LMFDB - Embedded newform 270.3.n.a.239.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [270,3,Mod(29,270)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(270, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([1, 9]))

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

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

chi := DirichletCharacter("270.29");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 270 = 2 \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	270.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:	$7.35696713773$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$36$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			239.5
Character	$\chi$	$=$	270.239
Dual form			270.3.n.a.209.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.32893 - 0.483690i) q^{2} +(-1.82117 + 2.38397i) q^{3} +(1.53209 + 1.28558i) q^{4} +(3.82198 + 3.22374i) q^{5} +(3.57331 - 2.28724i) q^{6} +(-7.39985 - 8.81880i) q^{7} +(-1.41421 - 2.44949i) q^{8} +(-2.36665 - 8.68326i) q^{9} +(-3.51984 - 6.13276i) q^{10} +(-7.46475 + 1.31624i) q^{11} +(-5.85498 + 1.31120i) q^{12} +(3.17789 + 8.73118i) q^{13} +(5.56829 + 15.2988i) q^{14} +(-14.6458 + 3.24050i) q^{15} +(0.694593 + 3.93923i) q^{16} +(15.9255 - 27.5838i) q^{17} +(-1.05490 + 12.6841i) q^{18} +(-3.87609 - 6.71358i) q^{19} +(1.71125 + 9.85249i) q^{20} +(34.5002 - 1.58047i) q^{21} +(10.5568 + 1.86144i) q^{22} +(4.47042 + 3.75113i) q^{23} +(8.41505 + 1.08950i) q^{24} +(4.21502 + 24.6421i) q^{25} -13.1402i q^{26} +(25.0107 + 10.1717i) q^{27} -23.0242i q^{28} +(18.6450 - 51.2268i) q^{29} +(21.0306 + 2.77763i) q^{30} +(-9.04603 - 7.59052i) q^{31} +(0.982302 - 5.57091i) q^{32} +(10.4567 - 20.1929i) q^{33} +(-34.5058 + 28.9538i) q^{34} +(0.147438 - 57.5604i) q^{35} +(7.53706 - 16.3460i) q^{36} +(-39.4679 - 22.7868i) q^{37} +(1.90374 + 10.7967i) q^{38} +(-26.6024 - 8.32500i) q^{39} +(2.49142 - 13.9209i) q^{40} +(-8.85524 - 24.3296i) q^{41} +(-46.6127 - 14.5870i) q^{42} +(22.9419 - 4.04528i) q^{43} +(-13.1288 - 7.57991i) q^{44} +(18.9473 - 40.8167i) q^{45} +(-4.12648 - 7.14727i) q^{46} +(28.0701 - 23.5536i) q^{47} +(-10.6560 - 5.51814i) q^{48} +(-14.5047 + 82.2600i) q^{49} +(6.31768 - 34.7863i) q^{50} +(36.7559 + 88.2008i) q^{51} +(-6.35578 + 17.4624i) q^{52} +99.3050 q^{53} +(-28.3175 - 25.6149i) q^{54} +(-32.7733 - 19.0338i) q^{55} +(-11.1366 + 30.5975i) q^{56} +(23.0640 + 2.98611i) q^{57} +(-49.5557 + 59.0582i) q^{58} +(-26.8660 - 4.73720i) q^{59} +(-26.6046 - 13.8635i) q^{60} +(14.8396 - 12.4519i) q^{61} +(8.35005 + 14.4627i) q^{62} +(-59.0630 + 85.1258i) q^{63} +(-4.00000 + 6.92820i) q^{64} +(-16.0012 + 43.6151i) q^{65} +(-23.6633 + 21.7770i) q^{66} +(-24.4146 - 67.0784i) q^{67} +(59.8603 - 21.7874i) q^{68} +(-17.0840 + 3.82590i) q^{69} +(-28.0373 + 76.4222i) q^{70} +(13.2366 + 7.64218i) q^{71} +(-17.9226 + 18.0771i) q^{72} +(6.00716 - 3.46824i) q^{73} +(41.4282 + 49.3722i) q^{74} +(-66.4224 - 34.8291i) q^{75} +(2.69230 - 15.2688i) q^{76} +(66.8457 + 56.0902i) q^{77} +(31.3259 + 23.9306i) q^{78} +(-1.96070 - 0.713637i) q^{79} +(-10.0443 + 17.2948i) q^{80} +(-69.7979 + 41.1005i) q^{81} +36.6154i q^{82} +(-125.248 - 45.5865i) q^{83} +(54.8892 + 41.9312i) q^{84} +(149.790 - 54.0849i) q^{85} +(-32.4448 - 5.72089i) q^{86} +(88.1674 + 137.742i) q^{87} +(13.7809 + 16.4234i) q^{88} +(-102.728 + 59.3103i) q^{89} +(-44.9221 + 45.0777i) q^{90} +(53.4826 - 92.6346i) q^{91} +(2.02673 + 11.4941i) q^{92} +(34.5700 - 7.74182i) q^{93} +(-48.6957 + 17.7238i) q^{94} +(6.82851 - 38.1546i) q^{95} +(11.4920 + 12.4874i) q^{96} +(13.0597 - 2.30278i) q^{97} +(59.0639 - 102.302i) q^{98} +(29.0957 + 61.7033i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 18 q^{5} + 12 q^{6} + 12 q^{9} - 36 q^{11} + 36 q^{14} + 18 q^{15} - 72 q^{20} + 360 q^{21} + 18 q^{25} - 36 q^{29} + 144 q^{30} + 180 q^{31} + 486 q^{35} - 192 q^{36} + 348 q^{39} - 72 q^{41} + 258 q^{45}+ \cdots - 1008 q^{99}+O(q^{100}) $ 216 * q - 18 * q^5 + 12 * q^6 + 12 * q^9 - 36 * q^11 + 36 * q^14 + 18 * q^15 - 72 * q^20 + 360 * q^21 + 18 * q^25 - 36 * q^29 + 144 * q^30 + 180 * q^31 + 486 * q^35 - 192 * q^36 + 348 * q^39 - 72 * q^41 + 258 * q^45 - 72 * q^49 - 288 * q^50 - 312 * q^51 - 360 * q^54 - 72 * q^56 - 612 * q^59 - 36 * q^60 - 144 * q^61 - 864 * q^64 - 234 * q^65 + 336 * q^69 + 288 * q^74 + 642 * q^75 + 72 * q^79 + 636 * q^81 - 216 * q^84 + 432 * q^86 - 1620 * q^89 - 240 * q^90 - 504 * q^94 + 108 * q^95 - 1008 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/270\mathbb{Z}\right)^\times$.

$n$	$191$	$217$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$-1$

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 $

$2$	−1.32893	−	0.483690i	−0.664463	−	0.241845i
$2$	−1.32893	−	0.483690i	−0.664463	−	0.241845i
$3$	−1.82117	+	2.38397i	−0.607058	+	0.794658i
$3$	−1.82117	+	2.38397i	−0.607058	+	0.794658i
$4$	1.53209	+	1.28558i	0.383022	+	0.321394i
$5$	3.82198	+	3.22374i	0.764395	+	0.644748i
$5$	3.82198	+	3.22374i	0.764395	+	0.644748i
$6$	3.57331	−	2.28724i	0.595551	−	0.381207i
$7$	−7.39985	−	8.81880i	−1.05712	−	1.25983i	−0.964488	−	0.264128i	$-0.914916\pi$
$7$	−7.39985	−	8.81880i	−1.05712	−	1.25983i	−0.0926339	−	0.995700i	$-0.529529\pi$
$8$	−1.41421	−	2.44949i	−0.176777	−	0.306186i
$9$	−2.36665	−	8.68326i	−0.262961	−	0.964806i
$10$	−3.51984	−	6.13276i	−0.351984	−	0.613276i
$11$	−7.46475	+	1.31624i	−0.678614	+	0.119658i	−0.502323	−	0.864680i	$-0.667521\pi$
$11$	−7.46475	+	1.31624i	−0.678614	+	0.119658i	−0.176291	+	0.984338i	$0.556410\pi$
$12$	−5.85498	+	1.31120i	−0.487915	+	0.109267i
$13$	3.17789	+	8.73118i	0.244453	+	0.671629i	0.999866	+	0.0163800i	$0.00521415\pi$
$13$	3.17789	+	8.73118i	0.244453	+	0.671629i	−0.755413	+	0.655249i	$0.772564\pi$
$14$	5.56829	+	15.2988i	0.397735	+	1.09277i
$15$	−14.6458	+	3.24050i	−0.976386	+	0.216033i
$16$	0.694593	+	3.93923i	0.0434120	+	0.246202i
$17$	15.9255	−	27.5838i	0.936794	−	1.62257i	0.165391	−	0.986228i	$-0.447111\pi$
$17$	15.9255	−	27.5838i	0.936794	−	1.62257i	0.771403	−	0.636347i	$-0.219555\pi$
$18$	−1.05490	+	12.6841i	−0.0586054	+	0.704674i
$19$	−3.87609	−	6.71358i	−0.204005	−	0.353346i	0.745811	−	0.666158i	$-0.232062\pi$
$19$	−3.87609	−	6.71358i	−0.204005	−	0.353346i	−0.949815	+	0.312812i	$0.898729\pi$
$20$	1.71125	+	9.85249i	0.0855625	+	0.492625i
$21$	34.5002	−	1.58047i	1.64287	−	0.0752607i
$22$	10.5568	+	1.86144i	0.479853	+	0.0846109i
$23$	4.47042	+	3.75113i	0.194366	+	0.163093i	0.734777	−	0.678309i	$-0.237287\pi$
$23$	4.47042	+	3.75113i	0.194366	+	0.163093i	−0.540411	+	0.841401i	$0.681731\pi$
$24$	8.41505	+	1.08950i	0.350627	+	0.0453959i
$25$	4.21502	+	24.6421i	0.168601	+	0.985684i
$26$		−	13.1402i		−	0.505392i
$27$	25.0107	+	10.1717i	0.926323	+	0.376729i
$28$		−	23.0242i		−	0.822295i
$29$	18.6450	−	51.2268i	0.642932	−	1.76644i	0.000616673	−	1.00000i	$-0.499804\pi$
$29$	18.6450	−	51.2268i	0.642932	−	1.76644i	0.642315	−	0.766441i	$-0.277974\pi$
$30$	21.0306	+	2.77763i	0.701019	+	0.0925877i
$31$	−9.04603	−	7.59052i	−0.291807	−	0.244855i	0.485117	−	0.874449i	$-0.338777\pi$
$31$	−9.04603	−	7.59052i	−0.291807	−	0.244855i	−0.776925	+	0.629594i	$0.783221\pi$
$32$	0.982302	−	5.57091i	0.0306970	−	0.174091i
$33$	10.4567	−	20.1929i	0.316871	−	0.611905i
$34$	−34.5058	+	28.9538i	−1.01488	+	0.851582i
$35$	0.147438	−	57.5604i	0.00421252	−	1.64458i
$36$	7.53706	−	16.3460i	0.209363	−	0.454056i
$37$	−39.4679	−	22.7868i	−1.06670	−	0.615860i	−0.139422	−	0.990233i	$-0.544525\pi$
$37$	−39.4679	−	22.7868i	−1.06670	−	0.615860i	−0.927278	+	0.374373i	$0.877858\pi$
$38$	1.90374	+	10.7967i	0.0500985	+	0.284123i
$39$	−26.6024	−	8.32500i	−0.682112	−	0.213461i
$40$	2.49142	−	13.9209i	0.0622855	−	0.348024i
$41$	−8.85524	−	24.3296i	−0.215981	−	0.593404i	0.783632	−	0.621226i	$-0.213365\pi$
$41$	−8.85524	−	24.3296i	−0.215981	−	0.593404i	−0.999613	+	0.0278220i	$0.991143\pi$
$42$	−46.6127	−	14.5870i	−1.10983	−	0.347311i
$43$	22.9419	−	4.04528i	0.533533	−	0.0940763i	0.0996108	−	0.995026i	$-0.468240\pi$
$43$	22.9419	−	4.04528i	0.533533	−	0.0940763i	0.433923	+	0.900950i	$0.357129\pi$
$44$	−13.1288	−	7.57991i	−0.298382	−	0.172271i
$45$	18.9473	−	40.8167i	0.421050	−	0.907037i
$46$	−4.12648	−	7.14727i	−0.0897061	−	0.155375i
$47$	28.0701	−	23.5536i	0.597236	−	0.501141i	−0.293320	−	0.956014i	$-0.594760\pi$
$47$	28.0701	−	23.5536i	0.597236	−	0.501141i	0.890556	+	0.454874i	$0.150316\pi$
$48$	−10.6560	−	5.51814i	−0.222000	−	0.114961i
$49$	−14.5047	+	82.2600i	−0.296013	+	1.67878i
$50$	6.31768	−	34.7863i	0.126354	−	0.695726i
$51$	36.7559	+	88.2008i	0.720703	+	1.72943i
$52$	−6.35578	+	17.4624i	−0.122227	+	0.335815i
$53$	99.3050			1.87368			0.936839	−	0.349760i	$-0.113737\pi$
$53$	99.3050			1.87368			0.936839	+	0.349760i	$0.113737\pi$
$54$	−28.3175	−	25.6149i	−0.524398	−	0.474349i
$55$	−32.7733	−	19.0338i	−0.595879	−	0.346069i
$56$	−11.1366	+	30.5975i	−0.198868	+	0.546384i
$57$	23.0640	+	2.98611i	0.404632	+	0.0523879i
$58$	−49.5557	+	59.0582i	−0.854409	+	1.01824i
$59$	−26.8660	−	4.73720i	−0.455356	−	0.0802915i	−0.0587341	−	0.998274i	$-0.518706\pi$
$59$	−26.8660	−	4.73720i	−0.455356	−	0.0802915i	−0.396622	+	0.917982i	$0.629818\pi$
$60$	−26.6046	−	13.8635i	−0.443409	−	0.231059i
$61$	14.8396	−	12.4519i	0.243272	−	0.204129i	−0.512997	−	0.858390i	$-0.671465\pi$
$61$	14.8396	−	12.4519i	0.243272	−	0.204129i	0.756269	+	0.654261i	$0.227020\pi$
$62$	8.35005	+	14.4627i	0.134678	+	0.233269i
$63$	−59.0630	+	85.1258i	−0.937509	+	1.35120i
$64$	−4.00000	+	6.92820i	−0.0625000	+	0.108253i
$65$	−16.0012	+	43.6151i	−0.246173	+	0.671001i
$66$	−23.6633	+	21.7770i	−0.358535	+	0.329955i
$67$	−24.4146	−	67.0784i	−0.364396	−	1.00117i	−0.977457	−	0.211135i	$-0.932284\pi$
$67$	−24.4146	−	67.0784i	−0.364396	−	1.00117i	0.613061	−	0.790036i	$-0.289938\pi$
$68$	59.8603	−	21.7874i	0.880298	−	0.320402i
$69$	−17.0840	+	3.82590i	−0.247594	+	0.0554479i
$70$	−28.0373	+	76.4222i	−0.400533	+	1.09175i
$71$	13.2366	+	7.64218i	0.186432	+	0.107636i	0.590311	−	0.807176i	$-0.299005\pi$
$71$	13.2366	+	7.64218i	0.186432	+	0.107636i	−0.403879	+	0.914812i	$0.632338\pi$
$72$	−17.9226	+	18.0771i	−0.248925	+	0.251070i
$73$	6.00716	−	3.46824i	0.0822899	−	0.0475101i	−0.458290	−	0.888802i	$-0.651538\pi$
$73$	6.00716	−	3.46824i	0.0822899	−	0.0475101i	0.540580	+	0.841292i	$0.318205\pi$
$74$	41.4282	+	49.3722i	0.559841	+	0.667192i
$75$	−66.4224	−	34.8291i	−0.885632	−	0.464388i
$76$	2.69230	−	15.2688i	0.0354250	−	0.200905i
$77$	66.8457	+	56.0902i	0.868126	+	0.728444i
$78$	31.3259	+	23.9306i	0.401614	+	0.306803i
$79$	−1.96070	−	0.713637i	−0.0248190	−	0.00903338i	0.329581	−	0.944127i	$-0.393093\pi$
$79$	−1.96070	−	0.713637i	−0.0248190	−	0.00903338i	−0.354400	+	0.935094i	$0.615315\pi$
$80$	−10.0443	+	17.2948i	−0.125554	+	0.216185i
$81$	−69.7979	+	41.1005i	−0.861703	+	0.507413i
$82$			36.6154i			0.446529i
$83$	−125.248	−	45.5865i	−1.50901	−	0.549235i	−0.550635	−	0.834746i	$-0.685614\pi$
$83$	−125.248	−	45.5865i	−1.50901	−	0.549235i	−0.958375	+	0.285511i	$0.907837\pi$
$84$	54.8892	+	41.9312i	0.653443	+	0.499181i
$85$	149.790	−	54.0849i	1.76223	−	0.636293i
$86$	−32.4448	−	5.72089i	−0.377265	−	0.0665220i
$87$	88.1674	+	137.742i	1.01342	+	1.58324i
$88$	13.7809	+	16.4234i	0.156601	+	0.186629i
$89$	−102.728	+	59.3103i	−1.15425	+	0.666408i	−0.949920	−	0.312493i	$-0.898836\pi$
$89$	−102.728	+	59.3103i	−1.15425	+	0.666408i	−0.204333	+	0.978901i	$0.565502\pi$
$90$	−44.9221	+	45.0777i	−0.499135	+	0.500864i
$91$	53.4826	−	92.6346i	0.587721	−	1.01796i
$92$	2.02673	+	11.4941i	0.0220296	+	0.124936i
$93$	34.5700	−	7.74182i	0.371720	−	0.0832454i
$94$	−48.6957	+	17.7238i	−0.518040	+	0.188551i
$95$	6.82851	−	38.1546i	0.0718790	−	0.401628i
$96$	11.4920	+	12.4874i	0.119708	+	0.130077i
$97$	13.0597	−	2.30278i	0.134636	−	0.0237400i	−0.105924	−	0.994374i	$-0.533780\pi$
$97$	13.0597	−	2.30278i	0.134636	−	0.0237400i	0.240560	+	0.970634i	$0.422669\pi$
$98$	59.0639	−	102.302i	0.602693	−	1.04390i
$99$	29.0957	+	61.7033i	0.293896	+	0.623266i
$100$	−25.2215	+	43.1726i	−0.252215	+	0.431726i
$101$	−20.6844	−	24.6507i	−0.204796	−	0.244066i	0.653864	−	0.756612i	$-0.273147\pi$
$101$	−20.6844	−	24.6507i	−0.204796	−	0.244066i	−0.858660	+	0.512546i	$0.828702\pi$
$102$	−6.18401	−	134.991i	−0.0606275	−	1.32344i
$103$	−182.340	−	32.1514i	−1.77029	−	0.312150i	−0.809024	−	0.587776i	$-0.800004\pi$
$103$	−182.340	−	32.1514i	−1.77029	−	0.312150i	−0.961265	+	0.275626i	$0.911115\pi$
$104$	16.8927	−	20.1320i	0.162430	−	0.193577i
$105$	136.954	+	105.179i	1.30432	+	1.00171i
$106$	−131.969	−	48.0328i	−1.24499	−	0.453139i
$107$	29.4166			0.274922			0.137461	−	0.990507i	$-0.456106\pi$
$107$	29.4166			0.274922			0.137461	+	0.990507i	$0.456106\pi$
$108$	25.2422	+	47.7371i	0.233724	+	0.442010i
$109$	−73.0657			−0.670327			−0.335164	−	0.942160i	$-0.608792\pi$
$109$	−73.0657			−0.670327			−0.335164	+	0.942160i	$0.608792\pi$
$110$	34.3469	+	41.1466i	0.312244	+	0.374060i
$111$	126.201	−	52.5917i	1.13695	−	0.473799i
$112$	29.5994	−	35.2752i	0.264280	−	0.314957i
$113$	−17.3508	+	98.4013i	−0.153547	+	0.870808i	0.806555	+	0.591159i	$0.201329\pi$
$113$	−17.3508	+	98.4013i	−0.153547	+	0.870808i	−0.960102	+	0.279649i	$0.909782\pi$
$114$	−29.2060	−	15.1241i	−0.256193	−	0.132668i
$115$	4.99319	+	28.7482i	0.0434191	+	0.249984i
$116$	94.4217	−	54.5144i	0.813980	−	0.469952i
$117$	68.2941	−	48.2581i	0.583710	−	0.412462i
$118$	33.4116	+	19.2902i	0.283149	+	0.163476i
$119$	−361.102	+	63.6720i	−3.03447	+	0.535059i
$120$	28.6498	+	31.2920i	0.238749	+	0.260766i
$121$	−59.7127	+	21.7337i	−0.493494	+	0.179617i
$122$	−25.7436	+	9.36989i	−0.211013	+	0.0768024i
$123$	74.1279	+	23.1977i	0.602666	+	0.188599i
$124$	−4.10113	−	23.2587i	−0.0330737	−	0.187570i
$125$	−63.3300	+	107.770i	−0.506640	+	0.862158i
$126$	119.665	−	84.5578i	0.949721	−	0.671093i
$127$	−83.5002	+	48.2088i	−0.657482	+	0.379597i	−0.791317	−	0.611406i	$-0.790604\pi$
$127$	−83.5002	+	48.2088i	−0.657482	+	0.379597i	0.133835	+	0.991004i	$0.457271\pi$
$128$	8.66680	−	7.27231i	0.0677094	−	0.0568149i
$129$	−32.1374	+	62.0601i	−0.249127	+	0.481086i
$130$	42.3606	−	50.2216i	0.325851	−	0.386320i
$131$	153.885	−	183.393i	1.17469	−	1.39995i	0.276121	−	0.961123i	$-0.410951\pi$
$131$	153.885	−	183.393i	1.17469	−	1.39995i	0.898573	−	0.438823i	$-0.144605\pi$
$132$	41.9801	−	17.4943i	0.318031	−	0.132533i
$133$	−30.5232	+	83.8619i	−0.229498	+	0.630541i
$134$			100.951i			0.753368i
$135$	62.7996	+	119.504i	0.465182	+	0.885215i
$136$	−90.0882			−0.662413
$137$	61.0116	+	22.2064i	0.445340	+	0.162090i	0.554949	−	0.831884i	$-0.312738\pi$
$137$	61.0116	+	22.2064i	0.445340	+	0.162090i	−0.109609	+	0.993975i	$0.534960\pi$
$138$	24.5539	+	3.17901i	0.177927	+	0.0230363i
$139$	95.9210	+	80.4873i	0.690079	+	0.579045i	0.918932	−	0.394416i	$-0.129053\pi$
$139$	95.9210	+	80.4873i	0.690079	+	0.579045i	−0.228853	+	0.973461i	$0.573498\pi$
$140$	74.2242	−	87.9982i	0.530173	−	0.628558i
$141$	5.03063	+	109.814i	0.0356782	+	0.778820i
$142$	−13.8941	−	16.5583i	−0.0978457	−	0.116608i
$143$	−35.2145	−	60.9932i	−0.246255	−	0.426526i
$144$	32.5615	−	15.3541i	0.226122	−	0.106626i
$145$	236.403	−	135.681i	1.63036	−	0.935730i
$146$	−9.66062	+	1.70343i	−0.0661686	+	0.0116673i
$147$	−169.690	−	184.389i	−1.15435	−	1.25434i
$148$	−31.1742	−	85.6504i	−0.210636	−	0.578719i
$149$	−34.8693	−	95.8026i	−0.234022	−	0.642970i	−1.00000		0.000103554i	$-0.999967\pi$
$149$	−34.8693	−	95.8026i	−0.234022	−	0.642970i	0.765978	−	0.642867i	$-0.222255\pi$
$150$	71.4240	+	78.4131i	0.476160	+	0.522754i
$151$	34.3402	+	194.753i	0.227418	+	1.28975i	0.858008	+	0.513637i	$0.171702\pi$
$151$	34.3402	+	194.753i	0.227418	+	1.28975i	−0.630589	+	0.776117i	$0.717187\pi$
$152$	−10.9632	+	18.9889i	−0.0721265	+	0.124927i
$153$	−277.207	−	73.0041i	−1.81181	−	0.477151i
$154$	−61.7027	−	106.872i	−0.400667	−	0.693976i
$155$	−10.1039	−	58.1728i	−0.0651862	−	0.375308i
$156$	−30.0548	−	46.9540i	−0.192659	−	0.300987i
$157$	−203.904	−	35.9538i	−1.29875	−	0.229005i	−0.518827	−	0.854879i	$-0.673631\pi$
$157$	−203.904	−	35.9538i	−1.29875	−	0.229005i	−0.779924	+	0.625874i	$0.784742\pi$
$158$	2.26045	+	1.89674i	0.0143066	+	0.0120047i
$159$	−180.852	+	236.740i	−1.13743	+	1.48893i
$160$	21.7135	−	18.1252i	0.135709	−	0.113283i
$161$		−	67.1816i		−	0.417277i
$162$	112.636	−	20.8590i	0.695285	−	0.128759i
$163$		−	261.578i		−	1.60477i	−0.596804	−	0.802387i	$-0.703563\pi$
$163$		−	261.578i		−	1.60477i	0.596804	−	0.802387i	$-0.296437\pi$
$164$	17.7105	−	48.6591i	0.107991	−	0.296702i
$165$	105.062	−	43.4669i	0.636739	−	0.263436i
$166$	144.395	+	121.162i	0.869852	+	0.729893i
$167$	34.0703	−	193.222i	0.204014	−	1.15702i	−0.694971	−	0.719038i	$-0.744583\pi$
$167$	34.0703	−	193.222i	0.204014	−	1.15702i	0.898984	−	0.437981i	$-0.144306\pi$
$168$	−52.6620	−	82.2727i	−0.313464	−	0.489719i
$169$	63.3270	−	53.1377i	0.374716	−	0.314424i
$170$	−225.220	−	0.576889i	−1.32482	−	0.00339346i
$171$	−49.1224	+	49.5457i	−0.287265	+	0.289741i
$172$	40.3496	+	23.2959i	0.234591	+	0.135441i
$173$	3.19536	+	18.1218i	0.0184703	+	0.104750i	0.992649	−	0.121027i	$-0.0386189\pi$
$173$	3.19536	+	18.1218i	0.0184703	+	0.104750i	−0.974179	+	0.225778i	$0.927508\pi$
$174$	−50.5435	−	225.695i	−0.290480	−	1.29710i
$175$	186.123	−	219.519i	1.06356	−	1.25440i
$176$	−10.3699	−	28.4911i	−0.0589200	−	0.161881i
$177$	60.2210	−	55.4205i	0.340232	−	0.313110i
$178$	165.206	−	29.1303i	0.928126	−	0.163654i
$179$	166.509	+	96.1340i	0.930218	+	0.537062i	0.886880	−	0.461999i	$-0.152868\pi$
$179$	166.509	+	96.1340i	0.930218	+	0.537062i	0.0433374	+	0.999060i	$0.486201\pi$
$180$	81.5018	−	38.1766i	0.452788	−	0.212092i
$181$	21.2045	+	36.7273i	0.117152	+	0.202913i	0.918638	−	0.395100i	$-0.129290\pi$
$181$	21.2045	+	36.7273i	0.117152	+	0.202913i	−0.801486	+	0.598014i	$0.795957\pi$
$182$	−115.881	+	97.2355i	−0.636708	+	0.534261i
$183$	2.65950	+	58.0542i	0.0145328	+	0.317236i
$184$	2.86622	−	16.2552i	0.0155773	−	0.0883432i
$185$	−77.3868	−	214.325i	−0.418307	−	1.15851i
$186$	−49.6856	−	6.43282i	−0.267127	−	0.0345851i
$187$	−82.5731	+	226.868i	−0.441568	+	1.21320i
$188$	73.2859			0.389818
$189$	−95.3736	−	295.834i	−0.504622	−	1.56526i
$190$	−27.5296	+	47.4018i	−0.144892	+	0.249483i
$191$	17.5695	−	48.2719i	0.0919870	−	0.252732i	−0.885164	−	0.465280i	$-0.845954\pi$
$191$	17.5695	−	48.2719i	0.0919870	−	0.252732i	0.977151	+	0.212547i	$0.0681760\pi$
$192$	−9.23195	−	22.1534i	−0.0480831	−	0.115382i
$193$	14.5082	−	17.2902i	0.0751720	−	0.0895865i	−0.727148	−	0.686481i	$-0.759154\pi$
$193$	14.5082	−	17.2902i	0.0751720	−	0.0895865i	0.802320	+	0.596895i	$0.203599\pi$
$194$	−18.4692	−	3.25662i	−0.0952020	−	0.0167867i
$195$	−74.8361	−	117.577i	−0.383775	−	0.602959i
$196$	−127.974	+	107.383i	−0.652928	+	0.547872i
$197$	113.858	+	197.208i	0.577960	+	1.00106i	0.995713	+	0.0924950i	$0.0294842\pi$
$197$	113.858	+	197.208i	0.577960	+	1.00106i	−0.417754	+	0.908560i	$0.637182\pi$
$198$	−8.82078	−	96.0724i	−0.0445494	−	0.485214i
$199$	2.50358	−	4.33632i	0.0125808	−	0.0217906i	−0.859666	−	0.510856i	$-0.829329\pi$
$199$	2.50358	−	4.33632i	0.0125808	−	0.0217906i	0.872247	+	0.489065i	$0.162662\pi$
$200$	54.3997	−	45.1739i	0.271998	−	0.225869i
$201$	204.376	+	63.9579i	1.01680	+	0.318198i
$202$	15.5647	+	42.7637i	0.0770531	+	0.211702i
$203$	−589.729	+	214.644i	−2.90507	+	1.05736i
$204$	−57.0755	+	182.384i	−0.279782	+	0.894039i
$205$	44.5876	−	121.534i	0.217501	−	0.592849i
$206$	226.765	+	130.923i	1.10080	+	0.635547i
$207$	21.9921	−	47.6954i	0.106242	−	0.230413i
$208$	−32.1868	+	18.5831i	−0.154744	+	0.0893416i
$209$	37.7707	+	45.0134i	0.180721	+	0.215375i
$210$	−131.128	−	206.018i	−0.624418	−	0.981040i
$211$	44.1325	−	250.288i	0.209159	−	1.18620i	−0.681601	−	0.731724i	$-0.738716\pi$
$211$	44.1325	−	250.288i	0.209159	−	1.18620i	0.890760	−	0.454475i	$-0.150173\pi$
$212$	152.144	+	127.664i	0.717661	+	0.602189i
$213$	−42.3250	+	17.6381i	−0.198709	+	0.0828078i
$214$	−39.0925	−	14.2285i	−0.182675	−	0.0664884i
$215$	100.724	+	58.4978i	0.468486	+	0.272083i
$216$	−10.4551	−	75.6485i	−0.0484030	−	0.350224i
$217$			135.944i			0.626469i
$218$	97.0989	+	35.3411i	0.445408	+	0.162115i
$219$	−2.67191	+	20.6372i	−0.0122005	+	0.0942336i
$220$	−25.7423	−	71.2940i	−0.117010	−	0.324064i
$221$	291.448	+	51.3902i	1.31877	+	0.232535i
$222$	−193.150	+	8.84831i	−0.870045	+	0.0398573i
$223$	150.578	+	179.452i	0.675240	+	0.804719i	0.989487	−	0.144622i	$-0.0461966\pi$
$223$	150.578	+	179.452i	0.675240	+	0.804719i	−0.314247	+	0.949341i	$0.601752\pi$
$224$	−56.3977	+	32.5612i	−0.251775	+	0.145363i
$225$	203.998	−	94.9194i	0.906659	−	0.421864i
$226$	70.6536	−	122.376i	0.312627	−	0.541485i
$227$	58.2346	+	330.265i	0.256540	+	1.45491i	0.792088	+	0.610407i	$0.208994\pi$
$227$	58.2346	+	330.265i	0.256540	+	1.45491i	−0.535548	+	0.844505i	$0.679895\pi$
$228$	31.4972	+	34.2255i	0.138146	+	0.150112i
$229$	354.918	−	129.180i	1.54986	−	0.564103i	0.581475	−	0.813564i	$-0.302476\pi$
$229$	354.918	−	129.180i	1.54986	−	0.564103i	0.968385	+	0.249461i	$0.0802534\pi$
$230$	7.26962	−	40.6194i	0.0316071	−	0.176606i
$231$	−255.455	+	57.2083i	−1.10587	+	0.247655i
$232$	−151.848	+	26.7748i	−0.654515	+	0.115409i
$233$	204.699	−	354.549i	0.878536	−	1.52167i	0.0255878	−	0.999673i	$-0.491854\pi$
$233$	204.699	−	354.549i	0.878536	−	1.52167i	0.852948	−	0.521996i	$-0.174812\pi$
$234$	−114.100	+	31.0983i	−0.487606	+	0.132899i
$235$	183.214	+	0.469293i	0.779634	+	0.00199699i
$236$	−35.0711	−	41.7961i	−0.148606	−	0.177102i
$237$	5.27207	−	3.37460i	0.0222450	−	0.0142388i
$238$	510.675	+	90.0459i	2.14570	+	0.378344i
$239$	35.1922	−	41.9405i	0.147248	−	0.175483i	−0.687379	−	0.726299i	$-0.741239\pi$
$239$	35.1922	−	41.9405i	0.147248	−	0.175483i	0.834627	+	0.550816i	$0.185683\pi$
$240$	−22.9379	−	55.4423i	−0.0955747	−	0.231010i
$241$	−177.163	−	64.4821i	−0.735117	−	0.267561i	−0.0527878	−	0.998606i	$-0.516811\pi$
$241$	−177.163	−	64.4821i	−0.735117	−	0.267561i	−0.682329	+	0.731045i	$0.739033\pi$
$242$	89.8662			0.371348
$243$	29.1318	−	241.247i	0.119884	−	0.992788i
$244$	38.7434			0.158784
$245$	−320.621	+	267.637i	−1.30866	+	1.09239i
$246$	−87.2900	−	66.6830i	−0.354838	−	0.271069i
$247$	46.2997	−	55.1778i	0.187448	−	0.223392i
$248$	−5.79988	+	32.8928i	−0.0233866	+	0.132632i
$249$	336.775	−	215.567i	1.35251	−	0.865729i
$250$	136.288	−	112.586i	0.545152	−	0.450344i
$251$	92.0594	−	53.1505i	0.366770	−	0.211755i	−0.305276	−	0.952264i	$-0.598749\pi$
$251$	92.0594	−	53.1505i	0.366770	−	0.211755i	0.672047	+	0.740509i	$0.265415\pi$
$252$	−199.925	+	54.4903i	−0.793355	+	0.216232i
$253$	−38.3080	−	22.1171i	−0.151415	−	0.0874195i
$254$	134.284	−	23.6778i	0.528676	−	0.0932198i
$255$	−143.856	+	455.593i	−0.564142	+	1.78664i
$256$	−15.0351	+	5.47232i	−0.0587308	+	0.0213763i
$257$	−328.998	+	119.745i	−1.28015	+	0.465935i	−0.890481	−	0.455021i	$-0.849632\pi$
$257$	−328.998	+	119.745i	−1.28015	+	0.465935i	−0.389666	+	0.920956i	$0.627410\pi$
$258$	72.7261	−	66.9288i	0.281884	−	0.259414i
$259$	91.1044	+	516.679i	0.351754	+	1.99490i
$260$	−80.5857	+	46.2514i	−0.309945	+	0.177890i
$261$	−488.942	−	40.6637i	−1.87334	−	0.155799i
$262$	−293.207	+	169.283i	−1.11911	+	0.646119i
$263$	−164.959	+	138.417i	−0.627220	+	0.526300i	−0.900064	−	0.435758i	$-0.856480\pi$
$263$	−164.959	+	138.417i	−0.627220	+	0.526300i	0.272844	+	0.962058i	$0.412036\pi$
$264$	−64.2503	+	2.94334i	−0.243372	+	0.0111490i
$265$	379.541	+	320.133i	1.43223	+	1.20805i
$266$	81.1262	−	96.6825i	0.304986	−	0.363468i
$267$	45.6923	−	352.916i	0.171132	−	1.32178i
$268$	48.8291	−	134.157i	0.182198	−	0.500585i
$269$			182.071i			0.676845i	0.940994	+	0.338423i	$0.109893\pi$
$269$			182.071i			0.676845i	−0.940994	+	0.338423i	$0.890107\pi$
$270$	−25.6531	−	189.188i	−0.0950116	−	0.700695i
$271$	−229.271			−0.846019			−0.423009	−	0.906125i	$-0.639026\pi$
$271$	−229.271			−0.846019			−0.423009	+	0.906125i	$0.639026\pi$
$272$	119.721	+	43.5747i	0.440149	+	0.160201i
$273$	123.437	+	296.205i	0.452151	+	1.08500i
$274$	−70.3389	−	59.0213i	−0.256711	−	0.215406i
$275$	−63.8990	−	178.399i	−0.232360	−	0.648725i
$276$	−31.0927	−	16.1012i	−0.112655	−	0.0583375i
$277$	69.4913	+	82.8165i	0.250871	+	0.298977i	0.876753	−	0.480942i	$-0.159705\pi$
$277$	69.4913	+	82.8165i	0.250871	+	0.298977i	−0.625881	+	0.779918i	$0.715261\pi$
$278$	−88.5410	−	153.358i	−0.318493	−	0.551646i
$279$	−44.5016	+	96.5131i	−0.159504	+	0.345925i
$280$	−141.202	+	81.0416i	−0.504294	+	0.289434i
$281$	−75.8567	+	13.3756i	−0.269953	+	0.0475999i	−0.306986	−	0.951714i	$-0.599320\pi$
$281$	−75.8567	+	13.3756i	−0.269953	+	0.0475999i	0.0370331	+	0.999314i	$0.488209\pi$
$282$	46.4304	−	148.367i	0.164647	−	0.526126i
$283$	83.0957	+	228.304i	0.293624	+	0.806726i	0.995529	+	0.0944555i	$0.0301110\pi$
$283$	83.0957	+	228.304i	0.293624	+	0.806726i	−0.701905	+	0.712271i	$0.747667\pi$
$284$	10.4551	+	28.7252i	0.0368138	+	0.101145i
$285$	78.5237	+	85.7652i	0.275522	+	0.300930i
$286$	17.2956	+	98.0884i	0.0604742	+	0.342966i
$287$	−149.030	+	258.128i	−0.519269	+	0.899400i
$288$	−50.6984	+	4.65482i	−0.176036	+	0.0161626i
$289$	−362.743	−	628.289i	−1.25517	−	2.17401i
$290$	−379.789	+	65.9644i	−1.30962	+	0.227464i
$291$	−18.2942	+	35.3277i	−0.0628667	+	0.121401i
$292$	13.6622	+	2.40901i	0.0467883	+	0.00825004i
$293$	−109.517	−	91.8958i	−0.373779	−	0.313637i	0.436476	−	0.899716i	$-0.356227\pi$
$293$	−109.517	−	91.8958i	−0.373779	−	0.313637i	−0.810254	+	0.586079i	$0.800671\pi$
$294$	136.319	+	327.116i	0.463669	+	1.11264i
$295$	−87.4097	−	104.714i	−0.296304	−	0.354964i
$296$			128.902i			0.435479i
$297$	−200.087	−	43.0091i	−0.673695	−	0.144812i
$298$			144.180i			0.483827i
$299$	−18.5453	+	50.9527i	−0.0620243	+	0.170410i
$300$	−56.9896	−	138.752i	−0.189965	−	0.462507i
$301$	−205.441	−	172.386i	−0.682530	−	0.572710i
$302$	48.5644	−	275.422i	0.160809	−	0.911994i
$303$	96.4363	−	4.41781i	0.318272	−	0.0145802i
$304$	23.7540	−	19.9320i	0.0781383	−	0.0655658i
$305$	96.8582	+	0.248097i	0.317568	+	0.000813433i
$306$	333.076	+	231.099i	1.08849	+	0.755226i
$307$	−112.635	−	65.0300i	−0.366890	−	0.211824i	0.305209	−	0.952285i	$-0.401274\pi$
$307$	−112.635	−	65.0300i	−0.366890	−	0.211824i	−0.672099	+	0.740461i	$0.734607\pi$
$308$	30.3054	+	171.870i	0.0983941	+	0.558021i
$309$	408.720	−	376.140i	1.32272	−	1.21728i
$310$	−14.7103	+	82.1945i	−0.0474525	+	0.265143i
$311$	180.722	+	496.530i	0.581100	+	1.59656i	0.786305	+	0.617839i	$0.211992\pi$
$311$	180.722	+	496.530i	0.581100	+	1.59656i	−0.205205	+	0.978719i	$0.565786\pi$
$312$	17.2295	+	76.9356i	0.0552226	+	0.246588i
$313$	346.159	−	61.0371i	1.10594	−	0.195007i	0.409279	−	0.912409i	$-0.365780\pi$
$313$	346.159	−	61.0371i	1.10594	−	0.195007i	0.696659	+	0.717402i	$0.254669\pi$
$314$	253.583	+	146.406i	0.807588	+	0.466261i
$315$	−500.161	+	134.945i	−1.58781	+	0.428397i
$316$	−2.08653	−	3.61398i	−0.00660296	−	0.0114367i
$317$	80.2228	−	67.3150i	0.253069	−	0.212350i	−0.507424	−	0.861697i	$-0.669402\pi$
$317$	80.2228	−	67.3150i	0.253069	−	0.212350i	0.760492	+	0.649347i	$0.224958\pi$
$318$	354.847	−	227.134i	1.11587	−	0.714259i
$319$	−71.7539	+	406.937i	−0.224934	+	1.27566i
$320$	−37.6226	+	13.5845i	−0.117571	+	0.0424515i
$321$	−53.5728	+	70.1284i	−0.166893	+	0.218469i
$322$	−32.4950	+	89.2793i	−0.100916	+	0.277265i
$323$	−246.914			−0.764441
$324$	−159.774	−	26.7609i	−0.493131	−	0.0825954i
$325$	−201.760	+	115.112i	−0.620799	+	0.354191i
$326$	−126.523	+	347.618i	−0.388106	+	1.06631i
$327$	133.065	−	174.187i	0.406927	−	0.532681i
$328$	−47.0718	+	56.0980i	−0.143512	+	0.171031i
$329$	−415.429	−	73.2514i	−1.26270	−	0.222649i
$330$	−160.644	+	6.94690i	−0.486800	+	0.0210512i
$331$	−103.981	+	87.2503i	−0.314141	+	0.263596i	−0.786201	−	0.617971i	$-0.787955\pi$
$331$	−103.981	+	87.2503i	−0.314141	+	0.263596i	0.472060	+	0.881567i	$0.343511\pi$
$332$	−133.286	−	230.858i	−0.401464	−	0.695356i
$333$	−104.457	+	396.639i	−0.313685	+	1.19111i
$334$	−138.736	+	240.298i	−0.415378	+	0.719456i
$335$	122.931	−	335.078i	0.366960	−	1.00023i
$336$	30.1894	+	134.806i	0.0898495	+	0.401210i
$337$	33.3298	+	91.5728i	0.0989014	+	0.271729i	0.979269	−	0.202562i	$-0.0649267\pi$
$337$	33.3298	+	91.5728i	0.0989014	+	0.271729i	−0.880368	+	0.474291i	$0.842704\pi$
$338$	−109.859	+	39.9854i	−0.325027	+	0.118300i
$339$	−202.987	−	220.570i	−0.598782	−	0.650648i
$340$	299.021	+	109.703i	0.879475	+	0.322656i
$341$	77.5173	+	44.7546i	0.227323	+	0.131245i
$342$	89.2448	−	42.0826i	0.260950	−	0.123049i
$343$	344.247	−	198.751i	1.00364	−	0.579449i
$344$	−42.3537	−	50.4751i	−0.123121	−	0.146730i
$345$	−77.6284	−	40.4519i	−0.225010	−	0.117252i
$346$	4.51892	−	25.6281i	0.0130605	−	0.0740696i
$347$	427.536	+	358.746i	1.23209	+	1.03385i	0.998100	+	0.0616105i	$0.0196237\pi$
$347$	427.536	+	358.746i	1.23209	+	1.03385i	0.233993	+	0.972238i	$0.424821\pi$
$348$	−41.9975	+	324.379i	−0.120683	+	0.932123i
$349$	−251.613	−	91.5796i	−0.720954	−	0.262406i	−0.0446230	−	0.999004i	$-0.514209\pi$
$349$	−251.613	−	91.5796i	−0.720954	−	0.262406i	−0.676331	+	0.736598i	$0.736431\pi$
$350$	−353.523	+	201.699i	−1.01007	+	0.576283i
$351$	−9.32955	+	250.698i	−0.0265799	+	0.714238i
$352$			42.8784i			0.121814i
$353$	254.314	+	92.5627i	0.720436	+	0.262217i	0.676111	−	0.736800i	$-0.263664\pi$
$353$	254.314	+	92.5627i	0.720436	+	0.262217i	0.0443254	+	0.999017i	$0.485886\pi$
$354$	−106.836	+	44.5215i	−0.301795	+	0.125767i
$355$	25.9538	+	71.8797i	0.0731092	+	0.202478i
$356$	−233.637	−	41.1965i	−0.656284	−	0.115721i
$357$	505.837	−	976.815i	1.41691	−	2.73618i
$358$	−174.779	−	208.294i	−0.488210	−	0.581826i
$359$	311.631	−	179.921i	0.868054	−	0.501171i	0.00135314	−	0.999999i	$-0.499569\pi$
$359$	311.631	−	179.921i	0.868054	−	0.501171i	0.866701	+	0.498828i	$0.166236\pi$
$360$	−126.776	+	11.3124i	−0.352154	+	0.0314232i
$361$	150.452	−	260.590i	0.416764	−	0.721857i
$362$	−10.4146	−	59.0642i	−0.0287696	−	0.163161i
$363$	56.9348	−	181.934i	0.156845	−	0.501197i
$364$	201.029	−	73.1685i	0.552277	−	0.201012i
$365$	34.1399	+	6.11000i	0.0935340	+	0.0167397i
$366$	24.5459	−	78.4361i	0.0670654	−	0.214306i
$367$	108.705	−	19.1677i	0.296200	−	0.0522280i	−0.0235736	−	0.999722i	$-0.507504\pi$
$367$	108.705	−	19.1677i	0.296200	−	0.0522280i	0.319773	+	0.947494i	$0.396393\pi$
$368$	−11.6714	+	20.2155i	−0.0317159	+	0.0549335i
$369$	−190.303	+	134.472i	−0.515725	+	0.364422i
$370$	−0.825435	+	322.253i	−0.00223090	+	0.870954i
$371$	−734.842	−	875.751i	−1.98071	−	2.36051i
$372$	62.9170	+	32.5811i	0.169132	+	0.0875837i
$373$	−280.667	−	49.4892i	−0.752460	−	0.132679i	−0.215753	−	0.976448i	$-0.569221\pi$
$373$	−280.667	−	49.4892i	−0.752460	−	0.132679i	−0.536707	+	0.843769i	$0.680332\pi$
$374$	219.467	−	261.551i	0.586811	−	0.699334i
$375$	−141.585	−	347.244i	−0.377560	−	0.925985i
$376$	−97.3915	−	35.4476i	−0.259020	−	0.0942755i
$377$	506.522			1.34356
$378$	−16.3472	+	439.272i	−0.0432466	+	1.16210i
$379$	551.847			1.45606			0.728030	−	0.685545i	$-0.240436\pi$
$379$	551.847			1.45606			0.728030	+	0.685545i	$0.240436\pi$
$380$	59.5125	−	49.6777i	0.156612	−	0.130731i
$381$	37.1398	−	286.859i	0.0974797	−	0.752910i
$382$	−46.6972	+	55.6516i	−0.122244	+	0.145685i
$383$	69.2607	−	392.797i	0.180837	−	1.02558i	−0.750351	−	0.661040i	$-0.770115\pi$
$383$	69.2607	−	392.797i	0.180837	−	1.02558i	0.931188	−	0.364539i	$-0.118773\pi$
$384$	1.55323	+	33.9056i	0.00404488	+	0.0882957i
$385$	74.6626	+	429.868i	0.193929	+	1.11654i
$386$	−27.6434	+	15.9599i	−0.0716150	+	0.0413470i
$387$	−89.4218	−	189.637i	−0.231064	−	0.490018i
$388$	22.9690	+	13.2612i	0.0591984	+	0.0341782i
$389$	115.578	−	20.3796i	0.297116	−	0.0523896i	−0.0231029	−	0.999733i	$-0.507355\pi$
$389$	115.578	−	20.3796i	0.297116	−	0.0523896i	0.320219	+	0.947343i	$0.396243\pi$
$390$	42.5808	+	192.449i	0.109182	+	0.493458i
$391$	174.664	−	63.5725i	0.446711	−	0.162590i
$392$	222.008	−	80.8042i	0.566346	−	0.206133i
$393$	156.952	+	700.848i	0.399370	+	1.78333i
$394$	−55.9215	−	317.147i	−0.141933	−	0.804941i
$395$	−5.19318	−	9.04829i	−0.0131473	−	0.0229071i
$396$	−34.7471	+	131.940i	−0.0877451	+	0.333181i
$397$	−181.811	+	104.968i	−0.457961	+	0.264404i	−0.711187	−	0.703003i	$-0.751842\pi$
$397$	−181.811	+	104.968i	−0.457961	+	0.264404i	0.253225	+	0.967407i	$0.418509\pi$
$398$	−5.42450	+	4.55170i	−0.0136294	+	0.0114364i
$399$	−144.336	−	225.494i	−0.361745	−	0.565147i
$400$	−94.1432	+	33.7202i	−0.235358	+	0.0843004i
$401$	−257.296	+	306.633i	−0.641635	+	0.764671i	−0.984628	−	0.174667i	$-0.944115\pi$
$401$	−257.296	+	306.633i	−0.641635	+	0.764671i	0.342992	+	0.939338i	$0.388560\pi$
$402$	−240.665	−	183.850i	−0.598670	−	0.457338i
$403$	37.5269	−	103.104i	0.0931188	−	0.255842i
$404$		−	64.3583i		−	0.159303i
$405$	−399.263	−	67.9252i	−0.985835	−	0.167717i
$406$	887.527			2.18603
$407$	324.611	+	118.149i	0.797570	+	0.290292i
$408$	164.066	−	214.768i	0.402123	−	0.526392i
$409$	470.357	+	394.676i	1.15002	+	0.964979i	0.999720	−	0.0236620i	$-0.00753255\pi$
$409$	470.357	+	394.676i	1.15002	+	0.964979i	0.150297	+	0.988641i	$0.451977\pi$
$410$	−118.038	+	139.943i	−0.287898	+	0.341325i
$411$	−164.052	+	105.008i	−0.399154	+	0.255494i
$412$	−238.028	−	283.670i	−0.577737	−	0.688520i
$413$	157.028	+	271.980i	0.380213	+	0.658548i
$414$	−52.2957	+	52.7464i	−0.126318	+	0.127407i
$415$	−331.736	−	577.997i	−0.799363	−	1.39276i
$416$	51.7623	−	9.12709i	0.124429	−	0.0219401i
$417$	−366.568	+	82.0917i	−0.879060	+	0.196863i
$418$	−28.4220	−	78.0887i	−0.0679951	−	0.186815i
$419$	−1.21929	−	3.34996i	−0.00290999	−	0.00799514i	0.938229	−	0.346015i	$-0.112465\pi$
$419$	−1.21929	−	3.34996i	−0.00290999	−	0.00799514i	−0.941139	+	0.338019i	$0.890243\pi$
$420$	74.6101	+	337.208i	0.177643	+	0.802877i
$421$	18.3778	+	104.226i	0.0436528	+	0.247567i	0.998824	−	0.0484873i	$-0.0154400\pi$
$421$	18.3778	+	104.226i	0.0436528	+	0.247567i	−0.955171	+	0.296055i	$0.904329\pi$
$422$	−179.711	+	311.268i	−0.425855	+	0.737602i
$423$	−270.954	−	187.997i	−0.640554	−	0.444437i
$424$	−140.438	−	243.247i	−0.331223	−	0.573695i
$425$	746.849	+	276.172i	1.75729	+	0.649816i
$426$	64.7781	−	2.96752i	0.152061	−	0.00696602i
$427$	−219.621	−	38.7252i	−0.514336	−	0.0906913i
$428$	45.0689	+	37.8173i	0.105301	+	0.0883581i
$429$	209.538	+	27.1290i	0.488433	+	0.0632377i
$430$	−105.561	−	126.459i	−0.245490	−	0.294090i
$431$			181.950i			0.422158i	0.977469	+	0.211079i	$0.0676977\pi$
$431$			181.950i			0.422158i	−0.977469	+	0.211079i	$0.932302\pi$
$432$	−22.6964	+	105.588i	−0.0525379	+	0.244417i
$433$			563.392i			1.30114i	0.759448	+	0.650568i	$0.225469\pi$
$433$			563.392i			1.30114i	−0.759448	+	0.650568i	$0.774531\pi$
$434$	65.7546	−	180.659i	0.151508	−	0.416265i
$435$	−107.071	+	810.676i	−0.246139	+	1.86362i
$436$	−111.943	−	93.9314i	−0.256750	−	0.215439i
$437$	7.85576	−	44.5522i	0.0179766	−	0.101950i
$438$	13.5327	−	26.1329i	0.0308967	−	0.0596641i
$439$	583.472	−	489.591i	1.32909	−	1.11524i	0.344804	−	0.938675i	$-0.387945\pi$
$439$	583.472	−	489.591i	1.32909	−	1.11524i	0.984289	−	0.176567i	$-0.0564991\pi$
$440$	−0.274576	+	107.196i	−0.000624037	+	0.243627i
$441$	748.612	−	68.7330i	1.69753	−	0.155857i
$442$	−362.456	−	209.264i	−0.820037	−	0.473449i
$443$	−76.7880	−	435.486i	−0.173336	−	0.983039i	−0.940047	−	0.341046i	$-0.889219\pi$
$443$	−76.7880	−	435.486i	−0.173336	−	0.983039i	0.766710	−	0.641993i	$-0.221892\pi$
$444$	260.962	+	81.6659i	0.587752	+	0.183932i
$445$	−583.827	−	104.487i	−1.31197	−	0.234802i
$446$	−113.308	−	311.312i	−0.254055	−	0.698009i
$447$	291.894	+	91.3458i	0.653006	+	0.204353i
$448$	90.6978	−	15.9925i	0.202451	−	0.0356975i
$449$	134.697	+	77.7671i	0.299992	+	0.173201i	0.642439	−	0.766336i	$-0.277922\pi$
$449$	134.697	+	77.7671i	0.299992	+	0.173201i	−0.342447	+	0.939537i	$0.611256\pi$
$450$	−317.010	+	27.4690i	−0.704467	+	0.0610422i
$451$	98.1256	+	169.959i	0.217573	+	0.376848i
$452$	−153.085	+	128.454i	−0.338684	+	0.284190i
$453$	−526.825	−	272.813i	−1.16297	−	0.602236i
$454$	82.3562	−	467.065i	0.181401	−	1.02878i
$455$	503.039	−	181.633i	1.10558	−	0.399194i
$456$	−25.3030	−	60.7181i	−0.0554890	−	0.133154i
$457$	−97.8045	+	268.716i	−0.214014	+	0.587999i	−0.999524	−	0.0308499i	$-0.990179\pi$
$457$	−97.8045	+	268.716i	−0.214014	+	0.587999i	0.785510	+	0.618849i	$0.212401\pi$
$458$	−534.143			−1.16625
$459$	678.882	−	527.901i	1.47905	−	1.15011i
$460$	−29.3080	+	50.4639i	−0.0637130	+	0.109704i
$461$	−48.8103	+	134.105i	−0.105879	+	0.290901i	−0.981307	−	0.192448i	$-0.938357\pi$
$461$	−48.8103	+	134.105i	−0.105879	+	0.290901i	0.875428	+	0.483348i	$0.160580\pi$
$462$	367.152	+	47.5354i	0.794701	+	0.102890i
$463$	18.6134	−	22.1825i	0.0402016	−	0.0479104i	−0.745569	−	0.666428i	$-0.767822\pi$
$463$	18.6134	−	22.1825i	0.0402016	−	0.0479104i	0.785771	+	0.618518i	$0.212267\pi$
$464$	214.745	+	37.8653i	0.462812	+	0.0816063i
$465$	157.083	+	81.8555i	0.337813	+	0.176033i
$466$	−443.521	+	372.158i	−0.951762	+	0.798623i
$467$	116.232	+	201.321i	0.248892	+	0.431093i	0.963219	−	0.268719i	$-0.0866003\pi$
$467$	116.232	+	201.321i	0.248892	+	0.431093i	−0.714327	+	0.699812i	$0.753267\pi$
$468$	166.672	+	13.8616i	0.356137	+	0.0296187i
$469$	−410.887	+	711.678i	−0.876092	+	1.51744i
$470$	−243.251	−	89.2424i	−0.517555	−	0.189877i
$471$	457.057	−	420.623i	0.970398	−	0.893043i
$472$	26.3905	+	72.5074i	0.0559121	+	0.153617i
$473$	−165.931	+	60.3941i	−0.350806	+	0.127683i
$474$	−8.63845	+	1.93455i	−0.0182246	+	0.00408133i
$475$	149.099	−	123.813i	0.313892	−	0.260659i
$476$	−635.096	−	366.673i	−1.33423	−	0.770321i
$477$	−235.020	−	862.291i	−0.492705	−	1.80774i
$478$	−67.0541	+	38.7137i	−0.140280	+	0.0809910i
$479$	−24.4024	−	29.0817i	−0.0509446	−	0.0607134i	0.739970	−	0.672639i	$-0.234839\pi$
$479$	−24.4024	−	29.0817i	−0.0509446	−	0.0607134i	−0.790915	+	0.611926i	$0.790395\pi$
$480$	3.66595	+	84.7736i	0.00763741	+	0.176612i
$481$	73.5311	−	417.015i	0.152871	−	0.866976i
$482$	204.247	+	171.384i	0.423750	+	0.355568i
$483$	160.159	+	122.349i	0.331592	+	0.253311i
$484$	−119.425	−	43.4673i	−0.246747	−	0.0898085i
$485$	57.3374	+	33.2999i	0.118221	+	0.0686595i
$486$	−155.403	+	306.509i	−0.319759	+	0.630678i
$487$		−	103.578i		−	0.212685i	−0.994330	−	0.106343i	$-0.966086\pi$
$487$		−	103.578i		−	0.212685i	0.994330	−	0.106343i	$-0.0339140\pi$
$488$	−51.4871	−	18.7398i	−0.105506	−	0.0384012i
$489$	623.595	+	476.379i	1.27525	+	0.974191i
$490$	555.535	−	200.588i	1.13374	−	0.409364i
$491$	−323.680	−	57.0736i	−0.659227	−	0.116239i	−0.165980	−	0.986129i	$-0.553079\pi$
$491$	−323.680	−	57.0736i	−0.659227	−	0.116239i	−0.493247	+	0.869890i	$0.664190\pi$
$492$	83.7482	+	130.838i	0.170220	+	0.265931i
$493$	−1116.10	−	1330.11i	−2.26389	−	2.69800i
$494$	−88.2178	+	50.9326i	−0.178578	+	0.103102i
$495$	−87.7122	+	329.626i	−0.177196	+	0.665910i
$496$	23.6175	−	40.9067i	0.0476159	−	0.0824732i
$497$	−30.5544	−	173.282i	−0.0614776	−	0.348657i
$498$	−551.816	+	123.577i	−1.10807	+	0.248147i
$499$	−625.580	+	227.692i	−1.25367	+	0.456298i	−0.881639	−	0.471924i	$-0.843560\pi$
$499$	−625.580	+	227.692i	−1.25367	+	0.456298i	−0.372028	+	0.928222i	$0.621337\pi$
$500$	−235.573	+	83.6973i	−0.471147	+	0.167395i
$501$	398.588	+	433.114i	0.795585	+	0.864498i
$502$	−148.048	+	26.1049i	−0.294917	+	0.0520019i
$503$	−220.580	+	382.056i	−0.438529	+	0.759554i	−0.997576	−	0.0695817i	$-0.977834\pi$
$503$	−220.580	+	382.056i	−0.438529	+	0.759554i	0.559048	+	0.829136i	$0.311167\pi$
$504$	292.043	+	24.2882i	0.579450	+	0.0481909i
$505$	0.412125	−	160.895i	0.000816089	−	0.318605i
$506$	40.2107	+	47.9212i	0.0794677	+	0.0947059i
$507$	11.3492	+	247.743i	0.0223851	+	0.488645i
$508$	−189.906	−	33.4855i	−0.373830	−	0.0659163i
$509$	164.382	−	195.903i	0.322951	−	0.384878i	−0.580003	−	0.814614i	$-0.696949\pi$
$509$	164.382	−	195.903i	0.322951	−	0.384878i	0.902955	+	0.429736i	$0.141393\pi$
$510$	411.540	−	535.867i	0.806941	−	1.05072i
$511$	−75.0378	−	27.3115i	−0.146845	−	0.0534472i
$512$	22.6274			0.0441942
$513$	−28.6553	−	207.338i	−0.0558582	−	0.404167i
$514$	495.133			0.963294
$515$	−593.251	−	710.698i	−1.15194	−	1.38000i
$516$	−129.020	+	53.7665i	−0.250039	+	0.104199i
$517$	−178.534	+	212.769i	−0.345328	+	0.411545i
$518$	128.841	−	730.694i	0.248728	−	1.41061i
$519$	−49.0212	−	25.3853i	−0.0944531	−	0.0489119i
$520$	129.464	−	22.4862i	0.248969	−	0.0432427i
$521$	516.815	−	298.383i	0.991968	−	0.572713i	0.0861057	−	0.996286i	$-0.472558\pi$
$521$	516.815	−	298.383i	0.991968	−	0.572713i	0.905862	+	0.423573i	$0.139224\pi$
$522$	630.099	+	290.535i	1.20709	+	0.556580i
$523$	620.460	+	358.223i	1.18635	+	0.684938i	0.957474	−	0.288518i	$-0.0931625\pi$
$523$	620.460	+	358.223i	1.18635	+	0.684938i	0.228873	+	0.973456i	$0.426496\pi$
$524$	471.531	−	83.1436i	0.899868	−	0.158671i
$525$	184.365	+	843.496i	0.351172	+	1.60666i
$526$	286.169	−	104.157i	0.544048	−	0.198017i
$527$	−353.438	+	128.641i	−0.670659	+	0.244100i
$528$	86.8075	+	27.1657i	0.164408	+	0.0514502i
$529$	−85.9462	−	487.425i	−0.162469	−	0.921408i
$530$	−349.537	−	609.014i	−0.659504	−	1.14908i
$531$	22.4481	+	244.496i	0.0422751	+	0.460444i
$532$	−154.575	+	89.2440i	−0.290555	+	0.167752i
$533$	184.285	−	154.633i	0.345750	−	0.290119i
$534$	−231.424	+	446.899i	−0.433377	+	0.836889i
$535$	112.430	+	94.8315i	0.210149	+	0.177255i
$536$	−129.781	+	154.666i	−0.242128	+	0.288557i
$537$	−532.423	+	221.876i	−0.991476	+	0.413177i
$538$	88.0660	−	241.959i	0.163691	−	0.449739i
$539$		−	633.142i		−	1.17466i
$540$	−57.4169	+	263.824i	−0.106328	+	0.488564i
$541$	−234.523			−0.433499			−0.216749	−	0.976227i	$-0.569545\pi$
$541$	−234.523			−0.433499			−0.216749	+	0.976227i	$0.569545\pi$
$542$	304.684	+	110.896i	0.562148	+	0.204605i
$543$	−126.174	−	16.3358i	−0.232364	−	0.0300843i
$544$	−138.023	−	115.815i	−0.253719	−	0.212896i
$545$	−279.255	−	235.545i	−0.512395	−	0.432192i
$546$	−20.7677	−	453.340i	−0.0380362	−	0.830292i
$547$	380.960	+	454.011i	0.696454	+	0.830001i	0.992120	−	0.125290i	$-0.0399862\pi$
$547$	380.960	+	454.011i	0.696454	+	0.830001i	−0.295667	+	0.955291i	$0.595542\pi$
$548$	64.9272	+	112.457i	0.118480	+	0.205214i
$549$	−143.243	−	99.3866i	−0.260916	−	0.181032i
$550$	−1.37288	+	267.987i	−0.00249614	+	0.487249i
$551$	−416.185	+	73.3846i	−0.755326	+	0.133184i
$552$	33.5320	+	36.4365i	0.0607463	+	0.0660081i
$553$	8.21547	+	22.5718i	0.0148562	+	0.0408171i
$554$	−52.2913	−	143.669i	−0.0943887	−	0.259331i
$555$	651.880	+	205.835i	1.17456	+	0.370874i
$556$	43.4870	+	246.627i	0.0782141	+	0.443574i
$557$	373.920	−	647.648i	0.671310	−	1.16274i	−0.306223	−	0.951960i	$-0.599065\pi$
$557$	373.920	−	647.648i	0.671310	−	1.16274i	0.977533	−	0.210783i	$-0.0676015\pi$
$558$	105.822	−	106.734i	0.189645	−	0.191279i
$559$	108.227	+	187.455i	0.193608	+	0.335339i
$560$	226.846	−	39.4003i	0.405083	−	0.0703576i
$561$	−390.467	−	610.018i	−0.696019	−	1.08738i
$562$	107.278	+	18.9159i	0.190885	+	0.0336582i
$563$	−379.982	−	318.843i	−0.674924	−	0.566328i	0.239595	−	0.970873i	$-0.422985\pi$
$563$	−379.982	−	318.843i	−0.674924	−	0.566328i	−0.914518	+	0.404545i	$0.867430\pi$
$564$	−133.466	+	174.711i	−0.236642	+	0.309772i
$565$	−383.535	+	320.153i	−0.678822	+	0.566643i
$566$		−	343.591i		−	0.607051i
$567$	878.951	+	311.397i	1.55018	+	0.549200i
$568$		−	43.2307i		−	0.0761104i
$569$	59.5163	−	163.520i	0.104598	−	0.287381i	−0.876343	−	0.481688i	$-0.840024\pi$
$569$	59.5163	−	163.520i	0.104598	−	0.287381i	0.980941	+	0.194307i	$0.0622460\pi$
$570$	−62.8685	−	151.957i	−0.110296	−	0.266591i
$571$	−68.7046	−	57.6500i	−0.120323	−	0.100963i	0.580641	−	0.814160i	$-0.302802\pi$
$571$	−68.7046	−	57.6500i	−0.120323	−	0.100963i	−0.700964	+	0.713197i	$0.747247\pi$
$572$	24.4597	−	138.718i	0.0427617	−	0.242514i
$573$	83.0817	+	129.797i	0.144994	+	0.226521i
$574$	322.904	−	270.948i	0.562550	−	0.472035i
$575$	−73.5928	+	125.972i	−0.127988	+	0.219081i
$576$	69.6260	+	18.3364i	0.120878	+	0.0318340i
$577$	−654.503	−	377.877i	−1.13432	−	0.654900i	−0.189302	−	0.981919i	$-0.560623\pi$
$577$	−654.503	−	377.877i	−1.13432	−	0.654900i	−0.945018	+	0.327019i	$0.893956\pi$
$578$	178.162	+	1010.41i	0.308238	+	1.74811i
$579$	14.7974	+	66.0756i	0.0255568	+	0.114120i
$580$	536.618	+	96.0381i	0.925203	+	0.165583i
$581$	524.797	+	1441.87i	0.903266	+	2.48170i
$582$	41.3993	−	38.0992i	0.0711328	−	0.0654625i
$583$	−741.287	+	130.709i	−1.27150	+	0.224201i
$584$	−16.9908	−	9.80965i	−0.0290939	−	0.0167973i
$585$	416.590	+	35.7211i	0.712120	+	0.0610617i
$586$	101.091	+	175.095i	0.172510	+	0.298797i
$587$	793.668	−	665.966i	1.35207	−	1.13453i	0.373731	−	0.927537i	$-0.378078\pi$
$587$	793.668	−	665.966i	1.35207	−	1.13453i	0.978343	−	0.206989i	$-0.0663663\pi$
$588$	−22.9350	−	500.649i	−0.0390051	−	0.851444i
$589$	−15.8964	+	90.1527i	−0.0269887	+	0.153061i
$590$	65.5118	+	181.437i	0.111037	+	0.307520i
$591$	−677.494	−	87.7155i	−1.14635	−	0.148419i
$592$	62.3484	−	171.301i	0.105318	−	0.289359i
$593$	30.0825			0.0507294			0.0253647	−	0.999678i	$-0.491925\pi$
$593$	30.0825			0.0507294			0.0253647	+	0.999678i	$0.491925\pi$
$594$	245.098	+	153.936i	0.412623	+	0.259152i
$595$	−1585.39	−	920.746i	−2.66451	−	1.54747i
$596$	69.7386	−	191.605i	0.117011	−	0.321485i
$597$	5.77823	+	13.8657i	0.00967877	+	0.0232256i
$598$	49.2906	−	58.7423i	0.0824258	−	0.0982312i
$599$	−309.176	−	54.5160i	−0.516153	−	0.0910117i	−0.0904970	−	0.995897i	$-0.528846\pi$
$599$	−309.176	−	54.5160i	−0.516153	−	0.0910117i	−0.425656	+	0.904885i	$0.639957\pi$
$600$	8.62200	+	211.957i	0.0143700	+	0.353261i
$601$	94.9714	−	79.6904i	0.158022	−	0.132596i	−0.560348	−	0.828257i	$-0.689333\pi$
$601$	94.9714	−	79.6904i	0.158022	−	0.132596i	0.718371	+	0.695661i	$0.244888\pi$
$602$	189.635	+	328.458i	0.315009	+	0.545611i
$603$	−524.679	+	370.749i	−0.870114	+	0.614841i
$604$	−197.757	+	342.526i	−0.327413	+	0.567095i
$605$	−298.284	−	109.433i	−0.493032	−	0.180881i
$606$	−130.294	−	40.7743i	−0.215006	−	0.0672843i
$607$	−114.998	−	315.953i	−0.189452	−	0.520516i	0.808207	−	0.588899i	$-0.200438\pi$
$607$	−114.998	−	315.953i	−0.189452	−	0.520516i	−0.997659	+	0.0683827i	$0.978216\pi$
$608$	−41.2083	+	14.9986i	−0.0677767	+	0.0246687i
$609$	562.294	−	1796.80i	0.923307	−	2.95041i
$610$	−128.597	−	47.1790i	−0.210815	−	0.0773426i
$611$	294.855	+	170.234i	0.482577	+	0.278616i
$612$	−330.854	−	468.219i	−0.540611	−	0.765064i
$613$	494.196	−	285.324i	0.806192	−	0.465455i	−0.0394395	−	0.999222i	$-0.512557\pi$
$613$	494.196	−	285.324i	0.806192	−	0.465455i	0.845632	+	0.533767i	$0.179224\pi$
$614$	118.230	+	140.901i	0.192556	+	0.229480i
$615$	208.532	+	327.630i	0.339076	+	0.532732i
$616$	42.8583	−	243.061i	0.0695751	−	0.394580i
$617$	342.354	+	287.269i	0.554868	+	0.465590i	0.876586	−	0.481246i	$-0.159816\pi$
$617$	342.354	+	287.269i	0.554868	+	0.465590i	−0.321717	+	0.946836i	$0.604260\pi$
$618$	−725.094	+	302.168i	−1.17329	+	0.488945i
$619$	792.722	+	288.527i	1.28065	+	0.466118i	0.890647	−	0.454695i	$-0.150252\pi$
$619$	792.722	+	288.527i	1.28065	+	0.466118i	0.390003	+	0.920814i	$0.372474\pi$
$620$	59.3055	−	102.115i	0.0956540	−	0.164702i
$621$	73.6532	+	139.290i	0.118604	+	0.224300i
$622$		−	747.264i		−	1.20139i
$623$	1283.22	+	467.054i	2.05975	+	0.749686i
$624$	14.3163	−	110.575i	0.0229427	−	0.177204i
$625$	−589.467	+	207.734i	−0.943147	+	0.332374i
$626$	−489.542	−	86.3195i	−0.782016	−	0.137891i
$627$	−176.098	+	8.06713i	−0.280857	+	0.0128662i
$628$	−266.178	−	317.218i	−0.423850	−	0.505125i
$629$	−1257.09	+	725.783i	−1.99856	+	1.15387i
$630$	729.949	+	62.5905i	1.15865	+	0.0993500i
$631$	−283.551	+	491.125i	−0.449368	+	0.778328i	−0.998345	−	0.0575093i	$-0.981684\pi$
$631$	−283.551	+	491.125i	−0.449368	+	0.778328i	0.548977	+	0.835837i	$0.315017\pi$
$632$	1.02480	+	5.81195i	0.00162152	+	0.00919612i
$633$	516.307	+	561.029i	0.815651	+	0.886302i
$634$	−139.170	+	50.6537i	−0.219511	+	0.0798953i
$635$	−474.548	−	84.9296i	−0.747320	−	0.133747i
$636$	−581.428	+	130.209i	−0.914195	+	0.204731i
$637$	−764.321	+	134.770i	−1.19988	+	0.211571i
$638$	292.187	−	506.082i	0.457973	−	0.793232i
$639$	35.0325	−	133.024i	0.0548240	−	0.208175i
$640$	56.5684	+	0.144897i	0.0883881	+	0.000226401i
$641$	612.866	+	730.385i	0.956109	+	1.13945i	0.990148	+	0.140026i	$0.0447186\pi$
$641$	612.866	+	730.385i	0.956109	+	1.13945i	−0.0340387	+	0.999421i	$0.510837\pi$
$642$	105.115	−	67.2829i	0.163730	−	0.104802i
$643$	298.081	+	52.5597i	0.463578	+	0.0817413i	0.400559	−	0.916271i	$-0.368816\pi$
$643$	298.081	+	52.5597i	0.463578	+	0.0817413i	0.0630192	+	0.998012i	$0.479927\pi$
$644$	86.3669	−	102.928i	0.134110	−	0.159826i
$645$	−322.894	+	133.590i	−0.500611	+	0.207116i
$646$	328.131	+	119.430i	0.507943	+	0.184876i
$647$	332.617			0.514091			0.257046	−	0.966399i	$-0.417251\pi$
$647$	332.617			0.514091			0.257046	+	0.966399i	$0.417251\pi$
$648$	199.384	+	112.844i	0.307692	+	0.174143i
$649$	206.783			0.318618
$650$	323.802	−	55.3862i	0.498157	−	0.0852096i
$651$	−324.086	−	247.577i	−0.497828	−	0.380303i
$652$	336.278	−	400.761i	0.515764	−	0.614664i
$653$	126.647	−	718.250i	0.193946	−	1.09992i	−0.719965	−	0.694010i	$-0.755842\pi$
$653$	126.647	−	718.250i	0.193946	−	1.09992i	0.913911	−	0.405914i	$-0.133047\pi$
$654$	−261.086	+	167.119i	−0.399214	+	0.255533i
$655$	1179.36	−	204.839i	1.80054	−	0.312731i
$656$	89.6890	−	51.7820i	0.136721	−	0.0789359i
$657$	−44.3324	−	43.9536i	−0.0674771	−	0.0669005i
$658$	516.644	+	298.285i	0.785173	+	0.453320i
$659$	858.018	−	151.292i	1.30200	−	0.229578i	0.520704	−	0.853738i	$-0.325670\pi$
$659$	858.018	−	151.292i	1.30200	−	0.229578i	0.781297	+	0.624160i	$0.214559\pi$
$660$	216.844	+	68.4699i	0.328552	+	0.103742i
$661$	−954.661	+	347.468i	−1.44427	+	0.525671i	−0.940984	−	0.338451i	$-0.890097\pi$
$661$	−954.661	+	347.468i	−1.44427	+	0.525671i	−0.503284	+	0.864121i	$0.667875\pi$
$662$	180.385	−	65.6547i	0.272485	−	0.0991763i
$663$	−653.291	+	601.214i	−0.985356	+	0.906809i
$664$	65.4636	+	371.262i	0.0985897	+	0.559130i
$665$	−387.008	+	222.119i	−0.581967	+	0.334014i
$666$	330.666	−	476.579i	0.496495	−	0.715583i
$667$	275.509	−	159.065i	0.413058	−	0.238479i
$668$	300.600	−	252.234i	0.450000	−	0.377595i
$669$	−702.039	+	32.1608i	−1.04939	+	0.0480730i
$670$	−325.441	+	385.834i	−0.485733	+	0.575871i
$671$	−94.3842	+	112.483i	−0.140662	+	0.167634i
$672$	25.0849	−	193.750i	0.0373288	−	0.288319i
$673$	−270.937	+	744.392i	−0.402581	+	1.10608i	0.558426	+	0.829554i	$0.311406\pi$
$673$	−270.937	+	744.392i	−0.402581	+	1.10608i	−0.961006	+	0.276526i	$0.910817\pi$
$674$		−	137.815i		−	0.204473i
$675$	−145.231	+	659.191i	−0.215157	+	0.976579i
$676$	165.335			0.244578
$677$	−838.302	−	305.117i	−1.23826	−	0.450690i	−0.361841	−	0.932240i	$-0.617852\pi$
$677$	−838.302	−	305.117i	−1.23826	−	0.450690i	−0.876419	+	0.481550i	$0.840074\pi$
$678$	163.068	+	391.304i	0.240513	+	0.577144i
$679$	−116.947	−	98.1306i	−0.172235	−	0.144522i
$680$	−344.315	−	290.421i	−0.506346	−	0.427090i
$681$	−893.398	−	462.640i	−1.31189	−	0.679354i
$682$	−81.3674	−	96.9699i	−0.119307	−	0.142185i
$683$	−266.684	−	461.910i	−0.390459	−	0.676296i	0.602051	−	0.798458i	$-0.294351\pi$
$683$	−266.684	−	461.910i	−0.390459	−	0.676296i	−0.992510	+	0.122162i	$0.961017\pi$
$684$	−138.955	+	12.7580i	−0.203150	+	0.0186520i
$685$	161.597	+	281.558i	0.235908	+	0.411033i
$686$	−553.613	+	97.6168i	−0.807015	+	0.142299i
$687$	−338.407	+	1081.37i	−0.492586	+	1.57405i
$688$	31.8706	+	87.5638i	0.0463236	+	0.127273i
$689$	315.580	+	867.050i	0.458026	+	1.25842i
$690$	83.5963	+	91.3056i	0.121154	+	0.132327i
$691$	192.060	+	1089.23i	0.277945	+	1.57630i	0.729449	+	0.684035i	$0.239776\pi$
$691$	192.060	+	1089.23i	0.277945	+	1.57630i	−0.451505	+	0.892269i	$0.649113\pi$
$692$	−18.4013	+	31.8721i	−0.0265915	+	0.0460579i
$693$	328.845	−	713.184i	0.474524	−	1.02913i
$694$	−394.643	−	683.541i	−0.568649	−	0.984930i
$695$	107.138	+	616.845i	0.154155	+	0.887546i
$696$	212.710	−	410.762i	0.305618	−	0.590175i
$697$	−812.125	−	143.200i	−1.16517	−	0.205451i
$698$	290.079	+	243.405i	0.415586	+	0.348718i
$699$	472.442	+	1133.69i	0.675883	+	1.62188i
$700$	567.366	−	97.0477i	0.810523	−	0.138640i
$701$		−	794.379i		−	1.13321i	−0.823990	−	0.566604i	$-0.808257\pi$
$701$		−	794.379i		−	1.13321i	0.823990	−	0.566604i	$-0.191743\pi$
$702$	133.658	−	328.646i	0.190396	−	0.468157i
$703$			353.295i			0.502553i
$704$	20.7399	−	56.9823i	0.0294600	−	0.0809407i
$705$	−334.783	+	435.923i	−0.474870	+	0.618330i
$706$	−293.193	−	246.018i	−0.415287	−	0.348468i
$707$	−64.3281	+	364.823i	−0.0909874	+	0.516015i
$708$	163.511	−	7.49054i	0.230948	−	0.0105799i
$709$	−921.539	+	773.263i	−1.29977	+	1.09064i	−0.309589	+	0.950870i	$0.600192\pi$
$709$	−921.539	+	773.263i	−1.29977	+	1.09064i	−0.990184	+	0.139769i	$0.955364\pi$
$710$	0.276832	−	108.076i	0.000389904	−	0.152220i
$711$	−1.55640	+	18.7142i	−0.00218903	+	0.0263210i
$712$	290.560	+	167.755i	0.408090	+	0.235611i
$713$	−11.9665	−	67.8656i	−0.0167834	−	0.0951832i
$714$	−1144.70	+	1053.45i	−1.60322	+	1.47542i
$715$	62.0374	−	346.637i	0.0867655	−	0.484807i
$716$	131.519	+	361.346i	0.183686	+	0.504673i
$717$	35.8938	+	160.278i	0.0500610	+	0.223540i
$718$	−501.161	+	88.3682i	−0.697996	+	0.123075i
$719$	−1073.70	−	619.902i	−1.49333	−	0.862172i	−0.493355	−	0.869828i	$-0.664230\pi$
$719$	−1073.70	−	619.902i	−1.49333	−	0.862172i	−0.999971	+	0.00765552i	$0.997563\pi$
$720$	173.947	+	46.2867i	0.241593	+	0.0642871i
$721$	1065.75	+	1845.93i	1.47816	+	2.56024i
$722$	−325.984	+	273.533i	−0.451502	+	0.378855i
$723$	476.369	−	304.919i	0.658878	−	0.421741i
$724$	−14.7285	+	83.5294i	−0.0203432	+	0.115372i
$725$	1340.92	+	243.531i	1.84955	+	0.335904i
$726$	−163.662	+	214.238i	−0.225430	+	0.295094i
$727$	139.140	−	382.285i	0.191390	−	0.525839i	−0.806467	−	0.591279i	$-0.798623\pi$
$727$	139.140	−	382.285i	0.191390	−	0.525839i	0.997856	+	0.0654407i	$0.0208453\pi$
$728$	−302.543			−0.415581
$729$	522.073	+	508.803i	0.716150	+	0.697946i
$730$	−42.4141	−	24.6329i	−0.0581015	−	0.0337436i
$731$	253.778	−	697.248i	0.347165	−	0.953828i
$732$	−70.5585	+	92.3632i	−0.0963913	+	0.126179i
$733$	−422.169	+	503.122i	−0.575947	+	0.686387i	−0.972840	−	0.231478i	$-0.925644\pi$
$733$	−422.169	+	503.122i	−0.575947	+	0.686387i	0.396893	+	0.917865i	$0.370088\pi$
$734$	−153.732	−	27.1072i	−0.209445	−	0.0369308i
$735$	−54.1314	−	1251.77i	−0.0736482	−	1.70308i
$736$	25.2885	−	21.2196i	0.0343594	−	0.0288310i
$737$	270.540	+	468.589i	0.367083	+	0.635806i
$738$	317.941	−	86.6558i	0.430814	−	0.117420i
$739$	−13.8328	+	23.9592i	−0.0187183	+	0.0324211i	−0.875233	−	0.483702i	$-0.839292\pi$
$739$	−13.8328	+	23.9592i	−0.0187183	+	0.0324211i	0.856515	+	0.516123i	$0.172625\pi$
$740$	156.967	−	427.851i	0.212118	−	0.578177i
$741$	47.2226	+	210.866i	0.0637282	+	0.284569i
$742$	552.959	+	1519.24i	0.745228	+	2.04750i
$743$	−280.507	+	102.096i	−0.377532	+	0.137411i	−0.523815	−	0.851832i	$-0.675492\pi$
$743$	−280.507	+	102.096i	−0.377532	+	0.137411i	0.146282	+	0.989243i	$0.453269\pi$
$744$	−67.8528	−	73.7302i	−0.0912001	−	0.0990997i
$745$	175.573	−	478.565i	0.235668	−	0.642369i
$746$	349.049	+	201.523i	0.467894	+	0.270139i
$747$	−99.4214	+	1195.45i	−0.133094	+	1.60033i
$748$	−418.165	+	241.428i	−0.559044	+	0.322764i
$749$	−217.679	−	259.419i	−0.290626	−	0.346354i
$750$	20.1976	+	529.945i	0.0269302	+	0.706594i
$751$	−39.0718	+	221.587i	−0.0520263	+	0.295056i	−0.999708	−	0.0241607i	$-0.992309\pi$
$751$	−39.0718	+	221.587i	−0.0520263	+	0.295056i	0.947682	+	0.319217i	$0.103420\pi$
$752$	112.280	+	94.2145i	0.149309	+	0.125285i
$753$	−40.9468	+	316.263i	−0.0543782	+	0.420004i
$754$	−673.130	−	244.999i	−0.892746	−	0.324933i
$755$	−496.585	+	855.045i	−0.657728	+	1.13251i
$756$	234.196	−	575.853i	0.309783	−	0.761711i
$757$			823.942i			1.08843i	0.838945	+	0.544216i	$0.183173\pi$
$757$			823.942i			1.08843i	−0.838945	+	0.544216i	$0.816827\pi$
$758$	−733.364	−	266.923i	−0.967499	−	0.352141i
$759$	122.492	−	51.0460i	0.161386	−	0.0672543i
$760$	−103.116	+	37.2324i	−0.135679	+	0.0489900i
$761$	475.894	+	83.9130i	0.625354	+	0.110267i	0.477340	−	0.878719i	$-0.341601\pi$
$761$	475.894	+	83.9130i	0.625354	+	0.110267i	0.148014	+	0.988985i	$0.452712\pi$
$762$	−188.107	+	363.250i	−0.246859	+	0.476706i
$763$	540.675	+	644.351i	0.708617	+	0.844497i
$764$	88.9752	−	51.3699i	0.116460	−	0.0672380i
$765$	−824.133	−	1172.66i	−1.07730	−	1.53289i
$766$	−282.034	+	488.497i	−0.368191	+	0.637725i
$767$	−44.0158	−	249.626i	−0.0573870	−	0.325458i
$768$	14.3356	−	45.8093i	0.0186662	−	0.0596475i
$769$	−556.721	+	202.630i	−0.723954	+	0.263498i	−0.677603	−	0.735427i	$-0.736981\pi$
$769$	−556.721	+	202.630i	−0.723954	+	0.263498i	−0.0463507	+	0.998925i	$0.514759\pi$
$770$	108.702	−	607.377i	0.141171	−	0.788801i
$771$	313.692	−	1002.40i	0.406864	−	1.30013i
$772$	44.4557	−	7.83874i	0.0575851	−	0.0101538i
$773$	294.856	−	510.706i	0.381444	−	0.660681i	−0.609825	−	0.792536i	$-0.708760\pi$
$773$	294.856	−	510.706i	0.381444	−	0.660681i	0.991269	+	0.131856i	$0.0420935\pi$
$774$	27.1095	+	295.266i	0.0350252	+	0.381480i
$775$	148.917	−	254.907i	0.192151	−	0.328913i
$776$	−24.1098	−	28.7330i	−0.0310693	−	0.0370270i
$777$	−1397.66	−	723.771i	−1.79880	−	0.931495i
$778$	−163.452	−	28.8211i	−0.210093	−	0.0370451i
$779$	−129.015	+	153.754i	−0.165616	+	0.197373i
$780$	36.4986	−	276.346i	0.0467931	−	0.354290i
$781$	−108.867	−	39.6244i	−0.139395	−	0.0507355i
$782$	−262.865			−0.336144
$783$	987.389	−	1091.57i	1.26103	−	1.39408i
$784$	−334.116			−0.426168
$785$	−663.411	−	794.747i	−0.845109	−	1.01242i
$786$	130.415	−	1007.29i	0.165922	−	1.28154i
$787$	−307.697	+	366.699i	−0.390974	+	0.465945i	−0.925246	−	0.379368i	$-0.876142\pi$
$787$	−307.697	+	366.699i	−0.390974	+	0.465945i	0.534272	+	0.845313i	$0.320586\pi$
$788$	−79.0850	+	448.513i	−0.100362	+	0.569179i
$789$	−29.5634	−	645.339i	−0.0374694	−	0.817920i
$790$	2.52478	+	14.5364i	0.00319593	+	0.0184005i
$791$	996.175	−	575.142i	1.25939	−	0.727107i
$792$	109.994	−	158.531i	0.138881	−	0.200166i
$793$	155.878	+	89.9963i	0.196568	+	0.113488i
$794$	292.385	−	51.5553i	0.368243	−	0.0649312i
$795$	−1454.40	+	321.798i	−1.82943	+	0.404777i
$796$	9.41037	−	3.42510i	0.0118221	−	0.00430288i
$797$	−456.066	+	165.994i	−0.572228	+	0.208274i	−0.611895	−	0.790939i	$-0.709592\pi$
$797$	−456.066	+	165.994i	−0.572228	+	0.208274i	0.0396671	+	0.999213i	$0.487370\pi$
$798$	82.7434	+	369.478i	0.103688	+	0.463005i
$799$	−202.667	−	1149.38i	−0.253651	−	1.43853i
$800$	141.420	+	0.724482i	0.176774	+	0.000905603i
$801$	758.129	+	751.651i	0.946478	+	0.938391i
$802$	490.242	−	283.041i	0.611275	−	0.352920i
$803$	−40.2769	+	33.7964i	−0.0501581	+	0.0420876i
$804$	230.900	+	360.730i	0.287189	+	0.448670i
$805$	216.576	−	256.766i	0.269038	−	0.318964i
$806$	−99.7409	+	118.867i	−0.123748	+	0.147477i
$807$	−434.053	−	331.584i	−0.537860	−	0.410884i
$808$	−31.1294	+	85.5275i	−0.0385265	+	0.105851i
$809$		−	259.067i		−	0.320231i	−0.987098	−	0.160115i	$-0.948813\pi$
$809$		−	259.067i		−	0.320231i	0.987098	−	0.160115i	$-0.0511866\pi$
$810$	497.737	+	283.387i	0.614490	+	0.349861i
$811$	1475.10			1.81887			0.909433	−	0.415850i	$-0.136516\pi$
$811$	1475.10			1.81887			0.909433	+	0.415850i	$0.136516\pi$
$812$	−1179.46	−	429.288i	−1.45253	−	0.528679i
$813$	417.542	−	546.576i	0.513582	−	0.672295i
$814$	−374.237	−	314.022i	−0.459750	−	0.385776i
$815$	843.259	−	999.745i	1.03467	−	1.22668i
$816$	−321.913	+	206.053i	−0.394501	+	0.252516i
$817$	−116.083	−	138.343i	−0.142085	−	0.169330i
$818$	−434.169	−	752.002i	−0.530769	−	0.919318i
$819$	−930.945	−	245.170i	−1.13668	−	0.299352i
$820$	224.553	−	128.880i	0.273845	−	0.157171i
$821$	−976.738	+	172.225i	−1.18969	+	0.209775i	−0.733239	−	0.679971i	$-0.761992\pi$
$821$	−976.738	+	172.225i	−1.18969	+	0.209775i	−0.456455	+	0.889747i	$0.650881\pi$
$822$	268.804	−	60.1978i	0.327013	−	0.0732334i
$823$	−200.329	−	550.401i	−0.243414	−	0.668773i	−0.999891	−	0.0147537i	$-0.995304\pi$
$823$	−200.329	−	550.401i	−0.243414	−	0.668773i	0.756478	−	0.654020i	$-0.226919\pi$
$824$	179.113	+	492.108i	0.217370	+	0.597219i
$825$	541.670	+	172.563i	0.656570	+	0.209167i
$826$	−77.1245	−	437.395i	−0.0933710	−	0.529533i
$827$	−31.1774	+	54.0008i	−0.0376994	+	0.0652972i	−0.884259	−	0.466996i	$-0.845336\pi$
$827$	−31.1774	+	54.0008i	−0.0376994	+	0.0652972i	0.846560	+	0.532293i	$0.178670\pi$
$828$	95.0099	−	44.8012i	0.114746	−	0.0541077i
$829$	247.131	+	428.043i	0.298107	+	0.516337i	0.975703	−	0.219098i	$-0.0703114\pi$
$829$	247.131	+	428.043i	0.298107	+	0.516337i	−0.677596	+	0.735435i	$0.736978\pi$
$830$	161.281	+	928.572i	0.194314	+	1.11876i
$831$	−323.988	+	14.8421i	−0.389877	+	0.0178605i
$832$	−73.2029	−	12.9077i	−0.0879843	−	0.0155140i
$833$	2038.05	+	1710.12i	2.44664	+	2.05297i
$834$	526.849	+	68.2114i	0.631713	+	0.0817883i
$835$	753.113	−	628.657i	0.901932	−	0.752882i
$836$			117.522i			0.140576i
$837$	−149.039	−	281.858i	−0.178064	−	0.336748i
$838$			5.04161i			0.00601624i
$839$	−480.440	+	1320.00i	−0.572634	+	1.57330i	0.227691	+	0.973733i	$0.426882\pi$
$839$	−480.440	+	1320.00i	−0.572634	+	1.57330i	−0.800325	+	0.599566i	$0.795340\pi$
$840$	63.9528	−	484.213i	0.0761343	−	0.576444i
$841$	−1632.30	−	1369.66i	−1.94091	−	1.62861i
$842$	25.9902	−	147.398i	0.0308672	−	0.175057i
$843$	106.261	−	205.200i	0.126051	−	0.243416i
$844$	389.379	−	326.728i	0.461350	−	0.387118i
$845$	413.336	+	1.05874i	0.489155	+	0.00125295i
$846$	269.146	+	380.892i	0.318140	+	0.450227i
$847$	633.530	+	365.769i	0.747970	+	0.431840i
$848$	68.9765	+	391.185i	0.0813402	+	0.461303i
$849$	−695.601	−	217.683i	−0.819318	−	0.256399i
$850$	−858.925	−	728.255i	−1.01050	−	0.856770i
$851$	−90.9620	−	249.916i	−0.106888	−	0.293673i
$852$	−87.5207	−	27.3889i	−0.102724	−	0.0321466i
$853$	1505.22	−	265.410i	1.76461	−	0.311149i	0.805169	−	0.593045i	$-0.202074\pi$
$853$	1505.22	−	265.410i	1.76461	−	0.311149i	0.959445	+	0.281896i	$0.0909634\pi$
$854$	273.130	+	157.691i	0.319824	+	0.184650i
$855$	−347.467	+	31.0050i	−0.406394	+	0.0362631i
$856$	−41.6014	−	72.0557i	−0.0485998	−	0.0841772i
$857$	−522.982	+	438.834i	−0.610247	+	0.512058i	−0.894721	−	0.446626i	$-0.852626\pi$
$857$	−522.982	+	438.834i	−0.610247	+	0.512058i	0.284474	+	0.958684i	$0.408181\pi$
$858$	−265.338	−	137.404i	−0.309252	−	0.160144i
$859$	−78.5591	+	445.531i	−0.0914541	+	0.518662i	0.904322	+	0.426850i	$0.140377\pi$
$859$	−78.5591	+	445.531i	−0.0914541	+	0.518662i	−0.995776	+	0.0918116i	$0.970734\pi$
$860$	79.1155	+	219.113i	0.0919948	+	0.254782i
$861$	−343.960	−	825.379i	−0.399488	−	0.958628i
$862$	88.0073	−	241.798i	0.102097	−	0.280508i
$863$	385.850			0.447104			0.223552	−	0.974692i	$-0.428235\pi$
$863$	385.850			0.447104			0.223552	+	0.974692i	$0.428235\pi$
$864$	81.2337	−	129.341i	0.0940205	−	0.149700i
$865$	−46.2073	+	79.5621i	−0.0534189	+	0.0919793i
$866$	272.507	−	748.707i	0.314673	−	0.864557i
$867$	2158.44	+	279.455i	2.48955	+	0.322324i
$868$	−174.766	+	208.278i	−0.201343	+	0.239952i
$869$	15.5755	+	2.74637i	0.0179234	+	0.00316038i
$870$	534.404	−	1025.54i	0.614258	−	1.17878i
$871$	508.087	−	426.336i	0.583338	−	0.489478i
$872$	103.330	+	178.974i	0.118498	+	0.205245i
$873$	−50.9033	−	107.951i	−0.0583085	−	0.123655i
$874$	−31.9892	+	55.4069i	−0.0366009	+	0.0633946i
$875$	1419.03	−	238.985i	1.62175	−	0.273126i
$876$	−30.6242	+	28.1830i	−0.0349592	+	0.0321724i
$877$	−128.755	−	353.752i	−0.146813	−	0.403366i	0.844388	−	0.535733i	$-0.179965\pi$
$877$	−128.755	−	353.752i	−0.146813	−	0.403366i	−0.991201	+	0.132367i	$0.957742\pi$
$878$	−1012.20	+	368.411i	−1.15285	+	0.419602i
$879$	418.527	−	93.7276i	0.476140	−	0.106630i
$880$	52.2144	−	142.322i	0.0593345	−	0.161730i
$881$	−322.870	−	186.409i	−0.366482	−	0.211588i	0.305439	−	0.952212i	$-0.401197\pi$
$881$	−322.870	−	186.409i	−0.366482	−	0.211588i	−0.671920	+	0.740623i	$0.734530\pi$
$882$	−1028.10	−	270.755i	−1.16564	−	0.306978i
$883$	1209.10	−	698.077i	1.36931	−	0.790574i	0.378474	−	0.925612i	$-0.376449\pi$
$883$	1209.10	−	698.077i	1.36931	−	0.790574i	0.990840	+	0.135038i	$0.0431157\pi$
$884$	380.459	+	453.413i	0.430383	+	0.512911i
$885$	408.825	−	17.6792i	0.461949	−	0.0199765i
$886$	−108.595	+	615.871i	−0.122567	+	0.695114i
$887$	216.113	+	181.340i	0.243644	+	0.204442i	0.756430	−	0.654075i	$-0.226942\pi$
$887$	216.113	+	181.340i	0.243644	+	0.204442i	−0.512785	+	0.858517i	$0.671386\pi$
$888$	−307.298	−	234.752i	−0.346056	−	0.264361i
$889$	1043.03	+	379.633i	1.17327	+	0.427034i
$890$	725.323	+	421.247i	0.814970	+	0.473311i
$891$	466.926	−	398.676i	0.524048	−	0.447447i
$892$			468.517i			0.525243i
$893$	−266.931	−	97.1550i	−0.298915	−	0.108796i
$894$	−343.722	−	262.578i	−0.384477	−	0.293711i
$895$	326.483	+	904.203i	0.364785	+	1.01028i
$896$	−128.266	−	22.6168i	−0.143154	−	0.0252419i
$897$	−87.6957	−	137.005i	−0.0977656	−	0.152737i
$898$	−141.387	−	168.498i	−0.157446	−	0.187637i
$899$	−557.501	+	321.873i	−0.620135	+	0.358035i
$900$	434.570	+	116.830i	0.482855	+	0.129811i
$901$	1581.48	−	2739.21i	1.75525	−	3.04018i
$902$	−48.1945	−	273.325i	−0.0534307	−	0.303021i
$903$	785.108	−	175.822i	0.869444	−	0.194709i
$904$	265.571	−	96.6599i	0.293773	−	0.106925i
$905$	−37.3560	+	208.728i	−0.0412773	+	0.230639i
$906$	568.155	+	617.368i	0.627102	+	0.681421i
$907$	947.252	−	167.026i	1.04438	−	0.184152i	0.374963	−	0.927040i	$-0.377655\pi$
$907$	947.252	−	167.026i	1.04438	−	0.184152i	0.669416	+	0.742888i	$0.266544\pi$
$908$	−335.360	+	580.860i	−0.369339	+	0.639714i
$909$	−165.095	+	237.947i	−0.181623	+	0.261768i
$910$	−756.356	−	1.93737i	−0.831160	−	0.00212897i
$911$	−77.4593	−	92.3124i	−0.0850267	−	0.101331i	0.721854	−	0.692046i	$-0.243290\pi$
$911$	−77.4593	−	92.3124i	−0.0850267	−	0.101331i	−0.806880	+	0.590715i	$0.798846\pi$
$912$	4.25711	+	92.9286i	0.00466789	+	0.101895i
$913$	994.947	+	175.436i	1.08976	+	0.192153i
$914$	259.950	−	309.796i	0.284409	−	0.338946i
$915$	−176.987	+	230.455i	−0.193428	+	0.251864i
$916$	709.836	+	258.359i	0.774930	+	0.282052i
$917$	−2756.03			−3.00549
$918$	−1157.52	+	373.173i	−1.26092	+	0.406507i
$919$	−1361.09			−1.48105			−0.740526	−	0.672028i	$-0.765424\pi$
$919$	−1361.09			−1.48105			−0.740526	+	0.672028i	$0.765424\pi$
$920$	63.3570	−	52.8869i	0.0688663	−	0.0574857i
$921$	360.158	−	150.088i	0.391051	−	0.162962i
$922$	129.731	−	154.607i	0.140706	−	0.167686i
$923$	−24.6607	+	139.858i	−0.0267179	+	0.151525i
$924$	−464.926	−	240.759i	−0.503166	−	0.260561i
$925$	395.157	−	1068.62i	0.427197	−	1.15526i
$926$	−35.4652	+	20.4759i	−0.0382994	+	0.0221122i
$927$	152.355	+	1659.39i	0.164353	+	1.79007i
$928$	−267.065	−	154.190i	−0.287785	−	0.166153i
$929$	−483.189	+	85.1992i	−0.520117	+	0.0917106i	−0.427543	−	0.903995i	$-0.640621\pi$
$929$	−483.189	+	85.1992i	−0.520117	+	0.0917106i	−0.0925742	+	0.995706i	$0.529510\pi$
$930$	−169.159	−	184.759i	−0.181892	−	0.198666i
$931$	608.480	−	221.469i	0.653577	−	0.237883i
$932$	769.416	−	280.044i	0.825554	−	0.300477i
$933$	−1512.84	−	473.430i	−1.62148	−	0.507428i
$934$	−57.0877	−	323.761i	−0.0611218	−	0.346639i
$935$	−1046.96	+	600.889i	−1.11974	+	0.642663i
$936$	−214.790	−	99.0385i	−0.229477	−	0.105810i
$937$	204.181	−	117.884i	0.217910	−	0.125810i	−0.387072	−	0.922049i	$-0.626514\pi$
$937$	204.181	−	117.884i	0.217910	−	0.125810i	0.604982	+	0.796239i	$0.293180\pi$
$938$	890.270	−	747.025i	0.949115	−	0.796402i
$939$	−484.904	+	936.392i	−0.516405	+	0.997223i
$940$	280.097	+	236.254i	0.297975	+	0.251335i
$941$	−1061.50	+	1265.05i	−1.12806	+	1.34437i	−0.196617	+	0.980480i	$0.562996\pi$
$941$	−1061.50	+	1265.05i	−1.12806	+	1.34437i	−0.931442	+	0.363889i	$0.881449\pi$
$942$	−810.846	+	337.903i	−0.860771	+	0.358709i
$943$	51.6767	−	141.981i	0.0548003	−	0.150563i
$944$		−	109.122i		−	0.115595i
$945$	589.175	−	1438.13i	0.623465	−	1.52183i
$946$	249.722			0.263977
$947$	−171.700	−	62.4938i	−0.181310	−	0.0659914i	0.249770	−	0.968305i	$-0.419645\pi$
$947$	−171.700	−	62.4938i	−0.181310	−	0.0659914i	−0.431080	+	0.902314i	$0.641867\pi$
$948$	12.4156	+	1.60745i	0.0130966	+	0.00169562i
$949$	49.3719	+	41.4279i	0.0520252	+	0.0436543i
$950$	−258.028	+	92.4205i	−0.271609	+	0.0972847i
$951$	14.3773	+	313.841i	0.0151180	+	0.330012i
$952$	666.639	+	794.470i	0.700252	+	0.834527i
$953$	−219.872	−	380.829i	−0.230715	−	0.399610i	0.727304	−	0.686316i	$-0.240773\pi$
$953$	−219.872	−	380.829i	−0.230715	−	0.399610i	−0.958019	+	0.286705i	$0.907440\pi$
$954$	−104.757	+	1259.60i	−0.109808	+	1.32033i
$955$	222.766	−	127.854i	0.233263	−	0.133879i
$956$	107.835	−	19.0143i	0.112798	−	0.0198894i
$957$	−839.449	−	912.161i	−0.877167	−	0.953147i
$958$	18.3625	+	50.4506i	0.0191676	+	0.0526625i
$959$	−255.643	−	702.373i	−0.266572	−	0.732401i
$960$	36.1323	−	114.431i	0.0376378	−	0.119199i
$961$	−142.661	−	809.072i	−0.148451	−	0.841907i
$962$	−299.423	+	518.616i	−0.311251	+	0.539102i
$963$	−69.6189	−	255.432i	−0.0722937	−	0.265246i
$964$	−188.533	−	326.549i	−0.195574	−	0.338744i
$965$	111.189	−	19.3121i	0.115222	−	0.0200125i
$966$	−153.660	−	240.060i	−0.159069	−	0.248510i
$967$	−510.467	−	90.0091i	−0.527887	−	0.0930807i	−0.0966483	−	0.995319i	$-0.530812\pi$
$967$	−510.467	−	90.0091i	−0.527887	−	0.0930807i	−0.431239	+	0.902238i	$0.641923\pi$
$968$	137.683	+	115.530i	0.142234	+	0.119349i
$969$	449.674	−	588.637i	0.464060	−	0.607469i
$970$	−60.0903	−	71.9865i	−0.0619488	−	0.0742129i
$971$		−	345.832i		−	0.356161i	−0.984016	−	0.178080i	$-0.943011\pi$
$971$		−	345.832i		−	0.356161i	0.984016	−	0.178080i	$-0.0569887\pi$
$972$	354.774	−	332.161i	0.364994	−	0.341730i
$973$		−	1441.50i		−	1.48150i
$974$	−50.0994	+	137.647i	−0.0514368	+	0.141321i
$975$	93.0159	−	690.629i	0.0954009	−	0.708337i
$976$	59.3583	+	49.8075i	0.0608180	+	0.0510323i
$977$	3.11533	−	17.6679i	0.00318867	−	0.0180838i	−0.983172	−	0.182683i	$-0.941522\pi$
$977$	3.11533	−	17.6679i	0.00318867	−	0.0180838i	0.986361	+	0.164599i	$0.0526330\pi$
$978$	−598.292	−	934.699i	−0.611750	−	0.955725i
$979$	688.776	−	577.952i	0.703551	−	0.590349i
$980$	−835.287	−	2.13955i	−0.852334	−	0.00218321i
$981$	172.921	+	634.448i	0.176270	+	0.646736i
$982$	402.541	+	232.407i	0.409920	+	0.236667i
$983$	−55.8439	−	316.706i	−0.0568096	−	0.322183i	0.943138	−	0.332401i	$-0.107859\pi$
$983$	−55.8439	−	316.706i	−0.0568096	−	0.322183i	−0.999948	+	0.0102175i	$0.996748\pi$
$984$	−48.0101	−	214.382i	−0.0487908	−	0.217868i
$985$	−200.584	+	1120.77i	−0.203638	+	1.13784i
$986$	839.848	+	2307.46i	0.851773	+	2.34023i
$987$	931.198	−	856.969i	0.943463	−	0.868256i
$988$	141.870	−	25.0156i	0.143594	−	0.0253194i
$989$	117.735	+	67.9741i	0.119044	+	0.0687301i
$990$	275.999	−	395.622i	0.278787	−	0.399619i
$991$	−263.037	−	455.594i	−0.265426	−	0.459731i	0.702249	−	0.711931i	$-0.252179\pi$
$991$	−263.037	−	455.594i	−0.265426	−	0.459731i	−0.967675	+	0.252200i	$0.918846\pi$
$992$	−51.1720	+	42.9384i	−0.0515847	+	0.0432847i
$993$	−18.6351	−	406.785i	−0.0187664	−	0.409653i
$994$	−43.2104	+	245.058i	−0.0434712	+	0.246537i
$995$	23.5478	−	8.50245i	0.0236661	−	0.00854518i
$996$	793.096	+	102.683i	0.796281	+	0.103095i
$997$	306.832	−	843.014i	0.307755	−	0.845550i	−0.685338	−	0.728225i	$-0.740346\pi$
$997$	306.832	−	843.014i	0.307755	−	0.845550i	0.993093	−	0.117326i	$-0.0374321\pi$
$998$	941.482			0.943369
$999$	−755.341	−	971.370i	−0.756097	−	0.972343i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	270.3.n.a.239.5	yes	216
5.4	even	2	inner	270.3.n.a.239.32	yes	216
27.20	odd	18	inner	270.3.n.a.209.32	yes	216
135.74	odd	18	inner	270.3.n.a.209.5	✓	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.3.n.a.209.5	✓	216	135.74	odd	18	inner
270.3.n.a.209.32	yes	216	27.20	odd	18	inner
270.3.n.a.239.5	yes	216	1.1	even	1	trivial
270.3.n.a.239.32	yes	216	5.4	even	2	inner

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:	\( N \)	\(=\)	\( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	270.n (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32893 - 0.483690i) q^{2} +(-1.82117 + 2.38397i) q^{3} +(1.53209 + 1.28558i) q^{4} +(3.82198 + 3.22374i) q^{5} +(3.57331 - 2.28724i) q^{6} +(-7.39985 - 8.81880i) q^{7} +(-1.41421 - 2.44949i) q^{8} +(-2.36665 - 8.68326i) q^{9} +(-3.51984 - 6.13276i) q^{10} +(-7.46475 + 1.31624i) q^{11} +(-5.85498 + 1.31120i) q^{12} +(3.17789 + 8.73118i) q^{13} +(5.56829 + 15.2988i) q^{14} +(-14.6458 + 3.24050i) q^{15} +(0.694593 + 3.93923i) q^{16} +(15.9255 - 27.5838i) q^{17} +(-1.05490 + 12.6841i) q^{18} +(-3.87609 - 6.71358i) q^{19} +(1.71125 + 9.85249i) q^{20} +(34.5002 - 1.58047i) q^{21} +(10.5568 + 1.86144i) q^{22} +(4.47042 + 3.75113i) q^{23} +(8.41505 + 1.08950i) q^{24} +(4.21502 + 24.6421i) q^{25} -13.1402i q^{26} +(25.0107 + 10.1717i) q^{27} -23.0242i q^{28} +(18.6450 - 51.2268i) q^{29} +(21.0306 + 2.77763i) q^{30} +(-9.04603 - 7.59052i) q^{31} +(0.982302 - 5.57091i) q^{32} +(10.4567 - 20.1929i) q^{33} +(-34.5058 + 28.9538i) q^{34} +(0.147438 - 57.5604i) q^{35} +(7.53706 - 16.3460i) q^{36} +(-39.4679 - 22.7868i) q^{37} +(1.90374 + 10.7967i) q^{38} +(-26.6024 - 8.32500i) q^{39} +(2.49142 - 13.9209i) q^{40} +(-8.85524 - 24.3296i) q^{41} +(-46.6127 - 14.5870i) q^{42} +(22.9419 - 4.04528i) q^{43} +(-13.1288 - 7.57991i) q^{44} +(18.9473 - 40.8167i) q^{45} +(-4.12648 - 7.14727i) q^{46} +(28.0701 - 23.5536i) q^{47} +(-10.6560 - 5.51814i) q^{48} +(-14.5047 + 82.2600i) q^{49} +(6.31768 - 34.7863i) q^{50} +(36.7559 + 88.2008i) q^{51} +(-6.35578 + 17.4624i) q^{52} +99.3050 q^{53} +(-28.3175 - 25.6149i) q^{54} +(-32.7733 - 19.0338i) q^{55} +(-11.1366 + 30.5975i) q^{56} +(23.0640 + 2.98611i) q^{57} +(-49.5557 + 59.0582i) q^{58} +(-26.8660 - 4.73720i) q^{59} +(-26.6046 - 13.8635i) q^{60} +(14.8396 - 12.4519i) q^{61} +(8.35005 + 14.4627i) q^{62} +(-59.0630 + 85.1258i) q^{63} +(-4.00000 + 6.92820i) q^{64} +(-16.0012 + 43.6151i) q^{65} +(-23.6633 + 21.7770i) q^{66} +(-24.4146 - 67.0784i) q^{67} +(59.8603 - 21.7874i) q^{68} +(-17.0840 + 3.82590i) q^{69} +(-28.0373 + 76.4222i) q^{70} +(13.2366 + 7.64218i) q^{71} +(-17.9226 + 18.0771i) q^{72} +(6.00716 - 3.46824i) q^{73} +(41.4282 + 49.3722i) q^{74} +(-66.4224 - 34.8291i) q^{75} +(2.69230 - 15.2688i) q^{76} +(66.8457 + 56.0902i) q^{77} +(31.3259 + 23.9306i) q^{78} +(-1.96070 - 0.713637i) q^{79} +(-10.0443 + 17.2948i) q^{80} +(-69.7979 + 41.1005i) q^{81} +36.6154i q^{82} +(-125.248 - 45.5865i) q^{83} +(54.8892 + 41.9312i) q^{84} +(149.790 - 54.0849i) q^{85} +(-32.4448 - 5.72089i) q^{86} +(88.1674 + 137.742i) q^{87} +(13.7809 + 16.4234i) q^{88} +(-102.728 + 59.3103i) q^{89} +(-44.9221 + 45.0777i) q^{90} +(53.4826 - 92.6346i) q^{91} +(2.02673 + 11.4941i) q^{92} +(34.5700 - 7.74182i) q^{93} +(-48.6957 + 17.7238i) q^{94} +(6.82851 - 38.1546i) q^{95} +(11.4920 + 12.4874i) q^{96} +(13.0597 - 2.30278i) q^{97} +(59.0639 - 102.302i) q^{98} +(29.0957 + 61.7033i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 18 q^{5} + 12 q^{6} + 12 q^{9} - 36 q^{11} + 36 q^{14} + 18 q^{15} - 72 q^{20} + 360 q^{21} + 18 q^{25} - 36 q^{29} + 144 q^{30} + 180 q^{31} + 486 q^{35} - 192 q^{36} + 348 q^{39} - 72 q^{41} + 258 q^{45}+ \cdots - 1008 q^{99}+O(q^{100}) \) 216 * q - 18 * q^5 + 12 * q^6 + 12 * q^9 - 36 * q^11 + 36 * q^14 + 18 * q^15 - 72 * q^20 + 360 * q^21 + 18 * q^25 - 36 * q^29 + 144 * q^30 + 180 * q^31 + 486 * q^35 - 192 * q^36 + 348 * q^39 - 72 * q^41 + 258 * q^45 - 72 * q^49 - 288 * q^50 - 312 * q^51 - 360 * q^54 - 72 * q^56 - 612 * q^59 - 36 * q^60 - 144 * q^61 - 864 * q^64 - 234 * q^65 + 336 * q^69 + 288 * q^74 + 642 * q^75 + 72 * q^79 + 636 * q^81 - 216 * q^84 + 432 * q^86 - 1620 * q^89 - 240 * q^90 - 504 * q^94 + 108 * q^95 - 1008 * q^99

Introduction

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