LMFDB - Embedded newform 200.4.f.b.149.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [200,4,Mod(149,200)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(200, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("200.149");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	200.f (of order $2$, degree $1$, not 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:	$11.8003820011$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{11} + 7x^{10} - 12x^{9} + 21x^{8} - 68x^{6} + 336x^{4} - 768x^{3} + 1792x^{2} - 4096x + 4096 $ x^12 - 4x^11 + 7x^10 - 12x^9 + 21x^8 - 68x^6 + 336x^4 - 768x^3 + 1792x^2 - 4096*x + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{15} $
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.9
Root			$-1.86176 - 0.730647i$ of defining polynomial
Character	$\chi$	$=$	200.149
Dual form			200.4.f.b.149.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.13111 - 2.59241i) q^{2} -6.25785 q^{3} +(-5.44116 - 5.86462i) q^{4} +(-7.07834 + 16.2229i) q^{6} -34.6280i q^{7} +(-21.3581 + 7.47214i) q^{8} +12.1606 q^{9} +O(q^{10})$	\(q+(1.13111 - 2.59241i) q^{2} -6.25785 q^{3} +(-5.44116 - 5.86462i) q^{4} +(-7.07834 + 16.2229i) q^{6} -34.6280i q^{7} +(-21.3581 + 7.47214i) q^{8} +12.1606 q^{9} -7.91595i q^{11} +(34.0499 + 36.6999i) q^{12} -11.0346 q^{13} +(-89.7698 - 39.1682i) q^{14} +(-4.78760 + 63.8207i) q^{16} +57.6152i q^{17} +(13.7551 - 31.5253i) q^{18} +141.133i q^{19} +216.696i q^{21} +(-20.5214 - 8.95385i) q^{22} -129.328i q^{23} +(133.655 - 46.7595i) q^{24} +(-12.4814 + 28.6062i) q^{26} +92.8625 q^{27} +(-203.080 + 188.416i) q^{28} +89.1664i q^{29} -78.3307 q^{31} +(160.034 + 84.5999i) q^{32} +49.5368i q^{33} +(149.362 + 65.1694i) q^{34} +(-66.1679 - 71.3175i) q^{36} -249.332 q^{37} +(365.874 + 159.637i) q^{38} +69.0530 q^{39} +91.8705 q^{41} +(561.766 + 245.109i) q^{42} +194.184 q^{43} +(-46.4240 + 43.0719i) q^{44} +(-335.270 - 146.285i) q^{46} -72.6149i q^{47} +(29.9600 - 399.380i) q^{48} -856.096 q^{49} -360.547i q^{51} +(60.0411 + 64.7139i) q^{52} -456.782 q^{53} +(105.038 - 240.737i) q^{54} +(258.745 + 739.586i) q^{56} -883.187i q^{57} +(231.156 + 100.857i) q^{58} -341.098i q^{59} -217.067i q^{61} +(-88.6011 + 203.065i) q^{62} -421.098i q^{63} +(400.334 - 319.181i) q^{64} +(128.420 + 56.0318i) q^{66} -529.237 q^{67} +(337.892 - 313.494i) q^{68} +809.314i q^{69} +381.540 q^{71} +(-259.728 + 90.8659i) q^{72} +876.902i q^{73} +(-282.023 + 646.370i) q^{74} +(827.690 - 767.926i) q^{76} -274.113 q^{77} +(78.1069 - 179.013i) q^{78} +203.950 q^{79} -909.456 q^{81} +(103.916 - 238.166i) q^{82} -996.654 q^{83} +(1270.84 - 1179.08i) q^{84} +(219.644 - 503.403i) q^{86} -557.989i q^{87} +(59.1491 + 169.069i) q^{88} -172.456 q^{89} +382.107i q^{91} +(-758.459 + 703.693i) q^{92} +490.182 q^{93} +(-188.247 - 82.1358i) q^{94} +(-1001.47 - 529.413i) q^{96} +1058.49i q^{97} +(-968.343 + 2219.35i) q^{98} -96.2629i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} - 12 q^{3} - 16 q^{4} - 36 q^{6} + 24 q^{8} + 108 q^{9}+O(q^{10}) $ 12 * q - 6 * q^2 - 12 * q^3 - 16 * q^4 - 36 * q^6 + 24 * q^8 + 108 * q^9	$ 12 q - 6 q^{2} - 12 q^{3} - 16 q^{4} - 36 q^{6} + 24 q^{8} + 108 q^{9} + 164 q^{12} - 68 q^{14} - 56 q^{16} - 450 q^{18} - 492 q^{22} - 360 q^{24} - 308 q^{26} - 432 q^{27} - 628 q^{28} - 264 q^{31} - 856 q^{32} + 180 q^{34} + 440 q^{36} - 136 q^{37} + 1388 q^{38} - 600 q^{39} + 40 q^{41} + 2332 q^{42} + 1204 q^{43} + 472 q^{44} - 1268 q^{46} + 2536 q^{48} - 1308 q^{49} + 1272 q^{52} - 1056 q^{53} + 1512 q^{54} - 728 q^{56} - 1528 q^{58} - 2104 q^{62} + 2048 q^{64} + 2928 q^{66} + 2412 q^{67} - 960 q^{68} - 1592 q^{71} - 744 q^{72} + 420 q^{74} + 2256 q^{76} - 824 q^{77} + 160 q^{78} - 2016 q^{79} + 2508 q^{81} - 352 q^{82} - 3556 q^{83} - 1048 q^{84} - 244 q^{86} - 1008 q^{88} + 424 q^{89} - 1068 q^{92} - 2784 q^{93} - 292 q^{94} - 5920 q^{96} - 638 q^{98}+O(q^{100}) $ 12 * q - 6 * q^2 - 12 * q^3 - 16 * q^4 - 36 * q^6 + 24 * q^8 + 108 * q^9 + 164 * q^12 - 68 * q^14 - 56 * q^16 - 450 * q^18 - 492 * q^22 - 360 * q^24 - 308 * q^26 - 432 * q^27 - 628 * q^28 - 264 * q^31 - 856 * q^32 + 180 * q^34 + 440 * q^36 - 136 * q^37 + 1388 * q^38 - 600 * q^39 + 40 * q^41 + 2332 * q^42 + 1204 * q^43 + 472 * q^44 - 1268 * q^46 + 2536 * q^48 - 1308 * q^49 + 1272 * q^52 - 1056 * q^53 + 1512 * q^54 - 728 * q^56 - 1528 * q^58 - 2104 * q^62 + 2048 * q^64 + 2928 * q^66 + 2412 * q^67 - 960 * q^68 - 1592 * q^71 - 744 * q^72 + 420 * q^74 + 2256 * q^76 - 824 * q^77 + 160 * q^78 - 2016 * q^79 + 2508 * q^81 - 352 * q^82 - 3556 * q^83 - 1048 * q^84 - 244 * q^86 - 1008 * q^88 + 424 * q^89 - 1068 * q^92 - 2784 * q^93 - 292 * q^94 - 5920 * q^96 - 638 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/200\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$177$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.13111	−	2.59241i	0.399910	−	0.916555i
$2$	1.13111	−	2.59241i	0.399910	−	0.916555i
$3$	−6.25785			−1.20432			−0.602161	−	0.798374i	$-0.705694\pi$
$3$	−6.25785			−1.20432			−0.602161	+	0.798374i	$0.705694\pi$
$4$	−5.44116	−	5.86462i	−0.680145	−	0.733078i
$5$		0			0
$5$		0			0
$6$	−7.07834	+	16.2229i	−0.481620	+	1.10383i
$7$		−	34.6280i		−	1.86973i	−0.354998	−	0.934867i	$-0.615518\pi$
$7$		−	34.6280i		−	1.86973i	0.354998	−	0.934867i	$-0.384482\pi$
$8$	−21.3581	+	7.47214i	−0.943902	+	0.330225i
$9$	12.1606			0.450394
$10$		0			0
$11$		−	7.91595i		−	0.216977i	−0.994098	−	0.108489i	$-0.965399\pi$
$11$		−	7.91595i		−	0.216977i	0.994098	−	0.108489i	$-0.0346011\pi$
$12$	34.0499	+	36.6999i	0.819114	+	0.882862i
$13$	−11.0346			−0.235420			−0.117710	−	0.993048i	$-0.537555\pi$
$13$	−11.0346			−0.235420			−0.117710	+	0.993048i	$0.537555\pi$
$14$	−89.7698	−	39.1682i	−1.71371	−	0.747725i
$15$		0			0
$16$	−4.78760	+	63.8207i	−0.0748062	+	0.997198i
$17$			57.6152i			0.821985i	0.911639	+	0.410992i	$0.134818\pi$
$17$			57.6152i			0.821985i	−0.911639	+	0.410992i	$0.865182\pi$
$18$	13.7551	−	31.5253i	0.180117	−	0.412810i
$19$			141.133i			1.70411i	0.523453	+	0.852055i	$0.324644\pi$
$19$			141.133i			1.70411i	−0.523453	+	0.852055i	$0.675356\pi$
$20$		0			0
$21$			216.696i			2.25176i
$22$	−20.5214	−	8.95385i	−0.198871	−	0.0867712i
$23$		−	129.328i		−	1.17247i	−0.810143	−	0.586233i	$-0.800610\pi$
$23$		−	129.328i		−	1.17247i	0.810143	−	0.586233i	$-0.199390\pi$
$24$	133.655	−	46.7595i	1.13676	−	0.397698i
$25$		0			0
$26$	−12.4814	+	28.6062i	−0.0941465	+	0.215775i
$27$	92.8625			0.661903
$28$	−203.080	+	188.416i	−1.37066	+	1.27169i
$29$			89.1664i			0.570958i	0.958385	+	0.285479i	$0.0921527\pi$
$29$			89.1664i			0.570958i	−0.958385	+	0.285479i	$0.907847\pi$
$30$		0			0
$31$	−78.3307			−0.453826			−0.226913	−	0.973915i	$-0.572863\pi$
$31$	−78.3307			−0.453826			−0.226913	+	0.973915i	$0.572863\pi$
$32$	160.034	+	84.5999i	0.884071	+	0.467353i
$33$			49.5368i			0.261310i
$34$	149.362	+	65.1694i	0.753394	+	0.328720i
$35$		0			0
$36$	−66.1679	−	71.3175i	−0.306333	−	0.330174i
$37$	−249.332			−1.10783			−0.553917	−	0.832572i	$-0.686868\pi$
$37$	−249.332			−1.10783			−0.553917	+	0.832572i	$0.686868\pi$
$38$	365.874	+	159.637i	1.56191	+	0.681489i
$39$	69.0530			0.283521
$40$		0			0
$41$	91.8705			0.349946			0.174973	−	0.984573i	$-0.444016\pi$
$41$	91.8705			0.349946			0.174973	+	0.984573i	$0.444016\pi$
$42$	561.766	+	245.109i	2.06386	+	0.900502i
$43$	194.184			0.688668			0.344334	−	0.938847i	$-0.388105\pi$
$43$	194.184			0.688668			0.344334	+	0.938847i	$0.388105\pi$
$44$	−46.4240	+	43.0719i	−0.159061	+	0.147576i
$45$		0			0
$46$	−335.270	−	146.285i	−1.07463	−	0.468880i
$47$		−	72.6149i		−	0.225361i	−0.993631	−	0.112680i	$-0.964056\pi$
$47$		−	72.6149i		−	0.225361i	0.993631	−	0.112680i	$-0.0359437\pi$
$48$	29.9600	−	399.380i	0.0900908	−	1.20095i
$49$	−856.096			−2.49591
$50$		0			0
$51$		−	360.547i		−	0.989935i
$52$	60.0411	+	64.7139i	0.160119	+	0.172581i
$53$	−456.782			−1.18385			−0.591923	−	0.805995i	$-0.701631\pi$
$53$	−456.782			−1.18385			−0.591923	+	0.805995i	$0.701631\pi$
$54$	105.038	−	240.737i	0.264701	−	0.606671i
$55$		0			0
$56$	258.745	+	739.586i	0.617433	+	1.76485i
$57$		−	883.187i		−	2.05230i
$58$	231.156	+	100.857i	0.523314	+	0.228331i
$59$		−	341.098i		−	0.752664i	−0.926485	−	0.376332i	$-0.877185\pi$
$59$		−	341.098i		−	0.752664i	0.926485	−	0.376332i	$-0.122815\pi$
$60$		0			0
$61$		−	217.067i		−	0.455616i	−0.973706	−	0.227808i	$-0.926844\pi$
$61$		−	217.067i		−	0.455616i	0.973706	−	0.227808i	$-0.0731559\pi$
$62$	−88.6011	+	203.065i	−0.181489	+	0.415957i
$63$		−	421.098i		−	0.842117i
$64$	400.334	−	319.181i	0.781903	−	0.623400i
$65$		0			0
$66$	128.420	+	56.0318i	0.239505	+	0.104501i
$67$	−529.237			−0.965024			−0.482512	−	0.875889i	$-0.660276\pi$
$67$	−529.237			−0.965024			−0.482512	+	0.875889i	$0.660276\pi$
$68$	337.892	−	313.494i	0.602579	−	0.559069i
$69$			809.314i			1.41203i
$70$		0			0
$71$	381.540			0.637754			0.318877	−	0.947796i	$-0.396694\pi$
$71$	381.540			0.637754			0.318877	+	0.947796i	$0.396694\pi$
$72$	−259.728	+	90.8659i	−0.425128	+	0.148731i
$73$			876.902i			1.40594i	0.711220	+	0.702970i	$0.248143\pi$
$73$			876.902i			1.40594i	−0.711220	+	0.702970i	$0.751857\pi$
$74$	−282.023	+	646.370i	−0.443034	+	1.01539i
$75$		0			0
$76$	827.690	−	767.926i	1.24924	−	1.15904i
$77$	−274.113			−0.405690
$78$	78.1069	−	179.013i	0.113383	−	0.259863i
$79$	203.950			0.290458			0.145229	−	0.989398i	$-0.453608\pi$
$79$	203.950			0.290458			0.145229	+	0.989398i	$0.453608\pi$
$80$		0			0
$81$	−909.456			−1.24754
$82$	103.916	−	238.166i	0.139947	−	0.320744i
$83$	−996.654			−1.31804			−0.659018	−	0.752127i	$-0.729028\pi$
$83$	−996.654			−1.31804			−0.659018	+	0.752127i	$0.729028\pi$
$84$	1270.84	−	1179.08i	1.65072	−	1.53153i
$85$		0			0
$86$	219.644	−	503.403i	0.275405	−	0.631202i
$87$		−	557.989i		−	0.687618i
$88$	59.1491	+	169.069i	0.0716513	+	0.204805i
$89$	−172.456			−0.205396			−0.102698	−	0.994713i	$-0.532748\pi$
$89$	−172.456			−0.205396			−0.102698	+	0.994713i	$0.532748\pi$
$90$		0			0
$91$			382.107i			0.440172i
$92$	−758.459	+	703.693i	−0.859509	+	0.797447i
$93$	490.182			0.546553
$94$	−188.247	−	82.1358i	−0.206556	−	0.0901240i
$95$		0			0
$96$	−1001.47	−	529.413i	−1.06471	−	0.562844i
$97$			1058.49i			1.10797i	0.832527	+	0.553984i	$0.186893\pi$
$97$			1058.49i			1.10797i	−0.832527	+	0.553984i	$0.813107\pi$
$98$	−968.343	+	2219.35i	−0.998137	+	2.28763i
$99$		−	96.2629i		−	0.0977251i
$100$		0			0
$101$		−	689.992i		−	0.679770i	−0.940467	−	0.339885i	$-0.889612\pi$
$101$		−	689.992i		−	0.679770i	0.940467	−	0.339885i	$-0.110388\pi$
$102$	−934.685	−	407.820i	−0.907330	−	0.395885i
$103$		−	1289.96i		−	1.23402i	−0.786956	−	0.617009i	$-0.788344\pi$
$103$		−	1289.96i		−	1.23402i	0.786956	−	0.617009i	$-0.211656\pi$
$104$	235.678	−	82.4523i	0.222213	−	0.0777414i
$105$		0			0
$106$	−516.673	+	1184.16i	−0.473431	+	1.08506i
$107$	−1843.74			−1.66580			−0.832902	−	0.553420i	$-0.813322\pi$
$107$	−1843.74			−1.66580			−0.832902	+	0.553420i	$0.813322\pi$
$108$	−505.279	−	544.603i	−0.450190	−	0.485227i
$109$		−	340.598i		−	0.299297i	−0.988739	−	0.149648i	$-0.952186\pi$
$109$		−	340.598i		−	0.299297i	0.988739	−	0.149648i	$-0.0478142\pi$
$110$		0			0
$111$	1560.28			1.33419
$112$	2209.98	+	165.785i	1.86450	+	0.139868i
$113$		−	157.831i		−	0.131393i	−0.997840	−	0.0656967i	$-0.979073\pi$
$113$		−	157.831i		−	0.131393i	0.997840	−	0.0656967i	$-0.0209270\pi$
$114$	−2289.58	−	998.986i	−1.88104	−	0.820733i
$115$		0			0
$116$	522.927	−	485.168i	0.418557	−	0.388334i
$117$	−134.188			−0.106031
$118$	−884.265	−	385.821i	−0.689858	−	0.300997i
$119$	1995.10			1.53689
$120$		0			0
$121$	1268.34			0.952921
$122$	−562.727	−	245.528i	−0.417597	−	0.182205i
$123$	−574.912			−0.421447
$124$	426.210	+	459.380i	0.308668	+	0.332690i
$125$		0			0
$126$	−1091.66	−	476.310i	−0.771846	−	0.336770i
$127$			494.704i			0.345652i	0.984952	+	0.172826i	$0.0552899\pi$
$127$			494.704i			0.345652i	−0.984952	+	0.172826i	$0.944710\pi$
$128$	−374.623	−	1398.86i	−0.258690	−	0.965960i
$129$	−1215.17			−0.829379
$130$		0			0
$131$		−	488.783i		−	0.325993i	−0.986627	−	0.162997i	$-0.947884\pi$
$131$		−	488.783i		−	0.325993i	0.986627	−	0.162997i	$-0.0521160\pi$
$132$	290.514	−	269.537i	0.191561	−	0.177729i
$133$	4887.14			3.18623
$134$	−598.628	+	1372.00i	−0.385922	+	0.884498i
$135$		0			0
$136$	−430.509	−	1230.55i	−0.271440	−	0.775873i
$137$		−	1532.13i		−	0.955464i	−0.878506	−	0.477732i	$-0.841459\pi$
$137$		−	1532.13i		−	0.955464i	0.878506	−	0.477732i	$-0.158541\pi$
$138$	2098.07	+	915.427i	1.29420	+	0.564683i
$139$		−	755.095i		−	0.460765i	−0.973100	−	0.230382i	$-0.926002\pi$
$139$		−	755.095i		−	0.460765i	0.973100	−	0.230382i	$-0.0739977\pi$
$140$		0			0
$141$			454.413i			0.271407i
$142$	431.566	−	989.108i	0.255044	−	0.584536i
$143$			87.3495i			0.0510807i
$144$	−58.2202	+	776.100i	−0.0336922	+	0.449132i
$145$		0			0
$146$	2273.29	+	991.877i	1.28862	+	0.562249i
$147$	5357.32			3.00588
$148$	1356.65	+	1462.24i	0.753488	+	0.812129i
$149$			1446.67i			0.795410i	0.917513	+	0.397705i	$0.130193\pi$
$149$			1446.67i			0.795410i	−0.917513	+	0.397705i	$0.869807\pi$
$150$		0			0
$151$	−1230.20			−0.662998			−0.331499	−	0.943456i	$-0.607554\pi$
$151$	−1230.20			−0.662998			−0.331499	+	0.943456i	$0.607554\pi$
$152$	−1054.56	−	3014.32i	−0.562739	−	1.60851i
$153$			700.637i			0.370217i
$154$	−310.053	+	710.613i	−0.162239	+	0.371837i
$155$		0			0
$156$	−375.728	−	404.970i	−0.192835	−	0.207843i
$157$	1773.74			0.901657			0.450828	−	0.892611i	$-0.351129\pi$
$157$	1773.74			0.901657			0.450828	+	0.892611i	$0.351129\pi$
$158$	230.691	−	528.722i	0.116157	−	0.266221i
$159$	2858.47			1.42573
$160$		0			0
$161$	−4478.36			−2.19220
$162$	−1028.70	+	2357.68i	−0.498903	+	1.14344i
$163$	−1711.28			−0.822319			−0.411159	−	0.911563i	$-0.634876\pi$
$163$	−1711.28			−0.822319			−0.411159	+	0.911563i	$0.634876\pi$
$164$	−499.882	−	538.786i	−0.238014	−	0.256537i
$165$		0			0
$166$	−1127.33	+	2583.73i	−0.527095	+	1.20805i
$167$			3913.26i			1.81328i	0.421909	+	0.906638i	$0.361360\pi$
$167$			3913.26i			1.81328i	−0.421909	+	0.906638i	$0.638640\pi$
$168$	−1619.19	−	4628.22i	−0.743589	−	2.12544i
$169$	−2075.24			−0.944578
$170$		0			0
$171$			1716.26i			0.767520i
$172$	−1056.58	−	1138.81i	−0.468394	−	0.504847i
$173$	−3985.34			−1.75144			−0.875722	−	0.482815i	$-0.839614\pi$
$173$	−3985.34			−1.75144			−0.875722	+	0.482815i	$0.839614\pi$
$174$	−1446.54	−	631.150i	−0.630239	−	0.274985i
$175$		0			0
$176$	505.201	+	37.8984i	0.216369	+	0.0162312i
$177$			2134.54i			0.906450i
$178$	−195.067	+	447.076i	−0.0821400	+	0.188257i
$179$		−	884.734i		−	0.369431i	−0.982792	−	0.184715i	$-0.940864\pi$
$179$		−	884.734i		−	0.369431i	0.982792	−	0.184715i	$-0.0591363\pi$
$180$		0			0
$181$			2810.77i			1.15427i	0.816649	+	0.577134i	$0.195829\pi$
$181$			2810.77i			1.15427i	−0.816649	+	0.577134i	$0.804171\pi$
$182$	990.576	+	432.206i	0.403442	+	0.176029i
$183$			1358.37i			0.548709i
$184$	966.356	+	2762.19i	0.387178	+	1.10669i
$185$		0			0
$186$	554.452	−	1270.75i	0.218572	−	0.500946i
$187$	456.079			0.178352
$188$	−425.859	+	395.109i	−0.165207	+	0.153278i
$189$		−	3215.64i		−	1.23758i
$190$		0			0
$191$	−749.321			−0.283869			−0.141935	−	0.989876i	$-0.545332\pi$
$191$	−749.321			−0.283869			−0.141935	+	0.989876i	$0.545332\pi$
$192$	−2505.23	+	1997.39i	−0.941663	+	0.750775i
$193$			3969.83i			1.48060i	0.672279	+	0.740298i	$0.265315\pi$
$193$			3969.83i			1.48060i	−0.672279	+	0.740298i	$0.734685\pi$
$194$	2744.03	+	1197.27i	1.01551	+	0.443087i
$195$		0			0
$196$	4658.15	+	5020.68i	1.69758	+	1.82969i
$197$	2243.20			0.811275			0.405638	−	0.914034i	$-0.367049\pi$
$197$	2243.20			0.811275			0.405638	+	0.914034i	$0.367049\pi$
$198$	−249.553	−	108.884i	−0.0895704	−	0.0390812i
$199$	672.030			0.239392			0.119696	−	0.992811i	$-0.461808\pi$
$199$	672.030			0.239392			0.119696	+	0.992811i	$0.461808\pi$
$200$		0			0
$201$	3311.89			1.16220
$202$	−1788.74	−	780.460i	−0.623046	−	0.271846i
$203$	3087.65			1.06754
$204$	−2114.47	+	1961.79i	−0.725700	+	0.673299i
$205$		0			0
$206$	−3344.11	−	1459.10i	−1.13104	−	0.493495i
$207$		−	1572.71i		−	0.528071i
$208$	52.8293	−	704.237i	0.0176108	−	0.234760i
$209$	1117.20			0.369753
$210$		0			0
$211$		−	1935.07i		−	0.631356i	−0.948866	−	0.315678i	$-0.897768\pi$
$211$		−	1935.07i		−	0.631356i	0.948866	−	0.315678i	$-0.102232\pi$
$212$	2485.42	+	2678.85i	0.805186	+	0.867851i
$213$	−2387.62			−0.768061
$214$	−2085.48	+	4779.73i	−0.666171	+	1.52680i
$215$		0			0
$216$	−1983.36	+	693.882i	−0.624772	+	0.218577i
$217$			2712.43i			0.848535i
$218$	−882.968	−	385.255i	−0.274322	−	0.119692i
$219$		−	5487.52i		−	1.69321i
$220$		0			0
$221$		−	635.762i		−	0.193511i
$222$	1764.86	−	4044.88i	0.533556	−	1.22286i
$223$		−	2492.56i		−	0.748494i	−0.927329	−	0.374247i	$-0.877901\pi$
$223$		−	2492.56i		−	0.748494i	0.927329	−	0.374247i	$-0.122099\pi$
$224$	2929.52	−	5541.65i	0.873826	−	1.65298i
$225$		0			0
$226$	−409.161	−	178.524i	−0.120429	−	0.0525455i
$227$	−3155.27			−0.922567			−0.461283	−	0.887253i	$-0.652611\pi$
$227$	−3155.27			−0.922567			−0.461283	+	0.887253i	$0.652611\pi$
$228$	−5179.56	+	4805.56i	−1.50449	+	1.39586i
$229$			2299.43i			0.663539i	0.943360	+	0.331770i	$0.107646\pi$
$229$			2299.43i			0.663539i	−0.943360	+	0.331770i	$0.892354\pi$
$230$		0			0
$231$	1715.36			0.488581
$232$	−666.264	−	1904.42i	−0.188545	−	0.538928i
$233$		−	741.991i		−	0.208624i	−0.994545	−	0.104312i	$-0.966736\pi$
$233$		−	741.991i		−	0.208624i	0.994545	−	0.104312i	$-0.0332641\pi$
$234$	−151.782	+	347.870i	−0.0424030	+	0.0971836i
$235$		0			0
$236$	−2000.41	+	1855.97i	−0.551761	+	0.511920i
$237$	−1276.29			−0.349806
$238$	2256.68	−	5172.11i	0.614618	−	1.40865i
$239$	−5786.01			−1.56597			−0.782984	−	0.622042i	$-0.786303\pi$
$239$	−5786.01			−1.56597			−0.782984	+	0.622042i	$0.786303\pi$
$240$		0			0
$241$	265.054			0.0708449			0.0354224	−	0.999372i	$-0.488722\pi$
$241$	265.054			0.0708449			0.0354224	+	0.999372i	$0.488722\pi$
$242$	1434.64	−	3288.05i	0.381082	−	0.873404i
$243$	3183.95			0.840537
$244$	−1273.02	+	1181.10i	−0.334002	+	0.309885i
$245$		0			0
$246$	−650.291	+	1490.41i	−0.168541	+	0.386280i
$247$		−	1557.35i		−	0.401181i
$248$	1672.99	−	585.298i	0.428368	−	0.149865i
$249$	6236.91			1.58734
$250$		0			0
$251$			1762.02i			0.443098i	0.975149	+	0.221549i	$0.0711113\pi$
$251$			1762.02i			0.443098i	−0.975149	+	0.221549i	$0.928889\pi$
$252$	−2469.58	+	2291.26i	−0.617337	+	0.572761i
$253$	−1023.75			−0.254398
$254$	1282.47	+	559.567i	0.316809	+	0.138230i
$255$		0			0
$256$	−4050.16	−	611.095i	−0.988808	−	0.149193i
$257$		−	1507.84i		−	0.365980i	−0.983115	−	0.182990i	$-0.941422\pi$
$257$		−	1507.84i		−	0.365980i	0.983115	−	0.182990i	$-0.0585775\pi$
$258$	−1374.50	+	3150.22i	−0.331677	+	0.760171i
$259$			8633.85i			2.07136i
$260$		0			0
$261$			1084.32i			0.257156i
$262$	−1267.12	−	552.869i	−0.298791	−	0.130368i
$263$		−	2772.54i		−	0.650046i	−0.945706	−	0.325023i	$-0.894628\pi$
$263$		−	2772.54i		−	0.650046i	0.945706	−	0.325023i	$-0.105372\pi$
$264$	−370.146	−	1058.01i	−0.0862913	−	0.246652i
$265$		0			0
$266$	5527.92	−	12669.5i	1.27420	−	2.92035i
$267$	1079.20			0.247364
$268$	2879.66	+	3103.78i	0.656356	+	0.707438i
$269$		−	5166.61i		−	1.17106i	−0.810652	−	0.585528i	$-0.800887\pi$
$269$		−	5166.61i		−	1.17106i	0.810652	−	0.585528i	$-0.199113\pi$
$270$		0			0
$271$	−1458.79			−0.326994			−0.163497	−	0.986544i	$-0.552277\pi$
$271$	−1458.79			−0.326994			−0.163497	+	0.986544i	$0.552277\pi$
$272$	−3677.04	−	275.838i	−0.819682	−	0.0614896i
$273$		−	2391.16i		−	0.530109i
$274$	−3971.90	−	1733.01i	−0.875735	−	0.382099i
$275$		0			0
$276$	4746.32	−	4403.60i	1.03513	−	0.960383i
$277$	−1994.60			−0.432650			−0.216325	−	0.976321i	$-0.569407\pi$
$277$	−1994.60			−0.432650			−0.216325	+	0.976321i	$0.569407\pi$
$278$	−1957.51	−	854.099i	−0.422316	−	0.184264i
$279$	−952.551			−0.204400
$280$		0			0
$281$	−311.583			−0.0661477			−0.0330739	−	0.999453i	$-0.510530\pi$
$281$	−311.583			−0.0661477			−0.0330739	+	0.999453i	$0.510530\pi$
$282$	1178.02	+	513.993i	0.248760	+	0.108538i
$283$	6072.33			1.27549			0.637743	−	0.770249i	$-0.279868\pi$
$283$	6072.33			1.27549			0.637743	+	0.770249i	$0.279868\pi$
$284$	−2076.02	−	2237.59i	−0.433765	−	0.467523i
$285$		0			0
$286$	226.446	+	98.8023i	0.0468182	+	0.0204276i
$287$		−	3181.29i		−	0.654305i
$288$	1946.11	+	1028.79i	0.398180	+	0.210493i
$289$	1593.49			0.324341
$290$		0			0
$291$		−	6623.84i		−	1.33435i
$292$	5142.70	−	4771.36i	1.03066	−	0.956243i
$293$	2321.06			0.462791			0.231395	−	0.972860i	$-0.425671\pi$
$293$	2321.06			0.462791			0.231395	+	0.972860i	$0.425671\pi$
$294$	6059.74	−	13888.3i	1.20208	−	2.75505i
$295$		0			0
$296$	5325.24	−	1863.04i	1.04569	−	0.365835i
$297$		−	735.095i		−	0.143618i
$298$	3750.37	+	1636.35i	0.729037	+	0.318092i
$299$			1427.08i			0.276021i
$300$		0			0
$301$		−	6724.19i		−	1.28763i
$302$	−1391.50	+	3189.19i	−0.265139	+	0.607674i
$303$			4317.86i			0.818662i
$304$	−9007.19	−	675.686i	−1.69933	−	0.127478i
$305$		0			0
$306$	1816.34	+	792.501i	0.339324	+	0.148053i
$307$	−2499.43			−0.464658			−0.232329	−	0.972637i	$-0.574635\pi$
$307$	−2499.43			−0.464658			−0.232329	+	0.972637i	$0.574635\pi$
$308$	1491.49	+	1607.57i	0.275928	+	0.297402i
$309$			8072.39i			1.48616i
$310$		0			0
$311$	−3052.83			−0.556624			−0.278312	−	0.960491i	$-0.589775\pi$
$311$	−3052.83			−0.556624			−0.278312	+	0.960491i	$0.589775\pi$
$312$	−1474.84	+	515.974i	−0.267616	+	0.0936258i
$313$		−	6179.23i		−	1.11588i	−0.829881	−	0.557941i	$-0.811592\pi$
$313$		−	6179.23i		−	1.11588i	0.829881	−	0.557941i	$-0.188408\pi$
$314$	2006.31	−	4598.27i	0.360581	−	0.826418i
$315$		0			0
$316$	−1109.73	−	1196.09i	−0.197554	−	0.212929i
$317$	−3116.20			−0.552124			−0.276062	−	0.961140i	$-0.589029\pi$
$317$	−3116.20			−0.552124			−0.276062	+	0.961140i	$0.589029\pi$
$318$	3233.26	−	7410.32i	0.570164	−	1.30676i
$319$	705.836			0.123885
$320$		0			0
$321$	11537.8			2.00617
$322$	−5065.54	+	11609.7i	−0.876682	+	2.00927i
$323$	−8131.39			−1.40075
$324$	4948.49	+	5333.62i	0.848507	+	0.914543i
$325$		0			0
$326$	−1935.66	+	4436.34i	−0.328853	+	0.753700i
$327$			2131.41i			0.360450i
$328$	−1962.18	+	686.469i	−0.330314	+	0.115561i
$329$	−2514.51			−0.421365
$330$		0			0
$331$		−	4157.26i		−	0.690343i	−0.938540	−	0.345171i	$-0.887821\pi$
$331$		−	4157.26i		−	0.690343i	0.938540	−	0.345171i	$-0.112179\pi$
$332$	5422.95	+	5845.00i	0.896455	+	0.966223i
$333$	−3032.03			−0.498962
$334$	10144.8	+	4426.35i	1.66197	+	0.725146i
$335$		0			0
$336$	−13829.7	−	1037.45i	−2.24545	−	0.168446i
$337$		−	8123.42i		−	1.31309i	−0.754287	−	0.656544i	$-0.772017\pi$
$337$		−	8123.42i		−	1.31309i	0.754287	−	0.656544i	$-0.227983\pi$
$338$	−2347.33	+	5379.86i	−0.377746	+	0.865757i
$339$			987.679i			0.158240i
$340$		0			0
$341$			620.062i			0.0984699i
$342$	4449.25	+	1941.29i	0.703474	+	0.306939i
$343$			17767.5i			2.79695i
$344$	−4147.39	+	1450.97i	−0.650035	+	0.227416i
$345$		0			0
$346$	−4507.88	+	10331.6i	−0.700419	+	1.60529i
$347$	−4620.55			−0.714824			−0.357412	−	0.933947i	$-0.616341\pi$
$347$	−4620.55			−0.714824			−0.357412	+	0.933947i	$0.616341\pi$
$348$	−3272.40	+	3036.11i	−0.504077	+	0.467680i
$349$		−	5560.98i		−	0.852929i	−0.904504	−	0.426465i	$-0.859759\pi$
$349$		−	5560.98i		−	0.852929i	0.904504	−	0.426465i	$-0.140241\pi$
$350$		0			0
$351$	−1024.70			−0.155825
$352$	669.689	−	1266.82i	0.101405	−	0.191823i
$353$		−	12031.8i		−	1.81413i	−0.420989	−	0.907066i	$-0.638317\pi$
$353$		−	12031.8i		−	1.81413i	0.420989	−	0.907066i	$-0.361683\pi$
$354$	5533.59	+	2414.41i	0.830811	+	0.362498i
$355$		0			0
$356$	938.359	+	1011.39i	0.139699	+	0.150572i
$357$	−12485.0			−1.85092
$358$	−2293.59	−	1000.74i	−0.338603	−	0.147739i
$359$	−1533.24			−0.225408			−0.112704	−	0.993629i	$-0.535951\pi$
$359$	−1533.24			−0.225408			−0.112704	+	0.993629i	$0.535951\pi$
$360$		0			0
$361$	−13059.5			−1.90399
$362$	7286.66	+	3179.30i	1.05795	+	0.461603i
$363$	−7937.06			−1.14762
$364$	2240.91	−	2079.10i	0.322680	−	0.299381i
$365$		0			0
$366$	3521.46	+	1536.48i	0.502922	+	0.219434i
$367$		−	5480.04i		−	0.779444i	−0.920933	−	0.389722i	$-0.872571\pi$
$367$		−	5480.04i		−	0.779444i	0.920933	−	0.389722i	$-0.127429\pi$
$368$	8253.79	+	619.169i	1.16918	+	0.0877077i
$369$	1117.20			0.157613
$370$		0			0
$371$			15817.4i			2.21348i
$372$	−2667.16	−	2874.73i	−0.371735	−	0.400666i
$373$	6225.70			0.864221			0.432111	−	0.901821i	$-0.357769\pi$
$373$	6225.70			0.864221			0.432111	+	0.901821i	$0.357769\pi$
$374$	515.878	−	1182.34i	0.0713246	−	0.163469i
$375$		0			0
$376$	542.588	+	1550.91i	0.0744198	+	0.212719i
$377$		−	983.917i		−	0.134415i
$378$	−8336.25	−	3637.26i	−1.13431	−	0.494921i
$379$			11172.0i			1.51416i	0.653325	+	0.757078i	$0.273374\pi$
$379$			11172.0i			1.51416i	−0.653325	+	0.757078i	$0.726626\pi$
$380$		0			0
$381$		−	3095.78i		−	0.416277i
$382$	−847.569	+	1942.55i	−0.113522	+	0.260182i
$383$		−	7621.03i		−	1.01675i	−0.861135	−	0.508376i	$-0.830246\pi$
$383$		−	7621.03i		−	1.01675i	0.861135	−	0.508376i	$-0.169754\pi$
$384$	2344.33	+	8753.85i	0.311546	+	1.16333i
$385$		0			0
$386$	10291.4	+	4490.34i	1.35705	+	0.592104i
$387$	2361.40			0.310172
$388$	6207.62	−	5759.39i	0.812227	−	0.753579i
$389$		−	5546.31i		−	0.722903i	−0.932391	−	0.361451i	$-0.882281\pi$
$389$		−	5546.31i		−	0.722903i	0.932391	−	0.361451i	$-0.117719\pi$
$390$		0			0
$391$	7451.25			0.963749
$392$	18284.6	−	6396.87i	2.35589	−	0.824211i
$393$			3058.73i			0.392601i
$394$	2537.31	−	5815.28i	0.324437	−	0.743578i
$395$		0			0
$396$	−564.546	+	523.782i	−0.0716401	+	0.0664672i
$397$	11025.2			1.39380			0.696900	−	0.717169i	$-0.254562\pi$
$397$	11025.2			1.39380			0.696900	+	0.717169i	$0.254562\pi$
$398$	760.143	−	1742.18i	0.0957350	−	0.219416i
$399$	−30583.0			−3.83725
$400$		0			0
$401$	10522.3			1.31037			0.655186	−	0.755467i	$-0.272590\pi$
$401$	10522.3			1.31037			0.655186	+	0.755467i	$0.272590\pi$
$402$	3746.12	−	8585.76i	0.464775	−	1.06522i
$403$	864.350			0.106840
$404$	−4046.54	+	3754.35i	−0.498324	+	0.462342i
$405$		0			0
$406$	3492.49	−	8004.45i	0.426919	−	0.978458i
$407$			1973.70i			0.240375i
$408$	2694.06	+	7700.59i	0.326901	+	0.934402i
$409$	−2320.17			−0.280502			−0.140251	−	0.990116i	$-0.544791\pi$
$409$	−2320.17			−0.280502			−0.140251	+	0.990116i	$0.544791\pi$
$410$		0			0
$411$			9587.82i			1.15069i
$412$	−7565.14	+	7018.89i	−0.904631	+	0.839310i
$413$	−11811.5			−1.40728
$414$	−4077.10	−	1778.91i	−0.484006	−	0.211181i
$415$		0			0
$416$	−1765.91	−	933.528i	−0.208128	−	0.110024i
$417$			4725.27i			0.554910i
$418$	1263.68	−	2896.24i	0.147868	−	0.338898i
$419$		−	9212.17i		−	1.07409i	−0.843554	−	0.537045i	$-0.819541\pi$
$419$		−	9212.17i		−	1.07409i	0.843554	−	0.537045i	$-0.180459\pi$
$420$		0			0
$421$			6967.70i			0.806615i	0.915064	+	0.403308i	$0.132140\pi$
$421$			6967.70i			0.806615i	−0.915064	+	0.403308i	$0.867860\pi$
$422$	−5016.50	−	2188.79i	−0.578672	−	0.252485i
$423$		−	883.042i		−	0.101501i
$424$	9755.98	−	3413.14i	1.11743	−	0.390935i
$425$		0			0
$426$	−2700.67	+	6189.69i	−0.307155	+	0.703970i
$427$	−7516.59			−0.851882
$428$	10032.1	+	10812.8i	1.13299	+	1.22116i
$429$		−	546.620i		−	0.0615176i
$430$		0			0
$431$	−11247.1			−1.25697			−0.628486	−	0.777821i	$-0.716325\pi$
$431$	−11247.1			−1.25697			−0.628486	+	0.777821i	$0.716325\pi$
$432$	−444.588	+	5926.55i	−0.0495145	+	0.660049i
$433$		−	2589.27i		−	0.287372i	−0.989623	−	0.143686i	$-0.954104\pi$
$433$		−	2589.27i		−	0.287372i	0.989623	−	0.143686i	$-0.0458956\pi$
$434$	7031.74	+	3068.07i	0.777728	+	0.339337i
$435$		0			0
$436$	−1997.48	+	1853.25i	−0.219408	+	0.203565i
$437$	18252.4			1.99801
$438$	−14225.9	−	6207.01i	−1.55192	−	0.677129i
$439$	−4220.01			−0.458793			−0.229396	−	0.973333i	$-0.573675\pi$
$439$	−4220.01			−0.458793			−0.229396	+	0.973333i	$0.573675\pi$
$440$		0			0
$441$	−10410.7			−1.12414
$442$	−1648.16	−	719.120i	−0.177364	−	0.0773870i
$443$	−9764.04			−1.04719			−0.523593	−	0.851969i	$-0.675409\pi$
$443$	−9764.04			−1.04719			−0.523593	+	0.851969i	$0.675409\pi$
$444$	−8489.73	−	9150.45i	−0.907443	−	0.978066i
$445$		0			0
$446$	−6461.73	−	2819.37i	−0.686035	−	0.299330i
$447$		−	9053.06i		−	0.957931i
$448$	−11052.6	−	13862.8i	−1.16559	−	1.46195i
$449$	17159.3			1.80355			0.901777	−	0.432202i	$-0.142263\pi$
$449$	17159.3			1.80355			0.901777	+	0.432202i	$0.142263\pi$
$450$		0			0
$451$		−	727.242i		−	0.0759302i
$452$	−925.617	+	858.781i	−0.0963216	+	0.0893665i
$453$	7698.43			0.798463
$454$	−3568.97	+	8179.75i	−0.368943	+	0.845583i
$455$		0			0
$456$	6599.30	+	18863.2i	0.677720	+	1.93717i
$457$			13027.3i			1.33346i	0.745299	+	0.666730i	$0.232307\pi$
$457$			13027.3i			1.33346i	−0.745299	+	0.666730i	$0.767693\pi$
$458$	5961.05	+	2600.92i	0.608170	+	0.265356i
$459$			5350.29i			0.544075i
$460$		0			0
$461$		−	313.396i		−	0.0316623i	−0.999875	−	0.0158312i	$-0.994961\pi$
$461$		−	313.396i		−	0.0316623i	0.999875	−	0.0158312i	$-0.00503943\pi$
$462$	1940.27	−	4446.91i	0.195388	−	0.447811i
$463$			12166.5i			1.22123i	0.791930	+	0.610613i	$0.209077\pi$
$463$			12166.5i			1.22123i	−0.791930	+	0.610613i	$0.790923\pi$
$464$	−5690.66	−	426.892i	−0.569358	−	0.0427112i
$465$		0			0
$466$	−1923.54	−	839.277i	−0.191216	−	0.0834308i
$467$	1844.42			0.182761			0.0913806	−	0.995816i	$-0.470872\pi$
$467$	1844.42			0.182761			0.0913806	+	0.995816i	$0.470872\pi$
$468$	730.138	+	786.962i	0.0721168	+	0.0777293i
$469$			18326.4i			1.80434i
$470$		0			0
$471$	−11099.8			−1.08589
$472$	2548.73	+	7285.19i	0.248548	+	0.710441i
$473$		−	1537.15i		−	0.149425i
$474$	−1443.63	+	3308.66i	−0.139891	+	0.320616i
$475$		0			0
$476$	−10855.6	−	11700.5i	−1.04531	−	1.12666i
$477$	−5554.75			−0.533196
$478$	−6544.65	+	14999.7i	−0.626245	+	1.43529i
$479$	16355.9			1.56017			0.780084	−	0.625675i	$-0.215176\pi$
$479$	16355.9			1.56017			0.780084	+	0.625675i	$0.215176\pi$
$480$		0			0
$481$	2751.28			0.260806
$482$	299.806	−	687.128i	0.0283315	−	0.0649332i
$483$	28024.9			2.64012
$484$	−6901.23	−	7438.32i	−0.648124	−	0.698565i
$485$		0			0
$486$	3601.41	−	8254.09i	0.336139	−	0.770398i
$487$			11824.6i			1.10025i	0.835082	+	0.550126i	$0.185420\pi$
$487$			11824.6i			1.10025i	−0.835082	+	0.550126i	$0.814580\pi$
$488$	1621.96	+	4636.13i	0.150456	+	0.430057i
$489$	10708.9			0.990337
$490$		0			0
$491$		−	7931.40i		−	0.729000i	−0.931203	−	0.364500i	$-0.881240\pi$
$491$		−	7931.40i		−	0.729000i	0.931203	−	0.364500i	$-0.118760\pi$
$492$	3128.18	+	3371.64i	0.286645	+	0.308954i
$493$	−5137.34			−0.469319
$494$	−4037.28	−	1761.54i	−0.367704	−	0.160436i
$495$		0			0
$496$	375.016	−	4999.12i	0.0339490	−	0.452555i
$497$		−	13212.0i		−	1.19243i
$498$	7054.66	−	16168.6i	0.634793	−	1.45488i
$499$		−	2734.69i		−	0.245333i	−0.992448	−	0.122667i	$-0.960855\pi$
$499$		−	2734.69i		−	0.245333i	0.992448	−	0.122667i	$-0.0391446\pi$
$500$		0			0
$501$		−	24488.6i		−	2.18377i
$502$	4567.87	+	1993.05i	0.406124	+	0.177199i
$503$		−	7297.64i		−	0.646890i	−0.946247	−	0.323445i	$-0.895159\pi$
$503$		−	7297.64i		−	0.646890i	0.946247	−	0.323445i	$-0.104841\pi$
$504$	3146.50	+	8993.84i	0.278088	+	0.794876i
$505$		0			0
$506$	−1157.98	+	2653.98i	−0.101736	+	0.233170i
$507$	12986.5			1.13758
$508$	2901.25	−	2691.76i	0.253390	−	0.235094i
$509$		−	10972.4i		−	0.955486i	−0.878500	−	0.477743i	$-0.841455\pi$
$509$		−	10972.4i		−	0.955486i	0.878500	−	0.477743i	$-0.158545\pi$
$510$		0			0
$511$	30365.3			2.62873
$512$	−6165.40	+	9808.44i	−0.532177	+	0.846633i
$513$			13105.9i			1.12796i
$514$	−3908.95	−	1705.55i	−0.335440	−	0.146359i
$515$		0			0
$516$	6611.94	+	7126.52i	0.564098	+	0.607999i
$517$	−574.815			−0.0488982
$518$	22382.5	+	9765.88i	1.89851	+	0.828355i
$519$	24939.7			2.10931
$520$		0			0
$521$	7693.43			0.646939			0.323470	−	0.946239i	$-0.395151\pi$
$521$	7693.43			0.646939			0.323470	+	0.946239i	$0.395151\pi$
$522$	2811.00	+	1226.49i	0.235697	+	0.102839i
$523$	14535.3			1.21527			0.607634	−	0.794217i	$-0.292119\pi$
$523$	14535.3			1.21527			0.607634	+	0.794217i	$0.292119\pi$
$524$	−2866.53	+	2659.54i	−0.238979	+	0.221723i
$525$		0			0
$526$	−7187.55	−	3136.06i	−0.595802	−	0.259959i
$527$		−	4513.04i		−	0.373038i
$528$	−3161.47	−	237.162i	−0.260578	−	0.0195476i
$529$	−4558.69			−0.374676
$530$		0			0
$531$		−	4147.97i		−	0.338995i
$532$	−26591.7	−	28661.2i	−2.16710	−	2.33576i
$533$	−1013.76			−0.0823840
$534$	1220.70	−	2797.73i	0.0989230	−	0.226722i
$535$		0			0
$536$	11303.5	−	3954.54i	0.910889	−	0.318675i
$537$			5536.53i			0.444914i
$538$	−13394.0	−	5844.03i	−1.07334	−	0.468316i
$539$			6776.81i			0.541555i
$540$		0			0
$541$			19131.8i			1.52040i	0.649686	+	0.760202i	$0.274900\pi$
$541$			19131.8i			1.52040i	−0.649686	+	0.760202i	$0.725100\pi$
$542$	−1650.06	+	3781.78i	−0.130768	+	0.299708i
$543$		−	17589.3i		−	1.39011i
$544$	−4874.24	+	9220.39i	−0.384157	+	0.726693i
$545$		0			0
$546$	−6198.87	−	2704.68i	−0.485874	−	0.211996i
$547$	−7142.78			−0.558324			−0.279162	−	0.960244i	$-0.590057\pi$
$547$	−7142.78			−0.558324			−0.279162	+	0.960244i	$0.590057\pi$
$548$	−8985.36	+	8336.55i	−0.700430	+	0.649854i
$549$		−	2639.67i		−	0.205207i
$550$		0			0
$551$	−12584.3			−0.972974
$552$	−6047.30	−	17285.4i	−0.466287	−	1.33282i
$553$		−	7062.39i		−	0.543080i
$554$	−2256.12	+	5170.82i	−0.173021	+	0.396547i
$555$		0			0
$556$	−4428.35	+	4108.59i	−0.337777	+	0.313387i
$557$	−11347.8			−0.863236			−0.431618	−	0.902057i	$-0.642057\pi$
$557$	−11347.8			−0.863236			−0.431618	+	0.902057i	$0.642057\pi$
$558$	−1077.44	+	2469.40i	−0.0817417	+	0.187344i
$559$	−2142.74			−0.162126
$560$		0			0
$561$	−2854.07			−0.214793
$562$	−352.437	+	807.751i	−0.0264531	+	0.0606280i
$563$	−8802.19			−0.658913			−0.329456	−	0.944171i	$-0.606865\pi$
$563$	−8802.19			−0.658913			−0.329456	+	0.944171i	$0.606865\pi$
$564$	2664.96	−	2472.53i	0.198963	−	0.184596i
$565$		0			0
$566$	6868.51	−	15742.0i	0.510079	−	1.16905i
$567$			31492.6i			2.33257i
$568$	−8148.96	+	2850.92i	−0.601977	+	0.210602i
$569$	−16714.7			−1.23149			−0.615744	−	0.787946i	$-0.711145\pi$
$569$	−16714.7			−1.23149			−0.615744	+	0.787946i	$0.711145\pi$
$570$		0			0
$571$		−	17386.8i		−	1.27428i	−0.770746	−	0.637142i	$-0.780116\pi$
$571$		−	17386.8i		−	1.27428i	0.770746	−	0.637142i	$-0.219884\pi$
$572$	512.272	−	475.283i	0.0374461	−	0.0347422i
$573$	4689.14			0.341870
$574$	−8247.20	−	3598.40i	−0.599706	−	0.261663i
$575$		0			0
$576$	4868.32	−	3881.44i	0.352164	−	0.280776i
$577$			2260.52i			0.163097i	0.996669	+	0.0815483i	$0.0259865\pi$
$577$			2260.52i			0.163097i	−0.996669	+	0.0815483i	$0.974014\pi$
$578$	1802.42	−	4130.97i	0.129707	−	0.297276i
$579$		−	24842.6i		−	1.78311i
$580$		0			0
$581$			34512.1i			2.46438i
$582$	−17171.7	−	7492.32i	−1.22301	−	0.533620i
$583$			3615.86i			0.256867i
$584$	−6552.33	−	18728.9i	−0.464276	−	1.32707i
$585$		0			0
$586$	2625.38	−	6017.13i	0.185074	−	0.424173i
$587$	25591.0			1.79941			0.899705	−	0.436498i	$-0.143781\pi$
$587$	25591.0			1.79941			0.899705	+	0.436498i	$0.143781\pi$
$588$	−29150.0	−	31418.6i	−2.04443	−	2.20354i
$589$		−	11055.0i		−	0.773369i
$590$		0			0
$591$	−14037.6			−0.977037
$592$	1193.70	−	15912.5i	0.0828729	−	1.10473i
$593$			10053.7i			0.696218i	0.937454	+	0.348109i	$0.113176\pi$
$593$			10053.7i			0.696218i	−0.937454	+	0.348109i	$0.886824\pi$
$594$	−1905.67	−	831.476i	−0.131634	−	0.0574342i
$595$		0			0
$596$	8484.20	−	7871.58i	0.583098	−	0.540994i
$597$	−4205.46			−0.288305
$598$	3699.58	+	1614.20i	0.252989	+	0.110384i
$599$	7086.68			0.483395			0.241698	−	0.970352i	$-0.422296\pi$
$599$	7086.68			0.483395			0.241698	+	0.970352i	$0.422296\pi$
$600$		0			0
$601$	6673.11			0.452915			0.226458	−	0.974021i	$-0.427286\pi$
$601$	6673.11			0.452915			0.226458	+	0.974021i	$0.427286\pi$
$602$	−17431.8	−	7605.83i	−1.18018	−	0.514934i
$603$	−6435.86			−0.434641
$604$	6693.74	+	7214.69i	0.450934	+	0.486029i
$605$		0			0
$606$	11193.7	+	4884.00i	0.750348	+	0.327391i
$607$		−	15205.6i		−	1.01677i	−0.861131	−	0.508383i	$-0.830243\pi$
$607$		−	15205.6i		−	1.01677i	0.861131	−	0.508383i	$-0.169757\pi$
$608$	−11939.8	+	22586.0i	−0.796420	+	1.50655i
$609$	−19322.0			−1.28566
$610$		0			0
$611$			801.278i			0.0530544i
$612$	4108.97	−	3812.28i	0.271398	−	0.251801i
$613$	−8147.64			−0.536836			−0.268418	−	0.963303i	$-0.586501\pi$
$613$	−8147.64			−0.536836			−0.268418	+	0.963303i	$0.586501\pi$
$614$	−2827.14	+	6479.55i	−0.185821	+	0.425885i
$615$		0			0
$616$	5854.53	−	2048.21i	0.382931	−	0.133969i
$617$			449.110i			0.0293039i	0.999893	+	0.0146519i	$0.00466402\pi$
$617$			449.110i			0.0293039i	−0.999893	+	0.0146519i	$0.995336\pi$
$618$	20926.9	+	9130.80i	1.36214	+	0.594328i
$619$		−	27800.4i		−	1.80516i	−0.430524	−	0.902579i	$-0.641671\pi$
$619$		−	27800.4i		−	1.80516i	0.430524	−	0.902579i	$-0.358329\pi$
$620$		0			0
$621$		−	12009.7i		−	0.776059i
$622$	−3453.10	+	7914.18i	−0.222599	+	0.510176i
$623$			5971.79i			0.384037i
$624$	−330.598	+	4407.01i	−0.0212091	+	0.282727i
$625$		0			0
$626$	−16019.1	−	6989.42i	−1.02277	−	0.446252i
$627$	−6991.26			−0.445302
$628$	−9651.22	−	10402.3i	−0.613257	−	0.660984i
$629$		−	14365.3i		−	0.910623i
$630$		0			0
$631$	14793.5			0.933315			0.466657	−	0.884438i	$-0.345458\pi$
$631$	14793.5			0.933315			0.466657	+	0.884438i	$0.345458\pi$
$632$	−4355.99	+	1523.95i	−0.274164	+	0.0959166i
$633$			12109.4i			0.760356i
$634$	−3524.78	+	8078.46i	−0.220800	+	0.506052i
$635$		0			0
$636$	−15553.4	−	16763.8i	−0.969704	−	1.04517i
$637$	9446.70			0.587585
$638$	798.382	−	1829.82i	0.0495427	−	0.113547i
$639$	4639.77			0.287240
$640$		0			0
$641$	−13853.8			−0.853655			−0.426828	−	0.904333i	$-0.640369\pi$
$641$	−13853.8			−0.853655			−0.426828	+	0.904333i	$0.640369\pi$
$642$	13050.6	−	29910.8i	0.802285	−	1.83876i
$643$	−4978.60			−0.305345			−0.152672	−	0.988277i	$-0.548788\pi$
$643$	−4978.60			−0.305345			−0.152672	+	0.988277i	$0.548788\pi$
$644$	24367.5	+	26263.9i	1.49101	+	1.60705i
$645$		0			0
$646$	−9197.54	+	21079.9i	−0.560174	+	1.28387i
$647$		−	1903.39i		−	0.115657i	−0.998327	−	0.0578284i	$-0.981582\pi$
$647$		−	1903.39i		−	0.115657i	0.998327	−	0.0578284i	$-0.0184176\pi$
$648$	19424.2	−	6795.58i	1.17756	−	0.411969i
$649$	−2700.11			−0.163311
$650$		0			0
$651$		−	16974.0i		−	1.02191i
$652$	9311.36	+	10036.0i	0.559296	+	0.602824i
$653$	10877.0			0.651839			0.325920	−	0.945397i	$-0.394326\pi$
$653$	10877.0			0.651839			0.325920	+	0.945397i	$0.394326\pi$
$654$	5525.48	+	2410.87i	0.330372	+	0.144147i
$655$		0			0
$656$	−439.839	+	5863.24i	−0.0261781	+	0.348965i
$657$			10663.7i			0.633226i
$658$	−2844.19	+	6518.62i	−0.168508	+	0.386204i
$659$			30611.3i			1.80948i	0.425965	+	0.904739i	$0.359935\pi$
$659$			30611.3i			1.80948i	−0.425965	+	0.904739i	$0.640065\pi$
$660$		0			0
$661$		−	16098.8i		−	0.947310i	−0.880710	−	0.473655i	$-0.842934\pi$
$661$		−	16098.8i		−	0.947310i	0.880710	−	0.473655i	$-0.157066\pi$
$662$	−10777.3	−	4702.34i	−0.632737	−	0.276075i
$663$			3978.50i			0.233050i
$664$	21286.6	−	7447.14i	1.24410	−	0.435249i
$665$		0			0
$666$	−3429.57	+	7860.26i	−0.199540	+	0.457326i
$667$	11531.7			0.669429
$668$	22949.8	−	21292.7i	1.32927	−	1.23329i
$669$			15598.0i			0.901428i
$670$		0			0
$671$	−1718.29			−0.0988583
$672$	−18332.5	+	34678.8i	−1.05237	+	1.99072i
$673$			23837.8i			1.36535i	0.730724	+	0.682673i	$0.239183\pi$
$673$			23837.8i			1.36535i	−0.730724	+	0.682673i	$0.760817\pi$
$674$	−21059.2	−	9188.52i	−1.20352	−	0.525117i
$675$		0			0
$676$	11291.7	+	12170.5i	0.642450	+	0.692449i
$677$	−25235.3			−1.43260			−0.716302	−	0.697791i	$-0.754167\pi$
$677$	−25235.3			−1.43260			−0.716302	+	0.697791i	$0.754167\pi$
$678$	2560.47	+	1117.18i	0.145036	+	0.0632817i
$679$	36653.2			2.07161
$680$		0			0
$681$	19745.2			1.11107
$682$	1607.45	+	701.361i	0.0902531	+	0.0393791i
$683$	−19975.3			−1.11909			−0.559543	−	0.828802i	$-0.689023\pi$
$683$	−19975.3			−1.11909			−0.559543	+	0.828802i	$0.689023\pi$
$684$	10065.2	−	9338.46i	0.562652	−	0.522025i
$685$		0			0
$686$	46060.5	+	20097.0i	2.56356	+	1.11853i
$687$		−	14389.5i		−	0.799115i
$688$	−929.673	+	12392.9i	−0.0515166	+	0.686739i
$689$	5040.42			0.278700
$690$		0			0
$691$			13772.3i			0.758209i	0.925354	+	0.379104i	$0.123768\pi$
$691$			13772.3i			0.758209i	−0.925354	+	0.379104i	$0.876232\pi$
$692$	21684.9	+	23372.5i	1.19124	+	1.28395i
$693$	−3333.39			−0.182720
$694$	−5226.37	+	11978.3i	−0.285865	+	0.655175i
$695$		0			0
$696$	4169.37	+	11917.6i	0.227069	+	0.649044i
$697$			5293.14i			0.287650i
$698$	−14416.3	−	6290.10i	−0.781756	−	0.341095i
$699$			4643.26i			0.251251i
$700$		0			0
$701$		−	6347.90i		−	0.342021i	−0.985269	−	0.171011i	$-0.945297\pi$
$701$		−	6347.90i		−	0.342021i	0.985269	−	0.171011i	$-0.0547032\pi$
$702$	−1159.06	+	2656.45i	−0.0623159	+	0.142822i
$703$		−	35188.9i		−	1.88787i
$704$	−2526.62	−	3169.02i	−0.135264	−	0.169655i
$705$		0			0
$706$	−31191.4	−	13609.4i	−1.66275	−	0.725488i
$707$	−23893.0			−1.27099
$708$	12518.3	−	11614.4i	0.664499	−	0.616517i
$709$		−	17910.5i		−	0.948719i	−0.880331	−	0.474360i	$-0.842680\pi$
$709$		−	17910.5i		−	0.948719i	0.880331	−	0.474360i	$-0.157320\pi$
$710$		0			0
$711$	2480.16			0.130821
$712$	3683.32	−	1288.61i	0.193874	−	0.0678270i
$713$			10130.3i			0.532096i
$714$	−14122.0	+	32366.3i	−0.740199	+	1.69647i
$715$		0			0
$716$	−5188.63	+	4813.98i	−0.270821	+	0.251266i
$717$	36208.0			1.88593
$718$	−1734.27	+	3974.78i	−0.0901426	+	0.206598i
$719$	−36601.6			−1.89849			−0.949243	−	0.314545i	$-0.898148\pi$
$719$	−36601.6			−1.89849			−0.949243	+	0.314545i	$0.898148\pi$
$720$		0			0
$721$	−44668.8			−2.30728
$722$	−14771.7	+	33855.4i	−0.761423	+	1.74511i
$723$	−1658.67			−0.0853201
$724$	16484.1	−	15293.8i	0.846169	−	0.785070i
$725$		0			0
$726$	−8977.73	+	20576.1i	−0.458946	+	1.05186i
$727$			2644.18i			0.134893i	0.997723	+	0.0674466i	$0.0214852\pi$
$727$			2644.18i			0.134893i	−0.997723	+	0.0674466i	$0.978515\pi$
$728$	−2855.15	−	8161.06i	−0.145356	−	0.415479i
$729$	4630.66			0.235262
$730$		0			0
$731$			11187.9i			0.566075i
$732$	7966.34	−	7391.12i	0.402247	−	0.373202i
$733$	33452.1			1.68565			0.842825	−	0.538188i	$-0.180891\pi$
$733$	33452.1			1.68565			0.842825	+	0.538188i	$0.180891\pi$
$734$	−14206.5	−	6198.56i	−0.714403	−	0.311707i
$735$		0			0
$736$	10941.1	−	20696.8i	0.547955	−	1.03654i
$737$			4189.42i			0.209388i
$738$	1263.69	−	2896.25i	0.0630310	−	0.144461i
$739$		−	25834.9i		−	1.28600i	−0.765867	−	0.642999i	$-0.777690\pi$
$739$		−	25834.9i		−	1.28600i	0.765867	−	0.642999i	$-0.222310\pi$
$740$		0			0
$741$			9745.64i			0.483151i
$742$	41005.2	+	17891.3i	2.02877	+	0.885190i
$743$		−	7625.09i		−	0.376497i	−0.982121	−	0.188249i	$-0.939719\pi$
$743$		−	7625.09i		−	0.376497i	0.982121	−	0.188249i	$-0.0602811\pi$
$744$	−10469.3	+	3662.71i	−0.515893	+	0.180486i
$745$		0			0
$746$	7041.98	−	16139.6i	0.345610	−	0.792106i
$747$	−12119.9			−0.593635
$748$	−2481.60	−	2674.73i	−0.121305	−	0.130746i
$749$			63845.0i			3.11461i
$750$		0			0
$751$	25362.7			1.23235			0.616177	−	0.787607i	$-0.288680\pi$
$751$	25362.7			1.23235			0.616177	+	0.787607i	$0.288680\pi$
$752$	4634.33	+	347.651i	0.224730	+	0.0168584i
$753$		−	11026.4i		−	0.533633i
$754$	−2550.72	−	1112.92i	−0.123198	−	0.0537537i
$755$		0			0
$756$	−18858.5	+	17496.8i	−0.907245	+	0.841736i
$757$	38948.0			1.87000			0.935000	−	0.354648i	$-0.115399\pi$
$757$	38948.0			1.87000			0.935000	+	0.354648i	$0.115399\pi$
$758$	28962.3	+	12636.8i	1.38781	+	0.605525i
$759$	6406.48			0.306378
$760$		0			0
$761$	−13722.2			−0.653654			−0.326827	−	0.945084i	$-0.605979\pi$
$761$	−13722.2			−0.653654			−0.326827	+	0.945084i	$0.605979\pi$
$762$	−8025.52	−	3501.68i	−0.381541	−	0.166473i
$763$	−11794.2			−0.559606
$764$	4077.18	+	4394.49i	0.193072	+	0.208098i
$765$		0			0
$766$	−19756.8	−	8620.26i	−0.931909	−	0.406609i
$767$			3763.89i			0.177192i
$768$	25345.3	+	3824.14i	1.19084	+	0.179677i
$769$	−18689.5			−0.876414			−0.438207	−	0.898874i	$-0.644386\pi$
$769$	−18689.5			−0.876414			−0.438207	+	0.898874i	$0.644386\pi$
$770$		0			0
$771$			9435.86i			0.440758i
$772$	23281.6	−	21600.5i	1.08539	−	1.00702i
$773$	6386.49			0.297162			0.148581	−	0.988900i	$-0.452529\pi$
$773$	6386.49			0.297162			0.148581	+	0.988900i	$0.452529\pi$
$774$	2671.01	−	6121.70i	0.124041	−	0.284289i
$775$		0			0
$776$	−7909.15	−	22607.2i	−0.365879	−	1.04581i
$777$		−	54029.3i		−	2.49458i
$778$	−14378.3	−	6273.52i	−0.662580	−	0.289096i
$779$			12965.9i			0.596345i
$780$		0			0
$781$		−	3020.25i		−	0.138378i
$782$	8428.22	−	19316.7i	0.385413	−	0.883329i
$783$			8280.21i			0.377919i
$784$	4098.64	−	54636.6i	0.186709	−	2.48891i
$785$		0			0
$786$	7929.47	+	3459.77i	0.359841	+	0.157005i
$787$	19410.3			0.879167			0.439583	−	0.898202i	$-0.355126\pi$
$787$	19410.3			0.879167			0.439583	+	0.898202i	$0.355126\pi$
$788$	−12205.6	−	13155.5i	−0.551785	−	0.594728i
$789$			17350.1i			0.782865i
$790$		0			0
$791$	−5465.35			−0.245671
$792$	719.290	+	2055.99i	0.0322713	+	0.0922429i
$793$			2395.25i			0.107261i
$794$	12470.8	−	28581.8i	0.557394	−	1.27749i
$795$		0			0
$796$	−3656.62	−	3941.20i	−0.162821	−	0.175493i
$797$	−30740.8			−1.36624			−0.683121	−	0.730305i	$-0.739378\pi$
$797$	−30740.8			−1.36624			−0.683121	+	0.730305i	$0.739378\pi$
$798$	−34592.8	+	79283.5i	−1.53455	+	3.51705i
$799$	4183.72			0.185243
$800$		0			0
$801$	−2097.17			−0.0925092
$802$	11902.0	−	27278.1i	0.524031	−	1.20103i
$803$	6941.51			0.305057
$804$	−18020.5	−	19423.0i	−0.790465	−	0.851984i
$805$		0			0
$806$	977.679	−	2240.75i	0.0427262	−	0.0979243i
$807$			32331.9i			1.41033i
$808$	5155.71	+	14736.9i	0.224477	+	0.641636i
$809$	−31805.5			−1.38223			−0.691114	−	0.722746i	$-0.742880\pi$
$809$	−31805.5			−1.38223			−0.691114	+	0.722746i	$0.742880\pi$
$810$		0			0
$811$			31014.7i			1.34288i	0.741060	+	0.671439i	$0.234323\pi$
$811$			31014.7i			1.34288i	−0.741060	+	0.671439i	$0.765677\pi$
$812$	−16800.4	−	18107.9i	−0.726081	−	0.782590i
$813$	9128.90			0.393806
$814$	5116.63	+	2232.48i	0.220317	+	0.0961281i
$815$		0			0
$816$	23010.4	+	1726.15i	0.987162	+	0.0740533i
$817$			27405.7i			1.17357i
$818$	−2624.38	+	6014.84i	−0.112175	+	0.257095i
$819$			4646.66i			0.198251i
$820$		0			0
$821$		−	12021.4i		−	0.511021i	−0.966806	−	0.255511i	$-0.917756\pi$
$821$		−	12021.4i		−	0.511021i	0.966806	−	0.255511i	$-0.0822436\pi$
$822$	24855.6	+	10844.9i	1.05467	+	0.460171i
$823$		−	15489.0i		−	0.656032i	−0.944672	−	0.328016i	$-0.893620\pi$
$823$		−	15489.0i		−	0.656032i	0.944672	−	0.328016i	$-0.106380\pi$
$824$	9638.78	+	27551.1i	0.407503	+	1.16479i
$825$		0			0
$826$	−13360.2	+	30620.3i	−0.562785	+	1.28985i
$827$	−17097.2			−0.718898			−0.359449	−	0.933165i	$-0.617035\pi$
$827$	−17097.2			−0.718898			−0.359449	+	0.933165i	$0.617035\pi$
$828$	−9223.34	+	8557.35i	−0.387117	+	0.359165i
$829$			9885.97i			0.414178i	0.978322	+	0.207089i	$0.0663990\pi$
$829$			9885.97i			0.414178i	−0.978322	+	0.207089i	$0.933601\pi$
$830$		0			0
$831$	12481.9			0.521050
$832$	−4417.54	+	3522.04i	−0.184075	+	0.146761i
$833$		−	49324.2i		−	2.05160i
$834$	12249.8	+	5344.82i	0.508605	+	0.221914i
$835$		0			0
$836$	−6078.86	−	6551.95i	−0.251485	−	0.271057i
$837$	−7273.99			−0.300389
$838$	−23881.7	−	10420.0i	−0.984462	−	0.429539i
$839$	39204.3			1.61321			0.806606	−	0.591090i	$-0.201302\pi$
$839$	39204.3			1.61321			0.806606	+	0.591090i	$0.201302\pi$
$840$		0			0
$841$	16438.4			0.674007
$842$	18063.1	+	7881.27i	0.739307	+	0.322573i
$843$	1949.84			0.0796632
$844$	−11348.5	+	10529.0i	−0.462833	+	0.429413i
$845$		0			0
$846$	−2289.21	−	998.822i	−0.0930314	−	0.0405913i
$847$		−	43920.0i		−	1.78171i
$848$	2186.89	−	29152.1i	0.0885589	−	1.18053i
$849$	−37999.7			−1.53610
$850$		0			0
$851$			32245.5i			1.29890i
$852$	12991.4	+	14002.5i	0.522393	+	0.563049i
$853$	−45054.1			−1.80847			−0.904234	−	0.427038i	$-0.859557\pi$
$853$	−45054.1			−1.80847			−0.904234	+	0.427038i	$0.859557\pi$
$854$	−8502.13	+	19486.1i	−0.340676	+	0.780796i
$855$		0			0
$856$	39378.7	−	13776.7i	1.57236	−	0.550090i
$857$		−	48464.2i		−	1.93174i	−0.259021	−	0.965872i	$-0.583400\pi$
$857$		−	48464.2i		−	1.93174i	0.259021	−	0.965872i	$-0.416600\pi$
$858$	−1417.06	−	618.290i	−0.0563842	−	0.0246015i
$859$		−	1000.76i		−	0.0397503i	−0.999802	−	0.0198751i	$-0.993673\pi$
$859$		−	1000.76i		−	0.0397503i	0.999802	−	0.0198751i	$-0.00632687\pi$
$860$		0			0
$861$			19908.0i			0.787995i
$862$	−12721.8	+	29157.1i	−0.502675	+	1.15208i
$863$		−	22485.5i		−	0.886922i	−0.896294	−	0.443461i	$-0.853750\pi$
$863$		−	22485.5i		−	0.886922i	0.896294	−	0.443461i	$-0.146250\pi$
$864$	14861.1	+	7856.16i	0.585170	+	0.309343i
$865$		0			0
$866$	−6712.44	−	2928.76i	−0.263392	−	0.114923i
$867$	−9971.79			−0.390611
$868$	15907.4	−	14758.8i	0.622042	−	0.577126i
$869$		−	1614.46i		−	0.0630228i
$870$		0			0
$871$	5839.94			0.227186
$872$	2544.99	+	7274.51i	0.0988353	+	0.282507i
$873$			12871.9i			0.499022i
$874$	20645.6	−	47317.6i	0.799023	−	1.83129i
$875$		0			0
$876$	−32182.2	+	29858.4i	−1.24125	+	1.15162i
$877$	−43726.2			−1.68361			−0.841806	−	0.539780i	$-0.818507\pi$
$877$	−43726.2			−1.68361			−0.841806	+	0.539780i	$0.818507\pi$
$878$	−4773.32	+	10940.0i	−0.183476	+	0.420509i
$879$	−14524.8			−0.557349
$880$		0			0
$881$	20290.0			0.775923			0.387962	−	0.921675i	$-0.373179\pi$
$881$	20290.0			0.775923			0.387962	+	0.921675i	$0.373179\pi$
$882$	−11775.7	+	26988.7i	−0.449554	+	1.03034i
$883$	−14887.3			−0.567382			−0.283691	−	0.958916i	$-0.591559\pi$
$883$	−14887.3			−0.567382			−0.283691	+	0.958916i	$0.591559\pi$
$884$	−3728.51	+	3459.28i	−0.141859	+	0.131616i
$885$		0			0
$886$	−11044.2	+	25312.4i	−0.418780	+	0.959803i
$887$			34359.3i			1.30065i	0.759658	+	0.650323i	$0.225367\pi$
$887$			34359.3i			1.30065i	−0.759658	+	0.650323i	$0.774633\pi$
$888$	−33324.6	+	11658.6i	−1.25935	+	0.440583i
$889$	17130.6			0.646278
$890$		0			0
$891$			7199.21i			0.270687i
$892$	−14617.9	+	13562.4i	−0.548704	+	0.509084i
$893$	10248.3			0.384040
$894$	−23469.2	−	10240.1i	−0.877996	−	0.383086i
$895$		0			0
$896$	−48439.7	+	12972.4i	−1.80609	+	0.483682i
$897$		−	8930.47i		−	0.332419i
$898$	19409.1	−	44483.8i	0.721258	−	1.65306i
$899$		−	6984.47i		−	0.259116i
$900$		0			0
$901$		−	26317.6i		−	0.973103i
$902$	−1885.31	−	822.595i	−0.0695941	−	0.0303652i
$903$			42078.9i			1.55072i
$904$	1179.33	+	3370.96i	0.0433894	+	0.124022i
$905$		0			0
$906$	8707.81	−	19957.5i	0.319313	−	0.731835i
$907$	−53363.9			−1.95360			−0.976802	−	0.214144i	$-0.931304\pi$
$907$	−53363.9			−1.95360			−0.976802	+	0.214144i	$0.931304\pi$
$908$	17168.3	+	18504.5i	0.627479	+	0.676313i
$909$		−	8390.73i		−	0.306164i
$910$		0			0
$911$	−25213.9			−0.916984			−0.458492	−	0.888699i	$-0.651610\pi$
$911$	−25213.9			−0.916984			−0.458492	+	0.888699i	$0.651610\pi$
$912$	56365.6	+	4228.34i	2.04655	+	0.153525i
$913$			7889.46i			0.285984i
$914$	33772.1	+	14735.4i	1.22219	+	0.533264i
$915$		0			0
$916$	13485.3	−	12511.6i	0.486426	−	0.451303i
$917$	−16925.5			−0.609521
$918$	13870.1	+	6051.80i	0.498674	+	0.217581i
$919$	−3747.02			−0.134497			−0.0672485	−	0.997736i	$-0.521422\pi$
$919$	−3747.02			−0.134497			−0.0672485	+	0.997736i	$0.521422\pi$
$920$		0			0
$921$	15641.1			0.559599
$922$	−812.452	−	354.487i	−0.0290202	−	0.0126621i
$923$	−4210.15			−0.150140
$924$	−9333.53	−	10059.9i	−0.332306	−	0.358168i
$925$		0			0
$926$	31540.6	+	13761.8i	1.11932	+	0.488380i
$927$		−	15686.8i		−	0.555794i
$928$	−7543.47	+	14269.6i	−0.266839	+	0.504767i
$929$	27726.7			0.979209			0.489604	−	0.871945i	$-0.337141\pi$
$929$	27726.7			0.979209			0.489604	+	0.871945i	$0.337141\pi$
$930$		0			0
$931$		−	120823.i		−	4.25330i
$932$	−4351.50	+	4037.29i	−0.152938	+	0.141895i
$933$	19104.1			0.670355
$934$	2086.25	−	4781.48i	0.0730879	−	0.167511i
$935$		0			0
$936$	2866.00	−	1002.67i	0.100083	−	0.0350143i
$937$			29333.2i			1.02270i	0.859371	+	0.511352i	$0.170855\pi$
$937$			29333.2i			1.02270i	−0.859371	+	0.511352i	$0.829145\pi$
$938$	47509.5	+	20729.3i	1.65378	+	0.721572i
$939$			38668.7i			1.34388i
$940$		0			0
$941$			24218.4i			0.838998i	0.907756	+	0.419499i	$0.137794\pi$
$941$			24218.4i			0.838998i	−0.907756	+	0.419499i	$0.862206\pi$
$942$	−12555.2	+	28775.2i	−0.434256	+	0.995274i
$943$		−	11881.4i		−	0.410299i
$944$	21769.1	+	1633.04i	0.750555	+	0.0563039i
$945$		0			0
$946$	−3984.91	−	1738.69i	−0.136956	−	0.0597566i
$947$	50824.6			1.74401			0.872005	−	0.489497i	$-0.162820\pi$
$947$	50824.6			1.74401			0.872005	+	0.489497i	$0.162820\pi$
$948$	6944.49	+	7484.96i	0.237918	+	0.256435i
$949$		−	9676.28i		−	0.330986i
$950$		0			0
$951$	19500.7			0.664935
$952$	−42611.4	+	14907.7i	−1.45068	+	0.507521i
$953$			10155.1i			0.345180i	0.984994	+	0.172590i	$0.0552136\pi$
$953$			10155.1i			0.345180i	−0.984994	+	0.172590i	$0.944786\pi$
$954$	−6283.06	+	14400.2i	−0.213230	+	0.488704i
$955$		0			0
$956$	31482.6	+	33932.8i	1.06508	+	1.14798i
$957$	−4417.01			−0.149197
$958$	18500.4	−	42401.2i	0.623926	−	1.42998i
$959$	−53054.5			−1.78646
$960$		0			0
$961$	−23655.3			−0.794042
$962$	3112.02	−	7132.45i	0.104299	−	0.239043i
$963$	−22421.0			−0.750268
$964$	−1442.20	−	1554.44i	−0.0481848	−	0.0519348i
$965$		0			0
$966$	31699.4	−	72651.9i	1.05581	−	2.41981i
$967$		−	28225.7i		−	0.938652i	−0.883025	−	0.469326i	$-0.844497\pi$
$967$		−	28225.7i		−	0.938652i	0.883025	−	0.469326i	$-0.155503\pi$
$968$	−27089.2	+	9477.20i	−0.899464	+	0.314678i
$969$	50885.0			1.68696
$970$		0			0
$971$		−	47631.4i		−	1.57422i	−0.616814	−	0.787109i	$-0.711577\pi$
$971$		−	47631.4i		−	1.57422i	0.616814	−	0.787109i	$-0.288423\pi$
$972$	−17324.4	−	18672.7i	−0.571687	−	0.616179i
$973$	−26147.4			−0.861508
$974$	30654.1	+	13375.0i	1.00844	+	0.440001i
$975$		0			0
$976$	13853.4	+	1039.23i	0.454340	+	0.0340829i
$977$			13542.4i			0.443460i	0.975108	+	0.221730i	$0.0711703\pi$
$977$			13542.4i			0.443460i	−0.975108	+	0.221730i	$0.928830\pi$
$978$	12113.0	−	27761.9i	0.396045	−	0.907698i
$979$			1365.15i			0.0445663i
$980$		0			0
$981$		−	4141.88i		−	0.134801i
$982$	−20561.4	−	8971.32i	−0.668168	−	0.291534i
$983$			35108.5i			1.13915i	0.821938	+	0.569576i	$0.192893\pi$
$983$			35108.5i			1.13915i	−0.821938	+	0.569576i	$0.807107\pi$
$984$	12279.0	−	4295.82i	0.397805	−	0.139172i
$985$		0			0
$986$	−5810.92	+	13318.1i	−0.187685	+	0.430156i
$987$	15735.4			0.507460
$988$	−9133.25	+	8473.77i	−0.294097	+	0.272861i
$989$		−	25113.4i		−	0.807440i
$990$		0			0
$991$	−42816.1			−1.37245			−0.686225	−	0.727390i	$-0.740733\pi$
$991$	−42816.1			−1.37245			−0.686225	+	0.727390i	$0.740733\pi$
$992$	−12535.6	−	6626.77i	−0.401215	−	0.212097i
$993$			26015.5i			0.831396i
$994$	−34250.8	−	14944.2i	−1.09293	−	0.476864i
$995$		0			0
$996$	−33936.0	−	36577.1i	−1.07962	−	1.16364i
$997$	13029.0			0.413873			0.206936	−	0.978354i	$-0.433651\pi$
$997$	13029.0			0.413873			0.206936	+	0.978354i	$0.433651\pi$
$998$	−7089.42	−	3093.24i	−0.224861	−	0.0981111i
$999$	−23153.6			−0.733280

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.4.f.b.149.9		12
4.3	odd	2		800.4.f.c.49.10		12
5.2	odd	4		200.4.d.b.101.12		12
5.3	odd	4		40.4.d.a.21.1	✓	12
5.4	even	2		200.4.f.c.149.4		12
8.3	odd	2		800.4.f.b.49.4		12
8.5	even	2		200.4.f.c.149.3		12
15.8	even	4		360.4.k.c.181.12		12
20.3	even	4		160.4.d.a.81.10		12
20.7	even	4		800.4.d.d.401.3		12
20.19	odd	2		800.4.f.b.49.3		12
40.3	even	4		160.4.d.a.81.3		12
40.13	odd	4		40.4.d.a.21.2	yes	12
40.19	odd	2		800.4.f.c.49.9		12
40.27	even	4		800.4.d.d.401.10		12
40.29	even	2	inner	200.4.f.b.149.10		12
40.37	odd	4		200.4.d.b.101.11		12
60.23	odd	4		1440.4.k.c.721.12		12
80.3	even	4		1280.4.a.ba.1.2		6
80.13	odd	4		1280.4.a.bc.1.5		6
80.43	even	4		1280.4.a.bd.1.5		6
80.53	odd	4		1280.4.a.bb.1.2		6
120.53	even	4		360.4.k.c.181.11		12
120.83	odd	4		1440.4.k.c.721.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.4.d.a.21.1	✓	12	5.3	odd	4
40.4.d.a.21.2	yes	12	40.13	odd	4
160.4.d.a.81.3		12	40.3	even	4
160.4.d.a.81.10		12	20.3	even	4
200.4.d.b.101.11		12	40.37	odd	4
200.4.d.b.101.12		12	5.2	odd	4
200.4.f.b.149.9		12	1.1	even	1	trivial
200.4.f.b.149.10		12	40.29	even	2	inner
200.4.f.c.149.3		12	8.5	even	2
200.4.f.c.149.4		12	5.4	even	2
360.4.k.c.181.11		12	120.53	even	4
360.4.k.c.181.12		12	15.8	even	4
800.4.d.d.401.3		12	20.7	even	4
800.4.d.d.401.10		12	40.27	even	4
800.4.f.b.49.3		12	20.19	odd	2
800.4.f.b.49.4		12	8.3	odd	2
800.4.f.c.49.9		12	40.19	odd	2
800.4.f.c.49.10		12	4.3	odd	2
1280.4.a.ba.1.2		6	80.3	even	4
1280.4.a.bb.1.2		6	80.53	odd	4
1280.4.a.bc.1.5		6	80.13	odd	4
1280.4.a.bd.1.5		6	80.43	even	4
1440.4.k.c.721.6		12	120.83	odd	4
1440.4.k.c.721.12		12	60.23	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	200.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.13111 - 2.59241i) q^{2} -6.25785 q^{3} +(-5.44116 - 5.86462i) q^{4} +(-7.07834 + 16.2229i) q^{6} -34.6280i q^{7} +(-21.3581 + 7.47214i) q^{8} +12.1606 q^{9} +O(q^{10})\)	\(q+(1.13111 - 2.59241i) q^{2} -6.25785 q^{3} +(-5.44116 - 5.86462i) q^{4} +(-7.07834 + 16.2229i) q^{6} -34.6280i q^{7} +(-21.3581 + 7.47214i) q^{8} +12.1606 q^{9} -7.91595i q^{11} +(34.0499 + 36.6999i) q^{12} -11.0346 q^{13} +(-89.7698 - 39.1682i) q^{14} +(-4.78760 + 63.8207i) q^{16} +57.6152i q^{17} +(13.7551 - 31.5253i) q^{18} +141.133i q^{19} +216.696i q^{21} +(-20.5214 - 8.95385i) q^{22} -129.328i q^{23} +(133.655 - 46.7595i) q^{24} +(-12.4814 + 28.6062i) q^{26} +92.8625 q^{27} +(-203.080 + 188.416i) q^{28} +89.1664i q^{29} -78.3307 q^{31} +(160.034 + 84.5999i) q^{32} +49.5368i q^{33} +(149.362 + 65.1694i) q^{34} +(-66.1679 - 71.3175i) q^{36} -249.332 q^{37} +(365.874 + 159.637i) q^{38} +69.0530 q^{39} +91.8705 q^{41} +(561.766 + 245.109i) q^{42} +194.184 q^{43} +(-46.4240 + 43.0719i) q^{44} +(-335.270 - 146.285i) q^{46} -72.6149i q^{47} +(29.9600 - 399.380i) q^{48} -856.096 q^{49} -360.547i q^{51} +(60.0411 + 64.7139i) q^{52} -456.782 q^{53} +(105.038 - 240.737i) q^{54} +(258.745 + 739.586i) q^{56} -883.187i q^{57} +(231.156 + 100.857i) q^{58} -341.098i q^{59} -217.067i q^{61} +(-88.6011 + 203.065i) q^{62} -421.098i q^{63} +(400.334 - 319.181i) q^{64} +(128.420 + 56.0318i) q^{66} -529.237 q^{67} +(337.892 - 313.494i) q^{68} +809.314i q^{69} +381.540 q^{71} +(-259.728 + 90.8659i) q^{72} +876.902i q^{73} +(-282.023 + 646.370i) q^{74} +(827.690 - 767.926i) q^{76} -274.113 q^{77} +(78.1069 - 179.013i) q^{78} +203.950 q^{79} -909.456 q^{81} +(103.916 - 238.166i) q^{82} -996.654 q^{83} +(1270.84 - 1179.08i) q^{84} +(219.644 - 503.403i) q^{86} -557.989i q^{87} +(59.1491 + 169.069i) q^{88} -172.456 q^{89} +382.107i q^{91} +(-758.459 + 703.693i) q^{92} +490.182 q^{93} +(-188.247 - 82.1358i) q^{94} +(-1001.47 - 529.413i) q^{96} +1058.49i q^{97} +(-968.343 + 2219.35i) q^{98} -96.2629i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} - 12 q^{3} - 16 q^{4} - 36 q^{6} + 24 q^{8} + 108 q^{9}+O(q^{10}) \) 12 * q - 6 * q^2 - 12 * q^3 - 16 * q^4 - 36 * q^6 + 24 * q^8 + 108 * q^9	\( 12 q - 6 q^{2} - 12 q^{3} - 16 q^{4} - 36 q^{6} + 24 q^{8} + 108 q^{9} + 164 q^{12} - 68 q^{14} - 56 q^{16} - 450 q^{18} - 492 q^{22} - 360 q^{24} - 308 q^{26} - 432 q^{27} - 628 q^{28} - 264 q^{31} - 856 q^{32} + 180 q^{34} + 440 q^{36} - 136 q^{37} + 1388 q^{38} - 600 q^{39} + 40 q^{41} + 2332 q^{42} + 1204 q^{43} + 472 q^{44} - 1268 q^{46} + 2536 q^{48} - 1308 q^{49} + 1272 q^{52} - 1056 q^{53} + 1512 q^{54} - 728 q^{56} - 1528 q^{58} - 2104 q^{62} + 2048 q^{64} + 2928 q^{66} + 2412 q^{67} - 960 q^{68} - 1592 q^{71} - 744 q^{72} + 420 q^{74} + 2256 q^{76} - 824 q^{77} + 160 q^{78} - 2016 q^{79} + 2508 q^{81} - 352 q^{82} - 3556 q^{83} - 1048 q^{84} - 244 q^{86} - 1008 q^{88} + 424 q^{89} - 1068 q^{92} - 2784 q^{93} - 292 q^{94} - 5920 q^{96} - 638 q^{98}+O(q^{100}) \) 12 * q - 6 * q^2 - 12 * q^3 - 16 * q^4 - 36 * q^6 + 24 * q^8 + 108 * q^9 + 164 * q^12 - 68 * q^14 - 56 * q^16 - 450 * q^18 - 492 * q^22 - 360 * q^24 - 308 * q^26 - 432 * q^27 - 628 * q^28 - 264 * q^31 - 856 * q^32 + 180 * q^34 + 440 * q^36 - 136 * q^37 + 1388 * q^38 - 600 * q^39 + 40 * q^41 + 2332 * q^42 + 1204 * q^43 + 472 * q^44 - 1268 * q^46 + 2536 * q^48 - 1308 * q^49 + 1272 * q^52 - 1056 * q^53 + 1512 * q^54 - 728 * q^56 - 1528 * q^58 - 2104 * q^62 + 2048 * q^64 + 2928 * q^66 + 2412 * q^67 - 960 * q^68 - 1592 * q^71 - 744 * q^72 + 420 * q^74 + 2256 * q^76 - 824 * q^77 + 160 * q^78 - 2016 * q^79 + 2508 * q^81 - 352 * q^82 - 3556 * q^83 - 1048 * q^84 - 244 * q^86 - 1008 * q^88 + 424 * q^89 - 1068 * q^92 - 2784 * q^93 - 292 * q^94 - 5920 * q^96 - 638 * q^98

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