LMFDB - Embedded newform 189.4.f.b.64.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,4,Mod(64,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("189.64");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	189.f (of order $3$, degree $2$, 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:	$11.1513609911$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 58 x^{14} - 129 x^{13} + 2107 x^{12} - 4455 x^{11} + 42901 x^{10} - 76404 x^{9} + \cdots + 21307456 $ x^16 - 3x^15 + 58x^14 - 129x^13 + 2107x^12 - 4455x^11 + 42901x^10 - 76404x^9 + 599392x^8 - 1089732x^7 + 4808401x^6 - 7939134x^5 + 26225236x^4 - 39450864x^3 + 62254768x^2 - 39660672*x + 21307456
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{14} $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			64.5
Root			$0.797492 + 1.38130i$ of defining polynomial
Character	$\chi$	$=$	189.64
Dual form			189.4.f.b.127.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.797492 + 1.38130i) q^{2} +(2.72801 - 4.72505i) q^{4} +(-1.27816 + 2.21384i) q^{5} +(3.50000 + 6.06218i) q^{7} +21.4622 q^{8} +O(q^{10})$	\(q+(0.797492 + 1.38130i) q^{2} +(2.72801 - 4.72505i) q^{4} +(-1.27816 + 2.21384i) q^{5} +(3.50000 + 6.06218i) q^{7} +21.4622 q^{8} -4.07730 q^{10} +(4.04539 + 7.00681i) q^{11} +(13.1187 - 22.7222i) q^{13} +(-5.58245 + 9.66908i) q^{14} +(-4.70819 - 8.15482i) q^{16} +69.7407 q^{17} +105.751 q^{19} +(6.97368 + 12.0788i) q^{20} +(-6.45233 + 11.1758i) q^{22} +(77.1585 - 133.642i) q^{23} +(59.2326 + 102.594i) q^{25} +41.8481 q^{26} +38.1922 q^{28} +(-36.3274 - 62.9209i) q^{29} +(-141.400 + 244.911i) q^{31} +(93.3581 - 161.701i) q^{32} +(55.6177 + 96.3327i) q^{34} -17.8943 q^{35} +25.7974 q^{37} +(84.3355 + 146.073i) q^{38} +(-27.4321 + 47.5138i) q^{40} +(-43.5544 + 75.4385i) q^{41} +(-44.5553 - 77.1721i) q^{43} +44.1434 q^{44} +246.133 q^{46} +(157.309 + 272.467i) q^{47} +(-24.5000 + 42.4352i) q^{49} +(-94.4751 + 163.636i) q^{50} +(-71.5757 - 123.973i) q^{52} -356.536 q^{53} -20.6826 q^{55} +(75.1175 + 130.107i) q^{56} +(57.9416 - 100.358i) q^{58} +(206.245 - 357.226i) q^{59} +(-73.3780 - 127.094i) q^{61} -451.060 q^{62} +222.479 q^{64} +(33.5355 + 58.0852i) q^{65} +(153.201 - 265.352i) q^{67} +(190.254 - 329.529i) q^{68} +(-14.2705 - 24.7173i) q^{70} -1038.77 q^{71} -1157.10 q^{73} +(20.5732 + 35.6339i) q^{74} +(288.490 - 499.679i) q^{76} +(-28.3177 + 49.0477i) q^{77} +(-373.147 - 646.309i) q^{79} +24.0713 q^{80} -138.937 q^{82} +(262.712 + 455.031i) q^{83} +(-89.1399 + 154.395i) q^{85} +(71.0651 - 123.088i) q^{86} +(86.8227 + 150.381i) q^{88} +643.894 q^{89} +183.661 q^{91} +(-420.978 - 729.156i) q^{92} +(-250.905 + 434.580i) q^{94} +(-135.167 + 234.116i) q^{95} +(-154.581 - 267.742i) q^{97} -78.1543 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} - 43 q^{4} + 30 q^{5} + 56 q^{7} - 12 q^{8}+O(q^{10}) $ 16 * q + 3 * q^2 - 43 * q^4 + 30 * q^5 + 56 * q^7 - 12 * q^8	$ 16 q + 3 q^{2} - 43 q^{4} + 30 q^{5} + 56 q^{7} - 12 q^{8} - 28 q^{10} + 24 q^{11} - 68 q^{13} - 21 q^{14} - 103 q^{16} - 336 q^{17} + 352 q^{19} + 330 q^{20} - 151 q^{22} + 228 q^{23} - 244 q^{25} - 1590 q^{26} - 602 q^{28} + 618 q^{29} - 72 q^{31} + 786 q^{32} + 261 q^{34} + 420 q^{35} + 420 q^{37} + 1032 q^{38} + 375 q^{40} + 420 q^{41} + 2 q^{43} - 774 q^{44} + 804 q^{46} + 570 q^{47} - 392 q^{49} + 1110 q^{50} + 431 q^{52} - 1056 q^{53} - 1676 q^{55} - 42 q^{56} - 37 q^{58} - 150 q^{59} - 578 q^{61} - 2340 q^{62} - 224 q^{64} - 366 q^{65} + 898 q^{67} + 2526 q^{68} - 98 q^{70} - 1764 q^{71} + 1944 q^{73} - 222 q^{74} - 1423 q^{76} - 168 q^{77} + 158 q^{79} - 4950 q^{80} - 422 q^{82} + 2958 q^{83} + 774 q^{85} - 114 q^{86} - 1317 q^{88} - 8760 q^{89} - 952 q^{91} + 4629 q^{92} + 3234 q^{94} + 930 q^{95} + 60 q^{97} - 294 q^{98}+O(q^{100}) $ 16 * q + 3 * q^2 - 43 * q^4 + 30 * q^5 + 56 * q^7 - 12 * q^8 - 28 * q^10 + 24 * q^11 - 68 * q^13 - 21 * q^14 - 103 * q^16 - 336 * q^17 + 352 * q^19 + 330 * q^20 - 151 * q^22 + 228 * q^23 - 244 * q^25 - 1590 * q^26 - 602 * q^28 + 618 * q^29 - 72 * q^31 + 786 * q^32 + 261 * q^34 + 420 * q^35 + 420 * q^37 + 1032 * q^38 + 375 * q^40 + 420 * q^41 + 2 * q^43 - 774 * q^44 + 804 * q^46 + 570 * q^47 - 392 * q^49 + 1110 * q^50 + 431 * q^52 - 1056 * q^53 - 1676 * q^55 - 42 * q^56 - 37 * q^58 - 150 * q^59 - 578 * q^61 - 2340 * q^62 - 224 * q^64 - 366 * q^65 + 898 * q^67 + 2526 * q^68 - 98 * q^70 - 1764 * q^71 + 1944 * q^73 - 222 * q^74 - 1423 * q^76 - 168 * q^77 + 158 * q^79 - 4950 * q^80 - 422 * q^82 + 2958 * q^83 + 774 * q^85 - 114 * q^86 - 1317 * q^88 - 8760 * q^89 - 952 * q^91 + 4629 * q^92 + 3234 * q^94 + 930 * q^95 + 60 * q^97 - 294 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.797492	+	1.38130i	0.281956	+	0.488362i	0.971866	−	0.235532i	$-0.0756834\pi$
$2$	0.797492	+	1.38130i	0.281956	+	0.488362i	−0.689910	+	0.723895i	$0.742350\pi$
$3$		0			0
$3$		0			0
$4$	2.72801	−	4.72505i	0.341001	−	0.590632i
$5$	−1.27816	+	2.21384i	−0.114322	+	0.198012i	−0.917509	−	0.397716i	$-0.869803\pi$
$5$	−1.27816	+	2.21384i	−0.114322	+	0.198012i	0.803186	+	0.595728i	$0.203136\pi$
$6$		0			0
$7$	3.50000	+	6.06218i	0.188982	+	0.327327i
$7$	3.50000	+	6.06218i	0.188982	+	0.327327i
$8$	21.4622			0.948502
$9$		0			0
$10$	−4.07730			−0.128935
$11$	4.04539	+	7.00681i	0.110885	+	0.192058i	0.916127	−	0.400888i	$-0.131298\pi$
$11$	4.04539	+	7.00681i	0.110885	+	0.192058i	−0.805243	+	0.592945i	$0.797965\pi$
$12$		0			0
$13$	13.1187	−	22.7222i	0.279882	−	0.484769i	−0.691473	−	0.722402i	$-0.743038\pi$
$13$	13.1187	−	22.7222i	0.279882	−	0.484769i	0.971355	+	0.237633i	$0.0763714\pi$
$14$	−5.58245	+	9.66908i	−0.106569	+	0.184584i
$15$		0			0
$16$	−4.70819	−	8.15482i	−0.0735654	−	0.127419i
$17$	69.7407			0.994977			0.497489	−	0.867471i	$-0.334256\pi$
$17$	69.7407			0.994977			0.497489	+	0.867471i	$0.334256\pi$
$18$		0			0
$19$	105.751			1.27689			0.638445	−	0.769667i	$-0.279578\pi$
$19$	105.751			1.27689			0.638445	+	0.769667i	$0.279578\pi$
$20$	6.97368	+	12.0788i	0.0779681	+	0.135045i
$21$		0			0
$22$	−6.45233	+	11.1758i	−0.0625291	+	0.108304i
$23$	77.1585	−	133.642i	0.699507	−	1.21158i	−0.269131	−	0.963104i	$-0.586737\pi$
$23$	77.1585	−	133.642i	0.699507	−	1.21158i	0.968638	−	0.248477i	$-0.0799302\pi$
$24$		0			0
$25$	59.2326	+	102.594i	0.473861	+	0.820751i
$26$	41.8481			0.315657
$27$		0			0
$28$	38.1922			0.257773
$29$	−36.3274	−	62.9209i	−0.232615	−	0.402900i	0.725962	−	0.687735i	$-0.241395\pi$
$29$	−36.3274	−	62.9209i	−0.232615	−	0.402900i	−0.958577	+	0.284834i	$0.908061\pi$
$30$		0			0
$31$	−141.400	+	244.911i	−0.819230	+	1.41895i	0.0870211	+	0.996206i	$0.472265\pi$
$31$	−141.400	+	244.911i	−0.819230	+	1.41895i	−0.906251	+	0.422741i	$0.861068\pi$
$32$	93.3581	−	161.701i	0.515736	−	0.893280i
$33$		0			0
$34$	55.6177	+	96.3327i	0.280540	+	0.485909i
$35$	−17.8943			−0.0864195
$36$		0			0
$37$	25.7974			0.114623			0.0573117	−	0.998356i	$-0.481747\pi$
$37$	25.7974			0.114623			0.0573117	+	0.998356i	$0.481747\pi$
$38$	84.3355	+	146.073i	0.360027	+	0.623585i
$39$		0			0
$40$	−27.4321	+	47.5138i	−0.108435	+	0.187815i
$41$	−43.5544	+	75.4385i	−0.165904	+	0.287354i	−0.936976	−	0.349394i	$-0.886387\pi$
$41$	−43.5544	+	75.4385i	−0.165904	+	0.287354i	0.771072	+	0.636748i	$0.219721\pi$
$42$		0			0
$43$	−44.5553	−	77.1721i	−0.158014	−	0.273689i	0.776138	−	0.630563i	$-0.217176\pi$
$43$	−44.5553	−	77.1721i	−0.158014	−	0.273689i	−0.934153	+	0.356874i	$0.883843\pi$
$44$	44.1434			0.151247
$45$		0			0
$46$	246.133			0.788921
$47$	157.309	+	272.467i	0.488209	+	0.845603i	0.999908	−	0.0135621i	$-0.00431707\pi$
$47$	157.309	+	272.467i	0.488209	+	0.845603i	−0.511699	+	0.859165i	$0.670984\pi$
$48$		0			0
$49$	−24.5000	+	42.4352i	−0.0714286	+	0.123718i
$50$	−94.4751	+	163.636i	−0.267216	+	0.462832i
$51$		0			0
$52$	−71.5757	−	123.973i	−0.190880	−	0.330614i
$53$	−356.536			−0.924038			−0.462019	−	0.886870i	$-0.652875\pi$
$53$	−356.536			−0.924038			−0.462019	+	0.886870i	$0.652875\pi$
$54$		0			0
$55$	−20.6826			−0.0507063
$56$	75.1175	+	130.107i	0.179250	+	0.310470i
$57$		0			0
$58$	57.9416	−	100.358i	0.131174	−	0.227200i
$59$	206.245	−	357.226i	0.455098	−	0.788252i	−0.543596	−	0.839347i	$-0.682938\pi$
$59$	206.245	−	357.226i	0.455098	−	0.788252i	0.998694	+	0.0510946i	$0.0162710\pi$
$60$		0			0
$61$	−73.3780	−	127.094i	−0.154018	−	0.266767i	0.778683	−	0.627417i	$-0.215888\pi$
$61$	−73.3780	−	127.094i	−0.154018	−	0.266767i	−0.932701	+	0.360651i	$0.882555\pi$
$62$	−451.060			−0.923947
$63$		0			0
$64$	222.479			0.434528
$65$	33.5355	+	58.0852i	0.0639934	+	0.110840i
$66$		0			0
$67$	153.201	−	265.352i	0.279350	−	0.483849i	−0.691873	−	0.722019i	$-0.743214\pi$
$67$	153.201	−	265.352i	0.279350	−	0.483849i	0.971223	+	0.238170i	$0.0765476\pi$
$68$	190.254	−	329.529i	0.339289	−	0.587665i
$69$		0			0
$70$	−14.2705	−	24.7173i	−0.0243665	−	0.0422040i
$71$	−1038.77			−1.73632			−0.868160	−	0.496284i	$-0.834698\pi$
$71$	−1038.77			−1.73632			−0.868160	+	0.496284i	$0.834698\pi$
$72$		0			0
$73$	−1157.10			−1.85518			−0.927590	−	0.373600i	$-0.878123\pi$
$73$	−1157.10			−1.85518			−0.927590	+	0.373600i	$0.878123\pi$
$74$	20.5732	+	35.6339i	0.0323188	+	0.0559777i
$75$		0			0
$76$	288.490	−	499.679i	0.435421	−	0.754172i
$77$	−28.3177	+	49.0477i	−0.0419104	+	0.0725910i
$78$		0			0
$79$	−373.147	−	646.309i	−0.531421	−	0.920449i	−0.999327	−	0.0366706i	$-0.988325\pi$
$79$	−373.147	−	646.309i	−0.531421	−	0.920449i	0.467906	−	0.883778i	$-0.345009\pi$
$80$	24.0713			0.0336407
$81$		0			0
$82$	−138.937			−0.187111
$83$	262.712	+	455.031i	0.347427	+	0.601761i	0.985792	−	0.167973i	$-0.0537222\pi$
$83$	262.712	+	455.031i	0.347427	+	0.601761i	−0.638365	+	0.769734i	$0.720389\pi$
$84$		0			0
$85$	−89.1399	+	154.395i	−0.113748	+	0.197017i
$86$	71.0651	−	123.088i	0.0891063	−	0.154337i
$87$		0			0
$88$	86.8227	+	150.381i	0.105174	+	0.182167i
$89$	643.894			0.766883			0.383441	−	0.923565i	$-0.374739\pi$
$89$	643.894			0.766883			0.383441	+	0.923565i	$0.374739\pi$
$90$		0			0
$91$	183.661			0.211571
$92$	−420.978	−	729.156i	−0.477066	−	0.826302i
$93$		0			0
$94$	−250.905	+	434.580i	−0.275307	+	0.476846i
$95$	−135.167	+	234.116i	−0.145977	+	0.252839i
$96$		0			0
$97$	−154.581	−	267.742i	−0.161808	−	0.280259i	0.773709	−	0.633541i	$-0.218399\pi$
$97$	−154.581	−	267.742i	−0.161808	−	0.280259i	−0.935517	+	0.353282i	$0.885066\pi$
$98$	−78.1543			−0.0805589
$99$		0			0
$100$	646.349			0.646349
$101$	560.283	+	970.439i	0.551983	+	0.956062i	0.998131	+	0.0611033i	$0.0194619\pi$
$101$	560.283	+	970.439i	0.551983	+	0.956062i	−0.446149	+	0.894959i	$0.647205\pi$
$102$		0			0
$103$	−282.613	+	489.500i	−0.270356	+	0.468271i	−0.968953	−	0.247245i	$-0.920475\pi$
$103$	−282.613	+	489.500i	−0.270356	+	0.468271i	0.698597	+	0.715516i	$0.253808\pi$
$104$	281.555	−	487.667i	0.265468	−	0.459805i
$105$		0			0
$106$	−284.335	−	492.483i	−0.260538	−	0.451266i
$107$	−1593.24			−1.43948			−0.719738	−	0.694246i	$-0.755738\pi$
$107$	−1593.24			−1.43948			−0.719738	+	0.694246i	$0.755738\pi$
$108$		0			0
$109$	−1498.64			−1.31691			−0.658457	−	0.752619i	$-0.728790\pi$
$109$	−1498.64			−1.31691			−0.658457	+	0.752619i	$0.728790\pi$
$110$	−16.4942	−	28.5689i	−0.0142969	−	0.0247630i
$111$		0			0
$112$	32.9573	−	57.0838i	0.0278051	−	0.0481599i
$113$	347.639	−	602.129i	0.289408	−	0.501270i	−0.684260	−	0.729238i	$-0.739875\pi$
$113$	347.639	−	602.129i	0.289408	−	0.501270i	0.973669	+	0.227968i	$0.0732081\pi$
$114$		0			0
$115$	197.242	+	341.633i	0.159938	+	0.277021i
$116$	−396.406			−0.317288
$117$		0			0
$118$	657.914			0.513270
$119$	244.093	+	422.781i	0.188033	+	0.325683i
$120$		0			0
$121$	632.770	−	1095.99i	0.475409	−	0.823433i
$122$	117.037	−	202.714i	0.0868526	−	0.150433i
$123$		0			0
$124$	771.479	+	1336.24i	0.558717	+	0.967726i
$125$	−622.376			−0.445336
$126$		0			0
$127$	−1377.51			−0.962475			−0.481237	−	0.876590i	$-0.659812\pi$
$127$	−1377.51			−0.962475			−0.481237	+	0.876590i	$0.659812\pi$
$128$	−569.440	−	986.299i	−0.393218	−	0.681073i
$129$		0			0
$130$	−53.4887	+	92.6451i	−0.0360867	+	0.0625039i
$131$	−1361.14	+	2357.56i	−0.907809	+	1.57237i	−0.0907071	+	0.995878i	$0.528913\pi$
$131$	−1361.14	+	2357.56i	−0.907809	+	1.57237i	−0.817102	+	0.576493i	$0.804421\pi$
$132$		0			0
$133$	370.128	+	641.081i	0.241310	+	0.417960i
$134$	488.706			0.315058
$135$		0			0
$136$	1496.79			0.943738
$137$	1176.31	+	2037.43i	0.733570	+	1.27058i	0.955348	+	0.295484i	$0.0954808\pi$
$137$	1176.31	+	2037.43i	0.733570	+	1.27058i	−0.221777	+	0.975097i	$0.571186\pi$
$138$		0			0
$139$	1024.35	−	1774.22i	0.625065	−	1.08264i	−0.363464	−	0.931608i	$-0.618406\pi$
$139$	1024.35	−	1774.22i	0.625065	−	1.08264i	0.988528	−	0.151036i	$-0.0482608\pi$
$140$	−48.8157	+	84.5514i	−0.0294692	+	0.0510421i
$141$		0			0
$142$	−828.408	−	1434.84i	−0.489566	−	0.847954i
$143$	212.280			0.124138
$144$		0			0
$145$	185.729			0.106372
$146$	−922.777	−	1598.30i	−0.523079	−	0.906000i
$147$		0			0
$148$	70.3756	−	121.894i	0.0390867	−	0.0677002i
$149$	646.993	−	1120.63i	0.355730	−	0.616142i	−0.631513	−	0.775366i	$-0.717566\pi$
$149$	646.993	−	1120.63i	0.355730	−	0.616142i	0.987243	+	0.159223i	$0.0508990\pi$
$150$		0			0
$151$	1070.84	+	1854.76i	0.577113	+	0.999589i	0.995809	+	0.0914626i	$0.0291542\pi$
$151$	1070.84	+	1854.76i	0.577113	+	0.999589i	−0.418695	+	0.908127i	$0.637512\pi$
$152$	2269.64			1.21113
$153$		0			0
$154$	−90.3326			−0.0472676
$155$	−361.463	−	626.072i	−0.187312	−	0.324434i
$156$		0			0
$157$	−1294.10	+	2241.44i	−0.657835	+	1.13940i	0.323340	+	0.946283i	$0.395194\pi$
$157$	−1294.10	+	2241.44i	−0.657835	+	1.13940i	−0.981175	+	0.193121i	$0.938139\pi$
$158$	595.163	−	1030.85i	0.299675	−	0.519052i
$159$		0			0
$160$	238.653	+	413.360i	0.117920	+	0.204244i
$161$	1080.22			0.528777
$162$		0			0
$163$	842.940			0.405056			0.202528	−	0.979276i	$-0.435084\pi$
$163$	842.940			0.405056			0.202528	+	0.979276i	$0.435084\pi$
$164$	237.634	+	411.594i	0.113147	+	0.195976i
$165$		0			0
$166$	−419.022	+	725.767i	−0.195918	+	0.339340i
$167$	828.694	−	1435.34i	0.383990	−	0.665089i	−0.607639	−	0.794213i	$-0.707883\pi$
$167$	828.694	−	1435.34i	0.383990	−	0.665089i	0.991628	+	0.129124i	$0.0412165\pi$
$168$		0			0
$169$	754.302	+	1306.49i	0.343333	+	0.594669i
$170$	−284.354			−0.128288
$171$		0			0
$172$	−486.190			−0.215533
$173$	973.548	+	1686.23i	0.427847	+	0.741052i	0.996682	−	0.0813995i	$-0.0259389\pi$
$173$	973.548	+	1686.23i	0.427847	+	0.741052i	−0.568835	+	0.822452i	$0.692606\pi$
$174$		0			0
$175$	−414.628	+	718.157i	−0.179103	+	0.310215i
$176$	38.0929	−	65.9788i	0.0163145	−	0.0282576i
$177$		0			0
$178$	513.500	+	889.409i	0.216227	+	0.374517i
$179$	841.904			0.351547			0.175773	−	0.984431i	$-0.443757\pi$
$179$	841.904			0.351547			0.175773	+	0.984431i	$0.443757\pi$
$180$		0			0
$181$	158.260			0.0649912			0.0324956	−	0.999472i	$-0.489655\pi$
$181$	158.260			0.0649912			0.0324956	+	0.999472i	$0.489655\pi$
$182$	146.468	+	253.691i	0.0596536	+	0.103323i
$183$		0			0
$184$	1655.99	−	2868.25i	0.663483	−	1.14919i
$185$	−32.9732	+	57.1113i	−0.0131040	+	0.0226968i
$186$		0			0
$187$	282.128	+	488.660i	0.110328	+	0.191093i
$188$	1716.56			0.665920
$189$		0			0
$190$	−431.178			−0.164636
$191$	−2309.48	−	4000.14i	−0.874912	−	1.51539i	−0.856857	−	0.515555i	$-0.827586\pi$
$191$	−2309.48	−	4000.14i	−0.874912	−	1.51539i	−0.0180552	−	0.999837i	$-0.505747\pi$
$192$		0			0
$193$	−2295.48	+	3975.89i	−0.856126	+	1.48285i	0.0194700	+	0.999810i	$0.493802\pi$
$193$	−2295.48	+	3975.89i	−0.856126	+	1.48285i	−0.875596	+	0.483044i	$0.839531\pi$
$194$	246.555	−	427.045i	0.0912453	−	0.158041i
$195$		0			0
$196$	133.673	+	231.528i	0.0487145	+	0.0843760i
$197$	2646.03			0.956965			0.478482	−	0.878097i	$-0.341187\pi$
$197$	2646.03			0.956965			0.478482	+	0.878097i	$0.341187\pi$
$198$		0			0
$199$	4741.58			1.68905			0.844527	−	0.535513i	$-0.179882\pi$
$199$	4741.58			1.68905			0.844527	+	0.535513i	$0.179882\pi$
$200$	1271.26	+	2201.89i	0.449458	+	0.778484i
$201$		0			0
$202$	−893.643	+	1547.84i	−0.311270	+	0.539135i
$203$	254.292	−	440.446i	0.0879201	−	0.152282i
$204$		0			0
$205$	−111.339	−	192.845i	−0.0379330	−	0.0657019i
$206$	−901.527			−0.304915
$207$		0			0
$208$	−247.060			−0.0823585
$209$	427.803	+	740.977i	0.141587	+	0.245236i
$210$		0			0
$211$	2290.39	−	3967.08i	0.747285	−	1.29434i	−0.201834	−	0.979420i	$-0.564690\pi$
$211$	2290.39	−	3967.08i	0.747285	−	1.29434i	0.949119	−	0.314916i	$-0.101977\pi$
$212$	−972.635	+	1684.65i	−0.315098	+	0.545766i
$213$		0			0
$214$	−1270.59	−	2200.73i	−0.405869	−	0.702986i
$215$	227.796			0.0722583
$216$		0			0
$217$	−1979.59			−0.619279
$218$	−1195.15	−	2070.07i	−0.371312	−	0.643131i
$219$		0			0
$220$	−56.4224	+	97.7265i	−0.0172909	+	0.0299487i
$221$	914.905	−	1584.66i	0.278476	−	0.482334i
$222$		0			0
$223$	−2238.14	−	3876.57i	−0.672093	−	1.16410i	−0.977309	−	0.211817i	$-0.932062\pi$
$223$	−2238.14	−	3876.57i	−0.672093	−	1.16410i	0.305216	−	0.952283i	$-0.401271\pi$
$224$	1307.01			0.389859
$225$		0			0
$226$	1108.96			0.326402
$227$	787.439	+	1363.88i	0.230239	+	0.398785i	0.957878	−	0.287175i	$-0.0927160\pi$
$227$	787.439	+	1363.88i	0.230239	+	0.398785i	−0.727640	+	0.685960i	$0.759383\pi$
$228$		0			0
$229$	−223.577	+	387.247i	−0.0645170	+	0.111747i	−0.896480	−	0.443085i	$-0.853884\pi$
$229$	−223.577	+	387.247i	−0.0645170	+	0.111747i	0.831963	+	0.554832i	$0.187217\pi$
$230$	−314.598	+	544.900i	−0.0901912	+	0.156216i
$231$		0			0
$232$	−779.664	−	1350.42i	−0.220635	−	0.382152i
$233$	−3933.72			−1.10604			−0.553018	−	0.833169i	$-0.686524\pi$
$233$	−3933.72			−1.10604			−0.553018	+	0.833169i	$0.686524\pi$
$234$		0			0
$235$	−804.263			−0.223253
$236$	−1125.28	−	1949.03i	−0.310378	−	0.537590i
$237$		0			0
$238$	−389.324	+	674.329i	−0.106034	+	0.183656i
$239$	−1839.53	+	3186.15i	−0.497862	+	0.862322i	−0.999997	−	0.00246688i	$-0.999215\pi$
$239$	−1839.53	+	3186.15i	−0.497862	+	0.862322i	0.502135	+	0.864789i	$0.332548\pi$
$240$		0			0
$241$	−416.504	−	721.407i	−0.111325	−	0.192821i	0.804980	−	0.593303i	$-0.202176\pi$
$241$	−416.504	−	721.407i	−0.111325	−	0.192821i	−0.916305	+	0.400481i	$0.868843\pi$
$242$	2018.52			0.536178
$243$		0			0
$244$	−800.705			−0.210081
$245$	−62.6299	−	108.478i	−0.0163317	−	0.0282874i
$246$		0			0
$247$	1387.31	−	2402.89i	0.357378	−	0.618997i
$248$	−3034.74	+	5256.32i	−0.777041	+	1.34587i
$249$		0			0
$250$	−496.340	−	859.686i	−0.125565	−	0.217485i
$251$	−7237.27			−1.81997			−0.909985	−	0.414640i	$-0.863907\pi$
$251$	−7237.27			−1.81997			−0.909985	+	0.414640i	$0.863907\pi$
$252$		0			0
$253$	1248.54			0.310258
$254$	−1098.55	−	1902.75i	−0.271376	−	0.470036i
$255$		0			0
$256$	1798.16	−	3114.51i	0.439004	−	0.760378i
$257$	−1539.39	+	2666.29i	−0.373635	+	0.647155i	−0.990122	−	0.140210i	$-0.955222\pi$
$257$	−1539.39	+	2666.29i	−0.373635	+	0.647155i	0.616487	+	0.787365i	$0.288555\pi$
$258$		0			0
$259$	90.2908	+	156.388i	0.0216618	+	0.0375193i
$260$	365.941			0.0872873
$261$		0			0
$262$	−4341.98			−1.02385
$263$	−1978.57	−	3426.99i	−0.463894	−	0.803488i	0.535257	−	0.844689i	$-0.320215\pi$
$263$	−1978.57	−	3426.99i	−0.463894	−	0.803488i	−0.999151	+	0.0412015i	$0.986881\pi$
$264$		0			0
$265$	455.711	−	789.315i	0.105638	−	0.182971i
$266$	−590.349	+	1022.51i	−0.136077	+	0.235693i
$267$		0			0
$268$	−835.868	−	1447.77i	−0.190518	−	0.329986i
$269$	2552.30			0.578499			0.289249	−	0.957254i	$-0.406594\pi$
$269$	2552.30			0.578499			0.289249	+	0.957254i	$0.406594\pi$
$270$		0			0
$271$	−1888.99			−0.423424			−0.211712	−	0.977332i	$-0.567904\pi$
$271$	−1888.99			−0.423424			−0.211712	+	0.977332i	$0.567904\pi$
$272$	−328.352	−	568.723i	−0.0731959	−	0.126779i
$273$		0			0
$274$	−1876.20	+	3249.67i	−0.413669	+	0.716496i
$275$	−479.237	+	830.064i	−0.105088	+	0.182017i
$276$		0			0
$277$	1476.48	+	2557.34i	0.320264	+	0.554713i	0.980542	−	0.196307i	$-0.0628951\pi$
$277$	1476.48	+	2557.34i	0.320264	+	0.554713i	−0.660278	+	0.751021i	$0.729562\pi$
$278$	3267.64			0.704963
$279$		0			0
$280$	−384.049			−0.0819691
$281$	603.238	+	1044.84i	0.128065	+	0.221814i	0.922927	−	0.384976i	$-0.125790\pi$
$281$	603.238	+	1044.84i	0.128065	+	0.221814i	−0.794862	+	0.606790i	$0.792457\pi$
$282$		0			0
$283$	−1848.75	+	3202.14i	−0.388329	+	0.672605i	−0.992225	−	0.124458i	$-0.960281\pi$
$283$	−1848.75	+	3202.14i	−0.388329	+	0.672605i	0.603896	+	0.797063i	$0.293614\pi$
$284$	−2833.76	+	4908.22i	−0.592088	+	1.02553i
$285$		0			0
$286$	169.292	+	293.222i	0.0350015	+	0.0606244i
$287$	−609.762			−0.125412
$288$		0			0
$289$	−49.2304			−0.0100204
$290$	148.117	+	256.547i	0.0299923	+	0.0519481i
$291$		0			0
$292$	−3156.58	+	5467.35i	−0.632619	+	1.09573i
$293$	1242.99	−	2152.92i	0.247837	−	0.429267i	−0.715088	−	0.699034i	$-0.753614\pi$
$293$	1242.99	−	2152.92i	0.247837	−	0.429267i	0.962925	+	0.269768i	$0.0869469\pi$
$294$		0			0
$295$	527.228	+	913.185i	0.104056	+	0.180230i
$296$	553.667			0.108720
$297$		0			0
$298$	2063.89			0.401201
$299$	−2024.43	−	3506.42i	−0.391558	−	0.678198i
$300$		0			0
$301$	311.887	−	540.205i	0.0597239	−	0.103445i
$302$	−1707.98	+	2958.31i	−0.325441	+	0.563681i
$303$		0			0
$304$	−497.895	−	862.379i	−0.0939350	−	0.162700i
$305$	375.156			0.0704307
$306$		0			0
$307$	−2167.98			−0.403040			−0.201520	−	0.979484i	$-0.564588\pi$
$307$	−2167.98			−0.403040			−0.201520	+	0.979484i	$0.564588\pi$
$308$	154.502	+	267.605i	0.0285830	+	0.0495072i
$309$		0			0
$310$	576.528	−	998.576i	0.105628	−	0.182953i
$311$	2330.99	−	4037.39i	0.425010	−	0.736140i	−0.571411	−	0.820664i	$-0.693604\pi$
$311$	2330.99	−	4037.39i	0.425010	−	0.736140i	0.996421	+	0.0845244i	$0.0269371\pi$
$312$		0			0
$313$	−249.595	−	432.311i	−0.0450733	−	0.0780693i	0.842609	−	0.538526i	$-0.181019\pi$
$313$	−249.595	−	432.311i	−0.0450733	−	0.0780693i	−0.887682	+	0.460457i	$0.847685\pi$
$314$	−4128.13			−0.741923
$315$		0			0
$316$	−4071.79			−0.724862
$317$	−4906.82	−	8498.87i	−0.869384	−	1.50582i	−0.862628	−	0.505840i	$-0.831183\pi$
$317$	−4906.82	−	8498.87i	−0.869384	−	1.50582i	−0.00675620	−	0.999977i	$-0.502151\pi$
$318$		0			0
$319$	293.916	−	509.078i	0.0515867	−	0.0893508i
$320$	−284.363	+	492.532i	−0.0496762	+	0.0860418i
$321$		0			0
$322$	861.466	+	1492.10i	0.149092	+	0.258235i
$323$	7375.14			1.27048
$324$		0			0
$325$	3108.21			0.530500
$326$	672.238	+	1164.35i	0.114208	+	0.197814i
$327$		0			0
$328$	−934.772	+	1619.07i	−0.157360	+	0.272556i
$329$	−1101.16	+	1907.27i	−0.184526	+	0.319608i
$330$		0			0
$331$	−5015.18	−	8686.55i	−0.832807	−	1.44246i	−0.895803	−	0.444451i	$-0.853399\pi$
$331$	−5015.18	−	8686.55i	−0.832807	−	1.44246i	0.0629962	−	0.998014i	$-0.479934\pi$
$332$	2866.73			0.473892
$333$		0			0
$334$	2643.51			0.433073
$335$	391.631	+	678.325i	0.0638719	+	0.110629i
$336$		0			0
$337$	4402.86	−	7625.97i	0.711688	−	1.23268i	−0.252535	−	0.967588i	$-0.581264\pi$
$337$	4402.86	−	7625.97i	0.711688	−	1.23268i	0.964223	−	0.265092i	$-0.0854023\pi$
$338$	−1203.10	+	2083.83i	−0.193609	+	0.335341i
$339$		0			0
$340$	486.349	+	842.382i	0.0775765	+	0.134366i
$341$	−2288.06			−0.363359
$342$		0			0
$343$	−343.000			−0.0539949
$344$	−956.253	−	1656.28i	−0.149877	−	0.259595i
$345$		0			0
$346$	−1552.79	+	2689.52i	−0.241268	+	0.417889i
$347$	3186.28	−	5518.79i	0.492934	−	0.853788i	−0.507032	−	0.861927i	$-0.669258\pi$
$347$	3186.28	−	5518.79i	0.492934	−	0.853788i	0.999967	+	0.00813945i	$0.00259090\pi$
$348$		0			0
$349$	1373.67	+	2379.26i	0.210690	+	0.364925i	0.951931	−	0.306314i	$-0.0990957\pi$
$349$	1373.67	+	2379.26i	0.210690	+	0.364925i	−0.741241	+	0.671239i	$0.765762\pi$
$350$	−1322.65			−0.201996
$351$		0			0
$352$	1510.68			0.228748
$353$	5139.65	+	8902.14i	0.774947	+	1.34225i	0.934824	+	0.355110i	$0.115557\pi$
$353$	5139.65	+	8902.14i	0.774947	+	1.34225i	−0.159878	+	0.987137i	$0.551110\pi$
$354$		0			0
$355$	1327.71	−	2299.66i	0.198500	−	0.343812i
$356$	1756.55	−	3042.43i	0.261508	−	0.452946i
$357$		0			0
$358$	671.412	+	1162.92i	0.0991208	+	0.171682i
$359$	10473.7			1.53978			0.769891	−	0.638176i	$-0.220311\pi$
$359$	10473.7			1.53978			0.769891	+	0.638176i	$0.220311\pi$
$360$		0			0
$361$	4324.25			0.630448
$362$	126.212	+	218.605i	0.0183247	+	0.0317393i
$363$		0			0
$364$	501.030	−	867.809i	0.0721459	−	0.124960i
$365$	1478.96	−	2561.63i	0.212088	−	0.367348i
$366$		0			0
$367$	−991.263	−	1716.92i	−0.140990	−	0.244203i	0.786879	−	0.617107i	$-0.211695\pi$
$367$	−991.263	−	1716.92i	−0.140990	−	0.244203i	−0.927870	+	0.372904i	$0.878362\pi$
$368$	−1453.11			−0.205838
$369$		0			0
$370$	−105.184			−0.0147790
$371$	−1247.88	−	2161.39i	−0.174627	−	0.302463i
$372$		0			0
$373$	−4670.83	+	8090.12i	−0.648382	+	1.12303i	0.335127	+	0.942173i	$0.391221\pi$
$373$	−4670.83	+	8090.12i	−0.648382	+	1.12303i	−0.983509	+	0.180858i	$0.942113\pi$
$374$	−449.990	+	779.406i	−0.0622151	+	0.107760i
$375$		0			0
$376$	3376.18	+	5847.72i	0.463067	+	0.802056i
$377$	−1906.27			−0.260418
$378$		0			0
$379$	8964.44			1.21497			0.607483	−	0.794333i	$-0.292179\pi$
$379$	8964.44			1.21497			0.607483	+	0.794333i	$0.292179\pi$
$380$	737.473	+	1277.34i	0.0995567	+	0.172437i
$381$		0			0
$382$	3683.59	−	6380.16i	0.493374	−	0.854548i
$383$	2285.75	−	3959.03i	0.304951	−	0.528190i	−0.672300	−	0.740279i	$-0.734693\pi$
$383$	2285.75	−	3959.03i	0.304951	−	0.528190i	0.977250	+	0.212089i	$0.0680266\pi$
$384$		0			0
$385$	−72.3892	−	125.382i	−0.00958258	−	0.0165975i
$386$	−7322.52			−0.965560
$387$		0			0
$388$	−1686.80			−0.220706
$389$	4418.60	+	7653.23i	0.575917	+	0.997517i	0.995941	+	0.0900045i	$0.0286881\pi$
$389$	4418.60	+	7653.23i	0.575917	+	0.997517i	−0.420024	+	0.907513i	$0.637979\pi$
$390$		0			0
$391$	5381.09	−	9320.32i	0.695993	−	1.20550i
$392$	−525.823	+	910.752i	−0.0677502	+	0.117347i
$393$		0			0
$394$	2110.19	+	3654.96i	0.269822	+	0.467346i
$395$	1907.77			0.243013
$396$		0			0
$397$	−3649.31			−0.461344			−0.230672	−	0.973032i	$-0.574092\pi$
$397$	−3649.31			−0.461344			−0.230672	+	0.973032i	$0.574092\pi$
$398$	3781.37	+	6549.53i	0.476239	+	0.824870i
$399$		0			0
$400$	557.757	−	966.063i	0.0697196	−	0.120758i
$401$	−509.732	+	882.882i	−0.0634784	+	0.109948i	−0.896018	−	0.444018i	$-0.853553\pi$
$401$	−509.732	+	882.882i	−0.0634784	+	0.109948i	0.832540	+	0.553965i	$0.186886\pi$
$402$		0			0
$403$	3709.95	+	6425.81i	0.458575	+	0.794274i
$404$	6113.84			0.752908
$405$		0			0
$406$	811.182			0.0991584
$407$	104.360	+	180.757i	0.0127100	+	0.0220143i
$408$		0			0
$409$	−690.083	+	1195.26i	−0.0834289	+	0.144503i	−0.904721	−	0.426005i	$-0.859920\pi$
$409$	−690.083	+	1195.26i	−0.0834289	+	0.144503i	0.821292	+	0.570508i	$0.193254\pi$
$410$	177.584	−	307.585i	0.0213909	−	0.0370501i
$411$		0			0
$412$	1541.94	+	2670.73i	0.184384	+	0.319362i
$413$	2887.42			0.344022
$414$		0			0
$415$	−1343.15			−0.158874
$416$	−2449.47	−	4242.60i	−0.288690	−	0.500025i
$417$		0			0
$418$	−682.339	+	1181.85i	−0.0798428	+	0.138292i
$419$	5644.76	−	9777.01i	0.658149	−	1.13995i	−0.322945	−	0.946418i	$-0.604673\pi$
$419$	5644.76	−	9777.01i	0.658149	−	1.13995i	0.981094	−	0.193530i	$-0.0619937\pi$
$420$		0			0
$421$	5670.06	+	9820.84i	0.656394	+	1.13691i	0.981542	+	0.191245i	$0.0612525\pi$
$421$	5670.06	+	9820.84i	0.656394	+	1.13691i	−0.325148	+	0.945663i	$0.605414\pi$
$422$	7306.29			0.842807
$423$		0			0
$424$	−7652.04			−0.876452
$425$	4130.93	+	7154.97i	0.471481	+	0.816629i
$426$		0			0
$427$	513.646	−	889.661i	0.0582133	−	0.100828i
$428$	−4346.37	+	7528.13i	−0.490863	+	0.850200i
$429$		0			0
$430$	181.665	+	314.653i	0.0203737	+	0.0352882i
$431$	−15264.9			−1.70600			−0.853000	−	0.521911i	$-0.825219\pi$
$431$	−15264.9			−1.70600			−0.853000	+	0.521911i	$0.825219\pi$
$432$		0			0
$433$	−3367.10			−0.373701			−0.186851	−	0.982388i	$-0.559828\pi$
$433$	−3367.10			−0.373701			−0.186851	+	0.982388i	$0.559828\pi$
$434$	−1578.71	−	2734.41i	−0.174610	−	0.302433i
$435$		0			0
$436$	−4088.30	+	7081.15i	−0.449069	+	0.777811i
$437$	8159.57	−	14132.8i	0.893193	−	1.54706i
$438$		0			0
$439$	−5526.68	−	9572.50i	−0.600852	−	1.04071i	−0.992692	−	0.120673i	$-0.961495\pi$
$439$	−5526.68	−	9572.50i	−0.600852	−	1.04071i	0.391840	−	0.920033i	$-0.371839\pi$
$440$	−443.894			−0.0480950
$441$		0			0
$442$	2918.52			0.314072
$443$	3869.09	+	6701.45i	0.414957	+	0.718726i	0.995424	−	0.0955576i	$-0.0304634\pi$
$443$	3869.09	+	6701.45i	0.414957	+	0.718726i	−0.580467	+	0.814284i	$0.697130\pi$
$444$		0			0
$445$	−823.000	+	1425.48i	−0.0876718	+	0.151852i
$446$	3569.80	−	6183.07i	0.379002	−	0.656450i
$447$		0			0
$448$	778.675	+	1348.70i	0.0821181	+	0.142233i
$449$	−1209.56			−0.127133			−0.0635665	−	0.997978i	$-0.520248\pi$
$449$	−1209.56			−0.127133			−0.0635665	+	0.997978i	$0.520248\pi$
$450$		0			0
$451$	−704.778			−0.0735847
$452$	−1896.73	−	3285.23i	−0.197377	−	0.341867i
$453$		0			0
$454$	−1255.95	+	2175.38i	−0.129834	+	0.224880i
$455$	−234.749	+	406.597i	−0.0241872	+	0.0418935i
$456$		0			0
$457$	7128.81	+	12347.5i	0.729697	+	1.26387i	0.957011	+	0.290051i	$0.0936722\pi$
$457$	7128.81	+	12347.5i	0.729697	+	1.26387i	−0.227314	+	0.973821i	$0.572994\pi$
$458$	−713.204			−0.0727638
$459$		0			0
$460$	2152.31			0.218157
$461$	5958.98	+	10321.2i	0.602033	+	1.04275i	0.992513	+	0.122140i	$0.0389758\pi$
$461$	5958.98	+	10321.2i	0.602033	+	1.04275i	−0.390480	+	0.920611i	$0.627691\pi$
$462$		0			0
$463$	−3930.43	+	6807.71i	−0.394520	+	0.683329i	−0.993040	−	0.117779i	$-0.962422\pi$
$463$	−3930.43	+	6807.71i	−0.394520	+	0.683329i	0.598520	+	0.801108i	$0.295756\pi$
$464$	−342.072	+	592.486i	−0.0342248	+	0.0592791i
$465$		0			0
$466$	−3137.11	−	5433.63i	−0.311854	−	0.540146i
$467$	−16152.3			−1.60051			−0.800257	−	0.599657i	$-0.795304\pi$
$467$	−16152.3			−1.60051			−0.800257	+	0.599657i	$0.795304\pi$
$468$		0			0
$469$	2144.81			0.211169
$470$	−641.394	−	1110.93i	−0.0629474	−	0.109028i
$471$		0			0
$472$	4426.45	−	7666.84i	0.431661	−	0.747659i
$473$	360.487	−	624.382i	0.0350427	−	0.0606958i
$474$		0			0
$475$	6263.90	+	10849.4i	0.605068	+	1.04801i
$476$	2663.55			0.256478
$477$		0			0
$478$	−5868.03			−0.561501
$479$	−5851.93	−	10135.8i	−0.558207	−	0.966844i	−0.997646	−	0.0685711i	$-0.978156\pi$
$479$	−5851.93	−	10135.8i	−0.558207	−	0.966844i	0.439439	−	0.898273i	$-0.355177\pi$
$480$		0			0
$481$	338.427	−	586.173i	0.0320810	−	0.0555659i
$482$	664.318	−	1150.63i	0.0627777	−	0.108734i
$483$		0			0
$484$	−3452.41	−	5979.74i	−0.324230	−	0.561584i
$485$	790.318			0.0739928
$486$		0			0
$487$	41.1258			0.00382667			0.00191333	−	0.999998i	$-0.499391\pi$
$487$	41.1258			0.00382667			0.00191333	+	0.999998i	$0.499391\pi$
$488$	−1574.85	−	2727.72i	−0.146086	−	0.253029i
$489$		0			0
$490$	99.8938	−	173.021i	0.00920967	−	0.0159516i
$491$	4217.83	−	7305.49i	0.387674	−	0.671471i	−0.604462	−	0.796634i	$-0.706612\pi$
$491$	4217.83	−	7305.49i	0.387674	−	0.671471i	0.992136	+	0.125163i	$0.0399453\pi$
$492$		0			0
$493$	−2533.50	−	4388.15i	−0.231446	−	0.400877i
$494$	4425.48			0.403060
$495$		0			0
$496$	2662.94			0.241068
$497$	−3635.68	−	6297.18i	−0.328134	−	0.568344i
$498$		0			0
$499$	−1093.08	+	1893.27i	−0.0980618	+	0.169848i	−0.910882	−	0.412666i	$-0.864598\pi$
$499$	−1093.08	+	1893.27i	−0.0980618	+	0.169848i	0.812821	+	0.582514i	$0.197931\pi$
$500$	−1697.85	+	2940.76i	−0.151860	+	0.263029i
$501$		0			0
$502$	−5771.67	−	9996.83i	−0.513152	−	0.888805i
$503$	−14676.6			−1.30098			−0.650492	−	0.759513i	$-0.725437\pi$
$503$	−14676.6			−1.30098			−0.650492	+	0.759513i	$0.725437\pi$
$504$		0			0
$505$	−2864.53			−0.252416
$506$	995.703	+	1724.61i	0.0874791	+	0.151518i
$507$		0			0
$508$	−3757.86	+	6508.81i	−0.328205	+	0.568468i
$509$	−6449.79	+	11171.4i	−0.561654	+	0.972814i	0.435698	+	0.900093i	$0.356502\pi$
$509$	−6449.79	+	11171.4i	−0.561654	+	0.972814i	−0.997352	+	0.0727208i	$0.976832\pi$
$510$		0			0
$511$	−4049.84	−	7014.54i	−0.350596	−	0.607250i
$512$	−3374.96			−0.291315
$513$		0			0
$514$	−4910.59			−0.421395
$515$	−722.451	−	1251.32i	−0.0618155	−	0.107068i
$516$		0			0
$517$	−1272.75	+	2204.46i	−0.108270	+	0.187528i
$518$	−144.013	+	249.437i	−0.0122153	+	0.0211576i
$519$		0			0
$520$	719.745	+	1246.63i	0.0606979	+	0.105132i
$521$	−11771.7			−0.989880			−0.494940	−	0.868927i	$-0.664810\pi$
$521$	−11771.7			−0.989880			−0.494940	+	0.868927i	$0.664810\pi$
$522$		0			0
$523$	5339.23			0.446402			0.223201	−	0.974772i	$-0.428349\pi$
$523$	5339.23			0.446402			0.223201	+	0.974772i	$0.428349\pi$
$524$	7426.39	+	12862.9i	0.619128	+	1.07236i
$525$		0			0
$526$	3155.80	−	5466.00i	0.261595	−	0.453097i
$527$	−9861.31	+	17080.3i	−0.815115	+	1.41182i
$528$		0			0
$529$	−5823.36	−	10086.3i	−0.478619	−	0.828992i
$530$	1453.70			0.119141
$531$		0			0
$532$	4038.85			0.329148
$533$	1142.75	+	1979.30i	0.0928669	+	0.160850i
$534$		0			0
$535$	2036.41	−	3527.17i	0.164564	−	0.285033i
$536$	3288.02	−	5695.02i	0.264964	−	0.458932i
$537$		0			0
$538$	2035.44	+	3525.48i	0.163111	+	0.282517i
$539$	−396.448			−0.0316813
$540$		0			0
$541$	828.599			0.0658489			0.0329244	−	0.999458i	$-0.489518\pi$
$541$	828.599			0.0658489			0.0329244	+	0.999458i	$0.489518\pi$
$542$	−1506.46	−	2609.26i	−0.119387	−	0.206784i
$543$		0			0
$544$	6510.86	−	11277.1i	0.513145	−	0.888793i
$545$	1915.50	−	3317.75i	0.150552	−	0.260765i
$546$		0			0
$547$	−6948.69	−	12035.5i	−0.543153	−	0.940768i	−0.998721	−	0.0505673i	$-0.983897\pi$
$547$	−6948.69	−	12035.5i	−0.543153	−	0.940768i	0.455568	−	0.890201i	$-0.349436\pi$
$548$	12836.0			1.00059
$549$		0			0
$550$	−1528.75			−0.118520
$551$	−3841.65	−	6653.93i	−0.297023	−	0.514459i
$552$		0			0
$553$	2612.03	−	4524.16i	0.200858	−	0.347897i
$554$	−2354.96	+	4078.92i	−0.180601	+	0.312810i
$555$		0			0
$556$	−5588.86	−	9680.19i	−0.426296	−	0.738366i
$557$	−11168.5			−0.849595			−0.424798	−	0.905288i	$-0.639655\pi$
$557$	−11168.5			−0.849595			−0.424798	+	0.905288i	$0.639655\pi$
$558$		0			0
$559$	−2338.02			−0.176901
$560$	84.2495	+	145.924i	0.00635749	+	0.0110115i
$561$		0			0
$562$	−962.156	+	1666.50i	−0.0722172	+	0.125084i
$563$	−322.865	+	559.218i	−0.0241689	+	0.0418618i	−0.877857	−	0.478923i	$-0.841027\pi$
$563$	−322.865	+	559.218i	−0.0241689	+	0.0418618i	0.853688	+	0.520785i	$0.174361\pi$
$564$		0			0
$565$	888.678	+	1539.23i	0.0661716	+	0.114613i
$566$	−5897.47			−0.437967
$567$		0			0
$568$	−22294.1			−1.64690
$569$	9542.50	+	16528.1i	0.703062	+	1.21774i	0.967386	+	0.253306i	$0.0815178\pi$
$569$	9542.50	+	16528.1i	0.703062	+	1.21774i	−0.264324	+	0.964434i	$0.585149\pi$
$570$		0			0
$571$	1409.15	−	2440.71i	0.103277	−	0.178880i	−0.809756	−	0.586766i	$-0.800401\pi$
$571$	1409.15	−	2440.71i	0.103277	−	0.178880i	0.913033	+	0.407886i	$0.133734\pi$
$572$	579.103	−	1003.04i	0.0423313	−	0.0733199i
$573$		0			0
$574$	−486.281	−	842.263i	−0.0353606	−	0.0612463i
$575$	18281.2			1.32588
$576$		0			0
$577$	16153.2			1.16546			0.582728	−	0.812667i	$-0.301985\pi$
$577$	16153.2			1.16546			0.582728	+	0.812667i	$0.301985\pi$
$578$	−39.2609	−	68.0019i	−0.00282533	−	0.00489361i
$579$		0			0
$580$	506.671	−	877.580i	0.0362730	−	0.0628267i
$581$	−1838.99	+	3185.22i	−0.131315	+	0.227444i
$582$		0			0
$583$	−1442.33	−	2498.18i	−0.102462	−	0.177469i
$584$	−24833.8			−1.75964
$585$		0			0
$586$	3965.10			0.279517
$587$	6970.50	+	12073.3i	0.490125	+	0.848921i	0.999935	−	0.0113658i	$-0.00361793\pi$
$587$	6970.50	+	12073.3i	0.490125	+	0.848921i	−0.509811	+	0.860287i	$0.670285\pi$
$588$		0			0
$589$	−14953.1	+	25899.6i	−1.04607	+	1.81184i
$590$	−840.920	+	1456.52i	−0.0586782	+	0.101634i
$591$		0			0
$592$	−121.459	−	210.373i	−0.00843232	−	0.0146052i
$593$	−203.913			−0.0141209			−0.00706046	−	0.999975i	$-0.502247\pi$
$593$	−203.913			−0.0141209			−0.00706046	+	0.999975i	$0.502247\pi$
$594$		0			0
$595$	−1247.96			−0.0859854
$596$	−3530.01	−	6114.16i	−0.242609	−	0.420211i
$597$		0			0
$598$	3228.94	−	5592.68i	0.220804	−	0.382444i
$599$	−1154.51	+	1999.67i	−0.0787514	+	0.136401i	−0.902711	−	0.430246i	$-0.858427\pi$
$599$	−1154.51	+	1999.67i	−0.0787514	+	0.136401i	0.823960	+	0.566648i	$0.191760\pi$
$600$		0			0
$601$	−11175.2	−	19356.0i	−0.758477	−	1.31372i	−0.943627	−	0.331010i	$-0.892611\pi$
$601$	−11175.2	−	19356.0i	−0.758477	−	1.31372i	0.185150	−	0.982710i	$-0.440723\pi$
$602$	994.911			0.0673580
$603$		0			0
$604$	11685.1			0.787186
$605$	1617.56	+	2801.70i	0.108700	+	0.188273i
$606$		0			0
$607$	8552.63	−	14813.6i	0.571895	−	0.990552i	−0.424476	−	0.905439i	$-0.639542\pi$
$607$	8552.63	−	14813.6i	0.571895	−	0.990552i	0.996371	−	0.0851126i	$-0.0271250\pi$
$608$	9872.70	−	17100.0i	0.658538	−	1.14062i
$609$		0			0
$610$	299.184	+	518.202i	0.0198584	+	0.0343957i
$611$	8254.71			0.546563
$612$		0			0
$613$	−7474.70			−0.492496			−0.246248	−	0.969207i	$-0.579198\pi$
$613$	−7474.70			−0.492496			−0.246248	+	0.969207i	$0.579198\pi$
$614$	−1728.95	−	2994.63i	−0.113639	−	0.196829i
$615$		0			0
$616$	−607.759	+	1052.67i	−0.0397521	+	0.0688527i
$617$	1802.12	−	3121.37i	0.117586	−	0.203665i	−0.801224	−	0.598364i	$-0.795818\pi$
$617$	1802.12	−	3121.37i	0.117586	−	0.203665i	0.918811	+	0.394699i	$0.129151\pi$
$618$		0			0
$619$	2271.30	+	3934.01i	0.147482	+	0.255446i	0.930296	−	0.366809i	$-0.119550\pi$
$619$	2271.30	+	3934.01i	0.147482	+	0.255446i	−0.782814	+	0.622256i	$0.786216\pi$
$620$	−3944.30			−0.255495
$621$		0			0
$622$	7435.78			0.479337
$623$	2253.63	+	3903.40i	0.144927	+	0.251021i
$624$		0			0
$625$	−6608.58	+	11446.4i	−0.422949	+	0.732569i
$626$	398.100	−	689.530i	0.0254174	−	0.0440242i
$627$		0			0
$628$	7060.62	+	12229.4i	0.448646	+	0.777077i
$629$	1799.13			0.114048
$630$		0			0
$631$	−11564.2			−0.729578			−0.364789	−	0.931090i	$-0.618859\pi$
$631$	−11564.2			−0.729578			−0.364789	+	0.931090i	$0.618859\pi$
$632$	−8008.53	−	13871.2i	−0.504054	−	0.873048i
$633$		0			0
$634$	7826.31	−	13555.6i	0.490256	−	0.849149i
$635$	1760.68	−	3049.59i	0.110032	−	0.190581i
$636$		0			0
$637$	642.814	+	1113.39i	0.0399831	+	0.0692527i
$638$	937.585			0.0581808
$639$		0			0
$640$	2911.34			0.179814
$641$	849.583	+	1471.52i	0.0523503	+	0.0906733i	0.891013	−	0.453978i	$-0.149995\pi$
$641$	849.583	+	1471.52i	0.0523503	+	0.0906733i	−0.838663	+	0.544651i	$0.816662\pi$
$642$		0			0
$643$	−14633.7	+	25346.3i	−0.897506	+	1.55453i	−0.0668341	+	0.997764i	$0.521290\pi$
$643$	−14633.7	+	25346.3i	−0.897506	+	1.55453i	−0.830672	+	0.556762i	$0.812044\pi$
$644$	2946.85	−	5104.09i	0.180314	−	0.312313i
$645$		0			0
$646$	5881.62	+	10187.3i	0.358219	+	0.620453i
$647$	−19018.7			−1.15564			−0.577822	−	0.816163i	$-0.696097\pi$
$647$	−19018.7			−1.15564			−0.577822	+	0.816163i	$0.696097\pi$
$648$		0			0
$649$	3337.36			0.201853
$650$	2478.77	+	4293.36i	0.149578	+	0.259076i
$651$		0			0
$652$	2299.55	−	3982.94i	0.138125	−	0.239239i
$653$	−4734.89	+	8201.06i	−0.283753	+	0.491474i	−0.972306	−	0.233712i	$-0.924913\pi$
$653$	−4734.89	+	8201.06i	−0.283753	+	0.491474i	0.688553	+	0.725186i	$0.258246\pi$
$654$		0			0
$655$	−3479.50	−	6026.67i	−0.207565	−	0.359514i
$656$	820.250			0.0488192
$657$		0			0
$658$	−3512.67			−0.208113
$659$	−8612.54	−	14917.4i	−0.509100	−	0.881787i	−0.999944	−	0.0105401i	$-0.996645\pi$
$659$	−8612.54	−	14917.4i	−0.509100	−	0.881787i	0.490844	−	0.871247i	$-0.336688\pi$
$660$		0			0
$661$	4939.90	−	8556.16i	0.290681	−	0.503474i	−0.683290	−	0.730147i	$-0.739452\pi$
$661$	4939.90	−	8556.16i	0.290681	−	0.503474i	0.973971	+	0.226673i	$0.0727849\pi$
$662$	7999.13	−	13854.9i	0.469630	−	0.813423i
$663$		0			0
$664$	5638.37	+	9765.94i	0.329535	+	0.570771i
$665$	−1892.33			−0.110348
$666$		0			0
$667$	−11211.9			−0.650862
$668$	−4521.37	−	7831.25i	−0.261882	−	0.453593i
$669$		0			0
$670$	−624.645	+	1081.92i	−0.0360181	+	0.0623853i
$671$	593.685	−	1028.29i	0.0341564	−	0.0591606i
$672$		0			0
$673$	15090.5	+	26137.5i	0.864334	+	1.49707i	0.867707	+	0.497076i	$0.165593\pi$
$673$	15090.5	+	26137.5i	0.864334	+	1.49707i	−0.00337288	+	0.999994i	$0.501074\pi$
$674$	14045.0			0.802659
$675$		0			0
$676$	8230.97			0.468308
$677$	−11225.4	−	19443.0i	−0.637265	−	1.10378i	−0.986030	−	0.166566i	$-0.946732\pi$
$677$	−11225.4	−	19443.0i	−0.637265	−	1.10378i	0.348765	−	0.937210i	$-0.386601\pi$
$678$		0			0
$679$	1082.07	−	1874.20i	0.0611575	−	0.105928i
$680$	−1913.13	+	3313.65i	−0.107890	+	0.186871i
$681$		0			0
$682$	−1824.71	−	3160.50i	−0.102451	−	0.177451i
$683$	12957.7			0.725933			0.362966	−	0.931802i	$-0.381764\pi$
$683$	12957.7			0.725933			0.362966	+	0.931802i	$0.381764\pi$
$684$		0			0
$685$	−6014.07			−0.335454
$686$	−273.540	−	473.785i	−0.0152242	−	0.0263691i
$687$		0			0
$688$	−419.550	+	726.681i	−0.0232488	+	0.0402681i
$689$	−4677.28	+	8101.28i	−0.258621	+	0.447945i
$690$		0			0
$691$	−285.528	−	494.549i	−0.0157192	−	0.0272265i	0.858059	−	0.513551i	$-0.171670\pi$
$691$	−285.528	−	494.549i	−0.0157192	−	0.0272265i	−0.873778	+	0.486325i	$0.838337\pi$
$692$	10623.4			0.583586
$693$		0			0
$694$	10164.1			0.555944
$695$	2618.56	+	4535.48i	0.142918	+	0.247541i
$696$		0			0
$697$	−3037.52	+	5261.14i	−0.165071	+	0.285911i
$698$	−2190.98	+	3794.89i	−0.118811	+	0.205786i
$699$		0			0
$700$	2262.22	+	3918.28i	0.122148	+	0.211567i
$701$	26258.8			1.41481			0.707404	−	0.706810i	$-0.249866\pi$
$701$	26258.8			1.41481			0.707404	+	0.706810i	$0.249866\pi$
$702$		0			0
$703$	2728.10			0.146361
$704$	900.011	+	1558.87i	0.0481825	+	0.0834545i
$705$		0			0
$706$	−8197.67	+	14198.8i	−0.437002	+	0.756910i
$707$	−3921.98	+	6793.07i	−0.208630	+	0.361358i
$708$		0			0
$709$	5120.65	+	8869.22i	0.271241	+	0.469803i	0.969180	−	0.246354i	$-0.0792326\pi$
$709$	5120.65	+	8869.22i	0.271241	+	0.469803i	−0.697939	+	0.716157i	$0.745899\pi$
$710$	4235.35			0.223873
$711$		0			0
$712$	13819.3			0.727390
$713$	21820.3	+	37794.0i	1.14611	+	1.98513i
$714$		0			0
$715$	−271.328	+	469.954i	−0.0141917	+	0.0245808i
$716$	2296.72	−	3978.04i	0.119878	−	0.207635i
$717$		0			0
$718$	8352.71	+	14467.3i	0.434151	+	0.751971i
$719$	9398.00			0.487464			0.243732	−	0.969843i	$-0.421628\pi$
$719$	9398.00			0.487464			0.243732	+	0.969843i	$0.421628\pi$
$720$		0			0
$721$	−3956.58			−0.204370
$722$	3448.55	+	5973.07i	0.177759	+	0.307887i
$723$		0			0
$724$	431.736	−	747.789i	0.0221621	−	0.0383859i
$725$	4303.53	−	7453.93i	0.220454	−	0.381837i
$726$		0			0
$727$	−3140.35	−	5439.24i	−0.160205	−	0.277483i	0.774737	−	0.632283i	$-0.217882\pi$
$727$	−3140.35	−	5439.24i	−0.160205	−	0.277483i	−0.934942	+	0.354800i	$0.884549\pi$
$728$	3941.77			0.200675
$729$		0			0
$730$	4717.83			0.239198
$731$	−3107.32	−	5382.04i	−0.157221	−	0.272314i
$732$		0			0
$733$	−5268.97	+	9126.13i	−0.265503	+	0.459865i	−0.967695	−	0.252122i	$-0.918872\pi$
$733$	−5268.97	+	9126.13i	−0.265503	+	0.459865i	0.702192	+	0.711988i	$0.252205\pi$
$734$	1581.05	−	2738.46i	0.0795063	−	0.137709i
$735$		0			0
$736$	−14406.7	−	24953.2i	−0.721521	−	1.24971i
$737$	2479.03			0.123902
$738$		0			0
$739$	20509.6			1.02092			0.510459	−	0.859902i	$-0.329475\pi$
$739$	20509.6			1.02092			0.510459	+	0.859902i	$0.329475\pi$
$740$	179.903	+	311.601i	0.00893696	+	0.0154793i
$741$		0			0
$742$	1990.35	−	3447.38i	0.0984742	−	0.170562i
$743$	−13139.5	+	22758.2i	−0.648776	+	1.12371i	0.334640	+	0.942346i	$0.391385\pi$
$743$	−13139.5	+	22758.2i	−0.648776	+	1.12371i	−0.983416	+	0.181367i	$0.941948\pi$
$744$		0			0
$745$	1653.92	+	2864.68i	0.0813357	+	0.140878i
$746$	−14899.8			−0.731261
$747$		0			0
$748$	3078.60			0.150487
$749$	−5576.33	−	9658.48i	−0.272035	−	0.471179i
$750$		0			0
$751$	688.771	−	1192.99i	0.0334668	−	0.0579663i	−0.848807	−	0.528703i	$-0.822679\pi$
$751$	688.771	−	1192.99i	0.0334668	−	0.0579663i	0.882274	+	0.470737i	$0.156012\pi$
$752$	1481.28	−	2565.65i	0.0718306	−	0.124414i
$753$		0			0
$754$	−1520.23	−	2633.12i	−0.0734265	−	0.127178i
$755$	−5474.85			−0.263907
$756$		0			0
$757$	13632.8			0.654549			0.327275	−	0.944929i	$-0.393870\pi$
$757$	13632.8			0.654549			0.327275	+	0.944929i	$0.393870\pi$
$758$	7149.07	+	12382.6i	0.342567	+	0.593344i
$759$		0			0
$760$	−2900.97	+	5024.62i	−0.138459	+	0.239819i
$761$	776.057	−	1344.17i	0.0369672	−	0.0640291i	−0.846950	−	0.531673i	$-0.821564\pi$
$761$	776.057	−	1344.17i	0.0369672	−	0.0640291i	0.883917	+	0.467644i	$0.154897\pi$
$762$		0			0
$763$	−5245.24	−	9085.01i	−0.248873	−	0.431061i
$764$	−25201.2			−1.19338
$765$		0			0
$766$	7291.46			0.343931
$767$	−5411.31	−	9372.66i	−0.254747	−	0.441235i
$768$		0			0
$769$	5314.20	−	9204.46i	0.249200	−	0.431627i	−0.714104	−	0.700040i	$-0.753166\pi$
$769$	5314.20	−	9204.46i	0.249200	−	0.431627i	0.963304	+	0.268412i	$0.0864990\pi$
$770$	115.460	−	199.982i	0.00540374	−	0.00935955i
$771$		0			0
$772$	12524.2	+	21692.6i	0.583881	+	1.01131i
$773$	20748.7			0.965432			0.482716	−	0.875777i	$-0.339650\pi$
$773$	20748.7			0.965432			0.482716	+	0.875777i	$0.339650\pi$
$774$		0			0
$775$	−33501.9			−1.55280
$776$	−3317.64	−	5746.33i	−0.153475	−	0.265826i
$777$		0			0
$778$	−7047.59	+	12206.8i	−0.324767	+	0.562512i
$779$	−4605.92	+	7977.69i	−0.211841	+	0.366920i
$780$		0			0
$781$	−4202.21	−	7278.44i	−0.192531	−	0.333474i
$782$	17165.5			0.784958
$783$		0			0
$784$	461.402			0.0210187
$785$	−3308.13	−	5729.85i	−0.150410	−	0.260518i
$786$		0			0
$787$	11193.0	−	19386.9i	0.506973	−	0.878103i	−0.492995	−	0.870032i	$-0.664098\pi$
$787$	11193.0	−	19386.9i	0.506973	−	0.878103i	0.999967	−	0.00807037i	$-0.00256891\pi$
$788$	7218.41	−	12502.7i	0.326326	−	0.565214i
$789$		0			0
$790$	1521.43	+	2635.19i	0.0685190	+	0.118678i
$791$	4866.95			0.218772
$792$		0			0
$793$	−3850.49			−0.172427
$794$	−2910.30	−	5040.78i	−0.130079	−	0.225303i
$795$		0			0
$796$	12935.1	−	22404.2i	0.575970	−	0.997609i
$797$	−518.525	+	898.112i	−0.0230453	+	0.0399156i	−0.877318	−	0.479909i	$-0.840670\pi$
$797$	−518.525	+	898.112i	−0.0230453	+	0.0399156i	0.854273	+	0.519825i	$0.174003\pi$
$798$		0			0
$799$	10970.8	+	19002.0i	0.485757	+	0.841355i
$800$	22119.4			0.977548
$801$		0			0
$802$	−1626.03			−0.0715925
$803$	−4680.91	−	8107.57i	−0.205711	−	0.356301i
$804$		0			0
$805$	−1380.69	+	2391.43i	−0.0604510	+	0.104704i
$806$	−5917.31	+	10249.1i	−0.258596	+	0.447901i
$807$		0			0
$808$	12024.9	+	20827.7i	0.523557	+	0.906827i
$809$	10345.1			0.449586			0.224793	−	0.974407i	$-0.427829\pi$
$809$	10345.1			0.449586			0.224793	+	0.974407i	$0.427829\pi$
$810$		0			0
$811$	8037.38			0.348003			0.174002	−	0.984745i	$-0.444330\pi$
$811$	8037.38			0.348003			0.174002	+	0.984745i	$0.444330\pi$
$812$	−1387.42	−	2403.08i	−0.0599617	−	0.103857i
$813$		0			0
$814$	−166.453	+	288.305i	−0.00716730	+	0.0124141i
$815$	−1077.41	+	1866.13i	−0.0463069	+	0.0802059i
$816$		0			0
$817$	−4711.76	−	8161.02i	−0.201767	−	0.349471i
$818$	−2201.34			−0.0940931
$819$		0			0
$820$	−1214.94			−0.0517408
$821$	−6094.85	−	10556.6i	−0.259089	−	0.448755i	0.706909	−	0.707304i	$-0.250089\pi$
$821$	−6094.85	−	10556.6i	−0.259089	−	0.448755i	−0.965998	+	0.258549i	$0.916756\pi$
$822$		0			0
$823$	8913.36	−	15438.4i	0.377521	−	0.653886i	−0.613180	−	0.789944i	$-0.710110\pi$
$823$	8913.36	−	15438.4i	0.377521	−	0.653886i	0.990701	+	0.136057i	$0.0434431\pi$
$824$	−6065.49	+	10505.7i	−0.256434	+	0.444156i
$825$		0			0
$826$	2302.70	+	3988.39i	0.0969990	+	0.168007i
$827$	41268.6			1.73525			0.867624	−	0.497220i	$-0.165646\pi$
$827$	41268.6			1.73525			0.867624	+	0.497220i	$0.165646\pi$
$828$		0			0
$829$	−42762.2			−1.79155			−0.895774	−	0.444509i	$-0.853378\pi$
$829$	−42762.2			−1.79155			−0.895774	+	0.444509i	$0.853378\pi$
$830$	−1071.16	−	1855.30i	−0.0447956	−	0.0775883i
$831$		0			0
$832$	2918.62	−	5055.20i	0.121616	−	0.210646i
$833$	−1708.65	+	2959.46i	−0.0710698	+	0.123097i
$834$		0			0
$835$	2118.41	+	3669.19i	0.0877971	+	0.152069i
$836$	4668.21			0.193126
$837$		0			0
$838$	18006.6			0.742277
$839$	−22207.9	−	38465.2i	−0.913828	−	1.58280i	−0.808608	−	0.588348i	$-0.799779\pi$
$839$	−22207.9	−	38465.2i	−0.913828	−	1.58280i	−0.105220	−	0.994449i	$-0.533555\pi$
$840$		0			0
$841$	9555.14	−	16550.0i	0.391781	−	0.678584i
$842$	−9043.67	+	15664.1i	−0.370149	+	0.641117i
$843$		0			0
$844$	−12496.4	−	21644.5i	−0.509651	−	0.882741i
$845$	−3856.48			−0.157002
$846$		0			0
$847$	8858.78			0.359376
$848$	1678.64	+	2907.49i	0.0679773	+	0.117740i
$849$		0			0
$850$	−6588.76	+	11412.1i	−0.265874	+	0.460507i
$851$	1990.49	−	3447.62i	0.0801798	−	0.138875i
$852$		0			0
$853$	−4585.60	−	7942.50i	−0.184066	−	0.318811i	0.759196	−	0.650863i	$-0.225593\pi$
$853$	−4585.60	−	7942.50i	−0.184066	−	0.318811i	−0.943261	+	0.332051i	$0.892259\pi$
$854$	1638.52			0.0656544
$855$		0			0
$856$	−34194.3			−1.36535
$857$	5911.62	+	10239.2i	0.235633	+	0.408128i	0.959456	−	0.281857i	$-0.0909504\pi$
$857$	5911.62	+	10239.2i	0.235633	+	0.408128i	−0.723824	+	0.689985i	$0.757617\pi$
$858$		0			0
$859$	−1386.20	+	2400.97i	−0.0550600	+	0.0953667i	−0.892242	−	0.451558i	$-0.850868\pi$
$859$	−1386.20	+	2400.97i	−0.0550600	+	0.0953667i	0.837182	+	0.546925i	$0.184202\pi$
$860$	621.429	−	1076.35i	0.0246402	−	0.0426780i
$861$		0			0
$862$	−12173.7	−	21085.4i	−0.481017	−	0.833146i
$863$	−7669.34			−0.302512			−0.151256	−	0.988495i	$-0.548332\pi$
$863$	−7669.34			−0.302512			−0.151256	+	0.988495i	$0.548332\pi$
$864$		0			0
$865$	−4977.41			−0.195650
$866$	−2685.24	−	4650.97i	−0.105367	−	0.182502i
$867$		0			0
$868$	−5400.36	+	9353.69i	−0.211175	+	0.365766i
$869$	3019.04	−	5229.14i	0.117853	−	0.204127i
$870$		0			0
$871$	−4019.58	−	6962.12i	−0.156370	−	0.270841i
$872$	−32164.0			−1.24910
$873$		0			0
$874$	26028.8			1.00737
$875$	−2178.31	−	3772.95i	−0.0841606	−	0.145770i
$876$		0			0
$877$	6933.86	−	12009.8i	0.266978	−	0.462420i	−0.701102	−	0.713061i	$-0.747308\pi$
$877$	6933.86	−	12009.8i	0.266978	−	0.462420i	0.968080	+	0.250642i	$0.0806415\pi$
$878$	8814.98	−	15268.0i	0.338828	−	0.586867i
$879$		0			0
$880$	97.3777	+	168.663i	0.00373023	+	0.00646095i
$881$	−19974.2			−0.763846			−0.381923	−	0.924194i	$-0.624738\pi$
$881$	−19974.2			−0.763846			−0.381923	+	0.924194i	$0.624738\pi$
$882$		0			0
$883$	22197.0			0.845969			0.422984	−	0.906137i	$-0.360983\pi$
$883$	22197.0			0.845969			0.422984	+	0.906137i	$0.360983\pi$
$884$	−4991.74	−	8645.95i	−0.189921	−	0.328953i
$885$		0			0
$886$	−6171.13	+	10688.7i	−0.233999	+	0.405298i
$887$	−16850.9	+	29186.6i	−0.637877	+	1.10484i	0.348021	+	0.937487i	$0.386854\pi$
$887$	−16850.9	+	29186.6i	−0.637877	+	1.10484i	−0.985898	+	0.167349i	$0.946479\pi$
$888$		0			0
$889$	−4821.29	−	8350.71i	−0.181891	−	0.315044i
$890$	−2625.34			−0.0988784
$891$		0			0
$892$	−24422.7			−0.916739
$893$	16635.5	+	28813.6i	0.623389	+	1.07974i
$894$		0			0
$895$	−1076.09	+	1863.84i	−0.0401896	+	0.0696104i
$896$	3986.08	−	6904.09i	0.148622	−	0.257421i
$897$		0			0
$898$	−964.616	−	1670.76i	−0.0358459	−	0.0620870i
$899$	20546.7			0.762259
$900$		0			0
$901$	−24865.1			−0.919397
$902$	−562.055	−	973.508i	−0.0207477	−	0.0359360i
$903$		0			0
$904$	7461.08	−	12923.0i	0.274504	−	0.475456i
$905$	−202.282	+	350.363i	−0.00742994	+	0.0128690i
$906$		0			0
$907$	11950.2	+	20698.3i	0.437485	+	0.757746i	0.997495	−	0.0707396i	$-0.0225359\pi$
$907$	11950.2	+	20698.3i	0.437485	+	0.757746i	−0.560010	+	0.828486i	$0.689203\pi$
$908$	8592.58			0.314047
$909$		0			0
$910$	−748.841			−0.0272789
$911$	−6376.80	−	11044.9i	−0.231913	−	0.401685i	0.726458	−	0.687211i	$-0.241165\pi$
$911$	−6376.80	−	11044.9i	−0.231913	−	0.401685i	−0.958371	+	0.285526i	$0.907832\pi$
$912$		0			0
$913$	−2125.54	+	3681.55i	−0.0770485	+	0.133452i
$914$	−11370.3	+	19694.0i	−0.411485	+	0.712713i
$915$		0			0
$916$	1219.84	+	2112.83i	0.0440008	+	0.0762115i
$917$	−19055.9			−0.686239
$918$		0			0
$919$	−10491.5			−0.376585			−0.188293	−	0.982113i	$-0.560295\pi$
$919$	−10491.5			−0.376585			−0.188293	+	0.982113i	$0.560295\pi$
$920$	4233.24	+	7332.18i	0.151702	+	0.262755i
$921$		0			0
$922$	−9504.48	+	16462.2i	−0.339494	+	0.588020i
$923$	−13627.2	+	23603.0i	−0.485964	+	0.841715i
$924$		0			0
$925$	1528.05	+	2646.65i	0.0543155	+	0.0940772i
$926$	−12538.0			−0.444949
$927$		0			0
$928$	−13565.8			−0.479870
$929$	−25022.9	−	43341.0i	−0.883720	−	1.53065i	−0.847174	−	0.531316i	$-0.821698\pi$
$929$	−25022.9	−	43341.0i	−0.883720	−	1.53065i	−0.0365465	−	0.999332i	$-0.511636\pi$
$930$		0			0
$931$	−2590.90	+	4487.56i	−0.0912064	+	0.157974i
$932$	−10731.2	+	18587.0i	−0.377160	+	0.653260i
$933$		0			0
$934$	−12881.4	−	22311.2i	−0.451275	−	0.781631i
$935$	−1442.42			−0.0504516
$936$		0			0
$937$	−35500.0			−1.23771			−0.618855	−	0.785505i	$-0.712403\pi$
$937$	−35500.0			−1.23771			−0.618855	+	0.785505i	$0.712403\pi$
$938$	1710.47	+	2962.62i	0.0595404	+	0.103127i
$939$		0			0
$940$	−2194.04	+	3800.19i	−0.0761294	+	0.131860i
$941$	21132.1	−	36601.8i	0.732078	−	1.26800i	−0.223916	−	0.974608i	$-0.571884\pi$
$941$	21132.1	−	36601.8i	0.732078	−	1.26800i	0.955994	−	0.293387i	$-0.0947826\pi$
$942$		0			0
$943$	6721.19	+	11641.4i	0.232102	+	0.402012i
$944$	−3884.15			−0.133918
$945$		0			0
$946$	1149.94			0.0395220
$947$	−24497.8	−	42431.4i	−0.840624	−	1.45600i	−0.889368	−	0.457193i	$-0.848855\pi$
$947$	−24497.8	−	42431.4i	−0.840624	−	1.45600i	0.0487434	−	0.998811i	$-0.484478\pi$
$948$		0			0
$949$	−15179.6	+	26291.8i	−0.519231	+	0.899334i
$950$	−9990.82	+	17304.6i	−0.341205	+	0.590985i
$951$		0			0
$952$	5238.75	+	9073.78i	0.178350	+	0.308911i
$953$	−5041.88			−0.171377			−0.0856886	−	0.996322i	$-0.527309\pi$
$953$	−5041.88			−0.171377			−0.0856886	+	0.996322i	$0.527309\pi$
$954$		0			0
$955$	11807.6			0.400087
$956$	10036.5	+	17383.7i	0.339543	+	0.588106i
$957$		0			0
$958$	9333.73	−	16166.5i	0.314780	−	0.545215i
$959$	−8234.19	+	14262.0i	−0.277264	+	0.480234i
$960$		0			0
$961$	−25092.2	−	43460.9i	−0.842274	−	1.45886i
$962$	1079.57			0.0361817
$963$		0			0
$964$	−4544.91			−0.151848
$965$	−5867.99	−	10163.7i	−0.195749	−	0.339046i
$966$		0			0
$967$	3479.68	−	6026.99i	0.115718	−	0.200429i	−0.802349	−	0.596856i	$-0.796417\pi$
$967$	3479.68	−	6026.99i	0.115718	−	0.200429i	0.918066	+	0.396427i	$0.129750\pi$
$968$	13580.6	−	23522.3i	0.450927	−	0.781028i
$969$		0			0
$970$	630.273	+	1091.66i	0.0208627	+	0.0361353i
$971$	12979.8			0.428983			0.214492	−	0.976726i	$-0.431191\pi$
$971$	12979.8			0.428983			0.214492	+	0.976726i	$0.431191\pi$
$972$		0			0
$973$	14340.9			0.472505
$974$	32.7975	+	56.8070i	0.00107895	+	0.00186880i
$975$		0			0
$976$	−690.955	+	1196.77i	−0.0226608	+	0.0392497i
$977$	−21131.1	+	36600.1i	−0.691958	+	1.19851i	0.279238	+	0.960222i	$0.409918\pi$
$977$	−21131.1	+	36600.1i	−0.691958	+	1.19851i	−0.971195	+	0.238284i	$0.923415\pi$
$978$		0			0
$979$	2604.80	+	4511.64i	0.0850354	+	0.147286i
$980$	−683.420			−0.0222766
$981$		0			0
$982$	13454.7			0.437228
$983$	27093.9	+	46927.9i	0.879105	+	1.52265i	0.852325	+	0.523013i	$0.175192\pi$
$983$	27093.9	+	46927.9i	0.879105	+	1.52265i	0.0267799	+	0.999641i	$0.491475\pi$
$984$		0			0
$985$	−3382.06	+	5857.90i	−0.109402	+	0.189490i
$986$	4040.89	−	6999.03i	0.130515	−	0.226059i
$987$		0			0
$988$	−7569.19	−	13110.2i	−0.243733	−	0.422158i
$989$	−13751.3			−0.442129
$990$		0			0
$991$	37682.0			1.20788			0.603940	−	0.797030i	$-0.293597\pi$
$991$	37682.0			1.20788			0.603940	+	0.797030i	$0.293597\pi$
$992$	26401.6	+	45728.9i	0.845012	+	1.46360i
$993$		0			0
$994$	5798.85	−	10043.9i	0.185039	−	0.320496i
$995$	−6060.51	+	10497.1i	−0.193096	+	0.334453i
$996$		0			0
$997$	24932.3	+	43184.1i	0.791991	+	1.37177i	0.924732	+	0.380618i	$0.124289\pi$
$997$	24932.3	+	43184.1i	0.791991	+	1.37177i	−0.132741	+	0.991151i	$0.542378\pi$
$998$	−3486.88			−0.110597
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.4.f.b.64.5		16
3.2	odd	2		63.4.f.b.22.4	✓	16
9.2	odd	6		63.4.f.b.43.4	yes	16
9.4	even	3		567.4.a.g.1.4		8
9.5	odd	6		567.4.a.i.1.5		8
9.7	even	3	inner	189.4.f.b.127.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.f.b.22.4	✓	16	3.2	odd	2
63.4.f.b.43.4	yes	16	9.2	odd	6
189.4.f.b.64.5		16	1.1	even	1	trivial
189.4.f.b.127.5		16	9.7	even	3	inner
567.4.a.g.1.4		8	9.4	even	3
567.4.a.i.1.5		8	9.5	odd	6

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	189.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.797492 + 1.38130i) q^{2} +(2.72801 - 4.72505i) q^{4} +(-1.27816 + 2.21384i) q^{5} +(3.50000 + 6.06218i) q^{7} +21.4622 q^{8} +O(q^{10})\)	\(q+(0.797492 + 1.38130i) q^{2} +(2.72801 - 4.72505i) q^{4} +(-1.27816 + 2.21384i) q^{5} +(3.50000 + 6.06218i) q^{7} +21.4622 q^{8} -4.07730 q^{10} +(4.04539 + 7.00681i) q^{11} +(13.1187 - 22.7222i) q^{13} +(-5.58245 + 9.66908i) q^{14} +(-4.70819 - 8.15482i) q^{16} +69.7407 q^{17} +105.751 q^{19} +(6.97368 + 12.0788i) q^{20} +(-6.45233 + 11.1758i) q^{22} +(77.1585 - 133.642i) q^{23} +(59.2326 + 102.594i) q^{25} +41.8481 q^{26} +38.1922 q^{28} +(-36.3274 - 62.9209i) q^{29} +(-141.400 + 244.911i) q^{31} +(93.3581 - 161.701i) q^{32} +(55.6177 + 96.3327i) q^{34} -17.8943 q^{35} +25.7974 q^{37} +(84.3355 + 146.073i) q^{38} +(-27.4321 + 47.5138i) q^{40} +(-43.5544 + 75.4385i) q^{41} +(-44.5553 - 77.1721i) q^{43} +44.1434 q^{44} +246.133 q^{46} +(157.309 + 272.467i) q^{47} +(-24.5000 + 42.4352i) q^{49} +(-94.4751 + 163.636i) q^{50} +(-71.5757 - 123.973i) q^{52} -356.536 q^{53} -20.6826 q^{55} +(75.1175 + 130.107i) q^{56} +(57.9416 - 100.358i) q^{58} +(206.245 - 357.226i) q^{59} +(-73.3780 - 127.094i) q^{61} -451.060 q^{62} +222.479 q^{64} +(33.5355 + 58.0852i) q^{65} +(153.201 - 265.352i) q^{67} +(190.254 - 329.529i) q^{68} +(-14.2705 - 24.7173i) q^{70} -1038.77 q^{71} -1157.10 q^{73} +(20.5732 + 35.6339i) q^{74} +(288.490 - 499.679i) q^{76} +(-28.3177 + 49.0477i) q^{77} +(-373.147 - 646.309i) q^{79} +24.0713 q^{80} -138.937 q^{82} +(262.712 + 455.031i) q^{83} +(-89.1399 + 154.395i) q^{85} +(71.0651 - 123.088i) q^{86} +(86.8227 + 150.381i) q^{88} +643.894 q^{89} +183.661 q^{91} +(-420.978 - 729.156i) q^{92} +(-250.905 + 434.580i) q^{94} +(-135.167 + 234.116i) q^{95} +(-154.581 - 267.742i) q^{97} -78.1543 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} - 43 q^{4} + 30 q^{5} + 56 q^{7} - 12 q^{8}+O(q^{10}) \) 16 * q + 3 * q^2 - 43 * q^4 + 30 * q^5 + 56 * q^7 - 12 * q^8	\( 16 q + 3 q^{2} - 43 q^{4} + 30 q^{5} + 56 q^{7} - 12 q^{8} - 28 q^{10} + 24 q^{11} - 68 q^{13} - 21 q^{14} - 103 q^{16} - 336 q^{17} + 352 q^{19} + 330 q^{20} - 151 q^{22} + 228 q^{23} - 244 q^{25} - 1590 q^{26} - 602 q^{28} + 618 q^{29} - 72 q^{31} + 786 q^{32} + 261 q^{34} + 420 q^{35} + 420 q^{37} + 1032 q^{38} + 375 q^{40} + 420 q^{41} + 2 q^{43} - 774 q^{44} + 804 q^{46} + 570 q^{47} - 392 q^{49} + 1110 q^{50} + 431 q^{52} - 1056 q^{53} - 1676 q^{55} - 42 q^{56} - 37 q^{58} - 150 q^{59} - 578 q^{61} - 2340 q^{62} - 224 q^{64} - 366 q^{65} + 898 q^{67} + 2526 q^{68} - 98 q^{70} - 1764 q^{71} + 1944 q^{73} - 222 q^{74} - 1423 q^{76} - 168 q^{77} + 158 q^{79} - 4950 q^{80} - 422 q^{82} + 2958 q^{83} + 774 q^{85} - 114 q^{86} - 1317 q^{88} - 8760 q^{89} - 952 q^{91} + 4629 q^{92} + 3234 q^{94} + 930 q^{95} + 60 q^{97} - 294 q^{98}+O(q^{100}) \) 16 * q + 3 * q^2 - 43 * q^4 + 30 * q^5 + 56 * q^7 - 12 * q^8 - 28 * q^10 + 24 * q^11 - 68 * q^13 - 21 * q^14 - 103 * q^16 - 336 * q^17 + 352 * q^19 + 330 * q^20 - 151 * q^22 + 228 * q^23 - 244 * q^25 - 1590 * q^26 - 602 * q^28 + 618 * q^29 - 72 * q^31 + 786 * q^32 + 261 * q^34 + 420 * q^35 + 420 * q^37 + 1032 * q^38 + 375 * q^40 + 420 * q^41 + 2 * q^43 - 774 * q^44 + 804 * q^46 + 570 * q^47 - 392 * q^49 + 1110 * q^50 + 431 * q^52 - 1056 * q^53 - 1676 * q^55 - 42 * q^56 - 37 * q^58 - 150 * q^59 - 578 * q^61 - 2340 * q^62 - 224 * q^64 - 366 * q^65 + 898 * q^67 + 2526 * q^68 - 98 * q^70 - 1764 * q^71 + 1944 * q^73 - 222 * q^74 - 1423 * q^76 - 168 * q^77 + 158 * q^79 - 4950 * q^80 - 422 * q^82 + 2958 * q^83 + 774 * q^85 - 114 * q^86 - 1317 * q^88 - 8760 * q^89 - 952 * q^91 + 4629 * q^92 + 3234 * q^94 + 930 * q^95 + 60 * q^97 - 294 * q^98

Introduction

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