LMFDB - Embedded newform 117.3.n.a.38.13

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			38.13
Character	$\chi$	$=$	117.38
Dual form			117.3.n.a.77.13

$q$-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} +(9.95015 + 8.36627i) 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} +(-26.9111 + 28.2275i) 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} +(-8.88602 + 50.0998i) 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} +(-12.1528 + 68.5181i) 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} +(-3.22338 - 10.9749i) 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	−0.900356	−	0.435154i	$-0.856694\pi$
$2$	−0.146647	+	0.254001i	−0.0733237	+	0.127000i	0.827032	+	0.562154i	$0.190027\pi$
$3$	−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	$0.0131304\pi$
$5$	2.67644	+	4.63573i	0.535288	+	0.927147i	−0.463861	+	0.885908i	$0.653536\pi$
$6$	−0.733091	−	0.486595i	−0.122182	−	0.0810992i
$7$	−8.20362	−	4.73636i	−1.17195	−	0.676623i	−0.217808	−	0.975992i	$-0.569891\pi$
$7$	−8.20362	−	4.73636i	−1.17195	−	0.676623i	−0.954138	+	0.299369i	$0.903224\pi$
$8$	−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	$-0.586070\pi$
$11$	7.71102	−	13.3559i	0.701001	−	1.21417i	0.968115	−	0.250505i	$-0.0805967\pi$
$12$	−10.5151	+	5.22555i	−0.876256	+	0.435462i
$13$	9.95015	+	8.36627i	0.765396	+	0.643559i
$13$	9.95015	+	8.36627i	0.765396	+	0.643559i
$14$	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	$0.340690\pi$
$19$			33.3392i			1.75470i	−0.479854	+	0.877348i	$0.659310\pi$
$20$	−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	−0.815560	−	0.578672i	$-0.803571\pi$
$31$	−22.3881	+	12.9257i	−0.722195	+	0.416960i	0.0933648	+	0.995632i	$0.470238\pi$
$32$	−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	$-0.923400\pi$
$37$		−	17.6365i		−	0.476662i	0.971184	−	0.238331i	$-0.0766003\pi$
$38$	−8.46819	−	4.88911i	−0.222847	−	0.128661i
$39$	−26.9111	+	28.2275i	−0.690028	+	0.723783i
$40$	−6.21236	−	10.7601i	−0.155309	−	0.269003i
$41$	28.3722	+	49.1420i	0.692004	+	1.19859i	0.971180	+	0.238346i	$0.0766052\pi$
$41$	28.3722	+	49.1420i	0.692004	+	1.19859i	−0.279177	+	0.960240i	$0.590061\pi$
$42$	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	−0.901884	−	0.431979i	$-0.857815\pi$
$47$	−3.61133	+	6.25502i	−0.0768369	+	0.133085i	0.825047	+	0.565065i	$0.191149\pi$
$48$	−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
$52$	−8.88602	+	50.0998i	−0.170885	+	0.963457i
$53$		−	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	$-0.814260\pi$
$59$	−52.7704	−	91.4009i	−0.894413	−	1.54917i	−0.0598833	−	0.998205i	$-0.519073\pi$
$60$	−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
$65$	−12.1528	+	68.5181i	−0.186966	+	1.05412i
$66$	−12.1518	+	6.03892i	−0.184118	+	0.0914988i
$67$	67.2001	−	38.7980i	1.00299	−	0.579075i	0.0938563	−	0.995586i	$-0.470081\pi$
$67$	67.2001	−	38.7980i	1.00299	−	0.579075i	0.909131	+	0.416511i	$0.136747\pi$
$68$	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	$-0.344074\pi$
$71$	66.8110			0.941000			0.470500	+	0.882400i	$0.344074\pi$
$72$	20.7277	+	2.59982i	0.287885	+	0.0361086i
$73$			54.1949i			0.742396i	0.928554	+	0.371198i	$0.121053\pi$
$73$			54.1949i			0.742396i	−0.928554	+	0.371198i	$0.878947\pi$
$74$	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
$78$	−3.22338	−	10.9749i	−0.0413253	−	0.140704i
$79$	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	−0.748263	−	0.663402i	$-0.769112\pi$
$83$	16.6325	−	28.8082i	0.200391	−	0.347087i	0.948654	+	0.316314i	$0.102445\pi$
$84$	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	$-0.636273\pi$
$89$	−73.8979			−0.830314			−0.415157	+	0.909750i	$0.636273\pi$
$90$	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	0.362323	−	0.932053i	$-0.381984\pi$
$97$	−25.5787	−	14.7678i	−0.263698	−	0.152246i	−0.626020	+	0.779807i	$0.715317\pi$
$98$	−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	$-0.470228\pi$
$104$	−23.0956	−	19.4192i	−0.222073	−	0.186723i
$105$	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	$0.00428839\pi$
$109$			2.93689i			0.0269439i	−0.999909	+	0.0134720i	$0.995712\pi$
$110$	−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
$117$	−79.4844	−	85.8559i	−0.679354	−	0.733811i
$118$	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
$130$	−15.6215	−	13.1348i	−0.120165	−	0.101037i
$131$	−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	−0.666440	−	0.745558i	$-0.732183\pi$
$137$	42.8060	−	74.1421i	0.312452	−	0.541183i	0.978893	+	0.204375i	$0.0655162\pi$
$138$	−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	0.632641	−	0.774445i	$-0.281971\pi$
$149$	−52.8009	−	91.4538i	−0.354368	−	0.613784i	−0.987010	+	0.160661i	$0.948637\pi$
$150$	2.87866	−	1.43057i	0.0191911	−	0.00953715i
$151$	−157.615	−	90.9988i	−1.04381	−	0.602641i	−0.122897	−	0.992419i	$-0.539218\pi$
$151$	−157.615	−	90.9988i	−1.04381	−	0.602641i	−0.920909	+	0.389778i	$0.872552\pi$
$152$		−	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
$156$	−148.345	−	35.9769i	−0.950929	−	0.230621i
$157$	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	$0.107311\pi$
$163$			107.833i			0.661553i	−0.943709	+	0.330777i	$0.892689\pi$
$164$	−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	0.741529	−	0.670921i	$-0.234101\pi$
$167$	−35.1152	−	60.8212i	−0.210270	−	0.364199i	−0.951799	+	0.306722i	$0.900768\pi$
$168$	−36.4785	+	54.9575i	−0.217134	+	0.327128i
$169$	29.0110	+	166.491i	0.171663	+	0.985156i
$170$			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	$0.620410\pi$
$182$	35.5628	+	6.30765i	0.195400	+	0.0346574i
$183$	−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	−0.417210	−	0.908810i	$-0.636992\pi$
$193$	31.1188	−	17.9665i	0.161237	−	0.0930904i	0.578448	+	0.815720i	$0.303659\pi$
$194$	7.50209	−	4.33133i	0.0386706	−	0.0223265i
$195$	−202.881	−	49.2032i	−1.04042	−	0.252324i
$196$	−79.7130	+	138.067i	−0.406699	+	0.704423i
$197$	31.9390			0.162127			0.0810633	−	0.996709i	$-0.474168\pi$
$197$	31.9390			0.162127			0.0810633	+	0.996709i	$0.474168\pi$
$198$	−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
$221$	17.7427	−	21.1017i	0.0802836	−	0.0954826i
$222$	−8.58183	+	12.9291i	−0.0386569	+	0.0582394i
$223$	−97.2097	−	56.1241i	−0.435918	−	0.251677i	0.265947	−	0.963988i	$-0.414316\pi$
$223$	−97.2097	−	56.1241i	−0.435918	−	0.251677i	−0.701865	+	0.712310i	$0.747649\pi$
$224$			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	−0.979416	−	0.201850i	$-0.935305\pi$
$227$	−71.4825	+	123.811i	−0.314901	+	0.545424i	0.664516	+	0.747274i	$0.268638\pi$
$228$	−174.216	−	350.564i	−0.764104	−	1.53756i
$229$	−69.2157	+	39.9617i	−0.302252	+	0.174505i	−0.643454	−	0.765485i	$-0.722499\pi$
$229$	−69.2157	+	39.9617i	−0.302252	+	0.174505i	0.341202	+	0.939990i	$0.389166\pi$
$230$	−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	$0.962042\pi$
$234$	33.4636	−	7.59854i	0.143007	−	0.0324724i
$235$	−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	$0.135486\pi$
$239$	194.301	+	336.539i	0.812974	+	1.40811i	−0.0978002	+	0.995206i	$0.531181\pi$
$240$	14.9933	−	240.013i	0.0624721	−	1.00005i
$241$	79.1067	+	45.6723i	0.328244	+	0.189512i	0.655061	−	0.755576i	$-0.272643\pi$
$241$	79.1067	+	45.6723i	0.328244	+	0.189512i	−0.326817	+	0.945087i	$0.605976\pi$
$242$	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
$247$	−278.925	+	331.730i	−1.12925	+	1.34304i
$248$	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	$-0.940456\pi$
$271$		−	100.797i		−	0.371945i	0.982555	−	0.185973i	$-0.0595435\pi$
$272$	27.5035	+	15.8792i	0.101116	+	0.0583793i
$273$	354.464	−	104.107i	1.29840	−	0.381346i
$274$	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	−0.757883	−	0.652391i	$-0.773766\pi$
$281$	52.2789	−	90.5497i	0.186046	−	0.322241i	0.943928	+	0.330150i	$0.107099\pi$
$282$	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
$286$	−10.2692	+	57.8980i	−0.0359061	+	0.202440i
$287$		−	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	0.896556	−	0.442931i	$-0.146061\pi$
$293$	18.9537	+	32.8288i	0.0646885	+	0.112044i	−0.831867	+	0.554975i	$0.812728\pi$
$294$	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
$299$	368.984	+	65.4454i	1.23406	+	0.218881i
$300$	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	$0.372024\pi$
$307$			565.040i			1.84052i	−0.391305	+	0.920261i	$0.627976\pi$
$308$	−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	$0.0201998\pi$
$312$	62.4641	−	65.5197i	0.200205	−	0.209999i
$313$	−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	−0.518077	−	0.855334i	$-0.673352\pi$
$317$	152.700	−	264.483i	0.481702	−	0.834332i	0.999779	+	0.0210013i	$0.00668542\pi$
$318$	−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	0.910273	−	0.414009i	$-0.135872\pi$
$331$	333.273	+	192.415i	1.00687	+	0.581314i	0.0965936	+	0.995324i	$0.469205\pi$
$332$	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	$0.863517\pi$
$338$	−46.5433	−	17.0467i	−0.137702	−	0.0504340i
$339$	−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	0.666973	−	0.745082i	$-0.267590\pi$
$349$	123.965	+	71.5710i	0.355199	+	0.205074i	−0.311774	+	0.950156i	$0.600923\pi$
$350$			10.1501i			0.0290003i
$351$	271.934	−	221.931i	0.774739	−	0.632281i
$352$	−210.922			−0.599209
$353$	−115.084	+	199.332i	−0.326018	+	0.564680i	−0.981718	−	0.190342i	$-0.939040\pi$
$353$	−115.084	+	199.332i	−0.326018	+	0.564680i	0.655700	+	0.755022i	$0.272374\pi$
$354$	−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	$-0.581901\pi$
$359$	−182.710			−0.508943			−0.254471	+	0.967080i	$0.581901\pi$
$360$	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
$364$	310.188	−	368.912i	0.852165	−	1.01349i
$365$	−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	$-0.969854\pi$
$379$		−	71.6797i		−	0.189128i	0.995519	−	0.0945642i	$-0.0301458\pi$
$380$	−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	0.838229	−	0.545318i	$-0.183591\pi$
$383$	−20.3546	−	35.2552i	−0.0531452	−	0.0920502i	−0.891374	+	0.453268i	$0.850258\pi$
$384$	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	$0.634979\pi$
$390$	42.2497	−	44.3165i	0.108332	−	0.113632i
$391$	−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	$-0.676585\pi$
$397$		−	674.923i		−	1.70006i	0.526737	−	0.850029i	$-0.323415\pi$
$398$	−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	0.787418	−	0.616419i	$-0.211417\pi$
$401$	−56.1904	−	97.3247i	−0.140126	−	0.242705i	−0.927544	+	0.373714i	$0.878084\pi$
$402$	−68.1427	−	4.25679i	−0.169509	−	0.0105890i
$403$	−330.905	−	58.6914i	−0.821104	−	0.145636i
$404$			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	−0.854797	−	0.518962i	$-0.826319\pi$
$409$	−340.599	+	196.645i	−0.832762	+	0.480795i	0.0220357	+	0.999757i	$0.492985\pi$
$410$	−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
$416$	31.0505	−	175.064i	0.0746406	−	0.420827i
$417$	−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	0.968235	−	0.250044i	$-0.0804450\pi$
$421$	520.275	+	300.381i	1.23581	+	0.713494i	0.267573	+	0.963538i	$0.413778\pi$
$422$	−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
$429$	169.492	+	577.084i	0.395085	+	1.34518i
$430$	−17.5314	+	30.3653i	−0.0407707	+	0.0706169i
$431$	−530.893			−1.23177			−0.615885	−	0.787836i	$-0.711201\pi$
$431$	−530.893			−1.23177			−0.615885	+	0.787836i	$0.711201\pi$
$432$	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	$-0.718421\pi$
$449$	−568.967			−1.26719			−0.633594	+	0.773666i	$0.718421\pi$
$450$	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
$455$	424.223	−	504.536i	0.932359	−	1.10887i
$456$	231.702	+	14.4742i	0.508119	+	0.0317416i
$457$	345.318	+	199.370i	0.755620	+	0.436257i	0.827721	−	0.561140i	$-0.189637\pi$
$457$	345.318	+	199.370i	0.755620	+	0.436257i	−0.0721010	+	0.997397i	$0.522970\pi$
$458$		−	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	$-0.617993\pi$
$461$	288.621	−	499.906i	0.626076	−	1.08440i	0.988332	−	0.152317i	$-0.0486733\pi$
$462$	128.291	+	8.01418i	0.277686	+	0.0173467i
$463$	456.842	−	263.758i	0.986700	−	0.569671i	0.0824134	−	0.996598i	$-0.473737\pi$
$463$	456.842	−	263.758i	0.986700	−	0.569671i	0.904286	+	0.426927i	$0.140404\pi$
$464$	−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	$-0.0910648\pi$
$468$	135.468	−	437.440i	0.289461	−	0.934700i
$469$	−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	−0.737358	−	0.675503i	$-0.763927\pi$
$479$	103.619	−	179.473i	0.216324	−	0.374683i	0.953681	+	0.300819i	$0.0972600\pi$
$480$	182.987	+	121.459i	0.381223	+	0.253040i
$481$	147.552	−	175.486i	0.306760	−	0.364835i
$482$	−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	$0.0881911\pi$
$487$			266.418i			0.547059i	−0.961864	+	0.273529i	$0.911809\pi$
$488$	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	−0.993827	−	0.110943i	$-0.964613\pi$
$499$	−695.936	+	401.799i	−1.39466	+	0.805208i	−0.400834	+	0.916151i	$0.631279\pi$
$500$	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
$507$	−503.929	+	55.7228i	−0.993942	+	0.109907i
$508$	−31.2607	−	54.1451i	−0.0615368	−	0.106585i
$509$	−138.478	−	239.850i	−0.272058	−	0.471218i	0.697331	−	0.716750i	$-0.254371\pi$
$509$	−138.478	−	239.850i	−0.272058	−	0.471218i	−0.969389	+	0.245531i	$0.921038\pi$
$510$	−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
$520$	28.2082	−	159.039i	0.0542466	−	0.305845i
$521$		−	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
$533$	−128.828	+	726.340i	−0.241704	+	1.36274i
$534$	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	$-0.735225\pi$
$541$		−	799.766i		−	1.47831i	0.673535	−	0.739155i	$-0.264775\pi$
$542$	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
$546$	−25.5379	+	105.301i	−0.0467727	+	0.192859i
$547$	−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	$-0.547075\pi$
$557$	−164.150			−0.294704			−0.147352	+	0.989084i	$0.547075\pi$
$558$	−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	$0.731391\pi$
$572$	600.606	+	505.001i	1.05001	+	0.882868i
$573$	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	$-0.870701\pi$
$577$		−	455.976i		−	0.790253i	0.918627	−	0.395126i	$-0.129299\pi$
$578$	−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
$585$	185.270	−	598.257i	0.316700	−	1.02266i
$586$	−11.1181			−0.0189728
$587$	−382.389	+	662.318i	−0.651430	+	1.12831i	0.331346	+	0.943509i	$0.392497\pi$
$587$	−382.389	+	662.318i	−0.651430	+	1.12831i	−0.982776	+	0.184801i	$0.940836\pi$
$588$	−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	$-0.509141\pi$
$593$	−34.0539			−0.0574265			−0.0287133	+	0.999588i	$0.509141\pi$
$594$	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
$598$	−70.7337	+	84.1248i	−0.118284	+	0.140677i
$599$	−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	$0.0525667\pi$
$613$			201.546i			0.328787i	−0.986395	+	0.164394i	$0.947433\pi$
$614$	−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	0.714540	−	0.699595i	$-0.246636\pi$
$617$	−153.384	−	265.670i	−0.248597	−	0.430583i	−0.963137	+	0.269012i	$0.913303\pi$
$618$	−9.21630	+	147.535i	−0.0149131	+	0.238729i
$619$	785.415	+	453.460i	1.26885	+	0.732568i	0.974769	−	0.223214i	$-0.0716549\pi$
$619$	785.415	+	453.460i	1.26885	+	0.732568i	0.294076	+	0.955782i	$0.404988\pi$
$620$		−	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
$624$	−164.580	−	560.361i	−0.263750	−	0.898015i
$625$	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	$0.281337\pi$
$631$			975.757i			1.54637i	−0.634183	+	0.773183i	$0.718663\pi$
$632$	−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
$637$	−92.4761	+	521.384i	−0.145174	+	0.818500i
$638$			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	−0.507966	−	0.861377i	$-0.669602\pi$
$643$	−10.2718	+	5.93041i	−0.0159748	+	0.00922303i	0.491991	+	0.870600i	$0.336269\pi$
$644$	−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
$650$	2.43268	−	13.7156i	0.00374259	−	0.0211009i
$651$	−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	−0.662648	−	0.748931i	$-0.730567\pi$
$661$	−228.295	+	131.806i	−0.345378	+	0.199404i	0.317270	+	0.948335i	$0.397234\pi$
$662$	−97.7471	+	56.4343i	−0.147654	+	0.0852482i
$663$	59.8632	+	57.0713i	0.0902914	+	0.0860804i
$664$	−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	$-0.391480\pi$
$683$	456.734			0.668717			0.334359	+	0.942446i	$0.391480\pi$
$684$	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
$689$	337.034	−	400.841i	0.489165	−	0.581772i
$690$	−60.4221	−	121.584i	−0.0875682	−	0.176208i
$691$	−980.035	−	565.824i	−1.41829	−	0.818847i	−0.422137	−	0.906532i	$-0.638720\pi$
$691$	−980.035	−	565.824i	−1.41829	−	0.818847i	−0.996148	+	0.0876845i	$0.972053\pi$
$692$		−	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	$0.974800\pi$
$702$	16.4922	+	101.617i	0.0234931	+	0.144753i
$703$	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	0.483604	−	0.875287i	$-0.339328\pi$
$709$	−23.1239	−	13.3506i	−0.0326148	−	0.0188302i	−0.516219	+	0.856457i	$0.672661\pi$
$710$	−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
$715$	821.408	+	690.655i	1.14882	+	0.965951i
$716$	−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	−0.00707285	−	0.999975i	$-0.502251\pi$
$733$	627.004	−	362.001i	0.855394	−	0.493862i	0.862467	+	0.506113i	$0.168918\pi$
$734$	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	$-0.876838\pi$
$739$		−	557.712i		−	0.754685i	0.926074	−	0.377342i	$-0.123162\pi$
$740$	319.999	+	184.752i	0.432432	+	0.249665i
$741$	−941.085	−	897.195i	−1.27002	−	1.21079i
$742$	−55.9618	−	96.9286i	−0.0754202	−	0.130632i
$743$	148.675	+	257.513i	0.200101	+	0.346586i	0.948561	−	0.316595i	$-0.102539\pi$
$743$	148.675	+	257.513i	0.200101	+	0.346586i	−0.748459	+	0.663181i	$0.769206\pi$
$744$	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
$754$	−100.999	−	17.9139i	−0.133951	−	0.0237584i
$755$		−	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	$0.0559990\pi$
$761$	489.973	+	848.658i	0.643854	+	1.11519i	−0.340711	+	0.940168i	$0.610668\pi$
$762$	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
$767$	239.612	−	1350.94i	0.312402	−	1.76134i
$768$	544.573	−	270.630i	0.709080	−	0.352383i
$769$	1032.58	−	596.163i	1.34276	−	0.775245i	0.355551	−	0.934657i	$-0.384293\pi$
$769$	1032.58	−	596.163i	1.34276	−	0.775245i	0.987212	+	0.159412i	$0.0509598\pi$
$770$	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} +(9.95015 + 8.36627i) 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} +(-26.9111 + 28.2275i) 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} +(-8.88602 + 50.0998i) 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} +(-12.1528 + 68.5181i) 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} +(-3.22338 - 10.9749i) 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

Properties

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