LMFDB - Embedded newform 117.3.n.a.77.13

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			77.13
Character	$\chi$	$=$	117.77
Dual form			117.3.n.a.38.13

$q$-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 $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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	$-0.190027\pi$
$2$	−0.146647	−	0.254001i	−0.0733237	−	0.127000i	−0.900356	+	0.435154i	$0.856694\pi$
$3$	−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	−0.463861	−	0.885908i	$-0.653536\pi$
$5$	2.67644	−	4.63573i	0.535288	−	0.927147i	0.999149	−	0.0412386i	$-0.0131304\pi$
$6$	−0.733091	+	0.486595i	−0.122182	+	0.0810992i
$7$	−8.20362	+	4.73636i	−1.17195	+	0.676623i	−0.954138	−	0.299369i	$-0.903224\pi$
$7$	−8.20362	+	4.73636i	−1.17195	+	0.676623i	−0.217808	+	0.975992i	$0.569891\pi$
$8$	−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	0.968115	+	0.250505i	$0.0805967\pi$
$11$	7.71102	+	13.3559i	0.701001	+	1.21417i	−0.267114	+	0.963665i	$0.586070\pi$
$12$	−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	$0.0198674\pi$
$17$			2.12074i			0.124749i	−0.998053	+	0.0623746i	$0.980133\pi$
$18$	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	0.932350	−	0.361557i	$-0.117755\pi$
$23$	24.9644	+	14.4132i	1.08541	+	0.626660i	0.153058	+	0.988217i	$0.451088\pi$
$24$	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	−0.0412625	−	0.999148i	$-0.513138\pi$
$29$	23.2984	−	13.4514i	0.803394	−	0.463840i	0.844657	+	0.535309i	$0.179805\pi$
$30$	0.293650	+	4.70075i	0.00978835	+	0.156692i
$31$	−22.3881	−	12.9257i	−0.722195	−	0.416960i	0.0933648	−	0.995632i	$-0.470238\pi$
$31$	−22.3881	−	12.9257i	−0.722195	−	0.416960i	−0.815560	+	0.578672i	$0.803571\pi$
$32$	−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
$39$	−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	−0.279177	−	0.960240i	$-0.590061\pi$
$41$	28.3722	−	49.1420i	0.692004	−	1.19859i	0.971180	−	0.238346i	$-0.0766052\pi$
$42$	3.70930	−	7.46402i	0.0883168	−	0.177715i
$43$	11.1667	+	19.3413i	0.259690	+	0.449797i	0.966159	−	0.257947i	$-0.0830462\pi$
$43$	11.1667	+	19.3413i	0.259690	+	0.449797i	−0.706469	+	0.707744i	$0.749713\pi$
$44$	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	$-0.191149\pi$
$47$	−3.61133	−	6.25502i	−0.0768369	−	0.133085i	−0.901884	+	0.431979i	$0.857815\pi$
$48$	−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	$0.124092\pi$
$53$			40.2849i			0.760092i	−0.924968	+	0.380046i	$0.875908\pi$
$54$	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	−0.0598833	+	0.998205i	$0.519073\pi$
$59$	−52.7704	+	91.4009i	−0.894413	+	1.54917i	−0.834530	+	0.550963i	$0.814260\pi$
$60$	−52.3672	+	34.7592i	−0.872787	+	0.579320i
$61$	−5.30723	−	9.19239i	−0.0870038	−	0.150695i	0.819240	−	0.573451i	$-0.194396\pi$
$61$	−5.30723	−	9.19239i	−0.0870038	−	0.150695i	−0.906243	+	0.422757i	$0.861063\pi$
$62$			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	0.909131	−	0.416511i	$-0.136747\pi$
$67$	67.2001	+	38.7980i	1.00299	+	0.579075i	0.0938563	+	0.995586i	$0.470081\pi$
$68$	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	$-0.878947\pi$
$73$		−	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
$78$	−3.22338	+	10.9749i	−0.0413253	+	0.140704i
$79$	30.9866	+	53.6704i	0.392235	+	0.679372i	0.992744	−	0.120247i	$-0.0383685\pi$
$79$	30.9866	+	53.6704i	0.392235	+	0.679372i	−0.600509	+	0.799618i	$0.705035\pi$
$80$	−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	$-0.102445\pi$
$83$	16.6325	+	28.8082i	0.200391	+	0.347087i	−0.748263	+	0.663402i	$0.769112\pi$
$84$	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	−0.626020	−	0.779807i	$-0.715317\pi$
$97$	−25.5787	+	14.7678i	−0.263698	+	0.152246i	0.362323	+	0.932053i	$0.381984\pi$
$98$	−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	−0.0989216	−	0.995095i	$-0.531539\pi$
$101$	72.0529	−	41.5998i	0.713395	−	0.411879i	0.812317	+	0.583216i	$0.198206\pi$
$102$	−1.03194	−	1.55469i	−0.0101171	−	0.0152421i
$103$	−84.0009	+	145.494i	−0.815542	+	1.41256i	0.0933953	+	0.995629i	$0.470228\pi$
$103$	−84.0009	+	145.494i	−0.815542	+	1.41256i	−0.908938	+	0.416932i	$0.863105\pi$
$104$	−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	$0.199429\pi$
$107$			125.475i			1.17266i	−0.810071	+	0.586332i	$0.800571\pi$
$108$	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	−0.351499	−	0.936188i	$-0.614328\pi$
$113$	−151.195	−	87.2926i	−1.33801	−	0.772501i	−0.986512	+	0.163687i	$0.947661\pi$
$114$	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	0.418848	−	0.908056i	$-0.362434\pi$
$131$	−20.7147	−	11.9596i	−0.158128	−	0.0912950i	−0.576976	+	0.816761i	$0.695767\pi$
$132$	−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	$-0.0655162\pi$
$137$	42.8060	+	74.1421i	0.312452	+	0.541183i	−0.666440	+	0.745558i	$0.732183\pi$
$138$	−25.3145	+	1.58137i	−0.183439	+	0.0114592i
$139$	38.8488	−	67.2881i	0.279488	−	0.484087i	−0.691770	−	0.722118i	$-0.743169\pi$
$139$	38.8488	−	67.2881i	0.279488	−	0.484087i	0.971258	+	0.238031i	$0.0765020\pi$
$140$	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	$-0.948637\pi$
$149$	−52.8009	+	91.4538i	−0.354368	+	0.613784i	0.632641	+	0.774445i	$0.281971\pi$
$150$	2.87866	+	1.43057i	0.0191911	+	0.00953715i
$151$	−157.615	+	90.9988i	−1.04381	+	0.602641i	−0.920909	−	0.389778i	$-0.872552\pi$
$151$	−157.615	+	90.9988i	−1.04381	+	0.602641i	−0.122897	+	0.992419i	$0.539218\pi$
$152$			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	−0.703800	−	0.710398i	$-0.748515\pi$
$157$	41.3417	−	71.6058i	0.263323	−	0.456088i	0.967123	+	0.254310i	$0.0818483\pi$
$158$	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	$-0.900768\pi$
$167$	−35.1152	+	60.8212i	−0.210270	+	0.364199i	0.741529	+	0.670921i	$0.234101\pi$
$168$	−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	−0.834033	−	0.551714i	$-0.813974\pi$
$173$	−133.772	+	77.2336i	−0.773251	+	0.446437i	0.0607819	+	0.998151i	$0.480641\pi$
$174$	−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	$-0.849077\pi$
$179$		−	163.453i		−	0.913147i	0.889686	−	0.456573i	$-0.150923\pi$
$180$	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	−0.824016	−	0.566566i	$-0.808272\pi$
$191$	−142.365	+	82.1942i	−0.745364	+	0.430336i	0.0786522	+	0.996902i	$0.474938\pi$
$192$	10.4536	+	167.342i	0.0544460	+	0.871571i
$193$	31.1188	+	17.9665i	0.161237	+	0.0930904i	0.578448	−	0.815720i	$-0.303659\pi$
$193$	31.1188	+	17.9665i	0.161237	+	0.0930904i	−0.417210	+	0.908810i	$0.636992\pi$
$194$	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	−0.798293	−	0.602269i	$-0.794263\pi$
$211$	25.8336	−	44.7451i	0.122434	−	0.212062i	0.920727	+	0.390207i	$0.127597\pi$
$212$	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	−0.701865	−	0.712310i	$-0.747649\pi$
$223$	−97.2097	+	56.1241i	−0.435918	+	0.251677i	0.265947	+	0.963988i	$0.414316\pi$
$224$		−	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	$-0.268638\pi$
$227$	−71.4825	−	123.811i	−0.314901	−	0.545424i	−0.979416	+	0.201850i	$0.935305\pi$
$228$	−174.216	+	350.564i	−0.764104	+	1.53756i
$229$	−69.2157	−	39.9617i	−0.302252	−	0.174505i	0.341202	−	0.939990i	$-0.389166\pi$
$229$	−69.2157	−	39.9617i	−0.302252	−	0.174505i	−0.643454	+	0.765485i	$0.722499\pi$
$230$	−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	$-0.962042\pi$
$233$		−	55.4387i		−	0.237934i	0.992898	−	0.118967i	$-0.0379583\pi$
$234$	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	−0.0978002	−	0.995206i	$-0.531181\pi$
$239$	194.301	−	336.539i	0.812974	−	1.40811i	0.910774	−	0.412906i	$-0.135486\pi$
$240$	14.9933	+	240.013i	0.0624721	+	1.00005i
$241$	79.1067	−	45.6723i	0.328244	−	0.189512i	−0.326817	−	0.945087i	$-0.605976\pi$
$241$	79.1067	−	45.6723i	0.328244	−	0.189512i	0.655061	+	0.755576i	$0.272643\pi$
$242$	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	$0.137690\pi$
$251$			210.440i			0.838405i	−0.907893	+	0.419203i	$0.862310\pi$
$252$	−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	0.970605	−	0.240679i	$-0.0773702\pi$
$257$	320.600	+	185.099i	1.24747	+	0.720229i	0.276868	+	0.960908i	$0.410704\pi$
$258$	−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	−0.539894	+	0.841733i	$0.681536\pi$
$263$	−404.705	+	233.657i	−1.53880	+	0.888429i	−0.998909	+	0.0466956i	$0.985131\pi$
$264$	−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	$0.00716638\pi$
$269$			12.1114i			0.0450239i	−0.999747	+	0.0225119i	$0.992834\pi$
$270$	−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
$273$	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	0.872366	−	0.488854i	$-0.162585\pi$
$277$	3.55206	+	6.15235i	0.0128233	+	0.0222106i	−0.859543	+	0.511064i	$0.829251\pi$
$278$	−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	$-0.107099\pi$
$281$	52.2789	+	90.5497i	0.186046	+	0.322241i	−0.757883	+	0.652391i	$0.773766\pi$
$282$	5.69109	+	2.82824i	0.0201812	+	0.0100292i
$283$	29.0002	−	50.2298i	0.102474	−	0.177491i	−0.810229	−	0.586113i	$-0.800657\pi$
$283$	29.0002	−	50.2298i	0.102474	−	0.177491i	0.912703	+	0.408623i	$0.133991\pi$
$284$	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	−0.831867	−	0.554975i	$-0.812728\pi$
$293$	18.9537	−	32.8288i	0.0646885	−	0.112044i	0.896556	+	0.442931i	$0.146061\pi$
$294$	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	$-0.627976\pi$
$307$		−	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	0.997987	−	0.0634169i	$-0.0201998\pi$
$311$	448.481	+	258.930i	1.44206	+	0.832574i	0.444073	+	0.895991i	$0.353533\pi$
$312$	62.4641	+	65.5197i	0.200205	+	0.209999i
$313$	−138.702	−	240.239i	−0.443138	−	0.767538i	0.554782	−	0.831996i	$-0.312802\pi$
$313$	−138.702	−	240.239i	−0.443138	−	0.767538i	−0.997920	+	0.0644575i	$0.979468\pi$
$314$	−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	$-0.00668542\pi$
$317$	152.700	+	264.483i	0.481702	+	0.834332i	−0.518077	+	0.855334i	$0.673352\pi$
$318$	−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	$-0.469205\pi$
$331$	333.273	−	192.415i	1.00687	−	0.581314i	0.910273	+	0.414009i	$0.135872\pi$
$332$	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	−0.909477	−	0.415755i	$-0.863517\pi$
$337$	−31.9085	+	55.2672i	−0.0946841	+	0.163998i	0.814793	+	0.579752i	$0.196851\pi$
$338$	−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	−0.393920	−	0.919145i	$-0.628881\pi$
$347$	−481.248	−	277.849i	−1.38688	−	0.800717i	−0.992963	+	0.118427i	$0.962215\pi$
$348$	−315.275	+	19.6949i	−0.905963	+	0.0565944i
$349$	123.965	−	71.5710i	0.355199	−	0.205074i	−0.311774	−	0.950156i	$-0.600923\pi$
$349$	123.965	−	71.5710i	0.355199	−	0.205074i	0.666973	+	0.745082i	$0.267590\pi$
$350$		−	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	0.655700	−	0.755022i	$-0.272374\pi$
$353$	−115.084	−	199.332i	−0.326018	−	0.564680i	−0.981718	+	0.190342i	$0.939040\pi$
$354$	−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	0.956092	−	0.293068i	$-0.0946762\pi$
$367$	82.2966	+	142.542i	0.224242	+	0.388398i	−0.731850	+	0.681466i	$0.761343\pi$
$368$		−	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	0.334644	+	0.942345i	$0.391384\pi$
$373$	−241.992	+	419.143i	−0.648772	+	1.12371i	−0.983416	+	0.181362i	$0.941949\pi$
$374$	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	$-0.850258\pi$
$383$	−20.3546	+	35.2552i	−0.0531452	+	0.0920502i	0.838229	+	0.545318i	$0.183591\pi$
$384$	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	−0.411454	−	0.911430i	$-0.634979\pi$
$389$	66.9628	−	38.6610i	0.172141	−	0.0993855i	0.583595	+	0.812045i	$0.301646\pi$
$390$	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	$0.323415\pi$
$397$			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	$-0.878084\pi$
$401$	−56.1904	+	97.3247i	−0.140126	+	0.242705i	0.787418	+	0.616419i	$0.211417\pi$
$402$	−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	0.0220357	−	0.999757i	$-0.492985\pi$
$409$	−340.599	−	196.645i	−0.832762	−	0.480795i	−0.854797	+	0.518962i	$0.826319\pi$
$410$	−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	−0.148381	−	0.988930i	$-0.547406\pi$
$419$	−452.106	−	261.023i	−1.07901	−	0.622967i	−0.930629	+	0.365963i	$0.880740\pi$
$420$	264.969	−	533.181i	0.630878	−	1.26948i
$421$	520.275	−	300.381i	1.23581	−	0.713494i	0.267573	−	0.963538i	$-0.413778\pi$
$421$	520.275	−	300.381i	1.23581	−	0.713494i	0.968235	+	0.250044i	$0.0804450\pi$
$422$	−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	−0.974959	−	0.222385i	$-0.928616\pi$
$439$	−298.551	−	517.105i	−0.680070	−	1.17792i	0.294889	−	0.955532i	$-0.404717\pi$
$440$	−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	−0.105703	−	0.994398i	$-0.533709\pi$
$443$	311.260	−	179.706i	0.702620	−	0.405658i	0.808322	+	0.588740i	$0.200376\pi$
$444$	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	−0.0721010	−	0.997397i	$-0.522970\pi$
$457$	345.318	−	199.370i	0.755620	−	0.436257i	0.827721	+	0.561140i	$0.189637\pi$
$458$			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	0.988332	+	0.152317i	$0.0486733\pi$
$461$	288.621	+	499.906i	0.626076	+	1.08440i	−0.362256	+	0.932079i	$0.617993\pi$
$462$	128.291	−	8.01418i	0.277686	−	0.0173467i
$463$	456.842	+	263.758i	0.986700	+	0.569671i	0.904286	−	0.426927i	$-0.140404\pi$
$463$	456.842	+	263.758i	0.986700	+	0.569671i	0.0824134	+	0.996598i	$0.473737\pi$
$464$	−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	$0.0910648\pi$
$467$			263.576i			0.564404i	−0.959355	+	0.282202i	$0.908935\pi$
$468$	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	0.953681	−	0.300819i	$-0.0972600\pi$
$479$	103.619	+	179.473i	0.216324	+	0.374683i	−0.737358	+	0.675503i	$0.763927\pi$
$480$	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	$-0.911809\pi$
$487$		−	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	0.755021	−	0.655701i	$-0.227627\pi$
$491$	277.257	+	160.074i	0.564678	+	0.326017i	−0.190343	+	0.981718i	$0.560960\pi$
$492$	−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	$-0.631279\pi$
$499$	−695.936	−	401.799i	−1.39466	−	0.805208i	−0.993827	+	0.110943i	$0.964613\pi$
$500$	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	$0.183427\pi$
$503$			548.156i			1.08977i	−0.838510	+	0.544887i	$0.816573\pi$
$504$	−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	−0.969389	−	0.245531i	$-0.921038\pi$
$509$	−138.478	+	239.850i	−0.272058	+	0.471218i	0.697331	+	0.716750i	$0.254371\pi$
$510$	−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	$0.129432\pi$
$521$			412.120i			0.791018i	−0.918462	+	0.395509i	$0.870568\pi$
$522$	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	$0.264775\pi$
$541$			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
$546$	−25.5379	−	105.301i	−0.0467727	−	0.192859i
$547$	−505.787	−	876.049i	−0.924657	−	1.60155i	−0.792112	−	0.610376i	$-0.791018\pi$
$547$	−505.787	−	876.049i	−0.924657	−	1.60155i	−0.132545	−	0.991177i	$-0.542315\pi$
$548$	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	0.700848	−	0.713311i	$-0.252805\pi$
$563$	244.075	+	140.917i	0.433526	+	0.250297i	−0.267321	+	0.963607i	$0.586139\pi$
$564$	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	0.369825	−	0.929102i	$-0.379418\pi$
$569$	773.477	−	446.567i	1.35936	−	0.784828i	0.989538	+	0.144273i	$0.0460845\pi$
$570$	156.720	−	9.79008i	0.274947	−	0.0171756i
$571$	179.759	−	311.352i	0.314814	−	0.545274i	−0.664584	−	0.747214i	$-0.731391\pi$
$571$	179.759	−	311.352i	0.314814	−	0.545274i	0.979398	+	0.201939i	$0.0647244\pi$
$572$	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	$0.129299\pi$
$577$			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
$585$	185.270	+	598.257i	0.316700	+	1.02266i
$586$	−11.1181			−0.0189728
$587$	−382.389	−	662.318i	−0.651430	−	1.12831i	−0.982776	−	0.184801i	$-0.940836\pi$
$587$	−382.389	−	662.318i	−0.651430	−	1.12831i	0.331346	−	0.943509i	$-0.392497\pi$
$588$	−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	−0.0743729	−	0.997230i	$-0.523696\pi$
$599$	−584.137	−	337.251i	−0.975186	−	0.563024i	−0.900813	+	0.434206i	$0.857029\pi$
$600$	21.1955	−	14.0687i	0.0353259	−	0.0234479i
$601$	−192.274	−	333.029i	−0.319924	−	0.554124i	0.660548	−	0.750784i	$-0.270324\pi$
$601$	−192.274	−	333.029i	−0.319924	−	0.554124i	−0.980472	+	0.196660i	$0.936991\pi$
$602$			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	0.160098	−	0.987101i	$-0.448819\pi$
$607$	567.487	−	982.915i	0.934904	−	1.61930i	0.774806	−	0.632200i	$-0.217848\pi$
$608$	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	$-0.913303\pi$
$617$	−153.384	+	265.670i	−0.248597	+	0.430583i	0.714540	+	0.699595i	$0.246636\pi$
$618$	−9.21630	−	147.535i	−0.0149131	−	0.238729i
$619$	785.415	−	453.460i	1.26885	−	0.732568i	0.294076	−	0.955782i	$-0.404988\pi$
$619$	785.415	−	453.460i	1.26885	−	0.732568i	0.974769	+	0.223214i	$0.0716549\pi$
$620$			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	$-0.718663\pi$
$631$		−	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
$637$	−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	−0.907619	−	0.419796i	$-0.862102\pi$
$641$	−639.637	+	369.295i	−0.997874	+	0.576123i	−0.0902554	+	0.995919i	$0.528768\pi$
$642$	−61.0556	−	91.9846i	−0.0951021	−	0.143278i
$643$	−10.2718	−	5.93041i	−0.0159748	−	0.00922303i	0.491991	−	0.870600i	$-0.336269\pi$
$643$	−10.2718	−	5.93041i	−0.0159748	−	0.00922303i	−0.507966	+	0.861377i	$0.669602\pi$
$644$	−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	$0.197542\pi$
$647$			752.487i			1.16304i	−0.813532	+	0.581520i	$0.802458\pi$
$648$	−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	0.337944	−	0.941166i	$-0.390268\pi$
$653$	−201.227	−	116.178i	−0.308157	−	0.177915i	−0.646102	+	0.763251i	$0.723602\pi$
$654$	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	0.478642	−	0.878010i	$-0.341129\pi$
$659$	974.227	−	562.470i	1.47834	−	0.853521i	0.999700	+	0.0244892i	$0.00779593\pi$
$660$	−868.043	−	431.381i	−1.31522	−	0.653608i
$661$	−228.295	−	131.806i	−0.345378	−	0.199404i	0.317270	−	0.948335i	$-0.397234\pi$
$661$	−228.295	−	131.806i	−0.345378	−	0.199404i	−0.662648	+	0.748931i	$0.730567\pi$
$662$	−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	0.592276	−	0.805735i	$-0.298230\pi$
$673$	−270.310	−	468.190i	−0.401649	−	0.695677i	−0.993925	+	0.110059i	$0.964896\pi$
$674$	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	−0.170601	−	0.985340i	$-0.554571\pi$
$677$	404.458	−	233.514i	0.597428	−	0.344925i	0.768029	+	0.640415i	$0.221238\pi$
$678$	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	−0.996148	−	0.0876845i	$-0.972053\pi$
$691$	−980.035	+	565.824i	−1.41829	+	0.818847i	−0.422137	+	0.906532i	$0.638720\pi$
$692$			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	$-0.974800\pi$
$701$		−	110.878i		−	0.158171i	0.996868	−	0.0790855i	$-0.0252000\pi$
$702$	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	−0.516219	−	0.856457i	$-0.672661\pi$
$709$	−23.1239	+	13.3506i	−0.0326148	+	0.0188302i	0.483604	+	0.875287i	$0.339328\pi$
$710$	−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	$0.0526235\pi$
$719$			236.651i			0.329139i	−0.986365	+	0.164570i	$0.947376\pi$
$720$	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	0.999075	+	0.0429910i	$0.0136887\pi$
$727$	390.231	+	675.900i	0.536769	+	0.929711i	−0.462306	+	0.886720i	$0.652978\pi$
$728$	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	$-0.168918\pi$
$733$	627.004	+	362.001i	0.855394	+	0.493862i	−0.00707285	+	0.999975i	$0.502251\pi$
$734$	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
$741$	−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	−0.748459	−	0.663181i	$-0.769206\pi$
$743$	148.675	−	257.513i	0.200101	−	0.346586i	0.948561	+	0.316595i	$0.102539\pi$
$744$	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	−0.964040	−	0.265758i	$-0.914378\pi$
$751$	−189.152	+	327.620i	−0.251866	+	0.436245i	0.712173	+	0.702004i	$0.247711\pi$
$752$	−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	−0.340711	−	0.940168i	$-0.610668\pi$
$761$	489.973	−	848.658i	0.643854	−	1.11519i	0.984565	−	0.175020i	$-0.0559990\pi$
$762$	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	0.987212	−	0.159412i	$-0.0509598\pi$
$769$	1032.58	+	596.163i	1.34276	+	0.775245i	0.355551	+	0.934657i	$0.384293\pi$
$770$	198.627	+	114.678i	0.257958	+	0.148932i
$771$	494.250	−	994.551i	0.641051	−	1.28995i
$772$	121.798	−	70.3203i	0.157770	−	0.0910885i
$773$	−948.513			−1.22705			−0.613527	−	0.789674i	$-0.710250\pi$
$773$	−948.513			−1.22705			−0.613527	+	0.789674i	$0.710250\pi$
$774$	−22.8932	+	54.3257i	−0.0295778	+	0.0701882i
$775$			94.4448i			0.121864i
$776$	59.3714	−	34.2781i	0.0765095	−	0.0441728i
$777$	−417.581	+	277.173i	−0.537427	+	0.356722i
$778$	−19.6398	−	11.3391i	−0.0252440	−	0.0145746i
$779$	−1638.36	−	945.906i	−2.10315	−	1.21426i
$780$	−230.257	+	783.977i	−0.295201	+	1.00510i
$781$	515.181	+	892.319i	0.659642	+	1.14253i
$782$	17.9300			0.0229284
$783$	473.894	+	550.493i	0.605229	+	0.703056i
$784$	−609.974			−0.778028
$785$	−221.297	−	383.298i	−0.281907	−	0.488277i
$786$	21.0053	−	1.31217i	0.0267242	−	0.00166943i
$787$	−915.970	−	528.836i	−1.16388	−	0.671964i	−0.211646	−	0.977346i	$-0.567882\pi$
$787$	−915.970	−	528.836i	−1.16388	−	0.671964i	−0.952230	+	0.305382i	$0.901216\pi$
$788$	62.5042	−	108.260i	0.0793200	−	0.137386i
$789$	775.303	+	1168.05i	0.982640	+	1.48042i
$790$	−48.6481	−	84.2610i	−0.0615799	−	0.106659i
$791$	1653.80			2.09077
$792$	194.555	+	256.790i	0.245650	+	0.324230i
$793$	−129.714	−	47.0639i	−0.163573	−	0.0593492i
$794$	171.431	−	98.9756i	0.215908	−	0.124654i
$795$	287.901	−	579.327i	0.362140	−	0.728713i
$796$	123.499	−	213.907i	0.155150	−	0.268727i
$797$	105.979	+	61.1867i	0.132972	+	0.0767713i	0.565010	−	0.825084i	$-0.308872\pi$
$797$	105.979	+	61.1867i	0.132972	+	0.0767713i	−0.432038	+	0.901855i	$0.642206\pi$
$798$	−248.845	−	123.665i	−0.311836	−	0.154969i
$799$	13.2652	−	7.65869i	0.0166023	−	0.00958535i
$800$	49.9657			0.0624571
$801$	659.911	−	82.7706i	0.823858	−	0.103334i
$802$	32.9607			0.0410981
$803$	723.820	−	417.898i	0.901395	−	0.520420i
$804$	−503.873	−	759.121i	−0.626708	−	0.944181i
$805$	−730.841	+	1265.85i	−0.907876	+	1.57249i
$806$	63.4340	+	75.4431i	0.0787022	+	0.0936019i
$807$	36.2636	−	2.26534i	0.0449363	−	0.00280712i
$808$	−167.244	+	96.5584i	−0.206985	+	0.119503i
$809$		−	529.452i		−	0.654453i	−0.944946	−	0.327226i	$-0.893886\pi$
$809$		−	529.452i		−	0.654453i	0.944946	−	0.327226i	$-0.106114\pi$
$810$	−123.229	+	31.4065i	−0.152134	+	0.0387734i
$811$			1178.67i			1.45336i	0.686977	+	0.726679i	$0.258937\pi$
$811$			1178.67i			1.45336i	−0.686977	+	0.726679i	$0.741063\pi$
$812$	498.723	+	863.813i	0.614191	+	1.06381i
$813$	301.803	−	18.8533i	0.371221	−	0.0231897i
$814$	69.0858	+	39.8867i	0.0848720	+	0.0490009i
$815$	−499.886	−	288.609i	−0.613357	−	0.354122i
$816$	−52.6891	−	79.3800i	−0.0645700	−	0.0972794i
$817$	644.823	−	372.289i	0.789257	−	0.455678i
$818$			115.350i			0.141015i
$819$	245.415	−	1080.80i	0.299652	−	1.31965i
$820$	−1188.85			−1.44982
$821$	627.687	+	1087.18i	0.764539	+	1.32422i	0.940490	+	0.339821i	$0.110367\pi$
$821$	627.687	+	1087.18i	0.764539	+	1.32422i	−0.175951	+	0.984399i	$0.556300\pi$
$822$	−67.4578	−	33.5237i	−0.0820655	−	0.0407831i
$823$	−192.191	+	332.885i	−0.233525	+	0.404477i	−0.958843	−	0.283937i	$-0.908359\pi$
$823$	−192.191	+	332.885i	−0.233525	+	0.404477i	0.725318	+	0.688414i	$0.241693\pi$
$824$	194.977	−	337.710i	0.236622	−	0.409842i
$825$	−151.366	−	75.2224i	−0.183474	−	0.0911787i
$826$	−253.939	+	146.612i	−0.307432	+	0.177496i
$827$	−1043.15			−1.26137			−0.630686	−	0.776038i	$-0.717226\pi$
$827$	−1043.15			−1.26137			−0.630686	+	0.776038i	$0.717226\pi$
$828$	−809.367	+	613.211i	−0.977497	+	0.740593i
$829$	215.798			0.260312			0.130156	−	0.991494i	$-0.458452\pi$
$829$	215.798			0.260312			0.130156	+	0.991494i	$0.458452\pi$
$830$	−26.1125	−	45.2282i	−0.0314608	−	0.0544918i
$831$	17.7567	−	11.7862i	0.0213679	−	0.0141831i
$832$	−556.107	+	467.585i	−0.668397	+	0.562001i
$833$	74.8097	+	43.1914i	0.0898076	+	0.0518504i
$834$	4.26237	+	68.2319i	0.00511075	+	0.0818129i
$835$	187.967	+	325.569i	0.225111	+	0.389903i
$836$		−	2012.41i		−	2.40718i
$837$	230.424	−	658.859i	0.275297	−	0.787168i
$838$			153.114i			0.182713i
$839$	147.757	+	255.923i	0.176111	+	0.305033i	0.940545	−	0.339669i	$-0.110315\pi$
$839$	147.757	+	255.923i	0.176111	+	0.305033i	−0.764434	+	0.644702i	$0.776982\pi$
$840$	−352.401	+	22.0141i	−0.419525	+	0.0262072i
$841$	−58.6222	+	101.537i	−0.0697053	+	0.120733i
$842$	−152.594	−	88.1002i	−0.181228	−	0.104632i
$843$	261.342	−	173.468i	0.310015	−	0.205775i
$844$	−101.112	−	175.131i	−0.119801	−	0.207502i
$845$	−694.163	−	580.092i	−0.821495	−	0.686499i
$846$	7.40373	−	17.5691i	0.00875145	−	0.0207672i
$847$		−	1106.78i		−	1.30671i
$848$	522.449	−	301.636i	0.616095	−	0.355703i
$849$	−155.821	−	77.4363i	−0.183534	−	0.0912088i
$850$	−1.96795	−	1.13620i	−0.00231523	−	0.00133670i
$851$	−254.198	+	440.284i	−0.298705	+	0.517373i
$852$	−702.522	−	349.124i	−0.824557	−	0.409770i
$853$	668.394	−	385.898i	0.783580	−	0.452400i	−0.0541172	−	0.998535i	$-0.517234\pi$
$853$	668.394	−	385.898i	0.783580	−	0.452400i	0.837698	+	0.546134i	$0.183901\pi$
$854$		−	29.4901i		−	0.0345318i
$855$	1480.10	+	623.723i	1.73111	+	0.729500i
$856$		−	291.244i		−	0.340238i
$857$	−406.517	+	234.703i	−0.474349	+	0.273866i	−0.718059	−	0.695983i	$-0.754969\pi$
$857$	−406.517	+	234.703i	−0.474349	+	0.273866i	0.243709	+	0.969848i	$0.421636\pi$
$858$	−171.435	+	41.5769i	−0.199808	+	0.0484579i
$859$	−667.222	+	1155.66i	−0.776743	+	1.34536i	0.157067	+	0.987588i	$0.449796\pi$
$859$	−667.222	+	1155.66i	−0.776743	+	1.34536i	−0.933810	+	0.357770i	$0.883537\pi$
$860$	233.954	−	405.220i	0.272040	−	0.471186i
$861$	1609.43	−	100.539i	1.86926	−	0.116770i
$862$	77.8540	+	134.847i	0.0903179	+	0.156435i
$863$	−919.885			−1.06592			−0.532958	−	0.846142i	$-0.678920\pi$
$863$	−919.885			−1.06592			−0.532958	+	0.846142i	$0.678920\pi$
$864$	−348.567	−	121.905i	−0.403434	−	0.141094i
$865$			826.845i			0.955890i
$866$	17.3363	+	30.0274i	0.0200189	+	0.0346737i
$867$	−53.2138	−	851.847i	−0.0613770	−	0.982522i
$868$	479.235	−	830.060i	0.552115	−	0.956290i
$869$	−477.876	+	827.706i	−0.549915	+	0.952481i
$870$	70.0731	+	105.570i	0.0805438	+	0.121345i
$871$	993.246	−	176.168i	1.14035	−	0.202260i
$872$			6.81690i			0.00781754i
$873$	211.877	−	160.527i	0.242700	−	0.183880i
$874$	−281.871			−0.322507
$875$	−937.395	+	541.205i	−1.07131	+	0.618520i
$876$	−283.198	+	569.863i	−0.323285	+	0.650529i
$877$	959.895	+	554.196i	1.09452	+	0.631922i	0.934777	−	0.355236i	$-0.115599\pi$
$877$	959.895	+	554.196i	1.09452	+	0.631922i	0.159745	+	0.987158i	$0.448933\pi$
$878$	−87.5634	+	151.664i	−0.0997305	+	0.172738i
$879$	−101.840	−	50.6102i	−0.115859	−	0.0575770i
$880$	−618.116	−	1070.61i	−0.702405	−	1.21660i
$881$		−	489.236i		−	0.555319i	−0.960680	−	0.277660i	$-0.910441\pi$
$881$		−	489.236i		−	0.555319i	0.960680	−	0.277660i	$-0.0895588\pi$
$882$	106.684	−	13.3810i	0.120957	−	0.0151712i
$883$	221.201			0.250511			0.125256	−	0.992125i	$-0.460025\pi$
$883$	221.201			0.250511			0.125256	+	0.992125i	$0.460025\pi$
$884$	106.248	−	18.8449i	0.120191	−	0.0213178i
$885$	1412.09	−	937.284i	1.59558	−	1.05908i
$886$	−91.2911	−	52.7069i	−0.103037	−	0.0594886i
$887$	453.335	+	261.733i	0.511087	+	0.295076i	0.733281	−	0.679926i	$-0.237988\pi$
$887$	453.335	+	261.733i	0.511087	+	0.295076i	−0.222193	+	0.975003i	$0.571322\pi$
$888$	−122.571	+	7.65685i	−0.138030	+	0.00862258i
$889$	131.044	−	75.6581i	0.147406	−	0.0851047i
$890$	116.018			0.130357
$891$	872.422	+	894.060i	0.979149	+	1.00343i
$892$			439.337i			0.492530i
$893$	−208.537	+	120.399i	−0.233525	+	0.134825i
$894$	−5.79314	−	92.7365i	−0.00648002	−	0.103732i
$895$	−757.726	−	437.473i	−0.846621	−	0.488797i
$896$	−583.266	−	336.749i	−0.650966	−	0.375836i
$897$	−264.970	−	1092.56i	−0.295395	−	1.21801i
$898$	83.4376	+	144.518i	0.0929149	+	0.160933i
$899$	−695.475			−0.773610
$900$	127.692	−	16.0160i	0.141880	−	0.0177956i
$901$	−85.4337			−0.0948210
$902$	−128.333	−	222.279i	−0.142276	−	0.246429i
$903$	−282.451	+	568.359i	−0.312791	+	0.629412i
$904$	350.944	+	202.617i	0.388212	+	0.224134i
$905$	−357.826	+	619.772i	−0.395387	+	0.684831i
$906$	71.2662	−	143.405i	0.0786603	−	0.158284i
$907$	402.236	+	696.693i	0.443479	+	0.768129i	0.997945	−	0.0640778i	$-0.0204106\pi$
$907$	402.236	+	696.693i	0.443479	+	0.768129i	−0.554465	+	0.832207i	$0.687077\pi$
$908$	−559.562			−0.616257
$909$	−596.840	+	452.191i	−0.656590	+	0.497460i
$910$	65.9413	−	181.742i	0.0724629	−	0.199716i
$911$	−463.788	+	267.768i	−0.509098	+	0.293928i	−0.732463	−	0.680807i	$-0.761629\pi$
$911$	−463.788	+	267.768i	−0.509098	+	0.293928i	0.223365	+	0.974735i	$0.428296\pi$
$912$	828.304	+	1247.90i	0.908228	+	1.36831i
$913$	−256.506	+	444.282i	−0.280949	+	0.486617i
$914$	−101.280	−	58.4741i	−0.110810	−	0.0639760i
$915$	10.6273	+	170.122i	0.0116146	+	0.185926i
$916$	−270.909	+	156.409i	−0.295752	+	0.170752i
$917$	226.581			0.247089
$918$	10.9566	+	12.7276i	0.0119353	+	0.0138645i
$919$	−693.391			−0.754506			−0.377253	−	0.926110i	$-0.623131\pi$
$919$	−693.391			−0.754506			−0.377253	+	0.926110i	$0.623131\pi$
$920$	−310.176	+	179.080i	−0.337147	+	0.194652i
$921$	−1691.82	+	105.686i	−1.83694	+	0.114751i
$922$	84.6510	−	146.620i	0.0918124	−	0.159024i
$923$	664.779	−	558.959i	0.720238	−	0.605589i
$924$	948.633	+	1429.18i	1.02666	+	1.54674i
$925$	55.8001	−	32.2162i	0.0603245	−	0.0348283i
$926$		−	154.718i		−	0.167082i
$927$	587.168	−	1393.35i	0.633406	−	1.50308i
$928$			367.939i			0.396486i
$929$	−485.591	−	841.069i	−0.522703	−	0.905349i	−0.999651	−	0.0264171i	$-0.991590\pi$
$929$	−485.591	−	841.069i	−0.522703	−	0.905349i	0.476948	−	0.878932i	$-0.341743\pi$
$930$	54.1865	−	109.036i	0.0582651	−	0.117243i
$931$	−1176.05	−	678.995i	−1.26321	−	0.729317i
$932$	−187.915	−	108.493i	−0.201626	−	0.116409i
$933$	691.395	−	1391.26i	0.741046	−	1.49116i
$934$	66.9486	−	38.6528i	0.0716795	−	0.0413842i
$935$			175.072i			0.187243i
$936$	184.493	−	199.283i	0.197108	−	0.212909i
$937$	1512.68			1.61438			0.807192	−	0.590289i	$-0.200986\pi$
$937$	1512.68			1.61438			0.807192	+	0.590289i	$0.200986\pi$
$938$	107.793	+	186.702i	0.114917	+	0.199043i
$939$	−693.373	+	460.232i	−0.738416	+	0.490130i
$940$	−75.6613	+	131.049i	−0.0804908	+	0.139414i
$941$	147.030	−	254.664i	0.156249	−	0.270631i	−0.777264	−	0.629174i	$-0.783393\pi$
$941$	147.030	−	254.664i	0.156249	−	0.270631i	0.933513	+	0.358543i	$0.116727\pi$
$942$	4.53587	+	72.6102i	0.00481515	+	0.0770809i
$943$	1416.59	−	817.867i	1.50221	−	0.867303i
$944$	1580.49			1.67424
$945$	−1345.16	+	254.746i	−1.42345	+	0.269573i
$946$	101.018			0.106785
$947$	−224.084	−	388.125i	−0.236625	−	0.409847i	0.723118	−	0.690724i	$-0.242708\pi$
$947$	−224.084	−	388.125i	−0.236625	−	0.409847i	−0.959744	+	0.280877i	$0.909375\pi$
$948$	−45.3692	−	726.270i	−0.0478578	−	0.766107i
$949$	−453.409	−	539.247i	−0.477776	−	0.568227i
$950$	30.9373	+	17.8617i	0.0325656	+	0.0188018i
$951$	763.345	−	506.677i	0.802676	−	0.532783i
$952$	23.3148	+	40.3823i	0.0244903	+	0.0424184i
$953$		−	1674.56i		−	1.75715i	−0.477608	−	0.878573i	$-0.658496\pi$
$953$		−	1674.56i		−	1.75715i	0.477608	−	0.878573i	$-0.341504\pi$
$954$	−84.7586	+	64.2167i	−0.0888455	+	0.0673131i
$955$			879.952i			0.921416i
$956$	−760.489	−	1317.21i	−0.795490	−	1.37783i
$957$	553.925	−	1114.63i	0.578814	−	1.16471i
$958$	30.3909	−	52.6386i	0.0317233	−	0.0549463i
$959$	−702.327	−	405.489i	−0.732354	−	0.422825i
$960$	803.729	+	399.420i	0.837218	+	0.416062i
$961$	−146.350	−	253.486i	−0.152289	−	0.263773i
$962$	22.9354	−	63.2128i	0.0238414	−	0.0657098i
$963$	−140.541	−	1120.50i	−0.145940	−	1.16355i
$964$		−	357.521i		−	0.370872i
$965$	166.575	−	96.1723i	0.172617	−	0.0996604i
$966$	200.181	−	132.872i	0.207227	−	0.137548i
$967$	−1422.81	−	821.462i	−1.47137	−	0.849495i	−0.471886	−	0.881660i	$-0.656427\pi$
$967$	−1422.81	−	821.462i	−1.47137	−	0.849495i	−0.999483	+	0.0321645i	$0.989760\pi$
$968$	135.599	−	234.865i	0.140082	−	0.242629i
$969$	−13.2246	−	211.699i	−0.0136476	−	0.218471i
$970$	40.1578	−	23.1851i	0.0413998	−	0.0239022i
$971$		−	324.950i		−	0.334655i	−0.985901	−	0.167327i	$-0.946486\pi$
$971$		−	324.950i		−	0.334655i	0.985901	−	0.167327i	$-0.0535137\pi$
$972$	−929.872	−	199.810i	−0.956658	−	0.205565i
$973$			736.008i			0.756432i
$974$	−67.6702	+	39.0694i	−0.0694766	+	0.0401124i
$975$	−40.1512	+	136.707i	−0.0411807	+	0.140212i
$976$	−79.4765	+	137.657i	−0.0814308	+	0.141042i
$977$	−874.564	+	1514.79i	−0.895152	+	1.55045i	−0.0615359	+	0.998105i	$0.519600\pi$
$977$	−874.564	+	1514.79i	−0.895152	+	1.55045i	−0.833616	+	0.552344i	$0.813733\pi$
$978$	52.4711	+	79.0515i	0.0536514	+	0.0808297i
$979$	−569.828	−	986.971i	−0.582051	−	1.00814i
$980$	−853.388			−0.870805
$981$	3.28951	+	26.2265i	0.00335323	+	0.0267345i
$982$		−	93.8979i		−	0.0956190i
$983$	807.157	+	1398.04i	0.821116	+	1.42222i	0.904852	+	0.425727i	$0.139982\pi$
$983$	807.157	+	1398.04i	0.821116	+	1.42222i	−0.0837352	+	0.996488i	$0.526685\pi$
$984$	353.847	+	175.847i	0.359600	+	0.178706i
$985$	85.4827	−	148.060i	0.0867845	−	0.150315i
$986$	8.36676	−	14.4916i	0.00848556	−	0.0146974i
$987$	91.3452	−	183.809i	0.0925484	−	0.186230i
$988$	−1670.29	+	296.253i	−1.69058	+	0.299851i
$989$			643.790i			0.650951i
$990$	131.594	+	173.688i	0.132923	+	0.175443i
$991$	586.232			0.591556			0.295778	−	0.955257i	$-0.404421\pi$
$991$	586.232			0.591556			0.295778	+	0.955257i	$0.404421\pi$
$992$	306.193	−	176.781i	0.308663	−	0.178207i
$993$	−638.458	−	961.883i	−0.642959	−	0.968664i
$994$	160.752	+	92.8105i	0.161723	+	0.0933707i
$995$	168.901	−	292.546i	0.169750	−	0.294016i
$996$	−24.3525	−	389.834i	−0.0244503	−	0.391400i
$997$	−124.344	−	215.369i	−0.124718	−	0.216017i	0.796905	−	0.604105i	$-0.206469\pi$
$997$	−124.344	−	215.369i	−0.124718	−	0.216017i	−0.921623	+	0.388087i	$0.873136\pi$
$998$			235.691i			0.236163i
$999$	−467.869	+	88.6049i	−0.468338	+	0.0886936i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.3.n.a.77.13	yes	52
3.2	odd	2		351.3.n.a.233.14		52
9.2	odd	6	inner	117.3.n.a.38.14	yes	52
9.7	even	3		351.3.n.a.116.13		52
13.12	even	2	inner	117.3.n.a.77.14	yes	52
39.38	odd	2		351.3.n.a.233.13		52
117.25	even	6		351.3.n.a.116.14		52
117.38	odd	6	inner	117.3.n.a.38.13	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.3.n.a.38.13	✓	52	117.38	odd	6	inner
117.3.n.a.38.14	yes	52	9.2	odd	6	inner
117.3.n.a.77.13	yes	52	1.1	even	1	trivial
117.3.n.a.77.14	yes	52	13.12	even	2	inner
351.3.n.a.116.13		52	9.7	even	3
351.3.n.a.116.14		52	117.25	even	6
351.3.n.a.233.13		52	39.38	odd	2
351.3.n.a.233.14		52	3.2	odd	2

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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