	+	0.00505819i
$481$	201318.			0.870148
$482$			197245.i			0.849008i
$483$	−10495.1	−	84965.6i	−0.0449878	−	0.364208i
$484$	−49511.4			−0.211356
$485$			4905.32i			0.0208537i
$486$	96292.8	+	136462.i	0.407682	+	0.577750i
$487$	20612.2			0.0869095			0.0434547	−	0.999055i	$-0.486164\pi$
$487$	20612.2			0.0869095			0.0434547	+	0.999055i	$0.486164\pi$
$488$			30448.5i			0.127857i
$489$	−309517.	+	38232.2i	−1.29439	+	0.159887i
$490$	−34036.1			−0.141758
$491$			175814.i			0.729273i	0.931150	+	0.364636i	$0.118807\pi$
$491$			175814.i			0.729273i	−0.931150	+	0.364636i	$0.881193\pi$
$492$	−27567.3	−	223177.i	−0.113884	−	0.921975i
$493$	−72138.7			−0.296807
$494$			112913.i			0.462689i
$495$	−42147.0	+	10573.5i	−0.172011	+	0.0431528i
$496$	71657.0			0.291270
$497$			97096.0i			0.393087i
$498$	−199290.	+	24616.7i	−0.803575	+	0.0992594i
$499$	103187.			0.414405			0.207203	−	0.978298i	$-0.433564\pi$
$499$	103187.			0.414405			0.207203	+	0.978298i	$0.433564\pi$
$500$		−	56762.2i		−	0.227049i
$501$	11110.9	+	89950.3i	0.0442662	+	0.358366i
$502$	223638.			0.887440
$503$		−	451090.i		−	1.78290i	−0.453119	−	0.891450i	$-0.649689\pi$
$503$		−	451090.i		−	1.78290i	0.453119	−	0.891450i	$-0.350311\pi$
$504$	−8208.39	−	32719.4i	−0.0323145	−	0.128808i
$505$	110075.			0.431624
$506$		−	134393.i		−	0.524899i
$507$	160459.	−	19820.2i	0.624234	−	0.0771068i
$508$	−164668.			−0.638091
$509$		−	5894.21i		−	0.0227505i	−0.999935	−	0.0113752i	$-0.996379\pi$
$509$		−	5894.21i		−	0.0227505i	0.999935	−	0.0113752i	$-0.00362093\pi$
$510$	−3811.40	−	30856.0i	−0.0146536	−	0.118631i
$511$	−1946.86			−0.00745576
$512$		−	11585.2i		−	0.0441942i
$513$	−263710.	+	101889.i	−1.00206	+	0.387162i
$514$	−240743.			−0.911228
$515$		−	61841.4i		−	0.233166i
$516$	−204729.	+	25288.6i	−0.768917	+	0.0949784i
$517$	−299047.			−1.11882
$518$		−	101808.i		−	0.379421i
$519$	57174.8	+	462870.i	0.212261	+	1.71840i
$520$	13591.7			0.0502653
$521$			322197.i			1.18699i	0.804839	+	0.593493i	$0.202252\pi$
$521$			322197.i			1.18699i	−0.804839	+	0.593493i	$0.797748\pi$
$522$	76587.6	−	19213.7i	0.281072	−	0.0705131i
$523$	510326.			1.86571			0.932856	−	0.360250i	$-0.117309\pi$
$523$	510326.			1.86571			0.932856	+	0.360250i	$0.117309\pi$
$524$		−	111135.i		−	0.404752i
$525$	97150.4	−	12000.2i	0.352473	−	0.0435383i
$526$	165765.			0.599132
$527$			234350.i			0.843809i
$528$	−6491.74	−	52555.2i	−0.0232859	−	0.188516i
$529$	12724.9			0.0454719
$530$		−	9.21018i		−	3.27881e-5i
$531$	8932.27	+	35604.9i	0.0316791	+	0.126276i
$532$	57100.6			0.201752
$533$			321508.i			1.13172i
$534$	299134.	−	36949.7i	1.04902	−	0.129577i
$535$	23086.6			0.0806588
$536$		−	149000.i		−	0.518629i
$537$	64514.3	+	522289.i	0.223721	+	1.81118i
$538$	−139064.			−0.480453
$539$		−	189593.i		−	0.652598i
$540$	12264.7	+	31743.7i	0.0420602	+	0.108861i
$541$	165093.			0.564070			0.282035	−	0.959404i	$-0.408991\pi$
$541$	165093.			0.564070			0.282035	+	0.959404i	$0.408991\pi$
$542$			249457.i			0.849175i
$543$	228489.	−	28223.5i	0.774937	−	0.0957220i
$544$	37888.8			0.128031
$545$		−	9042.65i		−	0.0304441i
$546$	5912.48	+	47865.7i	0.0198328	+	0.160561i
$547$	−174156.			−0.582055			−0.291028	−	0.956715i	$-0.593997\pi$
$547$	−174156.			−0.582055			−0.291028	+	0.956715i	$0.593997\pi$
$548$			29865.2i			0.0994498i
$549$	105721.	−	26522.5i	0.350766	−	0.0879974i
$550$	153666.			0.507987
$551$			133658.i			0.440241i
$552$	−104457.	+	12902.8i	−0.342816	+	0.0423454i
$553$	176457.			0.577016
$554$		−	139028.i		−	0.452984i
$555$	12590.7	+	101931.i	0.0408756	+	0.330917i
$556$	185332.			0.599517
$557$			230449.i			0.742786i	0.928476	+	0.371393i	$0.121120\pi$
$557$			230449.i			0.742786i	−0.928476	+	0.371393i	$0.878880\pi$
$558$	−62417.7	−	248803.i	−0.200465	−	0.799074i
$559$	294931.			0.943838
$560$		−	6873.41i		−	0.0219178i
$561$	171879.	−	21230.9i	0.546131	−	0.0674593i
$562$	313882.			0.993787
$563$			347408.i			1.09603i	0.836468	+	0.548016i	$0.184617\pi$
$563$			347408.i			1.09603i	−0.836468	+	0.548016i	$0.815383\pi$
$564$	28711.0	+	232435.i	0.0902588	+	0.730708i
$565$	9719.53			0.0304473
$566$			424071.i			1.32375i
$567$	−106456.	+	57001.2i	−0.331134	+	0.177304i
$568$	119371.			0.369999
$569$		−	222774.i		−	0.688081i	−0.938955	−	0.344040i	$-0.888204\pi$
$569$		−	222774.i		−	0.688081i	0.938955	−	0.344040i	$-0.111796\pi$
$570$	−57169.5	+	7061.71i	−0.175960	+	0.0217350i
$571$	−12033.9			−0.0369092			−0.0184546	−	0.999830i	$-0.505875\pi$
$571$	−12033.9			−0.0369092			−0.0184546	+	0.999830i	$0.505875\pi$
$572$			75710.9i			0.231401i
$573$	11599.1	+	93902.5i	0.0353275	+	0.286001i
$574$	162588.			0.493475
$575$		−	305423.i		−	0.923774i
$576$	−40225.5	+	10091.5i	−0.121243	+	0.0304165i
$577$	35228.3			0.105813			0.0529066	−	0.998599i	$-0.483151\pi$
$577$	35228.3			0.105813			0.0529066	+	0.998599i	$0.483151\pi$
$578$		−	112320.i		−	0.336202i
$579$	−185259.	+	22883.6i	−0.552614	+	0.0682601i
$580$	16088.9			0.0478266
$581$		−	145186.i		−	0.430103i
$582$	2623.37	+	21238.0i	0.00774485	+	0.0627000i
$583$	51.3040			0.000150944
$584$			2393.48i			0.00701785i
$585$	−11839.2	−	47192.3i	−0.0345949	−	0.137898i
$586$	−72273.5			−0.210467
$587$		−	1083.49i		−	0.00314446i	−0.999999	−	0.00157223i	$-0.999500\pi$
$587$		−	1083.49i		−	0.00314446i	0.999999	−	0.00157223i	$-0.000500457\pi$
$588$	−147362.	+	18202.5i	−0.426217	+	0.0526474i
$589$	434201.			1.25158
$590$			7479.57i			0.0214868i
$591$	−11717.7	−	94862.8i	−0.0335480	−	0.271594i
$592$	−125163.			−0.357136
$593$		−	337268.i		−	0.959103i	−0.877514	−	0.479551i	$-0.840799\pi$
$593$		−	337268.i		−	0.959103i	0.877514	−	0.479551i	$-0.159201\pi$
$594$	−176824.	+	68319.1i	−0.501151	+	0.193628i
$595$	22479.1			0.0634958
$596$			342248.i			0.963492i
$597$	−394003.	+	48668.1i	−1.10548	+	0.136551i
$598$	150481.			0.420803
$599$			342609.i			0.954871i	0.878667	+	0.477435i	$0.158434\pi$
$599$			342609.i			0.954871i	−0.878667	+	0.477435i	$0.841566\pi$
$600$	−14753.2	−	119437.i	−0.0409811	−	0.331771i
$601$	266078.			0.736649			0.368324	−	0.929697i	$-0.379932\pi$
$601$	266078.			0.736649			0.368324	+	0.929697i	$0.379932\pi$
$602$		−	149148.i		−	0.411553i
$603$	−517348.	+	129788.i	−1.42281	+	0.356944i
$604$	206882.			0.567086
$605$			36113.4i			0.0986638i
$606$	476578.	−	58868.0i	1.29774	−	0.160300i
$607$	49853.3			0.135306			0.0676530	−	0.997709i	$-0.478449\pi$
$607$	49853.3			0.135306			0.0676530	+	0.997709i	$0.478449\pi$
$608$		−	70199.9i		−	0.189902i
$609$	6998.75	+	56659.8i	0.0188706	+	0.152771i
$610$	22209.0			0.0596855
$611$		−	334845.i		−	0.896937i
$612$	−33003.5	−	131555.i	−0.0881166	−	0.351241i
$613$	390086.			1.03810			0.519051	−	0.854743i	$-0.326286\pi$
$613$	390086.			1.03810			0.519051	+	0.854743i	$0.326286\pi$
$614$			90372.4i			0.239717i
$615$	−162784.	+	20107.5i	−0.430390	+	0.0531628i
$616$	38287.4			0.100901
$617$			400521.i			1.05210i	0.850455	+	0.526048i	$0.176327\pi$
$617$			400521.i			1.05210i	−0.850455	+	0.526048i	$0.823673\pi$
$618$	−33072.8	−	267747.i	−0.0865951	−	0.701049i
$619$	−349779.			−0.912878			−0.456439	−	0.889755i	$-0.650875\pi$
$619$	−349779.			−0.912878			−0.456439	+	0.889755i	$0.650875\pi$
$620$		−	52266.4i		−	0.135969i
$621$	135789.	+	351451.i	0.352113	+	0.911342i
$622$	−444132.			−1.14797
$623$			217924.i			0.561473i
$624$	58846.5	−	7268.86i	0.151130	−	0.0186680i
$625$	327942.			0.839532
$626$			50815.1i			0.129671i
$627$	−39336.3	−	318455.i	−0.100059	−	0.810052i
$628$	110452.			0.280062
$629$		−	409339.i		−	1.03462i
$630$	−23865.4	+	5987.17i	−0.0601295	+	0.0150848i
$631$	308182.			0.774013			0.387006	−	0.922077i	$-0.373509\pi$
$631$	308182.			0.774013			0.387006	+	0.922077i	$0.373509\pi$
$632$		−	216937.i		−	0.543126i
$633$	−652149.	+	80554.9i	−1.62757	+	0.201041i
$634$	−72256.4			−0.179762
$635$			120108.i			0.297869i
$636$	−4.92560	−	39.8762i	−1.21771e−5	−	9.85825e-5i
$637$	212289.			0.523178
$638$			89620.8i			0.220175i
$639$	−103979.	−	414471.i	−0.254651	−	1.01506i
$640$	−8450.23			−0.0206304
$641$		−	690959.i		−	1.68165i	−0.541304	−	0.840827i	$-0.682069\pi$
$641$		−	690959.i		−	1.68165i	0.541304	−	0.840827i	$-0.317931\pi$
$642$	99955.2	−	12346.7i	0.242513	−	0.0299558i
$643$	658611.			1.59297			0.796484	−	0.604659i	$-0.206691\pi$
$643$	658611.			1.59297			0.796484	+	0.604659i	$0.206691\pi$
$644$		−	76099.0i		−	0.183488i
$645$	18445.4	+	149328.i	0.0443372	+	0.358941i
$646$	229585.			0.550146
$647$			76205.6i			0.182045i	0.995849	+	0.0910224i	$0.0290135\pi$
$647$			76205.6i			0.182045i	−0.995849	+	0.0910224i	$0.970987\pi$
$648$	70077.8	+	130878.i	0.166890	+	0.311685i
$649$	−41663.9			−0.0989169
$650$			172061.i			0.407245i
$651$	184065.	−	22736.2i	0.434320	−	0.0536482i
$652$	−277217.			−0.652116
$653$			587035.i			1.37669i	0.725382	+	0.688347i	$0.241663\pi$
$653$			587035.i			1.37669i	−0.725382	+	0.688347i	$0.758337\pi$
$654$	−4836.01	−	39150.9i	−0.0113066	−	0.0915348i
$655$	−81061.5			−0.188944
$656$		−	199887.i		−	0.464491i
$657$	8310.48	−	2084.87i	0.0192529	−	0.00483001i
$658$	−169333.			−0.391102
$659$		−	500449.i		−	1.15236i	−0.817322	−	0.576181i	$-0.804542\pi$
$659$		−	500449.i		−	1.15236i	0.817322	−	0.576181i	$-0.195458\pi$
$660$	−38333.6	+	4735.05i	−0.0880018	+	0.0108702i
$661$	−95665.5			−0.218954			−0.109477	−	0.993989i	$-0.534918\pi$
$661$	−95665.5			−0.218954			−0.109477	+	0.993989i	$0.534918\pi$
$662$			368152.i			0.840061i
$663$	23772.4	+	192454.i	0.0540811	+	0.437825i
$664$	−178493.			−0.404841
$665$		−	41649.0i		−	0.0941805i
$666$	109025.	+	434583.i	0.245797	+	0.979771i
$667$	178128.			0.400387
$668$			80563.5i			0.180545i
$669$	−380915.	+	47051.5i	−0.851091	+	0.105129i
$670$	−108680.			−0.242103
$671$			123712.i			0.274769i
$672$	−3675.90	−	29759.0i	−0.00814001	−	0.0658991i
$673$	−699854.			−1.54517			−0.772587	−	0.634909i	$-0.781037\pi$
$673$	−699854.			−1.54517			−0.772587	+	0.634909i	$0.781037\pi$
$674$		−	385184.i		−	0.847908i
$675$	−401852.	+	155262.i	−0.881979	+	0.340768i
$676$	143714.			0.314489
$677$		−	750216.i		−	1.63685i	−0.574613	−	0.818425i	$-0.694847\pi$
$677$		−	750216.i		−	1.63685i	0.574613	−	0.818425i	$-0.305153\pi$
$678$	42081.5	−	5198.00i	0.0915444	−	0.0113078i
$679$	−15472.2			−0.0335593
$680$		−	27636.0i		−	0.0597664i
$681$	29584.8	+	239509.i	0.0637931	+	0.516450i
$682$	291143.			0.625946
$683$			709646.i			1.52125i	0.649192	+	0.760625i	$0.275107\pi$
$683$			709646.i			1.52125i	−0.649192	+	0.760625i	$0.724893\pi$
$684$	−243744.	+	61148.5i	−0.520980	+	0.130699i
$685$	21783.5			0.0464245
$686$		−	232346.i		−	0.493727i
$687$	273820.	−	33822.8i	0.580164	−	0.0716632i
$688$	−183364.			−0.387381
$689$			57.4455i			0.000121009i
$690$	9411.27	+	76190.8i	0.0197674	+	0.160031i
$691$	415804.			0.870829			0.435414	−	0.900230i	$-0.356602\pi$
$691$	415804.			0.870829			0.435414	+	0.900230i	$0.356602\pi$
$692$			414567.i			0.865731i
$693$	−33350.7	−	132939.i	−0.0694445	−	0.276812i
$694$	425096.			0.882609
$695$		−	135181.i		−	0.279863i
$696$	69658.1	−	8604.32i	0.143798	−	0.0177623i
$697$	653720.			1.34563
$698$		−	185667.i		−	0.381086i
$699$	−25465.7	−	206163.i	−0.0521196	−	0.421945i
$700$	87012.2			0.177576
$701$		−	50726.5i		−	0.103228i	−0.998667	−	0.0516142i	$-0.983563\pi$
$701$		−	50726.5i		−	0.103228i	0.998667	−	0.0516142i	$-0.0164366\pi$
$702$	−76497.4	−	197991.i	−0.155229	−	0.401765i
$703$	−758418.			−1.53461
$704$		−	47070.8i		−	0.0949744i
$705$	169537.	−	20941.7i	0.341104	−	0.0421340i
$706$	−270146.			−0.541987
$707$			347195.i			0.694600i
$708$	4000.07	+	32383.4i	0.00797997	+	0.0646035i
$709$	−86836.5			−0.172747			−0.0863733	−	0.996263i	$-0.527528\pi$
$709$	−86836.5			−0.172747			−0.0863733	+	0.996263i	$0.527528\pi$
$710$		−	87068.5i		−	0.172721i
$711$	−753236.	+	188966.i	−1.49002	+	0.373804i
$712$	267918.			0.528496
$713$		−	578667.i		−	1.13828i
$714$	97325.0	−	12021.8i	0.190910	−	0.0235816i
$715$	55223.2			0.108021
$716$			467785.i			0.912474i
$717$	−91227.0	−	738547.i	−0.177454	−	1.43661i
$718$	−650453.			−1.26173
$719$		−	251293.i		−	0.486097i	−0.970014	−	0.243048i	$-0.921853\pi$
$719$		−	251293.i		−	0.486097i	0.970014	−	0.243048i	$-0.0781474\pi$
$720$	7360.67	+	29340.3i	0.0141988	+	0.0565978i
$721$	195058.			0.375227
$722$		−	56768.3i		−	0.108901i
$723$	622895.	−	76941.5i	1.19162	−	0.147192i
$724$	204645.			0.390413
$725$			203673.i			0.387487i
$726$	19313.4	+	156356.i	0.0366426	+	0.296648i
$727$	728266.			1.37791			0.688955	−	0.724804i	$-0.258070\pi$
$727$	728266.			1.37791			0.688955	+	0.724804i	$0.258070\pi$
$728$			42870.7i			0.0808905i
$729$	393383.	−	357322.i	0.740220	−	0.672364i
$730$	1745.80			0.00327603
$731$		−	599682.i		−	1.12224i
$732$	96155.7	−	11877.4i	0.179454	−	0.0221665i
$733$	−220300.			−0.410022			−0.205011	−	0.978760i	$-0.565723\pi$
$733$	−220300.			−0.410022			−0.205011	+	0.978760i	$0.565723\pi$
$734$			183371.i			0.340360i
$735$	13276.8	+	107485.i	0.0245765	+	0.198964i
$736$	−93556.7			−0.172711
$737$		−	605387.i		−	1.11455i
$738$	−694035.	+	174114.i	−1.27429	+	0.319684i
$739$	−1.04157e6			−1.90722			−0.953611	−	0.301043i	$-0.902665\pi$
$739$	−1.04157e6			−1.90722			−0.953611	+	0.301043i	$0.902665\pi$
$740$			91293.6i			0.166716i
$741$	356576.	−	44045.1i	0.649406	−	0.0802161i
$742$	29.0505			5.27650e−5
$743$			66611.3i			0.120662i	0.998178	+	0.0603310i	$0.0192156\pi$
$743$			66611.3i			0.120662i	−0.998178	+	0.0603310i	$0.980784\pi$
$744$	−27952.0	−	226292.i	−0.0504972	−	0.408811i
$745$	249634.			0.449771
$746$			719648.i			1.29313i
$747$	155478.	+	619751.i	0.278630	+	1.11065i
$748$	153942.			0.275141
$749$			72819.1i			0.129802i
$750$	−179254.	+	22141.9i	−0.318674	+	0.0393633i
$751$	648834.			1.15041			0.575206	−	0.818008i	$-0.304922\pi$
$751$	648834.			1.15041			0.575206	+	0.818008i	$0.304922\pi$
$752$			208179.i			0.368131i
$753$	−87237.1	−	706246.i	−0.153855	−	1.24556i
$754$	−100349.			−0.176511
$755$		−	150899.i		−	0.264723i
$756$	−100125.	+	38685.1i	−0.175186	+	0.0676863i
$757$	225381.			0.393301			0.196650	−	0.980474i	$-0.436994\pi$
$757$	225381.			0.393301			0.196650	+	0.980474i	$0.436994\pi$
$758$			478986.i			0.833651i
$759$	−424410.	+	52424.2i	−0.736720	+	0.0910014i
$760$	−51203.6			−0.0886488
$761$		−	838419.i		−	1.44774i	−0.689934	−	0.723872i	$-0.742360\pi$
$761$		−	838419.i		−	1.44774i	0.689934	−	0.723872i	$-0.257640\pi$
$762$	64233.9	+	520019.i	0.110625	+	0.895590i
$763$	28522.1			0.0489928
$764$			84103.3i			0.144087i
$765$	−95955.8	+	24072.6i	−0.163964	+	0.0411340i
$766$	449073.			0.765349
$767$		−	46651.4i		−	0.0793001i
$768$	−36585.9	+	4519.18i	−0.0620286	+	0.00766191i
$769$	−384416.			−0.650053			−0.325026	−	0.945705i	$-0.605373\pi$
$769$	−384416.			−0.650053			−0.325026	+	0.945705i	$0.605373\pi$
$770$		−	27926.7i		−	0.0471018i
$771$	93909.2	+	760261.i	0.157979	+	1.27895i
$772$	−165926.			−0.278407
$773$		−	123434.i		−	0.206574i	−0.994652	−	0.103287i	$-0.967064\pi$
$773$		−	123434.i		−	0.206574i	0.994652	−	0.103287i	$-0.0329360\pi$
$774$	159722.	+	636665.i	0.266613	+	1.06274i
$775$	661653.			1.10161
$776$			19021.7i			0.0315883i
$777$	−321507.	+	39713.2i	−0.532535	+	0.0657799i
$778$	452356.			0.747345
$779$		−	1.21120e6i		−	1.99591i
$780$	−5301.87	−	42922.4i	−0.00871445	−	0.0705497i
$781$	485003.			0.795137
$782$		−	305972.i		−	0.500343i
$783$	−90551.8	−	234367.i	−0.147698	−	0.382273i
$784$	−131984.			−0.214728
$785$		−	80563.2i		−	0.130737i
$786$	−350963.	+	43351.7i	−0.568088	+	0.0701716i
$787$	527357.			0.851443			0.425721	−	0.904854i	$-0.360020\pi$
$787$	527357.			0.851443			0.425721	+	0.904854i	$0.360020\pi$
$788$		−	84963.3i		−	0.136829i
$789$	−64661.9	−	523484.i	−0.103871	−	0.840910i
$790$	−158233.			−0.253538
$791$			30657.1i			0.0489979i
$792$	−163436.	+	41001.6i	−0.260554	+	0.0653658i
$793$	−138521.			−0.220278
$794$			491783.i			0.780069i
$795$	−29.0856	+	3.59272i	−4.60196e−5	+	5.68445e-6i
$796$	−352886.			−0.556940
$797$		−	328839.i		−	0.517686i	−0.965919	−	0.258843i	$-0.916659\pi$
$797$		−	328839.i		−	0.517686i	0.965919	−	0.258843i	$-0.0833413\pi$
$798$	−22273.9	−	180323.i	−0.0349776	−	0.283168i
$799$	−680839.			−1.06648
$800$		−	106974.i		−	0.167146i
$801$	−233373.	−	930246.i	−0.363735	−	1.44988i
$802$	−233429.			−0.362915
$803$			9724.71i			0.0150815i
$804$	−470539.	+	58122.0i	−0.727920	+	0.0899143i
$805$	−55506.3			−0.0856546
$806$			325995.i			0.501811i
$807$	54246.3	+	439162.i	0.0832958	+	0.674338i
$808$	426844.			0.653803
$809$			666332.i			1.01811i	0.860735	+	0.509053i	$0.170004\pi$
$809$			666332.i			1.01811i	−0.860735	+	0.509053i	$0.829996\pi$
$810$	95461.8	−	51114.4i	0.145499	−	0.0779065i
$811$	97916.2			0.148872			0.0744360	−	0.997226i	$-0.476284\pi$
$811$	97916.2			0.148872			0.0744360	+	0.997226i	$0.476284\pi$
$812$			50747.1i			0.0769660i
$813$	787781.	−	97308.5i	1.19186	−	0.147221i
$814$	−508538.			−0.767494
$815$			202201.i			0.304416i
$816$	−14779.7	−	119652.i	−0.0221966	−	0.179697i
$817$	−1.11108e6			−1.66457
$818$			214670.i			0.320822i
$819$	148853.	−	37343.0i	0.221916	−	0.0556726i
$820$	−145797.			−0.216831
$821$			529043.i			0.784882i	0.919777	+	0.392441i	$0.128369\pi$
$821$			529043.i			0.784882i	−0.919777	+	0.392441i	$0.871631\pi$
$822$	94313.6	−	11649.8i	0.139582	−	0.0172415i
$823$	−115727.			−0.170858			−0.0854288	−	0.996344i	$-0.527226\pi$
$823$	−115727.			−0.170858			−0.0854288	+	0.996344i	$0.527226\pi$
$824$		−	239806.i		−	0.353188i
$825$	−59942.2	−	485274.i	−0.0880694	−	0.712984i
$826$	−23591.8			−0.0345782
$827$			1.09630e6i			1.60294i	0.598036	+	0.801469i	$0.295948\pi$
$827$			1.09630e6i			1.60294i	−0.598036	+	0.801469i	$0.704052\pi$
$828$	81493.7	+	324841.i	0.118868	+	0.473817i
$829$	−460059.			−0.669429			−0.334714	−	0.942320i	$-0.608640\pi$
$829$	−460059.			−0.669429			−0.334714	+	0.942320i	$0.608640\pi$
$830$			130192.i			0.188985i
$831$	−439048.	+	54232.2i	−0.635784	+	0.0785335i
$832$	52705.6			0.0761394
$833$		−	431646.i		−	0.622068i
$834$	−72294.6	−	585276.i	−0.103938	−	0.841450i
$835$	58762.7			0.0842808
$836$		−	285222.i		−	0.408104i
$837$	−761366.	+	294167.i	−1.08678	+	0.419897i
$838$	620158.			0.883109
$839$		−	270241.i		−	0.383908i	−0.981404	−	0.191954i	$-0.938518\pi$
$839$		−	270241.i		−	0.383908i	0.981404	−	0.191954i	$-0.0614824\pi$
$840$	−21706.1	+	2681.19i	−0.0307626	+	0.00379987i
$841$	588495.			0.832053
$842$			93793.5i			0.132297i
$843$	−122439.	−	991232.i	−0.172292	−	1.39483i
$844$	−584093.			−0.819969
$845$		−	104824.i		−	0.146808i
$846$	722827.	−	181337.i	1.00994	−	0.253365i
$847$	−113908.			−0.158777
$848$		−	35.7149i		−	4.96659e-5i
$849$	1.33921e6	−	165422.i	1.85795	−	0.229498i
$850$	349851.			0.484222
$851$			1.01076e6i			1.39569i
$852$	−46564.2	−	376970.i	−0.0641465	−	0.519311i
$853$	−934159.			−1.28387			−0.641937	−	0.766757i	$-0.721869\pi$
$853$	−934159.			−1.28387			−0.641937	+	0.766757i	$0.721869\pi$
$854$			70051.0i			0.0960503i
$855$	44601.5	+	177786.i	0.0610122	+	0.243200i
$856$	89524.3			0.122178
$857$		−	854839.i		−	1.16392i	−0.813218	−	0.581960i	$-0.802286\pi$
$857$		−	854839.i		−	1.16392i	0.813218	−	0.581960i	$-0.197714\pi$
$858$	239093.	−	29533.4i	0.324783	−	0.0401179i
$859$	−1.01923e6			−1.38130			−0.690649	−	0.723190i	$-0.742675\pi$
$859$	−1.01923e6			−1.38130			−0.690649	+	0.723190i	$0.742675\pi$
$860$			133745.i			0.180834i
$861$	−63422.5	−	513450.i	−0.0855534	−	0.692615i
$862$	371779.			0.500346
$863$		−	928559.i		−	1.24678i	−0.781913	−	0.623388i	$-0.785756\pi$
$863$		−	928559.i		−	1.24678i	0.781913	−	0.623388i	$-0.214244\pi$
$864$	47559.8	+	123095.i	0.0637107	+	0.164897i
$865$	302384.			0.404135
$866$			160714.i			0.214298i
$867$	−354704.	+	43813.8i	−0.471876	+	0.0582871i
$868$	164857.			0.218811
$869$		−	881417.i		−	1.16719i
$870$	−6275.96	−	50808.3i	−0.00829166	−	0.0671269i
$871$	677856.			0.893514
$872$		−	35065.3i		−	0.0461152i
$873$	66045.8	−	16569.1i	0.0866596	−	0.0217405i
$874$	−566901.			−0.742137
$875$		−	130589.i		−	0.170566i
$876$	7558.57	−	933.651i	0.00984989	−	0.00121668i
$877$	265816.			0.345606			0.172803	−	0.984956i	$-0.444718\pi$
$877$	265816.			0.345606			0.172803	+	0.984956i	$0.444718\pi$
$878$			776975.i			1.00790i
$879$	28192.5	+	228238.i	0.0364885	+	0.295400i
$880$	−34333.3			−0.0443353
$881$			362393.i			0.466904i	0.972368	+	0.233452i	$0.0750021\pi$
$881$			362393.i			0.466904i	−0.972368	+	0.233452i	$0.924998\pi$
$882$	114966.	+	458266.i	0.147786	+	0.589089i
$883$	231036.			0.296318			0.148159	−	0.988964i	$-0.452665\pi$
$883$	231036.			0.296318			0.148159	+	0.988964i	$0.452665\pi$
$884$			172370.i			0.220576i
$885$	23620.3	−	2917.64i	0.0301578	−	0.00372516i
$886$	16416.0			0.0209122
$887$		−	363220.i		−	0.461660i	−0.972994	−	0.230830i	$-0.925856\pi$
$887$		−	363220.i		−	0.461660i	0.972994	−	0.230830i	$-0.0741441\pi$
$888$	48823.8	+	395263.i	0.0619164	+	0.501257i
$889$	−378843.			−0.479353
$890$		−	195418.i		−	0.246709i
$891$	284726.	+	531757.i	0.358651	+	0.669819i
$892$	−341165.			−0.428780
$893$			1.26145e6i			1.58186i
$894$	1.08081e6	−	133504.i	1.35231	−	0.167040i
$895$	341201.			0.425955
$896$		−	26653.5i		−	0.0332000i
$897$	−58699.7	−	475216.i	−0.0729544	−	0.590617i
$898$	−561987.			−0.696905
$899$			385888.i			0.477465i
$900$	−371426.	+	93180.6i	−0.458551	+	0.115038i
$901$	116.804			0.000143882
$902$		−	812142.i		−	0.998203i
$903$	−471008.	+	58179.9i	−0.577634	+	0.0713506i
$904$	37690.1			0.0461201
$905$		−	149267.i		−	0.182250i
$906$	−80700.7	−	653329.i	−0.0983153	−	0.795932i
$907$	−1.19620e6			−1.45409			−0.727043	−	0.686592i	$-0.759106\pi$
$907$	−1.19620e6			−1.45409			−0.727043	+	0.686592i	$0.759106\pi$
$908$			214515.i			0.260188i
$909$	−371808.	−	1.48206e6i	−0.449978	−	1.79365i
$910$	31269.7			0.0377608
$911$			1.05487e6i			1.27105i	0.772080	+	0.635525i	$0.219216\pi$
$911$			1.05487e6i			1.27105i	−0.772080	+	0.635525i	$0.780784\pi$
$912$	−221690.	+	27383.7i	−0.266536	+	0.0329232i
$913$	−725216.			−0.870013
$914$		−	41680.4i		−	0.0498929i
$915$	−8663.30	−	70135.5i	−0.0103476	−	0.0837714i
$916$	245245.			0.292287
$917$		−	255682.i		−	0.304062i
$918$	−402574.	+	155542.i	−0.477706	+	0.184570i
$919$	227019.			0.268801			0.134401	−	0.990927i	$-0.457089\pi$
$919$	227019.			0.268801			0.134401	+	0.990927i	$0.457089\pi$
$920$			68239.9i			0.0806237i
$921$	285394.	−	35252.5i	0.336454	−	0.0415596i
$922$	−694467.			−0.816939
$923$			543061.i			0.637449i
$924$	−14935.2	−	120911.i	−0.0174931	−	0.141619i
$925$	−1.15571e6			−1.35072
$926$			736173.i			0.858535i
$927$	−832640.	+	208886.i	−0.968942	+	0.243081i
$928$	62388.9			0.0724455
$929$			1.45378e6i			1.68449i	0.539095	+	0.842245i	$0.318766\pi$
$929$			1.45378e6i			1.68449i	−0.539095	+	0.842245i	$0.681234\pi$
$930$	−165056.	+	20388.1i	−0.190838	+	0.0235728i
$931$	−799748.			−0.922686
$932$		−	184649.i		−	0.212576i
$933$	173247.	+	1.40256e6i	0.199023	+	1.61123i
$934$	−410708.			−0.470803
$935$		−	112285.i		−	0.128439i
$936$	−45909.8	−	183001.i	−0.0524027	−	0.208882i
$937$	−1.20138e6			−1.36836			−0.684181	−	0.729312i	$-0.739840\pi$
$937$	−1.20138e6			−1.36836			−0.684181	+	0.729312i	$0.739840\pi$
$938$		−	342795.i		−	0.389609i
$939$	160473.	−	19822.0i	0.182000	−	0.0224810i
$940$	151845.			0.171848
$941$			1.18728e6i			1.34083i	0.741988	+	0.670413i	$0.233883\pi$
$941$			1.18728e6i			1.34083i	−0.741988	+	0.670413i	$0.766117\pi$
$942$	−43085.2	−	348805.i	−0.0485541	−	0.393080i
$943$	−1.61419e6			−1.81523
$944$			29004.0i			0.0325472i
$945$	28216.8	+	73030.9i	0.0315969	+	0.0817793i
$946$	−745009.			−0.832490
$947$			238948.i			0.266443i	0.991086	+	0.133221i	$0.0425321\pi$
$947$			238948.i			0.266443i	−0.991086	+	0.133221i	$0.957468\pi$
$948$	−685084.	+	84623.2i	−0.762302	+	0.0941613i
$949$	−10888.8			−0.0120906
$950$		−	648199.i		−	0.718226i
$951$	28185.8	+	228184.i	0.0311652	+	0.252304i
$952$	87168.6			0.0961803
$953$			543234.i			0.598137i	0.954232	+	0.299069i	$0.0966759\pi$
$953$			543234.i			0.598137i	−0.954232	+	0.299069i	$0.903324\pi$
$954$	−124.007	+	31.1099i	−0.000136254	+	3.41824e-5i
$955$	61344.6			0.0672620
$956$		−	661475.i		−	0.723766i
$957$	283021.	−	34959.4i	0.309025	−	0.0381715i
$958$	−143032.			−0.155849
$959$			68709.0i			0.0747096i
$960$	3296.27	+	26685.6i	0.00357668	+	0.0289558i
$961$	330076.			0.357410
$962$		−	569414.i		−	0.615288i
$963$	−77981.2	−	310840.i	−0.0840887	−	0.335185i
$964$	557893.			0.600339
$965$			121026.i			0.129964i
$966$	−240319.	+	29684.8i	−0.257534	+	0.0318111i
$967$	−1.45047e6			−1.55116			−0.775580	−	0.631250i	$-0.782542\pi$
$967$	−1.45047e6			−1.55116			−0.775580	+	0.631250i	$0.782542\pi$
$968$			140039.i			0.149451i
$969$	−89556.7	−	725024.i	−0.0953785	−	0.772156i
$970$	13874.3			0.0147458
$971$		−	1.16098e6i		−	1.23136i	−0.787995	−	0.615681i	$-0.788881\pi$
$971$		−	1.16098e6i		−	1.23136i	0.787995	−	0.615681i	$-0.211119\pi$
$972$	385974.	−	272357.i	0.408531	−	0.288275i
$973$	426383.			0.450375
$974$		−	58300.2i		−	0.0614543i
$975$	543366.	−	67117.8i	0.571588	−	0.0706038i
$976$	86121.3			0.0904088
$977$		−	565931.i		−	0.592891i	−0.955050	−	0.296445i	$-0.904199\pi$
$977$		−	565931.i		−	0.592891i	0.955050	−	0.296445i	$-0.0958012\pi$
$978$	108137.	+	875446.i	0.113057	+	0.915275i
$979$	1.08855e6			1.13575
$980$			96268.7i			0.100238i
$981$	−121751.	+	30544.0i	−0.126513	+	0.0317387i
$982$	497277.			0.515674
$983$			270237.i			0.279665i	0.990175	+	0.139832i	$0.0446564\pi$
$983$			270237.i			0.279665i	−0.990175	+	0.139832i	$0.955344\pi$
$984$	−631240.	+	77972.2i	−0.651935	+	0.0805285i
$985$	−61971.9			−0.0638737
$986$			204039.i			0.209874i
$987$	66053.6	+	534750.i	0.0678051	+	0.548930i
$988$	319366.			0.327171
$989$			1.48076e6i			1.51388i
$990$	29906.4	+	119210.i	0.0305136	+	0.121630i
$991$	308805.			0.314440			0.157220	−	0.987564i	$-0.449747\pi$
$991$	308805.			0.314440			0.157220	+	0.987564i	$0.449747\pi$
$992$		−	202677.i		−	0.205959i
$993$	1.16262e6	−	143609.i	1.17907	−	0.145641i
$994$	274629.			0.277954
$995$			257394.i			0.259987i
$996$	69626.6	+	563677.i	0.0701870	+	0.568213i
$997$	−206210.			−0.207453			−0.103726	−	0.994606i	$-0.533077\pi$
$997$	−206210.			−0.207453			−0.103726	+	0.994606i	$0.533077\pi$
$998$		−	291858.i		−	0.293029i
$999$	1.32988e6	−	513821.i	1.33254	−	0.514850i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.5.b.a.119.1	✓	76
3.2	odd	2	inner	354.5.b.a.119.39	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.5.b.a.119.1	✓	76	1.1	even	1	trivial
354.5.b.a.119.39	yes	76	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	354.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.82843i q^{2} +(-8.93212 + 1.10332i) q^{3} -8.00000 q^{4} +5.83517i q^{5} +(3.12065 + 25.2638i) q^{6} -18.4051 q^{7} +22.6274i q^{8} +(78.5654 - 19.7099i) q^{9} +O(q^{10})\)	\(q-2.82843i q^{2} +(-8.93212 + 1.10332i) q^{3} -8.00000 q^{4} +5.83517i q^{5} +(3.12065 + 25.2638i) q^{6} -18.4051 q^{7} +22.6274i q^{8} +(78.5654 - 19.7099i) q^{9} +16.5043 q^{10} +91.9352i q^{11} +(71.4569 - 8.82652i) q^{12} -102.941 q^{13} +52.0576i q^{14} +(-6.43803 - 52.1204i) q^{15} +64.0000 q^{16} +209.308i q^{17} +(-55.7480 - 222.216i) q^{18} +387.804 q^{19} -46.6813i q^{20} +(164.397 - 20.3067i) q^{21} +260.032 q^{22} -516.833i q^{23} +(-24.9652 - 202.111i) q^{24} +590.951 q^{25} +291.160i q^{26} +(-680.009 + 262.733i) q^{27} +147.241 q^{28} +344.653i q^{29} +(-147.419 + 18.2095i) q^{30} +1119.64 q^{31} -181.019i q^{32} +(-101.433 - 821.176i) q^{33} +592.013 q^{34} -107.397i q^{35} +(-628.523 + 157.679i) q^{36} -1955.68 q^{37} -1096.87i q^{38} +(919.477 - 113.576i) q^{39} -132.035 q^{40} -3123.24i q^{41} +(-57.4359 - 464.984i) q^{42} -2865.07 q^{43} -735.481i q^{44} +(115.010 + 458.442i) q^{45} -1461.82 q^{46} +3252.80i q^{47} +(-571.655 + 70.6122i) q^{48} -2062.25 q^{49} -1671.46i q^{50} +(-230.933 - 1869.57i) q^{51} +823.524 q^{52} -0.558046i q^{53} +(743.122 + 1923.36i) q^{54} -536.457 q^{55} -416.461i q^{56} +(-3463.91 + 427.870i) q^{57} +974.826 q^{58} +453.188i q^{59} +(51.5042 + 416.963i) q^{60} +1345.64 q^{61} -3166.82i q^{62} +(-1446.01 + 362.763i) q^{63} -512.000 q^{64} -600.675i q^{65} +(-2322.64 + 286.897i) q^{66} -6584.93 q^{67} -1674.47i q^{68} +(570.230 + 4616.41i) q^{69} -303.765 q^{70} -5275.49i q^{71} +(445.984 + 1777.73i) q^{72} +105.778 q^{73} +5531.49i q^{74} +(-5278.44 + 652.005i) q^{75} -3102.43 q^{76} -1692.08i q^{77} +(-321.241 - 2600.67i) q^{78} -9587.37 q^{79} +373.451i q^{80} +(5784.04 - 3097.03i) q^{81} -8833.85 q^{82} +7888.34i q^{83} +(-1315.17 + 162.453i) q^{84} -1221.35 q^{85} +8103.63i q^{86} +(-380.261 - 3078.48i) q^{87} -2080.26 q^{88} -11840.4i q^{89} +(1296.67 - 325.299i) q^{90} +1894.63 q^{91} +4134.66i q^{92} +(-10000.8 + 1235.32i) q^{93} +9200.32 q^{94} +2262.90i q^{95} +(199.721 + 1616.89i) q^{96} +840.648 q^{97} +5832.93i q^{98} +(1812.03 + 7222.92i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 608 q^{4} - 64 q^{6} - 184 q^{7} + 168 q^{9}+O(q^{10}) \) 76 * q - 608 * q^4 - 64 * q^6 - 184 * q^7 + 168 * q^9	\( 76 q - 608 q^{4} - 64 q^{6} - 184 q^{7} + 168 q^{9} + 256 q^{10} - 200 q^{13} - 26 q^{15} + 4864 q^{16} - 512 q^{18} + 616 q^{19} + 330 q^{21} + 640 q^{22} + 512 q^{24} - 10540 q^{25} - 354 q^{27} + 1472 q^{28} - 832 q^{30} - 3920 q^{31} - 188 q^{33} + 2560 q^{34} - 1344 q^{36} - 1440 q^{37} + 8204 q^{39} - 2048 q^{40} - 5760 q^{42} - 1944 q^{43} + 3886 q^{45} + 4864 q^{46} + 33636 q^{49} - 7544 q^{51} + 1600 q^{52} + 3392 q^{54} - 10536 q^{55} - 12182 q^{57} - 7168 q^{58} + 208 q^{60} + 6360 q^{61} + 10860 q^{63} - 38912 q^{64} + 19712 q^{66} + 30744 q^{67} - 34208 q^{69} - 23808 q^{70} + 4096 q^{72} + 4032 q^{73} + 22324 q^{75} - 4928 q^{76} + 12864 q^{78} - 29824 q^{79} - 22584 q^{81} + 13184 q^{82} - 2640 q^{84} + 9240 q^{85} + 32850 q^{87} - 5120 q^{88} - 16448 q^{90} - 31160 q^{91} - 1780 q^{93} + 5248 q^{94} - 4096 q^{96} + 77504 q^{97} - 15412 q^{99}+O(q^{100}) \) 76 * q - 608 * q^4 - 64 * q^6 - 184 * q^7 + 168 * q^9 + 256 * q^10 - 200 * q^13 - 26 * q^15 + 4864 * q^16 - 512 * q^18 + 616 * q^19 + 330 * q^21 + 640 * q^22 + 512 * q^24 - 10540 * q^25 - 354 * q^27 + 1472 * q^28 - 832 * q^30 - 3920 * q^31 - 188 * q^33 + 2560 * q^34 - 1344 * q^36 - 1440 * q^37 + 8204 * q^39 - 2048 * q^40 - 5760 * q^42 - 1944 * q^43 + 3886 * q^45 + 4864 * q^46 + 33636 * q^49 - 7544 * q^51 + 1600 * q^52 + 3392 * q^54 - 10536 * q^55 - 12182 * q^57 - 7168 * q^58 + 208 * q^60 + 6360 * q^61 + 10860 * q^63 - 38912 * q^64 + 19712 * q^66 + 30744 * q^67 - 34208 * q^69 - 23808 * q^70 + 4096 * q^72 + 4032 * q^73 + 22324 * q^75 - 4928 * q^76 + 12864 * q^78 - 29824 * q^79 - 22584 * q^81 + 13184 * q^82 - 2640 * q^84 + 9240 * q^85 + 32850 * q^87 - 5120 * q^88 - 16448 * q^90 - 31160 * q^91 - 1780 * q^93 + 5248 * q^94 - 4096 * q^96 + 77504 * q^97 - 15412 * q^99

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