LMFDB - Embedded newform 117.3.n.a.38.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,3,Mod(38,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("117.38");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	117.n (of order $6$, degree $2$, 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:	$3.18801909302$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			38.14
Character	$\chi$	$=$	117.38
Dual form			117.3.n.a.77.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.146647 - 0.254001i) q^{2} +(-0.187042 + 2.99416i) q^{3} +(1.95699 + 3.38960i) q^{4} +(-2.67644 - 4.63573i) q^{5} +(0.733091 + 0.486595i) q^{6} +(8.20362 + 4.73636i) q^{7} +2.32113 q^{8} +(-8.93003 - 1.12007i) q^{9} -1.56997 q^{10} +(-7.71102 + 13.3559i) q^{11} +(-10.5151 + 5.22555i) q^{12} +(2.27033 + 12.8002i) q^{13} +(2.40608 - 1.38915i) q^{14} +(14.3807 - 7.14663i) q^{15} +(-7.48757 + 12.9688i) q^{16} -2.12074i q^{17} +(-1.59406 + 2.10398i) q^{18} -33.3392i q^{19} +(10.4755 - 18.1442i) q^{20} +(-15.7159 + 23.6771i) q^{21} +(2.26160 + 3.91721i) q^{22} +(24.9644 - 14.4132i) q^{23} +(-0.434148 + 6.94984i) q^{24} +(-1.82668 + 3.16390i) q^{25} +(3.58420 + 1.30045i) q^{26} +(5.02395 - 26.5285i) q^{27} +37.0760i q^{28} +(23.2984 + 13.4514i) q^{29} +(0.293650 - 4.70075i) q^{30} +(22.3881 - 12.9257i) q^{31} +(6.83832 + 11.8443i) q^{32} +(-38.5474 - 25.5861i) q^{33} +(-0.538669 - 0.311001i) q^{34} -50.7064i q^{35} +(-13.6794 - 32.4612i) q^{36} +17.6365i q^{37} +(-8.46819 - 4.88911i) q^{38} +(-38.7506 + 4.40356i) q^{39} +(-6.21236 - 10.7601i) q^{40} +(-28.3722 - 49.1420i) q^{41} +(3.70930 + 7.46402i) q^{42} +(11.1667 - 19.3413i) q^{43} -60.3615 q^{44} +(18.7084 + 44.3950i) q^{45} -8.45463i q^{46} +(3.61133 - 6.25502i) q^{47} +(-37.4304 - 24.8447i) q^{48} +(20.3662 + 35.2753i) q^{49} +(0.535755 + 0.927955i) q^{50} +(6.34983 + 0.396666i) q^{51} +(-38.9447 + 32.7454i) q^{52} -40.2849i q^{53} +(-6.00150 - 5.16642i) q^{54} +82.5523 q^{55} +(19.0416 + 10.9937i) q^{56} +(99.8231 + 6.23583i) q^{57} +(6.83331 - 3.94521i) q^{58} +(52.7704 + 91.4009i) q^{59} +(52.3672 + 34.7592i) q^{60} +(-5.30723 + 9.19239i) q^{61} -7.58211i q^{62} +(-67.9535 - 51.4845i) q^{63} -55.8893 q^{64} +(53.2620 - 44.7837i) q^{65} +(-12.1518 + 6.03892i) q^{66} +(-67.2001 + 38.7980i) q^{67} +(7.18846 - 4.15026i) q^{68} +(38.4861 + 77.4433i) q^{69} +(-12.8795 - 7.43596i) q^{70} -66.8110 q^{71} +(-20.7277 - 2.59982i) q^{72} -54.1949i q^{73} +(4.47968 + 2.58635i) q^{74} +(-9.13157 - 6.06116i) q^{75} +(113.007 - 65.2445i) q^{76} +(-126.516 + 73.0443i) q^{77} +(-4.56417 + 10.4884i) q^{78} +(30.9866 - 53.6704i) q^{79} +80.1602 q^{80} +(78.4909 + 20.0045i) q^{81} -16.6428 q^{82} +(-16.6325 + 28.8082i) q^{83} +(-111.012 - 6.93476i) q^{84} +(-9.83117 + 5.67603i) q^{85} +(-3.27513 - 5.67269i) q^{86} +(-44.6333 + 67.2433i) q^{87} +(-17.8983 + 31.0007i) q^{88} +73.8979 q^{89} +(14.0199 + 1.75847i) q^{90} +(-42.0015 + 115.761i) q^{91} +(97.7100 + 56.4129i) q^{92} +(34.5143 + 69.4512i) q^{93} +(-1.05919 - 1.83456i) q^{94} +(-154.552 + 89.2305i) q^{95} +(-36.7429 + 18.2597i) q^{96} +(25.5787 + 14.7678i) q^{97} +11.9466 q^{98} +(83.8191 - 110.631i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 4 q^{3} - 50 q^{4} + 4 q^{9} + 8 q^{10} - 38 q^{12} - 6 q^{13} - 6 q^{14} - 90 q^{16} + 14 q^{22} + 138 q^{23} - 92 q^{25} - 76 q^{27} + 48 q^{29} + 186 q^{30} - 154 q^{36} + 324 q^{38} - 2 q^{39}+ \cdots + 504 q^{95}+O(q^{100}) $ 52 * q - 4 * q^3 - 50 * q^4 + 4 * q^9 + 8 * q^10 - 38 * q^12 - 6 * q^13 - 6 * q^14 - 90 * q^16 + 14 * q^22 + 138 * q^23 - 92 * q^25 - 76 * q^27 + 48 * q^29 + 186 * q^30 - 154 * q^36 + 324 * q^38 - 2 * q^39 - 68 * q^40 - 216 * q^42 + 62 * q^43 + 230 * q^48 + 70 * q^49 + 90 * q^51 - 4 * q^52 + 92 * q^55 - 276 * q^56 + 12 * q^61 + 12 * q^64 - 588 * q^65 + 762 * q^66 - 144 * q^68 - 414 * q^69 + 342 * q^74 - 620 * q^75 - 510 * q^77 - 162 * q^78 - 24 * q^79 + 532 * q^81 - 292 * q^82 - 330 * q^87 - 62 * q^88 + 258 * q^90 + 264 * q^91 - 396 * q^92 - 160 * q^94 + 504 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.146647	−	0.254001i	0.0733237	−	0.127000i	−0.827032	−	0.562154i	$-0.809973\pi$
$2$	0.146647	−	0.254001i	0.0733237	−	0.127000i	0.900356	+	0.435154i	$0.143306\pi$
$3$	−0.187042	+	2.99416i	−0.0623472	+	0.998055i
$3$	−0.187042	+	2.99416i	−0.0623472	+	0.998055i
$4$	1.95699	+	3.38960i	0.489247	+	0.847401i
$5$	−2.67644	−	4.63573i	−0.535288	−	0.927147i	−0.999149	−	0.0412386i	$-0.986870\pi$
$5$	−2.67644	−	4.63573i	−0.535288	−	0.927147i	0.463861	−	0.885908i	$-0.346464\pi$
$6$	0.733091	+	0.486595i	0.122182	+	0.0810992i
$7$	8.20362	+	4.73636i	1.17195	+	0.676623i	0.954138	−	0.299369i	$-0.0967761\pi$
$7$	8.20362	+	4.73636i	1.17195	+	0.676623i	0.217808	+	0.975992i	$0.430109\pi$
$8$	2.32113			0.290141
$9$	−8.93003	−	1.12007i	−0.992226	−	0.124452i
$10$	−1.56997			−0.156997
$11$	−7.71102	+	13.3559i	−0.701001	+	1.21417i	0.267114	+	0.963665i	$0.413930\pi$
$11$	−7.71102	+	13.3559i	−0.701001	+	1.21417i	−0.968115	+	0.250505i	$0.919403\pi$
$12$	−10.5151	+	5.22555i	−0.876256	+	0.435462i
$13$	2.27033	+	12.8002i	0.174641	+	0.984632i
$13$	2.27033	+	12.8002i	0.174641	+	0.984632i
$14$	2.40608	−	1.38915i	0.171863	−	0.0992250i
$15$	14.3807	−	7.14663i	0.958717	−	0.476442i
$16$	−7.48757	+	12.9688i	−0.467973	+	0.810553i
$17$		−	2.12074i		−	0.124749i	−0.998053	−	0.0623746i	$-0.980133\pi$
$17$		−	2.12074i		−	0.124749i	0.998053	−	0.0623746i	$-0.0198674\pi$
$18$	−1.59406	+	2.10398i	−0.0885591	+	0.116888i
$19$		−	33.3392i		−	1.75470i	−0.479854	−	0.877348i	$-0.659310\pi$
$19$		−	33.3392i		−	1.75470i	0.479854	−	0.877348i	$-0.340690\pi$
$20$	10.4755	−	18.1442i	0.523777	−	0.907208i
$21$	−15.7159	+	23.6771i	−0.748374	+	1.12748i
$22$	2.26160	+	3.91721i	0.102800	+	0.178055i
$23$	24.9644	−	14.4132i	1.08541	−	0.626660i	0.153058	−	0.988217i	$-0.451088\pi$
$23$	24.9644	−	14.4132i	1.08541	−	0.626660i	0.932350	+	0.361557i	$0.117755\pi$
$24$	−0.434148	+	6.94984i	−0.0180895	+	0.289577i
$25$	−1.82668	+	3.16390i	−0.0730671	+	0.126556i
$26$	3.58420	+	1.30045i	0.137854	+	0.0500174i
$27$	5.02395	−	26.5285i	0.186072	−	0.982536i
$28$			37.0760i			1.32414i
$29$	23.2984	+	13.4514i	0.803394	+	0.463840i	0.844657	−	0.535309i	$-0.179805\pi$
$29$	23.2984	+	13.4514i	0.803394	+	0.463840i	−0.0412625	+	0.999148i	$0.513138\pi$
$30$	0.293650	−	4.70075i	0.00978835	−	0.156692i
$31$	22.3881	−	12.9257i	0.722195	−	0.416960i	−0.0933648	−	0.995632i	$-0.529762\pi$
$31$	22.3881	−	12.9257i	0.722195	−	0.416960i	0.815560	+	0.578672i	$0.196429\pi$
$32$	6.83832	+	11.8443i	0.213698	+	0.370135i
$33$	−38.5474	−	25.5861i	−1.16810	−	0.775338i
$34$	−0.538669	−	0.311001i	−0.0158432	−	0.00914708i
$35$		−	50.7064i		−	1.44875i
$36$	−13.6794	−	32.4612i	−0.379983	−	0.901701i
$37$			17.6365i			0.476662i	0.971184	+	0.238331i	$0.0766003\pi$
$37$			17.6365i			0.476662i	−0.971184	+	0.238331i	$0.923400\pi$
$38$	−8.46819	−	4.88911i	−0.222847	−	0.128661i
$39$	−38.7506	+	4.40356i	−0.993605	+	0.112912i
$40$	−6.21236	−	10.7601i	−0.155309	−	0.269003i
$41$	−28.3722	−	49.1420i	−0.692004	−	1.19859i	−0.971180	−	0.238346i	$-0.923395\pi$
$41$	−28.3722	−	49.1420i	−0.692004	−	1.19859i	0.279177	−	0.960240i	$-0.409939\pi$
$42$	3.70930	+	7.46402i	0.0883168	+	0.177715i
$43$	11.1667	−	19.3413i	0.259690	−	0.449797i	−0.706469	−	0.707744i	$-0.749713\pi$
$43$	11.1667	−	19.3413i	0.259690	−	0.449797i	0.966159	+	0.257947i	$0.0830462\pi$
$44$	−60.3615			−1.37185
$45$	18.7084	+	44.3950i	0.415742	+	0.986556i
$46$		−	8.45463i		−	0.183796i
$47$	3.61133	−	6.25502i	0.0768369	−	0.133085i	−0.825047	−	0.565065i	$-0.808851\pi$
$47$	3.61133	−	6.25502i	0.0768369	−	0.133085i	0.901884	+	0.431979i	$0.142185\pi$
$48$	−37.4304	−	24.8447i	−0.779799	−	0.517598i
$49$	20.3662	+	35.2753i	0.415637	+	0.719905i
$50$	0.535755	+	0.927955i	0.0107151	+	0.0185591i
$51$	6.34983	+	0.396666i	0.124507	+	0.00777777i
$52$	−38.9447	+	32.7454i	−0.748936	+	0.629719i
$53$		−	40.2849i		−	0.760092i	−0.924968	−	0.380046i	$-0.875908\pi$
$53$		−	40.2849i		−	0.760092i	0.924968	−	0.380046i	$-0.124092\pi$
$54$	−6.00150	−	5.16642i	−0.111139	−	0.0956744i
$55$	82.5523			1.50095
$56$	19.0416	+	10.9937i	0.340029	+	0.196316i
$57$	99.8231	+	6.23583i	1.75128	+	0.109401i
$58$	6.83331	−	3.94521i	0.117816	−	0.0680209i
$59$	52.7704	+	91.4009i	0.894413	+	1.54917i	0.834530	+	0.550963i	$0.185740\pi$
$59$	52.7704	+	91.4009i	0.894413	+	1.54917i	0.0598833	+	0.998205i	$0.480927\pi$
$60$	52.3672	+	34.7592i	0.872787	+	0.579320i
$61$	−5.30723	+	9.19239i	−0.0870038	+	0.150695i	−0.906243	−	0.422757i	$-0.861063\pi$
$61$	−5.30723	+	9.19239i	−0.0870038	+	0.150695i	0.819240	+	0.573451i	$0.194396\pi$
$62$		−	7.58211i		−	0.122292i
$63$	−67.9535	−	51.4845i	−1.07863	−	0.817213i
$64$	−55.8893			−0.873270
$65$	53.2620	−	44.7837i	0.819415	−	0.688980i
$66$	−12.1518	+	6.03892i	−0.184118	+	0.0914988i
$67$	−67.2001	+	38.7980i	−1.00299	+	0.579075i	−0.909131	−	0.416511i	$-0.863253\pi$
$67$	−67.2001	+	38.7980i	−1.00299	+	0.579075i	−0.0938563	+	0.995586i	$0.529919\pi$
$68$	7.18846	−	4.15026i	0.105713	−	0.0610332i
$69$	38.4861	+	77.4433i	0.557769	+	1.12237i
$70$	−12.8795	−	7.43596i	−0.183992	−	0.106228i
$71$	−66.8110			−0.941000			−0.470500	−	0.882400i	$-0.655926\pi$
$71$	−66.8110			−0.941000			−0.470500	+	0.882400i	$0.655926\pi$
$72$	−20.7277	−	2.59982i	−0.287885	−	0.0361086i
$73$		−	54.1949i		−	0.742396i	−0.928554	−	0.371198i	$-0.878947\pi$
$73$		−	54.1949i		−	0.742396i	0.928554	−	0.371198i	$-0.121053\pi$
$74$	4.47968	+	2.58635i	0.0605363	+	0.0349506i
$75$	−9.13157	−	6.06116i	−0.121754	−	0.0808154i
$76$	113.007	−	65.2445i	1.48693	−	0.858481i
$77$	−126.516	+	73.0443i	−1.64307	+	0.948627i
$78$	−4.56417	+	10.4884i	−0.0585149	+	0.134467i
$79$	30.9866	−	53.6704i	0.392235	−	0.679372i	−0.600509	−	0.799618i	$-0.705035\pi$
$79$	30.9866	−	53.6704i	0.392235	−	0.679372i	0.992744	+	0.120247i	$0.0383685\pi$
$80$	80.1602			1.00200
$81$	78.4909	+	20.0045i	0.969023	+	0.246969i
$82$	−16.6428			−0.202961
$83$	−16.6325	+	28.8082i	−0.200391	+	0.347087i	−0.948654	−	0.316314i	$-0.897555\pi$
$83$	−16.6325	+	28.8082i	−0.200391	+	0.347087i	0.748263	+	0.663402i	$0.230888\pi$
$84$	−111.012	−	6.93476i	−1.32157	−	0.0825567i
$85$	−9.83117	+	5.67603i	−0.115661	+	0.0667768i
$86$	−3.27513	−	5.67269i	−0.0380829	−	0.0659615i
$87$	−44.6333	+	67.2433i	−0.513027	+	0.772912i
$88$	−17.8983	+	31.0007i	−0.203389	+	0.352281i
$89$	73.8979			0.830314			0.415157	−	0.909750i	$-0.363727\pi$
$89$	73.8979			0.830314			0.415157	+	0.909750i	$0.363727\pi$
$90$	14.0199	+	1.75847i	0.155777	+	0.0195386i
$91$	−42.0015	+	115.761i	−0.461555	+	1.27210i
$92$	97.7100	+	56.4129i	1.06207	+	0.613184i
$93$	34.5143	+	69.4512i	0.371122	+	0.746787i
$94$	−1.05919	−	1.83456i	−0.0112679	−	0.0195166i
$95$	−154.552	+	89.2305i	−1.62686	+	0.939269i
$96$	−36.7429	+	18.2597i	−0.382738	+	0.190205i
$97$	25.5787	+	14.7678i	0.263698	+	0.152246i	0.626020	−	0.779807i	$-0.284683\pi$
$97$	25.5787	+	14.7678i	0.263698	+	0.152246i	−0.362323	+	0.932053i	$0.618016\pi$
$98$	11.9466			0.121904
$99$	83.8191	−	110.631i	0.846657	−	1.11749i
$100$	−14.2992			−0.142992
$101$	72.0529	+	41.5998i	0.713395	+	0.411879i	0.812317	−	0.583216i	$-0.198206\pi$
$101$	72.0529	+	41.5998i	0.713395	+	0.411879i	−0.0989216	+	0.995095i	$0.531539\pi$
$102$	1.03194	−	1.55469i	0.0101171	−	0.0152421i
$103$	−84.0009	−	145.494i	−0.815542	−	1.41256i	−0.908938	−	0.416932i	$-0.863105\pi$
$103$	−84.0009	−	145.494i	−0.815542	−	1.41256i	0.0933953	−	0.995629i	$-0.470228\pi$
$104$	5.26972	+	29.7110i	0.0506704	+	0.285682i
$105$	151.823	+	9.48421i	1.44593	+	0.0903258i
$106$	−10.2324	−	5.90767i	−0.0965320	−	0.0557328i
$107$		−	125.475i		−	1.17266i	−0.810071	−	0.586332i	$-0.800571\pi$
$107$		−	125.475i		−	1.17266i	0.810071	−	0.586332i	$-0.199429\pi$
$108$	99.7529	−	34.8867i	0.923638	−	0.323025i
$109$		−	2.93689i		−	0.0269439i	−0.999909	−	0.0134720i	$-0.995712\pi$
$109$		−	2.93689i		−	0.0269439i	0.999909	−	0.0134720i	$-0.00428839\pi$
$110$	12.1061	−	20.9684i	0.110055	−	0.190621i
$111$	−52.8066	−	3.29876i	−0.475735	−	0.0297186i
$112$	−122.850	+	70.9277i	−1.09688	+	0.633283i
$113$	−151.195	+	87.2926i	−1.33801	+	0.772501i	−0.986512	−	0.163687i	$-0.947661\pi$
$113$	−151.195	+	87.2926i	−1.33801	+	0.772501i	−0.351499	+	0.936188i	$0.614328\pi$
$114$	16.2227	−	24.4407i	0.142304	−	0.214392i
$115$	−133.631	−	77.1521i	−1.16201	−	0.670888i
$116$			105.297i			0.907729i
$117$	−5.93700	−	116.849i	−0.0507436	−	0.998712i
$118$	30.9545			0.262327
$119$	10.0446	−	17.3977i	0.0844082	−	0.146199i
$120$	33.3796	−	16.5882i	0.278163	−	0.138235i
$121$	−58.4195	−	101.186i	−0.482806	−	0.836244i
$122$	1.55658	+	2.69608i	0.0127589	+	0.0220990i
$123$	152.446	−	75.7593i	1.23940	−	0.615929i
$124$	87.6264	+	50.5911i	0.706664	+	0.407993i
$125$	−114.266			−0.914129
$126$	−23.0423	+	9.71018i	−0.182875	+	0.0770649i
$127$	−15.9739			−0.125779			−0.0628893	−	0.998021i	$-0.520032\pi$
$127$	−15.9739			−0.125779			−0.0628893	+	0.998021i	$0.520032\pi$
$128$	−35.5493	+	61.5732i	−0.277729	+	0.481041i
$129$	55.8223	+	37.0525i	0.432731	+	0.287229i
$130$	−3.56435	−	20.0960i	−0.0274181	−	0.154585i
$131$	−20.7147	+	11.9596i	−0.158128	+	0.0912950i	−0.576976	−	0.816761i	$-0.695767\pi$
$131$	−20.7147	+	11.9596i	−0.158128	+	0.0912950i	0.418848	+	0.908056i	$0.362434\pi$
$132$	11.2901	−	180.732i	0.0855312	−	1.36918i
$133$	157.907	−	273.502i	1.18727	−	2.05641i
$134$			22.7585i			0.169840i
$135$	−136.425	+	47.7122i	−1.01056	+	0.353424i
$136$		−	4.92250i		−	0.0361949i
$137$	−42.8060	+	74.1421i	−0.312452	+	0.541183i	−0.978893	−	0.204375i	$-0.934484\pi$
$137$	−42.8060	+	74.1421i	−0.312452	+	0.541183i	0.666440	+	0.745558i	$0.267817\pi$
$138$	25.3145	+	1.58137i	0.183439	+	0.0114592i
$139$	38.8488	+	67.2881i	0.279488	+	0.484087i	0.971258	−	0.238031i	$-0.0765020\pi$
$139$	38.8488	+	67.2881i	0.279488	+	0.484087i	−0.691770	+	0.722118i	$0.743169\pi$
$140$	171.875	−	99.2318i	1.22768	−	0.708799i
$141$	18.0531	+	11.9829i	0.128036	+	0.0849849i
$142$	−9.79766	+	16.9700i	−0.0689976	+	0.119507i
$143$	−188.465	−	68.3805i	−1.31793	−	0.478185i
$144$	81.3902	−	107.426i	0.565210	−	0.746011i
$145$		−	144.007i		−	0.993152i
$146$	−13.7655	−	7.94754i	−0.0942845	−	0.0544352i
$147$	−109.429	+	54.3819i	−0.744418	+	0.369945i
$148$	−59.7808	+	34.5144i	−0.403924	+	0.233206i
$149$	52.8009	+	91.4538i	0.354368	+	0.613784i	0.987010	−	0.160661i	$-0.0513626\pi$
$149$	52.8009	+	91.4538i	0.354368	+	0.613784i	−0.632641	+	0.774445i	$0.718029\pi$
$150$	−2.87866	+	1.43057i	−0.0191911	+	0.00953715i
$151$	157.615	+	90.9988i	1.04381	+	0.602641i	0.920909	−	0.389778i	$-0.127448\pi$
$151$	157.615	+	90.9988i	1.04381	+	0.602641i	0.122897	+	0.992419i	$0.460782\pi$
$152$		−	77.3847i		−	0.509110i
$153$	−2.37537	+	18.9382i	−0.0155253	+	0.123779i
$154$			42.8470i			0.278227i
$155$	−119.841	−	69.1900i	−0.773165	−	0.446387i
$156$	−90.7608	−	122.731i	−0.581800	−	0.786740i
$157$	41.3417	+	71.6058i	0.263323	+	0.456088i	0.967123	−	0.254310i	$-0.0818483\pi$
$157$	41.3417	+	71.6058i	0.263323	+	0.456088i	−0.703800	+	0.710398i	$0.748515\pi$
$158$	−9.08821	−	15.7412i	−0.0575203	−	0.0996281i
$159$	120.620	+	7.53496i	0.758614	+	0.0473897i
$160$	36.6047	−	63.4013i	0.228780	−	0.396258i
$161$	273.064			1.69605
$162$	16.5916	−	17.0031i	0.102417	−	0.104958i
$163$		−	107.833i		−	0.661553i	−0.943709	−	0.330777i	$-0.892689\pi$
$163$		−	107.833i		−	0.661553i	0.943709	−	0.330777i	$-0.107311\pi$
$164$	111.048	−	192.341i	0.677122	−	1.17281i
$165$	−15.4407	+	247.175i	−0.0935802	+	1.49803i
$166$	4.87821	+	8.44931i	0.0293868	+	0.0508994i
$167$	35.1152	+	60.8212i	0.210270	+	0.364199i	0.951799	−	0.306722i	$-0.0992322\pi$
$167$	35.1152	+	60.8212i	0.210270	+	0.364199i	−0.741529	+	0.670921i	$0.765899\pi$
$168$	−36.4785	+	54.9575i	−0.217134	+	0.327128i
$169$	−158.691	+	58.1214i	−0.939001	+	0.343914i
$170$			3.32950i			0.0195853i
$171$	−37.3422	+	297.720i	−0.218375	+	1.74106i
$172$	87.4123			0.508211
$173$	−133.772	−	77.2336i	−0.773251	−	0.446437i	0.0607819	−	0.998151i	$-0.480641\pi$
$173$	−133.772	−	77.2336i	−0.773251	−	0.446437i	−0.834033	+	0.551714i	$0.813974\pi$
$174$	10.5345	+	21.1980i	0.0605431	+	0.121827i
$175$	−29.9707	+	17.3036i	−0.171261	+	0.0988778i
$176$	−115.474	−	200.006i	−0.656100	−	1.13640i
$177$	−283.540	+	140.907i	−1.60192	+	0.796086i
$178$	10.8369	−	18.7701i	0.0608817	−	0.105450i
$179$			163.453i			0.913147i	0.889686	+	0.456573i	$0.150923\pi$
$179$			163.453i			0.913147i	−0.889686	+	0.456573i	$0.849077\pi$
$180$	−113.870	+	150.295i	−0.632608	+	0.834970i
$181$	−133.695			−0.738644			−0.369322	−	0.929302i	$-0.620410\pi$
$181$	−133.695			−0.738644			−0.369322	+	0.929302i	$0.620410\pi$
$182$	23.2440	+	27.6445i	0.127714	+	0.151893i
$183$	−26.5308	−	17.6101i	−0.144977	−	0.0962299i
$184$	57.9455	−	33.4549i	0.314921	−	0.181820i
$185$	81.7581	−	47.2031i	0.441936	−	0.255152i
$186$	22.7021	+	1.41817i	0.122054	+	0.00762457i
$187$	28.3243	+	16.3530i	0.151467	+	0.0874494i
$188$	28.2694			0.150369
$189$	166.863	−	193.834i	0.882873	−	1.02558i
$190$			52.3417i			0.275483i
$191$	−142.365	−	82.1942i	−0.745364	−	0.430336i	0.0786522	−	0.996902i	$-0.474938\pi$
$191$	−142.365	−	82.1942i	−0.745364	−	0.430336i	−0.824016	+	0.566566i	$0.808272\pi$
$192$	10.4536	−	167.342i	0.0544460	−	0.871571i
$193$	−31.1188	+	17.9665i	−0.161237	+	0.0930904i	−0.578448	−	0.815720i	$-0.696341\pi$
$193$	−31.1188	+	17.9665i	−0.161237	+	0.0930904i	0.417210	+	0.908810i	$0.363008\pi$
$194$	7.50209	−	4.33133i	0.0386706	−	0.0223265i
$195$	124.127	+	167.852i	0.636551	+	0.860777i
$196$	−79.7130	+	138.067i	−0.406699	+	0.704423i
$197$	−31.9390			−0.162127			−0.0810633	−	0.996709i	$-0.525832\pi$
$197$	−31.9390			−0.162127			−0.0810633	+	0.996709i	$0.525832\pi$
$198$	−15.8086	−	37.5139i	−0.0798416	−	0.189464i
$199$	63.1067			0.317119			0.158560	−	0.987349i	$-0.449315\pi$
$199$	63.1067			0.317119			0.158560	+	0.987349i	$0.449315\pi$
$200$	−4.23996	+	7.34382i	−0.0211998	+	0.0367191i
$201$	−103.598	−	208.465i	−0.515415	−	1.03714i
$202$	21.1327	−	12.2010i	0.104618	−	0.0604010i
$203$	127.421	+	220.700i	0.627689	+	1.08719i
$204$	11.0820	+	22.2997i	0.0543236	+	0.109312i
$205$	−151.873	+	263.051i	−0.740843	+	1.28318i
$206$	−49.2740			−0.239194
$207$	−239.076	+	100.748i	−1.15496	+	0.486708i
$208$	−183.003	−	66.3990i	−0.879824	−	0.319226i
$209$	445.275	+	257.079i	2.13050	+	1.23004i
$210$	24.6735	−	37.1724i	0.117493	−	0.177011i
$211$	25.8336	+	44.7451i	0.122434	+	0.212062i	0.920727	−	0.390207i	$-0.127597\pi$
$211$	25.8336	+	44.7451i	0.122434	+	0.212062i	−0.798293	+	0.602269i	$0.794263\pi$
$212$	136.550	−	78.8371i	0.644103	−	0.371873i
$213$	12.4964	−	200.043i	0.0586687	−	0.939169i
$214$	−31.8708	−	18.4006i	−0.148929	−	0.0859841i
$215$	−119.548			−0.556037
$216$	11.6612	−	61.5760i	0.0539872	−	0.285074i
$217$	244.884			1.12850
$218$	−0.745972	−	0.430687i	−0.00342189	−	0.00197563i
$219$	162.268	+	10.1367i	0.740951	+	0.0462863i
$220$	161.554	+	279.820i	0.734336	+	1.27191i
$221$	27.1459	−	4.81477i	0.122832	−	0.0217863i
$222$	−8.58183	+	12.9291i	−0.0386569	+	0.0582394i
$223$	97.2097	+	56.1241i	0.435918	+	0.251677i	0.701865	−	0.712310i	$-0.252351\pi$
$223$	97.2097	+	56.1241i	0.435918	+	0.251677i	−0.265947	+	0.963988i	$0.585684\pi$
$224$			129.555i			0.578371i
$225$	19.8561	−	26.2077i	0.0882492	−	0.116479i
$226$			51.2049i			0.226571i
$227$	71.4825	−	123.811i	0.314901	−	0.545424i	−0.664516	−	0.747274i	$-0.731362\pi$
$227$	71.4825	−	123.811i	0.314901	−	0.545424i	0.979416	+	0.201850i	$0.0646954\pi$
$228$	174.216	+	350.564i	0.764104	+	1.53756i
$229$	69.2157	−	39.9617i	0.302252	−	0.174505i	−0.341202	−	0.939990i	$-0.610834\pi$
$229$	69.2157	−	39.9617i	0.302252	−	0.174505i	0.643454	+	0.765485i	$0.277501\pi$
$230$	−39.1934	+	22.6283i	−0.170406	+	0.0983840i
$231$	−195.043	−	392.473i	−0.844341	−	1.69902i
$232$	54.0786	+	31.2223i	0.233098	+	0.134579i
$233$			55.4387i			0.237934i	0.992898	+	0.118967i	$0.0379583\pi$
$233$			55.4387i			0.237934i	−0.992898	+	0.118967i	$0.962042\pi$
$234$	−30.5504	−	15.6276i	−0.130557	−	0.0667848i
$235$	−38.6621			−0.164520
$236$	−206.542	+	357.741i	−0.875178	+	1.51585i
$237$	154.902	+	102.818i	0.653595	+	0.433829i
$238$	−2.94602	−	5.10266i	−0.0123782	−	0.0214397i
$239$	−194.301	−	336.539i	−0.812974	−	1.40811i	−0.910774	−	0.412906i	$-0.864514\pi$
$239$	−194.301	−	336.539i	−0.812974	−	1.40811i	0.0978002	−	0.995206i	$-0.468819\pi$
$240$	−14.9933	+	240.013i	−0.0624721	+	1.00005i
$241$	−79.1067	−	45.6723i	−0.328244	−	0.189512i	0.326817	−	0.945087i	$-0.394024\pi$
$241$	−79.1067	−	45.6723i	−0.328244	−	0.189512i	−0.655061	+	0.755576i	$0.727357\pi$
$242$	−34.2683			−0.141604
$243$	−74.5777	+	231.273i	−0.306904	+	0.951740i
$244$	−41.5448			−0.170265
$245$	109.018	−	188.825i	0.444972	−	0.770713i
$246$	3.11290	−	49.8313i	0.0126541	−	0.202566i
$247$	426.750	−	75.6910i	1.72773	−	0.306441i
$248$	51.9655	−	30.0023i	0.209539	−	0.120977i
$249$	−83.1456	−	55.1886i	−0.333918	−	0.221641i
$250$	−16.7568	+	29.0237i	−0.0670273	+	0.116095i
$251$		−	210.440i		−	0.838405i	−0.907893	−	0.419203i	$-0.862310\pi$
$251$		−	210.440i		−	0.838405i	0.907893	−	0.419203i	$-0.137690\pi$
$252$	41.5276	−	331.090i	0.164792	−	1.31385i
$253$			444.561i			1.75716i
$254$	−2.34253	+	4.05738i	−0.00922255	+	0.0159739i
$255$	−15.1561	−	30.4978i	−0.0594358	−	0.119599i
$256$	−101.352	−	175.547i	−0.395907	−	0.685730i
$257$	320.600	−	185.099i	1.24747	−	0.720229i	0.276868	−	0.960908i	$-0.410704\pi$
$257$	320.600	−	185.099i	1.24747	−	0.720229i	0.970605	+	0.240679i	$0.0773702\pi$
$258$	17.5976	−	8.74525i	0.0682076	−	0.0338963i
$259$	−83.5328	+	144.683i	−0.322521	+	0.558622i
$260$	256.032	+	92.8959i	0.984739	+	0.357292i
$261$	−192.989	−	146.217i	−0.739422	−	0.560218i
$262$			7.01540i			0.0267763i
$263$	−404.705	−	233.657i	−1.53880	−	0.888429i	−0.998909	−	0.0466956i	$-0.985131\pi$
$263$	−404.705	−	233.657i	−1.53880	−	0.888429i	−0.539894	−	0.841733i	$-0.681536\pi$
$264$	−89.4734	−	59.3887i	−0.338914	−	0.224957i
$265$	−186.750	+	107.820i	−0.704717	+	0.406869i
$266$	−46.3132	−	80.2168i	−0.174110	−	0.301567i
$267$	−13.8220	+	221.262i	−0.0517678	+	0.828698i
$268$	−263.020	−	151.855i	−0.981417	−	0.566622i
$269$		−	12.1114i		−	0.0450239i	−0.999747	−	0.0225119i	$-0.992834\pi$
$269$		−	12.1114i		−	0.0450239i	0.999747	−	0.0225119i	$-0.00716638\pi$
$270$	−7.88747	+	41.6490i	−0.0292128	+	0.154255i
$271$			100.797i			0.371945i	0.982555	+	0.185973i	$0.0595435\pi$
$271$			100.797i			0.371945i	−0.982555	+	0.185973i	$0.940456\pi$
$272$	27.5035	+	15.8792i	0.101116	+	0.0583793i
$273$	−338.752	−	147.412i	−1.24085	−	0.539970i
$274$	12.5548	+	21.7455i	0.0458203	+	0.0793631i
$275$	−28.1711	−	48.7938i	−0.102440	−	0.177432i
$276$	−187.185	+	282.008i	−0.678208	+	1.02177i
$277$	3.55206	−	6.15235i	0.0128233	−	0.0222106i	−0.859543	−	0.511064i	$-0.829251\pi$
$277$	3.55206	−	6.15235i	0.0128233	−	0.0222106i	0.872366	+	0.488854i	$0.162585\pi$
$278$	22.7883			0.0819723
$279$	−214.404	+	90.3512i	−0.768472	+	0.323839i
$280$		−	117.696i		−	0.420343i
$281$	−52.2789	+	90.5497i	−0.186046	+	0.322241i	−0.943928	−	0.330150i	$-0.892901\pi$
$281$	−52.2789	+	90.5497i	−0.186046	+	0.322241i	0.757883	+	0.652391i	$0.226234\pi$
$282$	5.69109	−	2.82824i	0.0201812	−	0.0100292i
$283$	29.0002	+	50.2298i	0.102474	+	0.177491i	0.912703	−	0.408623i	$-0.133991\pi$
$283$	29.0002	+	50.2298i	0.102474	+	0.177491i	−0.810229	+	0.586113i	$0.800657\pi$
$284$	−130.748	−	226.463i	−0.460382	−	0.797404i
$285$	−238.263	−	479.443i	−0.836011	−	1.68226i
$286$	−45.0065	+	37.8423i	−0.157365	+	0.132316i
$287$		−	537.523i		−	1.87290i
$288$	−47.8000	−	113.430i	−0.165972	−	0.393853i
$289$	284.502			0.984438
$290$	−36.5779	−	21.1183i	−0.126131	−	0.0728216i
$291$	−49.0016	+	73.8245i	−0.168390	+	0.253692i
$292$	183.699	−	106.059i	0.629107	−	0.363215i
$293$	−18.9537	−	32.8288i	−0.0646885	−	0.112044i	0.831867	−	0.554975i	$-0.187272\pi$
$293$	−18.9537	−	32.8288i	−0.0646885	−	0.112044i	−0.896556	+	0.442931i	$0.853939\pi$
$294$	−2.23452	+	35.7701i	−0.00760039	+	0.121667i
$295$	282.474	−	489.259i	0.957538	−	1.65850i
$296$			40.9366i			0.138299i
$297$	315.571	+	271.661i	1.06253	+	0.914683i
$298$	30.9724			0.103934
$299$	241.169	+	286.827i	0.806586	+	0.959287i
$300$	2.67454	−	42.8140i	0.00891513	−	0.142713i
$301$	183.214	−	105.779i	0.608686	−	0.351425i
$302$	46.2275	−	26.6895i	0.153071	−	0.0883758i
$303$	−138.033	+	207.957i	−0.455556	+	0.686328i
$304$	432.372	+	249.630i	1.42227	+	0.821151i
$305$	56.8180			0.186288
$306$	4.46199	+	3.38059i	0.0145817	+	0.0110477i
$307$		−	565.040i		−	1.84052i	−0.391305	−	0.920261i	$-0.627976\pi$
$307$		−	565.040i		−	1.84052i	0.391305	−	0.920261i	$-0.372024\pi$
$308$	−495.183	−	285.894i	−1.60774	−	0.928227i
$309$	451.344	−	224.299i	1.46066	−	0.725887i
$310$	−35.1486	+	20.2931i	−0.113383	+	0.0654615i
$311$	448.481	−	258.930i	1.44206	−	0.832574i	0.444073	−	0.895991i	$-0.353533\pi$
$311$	448.481	−	258.930i	1.44206	−	0.832574i	0.997987	+	0.0634169i	$0.0201998\pi$
$312$	−89.9451	+	10.2212i	−0.288286	+	0.0327603i
$313$	−138.702	+	240.239i	−0.443138	+	0.767538i	−0.997920	−	0.0644575i	$-0.979468\pi$
$313$	−138.702	+	240.239i	−0.443138	+	0.767538i	0.554782	+	0.831996i	$0.312802\pi$
$314$	24.2506			0.0772312
$315$	−56.7945	+	452.809i	−0.180300	+	1.43749i
$316$	242.562			0.767600
$317$	−152.700	+	264.483i	−0.481702	+	0.834332i	−0.999779	−	0.0210013i	$-0.993315\pi$
$317$	−152.700	+	264.483i	−0.481702	+	0.834332i	0.518077	+	0.855334i	$0.326648\pi$
$318$	19.6024	−	29.5325i	0.0616429	−	0.0928694i
$319$	−359.309	+	207.447i	−1.12636	+	0.650305i
$320$	149.584	+	259.088i	0.467451	+	0.809649i
$321$	375.693	+	23.4691i	1.17038	+	0.0731124i
$322$	40.0442	−	69.3585i	0.124361	−	0.215399i
$323$	−70.7038			−0.218897
$324$	85.7986	+	305.202i	0.264810	+	0.941980i
$325$	−44.6458	−	16.1988i	−0.137372	−	0.0498424i
$326$	−27.3897	−	15.8134i	−0.0840175	−	0.0485075i
$327$	8.79353	+	0.549321i	0.0268915	+	0.00167988i
$328$	−65.8554	−	114.065i	−0.200779	−	0.347759i
$329$	59.2520	−	34.2092i	0.180097	−	0.103979i
$330$	60.5183	+	40.1695i	0.183389	+	0.121726i
$331$	−333.273	−	192.415i	−1.00687	−	0.581314i	−0.0965936	−	0.995324i	$-0.530795\pi$
$331$	−333.273	−	192.415i	−1.00687	−	0.581314i	−0.910273	+	0.414009i	$0.864128\pi$
$332$	−130.198			−0.392163
$333$	19.7541	−	157.494i	0.0593215	−	0.472956i
$334$	20.5982			0.0616712
$335$	359.714	+	207.681i	1.07377	+	0.619944i
$336$	−189.391	−	381.100i	−0.563663	−	1.13423i
$337$	−31.9085	−	55.2672i	−0.0946841	−	0.163998i	0.814793	−	0.579752i	$-0.196851\pi$
$337$	−31.9085	−	55.2672i	−0.0946841	−	0.163998i	−0.909477	+	0.415755i	$0.863517\pi$
$338$	−8.50877	+	48.8310i	−0.0251739	+	0.144471i
$339$	−233.089	−	469.031i	−0.687577	−	1.38357i
$340$	−38.4790	−	22.2159i	−0.113174	−	0.0653408i
$341$			398.683i			1.16916i
$342$	70.1451	+	53.1449i	0.205103	+	0.155394i
$343$		−	78.3161i		−	0.228327i
$344$	25.9193	−	44.8936i	0.0753468	−	0.130505i
$345$	256.001	−	385.684i	0.742031	−	1.11792i
$346$	−39.2348	+	22.6522i	−0.113395	+	0.0654688i
$347$	−481.248	+	277.849i	−1.38688	+	0.800717i	−0.992963	−	0.118427i	$-0.962215\pi$
$347$	−481.248	+	277.849i	−1.38688	+	0.800717i	−0.393920	+	0.919145i	$0.628881\pi$
$348$	−315.275	−	19.6949i	−0.905963	−	0.0565944i
$349$	−123.965	−	71.5710i	−0.355199	−	0.205074i	0.311774	−	0.950156i	$-0.399077\pi$
$349$	−123.965	−	71.5710i	−0.355199	−	0.205074i	−0.666973	+	0.745082i	$0.732410\pi$
$350$			10.1501i			0.0290003i
$351$	350.976	+	4.07934i	0.999932	+	0.0116221i
$352$	−210.922			−0.599209
$353$	115.084	−	199.332i	0.326018	−	0.564680i	−0.655700	−	0.755022i	$-0.727626\pi$
$353$	115.084	−	199.332i	0.326018	−	0.564680i	0.981718	+	0.190342i	$0.0609597\pi$
$354$	−5.78979	+	92.6830i	−0.0163553	+	0.261816i
$355$	178.816	+	309.718i	0.503706	+	0.872445i
$356$	144.617	+	250.485i	0.406229	+	0.703609i
$357$	50.2129	+	33.3292i	0.140652	+	0.0933591i
$358$	41.5173	+	23.9700i	0.115970	+	0.0669553i
$359$	182.710			0.508943			0.254471	−	0.967080i	$-0.418099\pi$
$359$	182.710			0.508943			0.254471	+	0.967080i	$0.418099\pi$
$360$	43.4245	+	103.047i	0.120624	+	0.286240i
$361$	−750.505			−2.07896
$362$	−19.6060	+	33.9585i	−0.0541601	+	0.0938080i
$363$	313.893	−	155.992i	0.864719	−	0.429729i
$364$	−474.581	+	84.1748i	−1.30379	+	0.231249i
$365$	−251.233	+	145.049i	−0.688310	+	0.397396i
$366$	−8.36365	+	4.15638i	−0.0228515	+	0.0113562i
$367$	82.2966	−	142.542i	0.224242	−	0.388398i	−0.731850	−	0.681466i	$-0.761343\pi$
$367$	82.2966	−	142.542i	0.224242	−	0.388398i	0.956092	+	0.293068i	$0.0946762\pi$
$368$			431.679i			1.17304i
$369$	198.322	+	470.618i	0.537458	+	1.27539i
$370$		−	27.6888i		−	0.0748346i
$371$	190.804	−	330.482i	0.514296	−	0.890787i
$372$	−167.868	+	252.905i	−0.451258	+	0.679852i
$373$	−241.992	−	419.143i	−0.648772	−	1.12371i	−0.983416	−	0.181362i	$-0.941949\pi$
$373$	−241.992	−	419.143i	−0.648772	−	1.12371i	0.334644	−	0.942345i	$-0.391384\pi$
$374$	8.30737	−	4.79626i	0.0222122	−	0.0128242i
$375$	21.3725	−	342.131i	0.0569934	−	0.912350i
$376$	8.38237	−	14.5187i	0.0222935	−	0.0386135i
$377$	−119.285	+	328.764i	−0.316406	+	0.872053i
$378$	−24.7640	−	70.8086i	−0.0655132	−	0.187324i
$379$			71.6797i			0.189128i	0.995519	+	0.0945642i	$0.0301458\pi$
$379$			71.6797i			0.189128i	−0.995519	+	0.0945642i	$0.969854\pi$
$380$	−604.912	−	349.246i	−1.59187	−	0.919069i
$381$	2.98778	−	47.8284i	0.00784195	−	0.125534i
$382$	−41.7548	+	24.1071i	−0.109306	+	0.0631077i
$383$	20.3546	+	35.2552i	0.0531452	+	0.0920502i	0.891374	−	0.453268i	$-0.149742\pi$
$383$	20.3546	+	35.2552i	0.0531452	+	0.0920502i	−0.838229	+	0.545318i	$0.816409\pi$
$384$	−177.711	−	117.957i	−0.462789	−	0.307180i
$385$	677.228	+	390.998i	1.75903	+	1.01558i
$386$			10.5389i			0.0273029i
$387$	−121.382	+	160.211i	−0.313650	+	0.413981i
$388$			115.602i			0.297943i
$389$	66.9628	+	38.6610i	0.172141	+	0.0993855i	0.583595	−	0.812045i	$-0.301646\pi$
$389$	66.9628	+	38.6610i	0.172141	+	0.0993855i	−0.411454	+	0.911430i	$0.634979\pi$
$390$	60.8374	−	6.91347i	0.155993	−	0.0177268i
$391$	−30.5666	−	52.9429i	−0.0781754	−	0.135404i
$392$	47.2726	+	81.8786i	0.120593	+	0.208874i
$393$	−31.9346	−	64.2602i	−0.0812585	−	0.163512i
$394$	−4.68376	+	8.11252i	−0.0118877	+	0.0205901i
$395$	−331.735			−0.839836
$396$	539.030	+	67.6089i	1.36119	+	0.170730i
$397$			674.923i			1.70006i	0.526737	+	0.850029i	$0.323415\pi$
$397$			674.923i			1.70006i	−0.526737	+	0.850029i	$0.676585\pi$
$398$	9.25443	−	16.0291i	0.0232523	−	0.0402742i
$399$	789.376	+	523.955i	1.97839	+	1.31317i
$400$	−27.3548	−	47.3798i	−0.0683869	−	0.118450i
$401$	56.1904	+	97.3247i	0.140126	+	0.242705i	0.927544	−	0.373714i	$-0.121916\pi$
$401$	56.1904	+	97.3247i	0.140126	+	0.242705i	−0.787418	+	0.616419i	$0.788583\pi$
$402$	−68.1427	−	4.25679i	−0.169509	−	0.0105890i
$403$	216.281	+	257.226i	0.536677	+	0.638279i
$404$			325.641i			0.806043i
$405$	−117.341	−	417.404i	−0.289731	−	1.03063i
$406$	74.7438			0.184098
$407$	−235.551	−	135.995i	−0.578749	−	0.334141i
$408$	14.7388	+	0.920714i	0.0361245	+	0.00225665i
$409$	340.599	−	196.645i	0.832762	−	0.480795i	−0.0220357	−	0.999757i	$-0.507015\pi$
$409$	340.599	−	196.645i	0.832762	−	0.480795i	0.854797	+	0.518962i	$0.173681\pi$
$410$	44.5435	+	77.1516i	0.108643	+	0.188175i
$411$	−213.987	−	142.036i	−0.520650	−	0.345586i
$412$	328.778	−	569.459i	0.798004	−	1.38218i
$413$			999.758i			2.42072i
$414$	−9.46975	+	75.5001i	−0.0228738	+	0.182367i
$415$	178.063			0.429068
$416$	−136.085	+	114.423i	−0.327127	+	0.275054i
$417$	−208.738	+	103.734i	−0.500571	+	0.248763i
$418$	130.597	−	75.4000i	0.312432	−	0.180383i
$419$	−452.106	+	261.023i	−1.07901	+	0.622967i	−0.930629	−	0.365963i	$-0.880740\pi$
$419$	−452.106	+	261.023i	−1.07901	+	0.622967i	−0.148381	+	0.988930i	$0.547406\pi$
$420$	264.969	+	533.181i	0.630878	+	1.26948i
$421$	−520.275	−	300.381i	−1.23581	−	0.713494i	−0.267573	−	0.963538i	$-0.586222\pi$
$421$	−520.275	−	300.381i	−1.23581	−	0.713494i	−0.968235	+	0.250044i	$0.919555\pi$
$422$	15.1537			0.0359093
$423$	−39.2554	+	51.8125i	−0.0928023	+	0.122488i
$424$		−	93.5064i		−	0.220534i
$425$	6.70980	+	3.87391i	0.0157878	+	0.00911507i
$426$	−48.9785	−	32.5099i	−0.114973	−	0.0763143i
$427$	−87.0770	+	50.2739i	−0.203927	+	0.117737i
$428$	425.311	−	245.553i	0.993717	−	0.573723i
$429$	239.993	−	551.504i	0.559424	−	1.28556i
$430$	−17.5314	+	30.3653i	−0.0407707	+	0.0706169i
$431$	530.893			1.23177			0.615885	−	0.787836i	$-0.288799\pi$
$431$	530.893			1.23177			0.615885	+	0.787836i	$0.288799\pi$
$432$	306.427	+	263.789i	0.709321	+	0.610622i
$433$	−118.218			−0.273020			−0.136510	−	0.990639i	$-0.543589\pi$
$433$	−118.218			−0.273020			−0.136510	+	0.990639i	$0.543589\pi$
$434$	35.9116	−	62.2007i	0.0827456	−	0.143320i
$435$	431.181	+	26.9353i	0.991220	+	0.0619203i
$436$	9.95490	−	5.74746i	0.0228323	−	0.0131823i
$437$	−480.525	−	832.293i	−1.09960	−	1.90456i
$438$	26.3710	−	39.7298i	0.0602077	−	0.0907072i
$439$	−298.551	+	517.105i	−0.680070	+	1.17792i	0.294889	+	0.955532i	$0.404717\pi$
$439$	−298.551	+	517.105i	−0.680070	+	1.17792i	−0.974959	+	0.222385i	$0.928616\pi$
$440$	191.615			0.435488
$441$	−142.360	−	337.821i	−0.322812	−	0.766035i
$442$	2.75792	−	7.60115i	0.00623964	−	0.0171972i
$443$	311.260	+	179.706i	0.702620	+	0.405658i	0.808322	−	0.588740i	$-0.200376\pi$
$443$	311.260	+	179.706i	0.702620	+	0.405658i	−0.105703	+	0.994398i	$0.533709\pi$
$444$	−92.1604	−	185.449i	−0.207568	−	0.417678i
$445$	−197.783	−	342.571i	−0.444457	−	0.769822i
$446$	28.5111	−	16.4609i	0.0639262	−	0.0369078i
$447$	−283.703	+	140.989i	−0.634683	+	0.315411i
$448$	−458.494	−	264.712i	−1.02342	−	0.590874i
$449$	568.967			1.26719			0.633594	−	0.773666i	$-0.281579\pi$
$449$	568.967			1.26719			0.633594	+	0.773666i	$0.281579\pi$
$450$	−3.74494	−	8.88675i	−0.00832209	−	0.0197483i
$451$	875.113			1.94038
$452$	−591.775	−	341.661i	−1.30924	−	0.755888i
$453$	−301.946	+	454.903i	−0.666547	+	1.00420i
$454$	−20.9654	−	36.3132i	−0.0461794	−	0.0799850i
$455$	649.053	−	115.120i	1.42649	−	0.253011i
$456$	231.702	+	14.4742i	0.508119	+	0.0317416i
$457$	−345.318	−	199.370i	−0.755620	−	0.436257i	0.0721010	−	0.997397i	$-0.477030\pi$
$457$	−345.318	−	199.370i	−0.755620	−	0.436257i	−0.827721	+	0.561140i	$0.810363\pi$
$458$		−	23.4411i		−	0.0511815i
$459$	−56.2599	−	10.6545i	−0.122571	−	0.0232124i
$460$		−	603.943i		−	1.31292i
$461$	−288.621	+	499.906i	−0.626076	+	1.08440i	0.362256	+	0.932079i	$0.382007\pi$
$461$	−288.621	+	499.906i	−0.626076	+	1.08440i	−0.988332	+	0.152317i	$0.951327\pi$
$462$	−128.291	−	8.01418i	−0.277686	−	0.0173467i
$463$	−456.842	+	263.758i	−0.986700	+	0.569671i	−0.904286	−	0.426927i	$-0.859596\pi$
$463$	−456.842	+	263.758i	−0.986700	+	0.569671i	−0.0824134	+	0.996598i	$0.526263\pi$
$464$	−348.897	+	201.436i	−0.751934	+	0.434129i
$465$	229.581	−	345.881i	0.493724	−	0.743830i
$466$	14.0815	+	8.12994i	0.0302177	+	0.0174462i
$467$		−	263.576i		−	0.564404i	−0.959355	−	0.282202i	$-0.908935\pi$
$467$		−	263.576i		−	0.564404i	0.959355	−	0.282202i	$-0.0910648\pi$
$468$	384.454	−	248.797i	0.821483	−	0.531617i
$469$	−735.046			−1.56726
$470$	−5.66970	+	9.82020i	−0.0120632	+	0.0208940i
$471$	−222.132	+	110.390i	−0.471618	+	0.234375i
$472$	122.487	+	212.153i	0.259506	+	0.449477i
$473$	172.213	+	298.282i	0.364087	+	0.630617i
$474$	48.8317	−	24.2673i	0.103020	−	0.0511969i
$475$	105.482	+	60.9001i	0.222067	+	0.128211i
$476$	78.6285			0.165186
$477$	−45.1218	+	359.745i	−0.0945949	+	0.754183i
$478$	−113.975			−0.238441
$479$	−103.619	+	179.473i	−0.216324	+	0.374683i	−0.953681	−	0.300819i	$-0.902740\pi$
$479$	−103.619	+	179.473i	−0.216324	+	0.374683i	0.737358	+	0.675503i	$0.236073\pi$
$480$	182.987	+	121.459i	0.381223	+	0.253040i
$481$	−225.751	+	40.0406i	−0.469337	+	0.0832446i
$482$	−23.2016	+	13.3954i	−0.0481361	+	0.0277914i
$483$	−51.0744	+	817.599i	−0.105744	+	1.69275i
$484$	228.653	−	396.038i	0.472423	−	0.818261i
$485$		−	158.101i		−	0.325982i
$486$	47.8069	+	52.8584i	0.0983680	+	0.108762i
$487$		−	266.418i		−	0.547059i	−0.961864	−	0.273529i	$-0.911809\pi$
$487$		−	266.418i		−	0.547059i	0.961864	−	0.273529i	$-0.0881911\pi$
$488$	−12.3188	+	21.3367i	−0.0252434	+	0.0437228i
$489$	322.870	+	20.1693i	0.660266	+	0.0412460i
$490$	−31.9744	−	55.3813i	−0.0652539	−	0.113023i
$491$	277.257	−	160.074i	0.564678	−	0.326017i	−0.190343	−	0.981718i	$-0.560960\pi$
$491$	277.257	−	160.074i	0.564678	−	0.326017i	0.755021	+	0.655701i	$0.227627\pi$
$492$	555.129	+	368.472i	1.12831	+	0.748926i
$493$	28.5268	−	49.4098i	0.0578637	−	0.100223i
$494$	43.3561	−	119.495i	0.0877654	−	0.241892i
$495$	−737.195	−	92.4641i	−1.48928	−	0.186796i
$496$			387.130i			0.780504i
$497$	−548.092	−	316.441i	−1.10280	−	0.636702i
$498$	−26.2110	+	13.0258i	−0.0526326	+	0.0261562i
$499$	695.936	−	401.799i	1.39466	−	0.805208i	0.400834	−	0.916151i	$-0.368721\pi$
$499$	695.936	−	401.799i	1.39466	−	0.805208i	0.993827	+	0.110943i	$0.0353872\pi$
$500$	−223.617	−	387.317i	−0.447235	−	0.774634i
$501$	−188.677	+	93.7644i	−0.376600	+	0.187155i
$502$	−53.4518	−	30.8604i	−0.106478	−	0.0614750i
$503$		−	548.156i		−	1.08977i	−0.838510	−	0.544887i	$-0.816573\pi$
$503$		−	548.156i		−	1.08977i	0.838510	−	0.544887i	$-0.183427\pi$
$504$	−157.729	−	119.502i	−0.312954	−	0.237107i
$505$		−	445.358i		−	0.881896i
$506$	112.919	+	65.1938i	0.223160	+	0.128841i
$507$	−144.343	−	486.019i	−0.284700	−	0.958617i
$508$	−31.2607	−	54.1451i	−0.0615368	−	0.106585i
$509$	138.478	+	239.850i	0.272058	+	0.471218i	0.969389	−	0.245531i	$-0.0789624\pi$
$509$	138.478	+	239.850i	0.272058	+	0.471218i	−0.697331	+	0.716750i	$0.745629\pi$
$510$	−9.96907	−	0.622755i	−0.0195472	−	0.00122109i
$511$	256.687	−	444.594i	0.502322	−	0.870047i
$512$	−343.846			−0.671575
$513$	−884.439	−	167.495i	−1.72405	−	0.326500i
$514$		−	108.577i		−	0.211239i
$515$	−449.647	+	778.811i	−0.873101	+	1.51225i
$516$	−16.3498	+	261.727i	−0.0316856	+	0.507223i
$517$	55.6941	+	96.4650i	0.107726	+	0.186586i
$518$	24.4997	+	42.4348i	0.0472968	+	0.0819204i
$519$	256.271	−	386.091i	0.493778	−	0.743913i
$520$	123.628	−	103.949i	0.237746	−	0.199901i
$521$		−	412.120i		−	0.791018i	−0.918462	−	0.395509i	$-0.870568\pi$
$521$		−	412.120i		−	0.791018i	0.918462	−	0.395509i	$-0.129432\pi$
$522$	−65.4405	+	27.5771i	−0.125365	+	0.0528297i
$523$	−658.680			−1.25943			−0.629713	−	0.776828i	$-0.716827\pi$
$523$	−658.680			−1.25943			−0.629713	+	0.776828i	$0.716827\pi$
$524$	−81.0769	−	46.8098i	−0.154727	−	0.0893316i
$525$	−46.2041	−	92.9738i	−0.0880078	−	0.177093i
$526$	−118.698	+	68.5303i	−0.225661	+	0.130286i
$527$	−27.4121	−	47.4792i	−0.0520154	−	0.0900933i
$528$	620.449	−	308.337i	1.17509	−	0.583972i
$529$	150.980	−	261.505i	0.285407	−	0.494339i
$530$			63.2462i			0.119332i
$531$	−368.866	−	875.320i	−0.694662	−	1.64844i
$532$	1236.09			2.32347
$533$	564.614	−	474.738i	1.05931	−	0.890691i
$534$	54.1739	+	35.9584i	0.101449	+	0.0673377i
$535$	−581.669	+	335.827i	−1.08723	+	0.627714i
$536$	−155.980	+	90.0552i	−0.291008	+	0.168013i
$537$	−489.406	−	30.5726i	−0.911370	−	0.0569322i
$538$	−3.07631	−	1.77611i	−0.00571805	−	0.00330132i
$539$	−628.177			−1.16545
$540$	−428.708	−	369.055i	−0.793904	−	0.683436i
$541$			799.766i			1.47831i	0.673535	+	0.739155i	$0.264775\pi$
$541$			799.766i			1.47831i	−0.673535	+	0.739155i	$0.735225\pi$
$542$	25.6025	+	14.7816i	0.0472372	+	0.0272724i
$543$	25.0065	−	400.303i	0.0460524	−	0.737207i
$544$	25.1187	−	14.5023i	0.0461741	−	0.0266586i
$545$	−13.6146	+	7.86041i	−0.0249810	+	0.0144228i
$546$	−87.1198	+	64.4257i	−0.159560	+	0.117996i
$547$	−505.787	+	876.049i	−0.924657	+	1.60155i	−0.132545	+	0.991177i	$0.542315\pi$
$547$	−505.787	+	876.049i	−0.924657	+	1.60155i	−0.792112	+	0.610376i	$0.791018\pi$
$548$	−335.083			−0.611466
$549$	57.6898	−	76.1439i	0.105082	−	0.138696i
$550$	−16.5249			−0.0300452
$551$	448.458	−	776.752i	0.813898	−	1.40971i
$552$	89.3311	+	179.756i	0.161832	+	0.325645i
$553$	508.404	−	293.527i	0.919357	−	0.530791i
$554$	−1.04180	−	1.80445i	−0.00188051	−	0.00325713i
$555$	126.041	+	253.626i	0.227102	+	0.456984i
$556$	−152.053	+	263.364i	−0.273477	+	0.473677i
$557$	164.150			0.294704			0.147352	−	0.989084i	$-0.452925\pi$
$557$	164.150			0.294704			0.147352	+	0.989084i	$0.452925\pi$
$558$	−8.49247	+	67.7085i	−0.0152195	+	0.121341i
$559$	272.925	+	99.0250i	0.488237	+	0.177147i
$560$	657.603	+	379.667i	1.17429	+	0.677978i
$561$	−54.2615	+	81.7489i	−0.0967228	+	0.145720i
$562$	15.3331	+	26.5578i	0.0272831	+	0.0472558i
$563$	244.075	−	140.917i	0.433526	−	0.250297i	−0.267321	−	0.963607i	$-0.586139\pi$
$563$	244.075	−	140.917i	0.433526	−	0.250297i	0.700848	+	0.713311i	$0.252805\pi$
$564$	−5.28755	+	84.6431i	−0.00937509	+	0.150076i
$565$	809.331	+	467.267i	1.43244	+	0.827022i
$566$	17.0112			0.0300551
$567$	549.161	+	535.870i	0.968538	+	0.945097i
$568$	−155.077			−0.273023
$569$	773.477	+	446.567i	1.35936	+	0.784828i	0.989538	−	0.144273i	$-0.0460845\pi$
$569$	773.477	+	446.567i	1.35936	+	0.784828i	0.369825	+	0.929102i	$0.379418\pi$
$570$	−156.720	−	9.79008i	−0.274947	−	0.0171756i
$571$	179.759	+	311.352i	0.314814	+	0.545274i	0.979398	−	0.201939i	$-0.0647244\pi$
$571$	179.759	+	311.352i	0.314814	+	0.545274i	−0.664584	+	0.747214i	$0.731391\pi$
$572$	−137.040	−	772.640i	−0.239581	−	1.35077i
$573$	272.731	−	410.889i	0.475970	−	0.717084i
$574$	−136.531	−	78.8264i	−0.237859	−	0.137328i
$575$			105.313i			0.183153i
$576$	499.093	+	62.5997i	0.866481	+	0.108680i
$577$			455.976i			0.790253i	0.918627	+	0.395126i	$0.129299\pi$
$577$			455.976i			0.790253i	−0.918627	+	0.395126i	$0.870701\pi$
$578$	41.7215	−	72.2638i	0.0721826	−	0.125024i
$579$	−47.9740	−	96.5353i	−0.0828566	−	0.166728i
$580$	488.127	−	281.820i	0.841598	−	0.485897i
$581$	−272.893	+	157.555i	−0.469695	+	0.271178i
$582$	11.5655	+	23.2726i	0.0198720	+	0.0399873i
$583$	538.040	+	310.637i	0.922881	+	0.532826i
$584$		−	125.793i		−	0.215399i
$585$	−525.792	+	340.263i	−0.898790	+	0.581645i
$586$	−11.1181			−0.0189728
$587$	382.389	−	662.318i	0.651430	−	1.12831i	−0.331346	−	0.943509i	$-0.607503\pi$
$587$	382.389	−	662.318i	0.651430	−	1.12831i	0.982776	−	0.184801i	$-0.0591639\pi$
$588$	−398.485	−	264.498i	−0.677696	−	0.449826i
$589$	−430.935	−	746.401i	−0.731638	−	1.26723i
$590$	−82.8480	−	143.497i	−0.140420	−	0.243215i
$591$	5.97392	−	95.6304i	0.0101082	−	0.161811i
$592$	−228.725	−	132.054i	−0.386360	−	0.223065i
$593$	34.0539			0.0574265			0.0287133	−	0.999588i	$-0.490859\pi$
$593$	34.0539			0.0574265			0.0287133	+	0.999588i	$0.490859\pi$
$594$	115.280	−	40.3169i	0.194074	−	0.0678736i
$595$	−107.535			−0.180731
$596$	−206.661	+	357.948i	−0.346747	+	0.600584i
$597$	−11.8036	+	188.952i	−0.0197715	+	0.316502i
$598$	108.221	−	19.1948i	0.180972	−	0.0320983i
$599$	−584.137	+	337.251i	−0.975186	+	0.563024i	−0.900813	−	0.434206i	$-0.857029\pi$
$599$	−584.137	+	337.251i	−0.975186	+	0.563024i	−0.0743729	+	0.997230i	$0.523696\pi$
$600$	−21.1955	−	14.0687i	−0.0353259	−	0.0234479i
$601$	−192.274	+	333.029i	−0.319924	+	0.554124i	−0.980472	−	0.196660i	$-0.936991\pi$
$601$	−192.274	+	333.029i	−0.319924	+	0.554124i	0.660548	+	0.750784i	$0.270324\pi$
$602$		−	62.0488i		−	0.103071i
$603$	643.556	−	271.199i	1.06726	−	0.449749i
$604$			712.335i			1.17936i
$605$	−312.713	+	541.635i	−0.516881	+	0.895264i
$606$	32.5791	+	65.5570i	0.0537609	+	0.108180i
$607$	567.487	+	982.915i	0.934904	+	1.61930i	0.774806	+	0.632200i	$0.217848\pi$
$607$	567.487	+	982.915i	0.934904	+	1.61930i	0.160098	+	0.987101i	$0.448819\pi$
$608$	394.881	−	227.984i	0.649475	−	0.374974i
$609$	−684.643	+	340.239i	−1.12421	+	0.558685i
$610$	8.33220	−	14.4318i	0.0136594	−	0.0236587i
$611$	88.2645	+	32.0249i	0.144459	+	0.0524140i
$612$	−68.8417	+	29.0104i	−0.112487	+	0.0474026i
$613$		−	201.546i		−	0.328787i	−0.986395	−	0.164394i	$-0.947433\pi$
$613$		−	201.546i		−	0.328787i	0.986395	−	0.164394i	$-0.0525667\pi$
$614$	−143.521	−	82.8617i	−0.233747	−	0.134954i
$615$	−759.213	−	503.934i	−1.23449	−	0.819404i
$616$	−293.661	+	169.545i	−0.476722	+	0.275236i
$617$	153.384	+	265.670i	0.248597	+	0.430583i	0.963137	−	0.269012i	$-0.0866972\pi$
$617$	153.384	+	265.670i	0.248597	+	0.430583i	−0.714540	+	0.699595i	$0.753364\pi$
$618$	9.21630	−	147.535i	0.0149131	−	0.238729i
$619$	−785.415	−	453.460i	−1.26885	−	0.732568i	−0.294076	−	0.955782i	$-0.595012\pi$
$619$	−785.415	−	453.460i	−1.26885	−	0.732568i	−0.974769	+	0.223214i	$0.928345\pi$
$620$		−	541.616i		−	0.873575i
$621$	−256.940	−	734.678i	−0.413752	−	1.18306i
$622$		−	151.886i		−	0.244190i
$623$	606.230	+	350.007i	0.973082	+	0.561809i
$624$	233.039	−	535.523i	0.373459	−	0.858209i
$625$	351.493	+	608.805i	0.562390	+	0.974087i
$626$	40.6807	+	70.4610i	0.0649851	+	0.112557i
$627$	−853.023	+	1285.14i	−1.36048	+	2.04967i
$628$	−161.810	+	280.264i	−0.257660	+	0.446280i
$629$	37.4024			0.0594632
$630$	106.685	+	80.8292i	0.169342	+	0.128300i
$631$		−	975.757i		−	1.54637i	−0.634183	−	0.773183i	$-0.718663\pi$
$631$		−	975.757i		−	1.54637i	0.634183	−	0.773183i	$-0.281337\pi$
$632$	71.9239	−	124.576i	0.113804	−	0.197114i
$633$	−138.806	+	68.9808i	−0.219283	+	0.108974i
$634$	44.7860	+	77.5716i	0.0706403	+	0.122353i
$635$	42.7532	+	74.0507i	0.0673278	+	0.116615i
$636$	210.511	+	423.598i	0.330992	+	0.666035i
$637$	−405.294	+	340.779i	−0.636254	+	0.534975i
$638$			121.686i			0.190731i
$639$	596.624	+	74.8328i	0.933684	+	0.117109i
$640$	380.582			0.594660
$641$	−639.637	−	369.295i	−0.997874	−	0.576123i	−0.0902554	−	0.995919i	$-0.528768\pi$
$641$	−639.637	−	369.295i	−0.997874	−	0.576123i	−0.907619	+	0.419796i	$0.862102\pi$
$642$	61.0556	−	91.9846i	0.0951021	−	0.143278i
$643$	10.2718	−	5.93041i	0.0159748	−	0.00922303i	−0.491991	−	0.870600i	$-0.663731\pi$
$643$	10.2718	−	5.93041i	0.0159748	−	0.00922303i	0.507966	+	0.861377i	$0.330398\pi$
$644$	534.384	+	925.580i	0.829789	+	1.43724i
$645$	22.3605	−	357.946i	0.0346674	−	0.554955i
$646$	−10.3685	+	17.9588i	−0.0160503	+	0.0278000i
$647$		−	752.487i		−	1.16304i	−0.813532	−	0.581520i	$-0.802458\pi$
$647$		−	752.487i		−	1.16304i	0.813532	−	0.581520i	$-0.197542\pi$
$648$	182.187	+	46.4329i	0.281153	+	0.0716558i
$649$	−1627.65			−2.50794
$650$	−10.6617	+	8.96455i	−0.0164026	+	0.0137916i
$651$	−45.8035	+	733.223i	−0.0703587	+	1.12630i
$652$	365.512	−	211.028i	0.560601	−	0.323663i
$653$	−201.227	+	116.178i	−0.308157	+	0.177915i	−0.646102	−	0.763251i	$-0.723602\pi$
$653$	−201.227	+	116.178i	−0.308157	+	0.177915i	0.337944	+	0.941166i	$0.390268\pi$
$654$	1.42908	−	2.15301i	0.00218513	−	0.00329206i
$655$	110.883	+	64.0186i	0.169288	+	0.0977383i
$656$	849.754			1.29536
$657$	−60.7019	+	483.962i	−0.0923926	+	0.736624i
$658$		−	20.0667i		−	0.0304966i
$659$	974.227	+	562.470i	1.47834	+	0.853521i	0.999700	−	0.0244892i	$-0.00779593\pi$
$659$	974.227	+	562.470i	1.47834	+	0.853521i	0.478642	+	0.878010i	$0.341129\pi$
$660$	−868.043	+	431.381i	−1.31522	+	0.653608i
$661$	228.295	−	131.806i	0.345378	−	0.199404i	−0.317270	−	0.948335i	$-0.602766\pi$
$661$	228.295	−	131.806i	0.345378	−	0.199404i	0.662648	+	0.748931i	$0.269433\pi$
$662$	−97.7471	+	56.4343i	−0.147654	+	0.0852482i
$663$	9.33879	+	82.1798i	0.0140857	+	0.123951i
$664$	−38.6061	+	66.8676i	−0.0581416	+	0.100704i
$665$	−1690.51			−2.54212
$666$	−37.1068	−	28.1137i	−0.0557160	−	0.0422128i
$667$	775.508			1.16268
$668$	−137.440	+	238.053i	−0.205748	+	0.356367i
$669$	−186.227	+	280.564i	−0.278366	+	0.419379i
$670$	105.502	−	60.9118i	0.157466	−	0.0909132i
$671$	−81.8482	−	141.765i	−0.121980	−	0.211275i
$672$	−387.909	−	24.2322i	−0.577245	−	0.0360598i
$673$	−270.310	+	468.190i	−0.401649	+	0.695677i	−0.993925	−	0.110059i	$-0.964896\pi$
$673$	−270.310	+	468.190i	−0.401649	+	0.695677i	0.592276	+	0.805735i	$0.298230\pi$
$674$	−18.7172			−0.0277703
$675$	74.7563	+	64.3543i	0.110750	+	0.0953397i
$676$	−507.566	−	424.158i	−0.750837	−	0.627452i
$677$	404.458	+	233.514i	0.597428	+	0.344925i	0.768029	−	0.640415i	$-0.221238\pi$
$677$	404.458	+	233.514i	0.597428	+	0.344925i	−0.170601	+	0.985340i	$0.554571\pi$
$678$	−153.316	−	9.57746i	−0.226130	−	0.0141260i
$679$	139.892	+	242.300i	0.206026	+	0.356848i
$680$	−22.8194	+	13.1748i	−0.0335580	+	0.0193747i
$681$	357.341	+	237.188i	0.524730	+	0.348294i
$682$	101.266	+	58.4658i	0.148483	+	0.0857269i
$683$	−456.734			−0.668717			−0.334359	−	0.942446i	$-0.608520\pi$
$683$	−456.734			−0.668717			−0.334359	+	0.942446i	$0.608520\pi$
$684$	−1082.23	+	456.060i	−1.58221	+	0.666755i
$685$	458.271			0.669008
$686$	−19.8924	−	11.4849i	−0.0289976	−	0.0167418i
$687$	106.706	+	214.718i	0.155321	+	0.312544i
$688$	167.223	+	289.638i	0.243056	+	0.420986i
$689$	515.656	−	91.4600i	0.748411	−	0.132743i
$690$	−60.4221	−	121.584i	−0.0875682	−	0.176208i
$691$	980.035	+	565.824i	1.41829	+	0.818847i	0.996148	−	0.0876845i	$-0.0279467\pi$
$691$	980.035	+	565.824i	1.41829	+	0.818847i	0.422137	+	0.906532i	$0.361280\pi$
$692$		−	604.581i		−	0.873672i
$693$	1211.61	−	510.581i	1.74836	−	0.736769i
$694$			162.983i			0.234846i
$695$	207.953	−	360.185i	0.299213	−	0.518253i
$696$	−103.600	+	156.080i	−0.148850	+	0.224253i
$697$	−104.217	+	60.1699i	−0.149523	+	0.0863270i
$698$	−36.3581	+	20.9914i	−0.0520890	+	0.0300736i
$699$	−165.993	−	10.3694i	−0.237471	−	0.0148346i
$700$	−117.305	−	67.7260i	−0.167578	−	0.0967514i
$701$			110.878i			0.158171i	0.996868	+	0.0790855i	$0.0252000\pi$
$701$			110.878i			0.158171i	−0.996868	+	0.0790855i	$0.974800\pi$
$702$	52.5059	−	88.5500i	0.0747947	−	0.126140i
$703$	587.987			0.836397
$704$	430.963	−	746.450i	0.612163	−	1.06030i
$705$	7.23143	−	115.761i	0.0102573	−	0.164200i
$706$	−33.7536	−	58.4630i	−0.0478097	−	0.0828088i
$707$	394.063	+	682.537i	0.557374	+	0.965399i
$708$	−1032.50	−	685.333i	−1.45834	−	0.967985i
$709$	23.1239	+	13.3506i	0.0326148	+	0.0188302i	0.516219	−	0.856457i	$-0.327339\pi$
$709$	23.1239	+	13.3506i	0.0326148	+	0.0188302i	−0.483604	+	0.875287i	$0.660672\pi$
$710$	104.891			0.147734
$711$	−336.826	+	444.571i	−0.473735	+	0.625276i
$712$	171.527			0.240908
$713$	372.603	−	645.367i	0.522584	−	0.905142i
$714$	15.8292	−	7.86646i	0.0221698	−	0.0110175i
$715$	187.421	+	1056.69i	0.262127	+	1.47789i
$716$	−554.042	+	319.876i	−0.773802	+	0.446755i
$717$	1043.99	−	518.821i	1.45606	−	0.723600i
$718$	26.7940	−	46.4086i	0.0373175	−	0.0646359i
$719$		−	236.651i		−	0.329139i	−0.986365	−	0.164570i	$-0.947376\pi$
$719$		−	236.651i		−	0.329139i	0.986365	−	0.164570i	$-0.0526235\pi$
$720$	−715.833	−	89.7848i	−0.994212	−	0.124701i
$721$		−	1591.43i		−	2.20726i
$722$	−110.060	+	190.629i	−0.152437	+	0.264029i
$723$	151.547	−	228.316i	0.209608	−	0.315789i
$724$	−261.639	−	453.172i	−0.361380	−	0.625928i
$725$	−85.1175	+	49.1426i	−0.117403	+	0.0677829i
$726$	6.40960	−	102.605i	0.00882865	−	0.141329i
$727$	390.231	−	675.900i	0.536769	−	0.929711i	−0.462306	−	0.886720i	$-0.652978\pi$
$727$	390.231	−	675.900i	0.536769	−	0.929711i	0.999075	−	0.0429910i	$-0.0136887\pi$
$728$	−97.4910	+	268.697i	−0.133916	+	0.369089i
$729$	−678.520	−	266.556i	−0.930754	−	0.365646i
$730$			85.0845i			0.116554i
$731$	−41.0178	−	23.6816i	−0.0561118	−	0.0323962i
$732$	7.77060	−	124.392i	0.0106156	−	0.169934i
$733$	−627.004	+	362.001i	−0.855394	+	0.493862i	−0.862467	−	0.506113i	$-0.831082\pi$
$733$	−627.004	+	362.001i	−0.855394	+	0.493862i	0.00707285	+	0.999975i	$0.497749\pi$
$734$	−24.1372	−	41.8068i	−0.0328844	−	0.0569575i
$735$	544.981	+	361.736i	0.741471	+	0.492158i
$736$	341.429	+	197.124i	0.463898	+	0.267832i
$737$		−	1196.69i		−	1.62373i
$738$	148.621	+	18.6411i	0.201383	+	0.0252589i
$739$			557.712i			0.754685i	0.926074	+	0.377342i	$0.123162\pi$
$739$			557.712i			0.754685i	−0.926074	+	0.377342i	$0.876838\pi$
$740$	319.999	+	184.752i	0.432432	+	0.249665i
$741$	146.811	+	1291.92i	0.198126	+	1.74348i
$742$	−55.9618	−	96.9286i	−0.0754202	−	0.130632i
$743$	−148.675	−	257.513i	−0.200101	−	0.346586i	0.748459	−	0.663181i	$-0.230794\pi$
$743$	−148.675	−	257.513i	−0.200101	−	0.346586i	−0.948561	+	0.316595i	$0.897461\pi$
$744$	80.1121	+	161.205i	0.107678	+	0.216673i
$745$	282.637	−	489.541i	0.379378	−	0.657102i
$746$	−141.950			−0.190282
$747$	180.795	−	238.629i	0.242029	−	0.319450i
$748$			128.011i			0.171138i
$749$	594.295	−	1029.35i	0.793452	−	1.37430i
$750$	−83.7674	−	55.6013i	−0.111690	−	0.0741351i
$751$	−189.152	−	327.620i	−0.251866	−	0.436245i	0.712173	−	0.702004i	$-0.247711\pi$
$751$	−189.152	−	327.620i	−0.251866	−	0.436245i	−0.964040	+	0.265758i	$0.914378\pi$
$752$	54.0802	+	93.6697i	0.0719152	+	0.124561i
$753$	630.091	+	39.3610i	0.836774	+	0.0522723i
$754$	66.0134	+	78.5109i	0.0875510	+	0.104126i
$755$		−	974.212i		−	1.29035i
$756$	983.570	+	186.268i	1.30102	+	0.246387i
$757$	521.787			0.689282			0.344641	−	0.938735i	$-0.388001\pi$
$757$	521.787			0.689282			0.344641	+	0.938735i	$0.388001\pi$
$758$	18.2067	+	10.5116i	0.0240194	+	0.0138676i
$759$	−1331.09	−	83.1515i	−1.75374	−	0.109554i
$760$	−358.735	+	207.115i	−0.472019	+	0.272520i
$761$	−489.973	−	848.658i	−0.643854	−	1.11519i	−0.984565	−	0.175020i	$-0.944001\pi$
$761$	−489.973	−	848.658i	−0.643854	−	1.11519i	0.340711	−	0.940168i	$-0.389332\pi$
$762$	−11.7103	−	7.77281i	−0.0153679	−	0.0102005i
$763$	13.9102	−	24.0931i	0.0182309	−	0.0315768i
$764$		−	643.413i		−	0.842163i
$765$	94.1502	−	39.6755i	0.123072	−	0.0518635i
$766$	11.9398			0.0155872
$767$	−1050.15	+	882.982i	−1.36916	+	1.15122i
$768$	544.573	−	270.630i	0.709080	−	0.352383i
$769$	−1032.58	+	596.163i	−1.34276	+	0.775245i	−0.987212	−	0.159412i	$-0.949040\pi$
$769$	−1032.58	+	596.163i	−1.34276	+	0.775245i	−0.355551	+	0.934657i	$0.615707\pi$
$770$	198.627	−	114.678i	0.257958	−	0.148932i
$771$	494.250	+	994.551i

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	117.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.146647 - 0.254001i) q^{2} +(-0.187042 + 2.99416i) q^{3} +(1.95699 + 3.38960i) q^{4} +(-2.67644 - 4.63573i) q^{5} +(0.733091 + 0.486595i) q^{6} +(8.20362 + 4.73636i) q^{7} +2.32113 q^{8} +(-8.93003 - 1.12007i) q^{9} -1.56997 q^{10} +(-7.71102 + 13.3559i) q^{11} +(-10.5151 + 5.22555i) q^{12} +(2.27033 + 12.8002i) q^{13} +(2.40608 - 1.38915i) q^{14} +(14.3807 - 7.14663i) q^{15} +(-7.48757 + 12.9688i) q^{16} -2.12074i q^{17} +(-1.59406 + 2.10398i) q^{18} -33.3392i q^{19} +(10.4755 - 18.1442i) q^{20} +(-15.7159 + 23.6771i) q^{21} +(2.26160 + 3.91721i) q^{22} +(24.9644 - 14.4132i) q^{23} +(-0.434148 + 6.94984i) q^{24} +(-1.82668 + 3.16390i) q^{25} +(3.58420 + 1.30045i) q^{26} +(5.02395 - 26.5285i) q^{27} +37.0760i q^{28} +(23.2984 + 13.4514i) q^{29} +(0.293650 - 4.70075i) q^{30} +(22.3881 - 12.9257i) q^{31} +(6.83832 + 11.8443i) q^{32} +(-38.5474 - 25.5861i) q^{33} +(-0.538669 - 0.311001i) q^{34} -50.7064i q^{35} +(-13.6794 - 32.4612i) q^{36} +17.6365i q^{37} +(-8.46819 - 4.88911i) q^{38} +(-38.7506 + 4.40356i) q^{39} +(-6.21236 - 10.7601i) q^{40} +(-28.3722 - 49.1420i) q^{41} +(3.70930 + 7.46402i) q^{42} +(11.1667 - 19.3413i) q^{43} -60.3615 q^{44} +(18.7084 + 44.3950i) q^{45} -8.45463i q^{46} +(3.61133 - 6.25502i) q^{47} +(-37.4304 - 24.8447i) q^{48} +(20.3662 + 35.2753i) q^{49} +(0.535755 + 0.927955i) q^{50} +(6.34983 + 0.396666i) q^{51} +(-38.9447 + 32.7454i) q^{52} -40.2849i q^{53} +(-6.00150 - 5.16642i) q^{54} +82.5523 q^{55} +(19.0416 + 10.9937i) q^{56} +(99.8231 + 6.23583i) q^{57} +(6.83331 - 3.94521i) q^{58} +(52.7704 + 91.4009i) q^{59} +(52.3672 + 34.7592i) q^{60} +(-5.30723 + 9.19239i) q^{61} -7.58211i q^{62} +(-67.9535 - 51.4845i) q^{63} -55.8893 q^{64} +(53.2620 - 44.7837i) q^{65} +(-12.1518 + 6.03892i) q^{66} +(-67.2001 + 38.7980i) q^{67} +(7.18846 - 4.15026i) q^{68} +(38.4861 + 77.4433i) q^{69} +(-12.8795 - 7.43596i) q^{70} -66.8110 q^{71} +(-20.7277 - 2.59982i) q^{72} -54.1949i q^{73} +(4.47968 + 2.58635i) q^{74} +(-9.13157 - 6.06116i) q^{75} +(113.007 - 65.2445i) q^{76} +(-126.516 + 73.0443i) q^{77} +(-4.56417 + 10.4884i) q^{78} +(30.9866 - 53.6704i) q^{79} +80.1602 q^{80} +(78.4909 + 20.0045i) q^{81} -16.6428 q^{82} +(-16.6325 + 28.8082i) q^{83} +(-111.012 - 6.93476i) q^{84} +(-9.83117 + 5.67603i) q^{85} +(-3.27513 - 5.67269i) q^{86} +(-44.6333 + 67.2433i) q^{87} +(-17.8983 + 31.0007i) q^{88} +73.8979 q^{89} +(14.0199 + 1.75847i) q^{90} +(-42.0015 + 115.761i) q^{91} +(97.7100 + 56.4129i) q^{92} +(34.5143 + 69.4512i) q^{93} +(-1.05919 - 1.83456i) q^{94} +(-154.552 + 89.2305i) q^{95} +(-36.7429 + 18.2597i) q^{96} +(25.5787 + 14.7678i) q^{97} +11.9466 q^{98} +(83.8191 - 110.631i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 4 q^{3} - 50 q^{4} + 4 q^{9} + 8 q^{10} - 38 q^{12} - 6 q^{13} - 6 q^{14} - 90 q^{16} + 14 q^{22} + 138 q^{23} - 92 q^{25} - 76 q^{27} + 48 q^{29} + 186 q^{30} - 154 q^{36} + 324 q^{38} - 2 q^{39}+ \cdots + 504 q^{95}+O(q^{100}) \) 52 * q - 4 * q^3 - 50 * q^4 + 4 * q^9 + 8 * q^10 - 38 * q^12 - 6 * q^13 - 6 * q^14 - 90 * q^16 + 14 * q^22 + 138 * q^23 - 92 * q^25 - 76 * q^27 + 48 * q^29 + 186 * q^30 - 154 * q^36 + 324 * q^38 - 2 * q^39 - 68 * q^40 - 216 * q^42 + 62 * q^43 + 230 * q^48 + 70 * q^49 + 90 * q^51 - 4 * q^52 + 92 * q^55 - 276 * q^56 + 12 * q^61 + 12 * q^64 - 588 * q^65 + 762 * q^66 - 144 * q^68 - 414 * q^69 + 342 * q^74 - 620 * q^75 - 510 * q^77 - 162 * q^78 - 24 * q^79 + 532 * q^81 - 292 * q^82 - 330 * q^87 - 62 * q^88 + 258 * q^90 + 264 * q^91 - 396 * q^92 - 160 * q^94 + 504 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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