LMFDB - Embedded newform 273.3.w.c.233.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,3,Mod(116,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4, 3]))

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

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

chi := DirichletCharacter("273.116");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	273.w (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.43871121704$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 16 x^{14} - 176 x^{13} + 344 x^{12} + 4576 x^{11} + 11040 x^{10} - 37664 x^{9} + \cdots + 97900608 $ x^16 - 16x^14 - 176x^13 + 344x^12 + 4576x^11 + 11040x^10 - 37664x^9 - 313120x^8 - 230912x^7 + 2040576x^6 + 9332224x^5 + 33838912x^4 + 73579264x^3 + 95390464x^2 + 117266688x + 97900608
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			233.6
Root			$0.144025 + 2.26426i$ of defining polynomial
Character	$\chi$	$=$	273.233
Dual form			273.3.w.c.116.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.759866 - 1.31613i) q^{2} +(2.79279 + 1.09560i) q^{3} +(0.845208 + 1.46394i) q^{4} +(0.681452 - 1.18031i) q^{5} +(3.56409 - 2.84316i) q^{6} +(0.736052 - 6.96119i) q^{7} +8.64790 q^{8} +(6.59934 + 6.11953i) q^{9} +O(q^{10})$	\(q+(0.759866 - 1.31613i) q^{2} +(2.79279 + 1.09560i) q^{3} +(0.845208 + 1.46394i) q^{4} +(0.681452 - 1.18031i) q^{5} +(3.56409 - 2.84316i) q^{6} +(0.736052 - 6.96119i) q^{7} +8.64790 q^{8} +(6.59934 + 6.11953i) q^{9} +(-1.03562 - 1.79375i) q^{10} +(2.96105 + 5.12869i) q^{11} +(0.756598 + 5.01449i) q^{12} -13.0000 q^{13} +(-8.60251 - 6.25831i) q^{14} +(3.19629 - 2.54976i) q^{15} +(3.19042 - 5.52596i) q^{16} +(8.60251 - 4.96666i) q^{17} +(13.0687 - 4.03554i) q^{18} +(-7.13265 - 4.11804i) q^{19} +2.30387 q^{20} +(9.68229 - 18.6347i) q^{21} +9.00000 q^{22} +(2.23720 + 1.29165i) q^{23} +(24.1518 + 9.47460i) q^{24} +(11.5712 + 20.0420i) q^{25} +(-9.87826 + 17.1096i) q^{26} +(11.7260 + 24.3208i) q^{27} +(10.8129 - 4.80612i) q^{28} -21.1583i q^{29} +(-0.927051 - 6.14420i) q^{30} +(-9.34080 + 5.39292i) q^{31} +(12.4472 + 21.5592i) q^{32} +(2.65062 + 17.5675i) q^{33} -15.0960i q^{34} +(-7.71478 - 5.61249i) q^{35} +(-3.38083 + 14.8333i) q^{36} +(-28.5306 - 16.4721i) q^{37} +(-10.8397 + 6.25831i) q^{38} +(-36.3063 - 14.2427i) q^{39} +(5.89313 - 10.2072i) q^{40} -16.9822 q^{41} +(-17.1684 - 26.9030i) q^{42} -3.30958 q^{43} +(-5.00540 + 8.66961i) q^{44} +(11.7201 - 3.61910i) q^{45} +(3.39995 - 1.96296i) q^{46} +(32.9393 - 57.0526i) q^{47} +(14.9644 - 11.9374i) q^{48} +(-47.9165 - 10.2476i) q^{49} +35.1704 q^{50} +(29.4664 - 4.44597i) q^{51} +(-10.9877 - 19.0313i) q^{52} +(-58.6730 + 33.8749i) q^{53} +(40.9194 + 3.04758i) q^{54} +8.07125 q^{55} +(6.36531 - 60.1997i) q^{56} +(-15.4083 - 19.3153i) q^{57} +(-27.8470 - 16.0775i) q^{58} +(-8.56949 - 14.8428i) q^{59} +(6.43423 + 2.52411i) q^{60} +(-9.60687 + 16.6396i) q^{61} +16.3916i q^{62} +(47.4567 - 41.4350i) q^{63} +63.3562 q^{64} +(-8.85887 + 15.3440i) q^{65} +(25.1351 + 9.86036i) q^{66} +(-88.3081 + 50.9847i) q^{67} +(14.5418 + 8.39572i) q^{68} +(4.83291 + 6.05837i) q^{69} +(-13.2489 + 5.88888i) q^{70} -27.8257 q^{71} +(57.0705 + 52.9211i) q^{72} +(-87.1163 + 50.2966i) q^{73} +(-43.3588 + 25.0332i) q^{74} +(10.3581 + 68.6505i) q^{75} -13.9224i q^{76} +(37.8813 - 16.8375i) q^{77} +(-46.3331 + 36.9610i) q^{78} +(28.4521 - 49.2804i) q^{79} +(-4.34823 - 7.53135i) q^{80} +(6.10263 + 80.7698i) q^{81} +(-12.9042 + 22.3507i) q^{82} -104.294 q^{83} +(35.4637 - 1.57590i) q^{84} -13.5382i q^{85} +(-2.51484 + 4.35583i) q^{86} +(23.1809 - 59.0907i) q^{87} +(25.6069 + 44.3524i) q^{88} +(43.7586 - 75.7921i) q^{89} +(4.14249 - 18.1751i) q^{90} +(-9.56867 + 90.4955i) q^{91} +4.36685i q^{92} +(-31.9954 + 4.82754i) q^{93} +(-50.0589 - 86.7046i) q^{94} +(-9.72111 + 5.61249i) q^{95} +(11.1423 + 73.8475i) q^{96} -27.8448i q^{97} +(-49.8972 + 55.2773i) q^{98} +(-11.8442 + 51.9662i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 24 q^{4} - 16 q^{9}+O(q^{10}) $ 16 * q - 24 * q^4 - 16 * q^9	$ 16 q - 24 q^{4} - 16 q^{9} + 96 q^{10} - 88 q^{12} - 208 q^{13} - 24 q^{16} + 144 q^{22} - 40 q^{25} + 264 q^{30} + 96 q^{36} + 432 q^{40} - 448 q^{42} - 128 q^{43} + 352 q^{48} - 504 q^{49} + 280 q^{51} + 312 q^{52} - 96 q^{55} + 184 q^{61} - 112 q^{64} - 448 q^{69} - 528 q^{75} + 80 q^{79} + 584 q^{81} + 544 q^{82} - 448 q^{87} + 72 q^{88} - 384 q^{90} - 88 q^{94}+O(q^{100}) $ 16 * q - 24 * q^4 - 16 * q^9 + 96 * q^10 - 88 * q^12 - 208 * q^13 - 24 * q^16 + 144 * q^22 - 40 * q^25 + 264 * q^30 + 96 * q^36 + 432 * q^40 - 448 * q^42 - 128 * q^43 + 352 * q^48 - 504 * q^49 + 280 * q^51 + 312 * q^52 - 96 * q^55 + 184 * q^61 - 112 * q^64 - 448 * q^69 - 528 * q^75 + 80 * q^79 + 584 * q^81 + 544 * q^82 - 448 * q^87 + 72 * q^88 - 384 * q^90 - 88 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.759866	−	1.31613i	0.379933	−	0.658063i	−0.611119	−	0.791539i	$-0.709280\pi$
$2$	0.759866	−	1.31613i	0.379933	−	0.658063i	0.991052	+	0.133475i	$0.0426137\pi$
$3$	2.79279	+	1.09560i	0.930930	+	0.365198i
$3$	2.79279	+	1.09560i	0.930930	+	0.365198i
$4$	0.845208	+	1.46394i	0.211302	+	0.365986i
$5$	0.681452	−	1.18031i	0.136290	−	0.236062i	−0.789799	−	0.613365i	$-0.789815\pi$
$5$	0.681452	−	1.18031i	0.136290	−	0.236062i	0.926090	+	0.377304i	$0.123149\pi$
$6$	3.56409	−	2.84316i	0.594014	−	0.473860i
$7$	0.736052	−	6.96119i	0.105150	−	0.994456i
$7$	0.736052	−	6.96119i	0.105150	−	0.994456i
$8$	8.64790			1.08099
$9$	6.59934	+	6.11953i	0.733260	+	0.679948i
$10$	−1.03562	−	1.79375i	−0.103562	−	0.179375i
$11$	2.96105	+	5.12869i	0.269186	+	0.466244i	0.968652	−	0.248422i	$-0.0799119\pi$
$11$	2.96105	+	5.12869i	0.269186	+	0.466244i	−0.699466	+	0.714666i	$0.746579\pi$
$12$	0.756598	+	5.01449i	0.0630499	+	0.417874i
$13$	−13.0000			−1.00000
$13$	−13.0000			−1.00000
$14$	−8.60251	−	6.25831i	−0.614465	−	0.447022i
$15$	3.19629	−	2.54976i	0.213086	−	0.169984i
$16$	3.19042	−	5.52596i	0.199401	−	0.345373i
$17$	8.60251	−	4.96666i	0.506030	−	0.292157i	−0.225170	−	0.974319i	$-0.572294\pi$
$17$	8.60251	−	4.96666i	0.506030	−	0.292157i	0.731200	+	0.682163i	$0.238961\pi$
$18$	13.0687	−	4.03554i	0.726038	−	0.224197i
$19$	−7.13265	−	4.11804i	−0.375403	−	0.216739i	0.300414	−	0.953809i	$-0.402875\pi$
$19$	−7.13265	−	4.11804i	−0.375403	−	0.216739i	−0.675816	+	0.737070i	$0.736209\pi$
$20$	2.30387			0.115194
$21$	9.68229	−	18.6347i	0.461061	−	0.887368i
$22$	9.00000			0.409091
$23$	2.23720	+	1.29165i	0.0972697	+	0.0561587i	0.547846	−	0.836579i	$-0.315448\pi$
$23$	2.23720	+	1.29165i	0.0972697	+	0.0561587i	−0.450576	+	0.892738i	$0.648781\pi$
$24$	24.1518	+	9.47460i	1.00632	+	0.394775i
$25$	11.5712	+	20.0420i	0.462850	+	0.801680i
$26$	−9.87826	+	17.1096i	−0.379933	+	0.658063i
$27$	11.7260	+	24.3208i	0.434298	+	0.900769i
$28$	10.8129	−	4.80612i	0.386175	−	0.171647i
$29$		−	21.1583i		−	0.729596i	−0.931087	−	0.364798i	$-0.881138\pi$
$29$		−	21.1583i		−	0.729596i	0.931087	−	0.364798i	$-0.118862\pi$
$30$	−0.927051	−	6.14420i	−0.0309017	−	0.204807i
$31$	−9.34080	+	5.39292i	−0.301316	+	0.173965i	−0.643034	−	0.765838i	$-0.722325\pi$
$31$	−9.34080	+	5.39292i	−0.301316	+	0.173965i	0.341718	+	0.939803i	$0.388991\pi$
$32$	12.4472	+	21.5592i	0.388976	+	0.673726i
$33$	2.65062	+	17.5675i	0.0803218	+	0.532347i
$34$		−	15.0960i		−	0.444000i
$35$	−7.71478	−	5.61249i	−0.220422	−	0.160357i
$36$	−3.38083	+	14.8333i	−0.0939120	+	0.412037i
$37$	−28.5306	−	16.4721i	−0.771097	−	0.445193i	0.0621687	−	0.998066i	$-0.480198\pi$
$37$	−28.5306	−	16.4721i	−0.771097	−	0.445193i	−0.833266	+	0.552872i	$0.813532\pi$
$38$	−10.8397	+	6.25831i	−0.285256	+	0.164692i
$39$	−36.3063	−	14.2427i	−0.930930	−	0.365198i
$40$	5.89313	−	10.2072i	0.147328	−	0.255180i
$41$	−16.9822			−0.414199			−0.207099	−	0.978320i	$-0.566402\pi$
$41$	−16.9822			−0.414199			−0.207099	+	0.978320i	$0.566402\pi$
$42$	−17.1684	−	26.9030i	−0.408772	−	0.640548i
$43$	−3.30958			−0.0769671			−0.0384835	−	0.999259i	$-0.512253\pi$
$43$	−3.30958			−0.0769671			−0.0384835	+	0.999259i	$0.512253\pi$
$44$	−5.00540	+	8.66961i	−0.113759	+	0.197037i
$45$	11.7201	−	3.61910i	0.260446	−	0.0804244i
$46$	3.39995	−	1.96296i	0.0739119	−	0.0426731i
$47$	32.9393	−	57.0526i	0.700837	−	1.21389i	−0.267336	−	0.963603i	$-0.586143\pi$
$47$	32.9393	−	57.0526i	0.700837	−	1.21389i	0.968173	−	0.250282i	$-0.0805233\pi$
$48$	14.9644	−	11.9374i	0.311758	−	0.248697i
$49$	−47.9165	−	10.2476i	−0.977887	−	0.209135i
$50$	35.1704			0.703408
$51$	29.4664	−	4.44597i	0.577773	−	0.0871759i
$52$	−10.9877	−	19.0313i	−0.211302	−	0.365986i
$53$	−58.6730	+	33.8749i	−1.10704	+	0.639148i	−0.938060	−	0.346472i	$-0.887380\pi$
$53$	−58.6730	+	33.8749i	−1.10704	+	0.639148i	−0.168977	+	0.985620i	$0.554046\pi$
$54$	40.9194	+	3.04758i	0.757767	+	0.0564366i
$55$	8.07125			0.146750
$56$	6.36531	−	60.1997i	0.113666	−	1.07500i
$57$	−15.4083	−	19.3153i	−0.270321	−	0.338865i
$58$	−27.8470	−	16.0775i	−0.480120	−	0.277198i
$59$	−8.56949	−	14.8428i	−0.145246	−	0.251573i	0.784219	−	0.620484i	$-0.213064\pi$
$59$	−8.56949	−	14.8428i	−0.145246	−	0.251573i	−0.929465	+	0.368911i	$0.879731\pi$
$60$	6.43423	+	2.52411i	0.107237	+	0.0420685i
$61$	−9.60687	+	16.6396i	−0.157490	+	0.272780i	−0.933963	−	0.357370i	$-0.883673\pi$
$61$	−9.60687	+	16.6396i	−0.157490	+	0.272780i	0.776473	+	0.630150i	$0.217007\pi$
$62$			16.3916i			0.264380i
$63$	47.4567	−	41.4350i	0.753281	−	0.657699i
$64$	63.3562			0.989941
$65$	−8.85887	+	15.3440i	−0.136290	+	0.236062i
$66$	25.1351	+	9.86036i	0.380835	+	0.149399i
$67$	−88.3081	+	50.9847i	−1.31803	+	0.760966i	−0.983412	−	0.181387i	$-0.941941\pi$
$67$	−88.3081	+	50.9847i	−1.31803	+	0.760966i	−0.334620	+	0.942353i	$0.608608\pi$
$68$	14.5418	+	8.39572i	0.213850	+	0.123467i
$69$	4.83291	+	6.05837i	0.0700422	+	0.0878025i
$70$	−13.2489	+	5.88888i	−0.189270	+	0.0841269i
$71$	−27.8257			−0.391911			−0.195955	−	0.980613i	$-0.562781\pi$
$71$	−27.8257			−0.391911			−0.195955	+	0.980613i	$0.562781\pi$
$72$	57.0705	+	52.9211i	0.792646	+	0.735016i
$73$	−87.1163	+	50.2966i	−1.19337	+	0.688995i	−0.959070	−	0.283168i	$-0.908615\pi$
$73$	−87.1163	+	50.2966i	−1.19337	+	0.688995i	−0.234304	+	0.972163i	$0.575281\pi$
$74$	−43.3588	+	25.0332i	−0.585930	+	0.338287i
$75$	10.3581	+	68.6505i	0.138109	+	0.915339i
$76$		−	13.9224i		−	0.183189i
$77$	37.8813	−	16.8375i	0.491965	−	0.218668i
$78$	−46.3331	+	36.9610i	−0.594014	+	0.473860i
$79$	28.4521	−	49.2804i	0.360153	−	0.623803i	−0.627833	−	0.778348i	$-0.716058\pi$
$79$	28.4521	−	49.2804i	0.360153	−	0.623803i	0.987986	+	0.154545i	$0.0493912\pi$
$80$	−4.34823	−	7.53135i	−0.0543529	−	0.0941419i
$81$	6.10263	+	80.7698i	0.0753411	+	0.997158i
$82$	−12.9042	+	22.3507i	−0.157368	+	0.272569i
$83$	−104.294			−1.25655			−0.628276	−	0.777990i	$-0.716239\pi$
$83$	−104.294			−1.25655			−0.628276	+	0.777990i	$0.716239\pi$
$84$	35.4637	−	1.57590i	0.422187	−	0.0187608i
$85$		−	13.5382i		−	0.159272i
$86$	−2.51484	+	4.35583i	−0.0292423	+	0.0506492i
$87$	23.1809	−	59.0907i	0.266447	−	0.679203i
$88$	25.6069	+	44.3524i	0.290987	+	0.504005i
$89$	43.7586	−	75.7921i	0.491669	−	0.851596i	−0.508285	−	0.861189i	$-0.669720\pi$
$89$	43.7586	−	75.7921i	0.491669	−	0.851596i	0.999954	+	0.00959299i	$0.00305359\pi$
$90$	4.14249	−	18.1751i	0.0460277	−	0.201946i
$91$	−9.56867	+	90.4955i	−0.105150	+	0.994456i
$92$			4.36685i			0.0474658i
$93$	−31.9954	+	4.82754i	−0.344036	+	0.0519090i
$94$	−50.0589	−	86.7046i	−0.532542	−	0.922390i
$95$	−9.72111	+	5.61249i	−0.102327	+	0.0590788i
$96$	11.1423	+	73.8475i	0.116066	+	0.769245i
$97$		−	27.8448i		−	0.287060i	−0.989646	−	0.143530i	$-0.954155\pi$
$97$		−	27.8448i		−	0.287060i	0.989646	−	0.143530i	$-0.0458453\pi$
$98$	−49.8972	+	55.2773i	−0.509155	+	0.564054i
$99$	−11.8442	+	51.9662i	−0.119638	+	0.524911i
$100$	−19.5602	+	33.8793i	−0.195602	+	0.338793i
$101$	145.044	−	83.7414i	1.43608	−	0.829123i	0.438508	−	0.898727i	$-0.355507\pi$
$101$	145.044	−	83.7414i	1.43608	−	0.829123i	0.997575	+	0.0696044i	$0.0221737\pi$
$102$	16.5391	−	42.1599i	0.162148	−	0.413332i
$103$	−68.0356	+	117.841i	−0.660540	+	1.14409i	0.319934	+	0.947440i	$0.396339\pi$
$103$	−68.0356	+	117.841i	−0.660540	+	1.14409i	−0.980474	+	0.196649i	$0.936994\pi$
$104$	−112.423			−1.08099
$105$	−15.3967	−	24.1268i	−0.146636	−	0.229779i
$106$			102.961i			0.971334i
$107$	103.923	+	59.9998i	0.971240	+	0.560746i	0.899614	−	0.436686i	$-0.143848\pi$
$107$	103.923	+	59.9998i	0.971240	+	0.560746i	0.0716262	+	0.997432i	$0.477181\pi$
$108$	−25.6933	+	37.7224i	−0.237901	+	0.349281i
$109$	−98.3325	+	56.7723i	−0.902133	+	0.520847i	−0.877892	−	0.478859i	$-0.841050\pi$
$109$	−98.3325	+	56.7723i	−0.902133	+	0.520847i	−0.0242417	+	0.999706i	$0.507717\pi$
$110$	6.13306	−	10.6228i	0.0557551	−	0.0965707i
$111$	−61.6331	−	77.2612i	−0.555253	−	0.696047i
$112$	−36.1190	−	26.2765i	−0.322491	−	0.234612i
$113$			82.4498i			0.729644i	0.931077	+	0.364822i	$0.118870\pi$
$113$			82.4498i			0.729644i	−0.931077	+	0.364822i	$0.881130\pi$
$114$	−37.1296	+	5.60221i	−0.325698	+	0.0491421i
$115$	3.04909	−	1.76039i	0.0265138	−	0.0153078i
$116$	30.9745	−	17.8832i	0.267022	−	0.154165i
$117$	−85.7914	−	79.5539i	−0.733260	−	0.679948i
$118$	−26.0467			−0.220734
$119$	−28.2420	−	63.5395i	−0.237328	−	0.533945i
$120$	27.6412	−	22.0501i	0.230344	−	0.183751i
$121$	42.9644	−	74.4165i	0.355077	−	0.615012i
$122$	14.5999	+	25.2877i	0.119671	+	0.207276i
$123$	−47.4276	−	18.6056i	−0.385590	−	0.151265i
$124$	−15.7898	−	9.11627i	−0.127337	−	0.0735183i
$125$	65.6136			0.524909
$126$	−18.4730	−	93.9441i	−0.146611	−	0.745588i
$127$	143.118			1.12691			0.563456	−	0.826146i	$-0.309471\pi$
$127$	143.118			1.12691			0.563456	+	0.826146i	$0.309471\pi$
$128$	−1.64670	+	2.85216i	−0.0128648	+	0.0222825i
$129$	−9.24297	−	3.62596i	−0.0716509	−	0.0281083i
$130$	13.4631	+	23.3188i	0.103562	+	0.179375i
$131$	−146.509	−	84.5872i	−1.11839	−	0.645704i	−0.177402	−	0.984139i	$-0.556769\pi$
$131$	−146.509	−	84.5872i	−1.11839	−	0.645704i	−0.940990	+	0.338435i	$0.890102\pi$
$132$	−23.4774	+	18.7285i	−0.177859	+	0.141883i
$133$	−33.9165	+	46.6207i	−0.255011	+	0.350531i
$134$			154.966i			1.15646i
$135$	36.6968	+	2.73308i	0.271828	+	0.0202451i
$136$	74.3937	−	42.9512i	0.547012	−	0.315818i
$137$	113.201	+	196.070i	0.826287	+	1.43117i	0.900932	+	0.433961i	$0.142884\pi$
$137$	113.201	+	196.070i	0.826287	+	1.43117i	−0.0746447	+	0.997210i	$0.523782\pi$
$138$	11.6459	−	1.75717i	0.0843909	−	0.0127331i
$139$	24.8821			0.179008			0.0895040	−	0.995986i	$-0.471472\pi$
$139$	24.8821			0.179008			0.0895040	+	0.995986i	$0.471472\pi$
$140$	1.69577	−	16.0377i	0.0121126	−	0.114555i
$141$	154.499	−	123.248i	1.09574	−	0.874097i
$142$	−21.1438	+	36.6221i	−0.148900	+	0.257902i
$143$	−38.4936	−	66.6729i	−0.269186	−	0.466244i
$144$	54.8710	−	16.9439i	0.381048	−	0.117666i
$145$	−24.9733	−	14.4184i	−0.172230	−	0.0994369i
$146$			152.875i			1.04709i
$147$	−122.593	−	81.1164i	−0.833968	−	0.551812i
$148$		−	55.6896i		−	0.376281i
$149$	13.3098	−	23.0532i	0.0893274	−	0.154720i	−0.817900	−	0.575361i	$-0.804862\pi$
$149$	13.3098	−	23.0532i	0.0893274	−	0.154720i	0.907227	+	0.420641i	$0.138195\pi$
$150$	98.2235	+	38.5325i	0.654823	+	0.256883i
$151$	5.60810	−	3.23784i	0.0371398	−	0.0214426i	−0.481315	−	0.876548i	$-0.659841\pi$
$151$	5.60810	−	3.23784i	0.0371398	−	0.0214426i	0.518455	+	0.855105i	$0.326507\pi$
$152$	−61.6825	−	35.6124i	−0.405806	−	0.234292i
$153$	87.1646	+	19.8666i	0.569703	+	0.129847i
$154$	6.62447	−	62.6507i	0.0430160	−	0.406823i
$155$			14.7000i			0.0948390i
$156$	−9.83578	−	65.1884i	−0.0630499	−	0.417874i
$157$	−110.262	−	190.979i	−0.702304	−	1.21643i	−0.967656	−	0.252274i	$-0.918822\pi$
$157$	−110.262	−	190.979i	−0.702304	−	1.21643i	0.265352	−	0.964152i	$-0.414512\pi$
$158$	−43.2395	−	74.8931i	−0.273668	−	0.474007i
$159$	−200.974	+	30.3235i	−1.26399	+	0.190714i
$160$	33.9288			0.212055
$161$	10.6381	−	14.6229i	0.0660753	−	0.0908254i
$162$	110.940	+	53.3424i	0.684817	+	0.329274i
$163$	−24.4470	−	14.1145i	−0.149982	−	0.0865920i	0.423131	−	0.906069i	$-0.360931\pi$
$163$	−24.4470	−	14.1145i	−0.149982	−	0.0865920i	−0.573113	+	0.819476i	$0.694264\pi$
$164$	−14.3534	−	24.8609i	−0.0875210	−	0.151591i
$165$	22.5413	+	8.84282i	0.136614	+	0.0535928i
$166$	−79.2494	+	137.264i	−0.477406	+	0.826891i
$167$	262.828			1.57382			0.786909	−	0.617069i	$-0.211680\pi$
$167$	262.828			1.57382			0.786909	+	0.617069i	$0.211680\pi$
$168$	83.7315	−	161.151i	0.498402	−	0.959235i
$169$	169.000			1.00000
$170$	−17.8179	−	10.2872i	−0.104811	−	0.0605128i
$171$	−21.8703	−	70.8248i	−0.127897	−	0.414180i
$172$	−2.79729	−	4.84504i	−0.0162633	−	0.0281689i
$173$	−97.5574	−	56.3248i	−0.563916	−	0.325577i	0.190800	−	0.981629i	$-0.438892\pi$
$173$	−97.5574	−	56.3248i	−0.563916	−	0.325577i	−0.754716	+	0.656052i	$0.772225\pi$
$174$	−60.1564	−	75.4100i	−0.345726	−	0.433391i
$175$	148.033	−	65.7978i	0.845904	−	0.375987i
$176$	37.7879			0.214704
$177$	−7.67109	−	50.8415i	−0.0433395	−	0.287240i
$178$	−66.5013	−	115.184i	−0.373603	−	0.647099i
$179$	128.612	−	74.2540i	0.718501	−	0.414827i	−0.0956998	−	0.995410i	$-0.530509\pi$
$179$	128.612	−	74.2540i	0.718501	−	0.414827i	0.814201	+	0.580584i	$0.197176\pi$
$180$	15.2040	+	14.0986i	0.0844669	+	0.0783257i
$181$	−42.0467			−0.232302			−0.116151	−	0.993232i	$-0.537056\pi$
$181$	−42.0467			−0.232302			−0.116151	+	0.993232i	$0.537056\pi$
$182$	111.833	+	81.3580i	0.614465	+	0.447022i
$183$	−45.0602	+	35.9456i	−0.246231	+	0.196424i
$184$	19.3471	+	11.1701i	0.105147	+	0.0607069i
$185$	−38.8844	+	22.4499i	−0.210186	+	0.121351i
$186$	−17.9585	+	45.7782i	−0.0965512	+	0.246119i
$187$	50.9449	+	29.4131i	0.272433	+	0.157289i
$188$	111.362			0.592353
$189$	177.933	−	63.7259i	0.941442	−	0.337174i
$190$			17.0589i			0.0897839i
$191$	−112.872	−	65.1664i	−0.590950	−	0.341185i	0.174523	−	0.984653i	$-0.444162\pi$
$191$	−112.872	−	65.1664i	−0.590950	−	0.341185i	−0.765473	+	0.643468i	$0.777495\pi$
$192$	176.941	+	69.4128i	0.921566	+	0.361525i
$193$	245.910	−	141.976i	1.27415	−	0.735628i	0.298380	−	0.954447i	$-0.403554\pi$
$193$	245.910	−	141.976i	1.27415	−	0.735628i	0.975765	+	0.218819i	$0.0702205\pi$
$194$	−36.6472	−	21.1583i	−0.188903	−	0.109063i
$195$	−41.5518	+	33.1469i	−0.213086	+	0.169984i
$196$	−25.4975	−	78.8083i	−0.130089	−	0.402083i
$197$	−11.8442			−0.0601228			−0.0300614	−	0.999548i	$-0.509570\pi$
$197$	−11.8442			−0.0601228			−0.0300614	+	0.999548i	$0.509570\pi$
$198$	59.3941	+	55.0758i	0.299970	+	0.278161i
$199$	−46.4987	−	80.5382i	−0.233662	−	0.404714i	0.725221	−	0.688516i	$-0.241738\pi$
$199$	−46.4987	−	80.5382i	−0.233662	−	0.404714i	−0.958883	+	0.283802i	$0.908404\pi$
$200$	100.067	+	173.321i	0.500335	+	0.866606i
$201$	−302.485	+	45.6396i	−1.50490	+	0.227063i
$202$		−	254.529i		−	1.26004i
$203$	−147.287	−	15.5736i	−0.725552	−	0.0767173i
$204$	31.4139	+	39.3794i	0.153990	+	0.193036i
$205$	−11.5725	+	20.0442i	−0.0564513	+	0.0977765i
$206$	103.396	+	179.087i	0.501922	+	0.869354i
$207$	6.85977	+	22.2147i	0.0331390	+	0.107317i
$208$	−41.4754	+	71.8375i	−0.199401	+	0.345373i
$209$		−	48.7748i		−	0.233372i
$210$	−43.4533	+	1.93094i	−0.206921	+	0.00919494i
$211$	189.047			0.895956			0.447978	−	0.894045i	$-0.352144\pi$
$211$	189.047			0.895956			0.447978	+	0.894045i	$0.352144\pi$
$212$	−99.1817	−	57.2626i	−0.467838	−	0.270107i
$213$	−77.7112	−	30.4857i	−0.364841	−	0.143125i
$214$	157.935	−	91.1836i	0.738012	−	0.426092i
$215$	−2.25532	+	3.90633i	−0.0104899	+	0.0181690i
$216$	101.406	+	210.324i	0.469471	+	0.973721i
$217$	30.6658	+	68.9926i	0.141317	+	0.317938i
$218$			172.557i			0.791548i
$219$	−298.402	+	45.0237i	−1.36257	+	0.205588i
$220$	6.82188	+	11.8158i	0.0310086	+	0.0537084i
$221$	−111.833	+	64.5666i	−0.506030	+	0.292157i
$222$	−148.518	+	22.4088i	−0.669002	+	0.100941i
$223$			265.517i			1.19066i	0.803481	+	0.595330i	$0.202979\pi$
$223$			265.517i			1.19066i	−0.803481	+	0.595330i	$0.797021\pi$
$224$	159.240	−	70.7789i	0.710892	−	0.315977i
$225$	−46.2850	+	203.075i	−0.205711	+	0.902554i
$226$	108.514	+	62.6507i	0.480152	+	0.277216i
$227$	20.7516	+	35.9429i	0.0914168	+	0.158339i	0.908108	−	0.418737i	$-0.137527\pi$
$227$	20.7516	+	35.9429i	0.0914168	+	0.158339i	−0.816691	+	0.577076i	$0.804194\pi$
$228$	15.2533	−	38.8823i	0.0669005	−	0.170536i
$229$	18.5243	+	10.6950i	0.0808921	+	0.0467031i	0.539900	−	0.841729i	$-0.318462\pi$
$229$	18.5243	+	10.6950i	0.0808921	+	0.0467031i	−0.459008	+	0.888432i	$0.651795\pi$
$230$		−	5.35065i		−	0.0232637i
$231$	124.241	−	5.52092i	0.537842	−	0.0239001i
$232$		−	182.975i		−	0.788685i
$233$	324.073	+	187.104i	1.39087	+	0.803019i	0.993412	−	0.114601i	$-0.0365589\pi$
$233$	324.073	+	187.104i	1.39087	+	0.803019i	0.397459	+	0.917620i	$0.369892\pi$
$234$	−169.893	+	52.4621i	−0.726038	+	0.224197i
$235$	−44.8931	−	77.7572i	−0.191035	−	0.330882i
$236$	14.4860	−	25.0905i	0.0613814	−	0.106316i
$237$	133.452	−	106.458i	0.563089	−	0.449190i
$238$	−105.086	−	11.1114i	−0.441538	−	0.0466867i
$239$	−301.411			−1.26113			−0.630567	−	0.776135i	$-0.717177\pi$
$239$	−301.411			−1.26113			−0.630567	+	0.776135i	$0.717177\pi$
$240$	−3.89237	−	25.7974i	−0.0162182	−	0.107489i
$241$	373.439	−	215.605i	1.54954	−	0.894626i	0.551361	−	0.834267i	$-0.314109\pi$
$241$	373.439	−	215.605i	1.54954	−	0.894626i	0.998177	−	0.0603596i	$-0.0192248\pi$
$242$	−65.2943	−	113.093i	−0.269811	−	0.467327i
$243$	−71.4476	+	232.259i	−0.294023	+	0.955798i
$244$	−32.4792			−0.133112
$245$	−44.7481	+	49.5730i	−0.182645	+	0.202339i
$246$	−60.5259	+	48.2829i	−0.246040	+	0.196272i
$247$	92.7244	+	53.5345i	0.375403	+	0.216739i
$248$	−80.7784	+	46.6374i	−0.325719	+	0.188054i
$249$	−291.271	−	114.264i	−1.16976	−	0.458891i
$250$	49.8575	−	86.3557i	0.199430	−	0.345423i
$251$		−	344.407i		−	1.37214i	−0.727536	−	0.686070i	$-0.759334\pi$
$251$		−	344.407i		−	1.37214i	0.727536	−	0.686070i	$-0.240666\pi$
$252$	100.769	+	34.4527i	0.399878	+	0.136717i
$253$			15.2986i			0.0604686i
$254$	108.750	−	188.361i	0.428151	−	0.741580i
$255$	14.8323	−	37.8092i	0.0581660	−	0.148271i
$256$	129.215	+	223.807i	0.504746	+	0.874246i
$257$	−180.999	−	104.500i	−0.704276	−	0.406614i	0.104662	−	0.994508i	$-0.466624\pi$
$257$	−180.999	−	104.500i	−0.704276	−	0.406614i	−0.808938	+	0.587894i	$0.799957\pi$
$258$	−11.7956	+	9.40967i	−0.0457196	+	0.0364716i
$259$	−135.666	+	186.483i	−0.523806	+	0.720010i
$260$	−29.9504			−0.115194
$261$	129.479	−	139.631i	0.496088	−	0.534984i
$262$	−222.655	+	128.550i	−0.849827	+	0.490648i
$263$	144.352	−	83.3415i	0.548866	−	0.316888i	−0.199798	−	0.979837i	$-0.564029\pi$
$263$	144.352	−	83.3415i	0.548866	−	0.316888i	0.748665	+	0.662949i	$0.230695\pi$
$264$	22.9223	+	151.922i	0.0868269	+	0.575461i
$265$			92.3363i			0.348439i
$266$	35.5867	+	80.0638i	0.133785	+	0.300992i
$267$	205.246	−	163.730i	0.768711	−	0.613219i
$268$	−149.277	−	86.1854i	−0.557005	−	0.321587i
$269$	330.092	−	190.579i	1.22711	−	0.708471i	0.260683	−	0.965424i	$-0.416052\pi$
$269$	330.092	−	190.579i	1.22711	−	0.708471i	0.966424	+	0.256954i	$0.0827188\pi$
$270$	31.4817	−	46.2208i	0.116599	−	0.171188i
$271$	315.379	+	182.084i	1.16376	+	0.671898i	0.952202	−	0.305468i	$-0.0988128\pi$
$271$	315.379	+	182.084i	1.16376	+	0.671898i	0.211558	+	0.977365i	$0.432146\pi$
$272$		−	63.3829i		−	0.233025i
$273$	−125.870	+	242.252i	−0.461061	+	0.887368i
$274$	344.071			1.25573
$275$	−68.5261	+	118.691i	−0.249186	+	0.431602i
$276$	−4.78430	+	12.1957i	−0.0173344	+	0.0441873i
$277$	3.36853	+	5.83447i	0.0121608	+	0.0210631i	0.872042	−	0.489431i	$-0.162796\pi$
$277$	3.36853	+	5.83447i	0.0121608	+	0.0210631i	−0.859881	+	0.510495i	$0.829462\pi$
$278$	18.9071	−	32.7480i	0.0680110	−	0.117799i
$279$	−94.6453	−	21.5717i	−0.339230	−	0.0773178i
$280$	−66.7166	−	48.5362i	−0.238274	−	0.173344i
$281$	−394.126			−1.40258			−0.701291	−	0.712875i	$-0.747393\pi$
$281$	−394.126			−1.40258			−0.701291	+	0.712875i	$0.747393\pi$
$282$	−44.8109	−	296.992i	−0.158904	−	1.05316i
$283$	−23.7973	−	41.2181i	−0.0840894	−	0.145647i	0.820913	−	0.571053i	$-0.193465\pi$
$283$	−23.7973	−	41.2181i	−0.0840894	−	0.145647i	−0.905003	+	0.425406i	$0.860131\pi$
$284$	−23.5185	−	40.7352i	−0.0828115	−	0.143434i
$285$	−33.2980	+	5.02409i	−0.116835	+	0.0176284i
$286$	−117.000			−0.409091
$287$	−12.4997	+	118.216i	−0.0435531	+	0.411903i
$288$	−49.7889	+	218.448i	−0.172878	+	0.758500i
$289$	−95.1646	+	164.830i	−0.329289	+	0.570345i
$290$	−37.9527	+	21.9120i	−0.130872	+	0.0755587i
$291$	30.5066	−	77.7646i	0.104834	−	0.267232i
$292$	−147.263	−	85.0222i	−0.504325	−	0.291172i
$293$	440.042			1.50185			0.750926	−	0.660387i	$-0.229608\pi$
$293$	440.042			1.50185			0.750926	+	0.660387i	$0.229608\pi$
$294$	−199.914	+	99.7107i	−0.679979	+	0.339152i
$295$	−23.3588			−0.0791823
$296$	−246.730	−	142.450i	−0.833547	−	0.481249i
$297$	−90.0123	+	132.154i	−0.303072	+	0.444964i
$298$	−20.2273	−	35.0347i	−0.0678769	−	0.117566i
$299$	−29.0836	−	16.7914i	−0.0972697	−	0.0561587i
$300$	−91.7456	+	73.1876i	−0.305819	+	0.243959i
$301$	−2.43603	+	23.0387i	−0.00809311	+	0.0765404i
$302$		−	9.84130i		−	0.0325871i
$303$	496.825	−	74.9622i	1.63969	−	0.247400i
$304$	−45.5122	+	26.2765i	−0.149711	+	0.0864359i
$305$	13.0932	+	22.6782i	0.0429286	+	0.0743546i
$306$	92.3804	−	99.6236i	0.301897	−	0.325567i
$307$			506.508i			1.64986i	0.565232	+	0.824932i	$0.308787\pi$
$307$			506.508i			1.64986i	−0.565232	+	0.824932i	$0.691213\pi$
$308$	56.6666	+	41.2249i	0.183983	+	0.133847i
$309$	−319.115	+	254.566i	−1.03274	+	0.823838i
$310$	19.3471	+	11.1701i	0.0624101	+	0.0360325i
$311$	−261.698	+	151.091i	−0.841472	+	0.485824i	−0.857764	−	0.514043i	$-0.828147\pi$
$311$	−261.698	+	151.091i	−0.841472	+	0.485824i	0.0162925	+	0.999867i	$0.494814\pi$
$312$	−313.973	−	123.170i	−1.00632	−	0.394775i
$313$	−138.858	+	240.508i	−0.443634	+	0.768397i	−0.997956	−	0.0639055i	$-0.979644\pi$
$313$	−138.858	+	240.508i	−0.443634	+	0.768397i	0.554322	+	0.832302i	$0.312978\pi$
$314$	−335.136			−1.06731
$315$	−16.5667	−	84.2495i	−0.0525925	−	0.267459i
$316$	96.1917			0.304404
$317$	243.071	−	421.012i	0.766786	−	1.32811i	−0.172511	−	0.985008i	$-0.555188\pi$
$317$	243.071	−	421.012i	0.766786	−	1.32811i	0.939297	−	0.343105i	$-0.111479\pi$
$318$	−112.804	+	287.549i	−0.354730	+	0.904243i
$319$	108.514	−	62.6507i	0.340170	−	0.196397i
$320$	43.1742	−	74.7799i	0.134919	−	0.233687i
$321$	224.499	+	281.424i	0.699373	+	0.876710i
$322$	−11.1620	−	25.1125i	−0.0346646	−	0.0779893i
$323$	−81.8116			−0.253287
$324$	−113.084	+	77.2012i	−0.349026	+	0.238275i
$325$	−150.426	−	260.546i	−0.462850	−	0.801680i
$326$	−37.1529	+	21.4503i	−0.113966	+	0.0657983i
$327$	−336.822	+	50.8204i	−1.03004	+	0.155414i
$328$	−146.860			−0.447744
$329$	−372.909	−	271.291i	−1.13346	−	0.824592i
$330$	28.7666	−	22.9478i	0.0871716	−	0.0695389i
$331$	496.394	+	286.593i	1.49968	+	0.865840i	1.00000		0.000370819i	$-0.000118035\pi$
$331$	496.394	+	286.593i	1.49968	+	0.865840i	0.499679	+	0.866211i	$0.333451\pi$
$332$	−88.1500	−	152.680i	−0.265512	−	0.459880i
$333$	−87.4813	−	283.299i	−0.262707	−	0.850749i
$334$	199.714	−	345.914i	0.597945	−	1.03567i
$335$			138.974i			0.414849i
$336$	−72.0843	−	112.957i	−0.214537	−	0.336180i
$337$	290.118			0.860884			0.430442	−	0.902618i	$-0.358358\pi$
$337$	290.118			0.860884			0.430442	+	0.902618i	$0.358358\pi$
$338$	128.417	−	222.425i	0.379933	−	0.658063i
$339$	−90.3316	+	230.265i	−0.266465	+	0.679247i
$340$	19.8191	−	11.4426i	0.0582914	−	0.0336546i
$341$	−55.3172	−	31.9374i	−0.162220	−	0.0936580i
$342$	−109.833	−	25.0332i	−0.321149	−	0.0731966i
$343$	−106.605	+	326.013i	−0.310800	+	0.950475i
$344$	−28.6210			−0.0832005
$345$	10.4441	−	1.57584i	0.0302729	−	0.00456765i
$346$	−148.261	+	85.5986i	−0.428500	+	0.247395i
$347$	−248.115	+	143.249i	−0.715029	+	0.412822i	−0.812920	−	0.582375i	$-0.802124\pi$
$347$	−248.115	+	143.249i	−0.715029	+	0.412822i	0.0978913	+	0.995197i	$0.468790\pi$
$348$	106.098	−	16.0083i	0.304879	−	0.0460010i
$349$		−	372.586i		−	1.06758i	−0.845616	−	0.533791i	$-0.820767\pi$
$349$		−	372.586i		−	1.06758i	0.845616	−	0.533791i	$-0.179233\pi$
$350$	25.8872	−	244.828i	0.0739635	−	0.699508i
$351$	−152.439	−	316.170i	−0.434298	−	0.900769i
$352$	−73.7137	+	127.676i	−0.209414	+	0.362716i
$353$	−185.062	−	320.536i	−0.524254	−	0.908035i	−0.999601	−	0.0282368i	$-0.991011\pi$
$353$	−185.062	−	320.536i	−0.524254	−	0.908035i	0.475347	−	0.879798i	$-0.342323\pi$
$354$	−72.7428	−	28.5366i	−0.205488	−	0.0806118i
$355$	−18.9618	+	32.8429i	−0.0534136	+	0.0925151i
$356$	147.940			0.415563
$357$	−9.26042	−	208.394i	−0.0259395	−	0.583737i
$358$		−	225.692i		−	0.630425i
$359$	−218.798	+	378.970i	−0.609466	+	1.05563i	0.381862	+	0.924219i	$0.375283\pi$
$359$	−218.798	+	378.970i	−0.609466	+	1.05563i	−0.991328	+	0.131407i	$0.958050\pi$
$360$	101.354	−	31.2976i	0.281539	−	0.0869378i
$361$	−146.584	−	253.890i	−0.406049	−	0.703297i
$362$	−31.9498	+	55.3387i	−0.0882592	+	0.152869i
$363$	201.521	−	160.758i	0.555154	−	0.442859i
$364$	−140.568	+	62.4795i	−0.386175	+	0.171647i
$365$			137.099i			0.375613i
$366$	13.0693	+	86.6188i	0.0357083	+	0.236663i
$367$	37.2604	+	64.5369i	0.101527	+	0.175850i	0.912314	−	0.409491i	$-0.134294\pi$
$367$	37.2604	+	64.5369i	0.101527	+	0.175850i	−0.810787	+	0.585341i	$0.800961\pi$
$368$	14.2752	−	8.24180i	0.0387913	−	0.0223962i
$369$	−112.071	−	103.923i	−0.303716	−	0.281634i
$370$			68.2358i			0.184421i
$371$	192.623	+	433.368i	0.519200	+	1.16811i
$372$	−34.1100	−	42.7591i	−0.0916934	−	0.114944i
$373$	−75.7137	+	131.140i	−0.202986	+	0.351582i	−0.949489	−	0.313800i	$-0.898398\pi$
$373$	−75.7137	+	131.140i	−0.202986	+	0.351582i	0.746503	+	0.665382i	$0.231731\pi$
$374$	77.4226	−	44.7000i	0.207012	−	0.119519i
$375$	183.245	+	71.8859i	0.488653	+	0.191696i
$376$	284.856	−	493.385i	0.757596	−	1.31220i
$377$			275.058i			0.729596i
$378$	51.3336	−	282.605i	0.135803	−	0.747632i
$379$			726.940i			1.91805i	0.283326	+	0.959024i	$0.408562\pi$
$379$			726.940i			1.91805i	−0.283326	+	0.959024i	$0.591438\pi$
$380$	−16.4327	−	9.48743i	−0.0432440	−	0.0249669i
$381$	399.698	+	156.799i	1.04908	+	0.411547i
$382$	−171.534	+	99.0355i	−0.449043	+	0.259255i
$383$	−115.240	+	199.602i	−0.300888	+	0.521153i	−0.976337	−	0.216253i	$-0.930616\pi$
$383$	−115.240	+	199.602i	−0.300888	+	0.521153i	0.675449	+	0.737406i	$0.263950\pi$
$384$	−7.72370	+	6.16138i	−0.0201138	+	0.0160453i
$385$	5.94086	−	56.1855i	0.0154308	−	0.145936i
$386$		−	431.531i		−	1.11796i
$387$	−21.8411	−	20.2531i	−0.0564369	−	0.0523336i
$388$	40.7632	−	23.5346i	0.105060	−	0.0606563i
$389$	42.2402	−	24.3874i	0.108587	−	0.0626926i	−0.444723	−	0.895668i	$-0.646698\pi$
$389$	42.2402	−	24.3874i	0.108587	−	0.0626926i	0.553310	+	0.832976i	$0.313365\pi$
$390$	12.0517	+	79.8746i	0.0309017	+	0.204807i
$391$	25.6607			0.0656285
$392$	−414.377	−	88.6203i	−1.05708	−	0.226072i
$393$	−316.496	−	396.749i	−0.805334	−	1.00954i
$394$	−9.00000	+	15.5885i	−0.0228426	+	0.0395646i
$395$	−38.7774	−	67.1645i	−0.0981707	−	0.170037i
$396$	−86.0864	+	26.5830i	−0.217390	+	0.0671288i
$397$	−425.769	−	245.818i	−1.07247	−	0.619188i	−0.143612	−	0.989634i	$-0.545872\pi$
$397$	−425.769	−	245.818i	−1.07247	−	0.619188i	−0.928854	+	0.370446i	$0.879205\pi$
$398$	−141.331			−0.355103
$399$	−145.799	+	93.0430i	−0.365411	+	0.233190i
$400$	147.668			0.369171
$401$	−234.688	+	406.492i	−0.585258	+	1.01370i	0.409586	+	0.912272i	$0.365673\pi$
$401$	−234.688	+	406.492i	−0.585258	+	1.01370i	−0.994843	+	0.101424i	$0.967660\pi$
$402$	−169.780	+	432.788i	−0.422339	+	1.07659i
$403$	121.430	−	70.1079i	0.301316	−	0.173965i
$404$	245.185	+	141.558i	0.606894	+	0.350391i
$405$	99.4919	+	47.8377i	0.245659	+	0.118118i
$406$	−132.415	+	182.014i	−0.326146	+	0.448311i
$407$		−	195.099i		−	0.479360i
$408$	254.823	−	38.4483i	0.624566	−	0.0942361i
$409$	481.463	−	277.973i	1.17717	−	0.679640i	0.221812	−	0.975089i	$-0.428803\pi$
$409$	481.463	−	277.973i	1.17717	−	0.679640i	0.955358	+	0.295449i	$0.0954694\pi$
$410$	17.5871	+	30.4618i	0.0428954	+	0.0742970i
$411$	101.334	+	671.606i	0.246554	+	1.63408i
$412$	−230.017			−0.558294
$413$	−109.631	+	48.7288i	−0.265451	+	0.117987i
$414$	34.4498	+	7.85184i	0.0832121	+	0.0189658i
$415$	−71.0712	+	123.099i	−0.171256	+	0.296624i
$416$	−161.814	−	280.270i	−0.388976	−	0.673726i
$417$	69.4905	+	27.2607i	0.166644	+	0.0653734i
$418$	−64.1938	−	37.0623i	−0.153574	−	0.0886659i
$419$			452.382i			1.07967i	0.841771	+	0.539835i	$0.181513\pi$
$419$			452.382i			1.07967i	−0.841771	+	0.539835i	$0.818487\pi$
$420$	22.3068	−	42.9321i	0.0531114	−	0.102219i
$421$		−	502.198i		−	1.19287i	−0.802662	−	0.596435i	$-0.796584\pi$
$421$		−	502.198i		−	1.19287i	0.802662	−	0.596435i	$-0.203416\pi$
$422$	143.650	−	248.809i	0.340403	−	0.589595i
$423$	566.513	−	174.936i	1.33927	−	0.413561i
$424$	−507.398	+	292.947i	−1.19669	+	0.690912i
$425$	199.084	+	114.941i	0.468432	+	0.270449i
$426$	−99.1730	+	79.1127i	−0.232801	+	0.185711i
$427$	108.760	+	79.1229i	0.254708	+	0.185300i
$428$			202.849i			0.473947i
$429$	−34.4581	−	228.377i	−0.0803218	−	0.532347i
$430$	3.42748	+	5.93658i	0.00797089	+	0.0138060i
$431$	177.101	+	306.748i	0.410907	+	0.711712i	0.994989	−	0.0999827i	$-0.0318787\pi$
$431$	177.101	+	306.748i	0.410907	+	0.711712i	−0.584082	+	0.811695i	$0.698545\pi$
$432$	171.807	+	12.7957i	0.397700	+	0.0296197i
$433$	−102.479			−0.236673			−0.118336	−	0.992974i	$-0.537756\pi$
$433$	−102.479			−0.236673			−0.118336	+	0.992974i	$0.537756\pi$
$434$	114.105	+	12.0650i	0.262915	+	0.0277996i
$435$	−53.9485	−	67.6281i	−0.124020	−	0.155467i
$436$	−166.223	−	95.9688i	−0.381245	−	0.220112i
$437$	−10.6381	−	18.4258i	−0.0243435	−	0.0421642i
$438$	−167.489	+	426.947i	−0.382395	+	0.974765i
$439$	56.2960	−	97.5076i	0.128237	−	0.222113i	−0.794757	−	0.606928i	$-0.792402\pi$
$439$	56.2960	−	97.5076i	0.128237	−	0.222113i	0.922994	+	0.384815i	$0.125735\pi$
$440$	69.7994			0.158635
$441$	−253.507	−	360.854i	−0.574845	−	0.818262i
$442$			196.248i			0.444000i
$443$	695.206	+	401.378i	1.56931	+	0.906044i	0.996249	+	0.0865352i	$0.0275795\pi$
$443$	695.206	+	401.378i	1.56931	+	0.906044i	0.573066	+	0.819509i	$0.305754\pi$
$444$	61.0132	−	155.529i	0.137417	−	0.350291i
$445$	−59.6387	−	103.297i	−0.134020	−	0.232129i
$446$	349.454	+	201.758i	0.783530	+	0.452371i
$447$	62.4284	−	49.8007i	0.139661	−	0.111411i
$448$	46.6335	−	441.035i	0.104093	−	0.984453i
$449$	784.854			1.74800			0.874002	−	0.485923i	$-0.161516\pi$
$449$	784.854			1.74800			0.874002	+	0.485923i	$0.161516\pi$
$450$	232.101	+	215.226i	0.515781	+	0.478281i
$451$	−50.2850	−	87.0962i	−0.111497	−	0.193118i
$452$	−120.702	+	69.6872i	−0.267039	+	0.154175i
$453$	19.2096	−	2.89839i	0.0424053	−	0.00639822i
$454$	63.0738			0.138929
$455$	100.292	+	72.9623i	0.220422	+	0.160357i
$456$	−133.249	−	167.037i	−0.292214	−	0.366309i
$457$	−197.681	−	114.131i	−0.432563	−	0.249741i	0.267875	−	0.963454i	$-0.413679\pi$
$457$	−197.681	−	114.131i	−0.432563	−	0.249741i	−0.700438	+	0.713713i	$0.747012\pi$
$458$	28.1519	−	16.2535i	0.0614671	−	0.0354881i
$459$	221.666	+	150.980i	0.482933	+	0.328933i
$460$	5.15423	+	2.97580i	0.0112049	+	0.00646912i
$461$	398.928			0.865353			0.432676	−	0.901549i	$-0.357569\pi$
$461$	398.928			0.865353			0.432676	+	0.901549i	$0.357569\pi$
$462$	87.1406	−	167.713i	0.188616	−	0.363014i
$463$		−	44.0935i		−	0.0952342i	−0.998866	−	0.0476171i	$-0.984837\pi$
$463$		−	44.0935i		−	0.0952342i	0.998866	−	0.0476171i	$-0.0151627\pi$
$464$	−116.920	−	67.5038i	−0.251983	−	0.145482i
$465$	−16.1053	+	41.0541i	−0.0346351	+	0.0882885i
$466$	492.504	−	284.347i	1.05687	−	0.610187i
$467$	399.258	+	230.512i	0.854943	+	0.493601i	0.862315	−	0.506372i	$-0.169014\pi$
$467$	399.258	+	230.512i	0.854943	+	0.493601i	−0.00737290	+	0.999973i	$0.502347\pi$
$468$	43.9508	−	192.833i	0.0939120	−	0.412037i
$469$	289.915	+	652.257i	0.618156	+	1.39074i
$470$	−136.451			−0.290321
$471$	−98.7021	−	654.166i	−0.209559	−	1.38889i
$472$	−74.1081	−	128.359i	−0.157009	−	0.271947i
$473$	−9.79984	−	16.9738i	−0.0207185	−	0.0358855i
$474$	−38.7064	−	256.534i	−0.0816591	−	0.541210i
$475$		−	190.603i		−	0.401270i
$476$	69.1478	−	95.0487i	0.145268	−	0.199682i
$477$	−594.501	−	135.499i	−1.24633	−	0.284066i
$478$	−229.032	+	396.695i	−0.479146	+	0.829905i
$479$	144.978	+	251.108i	0.302667	+	0.524235i	0.976739	−	0.214431i	$-0.0687896\pi$
$479$	144.978	+	251.108i	0.302667	+	0.524235i	−0.674072	+	0.738666i	$0.735456\pi$
$480$	94.7559	+	37.1722i	0.197408	+	0.0774420i
$481$	370.898	+	214.138i	0.771097	+	0.445193i
$482$		−	655.323i		−	1.35959i
$483$	45.7308	−	29.1836i	0.0946807	−	0.0604214i
$484$	145.255			0.300114
$485$	−32.8654	−	18.9749i	−0.0677638	−	0.0391234i
$486$	251.392	+	270.520i	0.517267	+	0.556625i
$487$	−46.1777	+	26.6607i	−0.0948208	+	0.0547448i	−0.546661	−	0.837354i	$-0.684101\pi$
$487$	−46.1777	+	26.6607i	−0.0948208	+	0.0547448i	0.451840	+	0.892099i	$0.350768\pi$
$488$	−83.0793	+	143.898i	−0.170244	+	0.294872i
$489$	−52.8116	−	66.2029i	−0.107999	−	0.135384i
$490$	31.2418	+	96.5629i	0.0637587	+	0.197067i
$491$		−	604.181i		−	1.23051i	−0.788328	−	0.615255i	$-0.789053\pi$
$491$		−	604.181i		−	1.23051i	0.788328	−	0.615255i	$-0.210947\pi$
$492$	−12.8487	−	85.1568i	−0.0261152	−	0.173083i
$493$	−105.086	−	182.014i	−0.213156	−	0.369198i
$494$	140.916	−	81.3580i	0.285256	−	0.164692i
$495$	53.2649	+	49.3923i	0.107606	+	0.0997824i
$496$			68.8226i			0.138755i
$497$	−20.4811	+	193.700i	−0.0412095	+	0.389738i
$498$	−371.712	+	296.524i	−0.746411	+	0.595430i
$499$	−211.439	−	122.074i	−0.423725	−	0.244637i	0.272945	−	0.962030i	$-0.412002\pi$
$499$	−211.439	−	122.074i	−0.423725	−	0.244637i	−0.696670	+	0.717392i	$0.745336\pi$
$500$	55.4571	+	96.0545i	0.110914	+	0.192109i
$501$	734.022	+	287.953i	1.46511	+	0.574756i
$502$	−453.283	−	261.703i	−0.902954	−	0.521321i
$503$			424.673i			0.844281i	0.906530	+	0.422141i	$0.138721\pi$
$503$			424.673i			0.844281i	−0.906530	+	0.422141i	$0.861279\pi$
$504$	410.401	−	358.326i	0.814288	−	0.710964i
$505$		−	228.263i		−	0.452006i
$506$	20.1348	+	11.6248i	0.0397921	+	0.0229740i
$507$	471.981	+	185.156i	0.930930	+	0.365198i
$508$	120.964	+	209.516i	0.238119	+	0.412434i
$509$	444.742	−	770.315i	0.873756	−	1.51339i	0.0156736	−	0.999877i	$-0.495011\pi$
$509$	444.742	−	770.315i	0.873756	−	1.51339i	0.858082	−	0.513512i	$-0.171656\pi$
$510$	−38.4911	−	48.2512i	−0.0754728	−	0.0946101i
$511$	286.003	+	643.455i	0.559692	+	1.25921i
$512$	379.571			0.741349
$513$	16.5161	−	221.760i	0.0321952	−	0.432280i
$514$	−275.070	+	158.812i	−0.535155	+	0.308972i
$515$	92.7260	+	160.606i	0.180050	+	0.311857i
$516$	−2.50403	−	16.5959i	−0.00485276	−	0.0321626i
$517$	390.140			0.754623
$518$	142.347	+	320.255i	0.274801	+	0.618253i
$519$	−210.748	−	264.187i	−0.406066	−	0.509030i
$520$	−76.6107	+	132.694i	−0.147328	+	0.255180i
$521$	265.480	−	153.275i	0.509558	−	0.294193i	−0.223094	−	0.974797i	$-0.571616\pi$
$521$	265.480	−	153.275i	0.509558	−	0.294193i	0.732652	+	0.680604i	$0.238282\pi$
$522$	−85.3852	−	276.511i	−0.163573	−	0.529715i
$523$	292.129	−	505.982i	0.558564	−	0.967461i	−0.439053	−	0.898461i	$-0.644686\pi$
$523$	292.129	−	505.982i	0.558564	−	0.967461i	0.997617	−	0.0689998i	$-0.0219808\pi$
$524$		−	285.975i		−	0.545754i
$525$	485.513	−	21.5748i	0.924787	−	0.0410948i
$526$		−	253.314i		−	0.481585i
$527$	−53.5696	+	92.7852i	−0.101650	+	0.176063i
$528$	105.534	+	41.4003i	0.199874	+	0.0784096i
$529$	−261.163	−	452.348i	−0.493692	−	0.855100i
$530$	121.526	+	70.1632i	0.229295	+	0.132383i
$531$	34.2780	−	150.394i	0.0645536	−	0.283228i
$532$	−96.9165	−	10.2476i	−0.182174	−	0.0192624i
$533$	220.768			0.414199
$534$	−59.5294	−	394.542i	−0.111478	−	0.738843i
$535$	141.637	−	81.7739i	0.264741	−	0.152848i
$536$	−763.680	+	440.911i	−1.42478	+	0.822595i
$537$	440.538	−	66.4694i	0.820368	−	0.123779i
$538$		−	579.257i		−	1.07669i
$539$	−89.3262	−	276.092i	−0.165726	−	0.512230i
$540$	27.0153	+	56.0320i	0.0500283	+	0.103763i
$541$	−222.619	−	128.529i	−0.411495	−	0.237577i	0.279937	−	0.960018i	$-0.409686\pi$
$541$	−222.619	−	128.529i	−0.411495	−	0.237577i	−0.691432	+	0.722442i	$0.743020\pi$
$542$	479.292	−	276.719i	0.884302	−	0.510552i
$543$	−117.427	−	46.0661i	−0.216257	−	0.0848363i
$544$	214.155	+	123.642i	0.393667	+	0.227284i
$545$			154.750i			0.283946i
$546$	223.189	+	349.739i	0.408772	+	0.640548i
$547$	−356.044			−0.650903			−0.325452	−	0.945559i	$-0.605516\pi$
$547$	−356.044			−0.650903			−0.325452	+	0.945559i	$0.605516\pi$
$548$	−191.357	+	331.441i	−0.349192	+	0.604819i
$549$	−165.226	+	51.0208i	−0.300957	+	0.0929340i
$550$	104.141	+	180.378i	0.189348	+	0.327960i
$551$	−87.1306	+	150.915i	−0.158132	+	0.273892i
$552$	41.7945	+	52.3922i	0.0757148	+	0.0949135i
$553$	−322.109	−	234.333i	−0.582475	−	0.423749i
$554$	10.2385			0.0184811
$555$	−133.192	+	20.0963i	−0.239986	+	0.0362096i
$556$	21.0305	+	36.4260i	0.0378247	+	0.0655143i
$557$	−254.710	−	441.171i	−0.457289	−	0.792048i	0.541528	−	0.840683i	$-0.317846\pi$
$557$	−254.710	−	441.171i	−0.457289	−	0.792048i	−0.998817	+	0.0486352i	$0.984513\pi$
$558$	−100.309	+	108.174i	−0.179765	+	0.193859i
$559$	43.0246			0.0769671
$560$	−55.6277	+	24.7254i	−0.0993352	+	0.0441525i
$561$	110.054	+	137.959i	0.196174	+	0.245917i
$562$	−299.483	+	518.719i	−0.532887	+	0.922988i
$563$	−711.106	+	410.557i	−1.26307	+	0.729231i	−0.973666	−	0.227977i	$-0.926789\pi$
$563$	−711.106	+	410.557i	−1.26307	+	0.729231i	−0.289399	+	0.957208i	$0.593456\pi$
$564$	311.012	+	122.008i	0.551439	+	0.216326i
$565$	97.3162	+	56.1855i	0.172241	+	0.0994434i
$566$	−72.3310			−0.127793
$567$	566.746	+	16.9691i	0.999552	+	0.0299280i
$568$	−240.634			−0.423651
$569$	−967.744	−	558.727i	−1.70078	−	0.981946i	−0.944971	−	0.327154i	$-0.893910\pi$
$569$	−967.744	−	558.727i	−1.70078	−	0.981946i	−0.755809	−	0.654792i	$-0.772756\pi$
$570$	−18.6897	+	47.6420i	−0.0327889	+	0.0835825i
$571$	−480.817	−	832.799i	−0.842061	−	1.45849i	−0.888149	−	0.459555i	$-0.848009\pi$
$571$	−480.817	−	832.799i	−0.842061	−	1.45849i	0.0460884	−	0.998937i	$-0.485324\pi$
$572$	65.0703	−	112.705i	0.113759	−	0.197037i
$573$	−243.830	−	305.658i	−0.425533	−	0.533434i
$574$	146.089	+	106.280i	0.254511	+	0.185156i
$575$			59.7840i			0.103972i
$576$	418.109	+	387.711i	0.725885	+	0.673109i
$577$	−856.777	+	494.660i	−1.48488	+	0.857297i	−0.999852	−	0.0172005i	$-0.994525\pi$
$577$	−856.777	+	494.660i	−1.48488	+	0.857297i	−0.485030	+	0.874498i	$0.661191\pi$
$578$	144.625	+	250.497i	0.250216	+	0.433386i
$579$	842.323	−	127.092i	1.45479	−	0.219502i
$580$		−	48.7460i		−	0.0840449i
$581$	−76.7657	+	726.010i	−0.132127	+	1.24959i
$582$	−79.1671	−	99.2412i	−0.136026	−	0.170518i
$583$	−347.467	−	200.610i	−0.595998	−	0.344100i
$584$	−753.374	+	434.961i	−1.29002	+	0.744795i
$585$	−152.361	+	47.0483i	−0.260446	+	0.0804244i
$586$	334.373	−	579.151i	0.570603	−	0.988313i
$587$	−725.629			−1.23616			−0.618082	−	0.786113i	$-0.712090\pi$
$587$	−725.629			−1.23616			−0.618082	+	0.786113i	$0.712090\pi$
$588$	15.1330	−	248.030i	0.0257364	−	0.421820i
$589$	88.8329			0.150820
$590$	−17.7495	+	30.7431i	−0.0300840	+	0.0521069i
$591$	−33.0783	−	12.9764i	−0.0559701	−	0.0219568i
$592$	−182.049	+	105.106i	−0.307515	+	0.177544i
$593$	54.7757	−	94.8742i	0.0923704	−	0.159990i	−0.816138	−	0.577857i	$-0.803889\pi$
$593$	54.7757	−	94.8742i	0.0923704	−	0.159990i	0.908508	+	0.417867i	$0.137222\pi$
$594$	105.534	+	218.887i	0.177667	+	0.368497i
$595$	−94.2418	−	9.96479i	−0.158389	−	0.0167475i
$596$	44.9982			0.0755003
$597$	−41.6239	−	275.870i	−0.0697218	−	0.462094i
$598$	−44.1993	+	25.5185i	−0.0739119	+	0.0426731i
$599$	519.534	−	299.953i	0.867335	−	0.500756i	0.000873542	−	1.00000i	$-0.499722\pi$
$599$	519.534	−	299.953i	0.867335	−	0.500756i	0.866462	+	0.499243i	$0.166389\pi$
$600$	89.5763	+	593.683i	0.149294	+	0.989471i
$601$	322.830			0.537155			0.268578	−	0.963258i	$-0.413446\pi$
$601$	322.830			0.537155			0.268578	+	0.963258i	$0.413446\pi$
$602$	28.4707	+	20.7124i	0.0472936	+	0.0344060i
$603$	−894.778	−	203.939i	−1.48388	−	0.338207i
$604$	9.48003	+	5.47330i	0.0156954	+	0.00906175i
$605$	−58.5563	−	101.422i	−0.0967873	−	0.167640i
$606$	278.861	−	710.846i	0.460166	−	1.17301i
$607$	112.203	−	194.341i	0.184848	−	0.320166i	−0.758677	−	0.651467i	$-0.774154\pi$
$607$	112.203	−	194.341i	0.184848	−	0.320166i	0.943525	+	0.331301i	$0.107487\pi$
$608$		−	205.033i		−	0.337225i
$609$	−394.279	−	204.861i	−0.647421	−	0.336389i
$610$	39.7964			0.0652400
$611$	−428.211	+	741.684i	−0.700837	+	1.21389i
$612$	44.5885	+	144.395i	0.0728571	+	0.235940i
$613$	−485.335	+	280.208i	−0.791737	+	0.457110i	−0.840574	−	0.541697i	$-0.817782\pi$
$613$	−485.335	+	280.208i	−0.791737	+	0.457110i	0.0488367	+	0.998807i	$0.484449\pi$
$614$	666.629	+	384.878i	1.08571	+	0.626837i
$615$	−54.2799	+	43.3004i	−0.0882600	+	0.0704071i
$616$	327.594	−	145.609i	0.531808	−	0.236378i
$617$	−610.674			−0.989748			−0.494874	−	0.868965i	$-0.664786\pi$
$617$	−610.674			−0.989748			−0.494874	+	0.868965i	$0.664786\pi$
$618$	92.5561	+	613.432i	0.149767	+	0.992609i
$619$	−634.279	+	366.201i	−1.02468	+	0.591602i	−0.915457	−	0.402415i	$-0.868171\pi$
$619$	−634.279	+	366.201i	−1.02468	+	0.591602i	−0.109227	+	0.994017i	$0.534837\pi$
$620$	−21.5200	+	12.4246i	−0.0347097	+	0.0200397i
$621$	−5.18039	+	69.5564i	−0.00834201	+	0.112007i
$622$			459.236i			0.738322i
$623$	−495.395	−	360.399i	−0.795176	−	0.578489i
$624$	−194.537	+	155.187i	−0.311758	+	0.248697i
$625$	−244.569	+	423.605i	−0.391310	+	0.677769i
$626$	211.026	+	365.508i	0.337102	+	0.583879i
$627$	53.4375	−	136.218i	0.0852272	−	0.217253i
$628$	186.388	−	322.834i	0.296796	−	0.514066i
$629$	−327.246			−0.520264
$630$	−123.471	−	42.2145i	−0.195986	−	0.0670072i
$631$			806.507i			1.27814i	0.769148	+	0.639070i	$0.220681\pi$
$631$			806.507i			1.27814i	−0.769148	+	0.639070i	$0.779319\pi$
$632$	246.051	−	426.173i	0.389321	−	0.674324i
$633$	527.967	+	207.119i	0.834072	+	0.327202i
$634$	−369.403	−	639.825i	−0.582654	−	1.00919i
$635$	97.5279	−	168.923i	0.153587	−	0.266021i
$636$	−214.257	−	268.585i	−0.336882	−	0.422304i
$637$	622.914	+	133.219i	0.977887	+	0.209135i
$638$		−	190.425i		−	0.298471i
$639$	−183.631	−	170.280i	−0.287372	−	0.266479i
$640$	2.24429	+	3.88722i	0.00350670	+	0.00607379i
$641$	406.049	−	234.433i	0.633462	−	0.365730i	−0.148629	−	0.988893i	$-0.547486\pi$
$641$	406.049	−	234.433i	0.633462	−	0.365730i	0.782092	+	0.623163i	$0.214153\pi$
$642$	540.978	−	81.6241i	0.842646	−	0.127140i
$643$			183.967i			0.286107i	0.989715	+	0.143054i	$0.0456921\pi$
$643$			183.967i			0.286107i	−0.989715	+	0.143054i	$0.954308\pi$
$644$	30.3985	+	3.21423i	0.0472026	+	0.00499104i
$645$	−10.5784	+	8.43864i	−0.0164006	+	0.0130832i
$646$	−62.1658	+	107.674i	−0.0962319	+	0.166679i
$647$	−557.646	+	321.957i	−0.861895	+	0.497615i	−0.864646	−	0.502381i	$-0.832458\pi$
$647$	−557.646	+	321.957i	−0.861895	+	0.497615i	0.00275144	+	0.999996i	$0.499124\pi$
$648$	52.7750	+	698.489i	0.0814429	+	1.07792i
$649$	50.7494	−	87.9005i	0.0781962	−	0.135440i
$650$	−457.215			−0.703408
$651$	10.0552	+	226.279i	0.0154457	+	0.347587i
$652$		−	47.7188i		−	0.0731883i
$653$	−349.801	−	201.957i	−0.535682	−	0.309276i	0.207645	−	0.978204i	$-0.433420\pi$
$653$	−349.801	−	201.957i	−0.535682	−	0.309276i	−0.743327	+	0.668928i	$0.766753\pi$
$654$	−189.053	+	481.916i	−0.289072	+	0.736875i
$655$	−199.678	+	115.284i	−0.304852	+	0.176006i
$656$	−54.1801	+	93.8427i	−0.0825917	+	0.143053i
$657$	−882.702	−	201.187i	−1.34353	−	0.306220i
$658$	−640.414	+	284.651i	−0.973273	+	0.432600i
$659$		−	970.422i		−	1.47257i	−0.676673	−	0.736284i	$-0.736579\pi$
$659$		−	970.422i		−	1.47257i	0.676673	−	0.736284i	$-0.263421\pi$
$660$	6.10669	+	40.4732i	0.00925256	+	0.0613230i
$661$	364.763	−	210.596i	0.551836	−	0.318602i	−0.198026	−	0.980197i	$-0.563453\pi$
$661$	364.763	−	210.596i	0.551836	−	0.318602i	0.749862	+	0.661594i	$0.230120\pi$
$662$	754.385	−	435.544i	1.13955	−	0.657922i
$663$	−383.064	+	57.7976i	−0.577773	+	0.0871759i
$664$	−901.924			−1.35832
$665$	31.9144	+	71.8016i	0.0479915	+	0.107972i
$666$	−439.332	−	100.133i	−0.659657	−	0.150350i
$667$	27.3291	−	47.3354i	0.0409732	−	0.0709676i
$668$	222.144	+	384.765i	0.332551	+	0.575995i
$669$	−290.900	+	741.534i	−0.434827	+	1.10842i
$670$	182.908	+	105.602i	0.272997	+	0.157615i
$671$	−113.786			−0.169576
$672$	522.268	−	23.2081i	0.777185	−	0.0345358i
$673$	441.956			0.656695			0.328348	−	0.944557i	$-0.393508\pi$
$673$	441.956			0.656695			0.328348	+	0.944557i	$0.393508\pi$
$674$	220.451	−	381.832i	0.327078	−	0.566516i
$675$	−351.752	+	516.435i	−0.521114	+	0.765089i
$676$	142.840	+	247.406i	0.211302	+	0.365986i
$677$	84.1342	+	48.5749i	0.124275	+	0.0717502i	0.560849	−	0.827918i	$-0.310475\pi$
$677$	84.1342	+	48.5749i	0.124275	+	0.0717502i	−0.436574	+	0.899668i	$0.643808\pi$
$678$	234.418	+	293.858i	0.345749	+	0.433419i
$679$	−193.833	−	20.4952i	−0.285468	−	0.0301844i
$680$		−	117.077i		−	0.172172i
$681$	18.5761	+	123.116i	0.0272776	+	0.180787i
$682$	−84.0672	+	48.5362i	−0.123266	+	0.0711675i
$683$	−581.988	−	1008.03i	−0.852105	−	1.47589i	−0.879305	−	0.476260i	$-0.841992\pi$
$683$	−581.988	−	1008.03i	−0.852105	−	1.47589i	0.0271990	−	0.999630i	$-0.491341\pi$
$684$	85.1985	−	91.8786i	0.124559	−	0.134325i
$685$	308.565			0.450460
$686$	348.069	+	388.031i	0.507389	+	0.565643i
$687$	40.0170	+	50.1640i	0.0582489	+	0.0730189i
$688$	−10.5589	+	18.2886i	−0.0153473	+	0.0265823i
$689$	762.749	−	440.373i	1.10704	−	0.639148i
$690$	5.86215	−	14.9432i	0.00849587	−	0.0216569i
$691$	−50.1221	−	28.9380i	−0.0725356	−	0.0418784i	0.463294	−	0.886205i	$-0.346668\pi$
$691$	−50.1221	−	28.9380i	−0.0725356	−	0.0418784i	−0.535829	+	0.844326i	$0.680001\pi$
$692$		−	190.425i		−	0.275180i
$693$	353.029	+	120.700i	0.509421	+	0.174170i
$694$			435.401i			0.627379i
$695$	16.9559	−	29.3686i	0.0243970	−	0.0422569i
$696$	200.466	−	511.010i	0.288027	−	0.734210i
$697$	−146.089	+	84.3446i	−0.209597	+	0.121011i
$698$	−490.371	−	283.116i	−0.702537	−	0.405610i
$699$	700.077	+	877.593i	1.00154	+	1.25550i
$700$	221.443	+	161.099i	0.316347	+	0.230142i
$701$			920.879i			1.31367i	0.754036	+	0.656833i	$0.228104\pi$
$701$			920.879i			1.31367i	−0.754036	+	0.656833i	$0.771896\pi$
$702$	−531.953	−	39.6185i	−0.757767	−	0.0564366i
$703$	135.666	+	234.980i	0.192981	+	0.334253i
$704$	187.601	+	324.934i	0.266479	+	0.461554i
$705$	−40.1866	−	266.344i	−0.0570023	−	0.377793i
$706$	−562.489			−0.796726
$707$	−476.180	−	1071.32i	−0.673522	−	1.51530i
$708$	67.9454	−	54.2017i	0.0959680	−	0.0765560i
$709$	−518.790	−	299.523i	−0.731721	−	0.422459i	0.0873307	−	0.996179i	$-0.472166\pi$
$709$	−518.790	−	299.523i	−0.731721	−	0.422459i	−0.819051	+	0.573720i	$0.805500\pi$
$710$	28.8169	+	49.9123i	0.0405872	+	0.0702991i
$711$	489.338	−	151.105i	0.688240	−	0.212525i
$712$	378.420	−	655.442i	0.531489	−	0.920565i
$713$	−27.8630			−0.0390786
$714$	−281.310	−	146.164i	−0.393991	−	0.204711i
$715$	−104.926			−0.146750
$716$	217.407	+	125.520i	0.303641	+	0.175307i
$717$	−841.777	−	330.224i	−1.17403	−	0.460564i
$718$	332.515	+	575.933i	0.463113	+	0.802135i
$719$	−453.270	−	261.695i	−0.630417	−	0.363971i	0.150497	−	0.988611i	$-0.451913\pi$
$719$	−453.270	−	261.695i	−0.630417	−	0.363971i	−0.780914	+	0.624639i	$0.785246\pi$
$720$	17.3929	−	76.3111i	0.0241568	−	0.105988i
$721$	770.237	+	560.346i	1.06829	+	0.777179i
$722$	−445.535			−0.617085
$723$	1279.15	−	193.001i	1.76923	−	0.266945i
$724$	−35.5382	−	61.5539i	−0.0490859	−	0.0850192i
$725$	424.054	−	244.828i	0.584902	−	0.337694i
$726$	−58.4490	−	387.381i	−0.0805083	−	0.533583i
$727$	−554.641			−0.762918			−0.381459	−	0.924386i	$-0.624578\pi$
$727$	−554.641			−0.762918			−0.381459	+	0.924386i	$0.624578\pi$
$728$	−82.7490	+	782.597i	−0.113666	+	1.07500i
$729$	−454.000	+	570.373i	−0.622771	+	0.782404i
$730$	180.439	+	104.177i	0.247177	+	0.142708i
$731$	−28.4707	+	16.4376i	−0.0389476	+	0.0224864i
$732$	−90.7076	−	35.5841i	−0.123917	−	0.0486121i
$733$	−640.607	−	369.855i	−0.873953	−	0.504577i	−0.00529302	−	0.999986i	$-0.501685\pi$
$733$	−640.607	−	369.855i	−0.873953	−	0.504577i	−0.868660	+	0.495409i	$0.835018\pi$
$734$	113.252			0.154294
$735$	−179.284	+	89.4211i	−0.243924	+	0.121661i
$736$			64.3099i			0.0873775i
$737$	−522.969	−	301.937i	−0.709592	−	0.409683i
$738$	−221.935	+	68.5322i	−0.300724	+	0.0928621i
$739$	−587.454	+	339.167i	−0.794931	+	0.458954i	−0.841696	−	0.539952i	$-0.818442\pi$
$739$	−587.454	+	339.167i	−0.794931	+	0.458954i	0.0467643	+	0.998906i	$0.485109\pi$
$740$	−65.7309	−	37.9497i	−0.0888255	−	0.0512834i
$741$	200.308	+	251.099i	0.270321	+	0.338865i
$742$	716.734	+	75.7849i	0.965949	+	0.102136i
$743$	891.716			1.20016			0.600078	−	0.799941i	$-0.295136\pi$
$743$	891.716			1.20016			0.600078	+	0.799941i	$0.295136\pi$
$744$	−276.693	+	41.7481i	−0.371899	+	0.0561130i
$745$	−18.1400	−	31.4193i	−0.0243489	−	0.0421736i
$746$	115.065	+	199.298i	0.154242	+	0.267155i
$747$	−688.271	−	638.230i	−0.921380	−	0.854391i
$748$			99.4406i			0.132942i
$749$	494.163	−	679.263i	0.659763	−	0.906894i
$750$	233.852	−	186.550i	0.311803	−	0.248733i
$751$	−439.436	+	761.125i	−0.585134	+	1.01348i	0.409724	+	0.912209i	$0.365625\pi$
$751$	−439.436	+	761.125i	−0.585134	+	1.01348i	−0.994859	+	0.101273i	$0.967708\pi$
$752$	−210.180	−	364.043i	−0.279495	−	0.484100i
$753$	377.331	−	961.856i	0.501103	−	1.27737i
$754$	362.011	+	209.007i	0.480120	+	0.277198i
$755$		−	8.82573i		−	0.0116897i
$756$	243.681	+	206.622i	0.322330	+	0.273309i
$757$	−262.211			−0.346382			−0.173191	−	0.984888i	$-0.555408\pi$
$757$	−262.211			−0.346382			−0.173191	+	0.984888i	$0.555408\pi$
$758$	956.745	+	552.377i	1.26220	+	0.728729i
$759$	−16.7610	+	42.7256i	−0.0220830	+	0.0562920i
$760$	−84.0672	+	48.5362i	−0.110615	+	0.0638635i
$761$	−286.792	+	496.739i	−0.376862	+	0.652745i	−0.990604	−	0.136762i	$-0.956330\pi$
$761$	−286.792	+	496.739i	−0.376862	+	0.652745i	0.613741	+	0.789507i	$0.289664\pi$
$762$	510.085	−	406.907i	0.669402	−	0.533998i
$763$	322.825	+	726.299i	0.423100	+	0.951899i
$764$		−	220.317i		−	0.288373i
$765$	82.8472	−	89.3429i	0.108297	−	0.116788i
$766$	175.134	+	303.341i	0.228634	+	0.396007i
$767$	111.403	+	192.956i	0.145246	+	0.251573i
$768$	115.668	+	766.613i	0.150610	+	0.998194i
$769$		−	951.682i		−	1.23756i	−0.785565	−	0.618779i	$-0.787628\pi$
$769$		−	951.682i		−	1.23756i	0.785565	−	0.618779i	$-0.212372\pi$
$770$	−69.4330	−	50.5124i	−0.0901727	−	0.0656005i
$771$	−391.003	−	490.148i	−0.507137	−	0.635730i
$772$	415.690	+	239.999i	0.538459	+	0.310879i
$773$	82.4071	+	142.733i	0.106607	+	0.184648i	0.914394	−	0.404826i	$-0.132668\pi$
$773$	82.4071	+	142.733i	0.106607	+	0.184648i	−0.807787	+	0.589475i	$0.799335\pi$
$774$	−43.2519	+	13.3560i	−0.0558811	+	0.0172558i
$775$	−216.170	−	124.806i	−0.278928	−	0.161039i
$776$		−	240.799i		−	0.310308i
$777$	−583.196	+	372.172i	−0.750573	+	0.478986i
$778$		−	74.1247i		−	0.0952759i
$779$	121.128	+	69.9331i	0.155491	+	0.0897730i
$780$	−83.6450	−	32.8135i	−0.107237	−	0.0420685i
$781$	−82.3931	−	142.709i	−0.105497	−	0.182726i
$782$	19.4987	−	33.7728i	0.0249344	−	0.0431877i
$783$	514.586	−	248.103i	0.657198	−	0.316862i
$784$	−209.501	+	232.090i	−0.267221	+	0.296034i
$785$	−300.552			−0.382869
$786$	−762.666	+	115.073i	−0.970313	+	0.146403i
$787$	−656.573	+	379.072i	−0.834273	+	0.481668i	−0.855313	−	0.518111i	$-0.826635\pi$
$787$	−656.573	+	379.072i	−0.834273	+	0.481668i	0.0210406	+	0.999779i	$0.493302\pi$
$788$	−10.0108	−	17.3392i	−0.0127041	−	0.0220041i
$789$	494.453	−	74.6042i	0.626683	−	0.0945554i
$790$	−117.863			−0.149193
$791$	573.949	+	60.6873i	0.725599	+	0.0767222i
$792$	−102.427	+	449.399i	−0.129328	+	0.567423i
$793$	124.889	−	216.315i	0.157490	−	0.272780i
$794$	−647.054	+	373.577i	−0.814930	+	0.470500i
$795$	−101.163	+	257.876i	−0.127249	+	0.324372i
$796$	78.6022	−	136.143i	0.0987465	−	0.171034i
$797$		−	329.799i		−	0.413801i	−0.978362	−	0.206900i	$-0.933662\pi$
$797$		−	329.799i		−	0.413801i	0.978362	−	0.206900i	$-0.0663376\pi$
$798$	11.6687	+	262.590i	0.0146225	+	0.329060i
$799$		−	654.394i		−	0.819016i
$800$	−288.060	+	498.935i	−0.360075	+	0.623668i
$801$	752.590	−	232.396i	0.939563	−	0.290132i
$802$	356.663	+	617.759i	0.444717	+	0.770273i
$803$	−515.911	−	297.862i	−0.642480	−	0.370936i
$804$	−322.476	−	404.245i	−0.401090	−	0.502793i
$805$	−10.0102	−	22.5211i	−0.0124350	−	0.0279765i
$806$		−	213.090i		−	0.264380i
$807$	1130.67	−	170.599i	1.40108	−	0.211399i
$808$	1254.33	−	724.188i	1.55239	−	0.896272i
$809$	1032.17	−	595.923i	1.27586	−	0.736617i	0.299774	−	0.954010i	$-0.403089\pi$
$809$	1032.17	−	595.923i	1.27586	−	0.736617i	0.976084	+	0.217393i	$0.0697554\pi$
$810$	138.561	−	94.5937i	0.171063	−	0.116782i
$811$			906.597i			1.11788i	0.829210	+	0.558938i	$0.188791\pi$
$811$			906.597i			1.11788i	−0.829210	+	0.558938i	$0.811209\pi$
$812$	−101.689	−	228.783i	−0.125233	−	0.281752i
$813$	681.297	+	854.051i	0.838004	+	1.05049i
$814$	−256.775	−	148.249i	−0.315449	−	0.182124i
$815$	−33.3189	+	19.2367i	−0.0408821	+	0.0236033i
$816$	69.4420	−	177.015i	0.0851004	−	0.216930i
$817$	23.6061	+	13.6290i	0.0288936	+	0.0166818i
$818$		−	844.888i		−	1.03287i
$819$	−616.937	+	538.655i	−0.753281	+	0.657699i
$820$	−39.1247			−0.0477131
$821$	234.515	−	406.191i	0.285645	−	0.494752i	−0.687120	−	0.726544i	$-0.741125\pi$
$821$	234.515	−	406.191i	0.285645	−	0.494752i	0.972765	+	0.231792i	$0.0744588\pi$
$822$	960.918	+	376.963i	1.16900	+	0.458592i
$823$	−386.069	−	668.691i	−0.469099	−	0.812504i	0.530277	−	0.847825i	$-0.322088\pi$
$823$	−386.069	−	668.691i	−0.469099	−	0.812504i	−0.999376	+	0.0353208i	$0.988755\pi$
$824$	−588.366	+	1019.08i	−0.714036	+	1.23675i
$825$	−321.416	+	256.401i	−0.389595	+	0.310789i
$826$	−19.1717	+	181.316i	−0.0232103	+	0.219511i
$827$	248.971			0.301053			0.150527	−	0.988606i	$-0.451903\pi$
$827$	248.971			0.301053			0.150527	+	0.988606i	$0.451903\pi$
$828$	−26.7231	+	28.8183i	−0.0322743	+	0.0348048i
$829$	14.0148	+	24.2744i	0.0169057	+	0.0292816i	0.874354	−	0.485288i	$-0.161285\pi$
$829$	14.0148	+	24.2744i	0.0169057	+	0.0292816i	−0.857449	+	0.514569i	$0.827952\pi$
$830$	108.009	+	187.077i	0.130132	+	0.225395i
$831$	3.01539	+	19.9850i	0.00362862	+	0.0240493i
$832$	−823.631			−0.989941
$833$	−463.098	+	149.830i	−0.555940	+	0.179868i
$834$	88.6820	−	70.7437i	0.106333	−	0.0848246i
$835$	179.104	−	310.218i	0.214496	−	0.371518i
$836$	71.4036	−	41.2249i	0.0854110	−	0.0493121i
$837$	−240.691	−	163.938i	−0.287563	−	0.195864i
$838$	595.392	+	343.750i	0.710491	+	0.410202i
$839$	−11.5043			−0.0137120			−0.00685598	−	0.999976i	$-0.502182\pi$
$839$	−11.5043			−0.0137120			−0.00685598	+	0.999976i	$0.502182\pi$
$840$	−133.149	−	208.646i	−0.158511	−	0.248388i
$841$	393.327			0.467689
$842$	−660.956	−	381.603i	−0.784983	−	0.453210i
$843$	−1100.71	−	431.802i	−1.30571	−	0.512221i
$844$	159.784	+	276.754i	0.189317	+	0.327907i
$845$	115.165	−	199.472i	0.136290	−	0.236062i
$846$	200.236	−	878.531i	0.236685	−	1.03845i
$847$	−486.404	−	353.858i	−0.574266	−	0.417778i
$848$			432.299i			0.509787i
$849$	−21.3024	−	141.186i	−0.0250912	−	0.166296i
$850$	302.554	−	174.679i	0.355945	−	0.205505i
$851$	−42.5525	−	73.7031i	−0.0500029	−	0.0866076i
$852$	−21.0528	−	139.531i	−0.0247099	−	0.163769i
$853$		−	1165.82i		−	1.36673i	−0.730077	−	0.683365i	$-0.760516\pi$
$853$		−	1165.82i		−	1.36673i	0.730077	−	0.683365i	$-0.239484\pi$
$854$	186.779	−	83.0194i	0.218711	−	0.0972125i
$855$	−98.4987	−	22.4499i	−0.115203	−	0.0262572i
$856$	898.714	+	518.873i	1.04990	+	0.606160i
$857$	−656.668	+	379.128i	−0.766241	+	0.442389i	−0.831532	−	0.555477i	$-0.812536\pi$
$857$	−656.668	+	379.128i	−0.766241	+	0.442389i	0.0652912	+	0.997866i	$0.479202\pi$
$858$	−326.756	−	128.185i	−0.380835	−	0.149399i
$859$	−59.6904	+	103.387i	−0.0694883	+	0.120357i	−0.898676	−	0.438613i	$-0.855470\pi$
$859$	−59.6904	+	103.387i	−0.0694883	+	0.120357i	0.829188	+	0.558970i	$0.188803\pi$
$860$	−7.62486			−0.00886612
$861$	−164.426	+	316.458i	−0.190971	+	0.367547i
$862$	538.292			0.624468
$863$	−30.3293	+	52.5319i	−0.0351441	+	0.0608713i	−0.883062	−	0.469255i	$-0.844522\pi$
$863$	−30.3293	+	52.5319i	−0.0351441	+	0.0608713i	0.847918	+	0.530127i	$0.177856\pi$
$864$	−378.381	+	555.531i	−0.437941	+	0.642976i
$865$	−132.961	+	76.7653i	−0.153713	+	0.0887460i
$866$	−77.8705	+	134.876i	−0.0899197	+	0.155745i
$867$	−446.361	+	356.073i	−0.514834	+	0.410696i
$868$	−75.0823	+	103.206i	−0.0865003	+	0.118901i
$869$	336.992			0.387793
$870$	−130.001	+	19.6148i	−0.149426	+	0.0225458i
$871$	1148.01	−	662.801i	1.31803	−	0.760966i
$872$	−850.370	+	490.962i	−0.975195	+	0.563029i
$873$	170.397	−	183.757i	0.195186	−	0.210489i
$874$	−32.3342			−0.0369956
$875$	48.2950	−	456.749i	0.0551943	−	0.521999i
$876$	−318.124	−	398.790i	−0.363155	−	0.455239i
$877$	1059.35	+	611.614i	1.20792	+	0.697393i	0.962305	−	0.271974i	$-0.0876764\pi$
$877$	1059.35	+	611.614i	1.20792	+	0.697393i	0.245616	+	0.969367i	$0.421010\pi$
$878$	−85.5548	−	148.185i	−0.0974429	−	0.168776i
$879$	1228.95	+	482.108i	1.39812	+	0.548474i
$880$	25.7506	−	44.6014i	0.0292621	−	0.0506834i
$881$			913.498i			1.03689i	0.855112	+	0.518444i	$0.173488\pi$
$881$			913.498i			1.03689i	−0.855112	+	0.518444i	$0.826512\pi$
$882$	−667.560	+	59.4462i	−0.756871	+	0.0673993i
$883$	299.052			0.338677			0.169338	−	0.985558i	$-0.445837\pi$
$883$	299.052			0.338677			0.169338	+	0.985558i	$0.445837\pi$
$884$	−189.044	−	109.144i	−0.213850	−	0.123467i
$885$	−65.2361	−	25.5918i	−0.0737131	−	0.0289172i
$886$	1056.53	−	609.986i	1.19247	−	0.688472i
$887$	527.257	+	304.412i	0.594427	+	0.343193i	0.766846	−	0.641831i	$-0.221825\pi$
$887$	527.257	+	304.412i	0.594427	+	0.343193i	−0.172419	+	0.985024i	$0.555158\pi$
$888$	−532.997	−	668.148i	−0.600222	−	0.752419i
$889$	105.342	−	996.272i	0.118495	−	1.12067i
$890$	−181.270			−0.203674
$891$	−396.173	+	270.462i	−0.444638	+	0.303549i
$892$	−388.702	+	224.417i	−0.435765	+	0.251589i
$893$	−469.889	+	271.291i	−0.526192	+	0.303797i
$894$	−18.1067	−	120.006i	−0.0202536	−	0.134234i
$895$		−	202.402i		−	0.226147i
$896$	18.6424	+	13.5623i	0.0208063	+	0.0151365i
$897$	−62.8278	−	78.7589i	−0.0700422	−	0.0878025i
$898$	596.383	−	1032.97i	0.664124	−	1.15030i
$899$	114.105	+	197.636i	0.126924	+	0.219839i
$900$	−336.410	+	103.882i	−0.373789	+	0.115424i
$901$	−336.490	+	582.818i	−0.373463	+	0.646856i
$902$	−152.839			−0.169445
$903$	−32.0444	+	61.6732i	−0.0354865	+	0.0682981i
$904$			713.018i			0.788736i
$905$	−28.6528	+	49.6280i	−0.0316605	+	0.0548376i
$906$	10.7821	−	27.4847i	0.0119007	−	0.0303363i
$907$	−393.512	−	681.583i	−0.433861	−	0.751470i	0.563341	−	0.826225i	$-0.309516\pi$
$907$	−393.512	−	681.583i	−0.433861	−	0.751470i	−0.997202	+	0.0747548i	$0.976183\pi$
$908$	−35.0789	+	60.7584i	−0.0386331	+	0.0669145i
$909$	1469.66	+	334.966i	1.61678	+	0.368499i
$910$	172.236	−	76.5555i	0.189270	−	0.0841269i
$911$			551.623i			0.605514i	0.953068	+	0.302757i	$0.0979070\pi$
$911$			551.623i			0.605514i	−0.953068	+	0.302757i	$0.902093\pi$
$912$	−155.894	+	23.5217i	−0.170937	+	0.0257914i
$913$	−308.819	−	534.891i	−0.338247	−	0.585861i
$914$	−300.423	+	173.449i	−0.328690	+	0.189769i
$915$	11.7206	+	77.6802i	0.0128094	+	0.0848964i
$916$			36.1580i			0.0394738i
$917$	−696.666	+	957.619i	−0.759723	+	1.04430i
$918$	367.146	−	177.016i	0.399941	−	0.192828i
$919$	13.0331	−	22.5740i	0.0141818	−	0.0245636i	−0.858847	−	0.512232i	$-0.828819\pi$
$919$	13.0331	−	22.5740i	0.0141818	−	0.0245636i	0.873029	+	0.487668i	$0.162152\pi$
$920$	26.3682	−	15.2237i	0.0286611	−	0.0165475i
$921$	−554.928	+	1414.57i	−0.602528	+	1.53591i
$922$	303.131	−	525.039i	0.328776	−	0.569457i
$923$	361.734			0.391911
$924$	113.092	+	177.216i	0.122394	+	0.191792i
$925$		−	762.413i		−	0.824230i
$926$	−58.0326	−	33.5051i	−0.0626701	−	0.0361826i
$927$	−1170.12	+	361.328i	−1.26227	+	0.389782i
$928$	456.157	−	263.362i	0.491548	−	0.283796i
$929$	−371.444	+	643.359i	−0.399832	+	0.692529i	−0.993705	−	0.112030i	$-0.964265\pi$
$929$	−371.444	+	643.359i	−0.399832	+	0.692529i	0.593873	+	0.804559i	$0.297598\pi$
$930$	41.7945	+	52.3922i	0.0449404	+	0.0563357i
$931$	299.571	+	270.414i	0.321774	+	0.290456i
$932$			632.565i			0.678718i
$933$	−896.401	+	135.251i	−0.960773	+	0.144964i
$934$	606.765	−	350.316i	0.649642	−	0.375071i
$935$	69.4330	−	40.0872i	0.0742599	−	0.0428740i
$936$	−741.916	−	687.975i	−0.792646	−	0.735016i
$937$	−621.718			−0.663519			−0.331760	−	0.943364i	$-0.607642\pi$
$937$	−621.718			−0.663519			−0.331760	+	0.943364i	$0.607642\pi$
$938$	1078.75	+	114.063i	1.15005	+	0.121603i
$939$	−651.299	+	519.557i	−0.693610	+	0.553309i
$940$	75.8881	−	131.442i	0.0807320	−	0.139832i
$941$	833.188	+	1443.12i	0.885428	+	1.53361i	0.845222	+	0.534415i	$0.179468\pi$
$941$	833.188	+	1443.12i	0.885428	+	1.53361i	0.0402064	+	0.999191i	$0.487198\pi$
$942$	−935.965	−	367.174i	−0.993593	−	0.389781i
$943$	−37.9925	−	21.9350i	−0.0402890	−	0.0232609i
$944$	−109.361			−0.115848
$945$	46.0362	−	253.442i	0.0487156	−	0.268192i
$946$	−29.7863			−0.0314865
$947$	720.823	−	1248.50i	0.761165	−	1.31838i	−0.181086	−	0.983467i	$-0.557961\pi$
$947$	720.823	−	1248.50i	0.761165	−	1.31838i	0.942251	−	0.334909i	$-0.108706\pi$
$948$	268.643	+	105.387i	0.283379	+	0.111168i
$949$	1132.51	−	653.856i	1.19337	−	0.688995i
$950$	−250.858	−	144.833i	−0.264061	−	0.152456i
$951$	1140.10	−	909.489i	1.19885	−	0.956350i
$952$	−244.234	−	549.483i	−0.256548	−	0.577188i
$953$		−	705.606i		−	0.740405i	−0.928951	−	0.370202i	$-0.879288\pi$
$953$		−	705.606i		−	0.740405i	0.928951	−	0.370202i	$-0.120712\pi$
$954$	−630.076	+	679.477i	−0.660457	+	0.712240i
$955$	−153.833	+	88.8155i	−0.161082	+	0.0930005i
$956$	−254.755	−	441.248i	−0.266480	−	0.461557i
$957$	371.697	−	56.0826i	0.388399	−	0.0586025i
$958$	440.654			0.459973
$959$	1448.21	−	643.698i	1.51012	−	0.671218i
$960$	202.505	−	161.543i	0.210943	−	0.168274i
$961$	−422.333	+	731.502i	−0.439472	+	0.761188i
$962$	563.665	−	325.432i	0.585930	−	0.338287i
$963$	318.651	+	1031.92i	0.330894	+	1.07157i
$964$	631.267	+	364.462i	0.654841	+	0.378073i
$965$		−	387.000i		−	0.401036i
$966$	−3.65997	−	82.3631i	−0.00378879	−	0.0852620i
$967$		−	1131.68i		−	1.17030i	−0.810925	−	0.585151i	$-0.801035\pi$
$967$		−	1131.68i		−	1.17030i	0.810925	−	0.585151i	$-0.198965\pi$
$968$	371.552	−	643.547i	0.383835	−	0.664821i
$969$	−228.482	−	89.6324i	−0.235792	−	0.0924999i
$970$	−49.9466	+	28.8367i	−0.0514914	+	0.0297286i
$971$	137.401	+	79.3285i	0.141505	+	0.0816978i	0.569081	−	0.822282i	$-0.307299\pi$
$971$	137.401	+	79.3285i	0.141505	+	0.0816978i	−0.427576	+	0.903979i	$0.640632\pi$
$972$	−400.402	+	91.7119i	−0.411936	+	0.0943538i
$973$	18.3145	−	173.209i	0.0188227	−	0.178016i
$974$			81.0343i			0.0831974i
$975$	−134.656	−	892.456i	−0.138109	−	0.915339i
$976$	61.2998	+	106.174i	0.0628072	+	0.108785i
$977$	−313.438	−	542.891i	−0.320817	−	0.555671i	0.659840	−	0.751406i	$-0.270624\pi$
$977$	−313.438	−	542.891i	−0.320817	−	0.555671i	−0.980657	+	0.195735i	$0.937291\pi$
$978$	−127.261	+	19.2015i	−0.130124	+	0.0196334i
$979$	518.285			0.529402
$980$	−110.393	−	23.6092i	−0.112646	−	0.0240910i
$981$	−996.350	−	227.089i	−1.01565	−	0.231488i
$982$	−795.178	−	459.096i	−0.809754	−	0.467512i
$983$	587.356	+	1017.33i	0.597513	+	1.03492i	0.993187	+	0.116532i	$0.0371779\pi$
$983$	587.356	+	1017.33i	0.597513	+	1.03492i	−0.395674	+	0.918391i	$0.629489\pi$
$984$	−410.149	−	160.899i	−0.416818	−	0.163515i
$985$	−8.07125	+	13.9798i	−0.00819416	+	0.0141927i
$986$	−319.405			−0.323940
$987$	−744.232	−	1166.22i	−0.754034	−	1.18158i
$988$			180.991i			0.183189i
$989$	−7.40421	−	4.27482i	−0.00748656	−	0.00432237i
$990$	105.481	−	32.5719i	0.106546	−	0.0329009i
$991$	−242.964	−	420.827i	−0.245171	−	0.424648i	0.717009	−	0.697064i	$-0.245511\pi$
$991$	−242.964	−	420.827i	−0.245171	−	0.424648i	−0.962180	+	0.272416i	$0.912177\pi$
$992$	−232.534	−	134.254i	−0.234410	−	0.135336i
$993$	1072.33	+	1344.24i	1.07989	+	1.35372i
$994$	239.370	+	174.142i	0.240815	+	0.175193i
$995$	−126.747			−0.127383
$996$	−78.9086	−	522.981i	−0.0792255	−	0.525081i
$997$	−568.005	−	983.813i	−0.569714	−	0.986773i	−0.996594	−	0.0824651i	$-0.973721\pi$
$997$	−568.005	−	983.813i	−0.569714	−	0.986773i	0.426880	−	0.904308i	$-0.359613\pi$
$998$	−321.330	+	185.520i	−0.321974	+	0.185892i
$999$	66.0645	−	887.039i	0.0661306	−	0.887927i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.3.w.c.233.6	yes	16
3.2	odd	2	inner	273.3.w.c.233.3	yes	16
7.4	even	3	inner	273.3.w.c.116.5	yes	16
13.12	even	2	inner	273.3.w.c.233.4	yes	16
21.11	odd	6	inner	273.3.w.c.116.4	yes	16
39.38	odd	2	inner	273.3.w.c.233.5	yes	16
91.25	even	6	inner	273.3.w.c.116.3	✓	16
273.116	odd	6	inner	273.3.w.c.116.6	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.3.w.c.116.3	✓	16	91.25	even	6	inner
273.3.w.c.116.4	yes	16	21.11	odd	6	inner
273.3.w.c.116.5	yes	16	7.4	even	3	inner
273.3.w.c.116.6	yes	16	273.116	odd	6	inner
273.3.w.c.233.3	yes	16	3.2	odd	2	inner
273.3.w.c.233.4	yes	16	13.12	even	2	inner
273.3.w.c.233.5	yes	16	39.38	odd	2	inner
273.3.w.c.233.6	yes	16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	273.w (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.759866 - 1.31613i) q^{2} +(2.79279 + 1.09560i) q^{3} +(0.845208 + 1.46394i) q^{4} +(0.681452 - 1.18031i) q^{5} +(3.56409 - 2.84316i) q^{6} +(0.736052 - 6.96119i) q^{7} +8.64790 q^{8} +(6.59934 + 6.11953i) q^{9} +O(q^{10})\)	\(q+(0.759866 - 1.31613i) q^{2} +(2.79279 + 1.09560i) q^{3} +(0.845208 + 1.46394i) q^{4} +(0.681452 - 1.18031i) q^{5} +(3.56409 - 2.84316i) q^{6} +(0.736052 - 6.96119i) q^{7} +8.64790 q^{8} +(6.59934 + 6.11953i) q^{9} +(-1.03562 - 1.79375i) q^{10} +(2.96105 + 5.12869i) q^{11} +(0.756598 + 5.01449i) q^{12} -13.0000 q^{13} +(-8.60251 - 6.25831i) q^{14} +(3.19629 - 2.54976i) q^{15} +(3.19042 - 5.52596i) q^{16} +(8.60251 - 4.96666i) q^{17} +(13.0687 - 4.03554i) q^{18} +(-7.13265 - 4.11804i) q^{19} +2.30387 q^{20} +(9.68229 - 18.6347i) q^{21} +9.00000 q^{22} +(2.23720 + 1.29165i) q^{23} +(24.1518 + 9.47460i) q^{24} +(11.5712 + 20.0420i) q^{25} +(-9.87826 + 17.1096i) q^{26} +(11.7260 + 24.3208i) q^{27} +(10.8129 - 4.80612i) q^{28} -21.1583i q^{29} +(-0.927051 - 6.14420i) q^{30} +(-9.34080 + 5.39292i) q^{31} +(12.4472 + 21.5592i) q^{32} +(2.65062 + 17.5675i) q^{33} -15.0960i q^{34} +(-7.71478 - 5.61249i) q^{35} +(-3.38083 + 14.8333i) q^{36} +(-28.5306 - 16.4721i) q^{37} +(-10.8397 + 6.25831i) q^{38} +(-36.3063 - 14.2427i) q^{39} +(5.89313 - 10.2072i) q^{40} -16.9822 q^{41} +(-17.1684 - 26.9030i) q^{42} -3.30958 q^{43} +(-5.00540 + 8.66961i) q^{44} +(11.7201 - 3.61910i) q^{45} +(3.39995 - 1.96296i) q^{46} +(32.9393 - 57.0526i) q^{47} +(14.9644 - 11.9374i) q^{48} +(-47.9165 - 10.2476i) q^{49} +35.1704 q^{50} +(29.4664 - 4.44597i) q^{51} +(-10.9877 - 19.0313i) q^{52} +(-58.6730 + 33.8749i) q^{53} +(40.9194 + 3.04758i) q^{54} +8.07125 q^{55} +(6.36531 - 60.1997i) q^{56} +(-15.4083 - 19.3153i) q^{57} +(-27.8470 - 16.0775i) q^{58} +(-8.56949 - 14.8428i) q^{59} +(6.43423 + 2.52411i) q^{60} +(-9.60687 + 16.6396i) q^{61} +16.3916i q^{62} +(47.4567 - 41.4350i) q^{63} +63.3562 q^{64} +(-8.85887 + 15.3440i) q^{65} +(25.1351 + 9.86036i) q^{66} +(-88.3081 + 50.9847i) q^{67} +(14.5418 + 8.39572i) q^{68} +(4.83291 + 6.05837i) q^{69} +(-13.2489 + 5.88888i) q^{70} -27.8257 q^{71} +(57.0705 + 52.9211i) q^{72} +(-87.1163 + 50.2966i) q^{73} +(-43.3588 + 25.0332i) q^{74} +(10.3581 + 68.6505i) q^{75} -13.9224i q^{76} +(37.8813 - 16.8375i) q^{77} +(-46.3331 + 36.9610i) q^{78} +(28.4521 - 49.2804i) q^{79} +(-4.34823 - 7.53135i) q^{80} +(6.10263 + 80.7698i) q^{81} +(-12.9042 + 22.3507i) q^{82} -104.294 q^{83} +(35.4637 - 1.57590i) q^{84} -13.5382i q^{85} +(-2.51484 + 4.35583i) q^{86} +(23.1809 - 59.0907i) q^{87} +(25.6069 + 44.3524i) q^{88} +(43.7586 - 75.7921i) q^{89} +(4.14249 - 18.1751i) q^{90} +(-9.56867 + 90.4955i) q^{91} +4.36685i q^{92} +(-31.9954 + 4.82754i) q^{93} +(-50.0589 - 86.7046i) q^{94} +(-9.72111 + 5.61249i) q^{95} +(11.1423 + 73.8475i) q^{96} -27.8448i q^{97} +(-49.8972 + 55.2773i) q^{98} +(-11.8442 + 51.9662i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 24 q^{4} - 16 q^{9}+O(q^{10}) \) 16 * q - 24 * q^4 - 16 * q^9	\( 16 q - 24 q^{4} - 16 q^{9} + 96 q^{10} - 88 q^{12} - 208 q^{13} - 24 q^{16} + 144 q^{22} - 40 q^{25} + 264 q^{30} + 96 q^{36} + 432 q^{40} - 448 q^{42} - 128 q^{43} + 352 q^{48} - 504 q^{49} + 280 q^{51} + 312 q^{52} - 96 q^{55} + 184 q^{61} - 112 q^{64} - 448 q^{69} - 528 q^{75} + 80 q^{79} + 584 q^{81} + 544 q^{82} - 448 q^{87} + 72 q^{88} - 384 q^{90} - 88 q^{94}+O(q^{100}) \) 16 * q - 24 * q^4 - 16 * q^9 + 96 * q^10 - 88 * q^12 - 208 * q^13 - 24 * q^16 + 144 * q^22 - 40 * q^25 + 264 * q^30 + 96 * q^36 + 432 * q^40 - 448 * q^42 - 128 * q^43 + 352 * q^48 - 504 * q^49 + 280 * q^51 + 312 * q^52 - 96 * q^55 + 184 * q^61 - 112 * q^64 - 448 * q^69 - 528 * q^75 + 80 * q^79 + 584 * q^81 + 544 * q^82 - 448 * q^87 + 72 * q^88 - 384 * q^90 - 88 * q^94

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