LMFDB - Embedded newform 135.3.n.a.104.26

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,3,Mod(14,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([17, 9]))

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

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

chi := DirichletCharacter("135.14");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	135.n (of order $18$, degree $6$, 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:	$3.67848356886$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			104.26
Character	$\chi$	$=$	135.104
Dual form			135.3.n.a.74.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.03789 + 0.741730i) q^{2} +(-2.69852 - 1.31073i) q^{3} +(0.538636 + 0.451970i) q^{4} +(-4.62185 - 1.90748i) q^{5} +(-4.52706 - 4.67268i) q^{6} +(-2.32404 - 2.76969i) q^{7} +(-3.57490 - 6.19192i) q^{8} +(5.56398 + 7.07404i) q^{9} +(-8.00397 - 7.31539i) q^{10} +(-8.70004 + 1.53405i) q^{11} +(-0.861110 - 1.92565i) q^{12} +(-3.15234 - 8.66099i) q^{13} +(-2.68178 - 7.36812i) q^{14} +(9.97195 + 11.2054i) q^{15} +(-3.18091 - 18.0399i) q^{16} +(9.89182 - 17.1331i) q^{17} +(6.09173 + 18.5431i) q^{18} +(12.1652 + 21.0707i) q^{19} +(-1.62737 - 3.11638i) q^{20} +(2.64116 + 10.5202i) q^{21} +(-18.8675 - 3.32686i) q^{22} +(-4.74988 - 3.98563i) q^{23} +(1.53102 + 21.3947i) q^{24} +(17.7230 + 17.6322i) q^{25} -19.9883i q^{26} +(-5.74235 - 26.3823i) q^{27} -2.54225i q^{28} +(-5.21445 + 14.3266i) q^{29} +(12.0103 + 30.2317i) q^{30} +(-9.90161 - 8.30843i) q^{31} +(1.93215 - 10.9578i) q^{32} +(25.4879 + 7.26372i) q^{33} +(32.8665 - 27.5783i) q^{34} +(5.45826 + 17.2342i) q^{35} +(-0.200289 + 6.32509i) q^{36} +(-9.23883 - 5.33404i) q^{37} +(9.16248 + 51.9630i) q^{38} +(-2.84556 + 27.5037i) q^{39} +(4.71171 + 35.4372i) q^{40} +(-23.8792 - 65.6075i) q^{41} +(-2.42079 + 23.3981i) q^{42} +(58.3296 - 10.2851i) q^{43} +(-5.37950 - 3.10586i) q^{44} +(-12.2223 - 43.3084i) q^{45} +(-6.72346 - 11.6454i) q^{46} +(-12.6408 + 10.6069i) q^{47} +(-15.0616 + 52.8502i) q^{48} +(6.23877 - 35.3818i) q^{49} +(23.0392 + 49.0781i) q^{50} +(-49.1501 + 33.2686i) q^{51} +(2.21654 - 6.08989i) q^{52} -85.3480 q^{53} +(7.86628 - 58.0234i) q^{54} +(43.1365 + 9.50501i) q^{55} +(-8.84144 + 24.2917i) q^{56} +(-5.20996 - 72.8049i) q^{57} +(-21.2529 + 25.3282i) q^{58} +(-60.9628 - 10.7494i) q^{59} +(0.306774 + 10.5426i) q^{60} +(55.8155 - 46.8348i) q^{61} +(-14.0157 - 24.2760i) q^{62} +(6.66196 - 31.8509i) q^{63} +(-24.5711 + 42.5584i) q^{64} +(-1.95102 + 46.0428i) q^{65} +(46.5538 + 33.7078i) q^{66} +(7.87234 + 21.6291i) q^{67} +(13.0717 - 4.75773i) q^{68} +(7.59357 + 16.9811i) q^{69} +(-1.65978 + 39.1698i) q^{70} +(49.0653 + 28.3279i) q^{71} +(23.9112 - 59.7407i) q^{72} +(101.360 - 58.5204i) q^{73} +(-14.8713 - 17.7229i) q^{74} +(-24.7149 - 70.8108i) q^{75} +(-2.97071 + 16.8478i) q^{76} +(24.4681 + 20.5312i) q^{77} +(-26.1992 + 53.9387i) q^{78} +(-7.55144 - 2.74850i) q^{79} +(-19.7090 + 89.4451i) q^{80} +(-19.0842 + 78.7197i) q^{81} -151.413i q^{82} +(-77.8706 - 28.3426i) q^{83} +(-3.33220 + 6.86031i) q^{84} +(-78.3997 + 60.3183i) q^{85} +(126.498 + 22.3050i) q^{86} +(32.8495 - 31.8258i) q^{87} +(40.6005 + 48.3858i) q^{88} +(102.638 - 59.2583i) q^{89} +(7.21547 - 97.3231i) q^{90} +(-16.6621 + 28.8595i) q^{91} +(-0.757079 - 4.29361i) q^{92} +(15.8295 + 35.3988i) q^{93} +(-33.6278 + 12.2395i) q^{94} +(-16.0337 - 120.591i) q^{95} +(-19.5766 + 27.0373i) q^{96} +(30.2613 - 5.33588i) q^{97} +(38.9576 - 67.4766i) q^{98} +(-59.2588 - 53.0090i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 12 q^{4} + 3 q^{5} - 24 q^{6} - 18 q^{9} - 3 q^{10} + 6 q^{11} - 48 q^{14} - 3 q^{15} + 12 q^{16} - 6 q^{19} + 63 q^{20} - 192 q^{21} + 42 q^{24} - 15 q^{25} + 96 q^{29} - 177 q^{30} - 102 q^{31}+ \cdots + 792 q^{99}+O(q^{100}) $ 204 * q - 12 * q^4 + 3 * q^5 - 24 * q^6 - 18 * q^9 - 3 * q^10 + 6 * q^11 - 48 * q^14 - 3 * q^15 + 12 * q^16 - 6 * q^19 + 63 * q^20 - 192 * q^21 + 42 * q^24 - 15 * q^25 + 96 * q^29 - 177 * q^30 - 102 * q^31 + 12 * q^34 - 252 * q^35 + 324 * q^36 - 258 * q^39 + 117 * q^40 + 96 * q^41 - 666 * q^44 - 279 * q^45 - 6 * q^46 + 60 * q^49 + 48 * q^50 + 270 * q^51 + 432 * q^54 - 12 * q^55 + 294 * q^56 + 510 * q^59 + 390 * q^60 + 132 * q^61 - 486 * q^64 + 147 * q^65 - 186 * q^66 - 84 * q^69 - 141 * q^70 - 18 * q^71 - 954 * q^74 - 285 * q^75 + 84 * q^76 - 48 * q^79 - 1026 * q^81 + 198 * q^84 + 69 * q^85 - 1506 * q^86 + 792 * q^89 - 180 * q^90 - 6 * q^91 + 492 * q^94 - 543 * q^95 + 654 * q^96 + 792 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	2.03789	+	0.741730i	1.01894	+	0.370865i	0.796861	−	0.604163i	$-0.206492\pi$
$2$	2.03789	+	0.741730i	1.01894	+	0.370865i	0.222082	+	0.975028i	$0.428715\pi$
$3$	−2.69852	−	1.31073i	−0.899505	−	0.436909i
$3$	−2.69852	−	1.31073i	−0.899505	−	0.436909i
$4$	0.538636	+	0.451970i	0.134659	+	0.112992i
$5$	−4.62185	−	1.90748i	−0.924370	−	0.381496i
$5$	−4.62185	−	1.90748i	−0.924370	−	0.381496i
$6$	−4.52706	−	4.67268i	−0.754510	−	0.778781i
$7$	−2.32404	−	2.76969i	−0.332006	−	0.395670i	0.574055	−	0.818817i	$-0.305370\pi$
$7$	−2.32404	−	2.76969i	−0.332006	−	0.395670i	−0.906061	+	0.423147i	$0.860925\pi$
$8$	−3.57490	−	6.19192i	−0.446863	−	0.773990i
$9$	5.56398	+	7.07404i	0.618220	+	0.786005i
$10$	−8.00397	−	7.31539i	−0.800397	−	0.731539i
$11$	−8.70004	+	1.53405i	−0.790913	+	0.139459i	−0.554489	−	0.832191i	$-0.687086\pi$
$11$	−8.70004	+	1.53405i	−0.790913	+	0.139459i	−0.236423	+	0.971650i	$0.575975\pi$
$12$	−0.861110	−	1.92565i	−0.0717592	−	0.160471i
$13$	−3.15234	−	8.66099i	−0.242488	−	0.666230i	−0.999911	−	0.0133060i	$-0.995764\pi$
$13$	−3.15234	−	8.66099i	−0.242488	−	0.666230i	0.757424	−	0.652924i	$-0.226458\pi$
$14$	−2.68178	−	7.36812i	−0.191555	−	0.526294i
$15$	9.97195	+	11.2054i	0.664797	+	0.747024i
$16$	−3.18091	−	18.0399i	−0.198807	−	1.12749i
$17$	9.89182	−	17.1331i	0.581872	−	1.00783i	−0.413386	−	0.910556i	$-0.635654\pi$
$17$	9.89182	−	17.1331i	0.581872	−	1.00783i	0.995258	−	0.0972754i	$-0.0310128\pi$
$18$	6.09173	+	18.5431i	0.338429	+	1.03017i
$19$	12.1652	+	21.0707i	0.640273	+	1.10899i	0.985372	+	0.170419i	$0.0545121\pi$
$19$	12.1652	+	21.0707i	0.640273	+	1.10899i	−0.345099	+	0.938566i	$0.612155\pi$
$20$	−1.62737	−	3.11638i	−0.0813687	−	0.155819i
$21$	2.64116	+	10.5202i	0.125770	+	0.500964i
$22$	−18.8675	−	3.32686i	−0.857615	−	0.151221i
$23$	−4.74988	−	3.98563i	−0.206517	−	0.173288i	0.533663	−	0.845697i	$-0.320815\pi$
$23$	−4.74988	−	3.98563i	−0.206517	−	0.173288i	−0.740180	+	0.672409i	$0.765260\pi$
$24$	1.53102	+	21.3947i	0.0637924	+	0.891447i
$25$	17.7230	+	17.6322i	0.708921	+	0.705288i
$26$		−	19.9883i		−	0.768780i
$27$	−5.74235	−	26.3823i	−0.212680	−	0.977122i
$28$		−	2.54225i		−	0.0907948i
$29$	−5.21445	+	14.3266i	−0.179808	+	0.494020i	−0.996551	−	0.0829826i	$-0.973555\pi$
$29$	−5.21445	+	14.3266i	−0.179808	+	0.494020i	0.816743	+	0.577002i	$0.195778\pi$
$30$	12.0103	+	30.2317i	0.400345	+	1.00772i
$31$	−9.90161	−	8.30843i	−0.319407	−	0.268014i	0.468960	−	0.883219i	$-0.344629\pi$
$31$	−9.90161	−	8.30843i	−0.319407	−	0.268014i	−0.788367	+	0.615205i	$0.789073\pi$
$32$	1.93215	−	10.9578i	0.0603798	−	0.342431i
$33$	25.4879	+	7.26372i	0.772361	+	0.220113i
$34$	32.8665	−	27.5783i	0.966663	−	0.811127i
$35$	5.45826	+	17.2342i	0.155950	+	0.492405i
$36$	−0.200289	+	6.32509i	−0.00556360	+	0.175697i
$37$	−9.23883	−	5.33404i	−0.249698	−	0.144163i	0.369928	−	0.929060i	$-0.379382\pi$
$37$	−9.23883	−	5.33404i	−0.249698	−	0.144163i	−0.619626	+	0.784897i	$0.712716\pi$
$38$	9.16248	+	51.9630i	0.241118	+	1.36745i
$39$	−2.84556	+	27.5037i	−0.0729630	+	0.705222i
$40$	4.71171	+	35.4372i	0.117793	+	0.885930i
$41$	−23.8792	−	65.6075i	−0.582419	−	1.60018i	−0.784033	−	0.620719i	$-0.786841\pi$
$41$	−23.8792	−	65.6075i	−0.582419	−	1.60018i	0.201614	−	0.979465i	$-0.435381\pi$
$42$	−2.42079	+	23.3981i	−0.0576378	+	0.557097i
$43$	58.3296	−	10.2851i	1.35650	−	0.239188i	0.552351	−	0.833612i	$-0.313731\pi$
$43$	58.3296	−	10.2851i	1.35650	−	0.239188i	0.804152	+	0.594424i	$0.202620\pi$
$44$	−5.37950	−	3.10586i	−0.122261	−	0.0705877i
$45$	−12.2223	−	43.3084i	−0.271607	−	0.962408i
$46$	−6.72346	−	11.6454i	−0.146162	−	0.253160i
$47$	−12.6408	+	10.6069i	−0.268952	+	0.225678i	−0.767282	−	0.641310i	$-0.778391\pi$
$47$	−12.6408	+	10.6069i	−0.268952	+	0.225678i	0.498330	+	0.866988i	$0.333947\pi$
$48$	−15.0616	+	52.8502i	−0.313783	+	1.10105i
$49$	6.23877	−	35.3818i	0.127322	−	0.722078i
$50$	23.0392	+	49.0781i	0.460784	+	0.981562i
$51$	−49.1501	+	33.2686i	−0.963728	+	0.652325i
$52$	2.21654	−	6.08989i	0.0426257	−	0.117113i
$53$	−85.3480			−1.61034			−0.805169	−	0.593045i	$-0.797926\pi$
$53$	−85.3480			−1.61034			−0.805169	+	0.593045i	$0.797926\pi$
$54$	7.86628	−	58.0234i	0.145672	−	1.07451i
$55$	43.1365	+	9.50501i	0.784299	+	0.172818i
$56$	−8.84144	+	24.2917i	−0.157883	+	0.433780i
$57$	−5.20996	−	72.8049i	−0.0914029	−	1.27728i
$58$	−21.2529	+	25.3282i	−0.366429	+	0.436693i
$59$	−60.9628	−	10.7494i	−1.03327	−	0.182193i	−0.368799	−	0.929509i	$-0.620231\pi$
$59$	−60.9628	−	10.7494i	−1.03327	−	0.182193i	−0.664469	+	0.747316i	$0.731342\pi$
$60$	0.306774	+	10.5426i	0.00511289	+	0.175711i
$61$	55.8155	−	46.8348i	0.915009	−	0.767784i	−0.0580564	−	0.998313i	$-0.518490\pi$
$61$	55.8155	−	46.8348i	0.915009	−	0.767784i	0.973065	+	0.230530i	$0.0740459\pi$
$62$	−14.0157	−	24.2760i	−0.226060	−	0.391548i
$63$	6.66196	−	31.8509i	0.105745	−	0.505570i
$64$	−24.5711	+	42.5584i	−0.383923	+	0.664974i
$65$	−1.95102	+	46.0428i	−0.0300157	+	0.708351i
$66$	46.5538	+	33.7078i	0.705360	+	0.510724i
$67$	7.87234	+	21.6291i	0.117498	+	0.322822i	0.984475	−	0.175526i	$-0.0561625\pi$
$67$	7.87234	+	21.6291i	0.117498	+	0.322822i	−0.866977	+	0.498348i	$0.833940\pi$
$68$	13.0717	−	4.75773i	0.192232	−	0.0699666i
$69$	7.59357	+	16.9811i	0.110052	+	0.246103i
$70$	−1.65978	+	39.1698i	−0.0237111	+	0.559569i
$71$	49.0653	+	28.3279i	0.691060	+	0.398984i	0.804009	−	0.594617i	$-0.202696\pi$
$71$	49.0653	+	28.3279i	0.691060	+	0.398984i	−0.112949	+	0.993601i	$0.536030\pi$
$72$	23.9112	−	59.7407i	0.332100	−	0.829733i
$73$	101.360	−	58.5204i	1.38850	−	0.801650i	0.395352	−	0.918530i	$-0.370623\pi$
$73$	101.360	−	58.5204i	1.38850	−	0.801650i	0.993146	+	0.116880i	$0.0372894\pi$
$74$	−14.8713	−	17.7229i	−0.200963	−	0.239498i
$75$	−24.7149	−	70.8108i	−0.329532	−	0.944145i
$76$	−2.97071	+	16.8478i	−0.0390883	+	0.221681i
$77$	24.4681	+	20.5312i	0.317768	+	0.266639i
$78$	−26.1992	+	53.9387i	−0.335887	+	0.691522i
$79$	−7.55144	−	2.74850i	−0.0955879	−	0.0347912i	0.293784	−	0.955872i	$-0.405086\pi$
$79$	−7.55144	−	2.74850i	−0.0955879	−	0.0347912i	−0.389371	+	0.921081i	$0.627308\pi$
$80$	−19.7090	+	89.4451i	−0.246362	+	1.11806i
$81$	−19.0842	+	78.7197i	−0.235607	+	0.971848i
$82$		−	151.413i		−	1.84649i
$83$	−77.8706	−	28.3426i	−0.938200	−	0.341477i	−0.172745	−	0.984967i	$-0.555264\pi$
$83$	−77.8706	−	28.3426i	−0.938200	−	0.341477i	−0.765455	+	0.643490i	$0.777486\pi$
$84$	−3.33220	+	6.86031i	−0.0396691	+	0.0816704i
$85$	−78.3997	+	60.3183i	−0.922349	+	0.709628i
$86$	126.498	+	22.3050i	1.47090	+	0.259360i
$87$	32.8495	−	31.8258i	0.377581	−	0.365813i
$88$	40.6005	+	48.3858i	0.461370	+	0.549839i
$89$	102.638	−	59.2583i	1.15324	−	0.665823i	0.203565	−	0.979061i	$-0.434747\pi$
$89$	102.638	−	59.2583i	1.15324	−	0.665823i	0.949675	+	0.313238i	$0.101414\pi$
$90$	7.21547	−	97.3231i	0.0801719	−	1.08137i
$91$	−16.6621	+	28.8595i	−0.183100	+	0.317138i
$92$	−0.757079	−	4.29361i	−0.00822912	−	0.0466696i
$93$	15.8295	+	35.3988i	0.170210	+	0.380632i
$94$	−33.6278	+	12.2395i	−0.357743	+	0.130208i
$95$	−16.0337	−	120.591i	−0.168776	−	1.26937i
$96$	−19.5766	+	27.0373i	−0.203923	+	0.281638i
$97$	30.2613	−	5.33588i	0.311972	−	0.0550090i	−0.0154702	−	0.999880i	$-0.504925\pi$
$97$	30.2613	−	5.33588i	0.311972	−	0.0550090i	0.327442	+	0.944871i	$0.393813\pi$
$98$	38.9576	−	67.4766i	0.397527	−	0.688537i
$99$	−59.2588	−	53.0090i	−0.598574	−	0.535445i
$100$	1.57705	+	17.5076i	0.0157705	+	0.175076i
$101$	69.5507	+	82.8873i	0.688621	+	0.820666i	0.991188	−	0.132462i	$-0.0422882\pi$
$101$	69.5507	+	82.8873i	0.688621	+	0.820666i	−0.302567	+	0.953128i	$0.597844\pi$
$102$	−124.839	+	31.3414i	−1.22391	+	0.307269i
$103$	−32.9784	−	5.81498i	−0.320179	−	0.0564561i	0.0112492	−	0.999937i	$-0.496419\pi$
$103$	−32.9784	−	5.81498i	−0.320179	−	0.0564561i	−0.331428	+	0.943481i	$0.607530\pi$
$104$	−42.3588	+	50.4812i	−0.407296	+	0.485396i
$105$	7.86010	−	53.6610i	0.0748581	−	0.511057i
$106$	−173.929	−	63.3051i	−1.64084	−	0.597218i
$107$	−183.486			−1.71482			−0.857411	−	0.514632i	$-0.827928\pi$
$107$	−183.486			−1.71482			−0.857411	+	0.514632i	$0.827928\pi$
$108$	8.83096	−	16.8058i	0.0817681	−	0.155610i
$109$	−75.0243			−0.688297			−0.344148	−	0.938915i	$-0.611832\pi$
$109$	−75.0243			−0.688297			−0.344148	+	0.938915i	$0.611832\pi$
$110$	80.8570	+	51.3657i	0.735064	+	0.466961i
$111$	17.9397	+	26.5036i	0.161618	+	0.238771i
$112$	−42.5722	+	50.7356i	−0.380109	+	0.452996i
$113$	31.4551	−	178.391i	0.278364	−	1.57868i	−0.449705	−	0.893177i	$-0.648471\pi$
$113$	31.4551	−	178.391i	0.278364	−	1.57868i	0.728069	−	0.685504i	$-0.240418\pi$
$114$	43.3843	−	152.232i	0.380564	−	1.33537i
$115$	14.3508	+	27.4813i	0.124789	+	0.238968i
$116$	−9.28387	+	5.36004i	−0.0800333	+	0.0462073i
$117$	43.7286	−	70.4894i	0.373749	−	0.602473i
$118$	−116.262	−	67.1239i	−0.985272	−	0.568847i
$119$	−70.4425	+	12.4209i	−0.591954	+	0.104377i
$120$	33.7339	−	101.804i	0.281116	−	0.848363i
$121$	−40.3654	+	14.6918i	−0.333599	+	0.121420i
$122$	148.484	−	54.0439i	1.21709	−	0.442983i
$123$	−21.5553	+	208.342i	−0.175246	+	1.69384i
$124$	−1.57821	−	8.95045i	−0.0127275	−	0.0721811i
$125$	−48.2801	−	115.300i	−0.386241	−	0.922398i
$126$	37.2011	−	59.9671i	0.295246	−	0.475929i
$127$	−107.545	+	62.0910i	−0.846809	+	0.488905i	−0.859573	−	0.511013i	$-0.829270\pi$
$127$	−107.545	+	62.0910i	−0.846809	+	0.488905i	0.0127639	+	0.999919i	$0.495937\pi$
$128$	−115.734	+	97.1127i	−0.904175	+	0.758693i
$129$	−170.884	−	48.6998i	−1.32468	−	0.377518i
$130$	−38.1273	+	92.3829i	−0.293287	+	0.710638i
$131$	79.4604	−	94.6972i	0.606568	−	0.722880i	−0.372131	−	0.928180i	$-0.621373\pi$
$131$	79.4604	−	94.6972i	0.606568	−	0.722880i	0.978699	+	0.205301i	$0.0658172\pi$
$132$	10.4457	+	15.4323i	0.0791344	+	0.116911i
$133$	30.0869	−	82.6631i	0.226217	−	0.621527i
$134$			49.9167i			0.372513i
$135$	−23.7835	+	132.888i	−0.176174	+	0.984359i
$136$	−141.449			−1.04007
$137$	178.739	+	65.0558i	1.30467	+	0.474860i	0.898514	−	0.438946i	$-0.144648\pi$
$137$	178.739	+	65.0558i	1.30467	+	0.474860i	0.406153	+	0.913805i	$0.366870\pi$
$138$	2.87945	+	40.2379i	0.0208656	+	0.291579i
$139$	183.719	+	154.158i	1.32172	+	1.10905i	0.985938	+	0.167110i	$0.0534436\pi$
$139$	183.719	+	154.158i	1.32172	+	1.10905i	0.335778	+	0.941941i	$0.391001\pi$
$140$	−4.84930	+	11.7499i	−0.0346379	+	0.0839280i
$141$	48.0140	−	12.0542i	0.340525	−	0.0854906i
$142$	78.9778	+	94.1221i	0.556182	+	0.662832i
$143$	40.7119	+	70.5151i	0.284699	+	0.493112i
$144$	109.916	−	122.875i	0.763307	−	0.853301i
$145$	51.4281	−	56.2688i	0.354676	−	0.388061i
$146$	249.967	−	44.0759i	1.71210	−	0.301890i
$147$	−63.2114	+	87.3011i	−0.430009	+	0.593885i
$148$	−2.56555	−	7.04878i	−0.0173348	−	0.0476269i
$149$	86.2208	+	236.890i	0.578663	+	1.58986i	0.790435	+	0.612545i	$0.209854\pi$
$149$	86.2208	+	236.890i	0.578663	+	1.58986i	−0.211772	+	0.977319i	$0.567923\pi$
$150$	2.15643	−	162.636i	0.0143762	−	1.08424i
$151$	32.4942	+	184.284i	0.215194	+	1.22042i	0.880570	+	0.473916i	$0.157160\pi$
$151$	32.4942	+	184.284i	0.215194	+	1.22042i	−0.665377	+	0.746508i	$0.731729\pi$
$152$	86.9788	−	150.652i	0.572229	−	0.991129i
$153$	176.238	−	25.3533i	1.15189	−	0.165708i
$154$	34.6346	+	59.9890i	0.224900	+	0.389539i
$155$	29.9156	+	57.2875i	0.193004	+	0.369597i
$156$	−13.9635	+	13.5284i	−0.0895099	+	0.0867204i
$157$	−87.5981	−	15.4459i	−0.557949	−	0.0983815i	−0.112440	−	0.993659i	$-0.535866\pi$
$157$	−87.5981	−	15.4459i	−0.557949	−	0.0983815i	−0.445510	+	0.895277i	$0.646978\pi$
$158$	−13.3503	−	11.2023i	−0.0844958	−	0.0709004i
$159$	230.313	+	111.868i	1.44851	+	0.703572i
$160$	−29.8319	+	46.9598i	−0.186450	+	0.293498i
$161$			22.4185i			0.139245i
$162$	−97.2802	+	146.266i	−0.600495	+	0.902879i
$163$			95.4121i			0.585350i	0.956212	+	0.292675i	$0.0945454\pi$
$163$			95.4121i			0.585350i	−0.956212	+	0.292675i	$0.905455\pi$
$164$	16.7904	−	46.1313i	0.102381	−	0.281288i
$165$	−103.946	−	82.1896i	−0.629976	−	0.498119i
$166$	−137.669	−	115.518i	−0.829330	−	0.695891i
$167$	−16.2091	+	91.9261i	−0.0970602	+	0.550456i	0.897036	+	0.441957i	$0.145716\pi$
$167$	−16.2091	+	91.9261i	−0.0970602	+	0.550456i	−0.994097	+	0.108499i	$0.965396\pi$
$168$	55.6986	−	53.9627i	0.331539	−	0.321207i
$169$	64.3861	−	54.0263i	0.380983	−	0.319682i
$170$	−204.509	+	64.7705i	−1.20300	+	0.381003i
$171$	−81.3683	+	203.294i	−0.475838	+	1.18885i
$172$	36.0670	+	20.8233i	0.209692	+	0.121066i
$173$	9.71927	+	55.1207i	0.0561808	+	0.318617i	0.999927	−	0.0120526i	$-0.00383655\pi$
$173$	9.71927	+	55.1207i	0.0561808	+	0.318617i	−0.943747	+	0.330670i	$0.892725\pi$
$174$	90.5497	−	40.4918i	0.520400	−	0.232712i
$175$	7.64658	−	90.0653i	0.0436947	−	0.514659i
$176$	55.3482	+	152.068i	0.314478	+	0.864022i
$177$	150.420	+	108.913i	0.849828	+	0.615328i
$178$	253.119	−	44.6317i	1.42202	−	0.250740i
$179$	−43.6437	−	25.1977i	−0.243820	−	0.140769i	0.373111	−	0.927787i	$-0.378291\pi$
$179$	−43.6437	−	25.1977i	−0.243820	−	0.140769i	−0.616931	+	0.787017i	$0.711624\pi$
$180$	12.9907	−	28.8516i	0.0721705	−	0.160287i
$181$	−120.436	−	208.601i	−0.665390	−	1.15249i	−0.979179	−	0.202997i	$-0.934932\pi$
$181$	−120.436	−	208.601i	−0.665390	−	1.15249i	0.313789	−	0.949493i	$-0.398402\pi$
$182$	−55.3613	+	46.4537i	−0.304183	+	0.255240i
$183$	−212.007	+	53.2255i	−1.15851	+	0.290850i
$184$	−7.69828	+	43.6591i	−0.0418385	+	0.237278i
$185$	32.5259	+	42.2760i	0.175816	+	0.228519i
$186$	6.00249	+	83.8799i	0.0322715	+	0.450967i
$187$	−59.7761	+	164.233i	−0.319658	+	0.878254i
$188$	−11.6027			−0.0617167
$189$	−59.7253	+	77.2182i	−0.316007	+	0.408562i
$190$	56.7708	−	257.642i	0.298794	−	1.35601i
$191$	112.920	−	310.246i	0.591206	−	1.62432i	−0.177065	−	0.984199i	$-0.556660\pi$
$191$	112.920	−	310.246i	0.591206	−	1.62432i	0.768271	−	0.640125i	$-0.221117\pi$
$192$	122.088	−	82.6384i	0.635874	−	0.430408i
$193$	55.0909	−	65.6548i	0.285445	−	0.340180i	−0.604200	−	0.796833i	$-0.706507\pi$
$193$	55.0909	−	65.6548i	0.285445	−	0.340180i	0.889645	+	0.456652i	$0.150952\pi$
$194$	65.6268	+	11.5718i	0.338282	+	0.0596483i
$195$	65.6145	−	121.690i	0.336485	−	0.624052i
$196$	19.3519	−	16.2382i	0.0987344	−	0.0828480i
$197$	81.4582	+	141.090i	0.413493	+	0.716191i	0.995269	−	0.0971578i	$-0.0309752\pi$
$197$	81.4582	+	141.090i	0.413493	+	0.716191i	−0.581776	+	0.813349i	$0.697642\pi$
$198$	−81.4443	−	151.980i	−0.411335	−	0.767577i
$199$	−90.2959	+	156.397i	−0.453748	+	0.785915i	−0.998615	−	0.0526075i	$-0.983247\pi$
$199$	−90.2959	+	156.397i	−0.453748	+	0.785915i	0.544867	+	0.838522i	$0.316580\pi$
$200$	45.8189	−	172.773i	0.229095	−	0.863865i
$201$	7.10620	−	68.6849i	0.0353542	−	0.341716i
$202$	80.2564	+	220.503i	0.397309	+	1.09160i
$203$	51.7988	−	18.8532i	0.255166	−	0.0928729i
$204$	−41.5104	−	4.29471i	−0.203482	−	0.0210525i
$205$	−14.7791	+	348.777i	−0.0720931	+	1.70135i
$206$	−62.8930	−	36.3113i	−0.305306	−	0.176269i
$207$	1.76622	−	55.7768i	0.00853248	−	0.269453i
$208$	−146.216	+	84.4176i	−0.702960	+	0.405854i
$209$	−138.161	−	164.654i	−0.661058	−	0.787818i
$210$	55.8199	−	103.525i	0.265809	−	0.492975i
$211$	27.1933	−	154.221i	0.128878	−	0.730906i	−0.850050	−	0.526702i	$-0.823428\pi$
$211$	27.1933	−	154.221i	0.128878	−	0.730906i	0.978928	−	0.204204i	$-0.0654605\pi$
$212$	−45.9715	−	38.5747i	−0.216847	−	0.181956i
$213$	−95.2734	−	140.754i	−0.447293	−	0.660819i
$214$	−373.923	−	136.097i	−1.74731	−	0.635967i
$215$	−289.209	−	63.7265i	−1.34516	−	0.296402i
$216$	−142.829	+	129.870i	−0.661244	+	0.601252i
$217$			46.7335i			0.215362i
$218$	−152.891	−	55.6478i	−0.701335	−	0.255265i
$219$	−350.227	+	25.0624i	−1.59921	+	0.114440i
$220$	18.9389	+	24.6161i	0.0860859	+	0.111891i
$221$	−179.572	−	31.6634i	−0.812544	−	0.143273i
$222$	16.9005	+	67.3177i	0.0761282	+	0.303233i
$223$	−7.70503	−	9.18250i	−0.0345517	−	0.0411771i	0.748492	−	0.663144i	$-0.230778\pi$
$223$	−7.70503	−	9.18250i	−0.0345517	−	0.0411771i	−0.783044	+	0.621967i	$0.786334\pi$
$224$	−34.8401	+	20.1149i	−0.155536	+	0.0897988i
$225$	−26.1203	+	223.479i	−0.116090	+	0.993239i
$226$	196.420	−	340.209i	0.869114	−	1.50535i
$227$	33.5298	+	190.157i	0.147709	+	0.837697i	0.965152	+	0.261689i	$0.0842793\pi$
$227$	33.5298	+	190.157i	0.147709	+	0.837697i	−0.817444	+	0.576008i	$0.804610\pi$
$228$	30.0993	−	41.5701i	0.132015	−	0.182325i
$229$	413.128	−	150.366i	1.80405	−	0.656622i	0.806163	−	0.591694i	$-0.201540\pi$
$229$	413.128	−	150.366i	1.80405	−	0.656622i	0.997890	−	0.0649279i	$-0.0206817\pi$
$230$	8.86150	+	66.6481i	0.0385283	+	0.289774i
$231$	−39.1168	−	87.4748i	−0.169337	−	0.378679i
$232$	107.350	−	18.9287i	0.462716	−	0.0815893i
$233$	79.8540	−	138.311i	0.342721	−	0.593611i	−0.642216	−	0.766524i	$-0.721985\pi$
$233$	79.8540	−	138.311i	0.342721	−	0.593611i	0.984937	+	0.172913i	$0.0553181\pi$
$234$	141.398	−	111.214i	0.604265	−	0.475275i
$235$	78.6561	−	24.9113i	0.334707	−	0.106005i
$236$	−27.9784	−	33.3434i	−0.118553	−	0.141285i
$237$	16.7752	+	17.3148i	0.0707813	+	0.0730581i
$238$	−152.767	−	26.9369i	−0.641877	−	0.113180i
$239$	−44.1733	+	52.6436i	−0.184825	+	0.220266i	−0.850499	−	0.525977i	$-0.823700\pi$
$239$	−44.1733	+	52.6436i	−0.184825	+	0.220266i	0.665674	+	0.746243i	$0.268144\pi$
$240$	170.423	−	215.536i	0.710097	−	0.898066i
$241$	−197.027	−	71.7120i	−0.817539	−	0.297560i	−0.100805	−	0.994906i	$-0.532142\pi$
$241$	−197.027	−	71.7120i	−0.817539	−	0.297560i	−0.716734	+	0.697346i	$0.754364\pi$
$242$	−93.1575			−0.384948
$243$	154.679	−	187.412i	0.636540	−	0.771244i
$244$	51.2322			0.209968
$245$	−96.3248	+	151.629i	−0.393163	+	0.618895i
$246$	−198.461	+	408.589i	−0.806751	+	1.66093i
$247$	144.144	−	171.785i	0.583581	−	0.695484i
$248$	−16.0478	+	91.0118i	−0.0647090	+	0.366983i
$249$	172.986	+	178.550i	0.694722	+	0.717069i
$250$	−12.8681	−	270.778i	−0.0514725	−	1.08311i
$251$	89.5394	−	51.6956i	0.356731	−	0.205959i	−0.310915	−	0.950438i	$-0.600635\pi$
$251$	89.5394	−	51.6956i	0.356731	−	0.205959i	0.667646	+	0.744479i	$0.267302\pi$
$252$	17.9840	−	14.1451i	0.0713651	−	0.0561312i
$253$	47.4383	+	27.3885i	0.187503	+	0.108255i
$254$	−265.219	+	46.7652i	−1.04417	+	0.184115i
$255$	290.624	−	60.0094i	1.13970	−	0.235331i
$256$	−123.171	+	44.8305i	−0.481136	+	0.175119i
$257$	−101.124	+	36.8062i	−0.393480	+	0.143215i	−0.531180	−	0.847259i	$-0.678251\pi$
$257$	−101.124	+	36.8062i	−0.393480	+	0.143215i	0.137700	+	0.990474i	$0.456029\pi$
$258$	−312.121	−	225.995i	−1.20977	−	0.875948i
$259$	6.69782	+	37.9852i	0.0258603	+	0.146661i
$260$	−21.8608	+	23.9185i	−0.0840802	+	0.0919944i
$261$	−130.360	+	42.8256i	−0.499463	+	0.164083i
$262$	232.171	−	134.044i	0.886149	−	0.511618i
$263$	29.1199	−	24.4345i	0.110722	−	0.0929069i	−0.585746	−	0.810495i	$-0.699198\pi$
$263$	29.1199	−	24.4345i	0.110722	−	0.0929069i	0.696468	+	0.717588i	$0.254754\pi$
$264$	−46.1405	−	183.786i	−0.174775	−	0.696160i
$265$	394.466	+	162.800i	1.48855	+	0.614338i
$266$	122.627	−	146.142i	0.461005	−	0.549404i
$267$	−354.643	+	25.3784i	−1.32825	+	0.0950504i
$268$	−5.53535	+	15.2083i	−0.0206543	+	0.0567472i
$269$		−	101.363i		−	0.376814i	−0.982091	−	0.188407i	$-0.939668\pi$
$269$		−	101.363i		−	0.376814i	0.982091	−	0.188407i	$-0.0603323\pi$
$270$	−147.035	+	253.171i	−0.544575	+	0.937669i
$271$	198.243			0.731524			0.365762	−	0.930708i	$-0.380808\pi$
$271$	198.243			0.731524			0.365762	+	0.930708i	$0.380808\pi$
$272$	−340.544	−	123.948i	−1.25200	−	0.455691i
$273$	82.7898	−	56.0385i	0.303259	−	0.205269i
$274$	315.996	+	265.152i	1.15327	+	0.967710i
$275$	−181.240	−	126.213i	−0.659054	−	0.458955i
$276$	−3.58476	+	12.5787i	−0.0129883	+	0.0455750i
$277$	−242.799	−	289.356i	−0.876529	−	1.04461i	−0.998642	−	0.0520907i	$-0.983412\pi$
$277$	−242.799	−	289.356i	−0.876529	−	1.04461i	0.122113	−	0.992516i	$-0.461033\pi$
$278$	260.054	+	450.426i	0.935445	+	1.62024i
$279$	3.68187	−	116.272i	0.0131967	−	0.416747i
$280$	87.1997	−	95.4076i	0.311428	−	0.340741i
$281$	−56.2501	+	9.91841i	−0.200178	+	0.0352968i	−0.272838	−	0.962060i	$-0.587962\pi$
$281$	−56.2501	+	9.91841i	−0.200178	+	0.0352968i	0.0726599	+	0.997357i	$0.476851\pi$
$282$	106.788	+	11.0484i	0.378681	+	0.0391786i
$283$	−173.966	−	477.966i	−0.614719	−	1.68893i	−0.719553	−	0.694437i	$-0.755653\pi$
$283$	−173.966	−	477.966i	−0.614719	−	1.68893i	0.104834	−	0.994490i	$-0.466569\pi$
$284$	13.6250	+	37.4344i	0.0479754	+	0.131811i
$285$	−114.794	+	346.432i	−0.402787	+	1.21555i
$286$	30.6631	+	173.899i	0.107213	+	0.608038i
$287$	−126.216	+	218.613i	−0.439778	+	0.761717i
$288$	88.2664	−	47.3008i	0.306481	−	0.164239i
$289$	−51.1962	−	88.6744i	−0.177149	−	0.306832i
$290$	146.541	−	76.5237i	0.505313	−	0.263875i
$291$	−88.6544	−	25.2653i	−0.304654	−	0.0868225i
$292$	81.0458	+	14.2906i	0.277554	+	0.0489403i
$293$	−161.315	−	135.359i	−0.550562	−	0.461976i	0.324569	−	0.945862i	$-0.394781\pi$
$293$	−161.315	−	135.359i	−0.550562	−	0.461976i	−0.875131	+	0.483886i	$0.839225\pi$
$294$	−193.571	+	131.024i	−0.658406	+	0.445659i
$295$	261.257	+	165.968i	0.885616	+	0.562602i
$296$			76.2747i			0.257685i
$297$	90.4305	+	220.718i	0.304480	+	0.743158i
$298$			546.707i			1.83459i
$299$	−19.5462	+	53.7027i	−0.0653719	+	0.179608i
$300$	18.6920	−	49.3117i	0.0623067	−	0.164372i
$301$	−164.047	−	137.652i	−0.545007	−	0.457315i
$302$	−70.4693	+	399.651i	−0.233342	+	1.32335i
$303$	−79.0410	−	314.835i	−0.260861	−	1.03906i
$304$	341.416	−	286.482i	1.12308	−	0.942376i
$305$	−347.308	+	109.996i	−1.13871	+	0.360644i
$306$	377.959	+	79.0542i	1.23516	+	0.258347i
$307$	46.5102	+	26.8527i	0.151499	+	0.0874681i	0.573833	−	0.818972i	$-0.305456\pi$
$307$	46.5102	+	26.8527i	0.151499	+	0.0874681i	−0.422334	+	0.906440i	$0.638789\pi$
$308$	3.89995	+	22.1177i	0.0126622	+	0.0718107i
$309$	81.3709	+	58.9175i	0.263336	+	0.190672i
$310$	18.4727	+	138.935i	0.0595893	+	0.448176i
$311$	−108.295	−	297.537i	−0.348215	−	0.956712i	−0.982932	−	0.183968i	$-0.941106\pi$
$311$	−108.295	−	297.537i	−0.348215	−	0.956712i	0.634718	−	0.772744i	$-0.281116\pi$
$312$	180.473	−	80.7036i	0.578439	−	0.258665i
$313$	−100.283	+	17.6826i	−0.320393	+	0.0564939i	−0.331532	−	0.943444i	$-0.607565\pi$
$313$	−100.283	+	17.6826i	−0.320393	+	0.0564939i	0.0111389	+	0.999938i	$0.496454\pi$
$314$	−167.058	−	96.4511i	−0.532032	−	0.307169i
$315$	−91.5456	+	134.503i	−0.290621	+	0.426992i
$316$	−2.82524	−	4.89347i	−0.00894065	−	0.0154857i
$317$	389.774	−	327.059i	1.22957	−	1.03173i	0.231304	−	0.972881i	$-0.425701\pi$
$317$	389.774	−	327.059i	1.22957	−	1.03173i	0.998267	−	0.0588511i	$-0.0187437\pi$
$318$	386.375	+	398.804i	1.21502	+	1.25410i
$319$	23.3882	−	132.641i	0.0733172	−	0.415802i
$320$	194.743	−	149.830i	0.608572	−	0.468217i
$321$	495.140	+	240.500i	1.54249	+	0.749222i
$322$	−16.6284	+	45.6863i	−0.0516411	+	0.141883i
$323$	481.343			1.49023
$324$	−45.8584	+	33.7758i	−0.141538	+	0.104246i
$325$	96.8432	−	209.082i	0.297979	−	0.643328i
$326$	−70.7700	+	194.439i	−0.217086	+	0.596438i
$327$	202.454	+	98.3365i	0.619127	+	0.300723i
$328$	−320.871	+	382.399i	−0.978264	+	1.16585i
$329$	58.7554	+	10.3602i	0.178588	+	0.0314898i
$330$	−150.868	−	244.593i	−0.457174	−	0.741190i
$331$	177.270	−	148.747i	0.535559	−	0.449387i	−0.334457	−	0.942411i	$-0.608553\pi$
$331$	177.270	−	148.747i	0.535559	−	0.449387i	0.870016	+	0.493024i	$0.164109\pi$
$332$	−29.1340	−	50.4615i	−0.0877529	−	0.151992i
$333$	−13.6714	−	95.0344i	−0.0410554	−	0.285389i
$334$	−101.217	+	175.312i	−0.303044	+	0.524887i
$335$	4.87227	−	114.983i	0.0145441	−	0.343232i
$336$	181.382	−	81.1102i	0.539829	−	0.241399i
$337$	57.8789	+	159.021i	0.171748	+	0.471873i	0.995465	−	0.0951279i	$-0.0303260\pi$
$337$	57.8789	+	159.021i	0.171748	+	0.471873i	−0.823718	+	0.567000i	$0.808104\pi$
$338$	171.284	−	62.3424i	0.506759	−	0.184445i
$339$	−318.704	+	440.162i	−0.940130	+	1.29841i
$340$	−69.4910	−	2.94461i	−0.204385	−	0.00866061i
$341$	98.8899	+	57.0941i	0.290000	+	0.167431i
$342$	−316.609	+	353.937i	−0.925756	+	1.03490i
$343$	−265.923	+	153.531i	−0.775287	+	0.447612i
$344$	−272.207	−	324.404i	−0.791300	−	0.943034i
$345$	−2.70524	−	92.9687i	−0.00784127	−	0.269474i
$346$	−21.0779	+	119.539i	−0.0609188	+	0.345488i
$347$	6.55502	+	5.50032i	0.0188905	+	0.0158511i	0.652184	−	0.758061i	$-0.273853\pi$
$347$	6.55502	+	5.50032i	0.0188905	+	0.0158511i	−0.633293	+	0.773912i	$0.718297\pi$
$348$	32.0782	−	2.29554i	0.0921788	−	0.00659637i
$349$	−397.135	−	144.545i	−1.13792	−	0.414170i	−0.296761	−	0.954952i	$-0.595906\pi$
$349$	−397.135	−	144.545i	−1.13792	−	0.414170i	−0.841163	+	0.540782i	$0.818129\pi$
$350$	82.3869	−	177.871i	0.235391	−	0.508203i
$351$	−210.395	+	132.900i	−0.599416	+	0.378634i
$352$			98.2973i			0.279254i
$353$	349.306	+	127.137i	0.989535	+	0.360161i	0.785540	−	0.618811i	$-0.212385\pi$
$353$	349.306	+	127.137i	0.989535	+	0.360161i	0.203995	+	0.978972i	$0.434607\pi$
$354$	225.754	+	333.523i	0.637723	+	0.942156i
$355$	−172.738	−	224.518i	−0.486585	−	0.632446i
$356$	82.0677	+	14.4707i	0.230527	+	0.0406482i
$357$	206.371	+	58.8129i	0.578069	+	0.164742i
$358$	−70.2510	−	83.7219i	−0.196232	−	0.233860i
$359$	615.787	−	355.525i	1.71528	−	0.990320i	0.788239	−	0.615369i	$-0.210993\pi$
$359$	615.787	−	355.525i	1.71528	−	0.990320i	0.927045	−	0.374950i	$-0.122340\pi$
$360$	−224.468	+	230.503i	−0.623523	+	0.640285i
$361$	−115.483	+	200.023i	−0.319899	+	0.554081i
$362$	−90.7088	−	514.435i	−0.250577	−	1.42109i
$363$	128.184	+	13.2620i	0.353123	+	0.0365345i
$364$	−22.0184	+	8.01405i	−0.0604902	+	0.0220166i
$365$	−580.099	+	77.1297i	−1.58931	+	0.211314i
$366$	−471.525	−	48.7844i	−1.28832	−	0.133291i
$367$	−597.597	+	105.372i	−1.62833	+	0.287118i	−0.911860	−	0.410501i	$-0.865354\pi$
$367$	−597.597	+	105.372i	−1.62833	+	0.287118i	−0.716469	+	0.697619i	$0.754243\pi$
$368$	−56.7912	+	98.3652i	−0.154324	+	0.267297i
$369$	331.247	−	533.962i	0.897689	−	1.44705i
$370$	34.9267	+	110.279i	0.0943965	+	0.298052i
$371$	198.352	+	236.387i	0.534643	+	0.637162i
$372$	−7.47279	+	26.2215i	−0.0200882	+	0.0704880i
$373$	−15.9903	−	2.81952i	−0.0428694	−	0.00755902i	0.152172	−	0.988354i	$-0.451373\pi$
$373$	−15.9903	−	2.81952i	−0.0428694	−	0.00755902i	−0.195042	+	0.980795i	$0.562484\pi$
$374$	−243.634	+	290.351i	−0.651427	+	0.776340i
$375$	−20.8419	+	374.420i	−0.0555785	+	0.998454i
$376$	110.866	+	40.3520i	0.294857	+	0.107319i
$377$	140.520			0.372732
$378$	−178.988	+	113.062i	−0.473514	+	0.299105i
$379$	−202.525			−0.534367			−0.267184	−	0.963646i	$-0.586093\pi$
$379$	−202.525			−0.534367			−0.267184	+	0.963646i	$0.586093\pi$
$380$	45.8670	−	72.2012i	0.120703	−	0.190003i
$381$	371.596	−	26.5916i	0.975317	−	0.0697942i
$382$	460.237	−	548.489i	1.20481	−	1.43584i
$383$	113.044	−	641.106i	0.295155	−	1.67391i	−0.371417	−	0.928466i	$-0.621128\pi$
$383$	113.044	−	641.106i	0.295155	−	1.67391i	0.666572	−	0.745441i	$-0.267761\pi$
$384$	439.600	−	110.364i	1.14479	−	0.287406i
$385$	−73.9252	−	141.565i	−0.192013	−	0.367700i
$386$	160.967	−	92.9344i	0.417013	−	0.240763i
$387$	397.302	+	355.400i	1.02662	+	0.918347i
$388$	18.7115	+	10.8031i	0.0482254	+	0.0278430i
$389$	−127.502	+	22.4820i	−0.327768	+	0.0577943i	−0.335111	−	0.942179i	$-0.608774\pi$
$389$	−127.502	+	22.4820i	−0.327768	+	0.0577943i	0.00734304	+	0.999973i	$0.497663\pi$
$390$	223.976	−	199.322i	0.574297	−	0.511083i
$391$	−115.271	+	41.9553i	−0.294811	+	0.107303i
$392$	−241.384	+	87.8567i	−0.615776	+	0.224124i
$393$	−338.548	+	151.391i	−0.861444	+	0.385219i
$394$	61.3520	+	347.945i	0.155716	+	0.883108i
$395$	29.6589	+	27.1074i	0.0750859	+	0.0686263i
$396$	−7.96049	−	55.3358i	−0.0201022	−	0.139737i
$397$	131.369	−	75.8460i	0.330904	−	0.191048i	−0.325338	−	0.945598i	$-0.605478\pi$
$397$	131.369	−	75.8460i	0.330904	−	0.191048i	0.656243	+	0.754550i	$0.272145\pi$
$398$	−300.017	+	251.744i	−0.753812	+	0.632523i
$399$	−189.539	+	183.632i	−0.475035	+	0.460230i
$400$	261.707	−	375.807i	0.654267	−	0.939519i
$401$	−164.397	+	195.920i	−0.409966	+	0.488579i	−0.931032	−	0.364938i	$-0.881090\pi$
$401$	−164.397	+	195.920i	−0.409966	+	0.488579i	0.521065	+	0.853517i	$0.325535\pi$
$402$	65.4272	−	134.701i	0.162754	−	0.335077i
$403$	−40.7460	+	111.949i	−0.101107	+	0.277788i
$404$			76.0809i			0.188319i
$405$	238.361	−	327.428i	0.588545	−	0.808464i
$406$	119.544			0.294443
$407$	88.5609	+	32.2335i	0.217594	+	0.0791978i
$408$	381.703	+	185.402i	0.935547	+	0.454416i
$409$	−475.249	−	398.781i	−1.16198	−	0.975015i	−0.162047	−	0.986783i	$-0.551809\pi$
$409$	−475.249	−	398.781i	−1.16198	−	0.975015i	−0.999931	+	0.0117684i	$0.996254\pi$
$410$	−288.817	+	699.806i	−0.704431	+	1.70684i
$411$	−397.060	−	409.833i	−0.966084	−	0.997160i
$412$	−15.1352	−	18.0374i	−0.0367358	−	0.0437801i
$413$	111.908	+	193.830i	0.270963	+	0.469322i
$414$	44.9707	−	112.357i	0.108625	−	0.271393i
$415$	305.843	+	279.532i	0.736972	+	0.673571i
$416$	−100.996	+	17.8083i	−0.242779	+	0.0428085i
$417$	−293.708	−	656.803i	−0.704336	−	1.57507i
$418$	−159.428	−	438.024i	−0.381406	−	1.04791i
$419$	52.8741	+	145.270i	0.126191	+	0.346707i	0.986660	−	0.162796i	$-0.0520513\pi$
$419$	52.8741	+	145.270i	0.126191	+	0.346707i	−0.860469	+	0.509504i	$0.829829\pi$
$420$	28.4869	−	25.3512i	0.0678259	−	0.0603601i
$421$	52.5666	+	298.120i	0.124861	+	0.708124i	0.981390	+	0.192025i	$0.0615053\pi$
$421$	52.5666	+	298.120i	0.124861	+	0.708124i	−0.856529	+	0.516099i	$0.827384\pi$
$422$	169.807	−	294.115i	0.402387	−	0.696955i
$423$	−145.366	−	30.4049i	−0.343655	−	0.0718792i
$424$	305.111	+	528.467i	0.719601	+	1.24639i
$425$	477.408	−	129.237i	1.12331	−	0.304086i
$426$	−89.7545	−	357.509i	−0.210691	−	0.839222i
$427$	−259.436	−	45.7455i	−0.607578	−	0.107132i
$428$	−98.8322	−	82.9301i	−0.230916	−	0.193762i
$429$	−17.4356	−	243.648i	−0.0406425	−	0.567945i
$430$	−542.108	−	344.382i	−1.26072	−	0.800889i
$431$			194.130i			0.450418i	0.974311	+	0.225209i	$0.0723064\pi$
$431$			194.130i			0.450418i	−0.974311	+	0.225209i	$0.927694\pi$
$432$	−457.667	+	187.511i	−1.05941	+	0.434053i
$433$			697.839i			1.61164i	0.592162	+	0.805819i	$0.298275\pi$
$433$			697.839i			1.61164i	−0.592162	+	0.805819i	$0.701725\pi$
$434$	−34.6637	+	95.2376i	−0.0798702	+	0.219441i
$435$	−212.533	+	84.4341i	−0.488581	+	0.194101i
$436$	−40.4108	−	33.9087i	−0.0926854	−	0.0777723i
$437$	26.1968	−	148.569i	0.0599469	−	0.339976i
$438$	−732.312	−	208.699i	−1.67194	−	0.476482i
$439$	307.468	−	257.996i	0.700382	−	0.587691i	−0.221500	−	0.975160i	$-0.571095\pi$
$439$	307.468	−	257.996i	0.700382	−	0.587691i	0.921882	+	0.387470i	$0.126651\pi$
$440$	−95.3546	−	301.077i	−0.216715	−	0.684266i
$441$	285.005	−	152.730i	0.646270	−	0.346328i
$442$	−342.462	−	197.720i	−0.774801	−	0.447331i
$443$	−0.222903	−	1.26415i	−0.000503168	−	0.00285361i	0.984555	−	0.175075i	$-0.0560167\pi$
$443$	−0.222903	−	1.26415i	−0.000503168	−	0.00285361i	−0.985058	+	0.172221i	$0.944906\pi$
$444$	−2.31587	+	22.3840i	−0.00521592	+	0.0504144i
$445$	−587.413	+	78.1022i	−1.32003	+	0.175511i
$446$	−8.89104	−	24.4279i	−0.0199351	−	0.0547711i
$447$	77.8298	−	752.263i	0.174116	−	1.68292i
$448$	174.978	−	30.8533i	0.390575	−	0.0688689i
$449$	581.893	+	335.956i	1.29597	+	0.748231i	0.979706	−	0.200439i	$-0.0642367\pi$
$449$	581.893	+	335.956i	1.29597	+	0.748231i	0.316268	+	0.948670i	$0.397570\pi$
$450$	−218.991	+	436.050i	−0.486647	+	0.969000i
$451$	308.395	+	534.156i	0.683803	+	1.18438i
$452$	97.5702	−	81.8711i	0.215863	−	0.181131i
$453$	153.860	−	539.884i	0.339647	−	1.19180i
$454$	−72.7153	+	412.389i	−0.160166	+	0.908345i
$455$	132.059	−	101.602i	0.290239	−	0.223301i
$456$	−432.177	+	292.530i	−0.947756	+	0.641514i
$457$	96.5574	−	265.289i	0.211285	−	0.580502i	−0.788100	−	0.615547i	$-0.788935\pi$
$457$	96.5574	−	265.289i	0.211285	−	0.580502i	0.999386	+	0.0350451i	$0.0111575\pi$
$458$	953.439			2.08174
$459$	−508.814	−	162.584i	−1.10853	−	0.354215i
$460$	−4.69087	+	21.2885i	−0.0101975	+	0.0462794i
$461$	−97.1395	+	266.889i	−0.210715	+	0.578934i	−0.999355	−	0.0359213i	$-0.988563\pi$
$461$	−97.1395	+	266.889i	−0.210715	+	0.578934i	0.788640	+	0.614855i	$0.210786\pi$
$462$	−14.8329	−	207.278i	−0.0321059	−	0.448653i
$463$	462.859	−	551.614i	0.999695	−	1.19139i	0.0182133	−	0.999834i	$-0.494202\pi$
$463$	462.859	−	551.614i	0.999695	−	1.19139i	0.981482	−	0.191556i	$-0.0613534\pi$
$464$	275.036	+	48.4963i	0.592750	+	0.104518i
$465$	−5.63934	−	193.802i	−0.0121276	−	0.416779i
$466$	265.323	−	222.632i	0.569363	−	0.477752i
$467$	−192.068	−	332.672i	−0.411281	−	0.712359i	0.583750	−	0.811934i	$-0.301585\pi$
$467$	−192.068	−	332.672i	−0.411281	−	0.712359i	−0.995030	+	0.0995750i	$0.968252\pi$
$468$	55.4129	−	18.2041i	0.118404	−	0.0388977i
$469$	41.6101	−	72.0708i	0.0887209	−	0.153669i
$470$	178.769	+	7.57517i	0.380361	+	0.0161174i
$471$	216.139	+	156.498i	0.458895	+	0.332268i
$472$	151.377	+	415.905i	0.320714	+	0.881154i
$473$	−491.692	+	178.961i	−1.03952	+	0.378354i
$474$	21.3430	+	47.7281i	0.0450274	+	0.100692i
$475$	−155.919	+	587.936i	−0.328251	+	1.23776i
$476$	−43.5568	−	25.1475i	−0.0915058	−	0.0528309i
$477$	−474.875	−	603.755i	−0.995544	−	1.26573i
$478$	−129.067	+	74.5171i	−0.270015	+	0.155894i
$479$	200.228	+	238.622i	0.418012	+	0.498167i	0.933424	−	0.358775i	$-0.116806\pi$
$479$	200.228	+	238.622i	0.418012	+	0.498167i	−0.515412	+	0.856943i	$0.672361\pi$
$480$	142.053	−	87.6201i	0.295945	−	0.182542i
$481$	−17.0741	+	96.8321i	−0.0354971	+	0.201314i
$482$	−348.328	−	292.282i	−0.722671	−	0.606393i
$483$	29.3845	−	60.4966i	0.0608375	−	0.125252i
$484$	−28.3826	−	10.3304i	−0.0586416	−	0.0213438i
$485$	−150.041	−	33.0612i	−0.309363	−	0.0681673i
$486$	454.228	−	267.195i	0.934625	−	0.549783i
$487$			144.089i			0.295871i	0.988997	+	0.147936i	$0.0472629\pi$
$487$			144.089i			0.295871i	−0.988997	+	0.147936i	$0.952737\pi$
$488$	−489.532	−	178.175i	−1.00314	−	0.365113i
$489$	125.059	−	257.471i	0.255745	−	0.526526i
$490$	−308.767	+	237.556i	−0.630136	+	0.484808i
$491$	135.820	+	23.9487i	0.276618	+	0.0487753i	0.310236	−	0.950659i	$-0.399592\pi$
$491$	135.820	+	23.9487i	0.276618	+	0.0487753i	−0.0336179	+	0.999435i	$0.510703\pi$
$492$	−105.775	+	102.478i	−0.214989	+	0.208289i
$493$	193.879	+	231.056i	0.393263	+	0.468673i
$494$	421.167	−	243.161i	0.852566	−	0.492229i
$495$	172.772	+	358.035i	0.349034	+	0.723303i
$496$	−118.387	+	205.052i	−0.238683	+	0.413411i
$497$	−35.5706	−	201.731i	−0.0715706	−	0.405897i
$498$	220.089	+	492.173i	0.441946	+	0.988300i
$499$	−449.216	+	163.501i	−0.900232	+	0.327658i	−0.750346	−	0.661045i	$-0.770113\pi$
$499$	−449.216	+	163.501i	−0.900232	+	0.327658i	−0.149886	+	0.988703i	$0.547891\pi$
$500$	26.1065	−	83.9258i	0.0522131	−	0.167852i
$501$	164.231	−	226.819i	0.327806	−	0.452732i
$502$	220.815	−	38.9357i	0.439871	−	0.0775611i
$503$	−293.589	+	508.511i	−0.583676	+	1.01096i	0.411363	+	0.911472i	$0.365053\pi$
$503$	−293.589	+	508.511i	−0.583676	+	1.01096i	−0.995039	+	0.0994853i	$0.968280\pi$
$504$	−221.034	+	72.6136i	−0.438559	+	0.144075i
$505$	−163.347	−	515.759i	−0.323459	−	1.02131i
$506$	76.3590	+	91.0011i	0.150907	+	0.179844i
$507$	−244.561	+	61.3983i	−0.482368	+	0.121101i
$508$	−85.9908	−	15.1625i	−0.169273	−	0.0298474i
$509$	−76.4269	+	91.0820i	−0.150151	+	0.178943i	−0.835877	−	0.548917i	$-0.815040\pi$
$509$	−76.4269	+	91.0820i	−0.150151	+	0.178943i	0.685726	+	0.727860i	$0.259485\pi$
$510$	636.769	+	93.2720i	1.24857	+	0.182886i
$511$	−397.649	−	144.733i	−0.778179	−	0.283234i
$512$	320.062			0.625121
$513$	486.037	−	441.941i	0.947441	−	0.861483i
$514$	−233.380			−0.454047
$515$	141.329	+	89.7816i	0.274426	+	0.174333i
$516$	−70.0337	−	103.466i	−0.135724	−	0.200516i
$517$	93.7036	−	111.672i	0.181245	−	0.215999i
$518$	−14.5254	+	82.3775i	−0.0280413	+	0.159030i
$519$	46.0207	−	161.484i	0.0886719	−	0.311144i
$520$	292.068	−	152.518i	0.561669	−	0.293304i
$521$	−617.263	+	356.377i	−1.18477	+	0.684025i	−0.957112	−	0.289717i	$-0.906439\pi$
$521$	−617.263	+	356.377i	−1.18477	+	0.684025i	−0.227654	+	0.973742i	$0.573105\pi$
$522$	−297.424	−	9.41818i	−0.569777	−	0.0180425i
$523$	632.955	+	365.437i	1.21024	+	0.698731i	0.962811	−	0.270175i	$-0.0870816\pi$
$523$	632.955	+	365.437i	1.21024	+	0.698731i	0.247427	+	0.968906i	$0.420415\pi$
$524$	85.6005	−	15.0937i	0.163360	−	0.0288047i
$525$	−138.686	+	233.020i	−0.264163	+	0.443848i
$526$	77.4668	−	28.1956i	0.147275	−	0.0536038i
$527$	−240.294	+	87.4600i	−0.455967	+	0.165958i
$528$	49.9617	−	482.904i	0.0946244	−	0.914591i
$529$	−85.1837	−	483.101i	−0.161028	−	0.913234i
$530$	683.122	+	624.354i	1.28891	+	1.17803i
$531$	−263.154	−	491.063i	−0.495583	−	0.924789i
$532$	53.5671	−	30.9270i	0.100690	−	0.0581334i
$533$	−492.951	+	413.635i	−0.924861	+	0.776050i
$534$	−741.545	−	211.331i	−1.38866	−	0.395750i
$535$	848.045	+	349.996i	1.58513	+	0.654198i
$536$	105.783	−	126.067i	0.197355	−	0.235199i
$537$	84.7460	+	125.202i	0.157814	+	0.233150i
$538$	75.1838	−	206.566i	0.139747	−	0.383951i
$539$			317.394i			0.588857i
$540$	−72.8722	+	60.8292i	−0.134949	+	0.112647i
$541$	−163.171			−0.301610			−0.150805	−	0.988564i	$-0.548187\pi$
$541$	−163.171			−0.301610			−0.150805	+	0.988564i	$0.548187\pi$
$542$	403.996	+	147.043i	0.745381	+	0.271296i
$543$	51.5788	+	720.771i	0.0949885	+	1.32739i
$544$	−168.629	−	141.496i	−0.309979	−	0.260104i
$545$	346.751	+	143.108i	0.636241	+	0.262583i
$546$	210.282	−	52.7923i	0.385131	−	0.0966892i
$547$	−429.435	−	511.781i	−0.785074	−	0.935615i	0.214077	−	0.976817i	$-0.431326\pi$
$547$	−429.435	−	511.781i	−0.785074	−	0.935615i	−0.999151	+	0.0412022i	$0.986881\pi$
$548$	66.8723	+	115.826i	0.122030	+	0.211362i
$549$	641.868	+	134.254i	1.16916	+	0.244542i
$550$	−275.730	−	391.638i	−0.501327	−	0.712069i
$551$	−365.306	+	64.4133i	−0.662987	+	0.116903i
$552$	77.9992	−	107.725i	0.141303	−	0.195153i
$553$	9.93740	+	27.3028i	0.0179700	+	0.0493721i
$554$	−280.172	−	769.765i	−0.505725	−	1.38947i
$555$	−32.3593	−	156.715i	−0.0583051	−	0.282370i
$556$	29.2827	+	166.070i	0.0526667	+	0.298688i
$557$	−429.574	+	744.043i	−0.771227	+	1.33581i	0.165663	+	0.986182i	$0.447024\pi$
$557$	−429.574	+	744.043i	−0.771227	+	1.33581i	−0.936891	+	0.349623i	$0.886310\pi$
$558$	93.7459	−	234.219i	0.168003	−	0.419747i
$559$	−272.954	−	472.770i	−0.488289	−	0.845742i
$560$	293.540	−	153.287i	0.524178	−	0.273726i
$561$	376.572	−	364.837i	0.671252	−	0.650333i
$562$	−121.988	−	21.5098i	−0.217061	−	0.0382736i
$563$	−51.6792	−	43.3640i	−0.0917926	−	0.0770232i	0.595737	−	0.803180i	$-0.296860\pi$
$563$	−51.6792	−	43.3640i	−0.0917926	−	0.0770232i	−0.687529	+	0.726157i	$0.741305\pi$
$564$	31.3102	+	15.2080i	0.0555145	+	0.0269646i
$565$	−485.658	+	764.496i	−0.859572	+	1.35309i
$566$		−	1103.08i		−	1.94890i
$567$	262.382	−	130.091i	0.462754	−	0.229437i
$568$		−	405.078i		−	0.713165i
$569$	16.2220	−	44.5695i	0.0285096	−	0.0783295i	−0.924621	−	0.380888i	$-0.875618\pi$
$569$	16.2220	−	44.5695i	0.0285096	−	0.0783295i	0.953131	+	0.302558i	$0.0978407\pi$
$570$	−490.896	+	620.841i	−0.861222	+	1.08920i
$571$	595.231	+	499.458i	1.04244	+	0.874707i	0.992278	−	0.124034i	$-0.0395832\pi$
$571$	595.231	+	499.458i	1.04244	+	0.874707i	0.0501575	+	0.998741i	$0.484028\pi$
$572$	−9.94176	+	56.3825i	−0.0173807	+	0.0985708i
$573$	−711.365	+	689.196i	−1.24148	+	1.20279i
$574$	−419.366	+	351.890i	−0.730602	+	0.613048i
$575$	−13.9070	−	154.388i	−0.0241861	−	0.268501i
$576$	−437.773	+	62.9770i	−0.760022	+	0.109335i
$577$	675.220	+	389.839i	1.17023	+	0.675630i	0.953733	−	0.300654i	$-0.0972050\pi$
$577$	675.220	+	389.839i	1.17023	+	0.675630i	0.216492	+	0.976284i	$0.430538\pi$
$578$	−38.5595	−	218.682i	−0.0667120	−	0.378342i
$579$	−234.719	+	104.961i	−0.405388	+	0.181280i
$580$	53.1328	−	7.06452i	0.0916083	−	0.0121802i
$581$	102.475	+	281.547i	0.176376	+	0.484590i
$582$	−161.927	−	117.245i	−0.278226	−	0.201453i
$583$	742.531	−	130.928i	1.27364	−	0.224577i
$584$	−724.707	−	418.410i	−1.24094	−	0.716455i
$585$	−336.564	+	242.380i	−0.575324	+	0.414325i
$586$	−228.341	−	395.498i	−0.389660	−	0.674912i
$587$	−80.5262	+	67.5695i	−0.137183	+	0.115110i	−0.708797	−	0.705412i	$-0.750762\pi$
$587$	−80.5262	+	67.5695i	−0.137183	+	0.115110i	0.571614	+	0.820522i	$0.306317\pi$
$588$	−73.5054	+	18.4539i	−0.125009	+	0.0313842i
$589$	54.6098	−	309.708i	0.0927161	−	0.525819i
$590$	409.308	+	532.005i	0.693743	+	0.901703i
$591$	−34.8860	−	487.502i	−0.0590287	−	0.824877i
$592$	−66.8374	+	183.634i	−0.112901	+	0.310193i
$593$	56.8607			0.0958864			0.0479432	−	0.998850i	$-0.484733\pi$
$593$	56.8607			0.0958864			0.0479432	+	0.998850i	$0.484733\pi$
$594$	20.5739	+	516.873i	0.0346361	+	0.870156i
$595$	349.267	+	76.9601i	0.587004	+	0.129345i
$596$	−60.6253	+	166.567i	−0.101720	+	0.279474i
$597$	448.659	−	303.687i	0.751523	−	0.508688i
$598$	−79.6658	+	94.9420i	−0.133220	+	0.158766i
$599$	356.770	+	62.9081i	0.595609	+	0.105022i	0.463323	−	0.886190i	$-0.346657\pi$
$599$	356.770	+	62.9081i	0.595609	+	0.105022i	0.132286	+	0.991212i	$0.457768\pi$
$600$	−350.102	+	406.174i	−0.583503	+	0.676957i
$601$	−189.072	+	158.650i	−0.314596	+	0.263977i	−0.786389	−	0.617732i	$-0.788052\pi$
$601$	−189.072	+	158.650i	−0.314596	+	0.263977i	0.471792	+	0.881710i	$0.343607\pi$
$602$	−232.209	−	402.197i	−0.385729	−	0.668102i
$603$	−109.203	+	176.033i	−0.181100	+	0.291929i
$604$	−65.7882	+	113.948i	−0.108921	+	0.188656i
$605$	214.587	+	9.09292i	0.354690	+	0.0150296i
$606$	72.4458	−	700.224i	0.119548	−	1.15549i
$607$	237.324	+	652.041i	0.390978	+	1.07420i	0.966556	+	0.256456i	$0.0825549\pi$
$607$	237.324	+	652.041i	0.390978	+	1.07420i	−0.575578	+	0.817747i	$0.695223\pi$
$608$	254.394	−	92.5917i	0.418411	−	0.152289i
$609$	−164.491	−	17.0184i	−0.270101	−	0.0279448i
$610$	−789.361	−	33.4484i	−1.29403	−	0.0548334i
$611$	131.714	+	76.0450i	0.215571	+	0.124460i
$612$	106.387	+	65.9982i	0.173836	+	0.107840i
$613$	−820.457	+	473.691i	−1.33843	+	0.772742i	−0.986574	−	0.163312i	$-0.947782\pi$
$613$	−820.457	+	473.691i	−1.33843	+	0.772742i	−0.351855	+	0.936055i	$0.614449\pi$
$614$	74.8651	+	89.2207i	0.121930	+	0.145311i
$615$	497.034	−	921.810i	0.808186	−	1.49888i
$616$	39.6562	−	224.902i	0.0643770	−	0.365100i
$617$	752.232	+	631.198i	1.21918	+	1.02301i	0.998867	+	0.0475809i	$0.0151512\pi$
$617$	752.232	+	631.198i	1.21918	+	1.02301i	0.220310	+	0.975430i	$0.429293\pi$
$618$	122.124	+	180.422i	0.197611	+	0.291946i
$619$	25.3213	+	9.21619i	0.0409067	+	0.0148888i	0.362392	−	0.932026i	$-0.381960\pi$
$619$	25.3213	+	9.21619i	0.0409067	+	0.0148888i	−0.321486	+	0.946914i	$0.604182\pi$
$620$	−9.77859	+	44.3781i	−0.0157719	+	0.0715775i
$621$	−77.8745	+	148.200i	−0.125402	+	0.238647i
$622$		−	686.673i		−	1.10398i
$623$	−402.663	−	146.557i	−0.646329	−	0.235245i
$624$	505.214	−	36.1534i	0.809638	−	0.0579382i
$625$	3.21146	+	624.992i	0.00513834	+	0.999987i
$626$	−217.481	−	38.3478i	−0.347414	−	0.0612584i
$627$	157.013	+	625.413i	0.250420	+	0.997470i
$628$	−40.2024	−	47.9114i	−0.0640166	−	0.0762920i
$629$	−182.778	+	105.527i	−0.290584	+	0.167769i
$630$	−286.324	+	206.199i	−0.454482	+	0.327300i
$631$	−127.491	+	220.821i	−0.202046	+	0.349955i	−0.949188	−	0.314711i	$-0.898093\pi$
$631$	−127.491	+	220.821i	−0.202046	+	0.349955i	0.747141	+	0.664665i	$0.231426\pi$
$632$	9.97721	+	56.5835i	0.0157867	+	0.0895309i
$633$	−275.524	+	380.525i	−0.435266	+	0.601146i
$634$	1036.90	−	377.402i	1.63550	−	0.595272i
$635$	615.493	−	81.8357i	0.969281	−	0.128875i
$636$	73.4940	+	164.351i	0.115557	+	0.258413i
$637$	−326.108	+	57.5017i	−0.511944	+	0.0902695i
$638$	146.046	−	252.959i	0.228912	−	0.396488i
$639$	72.6059	+	504.706i	0.113624	+	0.789837i
$640$	720.148	−	228.079i	1.12523	−	0.356374i
$641$	−425.457	−	507.040i	−0.663739	−	0.791014i	0.324178	−	0.945996i	$-0.394912\pi$
$641$	−425.457	−	507.040i	−0.663739	−	0.791014i	−0.987917	+	0.154983i	$0.950468\pi$
$642$	830.652	+	857.372i	1.29385	+	1.33547i
$643$	−110.331	−	19.4543i	−0.171587	−	0.0302555i	0.0871943	−	0.996191i	$-0.472210\pi$
$643$	−110.331	−	19.4543i	−0.171587	−	0.0302555i	−0.258782	+	0.965936i	$0.583321\pi$
$644$	−10.1325	+	12.0754i	−0.0157336	+	0.0187506i
$645$	696.908	+	551.042i	1.08048	+	0.854329i
$646$	980.922	+	357.027i	1.51846	+	0.552673i
$647$	10.7396			0.0165990			0.00829952	−	0.999966i	$-0.497358\pi$
$647$	10.7396			0.0165990			0.00829952	+	0.999966i	$0.497358\pi$
$648$	555.650	−	163.248i	0.857485	−	0.251925i
$649$	546.869			0.842633
$650$	352.437	−	354.253i	0.542211	−	0.545004i
$651$	61.2550	−	126.111i	0.0940937	−	0.193719i
$652$	−43.1234	+	51.3924i	−0.0661401	+	0.0788227i
$653$	135.331	−	767.498i	0.207244	−	1.17534i	−0.686624	−	0.727013i	$-0.740908\pi$
$653$	135.331	−	767.498i	0.207244	−	1.17534i	0.893869	−	0.448329i	$-0.147981\pi$
$654$	339.640	+	350.565i	0.519327	+	0.536032i
$655$	−547.887	+	286.107i	−0.836469	+	0.436805i
$656$	−1107.59	+	639.469i	−1.68840	+	0.974801i
$657$	977.943	+	391.421i	1.48850	+	0.595770i
$658$	112.052	+	64.6934i	0.170292	+	0.0983182i
$659$	735.143	−	129.626i	1.11554	−	0.196700i	0.414660	−	0.909976i	$-0.363901\pi$
$659$	735.143	−	129.626i	1.11554	−	0.196700i	0.700883	+	0.713276i	$0.252789\pi$
$660$	−18.8419	−	91.2507i	−0.0285483	−	0.138259i
$661$	509.948	−	185.606i	0.771480	−	0.280796i	0.0738649	−	0.997268i	$-0.476467\pi$
$661$	509.948	−	185.606i	0.771480	−	0.280796i	0.697615	+	0.716472i	$0.254244\pi$
$662$	471.586	−	171.643i	0.712365	−	0.259280i
$663$	443.076	+	320.815i	0.668290	+	0.483883i
$664$	102.885	+	583.490i	0.154947	+	0.878750i
$665$	−296.735	+	324.666i	−0.446219	+	0.488220i
$666$	42.6290	−	203.810i	0.0640075	−	0.306021i
$667$	81.8684	−	47.2667i	0.122741	−	0.0708647i
$668$	−50.2786	+	42.1888i	−0.0752674	+	0.0631568i
$669$	8.75639	+	34.8783i	0.0130888	+	0.0521350i
$670$	95.2152	−	230.708i	0.142112	−	0.344340i
$671$	−413.750	+	493.089i	−0.616618	+	0.734856i
$672$	120.382	−	8.61459i	0.179140	−	0.0128193i
$673$	256.931	−	705.911i	0.381769	−	1.04890i	−0.588842	−	0.808248i	$-0.700416\pi$
$673$	256.931	−	705.911i	0.381769	−	1.04890i	0.970611	−	0.240654i	$-0.0773619\pi$
$674$			366.997i			0.544506i
$675$	363.406	−	568.824i	0.538379	−	0.842703i
$676$	59.0990			0.0874245
$677$	89.4060	+	32.5411i	0.132062	+	0.0480667i	0.407206	−	0.913336i	$-0.366503\pi$
$677$	89.4060	+	32.5411i	0.132062	+	0.0480667i	−0.275144	+	0.961403i	$0.588725\pi$
$678$	−975.964	+	660.607i	−1.43947	+	0.974346i
$679$	−85.1072	−	71.4135i	−0.125342	−	0.105174i
$680$	653.757	+	269.812i	0.961408	+	0.396782i
$681$	158.764	−	557.091i	0.233133	−	0.818048i
$682$	159.178	+	189.701i	0.233399	+	0.278154i
$683$	−207.041	−	358.606i	−0.303135	−	0.525045i	0.673709	−	0.738996i	$-0.264700\pi$
$683$	−207.041	−	358.606i	−0.303135	−	0.525045i	−0.976844	+	0.213951i	$0.931367\pi$
$684$	−135.711	+	72.7256i	−0.198407	+	0.106324i
$685$	−702.014	−	641.620i	−1.02484	−	0.936672i
$686$	−655.800	+	115.635i	−0.955977	+	0.168565i
$687$	−1311.92	−	135.733i	−1.90964	−	0.197573i
$688$	−371.083	−	1019.54i	−0.539365	−	1.48189i
$689$	269.046	+	739.197i	0.390487	+	1.07286i
$690$	63.4446	−	191.466i	0.0919488	−	0.277487i
$691$	−36.2485	−	205.575i	−0.0524580	−	0.297504i	0.947280	−	0.320408i	$-0.103820\pi$
$691$	−36.2485	−	205.575i	−0.0524580	−	0.297504i	−0.999738	+	0.0229038i	$0.992709\pi$
$692$	−19.6777	+	34.0829i	−0.0284360	+	0.0492527i
$693$	−9.09836	+	287.324i	−0.0131289	+	0.414609i
$694$	9.27863	+	16.0711i	0.0133698	+	0.0231572i
$695$	−555.066	−	1062.94i	−0.798656	−	1.52940i
$696$	−314.496	−	89.6273i	−0.451863	−	0.128775i
$697$	−1360.27	−	239.853i	−1.95161	−	0.344121i
$698$	−702.103	−	589.134i	−1.00588	−	0.844032i
$699$	−396.776	+	268.568i	−0.567634	+	0.384218i
$700$	44.8255	−	45.0564i	0.0640364	−	0.0643663i
$701$			128.633i			0.183499i	0.995782	+	0.0917494i	$0.0292459\pi$
$701$			128.633i			0.183499i	−0.995782	+	0.0917494i	$0.970754\pi$
$702$	−527.337	+	114.780i	−0.751192	+	0.163504i
$703$		−	259.558i		−	0.369215i
$704$	148.483	−	407.953i	0.210913	−	0.579478i
$705$	−244.907	−	35.8732i	−0.347385	−	0.0508840i
$706$	617.544	+	518.181i	0.874708	+	0.733967i
$707$	67.9331	−	385.268i	0.0960864	−	0.544933i
$708$	31.7961	+	126.650i	0.0449097	+	0.178884i
$709$	−30.2527	+	25.3851i	−0.0426696	+	0.0358040i	−0.663873	−	0.747845i	$-0.731088\pi$
$709$	−30.2527	+	25.3851i	−0.0426696	+	0.0358040i	0.621203	+	0.783649i	$0.286644\pi$
$710$	−185.488	−	585.667i	−0.261250	−	0.824883i
$711$	−22.5731	−	68.7119i	−0.0317484	−	0.0966412i
$712$	−733.845	−	423.685i	−1.03068	−	0.595064i
$713$	13.9172	+	78.9282i	0.0195192	+	0.110699i
$714$	376.936	+	272.925i	0.527922	+	0.382248i
$715$	−53.6581	−	403.567i	−0.0750464	−	0.564430i
$716$	−12.1195	−	33.2981i	−0.0169267	−	0.0465057i
$717$	188.204	−	84.1606i	0.262488	−	0.117379i
$718$	1518.61	−	267.771i	2.11505	−	0.372941i
$719$	−1187.82	−	685.786i	−1.65204	−	0.953806i	−0.976232	−	0.216728i	$-0.930461\pi$
$719$	−1187.82	−	685.786i	−1.65204	−	0.953806i	−0.675808	−	0.737077i	$-0.736205\pi$
$720$	−742.399	+	358.249i	−1.03111	+	0.497568i
$721$	60.5376	+	104.854i	0.0839633	+	0.145429i
$722$	−383.705	+	321.967i	−0.531448	+	0.445937i
$723$	437.686	+	451.765i	0.605374	+	0.624848i
$724$	29.4101	−	166.793i	0.0406217	−	0.230377i
$725$	−345.025	+	161.968i	−0.475896	+	0.223404i
$726$	251.387	+	122.104i	0.346263	+	0.168188i
$727$	−290.996	+	799.505i	−0.400270	+	1.09973i	0.561882	+	0.827217i	$0.310078\pi$
$727$	−290.996	+	799.505i	−0.400270	+	1.09973i	−0.962152	+	0.272515i	$0.912145\pi$
$728$	238.261			0.327282
$729$	−663.051	+	302.993i	−0.909535	+	0.415628i
$730$	−1239.38	−	273.095i	−1.69779	−	0.374103i
$731$	400.770	−	1101.11i	0.548249	−	1.50630i
$732$	−138.251	−	67.1515i	−0.188867	−	0.0917370i
$733$	−440.220	+	524.633i	−0.600573	+	0.715735i	−0.977601	−	0.210467i	$-0.932501\pi$
$733$	−440.220	+	524.633i	−0.600573	+	0.715735i	0.377028	+	0.926202i	$0.376946\pi$
$734$	−1295.99	−	228.518i	−1.76566	−	0.311333i
$735$	458.679	−	282.918i	0.624053	−	0.384923i
$736$	−52.8512	+	44.3474i	−0.0718087	+	0.0602546i
$737$	−101.670	−	176.097i	−0.137951	−	0.238938i
$738$	1071.10	−	842.457i	1.45135	−	1.14154i
$739$	439.434	−	761.121i	0.594633	−	1.02993i	−0.398966	−	0.916966i	$-0.630631\pi$
$739$	439.434	−	761.121i	0.594633	−	1.02993i	0.993599	−	0.112968i	$-0.0360359\pi$
$740$	−1.58784	+	37.4721i	−0.00214573	+	0.0506380i
$741$	−614.139	+	274.629i	−0.828797	+	0.370620i
$742$	228.884	+	628.854i	0.308469	+	0.847512i
$743$	403.184	−	146.747i	0.542643	−	0.197506i	−0.0561318	−	0.998423i	$-0.517877\pi$
$743$	403.184	−	146.747i	0.542643	−	0.197506i	0.598775	+	0.800918i	$0.295654\pi$
$744$	162.597	−	224.562i	0.218544	−	0.301831i
$745$	53.3630	−	1259.33i	0.0716282	−	1.69038i
$746$	−30.4950	−	17.6063i	−0.0408780	−	0.0236009i
$747$	−232.774	−	708.558i	−0.311612	−	0.948538i
$748$	−106.426	+	61.4452i	−0.142281	+	0.0821459i
$749$	426.430	+	508.199i	0.569332	+	0.678503i
$750$	−320.192	+	747.567i	−0.426923	+	0.996756i
$751$	−75.6930	+	429.277i	−0.100790	+	0.571607i	0.892029	+	0.451978i	$0.149281\pi$
$751$	−75.6930	+	429.277i	−0.100790	+	0.571607i	−0.992819	+	0.119629i	$0.961830\pi$
$752$	231.555	+	194.298i	0.307919	+	0.258375i
$753$	−309.382	+	22.1396i	−0.410866	+	0.0294018i
$754$	286.364	+	104.228i	0.379793	+	0.138233i
$755$	201.335	−	913.715i	0.266668	−	1.21022i
$756$	−67.0705	+	14.5985i	−0.0887175	+	0.0193102i
$757$		−	387.406i		−	0.511765i	−0.966708	−	0.255883i	$-0.917634\pi$
$757$		−	387.406i		−	0.511765i	0.966708	−	0.255883i	$-0.0823660\pi$
$758$	−412.723	−	150.219i	−0.544490	−	0.198178i
$759$	−92.1142	−	136.087i	−0.121363	−	0.179298i
$760$	−689.368	+	530.379i	−0.907063	+	0.697867i
$761$	−819.711	−	144.537i	−1.07715	−	0.189931i	−0.393195	−	0.919455i	$-0.628630\pi$
$761$	−819.711	−	144.537i	−1.07715	−	0.189931i	−0.683955	+	0.729524i	$0.739741\pi$
$762$	776.993	+	221.433i	1.01968	+	0.290594i
$763$	174.360	+	207.794i	0.228519	+	0.272338i
$764$	201.045	−	116.073i	0.263148	−	0.151928i
$765$	−862.909	−	218.992i	−1.12799	−	0.286265i
$766$	705.899	−	1222.65i	0.921539	−	1.59615i
$767$	99.0753	+	561.884i	0.129172	+	0.732573i
$768$	391.139	+	40.4676i	0.509296	+	0.0526922i
$769$	−527.601	+	192.031i	−0.686087	+	0.249715i	−0.661459	−	0.749981i	$-0.730062\pi$
$769$	−527.601	+	192.031i	−0.686087	+	0.249715i	−0.0246284	+	0.999697i	$0.507840\pi$
$770$	−45.6484	−	343.325i	−0.0592836	−	0.445877i
$771$	321.129	+	33.2243i	0.416509	+	0.0430924i
$772$	59.3480	−	10.4646i	0.0768756	−	0.0135552i
$773$	−189.771	+	328.693i	−0.245499	+	0.425217i	−0.962272	−	0.272090i	$-0.912285\pi$
$773$	−189.771	+	328.693i	−0.245499	+	0.425217i	0.716773	+	0.697307i	$0.245618\pi$
$774$	546.045	+	1018.96i	0.705485	+	1.31648i
$775$	−28.9905	−	321.838i	−0.0374071	−	0.415274i
$776$	−141.220	−	168.300i	−0.181985	−	0.216881i
$777$	31.7141	−	111.283i	0.0408161	−	0.143221i
$778$	−276.509	−	48.7560i	−0.355410	−	0.0626684i
$779$	1091.90	−	1301.28i	1.40167	−	1.67045i
$780$	90.3426	−	35.8909i	0.115824	−	0.0460140i
$781$	−470.326	−	171.185i	−0.602210	−	0.219187i
$782$	−266.029			−0.340191
$783$	407.911	+	55.3009i	0.520959	+	0.0706269i
$784$	−658.128			−0.839449
$785$	375.403	+	238.480i	0.478220	+	0.303797i
$786$	−802.212	+	57.4068i	−1.02063	+	0.0730366i
$787$	646.804	−	770.831i	0.821860	−	0.979455i	−0.178130	−	0.984007i	$-0.557005\pi$
$787$	646.804	−	770.831i	0.821860	−	0.979455i	0.999990	+	0.00455231i	$0.00144905\pi$
$788$	−19.8919	+	112.813i	−0.0252436	+	0.143163i
$789$	−110.608	+	27.7686i	−0.140187	+	0.0351947i
$790$	40.3352	+	77.2407i	0.0510572	+	0.0977730i
$791$	−567.190	+	327.468i	−0.717055	+	0.413992i
$792$	−116.383	+	556.428i	−0.146948	+	0.702560i
$793$	−581.585	−	335.778i	−0.733399	−	0.423428i
$794$	323.972	−	57.1251i	0.408026	−	0.0719459i
$795$	−851.086	−	956.355i	−1.07055	−	1.20296i
$796$	−119.323	+	43.4302i	−0.149904	+	0.0545605i
$797$	11.4218	−	4.15721i	0.0143310	−	0.00521607i	−0.334845	−	0.942273i	$-0.608684\pi$
$797$	11.4218	−	4.15721i	0.0143310	−	0.00521607i	0.349176	+	0.937057i	$0.386462\pi$
$798$	−522.464	+	233.634i	−0.654716	+	0.292775i
$799$	56.6886	+	321.497i	0.0709494	+	0.402374i
$800$	227.454	−	160.137i	0.284317	−	0.200171i
$801$	990.274	+	396.356i	1.23630	+	0.494827i
$802$	−480.341	+	277.325i	−0.598929	+	0.345792i
$803$	−792.066	+	664.622i	−0.986383	+	0.827674i
$804$	34.8711	−	33.7844i	0.0433721	−	0.0420204i
$805$	42.7628	−	103.615i	0.0531215	−	0.128714i
$806$	−166.071	+	197.916i	−0.206044	+	0.245553i
$807$	−132.859	+	273.529i	−0.164633	+	0.338946i
$808$	264.594	−	726.966i	0.327468	−	0.899711i
$809$			1078.95i			1.33368i	0.745199	+	0.666842i	$0.232354\pi$
$809$			1078.95i			1.33368i	−0.745199	+	0.666842i	$0.767646\pi$
$810$	728.615	−	490.462i	0.899525	−	0.605508i
$811$	1043.57			1.28677			0.643386	−	0.765542i	$-0.277529\pi$
$811$	1043.57			1.28677			0.643386	+	0.765542i	$0.277529\pi$
$812$	36.4218	+	13.2564i	0.0448544	+	0.0163257i
$813$	−534.962	−	259.843i	−0.658010	−	0.319610i
$814$	156.568	+	131.376i	0.192344	+	0.161396i
$815$	181.997	−	440.981i	0.223309	−	0.541080i
$816$	756.502	+	780.837i	0.927086	+	0.956908i
$817$	926.304	+	1103.93i	1.13379	+	1.35120i
$818$	−672.715	−	1165.18i	−0.822390	−	1.42442i
$819$	−296.861	+	42.7058i	−0.362468	+	0.0521438i
$820$	−165.597	+	181.185i	−0.201948	+	0.220957i
$821$	381.096	−	67.1976i	0.464186	−	0.0818484i	0.0633359	−	0.997992i	$-0.479826\pi$
$821$	381.096	−	67.1976i	0.464186	−	0.0818484i	0.400850	+	0.916144i	$0.368715\pi$
$822$	−505.179	−	1129.70i	−0.614573	−	1.37434i
$823$	−338.120	−	928.977i	−0.410838	−	1.12877i	−0.956746	−	0.290924i	$-0.906037\pi$
$823$	−338.120	−	928.977i	−0.410838	−	1.12877i	0.545908	−	0.837845i	$-0.316185\pi$
$824$	81.8887	+	224.987i	0.0993795	+	0.273043i
$825$	323.648	+	578.143i	0.392300	+	0.700780i
$826$	84.2859	+	478.009i	0.102041	+	0.578703i
$827$	−24.4367	+	42.3257i	−0.0295486	+	0.0511798i	−0.880422	−	0.474192i	$-0.842740\pi$
$827$	−24.4367	+	42.3257i	−0.0295486	+	0.0511798i	0.850873	+	0.525372i	$0.176074\pi$
$828$	26.1608	−	29.2452i	0.0315952	−	0.0353202i
$829$	−546.065	−	945.813i	−0.658704	−	1.14091i	−0.980952	−	0.194253i	$-0.937772\pi$
$829$	−546.065	−	945.813i	−0.658704	−	1.14091i	0.322248	−	0.946655i	$-0.395562\pi$
$830$	415.937	+	796.507i	0.501129	+	0.959647i
$831$	275.929	+	1099.08i	0.332044	+	1.32259i
$832$	446.054	+	78.6513i	0.536122	+	0.0945328i
$833$	−544.489	−	456.880i	−0.653648	−	0.548476i
$834$	−111.373	−	1556.34i	−0.133540	−	1.86612i
$835$	250.263	−	393.951i	0.299717	−	0.471797i
$836$		−	151.133i		−	0.180781i
$837$	−162.337	+	308.937i	−0.193951	+	0.369100i
$838$			335.263i			0.400075i
$839$	34.5885	−	95.0311i	0.0412259	−	0.113267i	−0.917372	−	0.398032i	$-0.869693\pi$
$839$	34.5885	−	95.0311i	0.0412259	−	0.113267i	0.958597	+	0.284765i	$0.0919155\pi$
$840$	−360.363	+	143.164i	−0.429004	+	0.170433i
$841$	466.183	+	391.174i	0.554320	+	0.465130i
$842$	−114.000	+	646.525i	−0.135392	+	0.767844i
$843$	164.792	+	46.9636i	0.195483	+	0.0557101i
$844$	84.3506	−	70.7785i	0.0999414	−	0.0838608i
$845$	−400.637	+	126.886i	−0.474127	+	0.150161i
$846$	−273.688	−	169.784i	−0.323508	−	0.200691i
$847$	134.503	+	77.6553i	0.158799	+	0.0916827i
$848$	271.485	+	1539.67i	0.320147	+	1.81564i
$849$	−157.035	+	1517.82i	−0.184965	+	1.78778i
$850$	1068.76	+	90.7382i	1.25737	+	0.106751i
$851$	22.6239	+	62.1586i	0.0265850	+	0.0730418i
$852$	12.2990	−	118.876i	0.0144355	−	0.139526i
$853$	−490.805	+	86.5422i	−0.575387	+	0.101456i	−0.453767	−	0.891120i	$-0.649920\pi$
$853$	−490.805	+	86.5422i	−0.575387	+	0.101456i	−0.121620	+	0.992577i	$0.538809\pi$
$854$	−494.769	−	285.655i	−0.579355	−	0.334491i
$855$	763.852	−	784.387i	0.893394	−	0.917412i
$856$	655.945	+	1136.13i	0.766291	+	1.32725i
$857$	599.546	−	503.079i	0.699587	−	0.587024i	−0.222069	−	0.975031i	$-0.571281\pi$
$857$	599.546	−	503.079i	0.699587	−	0.587024i	0.921656	+	0.388007i	$0.126837\pi$
$858$	145.189	−	509.460i	0.169218	−	0.593776i
$859$	−105.854	+	600.327i	−0.123229	+	0.698867i	0.859115	+	0.511783i	$0.171015\pi$
$859$	−105.854	+	600.327i	−0.123229	+	0.698867i	−0.982344	+	0.187084i	$0.940096\pi$
$860$	−126.976	−	165.039i	−0.147647	−	0.191906i
$861$	627.138	−	424.495i	0.728384	−	0.493026i
$862$	−143.992	+	395.615i	−0.167044	+	0.458950i
$863$	−72.8410			−0.0844044			−0.0422022	−	0.999109i	$-0.513437\pi$
$863$	−72.8410			−0.0844044			−0.0422022	+	0.999109i	$0.513437\pi$
$864$	−300.187	+	11.9488i	−0.347439	+	0.0138296i
$865$	60.2207	−	273.299i	0.0696194	−	0.315953i
$866$	−517.608	+	1422.12i	−0.597700	+	1.64217i
$867$	21.9257	+	306.394i	0.0252892	+	0.353395i
$868$	−21.1221	+	25.1724i	−0.0243343	+	0.0290004i
$869$	69.9142	+	12.3278i	0.0804536	+	0.0141861i
$870$	−495.744	+	14.4254i	−0.569821	+	0.0165809i
$871$	162.513	−	136.364i	0.186582	−	0.156561i
$872$	268.205	+	464.544i	0.307574	+	0.532734i
$873$	206.119	+	184.381i	0.236105	+	0.211204i
$874$	163.584	−	283.336i	0.187167	−	0.324184i
$875$	−207.139	+	401.683i	−0.236731	+	0.459066i
$876$	−199.972	−	144.792i	−0.228279	−	0.165288i
$877$	544.678	+	1496.49i	0.621070	+	1.70638i	0.704353	+	0.709849i	$0.251237\pi$
$877$	544.678	+	1496.49i	0.621070	+	1.70638i	−0.0832836	+	0.996526i	$0.526541\pi$
$878$	817.948	−	297.709i	0.931603	−	0.339076i
$879$	257.891	+	576.708i	0.293392	+	0.656096i
$880$	34.2556	−	808.410i	0.0389268	−	0.918648i
$881$	597.963	+	345.234i	0.678732	+	0.391866i	0.799377	−	0.600830i	$-0.205163\pi$
$881$	597.963	+	345.234i	0.678732	+	0.391866i	−0.120645	+	0.992696i	$0.538496\pi$
$882$	694.092	−	99.8506i	0.786953	−	0.113209i
$883$	858.918	−	495.896i	0.972727	−	0.561604i	0.0726604	−	0.997357i	$-0.476851\pi$
$883$	858.918	−	495.896i	0.972727	−	0.561604i	0.900066	+	0.435753i	$0.143518\pi$
$884$	−82.4132	−	98.2163i	−0.0932276	−	0.111104i
$885$	−487.468	−	790.303i	−0.550811	−	0.892998i
$886$	0.483404	−	2.74152i	0.000545603	−	0.00309427i
$887$	861.700	+	723.052i	0.971477	+	0.815166i	0.982782	−	0.184770i	$-0.0591542\pi$
$887$	861.700	+	723.052i	0.971477	+	0.815166i	−0.0113051	+	0.999936i	$0.503599\pi$
$888$	99.9755	−	205.829i	0.112585	−	0.231789i
$889$	421.912	+	153.563i	0.474591	+	0.172737i
$890$	−1255.01	−	276.538i	−1.41013	−	0.310717i
$891$	45.2732	−	714.141i	0.0508117	−	0.801505i
$892$		−	8.42847i		−	0.00944895i
$893$	−377.271	−	137.315i	−0.422476	−	0.153769i
$894$	716.584	−	1475.30i	0.801548	−	1.65022i
$895$	153.651	+	199.710i	0.171677	+	0.223139i
$896$	537.944	+	94.8540i	0.600384	+	0.105864i
$897$	123.135	−	119.298i	0.137275	−	0.132997i
$898$	936.642	+	1116.25i	1.04303	+	1.24304i
$899$	170.663	−	98.5322i	0.189836	−	0.109602i
$900$	−115.075	+	108.568i	−0.127861	+	0.120631i
$901$	−844.247	+	1462.28i	−0.937011	+	1.62295i
$902$	232.275	+	1317.30i	0.257511	+	1.46042i
$903$	262.260	+	586.477i	0.290431	+	0.649476i
$904$	−1217.03	+	442.963i	−1.34627	+	0.490003i
$905$	158.734	+	1193.85i	0.175396	+	1.31917i
$906$	713.997	−	986.100i	0.788076	−	1.08841i
$907$	784.120	−	138.261i	0.864520	−	0.152438i	0.276233	−	0.961091i	$-0.410914\pi$
$907$	784.120	−	138.261i	0.864520	−	0.152438i	0.588287	+	0.808652i	$0.299803\pi$
$908$	−67.8849	+	117.580i	−0.0747631	+	0.129493i
$909$	−199.370	+	953.188i	−0.219328	+	1.04861i
$910$	344.481	−	109.101i	0.378551	−	0.119891i
$911$	−254.988	−	303.883i	−0.279899	−	0.333571i	0.607718	−	0.794153i	$-0.292085\pi$
$911$	−254.988	−	303.883i	−0.279899	−	0.333571i	−0.887617	+	0.460582i	$0.847641\pi$
$912$	−1296.82	+	325.573i	−1.42195	+	0.356988i
$913$	720.956	+	127.124i	0.789656	+	0.139238i
$914$	393.546	−	469.010i	0.430575	−	0.513140i
$915$	1081.39	+	158.399i	1.18185	+	0.173114i
$916$	290.487	+	105.729i	0.317125	+	0.115424i
$917$	−446.951			−0.487406
$918$	−916.310	−	708.731i	−0.998159	−	0.772038i
$919$	1270.39			1.38236			0.691179	−	0.722684i	$-0.257092\pi$
$919$	1270.39			1.38236			0.691179	+	0.722684i	$0.257092\pi$
$920$	118.859	−	187.102i	0.129195	−	0.203371i
$921$	−90.3120	−	133.425i	−0.0980587	−	0.144869i
$922$	−395.918	+	471.837i	−0.429413	+	0.511754i
$923$	90.6767	−	514.253i	0.0982412	−	0.557154i
$924$	18.4662	−	64.7968i	0.0199851	−	0.0701264i
$925$	−69.6892	−	257.436i	−0.0753397	−	0.278309i
$926$	1352.40	−	780.809i	1.46048	−	0.843207i
$927$	−142.356	−	265.645i	−0.153566	−	0.286564i
$928$	146.913	+	84.8200i	0.158311	+	0.0914008i
$929$	482.079	−	85.0036i	0.518923	−	0.0915001i	0.0919483	−	0.995764i	$-0.470691\pi$
$929$	482.079	−	85.0036i	0.518923	−	0.0915001i	0.426974	+	0.904264i	$0.359579\pi$
$930$	132.257	−	399.130i	0.142211	−	0.429172i
$931$	821.416	−	298.971i	0.882294	−	0.321129i
$932$	105.525	−	38.4079i	0.113224	−	0.0412102i
$933$	−97.7555	+	944.855i	−0.104775	+	1.01271i
$934$	−144.660	−	820.409i	−0.154882	−	0.878382i
$935$	589.549	−	645.041i	0.630533	−	0.689883i
$936$	−592.790	−	18.7712i	−0.633323	−	0.0200547i
$937$	417.683	−	241.149i	0.445766	−	0.257363i	−0.260274	−	0.965535i	$-0.583813\pi$
$937$	417.683	−	241.149i	0.445766	−	0.257363i	0.706040	+	0.708172i	$0.250480\pi$
$938$	138.254	−	116.009i	0.147392	−	0.123677i
$939$	293.792	+	83.7270i	0.312878	+	0.0891661i
$940$	53.6262	+	22.1320i	0.0570491	+	0.0235447i
$941$	−167.759	+	199.928i	−0.178278	+	0.212463i	−0.847782	−	0.530345i	$-0.822062\pi$
$941$	−167.759	+	199.928i	−0.178278	+	0.212463i	0.669504	+	0.742809i	$0.266507\pi$
$942$	324.388	+	479.243i	0.344361	+	0.508750i
$943$	−148.064	+	406.802i	−0.157014	+	0.431391i
$944$			1133.95i			1.20122i
$945$	423.334	−	242.966i	0.447972	−	0.257107i
$946$	−1134.75			−1.19953
$947$	161.848	+	58.9078i	0.170906	+	0.0622046i	0.426056	−	0.904697i	$-0.359903\pi$
$947$	161.848	+	58.9078i	0.170906	+	0.0622046i	−0.255150	+	0.966901i	$0.582125\pi$
$948$	1.20996	+	16.9082i	0.00127633	+	0.0178357i
$949$	−826.367	−	693.404i	−0.870776	−	0.730668i
$950$	−753.835	+	1082.50i	−0.793510	+	1.13947i
$951$	−1480.50	+	371.687i	−1.55678	+	0.390838i
$952$	328.734	+	391.770i	0.345309	+	0.411524i
$953$	825.741	+	1430.23i	0.866465	+	1.50076i	0.865585	+	0.500761i	$0.166947\pi$
$953$	825.741	+	1430.23i	0.866465	+	1.50076i	0.000879492		1.00000i	$0.499720\pi$
$954$	−519.917	−	1582.61i	−0.544986	−	1.65892i
$955$	−1113.69	+	1218.52i	−1.16617	+	1.27593i
$956$	−47.5867	+	8.39081i	−0.0497768	+	0.00877700i
$957$	−236.970	+	327.278i	−0.247617	+	0.341984i
$958$	231.048	+	634.800i	0.241178	+	0.662630i
$959$	−235.214	−	646.245i	−0.245270	−	0.673874i
$960$	−721.903	+	149.062i	−0.751983	+	0.155273i
$961$	−137.864	−	781.867i	−0.143459	−	0.813597i
$962$	−106.618	+	184.668i	−0.110830	+	0.191963i
$963$	−1020.91	−	1297.99i	−1.06014	−	1.34786i
$964$	−73.7143	−	127.677i	−0.0764671	−	0.132445i
$965$	−379.857	+	198.362i	−0.393635	+	0.205556i
$966$	104.754	−	101.490i	0.108441	−	0.105062i
$967$	−1336.23	−	235.614i	−1.38183	−	0.243654i	−0.567175	−	0.823597i	$-0.691964\pi$
$967$	−1336.23	−	235.614i	−1.38183	−	0.243654i	−0.814657	+	0.579943i	$0.803075\pi$
$968$	235.273	+	197.418i	0.243051	+	0.203944i
$969$	−1298.91	−	630.910i	−1.34047	−	0.651094i
$970$	−281.244	−	178.665i	−0.289942	−	0.184191i
$971$			563.556i			0.580387i	0.956968	+	0.290194i	$0.0937197\pi$
$971$			563.556i			0.580387i	−0.956968	+	0.290194i	$0.906280\pi$
$972$	168.020	−	31.0368i	0.172861	−	0.0319308i
$973$		−	867.114i		−	0.891175i
$974$	−106.875	+	293.638i	−0.109728	+	0.301476i
$975$	−535.382	+	437.275i	−0.549110	+	0.448487i
$976$	−1022.44	−	857.927i	−1.04758	−	0.879024i
$977$	−28.6746	+	162.622i	−0.0293497	+	0.166450i	−0.995960	−	0.0898018i	$-0.971377\pi$
$977$	−28.6746	+	162.622i	−0.0293497	+	0.166450i	0.966610	+	0.256252i	$0.0824877\pi$
$978$	445.831	−	431.936i	0.455859	−	0.441653i
$979$	−802.052	+	673.002i	−0.819257	+	0.687438i
$980$	−120.416	+	38.1371i	−0.122873	+	0.0389154i
$981$	−417.434	−	530.725i	−0.425519	−	0.541004i
$982$	259.021	+	149.546i	0.263769	+	0.152287i
$983$	72.9652	+	413.806i	0.0742271	+	0.420963i	0.999165	+	0.0408456i	$0.0130052\pi$
$983$	72.9652	+	413.806i	0.0742271	+	0.420963i	−0.924938	+	0.380117i	$0.875884\pi$
$984$	1367.10	−	611.335i	1.38932	−	0.621275i
$985$	−107.362	−	807.476i	−0.108997	−	0.819772i
$986$	223.722	+	614.671i	0.226898	+	0.623398i
$987$	−144.973	−	104.969i	−0.146882	−	0.106352i
$988$	155.283	−	27.3806i	0.157169	−	0.0277131i
$989$	−318.051	−	183.627i	−0.321589	−	0.185669i
$990$	86.5238	+	857.784i	0.0873978	+	0.866449i
$991$	−402.904	−	697.851i	−0.406564	−	0.704189i	0.587939	−	0.808906i	$-0.299940\pi$
$991$	−402.904	−	697.851i	−0.406564	−	0.704189i	−0.994502	+	0.104717i	$0.966606\pi$
$992$	−110.174	+	92.4466i	−0.111062	+	0.0931921i
$993$	−673.333	+	169.044i	−0.678079	+	0.170235i
$994$	77.1409	−	437.488i	0.0776066	−	0.440129i
$995$	715.659	−	550.606i	0.719255	−	0.553373i
$996$	12.4772	+	174.358i	0.0125273	+	0.175058i
$997$	667.318	−	1833.44i	0.669326	−	1.83896i	0.140804	−	0.990037i	$-0.455031\pi$
$997$	667.318	−	1833.44i	0.669326	−	1.83896i	0.528522	−	0.848920i	$-0.322747\pi$
$998$	−1036.72			−1.03880
$999$	−87.6716	+	274.371i	−0.0877594	+	0.274646i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.3.n.a.104.26	yes	204
3.2	odd	2		405.3.n.a.179.9		204
5.4	even	2	inner	135.3.n.a.104.9	yes	204
15.14	odd	2		405.3.n.a.179.26		204
27.7	even	9		405.3.n.a.224.26		204
27.20	odd	18	inner	135.3.n.a.74.9	✓	204
135.34	even	18		405.3.n.a.224.9		204
135.74	odd	18	inner	135.3.n.a.74.26	yes	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.3.n.a.74.9	✓	204	27.20	odd	18	inner
135.3.n.a.74.26	yes	204	135.74	odd	18	inner
135.3.n.a.104.9	yes	204	5.4	even	2	inner
135.3.n.a.104.26	yes	204	1.1	even	1	trivial
405.3.n.a.179.9		204	3.2	odd	2
405.3.n.a.179.26		204	15.14	odd	2
405.3.n.a.224.9		204	135.34	even	18
405.3.n.a.224.26		204	27.7	even	9

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	135.n (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(2.03789 + 0.741730i) q^{2} +(-2.69852 - 1.31073i) q^{3} +(0.538636 + 0.451970i) q^{4} +(-4.62185 - 1.90748i) q^{5} +(-4.52706 - 4.67268i) q^{6} +(-2.32404 - 2.76969i) q^{7} +(-3.57490 - 6.19192i) q^{8} +(5.56398 + 7.07404i) q^{9} +(-8.00397 - 7.31539i) q^{10} +(-8.70004 + 1.53405i) q^{11} +(-0.861110 - 1.92565i) q^{12} +(-3.15234 - 8.66099i) q^{13} +(-2.68178 - 7.36812i) q^{14} +(9.97195 + 11.2054i) q^{15} +(-3.18091 - 18.0399i) q^{16} +(9.89182 - 17.1331i) q^{17} +(6.09173 + 18.5431i) q^{18} +(12.1652 + 21.0707i) q^{19} +(-1.62737 - 3.11638i) q^{20} +(2.64116 + 10.5202i) q^{21} +(-18.8675 - 3.32686i) q^{22} +(-4.74988 - 3.98563i) q^{23} +(1.53102 + 21.3947i) q^{24} +(17.7230 + 17.6322i) q^{25} -19.9883i q^{26} +(-5.74235 - 26.3823i) q^{27} -2.54225i q^{28} +(-5.21445 + 14.3266i) q^{29} +(12.0103 + 30.2317i) q^{30} +(-9.90161 - 8.30843i) q^{31} +(1.93215 - 10.9578i) q^{32} +(25.4879 + 7.26372i) q^{33} +(32.8665 - 27.5783i) q^{34} +(5.45826 + 17.2342i) q^{35} +(-0.200289 + 6.32509i) q^{36} +(-9.23883 - 5.33404i) q^{37} +(9.16248 + 51.9630i) q^{38} +(-2.84556 + 27.5037i) q^{39} +(4.71171 + 35.4372i) q^{40} +(-23.8792 - 65.6075i) q^{41} +(-2.42079 + 23.3981i) q^{42} +(58.3296 - 10.2851i) q^{43} +(-5.37950 - 3.10586i) q^{44} +(-12.2223 - 43.3084i) q^{45} +(-6.72346 - 11.6454i) q^{46} +(-12.6408 + 10.6069i) q^{47} +(-15.0616 + 52.8502i) q^{48} +(6.23877 - 35.3818i) q^{49} +(23.0392 + 49.0781i) q^{50} +(-49.1501 + 33.2686i) q^{51} +(2.21654 - 6.08989i) q^{52} -85.3480 q^{53} +(7.86628 - 58.0234i) q^{54} +(43.1365 + 9.50501i) q^{55} +(-8.84144 + 24.2917i) q^{56} +(-5.20996 - 72.8049i) q^{57} +(-21.2529 + 25.3282i) q^{58} +(-60.9628 - 10.7494i) q^{59} +(0.306774 + 10.5426i) q^{60} +(55.8155 - 46.8348i) q^{61} +(-14.0157 - 24.2760i) q^{62} +(6.66196 - 31.8509i) q^{63} +(-24.5711 + 42.5584i) q^{64} +(-1.95102 + 46.0428i) q^{65} +(46.5538 + 33.7078i) q^{66} +(7.87234 + 21.6291i) q^{67} +(13.0717 - 4.75773i) q^{68} +(7.59357 + 16.9811i) q^{69} +(-1.65978 + 39.1698i) q^{70} +(49.0653 + 28.3279i) q^{71} +(23.9112 - 59.7407i) q^{72} +(101.360 - 58.5204i) q^{73} +(-14.8713 - 17.7229i) q^{74} +(-24.7149 - 70.8108i) q^{75} +(-2.97071 + 16.8478i) q^{76} +(24.4681 + 20.5312i) q^{77} +(-26.1992 + 53.9387i) q^{78} +(-7.55144 - 2.74850i) q^{79} +(-19.7090 + 89.4451i) q^{80} +(-19.0842 + 78.7197i) q^{81} -151.413i q^{82} +(-77.8706 - 28.3426i) q^{83} +(-3.33220 + 6.86031i) q^{84} +(-78.3997 + 60.3183i) q^{85} +(126.498 + 22.3050i) q^{86} +(32.8495 - 31.8258i) q^{87} +(40.6005 + 48.3858i) q^{88} +(102.638 - 59.2583i) q^{89} +(7.21547 - 97.3231i) q^{90} +(-16.6621 + 28.8595i) q^{91} +(-0.757079 - 4.29361i) q^{92} +(15.8295 + 35.3988i) q^{93} +(-33.6278 + 12.2395i) q^{94} +(-16.0337 - 120.591i) q^{95} +(-19.5766 + 27.0373i) q^{96} +(30.2613 - 5.33588i) q^{97} +(38.9576 - 67.4766i) q^{98} +(-59.2588 - 53.0090i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 12 q^{4} + 3 q^{5} - 24 q^{6} - 18 q^{9} - 3 q^{10} + 6 q^{11} - 48 q^{14} - 3 q^{15} + 12 q^{16} - 6 q^{19} + 63 q^{20} - 192 q^{21} + 42 q^{24} - 15 q^{25} + 96 q^{29} - 177 q^{30} - 102 q^{31}+ \cdots + 792 q^{99}+O(q^{100}) \) 204 * q - 12 * q^4 + 3 * q^5 - 24 * q^6 - 18 * q^9 - 3 * q^10 + 6 * q^11 - 48 * q^14 - 3 * q^15 + 12 * q^16 - 6 * q^19 + 63 * q^20 - 192 * q^21 + 42 * q^24 - 15 * q^25 + 96 * q^29 - 177 * q^30 - 102 * q^31 + 12 * q^34 - 252 * q^35 + 324 * q^36 - 258 * q^39 + 117 * q^40 + 96 * q^41 - 666 * q^44 - 279 * q^45 - 6 * q^46 + 60 * q^49 + 48 * q^50 + 270 * q^51 + 432 * q^54 - 12 * q^55 + 294 * q^56 + 510 * q^59 + 390 * q^60 + 132 * q^61 - 486 * q^64 + 147 * q^65 - 186 * q^66 - 84 * q^69 - 141 * q^70 - 18 * q^71 - 954 * q^74 - 285 * q^75 + 84 * q^76 - 48 * q^79 - 1026 * q^81 + 198 * q^84 + 69 * q^85 - 1506 * q^86 + 792 * q^89 - 180 * q^90 - 6 * q^91 + 492 * q^94 - 543 * q^95 + 654 * q^96 + 792 * q^99

Introduction

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