LMFDB - Embedded newform 105.3.t.a.86.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,3,Mod(11,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 4]))

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

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

chi := DirichletCharacter("105.11");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.t (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:	$2.86104277578$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.3317760000.8
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 4x^{6} + 7x^{4} + 36x^{2} + 81 $ x^8 + 4x^6 + 7x^4 + 36*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			86.2
Root			$1.40294 - 1.01575i$ of defining polynomial
Character	$\chi$	$=$	105.86
Dual form			105.3.t.a.11.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.711747 - 0.410927i) q^{2} +(-2.25829 + 1.97487i) q^{3} +(-1.66228 - 2.87915i) q^{4} +(1.93649 + 1.11803i) q^{5} +(2.41886 - 0.477612i) q^{6} +7.00000 q^{7} +6.01972i q^{8} +(1.19979 - 8.91967i) q^{9} +O(q^{10})$	\(q+(-0.711747 - 0.410927i) q^{2} +(-2.25829 + 1.97487i) q^{3} +(-1.66228 - 2.87915i) q^{4} +(1.93649 + 1.11803i) q^{5} +(2.41886 - 0.477612i) q^{6} +7.00000 q^{7} +6.01972i q^{8} +(1.19979 - 8.91967i) q^{9} +(-0.918861 - 1.59151i) q^{10} +(9.48371 - 5.47542i) q^{11} +(9.43985 + 3.21919i) q^{12} +16.8114 q^{13} +(-4.98223 - 2.87649i) q^{14} +(-6.58114 + 1.29947i) q^{15} +(-4.17544 + 7.23208i) q^{16} +(16.7167 - 9.65138i) q^{17} +(-4.51928 + 5.85552i) q^{18} +(-6.56797 + 11.3761i) q^{19} -7.43393i q^{20} +(-15.8081 + 13.8241i) q^{21} -9.00000 q^{22} +(-17.6594 - 10.1957i) q^{23} +(-11.8882 - 13.5943i) q^{24} +(2.50000 + 4.33013i) q^{25} +(-11.9655 - 6.90826i) q^{26} +(14.9057 + 22.5127i) q^{27} +(-11.6359 - 20.1540i) q^{28} -10.8175i q^{29} +(5.21809 + 1.77948i) q^{30} +(-8.06797 - 13.9741i) q^{31} +(26.7966 - 15.4710i) q^{32} +(-10.6038 + 31.0942i) q^{33} -15.8641 q^{34} +(13.5554 + 7.82624i) q^{35} +(-27.6754 + 11.3726i) q^{36} +(-22.0548 + 38.2000i) q^{37} +(9.34947 - 5.39792i) q^{38} +(-37.9651 + 33.2003i) q^{39} +(-6.73025 + 11.6571i) q^{40} -20.1246i q^{41} +(16.9320 - 3.34328i) q^{42} -9.81139 q^{43} +(-31.5291 - 18.2033i) q^{44} +(12.2959 - 15.9315i) q^{45} +(8.37936 + 14.5135i) q^{46} +(57.0178 + 32.9192i) q^{47} +(-4.85303 - 24.5781i) q^{48} +49.0000 q^{49} -4.10927i q^{50} +(-18.6910 + 54.8089i) q^{51} +(-27.9452 - 48.4025i) q^{52} +(2.59724 - 1.49952i) q^{53} +(-1.35801 - 22.1485i) q^{54} +24.4868 q^{55} +42.1380i q^{56} +(-7.63381 - 38.6614i) q^{57} +(-4.44520 + 7.69930i) q^{58} +(-74.9082 + 43.2483i) q^{59} +(14.6810 + 16.7880i) q^{60} +(55.1359 - 95.4983i) q^{61} +13.2614i q^{62} +(8.39853 - 62.4377i) q^{63} +7.97367 q^{64} +(32.5551 + 18.7957i) q^{65} +(20.3247 - 17.7738i) q^{66} +(29.6754 + 51.3994i) q^{67} +(-55.5755 - 32.0865i) q^{68} +(60.0153 - 11.8502i) q^{69} +(-6.43203 - 11.1406i) q^{70} -48.0460i q^{71} +(53.6939 + 7.22240i) q^{72} +(-47.0680 - 81.5241i) q^{73} +(31.3949 - 18.1258i) q^{74} +(-14.1972 - 4.84153i) q^{75} +43.6712 q^{76} +(66.3860 - 38.3280i) q^{77} +(40.6644 - 8.02931i) q^{78} +(-47.7434 + 82.6940i) q^{79} +(-16.1714 + 9.33658i) q^{80} +(-78.1210 - 21.4035i) q^{81} +(-8.26975 + 14.3236i) q^{82} +114.706i q^{83} +(66.0790 + 22.5343i) q^{84} +43.1623 q^{85} +(6.98322 + 4.03177i) q^{86} +(21.3631 + 24.4290i) q^{87} +(32.9605 + 57.0893i) q^{88} +(-45.2833 - 26.1443i) q^{89} +(-15.2982 + 6.28646i) q^{90} +117.680 q^{91} +67.7922i q^{92} +(45.8169 + 15.6245i) q^{93} +(-27.0548 - 46.8603i) q^{94} +(-25.4376 + 14.6864i) q^{95} +(-29.9614 + 87.8580i) q^{96} -40.1886 q^{97} +(-34.8756 - 20.1354i) q^{98} +(-37.4605 - 91.1609i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} + 12 q^{4} + 32 q^{6} + 56 q^{7} + 8 q^{9}+O(q^{10}) $ 8 * q - 4 * q^3 + 12 * q^4 + 32 * q^6 + 56 * q^7 + 8 * q^9	$ 8 q - 4 q^{3} + 12 q^{4} + 32 q^{6} + 56 q^{7} + 8 q^{9} - 20 q^{10} + 52 q^{12} + 8 q^{13} - 40 q^{15} - 84 q^{16} - 52 q^{18} + 36 q^{19} - 28 q^{21} - 72 q^{22} + 24 q^{24} + 20 q^{25} + 56 q^{27} + 84 q^{28} - 40 q^{30} + 24 q^{31} - 72 q^{33} - 304 q^{34} - 272 q^{36} - 12 q^{37} + 96 q^{39} + 60 q^{40} + 224 q^{42} + 48 q^{43} + 20 q^{45} - 148 q^{46} + 328 q^{48} + 392 q^{49} - 164 q^{51} - 388 q^{52} - 160 q^{54} + 120 q^{55} - 352 q^{57} - 200 q^{58} - 20 q^{60} + 264 q^{61} + 56 q^{63} - 88 q^{64} + 36 q^{66} + 288 q^{67} + 88 q^{69} - 140 q^{70} + 348 q^{72} - 288 q^{73} + 20 q^{75} + 1336 q^{76} - 168 q^{78} - 344 q^{79} - 28 q^{81} - 180 q^{82} + 364 q^{84} + 320 q^{85} + 140 q^{87} + 36 q^{88} + 80 q^{90} + 56 q^{91} + 164 q^{93} - 52 q^{94} - 320 q^{96} - 448 q^{97} - 72 q^{99}+O(q^{100}) $ 8 * q - 4 * q^3 + 12 * q^4 + 32 * q^6 + 56 * q^7 + 8 * q^9 - 20 * q^10 + 52 * q^12 + 8 * q^13 - 40 * q^15 - 84 * q^16 - 52 * q^18 + 36 * q^19 - 28 * q^21 - 72 * q^22 + 24 * q^24 + 20 * q^25 + 56 * q^27 + 84 * q^28 - 40 * q^30 + 24 * q^31 - 72 * q^33 - 304 * q^34 - 272 * q^36 - 12 * q^37 + 96 * q^39 + 60 * q^40 + 224 * q^42 + 48 * q^43 + 20 * q^45 - 148 * q^46 + 328 * q^48 + 392 * q^49 - 164 * q^51 - 388 * q^52 - 160 * q^54 + 120 * q^55 - 352 * q^57 - 200 * q^58 - 20 * q^60 + 264 * q^61 + 56 * q^63 - 88 * q^64 + 36 * q^66 + 288 * q^67 + 88 * q^69 - 140 * q^70 + 348 * q^72 - 288 * q^73 + 20 * q^75 + 1336 * q^76 - 168 * q^78 - 344 * q^79 - 28 * q^81 - 180 * q^82 + 364 * q^84 + 320 * q^85 + 140 * q^87 + 36 * q^88 + 80 * q^90 + 56 * q^91 + 164 * q^93 - 52 * q^94 - 320 * q^96 - 448 * q^97 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−0.711747	−	0.410927i	−0.355873	−	0.205464i	0.311396	−	0.950280i	$-0.399204\pi$
$2$	−0.711747	−	0.410927i	−0.355873	−	0.205464i	−0.667269	+	0.744817i	$0.732537\pi$
$3$	−2.25829	+	1.97487i	−0.752765	+	0.658289i
$3$	−2.25829	+	1.97487i	−0.752765	+	0.658289i
$4$	−1.66228	−	2.87915i	−0.415569	−	0.719787i
$5$	1.93649	+	1.11803i	0.387298	+	0.223607i
$5$	1.93649	+	1.11803i	0.387298	+	0.223607i
$6$	2.41886	−	0.477612i	0.403144	−	0.0796019i
$7$	7.00000			1.00000
$7$	7.00000			1.00000
$8$			6.01972i			0.752465i
$9$	1.19979	−	8.91967i	0.133310	−	0.991074i
$10$	−0.918861	−	1.59151i	−0.0918861	−	0.159151i
$11$	9.48371	−	5.47542i	0.862155	−	0.497766i	−0.00257807	−	0.999997i	$-0.500821\pi$
$11$	9.48371	−	5.47542i	0.862155	−	0.497766i	0.864733	+	0.502231i	$0.167487\pi$
$12$	9.43985	+	3.21919i	0.786654	+	0.268266i
$13$	16.8114			1.29318			0.646592	−	0.762836i	$-0.276194\pi$
$13$	16.8114			1.29318			0.646592	+	0.762836i	$0.276194\pi$
$14$	−4.98223	−	2.87649i	−0.355873	−	0.205464i
$15$	−6.58114	+	1.29947i	−0.438743	+	0.0866311i
$16$	−4.17544	+	7.23208i	−0.260965	+	0.452005i
$17$	16.7167	−	9.65138i	0.983334	−	0.567728i	0.0800590	−	0.996790i	$-0.474489\pi$
$17$	16.7167	−	9.65138i	0.983334	−	0.567728i	0.903275	+	0.429062i	$0.141156\pi$
$18$	−4.51928	+	5.85552i	−0.251071	+	0.325307i
$19$	−6.56797	+	11.3761i	−0.345683	+	0.598740i	−0.985478	−	0.169806i	$-0.945686\pi$
$19$	−6.56797	+	11.3761i	−0.345683	+	0.598740i	0.639795	+	0.768546i	$0.279019\pi$
$20$		−	7.43393i		−	0.371697i
$21$	−15.8081	+	13.8241i	−0.752765	+	0.658289i
$22$	−9.00000			−0.409091
$23$	−17.6594	−	10.1957i	−0.767801	−	0.443290i	0.0642885	−	0.997931i	$-0.479522\pi$
$23$	−17.6594	−	10.1957i	−0.767801	−	0.443290i	−0.832090	+	0.554641i	$0.812856\pi$
$24$	−11.8882	−	13.5943i	−0.495340	−	0.566429i
$25$	2.50000	+	4.33013i	0.100000	+	0.173205i
$26$	−11.9655	−	6.90826i	−0.460210	−	0.265702i
$27$	14.9057	+	22.5127i	0.552063	+	0.833803i
$28$	−11.6359	−	20.1540i	−0.415569	−	0.719787i
$29$		−	10.8175i		−	0.373016i	−0.982453	−	0.186508i	$-0.940283\pi$
$29$		−	10.8175i		−	0.373016i	0.982453	−	0.186508i	$-0.0597171\pi$
$30$	5.21809	+	1.77948i	0.173936	+	0.0593159i
$31$	−8.06797	−	13.9741i	−0.260257	−	0.450779i	0.706053	−	0.708159i	$-0.250474\pi$
$31$	−8.06797	−	13.9741i	−0.260257	−	0.450779i	−0.966310	+	0.257380i	$0.917141\pi$
$32$	26.7966	−	15.4710i	0.837395	−	0.483470i
$33$	−10.6038	+	31.0942i	−0.321326	+	0.942248i
$34$	−15.8641			−0.466590
$35$	13.5554	+	7.82624i	0.387298	+	0.223607i
$36$	−27.6754	+	11.3726i	−0.768762	+	0.315905i
$37$	−22.0548	+	38.2000i	−0.596076	+	1.03243i	0.397318	+	0.917681i	$0.369941\pi$
$37$	−22.0548	+	38.2000i	−0.596076	+	1.03243i	−0.993394	+	0.114753i	$0.963392\pi$
$38$	9.34947	−	5.39792i	0.246039	−	0.142050i
$39$	−37.9651	+	33.2003i	−0.973463	+	0.851289i
$40$	−6.73025	+	11.6571i	−0.168256	+	0.291428i
$41$		−	20.1246i		−	0.490844i	−0.969416	−	0.245422i	$-0.921073\pi$
$41$		−	20.1246i		−	0.490844i	0.969416	−	0.245422i	$-0.0789266\pi$
$42$	16.9320	−	3.34328i	0.403144	−	0.0796019i
$43$	−9.81139			−0.228172			−0.114086	−	0.993471i	$-0.536394\pi$
$43$	−9.81139			−0.228172			−0.114086	+	0.993471i	$0.536394\pi$
$44$	−31.5291	−	18.2033i	−0.716571	−	0.413712i
$45$	12.2959	−	15.9315i	0.273242	−	0.354032i
$46$	8.37936	+	14.5135i	0.182160	+	0.315510i
$47$	57.0178	+	32.9192i	1.21314	+	0.700409i	0.963443	−	0.267914i	$-0.0863343\pi$
$47$	57.0178	+	32.9192i	1.21314	+	0.700409i	0.249701	+	0.968323i	$0.419668\pi$
$48$	−4.85303	−	24.5781i	−0.101105	−	0.512044i
$49$	49.0000			1.00000
$50$		−	4.10927i		−	0.0821854i
$51$	−18.6910	+	54.8089i	−0.366490	+	1.07468i
$52$	−27.9452	−	48.4025i	−0.537408	−	0.930817i
$53$	2.59724	−	1.49952i	0.0490046	−	0.0282928i	−0.475298	−	0.879825i	$-0.657660\pi$
$53$	2.59724	−	1.49952i	0.0490046	−	0.0282928i	0.524302	+	0.851532i	$0.324326\pi$
$54$	−1.35801	−	22.1485i	−0.0251484	−	0.410157i
$55$	24.4868			0.445215
$56$			42.1380i			0.752465i
$57$	−7.63381	−	38.6614i	−0.133926	−	0.678270i
$58$	−4.44520	+	7.69930i	−0.0766413	+	0.132747i
$59$	−74.9082	+	43.2483i	−1.26963	+	0.733021i	−0.974918	−	0.222565i	$-0.928557\pi$
$59$	−74.9082	+	43.2483i	−1.26963	+	0.733021i	−0.294712	+	0.955586i	$0.595224\pi$
$60$	14.6810	+	16.7880i	0.244684	+	0.279800i
$61$	55.1359	−	95.4983i	0.903868	−	1.56555i	0.0814382	−	0.996678i	$-0.474049\pi$
$61$	55.1359	−	95.4983i	0.903868	−	1.56555i	0.822430	−	0.568867i	$-0.192618\pi$
$62$			13.2614i			0.213893i
$63$	8.39853	−	62.4377i	0.133310	−	0.991074i
$64$	7.97367			0.124589
$65$	32.5551	+	18.7957i	0.500848	+	0.289165i
$66$	20.3247	−	17.7738i	0.307949	−	0.269300i
$67$	29.6754	+	51.3994i	0.442917	+	0.767155i	0.997905	−	0.0647038i	$-0.0206103\pi$
$67$	29.6754	+	51.3994i	0.442917	+	0.767155i	−0.554987	+	0.831859i	$0.687277\pi$
$68$	−55.5755	−	32.0865i	−0.817287	−	0.471861i
$69$	60.0153	−	11.8502i	0.869787	−	0.171742i
$70$	−6.43203	−	11.1406i	−0.0918861	−	0.159151i
$71$		−	48.0460i		−	0.676704i	−0.941020	−	0.338352i	$-0.890130\pi$
$71$		−	48.0460i		−	0.676704i	0.941020	−	0.338352i	$-0.109870\pi$
$72$	53.6939	+	7.22240i	0.745749	+	0.100311i
$73$	−47.0680	−	81.5241i	−0.644767	−	1.11677i	−0.984355	−	0.176195i	$-0.943621\pi$
$73$	−47.0680	−	81.5241i	−0.644767	−	1.11677i	0.339589	−	0.940574i	$-0.389712\pi$
$74$	31.3949	−	18.1258i	0.424255	−	0.244944i
$75$	−14.1972	−	4.84153i	−0.189296	−	0.0645538i
$76$	43.6712			0.574621
$77$	66.3860	−	38.3280i	0.862155	−	0.497766i
$78$	40.6644	−	8.02931i	0.521339	−	0.102940i
$79$	−47.7434	+	82.6940i	−0.604347	+	1.04676i	0.387807	+	0.921740i	$0.373233\pi$
$79$	−47.7434	+	82.6940i	−0.604347	+	1.04676i	−0.992154	+	0.125019i	$0.960101\pi$
$80$	−16.1714	+	9.33658i	−0.202143	+	0.116707i
$81$	−78.1210	−	21.4035i	−0.964457	−	0.264240i
$82$	−8.26975	+	14.3236i	−0.100851	+	0.174678i
$83$			114.706i			1.38200i	0.722853	+	0.691002i	$0.242830\pi$
$83$			114.706i			1.38200i	−0.722853	+	0.691002i	$0.757170\pi$
$84$	66.0790	+	22.5343i	0.786654	+	0.268266i
$85$	43.1623			0.507792
$86$	6.98322	+	4.03177i	0.0812003	+	0.0468810i
$87$	21.3631	+	24.4290i	0.245553	+	0.280794i
$88$	32.9605	+	57.0893i	0.374551	+	0.648742i
$89$	−45.2833	−	26.1443i	−0.508801	−	0.293757i	0.223540	−	0.974695i	$-0.428239\pi$
$89$	−45.2833	−	26.1443i	−0.508801	−	0.293757i	−0.732341	+	0.680938i	$0.761572\pi$
$90$	−15.2982	+	6.28646i	−0.169980	+	0.0698495i
$91$	117.680			1.29318
$92$			67.7922i			0.736871i
$93$	45.8169	+	15.6245i	0.492655	+	0.168006i
$94$	−27.0548	−	46.8603i	−0.287817	−	0.498514i
$95$	−25.4376	+	14.6864i	−0.267765	+	0.154594i
$96$	−29.9614	+	87.8580i	−0.312098	+	0.915188i
$97$	−40.1886			−0.414316			−0.207158	−	0.978308i	$-0.566421\pi$
$97$	−40.1886			−0.414316			−0.207158	+	0.978308i	$0.566421\pi$
$98$	−34.8756	−	20.1354i	−0.355873	−	0.205464i
$99$	−37.4605	−	91.1609i	−0.378389	−	0.920817i
$100$	8.31139	−	14.3957i	0.0831139	−	0.143957i
$101$	14.9279	−	8.61865i	0.147801	−	0.0853332i	−0.424276	−	0.905533i	$-0.639471\pi$
$101$	14.9279	−	8.61865i	0.147801	−	0.0853332i	0.572077	+	0.820200i	$0.306138\pi$
$102$	35.8257	−	31.3294i	0.351232	−	0.307151i
$103$	−72.9210	+	126.303i	−0.707971	+	1.22624i	0.257638	+	0.966242i	$0.417056\pi$
$103$	−72.9210	+	126.303i	−0.707971	+	1.22624i	−0.965609	+	0.260000i	$0.916277\pi$
$104$			101.200i			0.973075i
$105$	−46.0680	+	9.09626i	−0.438743	+	0.0866311i
$106$	−2.46477			−0.0232526
$107$	−157.992	−	91.2168i	−1.47656	−	0.852493i	−0.476912	−	0.878951i	$-0.658244\pi$
$107$	−157.992	−	91.2168i	−1.47656	−	0.852493i	−0.999650	+	0.0264580i	$0.991577\pi$
$108$	40.0399	−	80.3380i	0.370740	−	0.743871i
$109$	−68.8530	−	119.257i	−0.631679	−	1.09410i	−0.987208	−	0.159435i	$-0.949033\pi$
$109$	−68.8530	−	119.257i	−0.631679	−	1.09410i	0.355529	−	0.934665i	$-0.384301\pi$
$110$	−17.4284	−	10.0623i	−0.158440	−	0.0914755i
$111$	−25.6338	−	129.822i	−0.230935	−	1.16957i
$112$	−29.2281	+	50.6246i	−0.260965	+	0.452005i
$113$			153.200i			1.35575i	0.735176	+	0.677877i	$0.237100\pi$
$113$			153.200i			1.35575i	−0.735176	+	0.677877i	$0.762900\pi$
$114$	−10.4537	+	30.6541i	−0.0916989	+	0.268895i
$115$	−22.7982	−	39.4877i	−0.198245	−	0.343371i
$116$	−31.1451	+	17.9816i	−0.268492	+	0.155014i
$117$	20.1701	−	149.952i	0.172394	−	1.28164i
$118$	71.0875			0.602437
$119$	117.017	−	67.5597i	0.983334	−	0.567728i
$120$	−7.82242	−	39.6166i	−0.0651868	−	0.330138i
$121$	−0.539501	+	0.934443i	−0.00445869	+	0.00772267i
$122$	−78.4857	+	45.3137i	−0.643325	+	0.371424i
$123$	39.7435	+	45.4473i	0.323118	+	0.369490i
$124$	−26.8224	+	46.4578i	−0.216310	+	0.374660i
$125$			11.1803i			0.0894427i
$126$	−31.6350	+	40.9886i	−0.251071	+	0.325307i
$127$	−215.868			−1.69975			−0.849875	−	0.526984i	$-0.823323\pi$
$127$	−215.868			−1.69975			−0.849875	+	0.526984i	$0.823323\pi$
$128$	−112.862	−	65.1608i	−0.881733	−	0.509069i
$129$	22.1570	−	19.3762i	0.171760	−	0.150203i
$130$	−15.4473	−	26.7556i	−0.118826	−	0.205812i
$131$	103.590	+	59.8079i	0.790766	+	0.456549i	0.840232	−	0.542227i	$-0.182419\pi$
$131$	103.590	+	59.8079i	0.790766	+	0.456549i	−0.0494663	+	0.998776i	$0.515752\pi$
$132$	107.151	−	21.1573i	0.811752	−	0.160283i
$133$	−45.9758	+	79.6324i	−0.345683	+	0.598740i
$134$		−	48.7778i		−	0.364013i
$135$	3.69482	+	60.2607i	0.0273691	+	0.446375i
$136$	58.0986	+	100.630i	0.427195	+	0.739924i
$137$	−45.1491	+	26.0668i	−0.329555	+	0.190269i	−0.655644	−	0.755070i	$-0.727603\pi$
$137$	−45.1491	+	26.0668i	−0.329555	+	0.190269i	0.326088	+	0.945339i	$0.394269\pi$
$138$	−47.5853	−	16.2276i	−0.344821	−	0.117591i
$139$	−63.6228			−0.457718			−0.228859	−	0.973460i	$-0.573499\pi$
$139$	−63.6228			−0.457718			−0.228859	+	0.973460i	$0.573499\pi$
$140$		−	52.0375i		−	0.371697i
$141$	−193.774	+	38.2613i	−1.37428	+	0.271357i
$142$	−19.7434	+	34.1966i	−0.139038	+	0.240821i
$143$	159.434	−	92.0495i	1.11493	−	0.643702i
$144$	59.4981	+	45.9206i	0.413181	+	0.318893i
$145$	12.0943	−	20.9480i	0.0834090	−	0.144469i
$146$			77.3660i			0.529904i
$147$	−110.656	+	96.7686i	−0.752765	+	0.658289i
$148$	146.645			0.990843
$149$	187.155	+	108.054i	1.25607	+	0.725194i	0.972309	−	0.233700i	$-0.0750832\pi$
$149$	187.155	+	108.054i	1.25607	+	0.725194i	0.283765	+	0.958894i	$0.408417\pi$
$150$	8.11527	+	9.27995i	0.0541018	+	0.0618663i
$151$	−19.5658	−	33.8890i	−0.129575	−	0.224431i	0.793937	−	0.608000i	$-0.208028\pi$
$151$	−19.5658	−	33.8890i	−0.129575	−	0.224431i	−0.923512	+	0.383570i	$0.874695\pi$
$152$	−68.4807	−	39.5373i	−0.450531	−	0.260114i
$153$	−66.0306	−	160.687i	−0.431573	−	1.05024i
$154$	−63.0000			−0.409091
$155$		−	36.0811i		−	0.232781i
$156$	158.697	+	54.1190i	1.01729	+	0.346917i
$157$	23.8399	+	41.2918i	0.151846	+	0.263005i	0.931906	−	0.362699i	$-0.118145\pi$
$157$	23.8399	+	41.2918i	0.151846	+	0.263005i	−0.780060	+	0.625705i	$0.784811\pi$
$158$	67.9624	−	39.2381i	0.430142	−	0.248343i
$159$	−2.90399	+	8.51557i	−0.0182641	+	0.0535570i
$160$	69.1886			0.432429
$161$	−123.616	−	71.3697i	−0.767801	−	0.443290i
$162$	46.8071	+	47.3359i	0.288933	+	0.292197i
$163$	63.2719	−	109.590i	0.388171	−	0.672332i	−0.604032	−	0.796960i	$-0.706440\pi$
$163$	63.2719	−	109.590i	0.388171	−	0.672332i	0.992204	+	0.124628i	$0.0397736\pi$
$164$	−57.9418	+	33.4527i	−0.353303	+	0.203980i
$165$	−55.2985	+	48.3583i	−0.335142	+	0.293080i
$166$	47.1359	−	81.6418i	0.283951	−	0.491818i
$167$			54.3325i			0.325344i	0.986680	+	0.162672i	$0.0520113\pi$
$167$			54.3325i			0.325344i	−0.986680	+	0.162672i	$0.947989\pi$
$168$	−83.2171	−	95.1601i	−0.495340	−	0.566429i
$169$	113.623			0.672324
$170$	−30.7206	−	17.7366i	−0.180709	−	0.104333i
$171$	93.5905	+	72.2330i	0.547313	+	0.422415i
$172$	16.3093	+	28.2485i	0.0948212	+	0.164235i
$173$	241.363	+	139.351i	1.39516	+	0.805498i	0.993881	−	0.110457i	$-0.0352313\pi$
$173$	241.363	+	139.351i	1.39516	+	0.805498i	0.401282	+	0.915954i	$0.368565\pi$
$174$	−5.16655	−	26.1660i	−0.0296928	−	0.150379i
$175$	17.5000	+	30.3109i	0.100000	+	0.173205i
$176$			91.4493i			0.519598i
$177$	83.7551	−	245.601i	0.473193	−	1.38758i
$178$	21.4868	+	37.2163i	0.120713	+	0.209080i
$179$	102.629	−	59.2528i	0.573345	−	0.331021i	−0.185139	−	0.982712i	$-0.559274\pi$
$179$	102.629	−	59.2528i	0.573345	−	0.331021i	0.758484	+	0.651691i	$0.225940\pi$
$180$	−66.3082	−	8.91916i	−0.368379	−	0.0495509i
$181$	−28.9431			−0.159906			−0.0799532	−	0.996799i	$-0.525477\pi$
$181$	−28.9431			−0.159906			−0.0799532	+	0.996799i	$0.525477\pi$
$182$	−83.7582	−	48.3578i	−0.460210	−	0.265702i
$183$	64.0833	+	324.549i	0.350182	+	1.77349i
$184$	61.3751	−	106.305i	0.333560	−	0.577743i
$185$	−85.4179	+	49.3160i	−0.461718	+	0.266573i
$186$	−26.1895	−	29.9481i	−0.140804	−	0.161012i
$187$	105.691	−	183.062i	0.565191	−	0.978940i
$188$		−	218.884i		−	1.16427i
$189$	104.340	+	157.589i	0.552063	+	0.833803i
$190$	24.1402			0.127054
$191$	−268.488	−	155.011i	−1.40569	−	0.811578i	−0.410725	−	0.911759i	$-0.634724\pi$
$191$	−268.488	−	155.011i	−1.40569	−	0.811578i	−0.994969	+	0.100181i	$0.968058\pi$
$192$	−18.0069	+	15.7469i	−0.0937859	+	0.0820153i
$193$	−128.774	−	223.043i	−0.667223	−	1.15566i	−0.978677	−	0.205403i	$-0.934150\pi$
$193$	−128.774	−	223.043i	−0.667223	−	1.15566i	0.311455	−	0.950261i	$-0.399184\pi$
$194$	28.6041	+	16.5146i	0.147444	+	0.0851268i
$195$	−110.638	+	21.8458i	−0.567375	+	0.112030i
$196$	−81.4516	−	141.078i	−0.415569	−	0.719787i
$197$		−	83.7642i		−	0.425199i	−0.977139	−	0.212600i	$-0.931807\pi$
$197$		−	83.7642i		−	0.425199i	0.977139	−	0.212600i	$-0.0681930\pi$
$198$	−10.7981	+	80.2770i	−0.0545359	+	0.405440i
$199$	139.434	+	241.507i	0.700674	+	1.21360i	0.968230	+	0.250061i	$0.0804507\pi$
$199$	139.434	+	241.507i	0.700674	+	1.21360i	−0.267556	+	0.963542i	$0.586216\pi$
$200$	−26.0661	+	15.0493i	−0.130331	+	0.0752465i
$201$	−168.523	−	57.4698i	−0.838422	−	0.285920i
$202$	−14.1666			−0.0701314
$203$		−	75.7223i		−	0.373016i
$204$	188.873	−	37.2935i	0.925846	−	0.182811i
$205$	22.5000	−	38.9711i	0.109756	−	0.190103i
$206$	103.803	−	59.9304i	0.503896	−	0.290924i
$207$	−112.130	+	145.284i	−0.541689	+	0.701853i
$208$	−70.1950	+	121.581i	−0.337476	+	0.584526i
$209$			143.850i			0.688276i
$210$	36.5266	+	12.4563i	0.173936	+	0.0593159i
$211$	136.057			0.644820			0.322410	−	0.946600i	$-0.395507\pi$
$211$	136.057			0.644820			0.322410	+	0.946600i	$0.395507\pi$
$212$	−8.63468	−	4.98523i	−0.0407296	−	0.0235153i
$213$	94.8846	+	108.502i	0.445467	+	0.509399i
$214$	74.9669	+	129.846i	0.350313	+	0.606759i
$215$	−18.9997	−	10.9695i	−0.0883706	−	0.0510208i
$216$	−135.520	+	89.7281i	−0.627407	+	0.415408i
$217$	−56.4758	−	97.8190i	−0.260257	−	0.450779i
$218$			113.174i			0.519148i
$219$	267.293	+	91.1524i	1.22051	+	0.416221i
$220$	−40.7039	−	70.5012i	−0.185018	−	0.320460i
$221$	281.031	−	162.253i	1.27163	−	0.734177i
$222$	−35.1027	+	102.934i	−0.158120	+	0.463668i
$223$	−65.8861			−0.295453			−0.147727	−	0.989028i	$-0.547196\pi$
$223$	−65.8861			−0.295453			−0.147727	+	0.989028i	$0.547196\pi$
$224$	187.576	−	108.297i	0.837395	−	0.483470i
$225$	41.6228	−	17.1039i	0.184990	−	0.0760175i
$226$	62.9541	−	109.040i	0.278558	−	0.482476i
$227$	−24.8924	+	14.3716i	−0.109658	+	0.0633111i	−0.553826	−	0.832632i	$-0.686833\pi$
$227$	−24.8924	+	14.3716i	−0.109658	+	0.0633111i	0.444168	+	0.895944i	$0.353499\pi$
$228$	−98.6224	+	86.2448i	−0.432554	+	0.378267i
$229$	41.3135	−	71.5571i	0.180408	−	0.312477i	−0.761611	−	0.648034i	$-0.775591\pi$
$229$	41.3135	−	71.5571i	0.180408	−	0.312477i	0.942020	+	0.335558i	$0.108925\pi$
$230$			37.4736i			0.162929i
$231$	−74.2264	+	217.659i	−0.321326	+	0.942248i
$232$	65.1182			0.280682
$233$	−220.261	−	127.167i	−0.945324	−	0.545783i	−0.0536989	−	0.998557i	$-0.517101\pi$
$233$	−220.261	−	127.167i	−0.945324	−	0.545783i	−0.891625	+	0.452774i	$0.850434\pi$
$234$	−75.9754	+	98.4394i	−0.324681	+	0.420681i
$235$	73.6096	+	127.496i	0.313232	+	0.542534i
$236$	249.036	+	143.781i	1.05524	+	0.609243i
$237$	−55.4911	−	281.034i	−0.234140	−	1.18580i
$238$	−111.048			−0.466590
$239$		−	468.377i		−	1.95974i	−0.199641	−	0.979869i	$-0.563977\pi$
$239$		−	468.377i		−	1.95974i	0.199641	−	0.979869i	$-0.436023\pi$
$240$	18.0813	−	53.0212i	0.0753389	−	0.220922i
$241$	84.3904	+	146.168i	0.350168	+	0.606508i	0.986279	−	0.165089i	$-0.0527913\pi$
$241$	84.3904	+	146.168i	0.350168	+	0.606508i	−0.636111	+	0.771598i	$0.719458\pi$
$242$	0.767976	−	0.443391i	0.00317346	−	0.00183220i
$243$	218.689	−	105.943i	0.899956	−	0.435981i
$244$	−366.605			−1.50248
$245$	94.8881	+	54.7837i	0.387298	+	0.223607i
$246$	−9.61175	−	48.6786i	−0.0390721	−	0.197881i
$247$	−110.417	+	191.247i	−0.447031	+	0.774281i
$248$	84.1204	−	48.5669i	0.339195	−	0.195834i
$249$	−226.530	−	259.041i	−0.909758	−	1.04032i
$250$	4.59431	−	7.95757i	0.0183772	−	0.0318303i
$251$		−	61.6391i		−	0.245574i	−0.992433	−	0.122787i	$-0.960817\pi$
$251$		−	61.6391i		−	0.245574i	0.992433	−	0.122787i	$-0.0391832\pi$
$252$	−193.728	+	79.6082i	−0.768762	+	0.315905i
$253$	−223.302			−0.882619
$254$	153.644	+	88.7062i	0.604896	+	0.349237i
$255$	−97.4731	+	85.2398i	−0.382248	+	0.334274i
$256$	37.6053	+	65.1344i	0.146896	+	0.254431i
$257$	−14.0039	−	8.08518i	−0.0544900	−	0.0314598i	0.472507	−	0.881327i	$-0.343349\pi$
$257$	−14.0039	−	8.08518i	−0.0544900	−	0.0314598i	−0.526998	+	0.849867i	$0.676682\pi$
$258$	−23.7324	+	4.68603i	−0.0919860	+	0.0181629i
$259$	−154.384	+	267.400i	−0.596076	+	1.03243i
$260$		−	124.975i		−	0.480672i
$261$	−96.4883	−	12.9787i	−0.369687	−	0.0497268i
$262$	−49.1534	−	85.1362i	−0.187608	−	0.324947i
$263$	69.4827	−	40.1159i	0.264193	−	0.152532i	−0.362053	−	0.932158i	$-0.617924\pi$
$263$	69.4827	−	40.1159i	0.264193	−	0.152532i	0.626246	+	0.779626i	$0.284591\pi$
$264$	−187.178	−	63.8317i	−0.709009	−	0.241787i
$265$	6.70605			0.0253059
$266$	65.4463	−	37.7854i	0.246039	−	0.142050i
$267$	153.895	−	30.3870i	0.576385	−	0.113809i
$268$	98.6577	−	170.880i	0.368126	−	0.637612i
$269$	−439.597	+	253.802i	−1.63419	+	0.943500i	−0.651409	+	0.758727i	$0.725822\pi$
$269$	−439.597	+	253.802i	−1.63419	+	0.943500i	−0.982781	+	0.184773i	$0.940845\pi$
$270$	22.1330	−	44.4086i	0.0819740	−	0.164476i
$271$	44.7061	−	77.4332i	0.164967	−	0.285731i	−0.771677	−	0.636015i	$-0.780582\pi$
$271$	44.7061	−	77.4332i	0.164967	−	0.285731i	0.936644	+	0.350284i	$0.113915\pi$
$272$			161.195i			0.592629i
$273$	−265.755	+	232.402i	−0.973463	+	0.851289i
$274$	42.8463			0.156373
$275$	47.4185	+	27.3771i	0.172431	+	0.0995531i
$276$	−133.881	−	153.095i	−0.485075	−	0.554691i
$277$	4.84200	+	8.38658i	0.0174801	+	0.0302765i	0.874633	−	0.484785i	$-0.161102\pi$
$277$	4.84200	+	8.38658i	0.0174801	+	0.0302765i	−0.857153	+	0.515062i	$0.827769\pi$
$278$	45.2833	+	26.1443i	0.162890	+	0.0940444i
$279$	−134.325	+	55.1976i	−0.481450	+	0.197841i
$280$	−47.1117	+	81.5999i	−0.168256	+	0.291428i
$281$			290.277i			1.03301i	0.856283	+	0.516506i	$0.172768\pi$
$281$			290.277i			1.03301i	−0.856283	+	0.516506i	$0.827232\pi$
$282$	153.641	+	52.3947i	0.544825	+	0.185797i
$283$	231.947	+	401.745i	0.819602	+	1.41959i	0.905976	+	0.423329i	$0.139139\pi$
$283$	231.947	+	401.745i	0.819602	+	1.41959i	−0.0863740	+	0.996263i	$0.527528\pi$
$284$	−138.332	+	79.8658i	−0.487083	+	0.281218i
$285$	28.4419	−	83.4023i	0.0997962	−	0.292640i
$286$	−151.302			−0.529030
$287$		−	140.872i		−	0.490844i
$288$	−105.846	−	257.579i	−0.367522	−	0.894372i
$289$	41.7982	−	72.3966i	0.144631	−	0.250507i
$290$	−17.2162	+	9.93976i	−0.0593661	+	0.0342750i
$291$	90.7577	−	79.3672i	0.311882	−	0.272740i
$292$	−156.480	+	271.031i	−0.535891	+	0.928190i
$293$			120.503i			0.411272i	0.978629	+	0.205636i	$0.0659262\pi$
$293$			120.503i			0.411272i	−0.978629	+	0.205636i	$0.934074\pi$
$294$	118.524	−	23.4030i	0.403144	−	0.0796019i
$295$	−193.412			−0.655634
$296$	−229.953	−	132.764i	−0.776870	−	0.448526i
$297$	264.628	+	131.889i	0.891002	+	0.444070i
$298$	−88.8046	−	153.814i	−0.298002	−	0.516155i
$299$	−296.879	−	171.403i	−0.992908	−	0.573256i
$300$	9.66014	+	48.9237i	0.0322005	+	0.163079i
$301$	−68.6797			−0.228172
$302$			32.1605i			0.106492i
$303$	−16.6910	+	48.9442i	−0.0550858	+	0.161532i
$304$	−54.8484	−	95.0002i	−0.180422	−	0.312501i
$305$	213.541	−	123.288i	0.700133	−	0.404222i
$306$	−19.0335	+	141.502i	−0.0622011	+	0.462425i
$307$	−84.7936			−0.276201			−0.138100	−	0.990418i	$-0.544100\pi$
$307$	−84.7936			−0.276201			−0.138100	+	0.990418i	$0.544100\pi$
$308$	−220.704	−	127.423i	−0.716571	−	0.413712i
$309$	−84.7544	−	429.238i	−0.274286	−	1.38912i
$310$	−14.8267	+	25.6806i	−0.0478280	+	0.0828406i
$311$	−442.101	+	255.247i	−1.42155	+	0.820730i	−0.996431	−	0.0844100i	$-0.973099\pi$
$311$	−442.101	+	255.247i	−1.42155	+	0.820730i	−0.425114	+	0.905140i	$0.639766\pi$
$312$	−199.856	−	228.539i	−0.640565	−	0.732497i
$313$	57.4605	−	99.5245i	0.183580	−	0.317970i	−0.759517	−	0.650487i	$-0.774565\pi$
$313$	57.4605	−	99.5245i	0.183580	−	0.317970i	0.943097	+	0.332518i	$0.107898\pi$
$314$		−	39.1858i		−	0.124795i
$315$	86.0711	−	111.520i	0.273242	−	0.354032i
$316$	317.451			1.00459
$317$	423.015	+	244.228i	1.33443	+	0.770434i	0.985975	−	0.166891i	$-0.0533728\pi$
$317$	423.015	+	244.228i	1.33443	+	0.770434i	0.348456	+	0.937325i	$0.386706\pi$
$318$	5.56618	−	4.86760i	0.0175037	−	0.0153069i
$319$	−59.2302	−	102.590i	−0.185675	−	0.321598i
$320$	15.4409	+	8.91483i	0.0482529	+	0.0278588i
$321$	536.934	−	106.019i	1.67269	−	0.330278i
$322$	58.6555	+	101.594i	0.182160	+	0.315510i
$323$			253.560i			0.785015i
$324$	68.2351	+	260.501i	0.210602	+	0.804014i
$325$	42.0285	+	72.7954i	0.129318	+	0.223986i
$326$	−90.0671	+	52.0003i	−0.276280	+	0.159510i
$327$	391.007	+	133.342i	1.19574	+	0.407773i
$328$	121.144			0.369343
$329$	399.124	+	230.435i	1.21314	+	0.700409i
$330$	59.2302	−	11.6952i	0.179486	−	0.0354400i
$331$	106.568	−	184.581i	0.321958	−	0.557647i	−0.658934	−	0.752201i	$-0.728992\pi$
$331$	106.568	−	184.581i	0.321958	−	0.557647i	0.980892	+	0.194554i	$0.0623258\pi$
$332$	330.257	−	190.674i	0.994749	−	0.574318i
$333$	314.271	+	242.554i	0.943756	+	0.728389i
$334$	22.3267	−	38.6710i	0.0668464	−	0.115781i
$335$			132.713i			0.396157i
$336$	−33.9712	−	172.047i	−0.101105	−	0.512044i
$337$	137.925			0.409274			0.204637	−	0.978838i	$-0.434399\pi$
$337$	137.925			0.409274			0.204637	+	0.978838i	$0.434399\pi$
$338$	−80.8706	−	46.6907i	−0.239262	−	0.138138i
$339$	−302.550	−	345.971i	−0.892478	−	1.02056i
$340$	−71.7477	−	124.271i	−0.211023	−	0.365502i
$341$	−153.029	−	88.3511i	−0.448764	−	0.259094i
$342$	−36.9302	−	89.8705i	−0.107983	−	0.262779i
$343$	343.000			1.00000
$344$		−	59.0618i		−	0.171691i
$345$	129.468	+	44.1513i	0.375270	+	0.127975i
$346$	−114.526	−	198.365i	−0.331001	−	0.573310i
$347$	19.3327	−	11.1617i	0.0557137	−	0.0321663i	−0.471884	−	0.881660i	$-0.656426\pi$
$347$	19.3327	−	11.1617i	0.0557137	−	0.0321663i	0.527598	+	0.849494i	$0.323093\pi$
$348$	34.8235	−	102.115i	0.100068	−	0.293435i
$349$	360.302			1.03239			0.516193	−	0.856472i	$-0.327349\pi$
$349$	360.302			1.03239			0.516193	+	0.856472i	$0.327349\pi$
$350$		−	28.7649i		−	0.0821854i
$351$	250.585	+	378.469i	0.713919	+	1.07826i
$352$	169.421	−	293.446i	0.481310	−	0.833653i
$353$	64.2507	−	37.0952i	0.182013	−	0.105085i	−0.406225	−	0.913773i	$-0.633155\pi$
$353$	64.2507	−	37.0952i	0.182013	−	0.105085i	0.588238	+	0.808688i	$0.299822\pi$
$354$	−160.537	+	140.389i	−0.453493	+	0.396578i
$355$	53.7171	−	93.0407i	0.151316	−	0.262087i
$356$			173.837i			0.488305i
$357$	−130.837	+	383.662i	−0.366490	+	1.07468i
$358$	−97.3943			−0.272051
$359$	−258.985	−	149.525i	−0.721407	−	0.416505i	0.0938632	−	0.995585i	$-0.470078\pi$
$359$	−258.985	−	149.525i	−0.721407	−	0.416505i	−0.815270	+	0.579080i	$0.803412\pi$
$360$	95.9029	+	74.0177i	0.266397	+	0.205605i
$361$	94.2235	+	163.200i	0.261007	+	0.452077i
$362$	20.6001	+	11.8935i	0.0569064	+	0.0328549i
$363$	−0.627050	−	3.17569i	−0.00172741	−	0.00874846i
$364$	−195.616	−	338.817i	−0.537408	−	0.930817i
$365$		−	210.494i		−	0.576697i
$366$	87.7551	−	257.331i	0.239768	−	0.703089i
$367$	−37.8246	−	65.5141i	−0.103064	−	0.178512i	0.809881	−	0.586594i	$-0.199531\pi$
$367$	−37.8246	−	65.5141i	−0.103064	−	0.178512i	−0.912946	+	0.408081i	$0.866198\pi$
$368$	147.472	−	85.1429i	0.400739	−	0.231367i
$369$	−179.505	−	24.1453i	−0.486463	−	0.0654344i
$370$	81.0612			0.219084
$371$	18.1807	−	10.4966i	0.0490046	−	0.0282928i
$372$	−31.1751	−	157.886i	−0.0838040	−	0.424425i
$373$	40.6712	−	70.4445i	0.109038	−	0.188859i	−0.806343	−	0.591448i	$-0.798556\pi$
$373$	40.6712	−	70.4445i	0.109038	−	0.188859i	0.915381	+	0.402589i	$0.131890\pi$
$374$	−150.450	+	86.8624i	−0.402273	+	0.232252i
$375$	−22.0797	−	25.2485i	−0.0588792	−	0.0673293i
$376$	−198.164	+	343.231i	−0.527033	+	0.912848i
$377$		−	181.857i		−	0.482379i
$378$	−9.50608	−	155.039i	−0.0251484	−	0.410157i
$379$	195.302			0.515310			0.257655	−	0.966237i	$-0.417050\pi$
$379$	195.302			0.515310			0.257655	+	0.966237i	$0.417050\pi$
$380$	84.5689	+	48.8259i	0.222550	+	0.128489i
$381$	487.494	−	426.312i	1.27951	−	1.11893i
$382$	127.397	+	220.658i	0.333499	+	0.577638i
$383$	−146.198	−	84.4077i	−0.381719	−	0.220386i	0.296847	−	0.954925i	$-0.404065\pi$
$383$	−146.198	−	84.4077i	−0.381719	−	0.220386i	−0.678566	+	0.734540i	$0.737398\pi$
$384$	383.559	−	75.7349i	0.998852	−	0.197226i
$385$	171.408			0.445215
$386$			211.667i			0.548360i
$387$	−11.7716	+	87.5143i	−0.0304176	+	0.226135i
$388$	66.8046	+	115.709i	0.172177	+	0.298219i
$389$	−561.384	+	324.115i	−1.44315	+	0.833201i	−0.998058	−	0.0622862i	$-0.980161\pi$
$389$	−561.384	+	324.115i	−1.44315	+	0.833201i	−0.445088	+	0.895487i	$0.646828\pi$
$390$	87.7233	+	29.9155i	0.224932	+	0.0767064i
$391$	−393.609			−1.00667
$392$			294.966i			0.752465i
$393$	−352.050	+	69.5134i	−0.895802	+	0.176879i
$394$	−34.4210	+	59.6189i	−0.0873629	+	0.151317i
$395$	−184.909	+	106.758i	−0.468125	+	0.270272i
$396$	−200.196	+	259.389i	−0.505546	+	0.655023i
$397$	25.3552	−	43.9164i	0.0638669	−	0.110621i	−0.832324	−	0.554290i	$-0.812990\pi$
$397$	25.3552	−	43.9164i	0.0638669	−	0.110621i	0.896191	+	0.443669i	$0.146323\pi$
$398$		−	229.189i		−	0.575852i
$399$	−53.4366	−	270.630i	−0.133926	−	0.678270i
$400$	−41.7544			−0.104386
$401$	−16.4294	−	9.48555i	−0.0409712	−	0.0236547i	0.479374	−	0.877610i	$-0.340864\pi$
$401$	−16.4294	−	9.48555i	−0.0409712	−	0.0236547i	−0.520346	+	0.853956i	$0.674197\pi$
$402$	96.3297	+	110.155i	0.239626	+	0.274016i
$403$	−135.634	−	234.925i	−0.336560	−	0.582940i
$404$	−49.6288	−	28.6532i	−0.122843	−	0.0709237i
$405$	−127.351	−	128.790i	−0.314447	−	0.317999i
$406$	−31.1164	+	53.8951i	−0.0766413	+	0.132747i
$407$			483.037i			1.18682i
$408$	−329.934	−	112.514i	−0.808662	−	0.275771i
$409$	24.0527	+	41.6604i	0.0588085	+	0.101859i	0.893931	−	0.448205i	$-0.147937\pi$
$409$	24.0527	+	41.6604i	0.0588085	+	0.101859i	−0.835122	+	0.550064i	$0.814603\pi$
$410$	−32.0286	+	18.4917i	−0.0781186	+	0.0451018i
$411$	50.4813	−	148.030i	0.122826	−	0.360170i
$412$	484.860			1.17684
$413$	−524.357	+	302.738i	−1.26963	+	0.733021i
$414$	139.509	−	57.3280i	0.336978	−	0.138473i
$415$	−128.246	+	222.128i	−0.309025	+	0.535248i
$416$	450.489	−	260.090i	1.08291	−	0.625216i
$417$	143.679	−	125.647i	0.344554	−	0.301311i
$418$	59.1117	−	102.385i	0.141416	−	0.244939i
$419$			257.824i			0.615332i	0.951494	+	0.307666i	$0.0995480\pi$
$419$			257.824i			0.615332i	−0.951494	+	0.307666i	$0.900452\pi$
$420$	102.767	+	117.516i	0.244684	+	0.279800i
$421$	−640.719			−1.52190			−0.760949	−	0.648812i	$-0.775266\pi$
$421$	−640.719			−1.52190			−0.760949	+	0.648812i	$0.775266\pi$
$422$	−96.8381	−	55.9095i	−0.229474	−	0.132487i
$423$	362.038	−	469.083i	0.855882	−	1.10894i
$424$	9.02668	+	15.6347i	0.0212893	+	0.0368742i
$425$	83.5834	+	48.2569i	0.196667	+	0.113546i
$426$	−22.9473	−	116.217i	−0.0538670	−	0.272809i
$427$	385.952	−	668.488i	0.903868	−	1.56555i
$428$			606.510i			1.41708i
$429$	−178.264	+	522.737i	−0.415534	+	1.21850i
$430$	9.01530	+	15.6150i	0.0209658	+	0.0363139i
$431$	237.998	−	137.408i	0.552200	−	0.318813i	−0.197809	−	0.980241i	$-0.563383\pi$
$431$	237.998	−	137.408i	0.552200	−	0.318813i	0.750009	+	0.661428i	$0.230049\pi$
$432$	−225.051	+	13.7988i	−0.520952	+	0.0319417i
$433$	−57.2456			−0.132207			−0.0661034	−	0.997813i	$-0.521057\pi$
$433$	−57.2456			−0.132207			−0.0661034	+	0.997813i	$0.521057\pi$
$434$			92.8298i			0.213893i
$435$	14.0569	+	71.1913i	0.0323148	+	0.163658i
$436$	−228.906	+	396.476i	−0.525013	+	0.909349i
$437$	231.973	−	133.930i	0.530831	−	0.306476i
$438$	−152.788	−	174.715i	−0.348830	−	0.398893i
$439$	101.958	−	176.597i	0.232251	−	0.402271i	−0.726219	−	0.687464i	$-0.758724\pi$
$439$	101.958	−	176.597i	0.232251	−	0.402271i	0.958470	+	0.285192i	$0.0920575\pi$
$440$			147.404i			0.335009i
$441$	58.7897	−	437.064i	0.133310	−	0.991074i
$442$	−266.697			−0.603386
$443$	−230.300	−	132.964i	−0.519865	−	0.300144i	0.217015	−	0.976168i	$-0.430368\pi$
$443$	−230.300	−	132.964i	−0.519865	−	0.300144i	−0.736879	+	0.676024i	$0.763701\pi$
$444$	−331.167	+	289.604i	−0.745872	+	0.652262i
$445$	−58.4605	−	101.257i	−0.131372	−	0.227543i
$446$	46.8942	+	27.0744i	0.105144	+	0.0607049i
$447$	−636.043	+	125.589i	−1.42292	+	0.280959i
$448$	55.8157			0.124589
$449$		−	281.215i		−	0.626313i	−0.949702	−	0.313157i	$-0.898614\pi$
$449$		−	281.215i		−	0.626313i	0.949702	−	0.313157i	$-0.101386\pi$
$450$	−36.6533	−	4.93026i	−0.0814519	−	0.0109561i
$451$	−110.191	−	190.856i	−0.244325	−	0.423184i
$452$	441.086	−	254.661i	0.975854	−	0.563410i
$453$	111.112	+	37.8914i	0.245280	+	0.0836456i
$454$	23.6228			0.0520325
$455$	227.886	+	131.570i	0.500848	+	0.289165i
$456$	232.731	−	45.9534i	0.510374	−	0.100775i
$457$	−345.228	+	597.952i	−0.755422	+	1.30843i	0.189743	+	0.981834i	$0.439235\pi$
$457$	−345.228	+	597.952i	−0.755422	+	1.30843i	−0.945164	+	0.326595i	$0.894099\pi$
$458$	−58.8095	+	33.9537i	−0.128405	+	0.0741347i
$459$	466.452	+	232.477i	1.01624	+	0.506485i
$460$	−75.7939	+	131.279i	−0.164769	+	0.285389i
$461$		−	1.75543i		−	0.00380788i	−0.999998	−	0.00190394i	$-0.999394\pi$
$461$		−	1.75543i		−	0.00380788i	0.999998	−	0.00190394i	$-0.000606044\pi$
$462$	142.273	−	124.417i	0.307949	−	0.269300i
$463$	−635.491			−1.37255			−0.686275	−	0.727342i	$-0.740756\pi$
$463$	−635.491			−1.37255			−0.686275	+	0.727342i	$0.740756\pi$
$464$	78.2329	+	45.1678i	0.168605	+	0.0973443i
$465$	71.2554	+	81.4817i	0.153237	+	0.175229i
$466$	104.513	+	181.022i	0.224277	+	0.388459i
$467$	−181.111	−	104.565i	−0.387819	−	0.223907i	0.293396	−	0.955991i	$-0.405215\pi$
$467$	−181.111	−	104.565i	−0.387819	−	0.223907i	−0.681215	+	0.732084i	$0.738548\pi$
$468$	−465.263	+	191.189i	−0.994151	+	0.408524i
$469$	207.728	+	359.796i	0.442917	+	0.767155i
$470$		−	120.993i		−	0.257431i
$471$	−135.383	−	46.1686i	−0.287438	−	0.0980225i
$472$	−260.342	−	450.926i	−0.551573	−	0.955352i
$473$	−93.0484	+	53.7215i	−0.196720	+	0.113576i
$474$	−75.9891	+	222.828i	−0.160315	+	0.470102i
$475$	−65.6797			−0.138273
$476$	−389.029	−	224.606i	−0.817287	−	0.471861i
$477$	−10.2591	−	24.9657i	−0.0215075	−	0.0523389i
$478$	−192.469	+	333.366i	−0.402655	+	0.697419i
$479$	133.986	−	77.3570i	0.279721	−	0.161497i	−0.353576	−	0.935406i	$-0.615035\pi$
$479$	133.986	−	77.3570i	0.279721	−	0.161497i	0.633297	+	0.773909i	$0.281701\pi$
$480$	−156.248	+	136.638i	−0.325517	+	0.284663i
$481$	−370.772	+	642.196i	−0.770836	+	1.33513i
$482$		−	138.713i		−	0.287787i
$483$	420.107	−	82.9514i	0.869787	−	0.171742i
$484$	3.58720			0.00741157
$485$	−77.8249	−	44.9322i	−0.160464	−	0.0926438i
$486$	−199.186	−	14.4605i	−0.409849	−	0.0297541i
$487$	161.895	+	280.410i	0.332433	+	0.575790i	0.982988	−	0.183668i	$-0.0587973\pi$
$487$	161.895	+	280.410i	0.332433	+	0.575790i	−0.650556	+	0.759459i	$0.725464\pi$
$488$	574.873	+	331.903i	1.17802	+	0.680129i
$489$	73.5395	+	372.440i	0.150388	+	0.761637i
$490$	−45.0242	−	77.9842i	−0.0918861	−	0.159151i
$491$		−	473.929i		−	0.965231i	−0.875832	−	0.482616i	$-0.839687\pi$
$491$		−	473.929i		−	0.965231i	0.875832	−	0.482616i	$-0.160313\pi$
$492$	64.7849	−	189.973i	0.131677	−	0.386125i
$493$	−104.404	−	180.832i	−0.211772	−	0.366800i
$494$	157.178	−	90.7465i	0.318173	−	0.183697i
$495$	29.3791	−	218.414i	0.0593516	−	0.441241i
$496$	134.749			0.271672
$497$		−	336.322i		−	0.676704i
$498$	54.7851	+	277.459i	0.110010	+	0.557146i
$499$	279.302	−	483.766i	0.559724	−	0.969471i	−0.437795	−	0.899075i	$-0.644240\pi$
$499$	279.302	−	483.766i	0.559724	−	0.969471i	0.997519	−	0.0703962i	$-0.0224263\pi$
$500$	32.1899	−	18.5848i	0.0643797	−	0.0371697i
$501$	−107.299	−	122.699i	−0.214171	−	0.244908i
$502$	−25.3292	+	43.8714i	−0.0504565	+	0.0873933i
$503$		−	549.856i		−	1.09315i	−0.837409	−	0.546577i	$-0.815931\pi$
$503$		−	549.856i		−	1.09315i	0.837409	−	0.546577i	$-0.184069\pi$
$504$	375.857	+	50.5568i	0.745749	+	0.100311i
$505$	38.5438			0.0763243
$506$	158.935	+	91.7611i	0.314100	+	0.181346i
$507$	−256.594	+	224.390i	−0.506102	+	0.442584i
$508$	358.833	+	621.517i	0.706364	+	1.22346i
$509$	−394.701	−	227.881i	−0.775444	−	0.447703i	0.0593694	−	0.998236i	$-0.481091\pi$
$509$	−394.701	−	227.881i	−0.775444	−	0.447703i	−0.834813	+	0.550533i	$0.814424\pi$
$510$	104.404	−	20.6148i	0.204713	−	0.0404212i
$511$	−329.476	−	570.669i	−0.644767	−	1.11677i
$512$			459.474i			0.897410i
$513$	−354.006	+	21.7055i	−0.690070	+	0.0423109i
$514$	6.64484	+	11.5092i	0.0129277	+	0.0223914i
$515$	−282.422	+	163.056i	−0.548392	+	0.316614i
$516$	−92.6181	−	31.5847i	−0.179492	−	0.0612107i
$517$	720.986			1.39456
$518$	219.764	−	126.881i	0.424255	−	0.244944i
$519$	−820.269	+	161.965i	−1.58048	+	0.312071i
$520$	−113.145	+	195.973i	−0.217586	+	0.376870i
$521$	183.521	−	105.956i	0.352248	−	0.203371i	−0.313427	−	0.949612i	$-0.601477\pi$
$521$	183.521	−	105.956i	0.352248	−	0.203371i	0.665675	+	0.746242i	$0.268144\pi$
$522$	63.3419	+	48.8872i	0.121345	+	0.0936537i
$523$	306.427	−	530.748i	0.585903	−	1.01481i	−0.408859	−	0.912598i	$-0.634073\pi$
$523$	306.427	−	530.748i	0.585903	−	1.01481i	0.994762	−	0.102217i	$-0.0325935\pi$
$524$		−	397.669i		−	0.758911i
$525$	−99.3802	−	33.8907i	−0.189296	−	0.0645538i
$526$	−65.9388			−0.125359
$527$	−269.739	−	155.734i	−0.511839	−	0.295511i
$528$	−180.600	−	206.519i	−0.342046	−	0.391135i
$529$	−56.5964	−	98.0279i	−0.106988	−	0.185308i
$530$	−4.77301	−	2.75570i	−0.00900568	−	0.00519943i
$531$	295.886	+	720.045i	0.557224	+	1.35602i
$532$	305.698			0.574621
$533$		−	338.323i		−	0.634752i
$534$	−122.021	−	41.6117i	−0.228503	−	0.0779245i
$535$	−203.967	−	353.281i	−0.381247	−	0.660338i
$536$	−309.410	+	178.638i	−0.577257	+	0.333280i
$537$	−114.750	+	336.489i	−0.213687	+	0.626608i
$538$	417.176			0.775420
$539$	464.702	−	268.296i	0.862155	−	0.497766i
$540$	167.358	−	110.808i	0.309922	−	0.205200i
$541$	−147.985	+	256.317i	−0.273539	+	0.473784i	−0.969766	−	0.244039i	$-0.921528\pi$
$541$	−147.985	+	256.317i	−0.273539	+	0.473784i	0.696226	+	0.717822i	$0.254861\pi$
$542$	−63.6388	+	36.7419i	−0.117415	+	0.0677894i
$543$	65.3620	−	57.1587i	0.120372	−	0.105265i
$544$	298.634	−	517.249i	0.548959	−	0.950825i
$545$		−	307.920i		−	0.564991i
$546$	284.651	−	56.2052i	0.521339	−	0.102940i
$547$	517.246			0.945604			0.472802	−	0.881169i	$-0.343243\pi$
$547$	517.246			0.945604			0.472802	+	0.881169i	$0.343243\pi$
$548$	150.101	+	86.6606i	0.273906	+	0.158140i
$549$	−785.661	−	606.372i	−1.43108	−	1.10450i
$550$	−22.5000	−	38.9711i	−0.0409091	−	0.0708566i
$551$	123.060	+	71.0489i	0.223340	+	0.128945i
$552$	71.3349	+	361.275i	0.129230	+	0.654484i
$553$	−334.204	+	578.858i	−0.604347	+	1.04676i
$554$		−	7.95883i		−	0.0143661i
$555$	95.5061	−	280.059i	0.172083	−	0.504611i
$556$	105.759	+	183.179i	0.190214	+	0.329459i
$557$	−521.373	+	301.015i	−0.936038	+	0.540422i	−0.888716	−	0.458458i	$-0.848402\pi$
$557$	−521.373	+	301.015i	−0.936038	+	0.540422i	−0.0473217	+	0.998880i	$0.515069\pi$
$558$	118.287	+	15.9109i	0.211984	+	0.0285141i
$559$	−164.943			−0.295068
$560$	−113.200	+	65.3560i	−0.202143	+	0.116707i
$561$	122.842	+	622.133i	0.218970	+	1.10897i
$562$	119.283	−	206.603i	0.212247	−	0.367622i
$563$	314.754	−	181.723i	0.559066	−	0.322777i	−0.193704	−	0.981060i	$-0.562050\pi$
$563$	314.754	−	181.723i	0.559066	−	0.322777i	0.752771	+	0.658283i	$0.228717\pi$
$564$	432.266	+	494.304i	0.766429	+	0.876425i
$565$	−171.283	+	296.671i	−0.303156	+	0.525081i
$566$		−	381.254i		−	0.673593i
$567$	−546.847	−	149.824i	−0.964457	−	0.264240i
$568$	289.223			0.509196
$569$	922.402	+	532.549i	1.62109	+	0.935938i	0.986628	+	0.162986i	$0.0521124\pi$
$569$	922.402	+	532.549i	1.62109	+	0.935938i	0.634464	+	0.772952i	$0.281221\pi$
$570$	−54.5157	+	47.6738i	−0.0956416	+	0.0836382i
$571$	−49.9125	−	86.4509i	−0.0874123	−	0.151403i	0.819004	−	0.573787i	$-0.194526\pi$
$571$	−49.9125	−	86.4509i	−0.0874123	−	0.151403i	−0.906417	+	0.422385i	$0.861193\pi$
$572$	−530.048	−	306.023i	−0.926658	−	0.535006i
$573$	912.451	−	180.166i	1.59241	−	0.314426i
$574$	−57.8883	+	100.265i	−0.100851	+	0.174678i
$575$		−	101.957i		−	0.177316i
$576$	9.56672	−	71.1225i	0.0166089	−	0.123477i
$577$	−464.160	−	803.948i	−0.804436	−	1.39332i	−0.916671	−	0.399643i	$-0.869134\pi$
$577$	−464.160	−	803.948i	−0.804436	−	1.39332i	0.112235	−	0.993682i	$-0.464199\pi$
$578$	−59.4995	+	34.3521i	−0.102940	+	0.0594326i
$579$	731.291	+	249.385i	1.26302	+	0.430717i
$580$	−80.4164			−0.138649
$581$			802.944i			1.38200i
$582$	−97.2107	+	19.1945i	−0.167029	+	0.0329803i
$583$	16.4210	−	28.4420i	0.0281664	−	0.0487856i
$584$	490.752	−	283.336i	0.840329	−	0.485164i
$585$	206.711	−	267.830i	0.353352	−	0.457829i
$586$	49.5178	−	85.7673i	0.0845013	−	0.146361i
$587$			524.505i			0.893535i	0.894650	+	0.446768i	$0.147425\pi$
$587$			524.505i			0.893535i	−0.894650	+	0.446768i	$0.852575\pi$
$588$	462.553	+	157.740i	0.786654	+	0.268266i
$589$	211.961			0.359866
$590$	137.660	+	79.4783i	0.233323	+	0.134709i
$591$	165.423	+	189.164i	0.279904	+	0.320075i
$592$	−184.177	−	319.004i	−0.311110	−	0.538859i
$593$	8.04147	+	4.64275i	0.0135607	+	0.00782925i	0.506765	−	0.862084i	$-0.330841\pi$
$593$	8.04147	+	4.64275i	0.0135607	+	0.00782925i	−0.493204	+	0.869913i	$0.664175\pi$
$594$	−134.151	−	202.614i	−0.225844	−	0.341101i
$595$	302.136			0.507792
$596$		−	718.463i		−	1.20547i
$597$	−791.828	−	270.030i	−1.32635	−	0.452312i
$598$	140.869	+	243.992i	0.235566	+	0.408013i
$599$	362.110	−	209.065i	0.604525	−	0.349023i	−0.166295	−	0.986076i	$-0.553180\pi$
$599$	362.110	−	209.065i	0.604525	−	0.349023i	0.770820	+	0.637053i	$0.219847\pi$
$600$	29.1447	−	85.4629i	0.0485744	−	0.142438i
$601$	500.377			0.832574			0.416287	−	0.909233i	$-0.363331\pi$
$601$	500.377			0.832574			0.416287	+	0.909233i	$0.363331\pi$
$602$	48.8826	+	28.2224i	0.0812003	+	0.0468810i
$603$	494.070	−	203.027i	0.819353	−	0.336694i
$604$	−65.0477	+	112.666i	−0.107695	+	0.186533i
$605$	−2.08948	+	1.20636i	−0.00345368	+	0.00199399i
$606$	31.9922	−	27.9771i	0.0527925	−	0.0461668i
$607$	−196.368	+	340.120i	−0.323506	+	0.560329i	−0.981209	−	0.192948i	$-0.938195\pi$
$607$	−196.368	+	340.120i	−0.323506	+	0.560329i	0.657703	+	0.753278i	$0.271528\pi$
$608$			406.454i			0.668509i
$609$	149.542	+	171.003i	0.245553	+	0.280794i
$610$	−202.649			−0.332212
$611$	958.548	+	553.418i	1.56882	+	0.905757i
$612$	−352.880	+	457.218i	−0.576602	+	0.747089i
$613$	−104.735	−	181.406i	−0.170856	−	0.295931i	0.767864	−	0.640613i	$-0.221320\pi$
$613$	−104.735	−	181.406i	−0.170856	−	0.295931i	−0.938719	+	0.344683i	$0.887987\pi$
$614$	60.3516	+	34.8440i	0.0982925	+	0.0567492i
$615$	26.1512	+	132.443i	0.0425224	+	0.215354i
$616$	230.723	+	399.625i	0.374551	+	0.648742i
$617$		−	1002.43i		−	1.62469i	−0.583176	−	0.812346i	$-0.698190\pi$
$617$		−	1002.43i		−	1.62469i	0.583176	−	0.812346i	$-0.301810\pi$
$618$	−116.062	+	340.337i	−0.187803	+	0.550707i
$619$	272.870	+	472.626i	0.440825	+	0.763531i	0.997751	−	0.0670313i	$-0.0213527\pi$
$619$	272.870	+	472.626i	0.440825	+	0.763531i	−0.556926	+	0.830562i	$0.688019\pi$
$620$	−103.883	+	59.9768i	−0.167553	+	0.0967367i
$621$	−33.6942	−	549.534i	−0.0542579	−	0.884919i
$622$	419.552			0.674520
$623$	−316.983	−	183.010i	−0.508801	−	0.293757i
$624$	−81.5861	−	413.192i	−0.130747	−	0.662167i
$625$	−12.5000	+	21.6506i	−0.0200000	+	0.0346410i
$626$	−81.7947	+	47.2242i	−0.130662	+	0.0754380i
$627$	−284.084	−	324.855i	−0.453085	−	0.518110i
$628$	79.2569	−	137.277i	0.126205	−	0.218594i
$629$			851.437i			1.35364i
$630$	−107.088	+	44.0052i	−0.169980	+	0.0698495i
$631$	−101.662			−0.161112			−0.0805562	−	0.996750i	$-0.525670\pi$
$631$	−101.662			−0.161112			−0.0805562	+	0.996750i	$0.525670\pi$
$632$	−497.795	−	287.402i	−0.787650	−	0.454750i
$633$	−307.257	+	268.695i	−0.485398	+	0.424478i
$634$	−200.720	−	347.656i	−0.316592	−	0.548354i
$635$	−418.027	−	241.348i	−0.658311	−	0.380076i
$636$	29.3448	−	5.79423i	0.0461397	−	0.00911042i
$637$	823.758			1.29318
$638$			97.3573i			0.152598i
$639$	−428.555	−	57.6451i	−0.670664	−	0.0902115i
$640$	−145.704	−	252.367i	−0.227662	−	0.394323i
$641$	−296.558	+	171.218i	−0.462649	+	0.267110i	−0.713157	−	0.701004i	$-0.752735\pi$
$641$	−296.558	+	171.218i	−0.462649	+	0.267110i	0.250509	+	0.968114i	$0.419402\pi$
$642$	−425.727	−	145.182i	−0.663126	−	0.226140i
$643$	−362.904			−0.564392			−0.282196	−	0.959357i	$-0.591063\pi$
$643$	−362.904			−0.564392			−0.282196	+	0.959357i	$0.591063\pi$
$644$			474.545i			0.736871i
$645$	64.5701	−	12.7496i	0.100109	−	0.0197668i
$646$	104.195	−	180.470i	0.161292	−	0.279366i
$647$	−399.162	+	230.456i	−0.616942	+	0.356192i	−0.775678	−	0.631129i	$-0.782592\pi$
$647$	−399.162	+	230.456i	−0.616942	+	0.356192i	0.158735	+	0.987321i	$0.449258\pi$
$648$	128.843	−	470.266i	0.198831	−	0.725720i
$649$	−473.605	+	820.308i	−0.729746	+	1.26396i
$650$		−	69.0826i		−	0.106281i
$651$	320.719	+	109.372i	0.492655	+	0.168006i
$652$	−420.702			−0.645248
$653$	636.951	+	367.744i	0.975422	+	0.563160i	0.900885	−	0.434058i	$-0.142919\pi$
$653$	636.951	+	367.744i	0.975422	+	0.563160i	0.0745371	+	0.997218i	$0.476252\pi$
$654$	−223.504	−	255.581i	−0.341750	−	0.390797i
$655$	133.735	+	231.635i	0.204175	+	0.353641i
$656$	145.543	+	84.0292i	0.221864	+	0.128093i
$657$	−783.640	+	322.019i	−1.19275	+	0.490135i
$658$	−189.384	−	328.022i	−0.287817	−	0.498514i
$659$		−	959.450i		−	1.45592i	−0.685621	−	0.727959i	$-0.740469\pi$
$659$		−	959.450i		−	1.45592i	0.685621	−	0.727959i	$-0.259531\pi$
$660$	231.152	+	78.8277i	0.350230	+	0.119436i
$661$	−124.816	−	216.187i	−0.188829	−	0.327061i	0.756031	−	0.654535i	$-0.227136\pi$
$661$	−124.816	−	216.187i	−0.188829	−	0.327061i	−0.944860	+	0.327475i	$0.893802\pi$
$662$	−151.699	+	87.5834i	−0.229152	+	0.132301i
$663$	−314.221	+	921.414i	−0.473939	+	1.38976i
$664$	−690.500			−1.03991
$665$	−178.064	+	102.805i	−0.267765	+	0.154594i
$666$	−124.009	−	301.779i	−0.186200	−	0.453122i
$667$	−110.291	+	191.030i	−0.165355	+	0.286402i
$668$	156.431	−	90.3157i	0.234179	−	0.135203i
$669$	148.790	−	130.116i	0.222407	−	0.194494i
$670$	54.5352	−	94.4578i	0.0813959	−	0.140982i
$671$		−	1207.57i		−	1.79966i
$672$	−209.730	+	615.006i	−0.312098	+	0.915188i
$673$	527.512			0.783822			0.391911	−	0.920003i	$-0.371814\pi$
$673$	527.512			0.783822			0.391911	+	0.920003i	$0.371814\pi$
$674$	−98.1679	−	56.6772i	−0.145650	−	0.0840909i
$675$	−60.2185	+	120.825i	−0.0892126	+	0.179000i
$676$	−188.873	−	327.137i	−0.279397	−	0.483930i
$677$	433.266	+	250.146i	0.639980	+	0.369493i	0.784607	−	0.619994i	$-0.212865\pi$
$677$	433.266	+	250.146i	0.639980	+	0.369493i	−0.144627	+	0.989486i	$0.546198\pi$
$678$	73.1701	+	370.570i	0.107921	+	0.546563i
$679$	−281.320			−0.414316
$680$			259.825i			0.382095i
$681$	27.8323	−	81.6146i	0.0408697	−	0.119845i
$682$	72.6117	+	125.767i	0.106469	+	0.184409i
$683$	−12.3930	+	7.15511i	−0.0181450	+	0.0104760i	−0.509045	−	0.860740i	$-0.670001\pi$
$683$	−12.3930	+	7.15511i	−0.0181450	+	0.0104760i	0.490900	+	0.871216i	$0.336668\pi$
$684$	52.3962	−	389.532i	0.0766027	−	0.569492i
$685$	−116.574			−0.170182
$686$	−244.129	−	140.948i	−0.355873	−	0.205464i
$687$	48.0178	+	243.186i	0.0698949	+	0.353982i
$688$	40.9669	−	70.9568i	0.0595449	−	0.103135i
$689$	43.6633	−	25.2090i	0.0633719	−	0.0365878i
$690$	−74.0055	−	84.6265i	−0.107254	−	0.122647i
$691$	268.562	−	465.162i	0.388656	−	0.673173i	−0.603613	−	0.797278i	$-0.706273\pi$
$691$	268.562	−	465.162i	0.388656	−	0.673173i	0.992269	+	0.124105i	$0.0396060\pi$
$692$		−	926.561i		−	1.33896i
$693$	−262.223	−	638.126i	−0.378389	−	0.920817i
$694$	−18.3466			−0.0264360
$695$	−123.205	−	71.1324i	−0.177273	−	0.102349i
$696$	−147.056	+	128.600i	−0.211287	+	0.184770i
$697$	−194.230	−	336.417i	−0.278666	−	0.482664i
$698$	−256.444	−	148.058i	−0.367398	−	0.212118i
$699$	748.552	−	147.804i	1.07089	−	0.211451i
$700$	58.1797	−	100.770i	0.0831139	−	0.143957i
$701$			618.842i			0.882799i	0.897311	+	0.441399i	$0.145518\pi$
$701$			618.842i			0.882799i	−0.897311	+	0.441399i	$0.854482\pi$
$702$	−22.8301	−	372.347i	−0.0325215	−	0.530408i
$703$	−289.711	−	501.794i	−0.412106	−	0.713789i
$704$	75.6199	−	43.6592i	0.107415	−	0.0620159i
$705$	−418.019	−	142.553i	−0.592935	−	0.202203i
$706$	−60.9737			−0.0863650
$707$	104.496	−	60.3305i	0.147801	−	0.0853332i
$708$	−846.347	+	167.114i	−1.19540	+	0.236036i
$709$	242.721	−	420.406i	0.342343	−	0.592956i	−0.642524	−	0.766265i	$-0.722113\pi$
$709$	242.721	−	420.406i	0.342343	−	0.592956i	0.984867	+	0.173310i	$0.0554461\pi$
$710$	−76.4659	+	44.1476i	−0.107698	+	0.0621797i
$711$	680.321	+	525.071i	0.956851	+	0.738496i
$712$	157.381	−	272.593i	0.221041	−	0.382855i
$713$			329.034i			0.461478i
$714$	250.780	−	219.306i	0.351232	−	0.307151i
$715$	411.658			0.575745
$716$	−341.195	−	196.989i	−0.476530	−	0.275125i
$717$	924.984	+	1057.73i	1.29008	+	1.47522i
$718$	122.888	+	212.848i	0.171153	+	0.296446i
$719$	750.521	+	433.314i	1.04384	+	0.602661i	0.920919	−	0.389755i	$-0.127440\pi$
$719$	750.521	+	433.314i	1.04384	+	0.602661i	0.122922	+	0.992416i	$0.460774\pi$
$720$	63.8769	+	155.446i	0.0887179	+	0.215897i
$721$	−510.447	+	884.120i	−0.707971	+	1.22624i
$722$		−	154.876i		−	0.214510i
$723$	−479.242	−	163.432i	−0.662852	−	0.226046i
$724$	48.1114	+	83.3314i	0.0664522	+	0.115099i
$725$	46.8410	−	27.0437i	0.0646083	−	0.0373016i
$726$	−0.858677	+	2.51796i	−0.00118275	+	0.00346827i
$727$	−823.719			−1.13304			−0.566519	−	0.824049i	$-0.691710\pi$
$727$	−823.719			−1.13304			−0.566519	+	0.824049i	$0.691710\pi$
$728$			708.399i			0.973075i
$729$	−284.641	+	671.134i	−0.390453	+	0.920623i
$730$	−86.4979	+	149.819i	−0.118490	+	0.205231i
$731$	−164.014	+	94.6934i	−0.224369	+	0.129540i
$732$	827.902	−	723.997i	1.13101	−	0.989066i
$733$	−385.164	+	667.124i	−0.525463	+	0.910129i	0.474097	+	0.880473i	$0.342775\pi$
$733$	−385.164	+	667.124i	−0.525463	+	0.910129i	−0.999560	+	0.0296561i	$0.990559\pi$
$734$			62.1726i			0.0847038i
$735$	−322.476	+	63.6738i	−0.438743	+	0.0866311i
$736$	−630.951			−0.857270
$737$	562.867	+	324.971i	0.763727	+	0.440938i
$738$	117.840	+	90.9488i	0.159675	+	0.123237i
$739$	473.730	+	820.525i	0.641042	+	1.11032i	0.985200	+	0.171406i	$0.0548310\pi$
$739$	473.730	+	820.525i	0.641042	+	1.11032i	−0.344158	+	0.938912i	$0.611836\pi$
$740$	283.977	+	163.954i	0.383752	+	0.221559i
$741$	−128.335	−	649.951i	−0.173191	−	0.877127i
$742$	−17.2534			−0.0232526
$743$		−	453.804i		−	0.610773i	−0.952229	−	0.305386i	$-0.901214\pi$
$743$		−	453.804i		−	0.610773i	0.952229	−	0.305386i	$-0.0987856\pi$
$744$	−94.0553	+	275.805i	−0.126418	+	0.370706i
$745$	241.616	+	418.491i	0.324317	+	0.561733i
$746$	−57.8952	+	33.4258i	−0.0776074	+	0.0448067i
$747$	1023.14	+	137.623i	1.36967	+	0.184235i
$748$	−702.749			−0.939505
$749$	−1105.94	−	638.517i	−1.47656	−	0.852493i
$750$	5.33986	+	27.0437i	0.00711981	+	0.0360583i
$751$	−284.698	+	493.111i	−0.379091	+	0.656605i	−0.990930	−	0.134377i	$-0.957097\pi$
$751$	−284.698	+	493.111i	−0.379091	+	0.656605i	0.611839	+	0.790982i	$0.290430\pi$
$752$	−476.149	+	274.905i	−0.633177	+	0.365565i
$753$	121.729	+	139.199i	0.161659	+	0.184860i
$754$	−74.7299	+	129.436i	−0.0991113	+	0.171666i
$755$		−	87.5011i		−	0.115895i
$756$	280.280	−	562.366i	0.370740	−	0.743871i
$757$	58.6050			0.0774174			0.0387087	−	0.999251i	$-0.487676\pi$
$757$	58.6050			0.0774174			0.0387087	+	0.999251i	$0.487676\pi$
$758$	−139.006	−	80.2551i	−0.183385	−	0.105877i
$759$	504.283	−	440.993i	0.664404	−	0.581018i
$760$	−88.4082	−	153.127i	−0.116327	−	0.201483i
$761$	211.873	+	122.325i	0.278413	+	0.160742i	0.632705	−	0.774393i	$-0.281945\pi$
$761$	211.873	+	122.325i	0.278413	+	0.160742i	−0.354292	+	0.935135i	$0.615278\pi$
$762$	−522.156	+	103.101i	−0.685243	+	0.135303i
$763$	−481.971	−	834.799i	−0.631679	−	1.09410i
$764$			1030.69i			1.34907i
$765$	51.7857	−	384.993i	0.0676937	−	0.503259i
$766$	69.3708	+	120.154i	0.0905624	+	0.156859i
$767$	−1259.31	+	727.063i	−1.64187	+	0.947931i
$768$	−213.556	−	72.8270i	−0.278067	−	0.0948268i
$769$	113.790			0.147971			0.0739857	−	0.997259i	$-0.476428\pi$
$769$	113.790			0.147971			0.0739857	+	0.997259i	$0.476428\pi$
$770$	−121.999	−	70.4361i	−0.158440	−	0.0914755i
$771$	47.5922	−	9.39722i	0.0617278	−	0.0121884i
$772$	−428.116	+	741.519i	−0.554555	+	0.960517i
$773$	−47.5310	+	27.4420i	−0.0614890	+	0.0355007i	−0.530429	−	0.847729i	$-0.677969\pi$
$773$	−47.5310	+	27.4420i	−0.0614890	+	0.0355007i	0.468940	+	0.883230i	$0.344636\pi$
$774$	44.3404	−	57.4508i	0.0572874	−	0.0742258i
$775$	40.3399	−	69.8707i	0.0520514	−	0.0901557i
$776$		−	241.924i		−	0.311758i
$777$	−179.437	−	908.756i	−0.230935	−	1.16957i
$778$	532.751			0.684770
$779$	228.939	+	132.178i	0.293888	+	0.169676i
$780$	246.809	+	282.230i	0.316421	+	0.361833i
$781$	−263.072	−	455.654i	−0.336840	−	0.583424i
$782$	280.150	+	161.745i	0.358248	+	0.206835i
$783$	243.530	−	161.242i	0.311022	−	0.205928i
$784$	−204.597	+	354.372i	−0.260965	+	0.452005i
$785$			106.615i			0.135815i
$786$	279.136	+	95.1911i	0.355134	+	0.121108i
$787$	76.6100	+	132.692i	0.0973443	+	0.168605i	0.910585	−	0.413323i	$-0.135632\pi$
$787$	76.6100	+	132.692i	0.0973443	+	0.168605i	−0.813240	+	0.581928i	$0.802299\pi$
$788$	−241.170	+	139.239i	−0.306053	+	0.176700i
$789$	−77.6889	+	227.813i	−0.0984650	+	0.288736i
$790$	175.478			0.222124
$791$			1072.40i			1.35575i
$792$	548.763	−	225.502i	0.692883	−	0.284724i
$793$	926.912	−	1605.46i	1.16887	−	2.02454i
$794$	−36.0929	+	20.8383i	−0.0454571	+	0.0262447i
$795$	−15.1442	+	13.2436i	−0.0190494	+	0.0166586i
$796$	463.557	−	802.904i	0.582358	−	1.00867i
$797$		−	137.401i		−	0.172398i	−0.996278	−	0.0861990i	$-0.972528\pi$
$797$		−	137.401i		−	0.172398i	0.996278	−	0.0861990i	$-0.0274721\pi$
$798$	−73.1757	+	214.578i	−0.0916989	+	0.268895i
$799$	1270.86			1.59057
$800$	133.983	+	77.3552i	0.167479	+	0.0966940i
$801$	−287.529	+	372.544i	−0.358963	+	0.465099i
$802$	7.79574	+	13.5026i	0.00972037	+	0.0168362i
$803$	−892.758	−	515.434i	−1.11178	−	0.641885i
$804$	114.668	+	580.733i	0.142621	+	0.722305i
$805$	−159.588	−	276.414i	−0.198245	−	0.343371i
$806$			222.942i			0.276604i
$807$	491.515	−	1441.31i	0.609065	−	1.78600i
$808$	51.8818	+	89.8620i	0.0642102	+	0.111215i
$809$	−673.166	+	388.652i	−0.832096	+	0.480411i	−0.854570	−	0.519337i	$-0.826179\pi$
$809$	−673.166	+	388.652i	−0.832096	+	0.480411i	0.0224739	+	0.999747i	$0.492846\pi$
$810$	37.7185	+	143.998i	0.0465660	+	0.177775i
$811$	−592.584			−0.730683			−0.365341	−	0.930874i	$-0.619048\pi$
$811$	−592.584			−0.730683			−0.365341	+	0.930874i	$0.619048\pi$
$812$	−218.016	+	125.872i	−0.268492	+	0.155014i
$813$	51.9608	+	263.155i	0.0639125	+	0.323684i
$814$	198.493	−	343.800i	0.243849	−	0.422359i
$815$	245.051	−	141.480i	0.300676	−	0.173595i
$816$	−318.339	−	364.026i	−0.390122	−	0.446111i
$817$	64.4409	−	111.615i	0.0788751	−	0.136616i
$818$		−	39.5356i		−	0.0483320i
$819$	141.191	−	1049.66i	0.172394	−	1.28164i
$820$	−149.605			−0.182445
$821$	−486.079	−	280.638i	−0.592057	−	0.341824i	0.173853	−	0.984772i	$-0.444378\pi$
$821$	−486.079	−	280.638i	−0.592057	−	0.341824i	−0.765911	+	0.642947i	$0.777711\pi$
$822$	−96.7595	+	84.6157i	−0.117712	+	0.102939i
$823$	477.065	+	826.302i	0.579666	+	1.00401i	0.995517	+	0.0945789i	$0.0301505\pi$
$823$	477.065	+	826.302i	0.579666	+	1.00401i	−0.415851	+	0.909433i	$0.636516\pi$
$824$	−760.308	−	438.964i	−0.922704	−	0.532723i
$825$	−161.151	+	31.8198i	−0.195335	+	0.0385695i
$826$	497.613			0.602437
$827$			803.925i			0.972097i	0.873932	+	0.486049i	$0.161562\pi$
$827$			803.925i			0.972097i	−0.873932	+	0.486049i	$0.838438\pi$
$828$	604.684	+	81.3364i	0.730294	+	0.0982323i
$829$	647.028	+	1120.69i	0.780492	+	1.35185i	0.931655	+	0.363343i	$0.118365\pi$
$829$	647.028	+	1120.69i	0.780492	+	1.35185i	−0.151163	+	0.988509i	$0.548302\pi$
$830$	182.557	−	105.399i	0.219948	−	0.126987i
$831$	−27.4971	−	9.37707i	−0.0330891	−	0.0112841i
$832$	134.048			0.161116
$833$	819.117	−	472.918i	0.983334	−	0.567728i
$834$	−153.895	+	30.3870i	−0.184526	+	0.0364352i
$835$	−60.7456	+	105.214i	−0.0727492	+	0.126005i
$836$	414.165	−	239.118i	0.495412	−	0.286026i
$837$	194.336	−	389.926i	0.232182	−	0.465861i
$838$	105.947	−	183.506i	0.126428	−	0.218980i
$839$		−	763.470i		−	0.909976i	−0.890498	−	0.454988i	$-0.849644\pi$
$839$		−	763.470i		−	0.909976i	0.890498	−	0.454988i	$-0.150356\pi$
$840$	−54.7569	−	277.316i	−0.0651868	−	0.330138i
$841$	723.982			0.860859
$842$	456.030	+	263.289i	0.541603	+	0.312695i
$843$	−573.258	−	655.530i	−0.680022	−	0.777616i
$844$	−226.164	−	391.728i	−0.267967	−	0.464133i
$845$	220.030	+	127.034i	0.260390	+	0.150336i
$846$	−450.438	+	185.097i	−0.532433	+	0.218791i
$847$	−3.77651	+	6.54110i	−0.00445869	+	0.00772267i
$848$			25.0446i			0.0295338i
$849$	−1317.20	−	449.192i	−1.55147	−	0.529084i
$850$	−39.6601	−	68.6934i	−0.0466590	−	0.0808157i
$851$	778.950	−	449.727i	0.915335	−	0.528469i
$852$	154.669	−	453.547i	0.181537	−	0.532333i
$853$	−697.530			−0.817738			−0.408869	−	0.912593i	$-0.634077\pi$
$853$	−697.530			−0.817738			−0.408869	+	0.912593i	$0.634077\pi$
$854$	−549.400	+	317.196i	−0.643325	+	0.371424i
$855$	100.478	+	244.516i	0.117518	+	0.285984i
$856$	549.099	−	951.068i	0.641471	−	1.11106i
$857$	864.347	−	499.031i	1.00857	−	0.582300i	0.0977997	−	0.995206i	$-0.468820\pi$
$857$	864.347	−	499.031i	1.00857	−	0.582300i	0.910774	+	0.412906i	$0.135486\pi$
$858$	341.686	−	298.803i	0.398235	−	0.348255i
$859$	774.157	−	1340.88i	0.901231	−	1.56098i	0.0753326	−	0.997158i	$-0.475998\pi$
$859$	774.157	−	1340.88i	0.901231	−	1.56098i	0.825898	−	0.563819i	$-0.190669\pi$
$860$			72.9372i			0.0848107i
$861$	278.204	+	318.131i	0.323118	+	0.369490i
$862$	−225.859			−0.262018
$863$	633.732	+	365.885i	0.734336	+	0.423969i	0.820006	−	0.572354i	$-0.193970\pi$
$863$	633.732	+	365.885i	0.734336	+	0.423969i	−0.0856701	+	0.996324i	$0.527303\pi$
$864$	747.717	+	372.657i	0.865413	+	0.431316i
$865$	311.599	+	539.705i	0.360230	+	0.623936i
$866$	40.7443	+	23.5238i	0.0470489	+	0.0271637i
$867$	48.5811	+	246.039i	0.0560336	+	0.283782i
$868$	−187.757	+	325.205i	−0.216310	+	0.374660i
$869$			1045.66i			1.20329i
$870$	19.2495	−	56.4466i	0.0221258	−	0.0648811i
$871$	498.885	+	864.095i	0.572773	+	0.992072i
$872$	717.893	−	414.476i	0.823272	−	0.475316i
$873$	−48.2179	+	358.469i	−0.0552324	+	0.410618i
$874$	−220.142			−0.251878
$875$			78.2624i			0.0894427i
$876$	−181.873	−	921.096i	−0.207618	−	1.05148i
$877$	−71.6249	+	124.058i	−0.0816704	+	0.141457i	−0.903968	−	0.427601i	$-0.859359\pi$
$877$	−71.6249	+	124.058i	−0.0816704	+	0.141457i	0.822297	+	0.569058i	$0.192692\pi$
$878$	−145.137	+	83.7949i	−0.165304	+	0.0954384i
$879$	−237.977	−	272.130i	−0.270736	−	0.309591i
$880$	−102.243	+	177.091i	−0.116186	+	0.201240i
$881$			1661.69i			1.88614i	0.332591	+	0.943071i	$0.392077\pi$
$881$			1661.69i			1.88614i	−0.332591	+	0.943071i	$0.607923\pi$
$882$	−221.445	+	286.920i	−0.251071	+	0.325307i
$883$	565.057			0.639929			0.319964	−	0.947430i	$-0.396329\pi$
$883$	565.057			0.639929			0.319964	+	0.947430i	$0.396329\pi$
$884$	−934.302	−	539.419i	−1.05690	−	0.610203i
$885$	436.782	−	381.963i	0.493538	−	0.431597i
$886$	109.277	+	189.273i	0.123337	+	0.213626i
$887$	−110.302	−	63.6829i	−0.124354	−	0.0717958i	0.436533	−	0.899688i	$-0.356206\pi$
$887$	−110.302	−	63.6829i	−0.124354	−	0.0717958i	−0.560887	+	0.827893i	$0.689540\pi$
$888$	781.494	−	154.308i	0.880060	−	0.173771i
$889$	−1511.08			−1.69975
$890$			96.0920i			0.107969i
$891$	−858.070	+	224.761i	−0.963041	+	0.252257i
$892$	109.521	+	189.696i	0.122781	+	0.212664i
$893$	−748.982	+	432.425i	−0.838726	+	0.484239i
$894$	504.310	+	171.980i	0.564105	+	0.192372i
$895$	264.986			0.296074
$896$	−790.032	−	456.125i	−0.881733	−	0.509069i
$897$	1008.94	−	199.218i	1.12479	−	0.222094i
$898$	−115.559	+	200.154i	−0.128685	+	0.222888i
$899$	−151.165	+	87.2751i	−0.168148	+	0.0970802i
$900$	−118.433	−	91.4067i	−0.131593	−	0.101563i
$901$	28.9448	−	50.1339i	0.0321252	−	0.0556426i
$902$			181.122i			0.200800i
$903$	155.099	−	135.633i	0.171760	−	0.150203i
$904$	−922.221			−1.02016
$905$	−56.0480	−	32.3593i	−0.0619315	−	0.0357562i
$906$	−63.5128	−	72.6280i	−0.0701025	−	0.0801633i
$907$	−16.7189	−	28.9579i	−0.0184332	−	0.0319272i	0.856662	−	0.515879i	$-0.172534\pi$
$907$	−16.7189	−	28.9579i	−0.0184332	−	0.0319272i	−0.875095	+	0.483951i	$0.839201\pi$
$908$	82.7561	+	47.7793i	0.0911411	+	0.0526204i
$909$	−58.9651	−	143.493i	−0.0648681	−	0.157858i
$910$	−108.131	−	187.289i	−0.118826	−	0.205812i
$911$		−	105.154i		−	0.115427i	−0.998333	−	0.0577135i	$-0.981619\pi$
$911$		−	105.154i		−	0.115427i	0.998333	−	0.0577135i	$-0.0183810\pi$
$912$	311.477	+	106.220i	0.341532	+	0.116469i
$913$	628.065	+	1087.84i	0.687914	+	1.19150i
$914$	491.430	−	283.727i	0.537669	−	0.310423i
$915$	−238.761	+	700.135i	−0.260941	+	0.765174i
$916$	−274.698			−0.299889
$917$	725.132	+	418.655i	0.790766	+	0.456549i
$918$	−236.465	−	357.142i	−0.257587	−	0.389044i
$919$	62.4231	−	108.120i	0.0679251	−	0.117650i	−0.830063	−	0.557670i	$-0.811695\pi$
$919$	62.4231	−	108.120i	0.0679251	−	0.117650i	0.897988	+	0.440020i	$0.145029\pi$
$920$	237.705	−	137.239i	0.258375	−	0.149173i
$921$	191.489	−	167.456i	0.207914	−	0.181820i
$922$	−0.721356	+	1.24943i	−0.000782382	+	0.00135512i
$923$		−	807.720i		−	0.875103i
$924$	750.059	−	148.101i	0.811752	−	0.160283i
$925$	−220.548			−0.238430
$926$	452.309	+	261.141i	0.488454	+	0.282009i
$927$	1039.09	+	801.968i	1.12092	+	0.865122i
$928$	−167.358	−	289.872i	−0.180342	−	0.312362i
$929$	362.569	+	209.330i	0.390279	+	0.225328i	0.682281	−	0.731090i	$-0.260988\pi$
$929$	362.569	+	209.330i	0.390279	+	0.225328i	−0.292002	+	0.956418i	$0.594321\pi$
$930$	−17.2327	−	87.2751i	−0.0185298	−	0.0938442i
$931$	−321.831	+	557.427i	−0.345683	+	0.598740i
$932$			845.551i			0.907243i
$933$	494.314	−	1449.51i	0.529812	−	1.55360i
$934$	85.9370	+	148.847i	0.0920096	+	0.159365i
$935$	409.339	−	236.332i	0.437795	−	0.252761i
$936$	902.669	+	121.419i	0.964390	+	0.129721i
$937$	991.740			1.05842			0.529210	−	0.848491i	$-0.322488\pi$
$937$	991.740			1.05842			0.529210	+	0.848491i	$0.322488\pi$
$938$		−	341.445i		−	0.364013i
$939$	66.7851	+	338.233i	0.0711236	+	0.360205i
$940$	244.719	−	423.866i	0.260340	−	0.450921i
$941$	−666.760	+	384.954i	−0.708565	+	0.409090i	−0.810530	−	0.585698i	$-0.800821\pi$
$941$	−666.760	+	384.954i	−0.708565	+	0.409090i	0.101964	+	0.994788i	$0.467487\pi$
$942$	77.3868	+	88.4931i	0.0821516	+	0.0939417i
$943$	−205.184	+	355.389i	−0.217586	+	0.376871i
$944$		−	722.323i		−	0.765173i
$945$	25.8638	+	421.825i	0.0273691	+	0.446375i
$946$	88.3025			0.0933430
$947$	1200.26	+	692.971i	1.26743	+	0.731754i	0.974502	−	0.224379i	$-0.0720355\pi$
$947$	1200.26	+	692.971i	1.26743	+	0.731754i	0.292933	+	0.956133i	$0.405369\pi$
$948$	−716.898	+	626.924i	−0.756222	+	0.661313i
$949$	−791.278	−	1370.53i	−0.833802	−	1.44419i
$950$	46.7473	+	26.9896i	0.0492077	+	0.0284101i
$951$	−1437.61	+	283.860i	−1.51168	+	0.298486i
$952$	406.690	+	704.408i	0.427195	+	0.739924i
$953$		−	665.132i		−	0.697935i	−0.937135	−	0.348968i	$-0.886532\pi$
$953$		−	665.132i		−	0.697935i	0.937135	−	0.348968i	$-0.113468\pi$
$954$	−2.95721	+	21.9850i	−0.00309980	+	0.0230450i
$955$	−346.616	−	600.357i	−0.362949	−	0.628646i
$956$	−1348.53	+	778.573i	−1.41059	+	0.814407i
$957$	336.361	+	114.706i	0.351474	+	0.119860i
$958$	−127.152			−0.132727
$959$	−316.043	+	182.468i	−0.329555	+	0.190269i
$960$	−52.4758	+	10.3615i	−0.0546623	+	0.0107932i
$961$	350.316	−	606.765i	0.364532	−	0.631389i
$962$	527.791	−	304.721i	0.548640	−	0.316757i
$963$	−1003.18	+	1299.80i	−1.04172	+	1.34974i
$964$	280.561	−	485.945i	0.291038	−	0.504092i
$965$		−	575.895i		−	0.596782i
$966$	−333.097	−	113.593i	−0.344821	−	0.117591i
$967$	−1158.19			−1.19772			−0.598858	−	0.800855i	$-0.704379\pi$
$967$	−1158.19			−1.19772			−0.598858	+	0.800855i	$0.704379\pi$
$968$	−5.62508	−	3.24764i	−0.00581104	−	0.00335500i
$969$	−500.747	−	572.613i	−0.516767	−	0.590932i
$970$	36.9278	+	63.9607i	0.0380699	+	0.0659389i
$971$	−1639.61	−	946.628i	−1.68858	−	0.974900i	−0.955610	−	0.294636i	$-0.904802\pi$
$971$	−1639.61	−	946.628i	−1.68858	−	0.974900i	−0.732967	−	0.680264i	$-0.761865\pi$
$972$	−668.549	−	453.532i	−0.687808	−	0.466596i
$973$	−445.359			−0.457718
$974$		−	266.108i		−	0.273211i
$975$	−238.674	−	81.3929i	−0.244794	−	0.0834799i
$976$	460.434	+	797.495i	0.471756	+	0.817106i
$977$	1319.18	−	761.632i	1.35024	−	0.779561i	0.361957	−	0.932195i	$-0.382109\pi$
$977$	1319.18	−	761.632i	1.35024	−	0.779561i	0.988283	+	0.152633i	$0.0487753\pi$
$978$	100.704	−	295.303i	0.102970	−	0.301945i
$979$	−572.605			−0.584888
$980$		−	364.263i		−	0.371697i
$981$	−1146.34	+	471.063i	−1.16854	+	0.480187i
$982$	−194.750	+	337.317i	−0.198320	+	0.343500i
$983$	−329.604	+	190.297i	−0.335304	+	0.193588i	−0.658194	−	0.752849i	$-0.728679\pi$
$983$	−329.604	+	190.297i	−0.335304	+	0.193588i	0.322889	+	0.946437i	$0.395346\pi$
$984$	−273.580	+	239.244i	−0.278028	+	0.243135i
$985$	93.6512	−	162.209i	0.0950774	−	0.164679i
$986$			171.609i			0.174046i
$987$	−1356.42	+	267.829i	−1.37428	+	0.271357i
$988$	734.173			0.743090
$989$	173.263	+	100.034i	0.175191	+	0.101146i
$990$	−110.663	+	143.383i	−0.111781	+	0.144831i
$991$	−643.339	−	1114.30i	−0.649182	−	1.12442i	−0.983319	−	0.181891i	$-0.941778\pi$
$991$	−643.339	−	1114.30i	−0.649182	−	1.12442i	0.334137	−	0.942525i	$-0.391555\pi$
$992$	−432.389	−	249.640i	−0.435876	−	0.251653i
$993$	123.862	+	627.296i	0.124735	+	0.631718i
$994$	−138.204	+	239.376i	−0.139038	+	0.240821i
$995$			623.569i			0.626702i
$996$	−369.261	+	1082.81i	−0.370744	+	1.08716i
$997$	−948.355	−	1642.60i	−0.951209	−	1.64754i	−0.742815	−	0.669497i	$-0.766510\pi$
$997$	−948.355	−	1642.60i	−0.951209	−	1.64754i	−0.208394	−	0.978045i	$-0.566824\pi$
$998$	−397.585	+	229.546i	−0.398382	+	0.230006i
$999$	−1188.73	+	72.8856i	−1.18992	+	0.0729586i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.t.a.86.2	yes	8
3.2	odd	2	inner	105.3.t.a.86.3	yes	8
7.4	even	3	inner	105.3.t.a.11.3	yes	8
21.11	odd	6	inner	105.3.t.a.11.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.t.a.11.2	✓	8	21.11	odd	6	inner
105.3.t.a.11.3	yes	8	7.4	even	3	inner
105.3.t.a.86.2	yes	8	1.1	even	1	trivial
105.3.t.a.86.3	yes	8	3.2	odd	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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.711747 - 0.410927i) q^{2} +(-2.25829 + 1.97487i) q^{3} +(-1.66228 - 2.87915i) q^{4} +(1.93649 + 1.11803i) q^{5} +(2.41886 - 0.477612i) q^{6} +7.00000 q^{7} +6.01972i q^{8} +(1.19979 - 8.91967i) q^{9} +O(q^{10})\)	\(q+(-0.711747 - 0.410927i) q^{2} +(-2.25829 + 1.97487i) q^{3} +(-1.66228 - 2.87915i) q^{4} +(1.93649 + 1.11803i) q^{5} +(2.41886 - 0.477612i) q^{6} +7.00000 q^{7} +6.01972i q^{8} +(1.19979 - 8.91967i) q^{9} +(-0.918861 - 1.59151i) q^{10} +(9.48371 - 5.47542i) q^{11} +(9.43985 + 3.21919i) q^{12} +16.8114 q^{13} +(-4.98223 - 2.87649i) q^{14} +(-6.58114 + 1.29947i) q^{15} +(-4.17544 + 7.23208i) q^{16} +(16.7167 - 9.65138i) q^{17} +(-4.51928 + 5.85552i) q^{18} +(-6.56797 + 11.3761i) q^{19} -7.43393i q^{20} +(-15.8081 + 13.8241i) q^{21} -9.00000 q^{22} +(-17.6594 - 10.1957i) q^{23} +(-11.8882 - 13.5943i) q^{24} +(2.50000 + 4.33013i) q^{25} +(-11.9655 - 6.90826i) q^{26} +(14.9057 + 22.5127i) q^{27} +(-11.6359 - 20.1540i) q^{28} -10.8175i q^{29} +(5.21809 + 1.77948i) q^{30} +(-8.06797 - 13.9741i) q^{31} +(26.7966 - 15.4710i) q^{32} +(-10.6038 + 31.0942i) q^{33} -15.8641 q^{34} +(13.5554 + 7.82624i) q^{35} +(-27.6754 + 11.3726i) q^{36} +(-22.0548 + 38.2000i) q^{37} +(9.34947 - 5.39792i) q^{38} +(-37.9651 + 33.2003i) q^{39} +(-6.73025 + 11.6571i) q^{40} -20.1246i q^{41} +(16.9320 - 3.34328i) q^{42} -9.81139 q^{43} +(-31.5291 - 18.2033i) q^{44} +(12.2959 - 15.9315i) q^{45} +(8.37936 + 14.5135i) q^{46} +(57.0178 + 32.9192i) q^{47} +(-4.85303 - 24.5781i) q^{48} +49.0000 q^{49} -4.10927i q^{50} +(-18.6910 + 54.8089i) q^{51} +(-27.9452 - 48.4025i) q^{52} +(2.59724 - 1.49952i) q^{53} +(-1.35801 - 22.1485i) q^{54} +24.4868 q^{55} +42.1380i q^{56} +(-7.63381 - 38.6614i) q^{57} +(-4.44520 + 7.69930i) q^{58} +(-74.9082 + 43.2483i) q^{59} +(14.6810 + 16.7880i) q^{60} +(55.1359 - 95.4983i) q^{61} +13.2614i q^{62} +(8.39853 - 62.4377i) q^{63} +7.97367 q^{64} +(32.5551 + 18.7957i) q^{65} +(20.3247 - 17.7738i) q^{66} +(29.6754 + 51.3994i) q^{67} +(-55.5755 - 32.0865i) q^{68} +(60.0153 - 11.8502i) q^{69} +(-6.43203 - 11.1406i) q^{70} -48.0460i q^{71} +(53.6939 + 7.22240i) q^{72} +(-47.0680 - 81.5241i) q^{73} +(31.3949 - 18.1258i) q^{74} +(-14.1972 - 4.84153i) q^{75} +43.6712 q^{76} +(66.3860 - 38.3280i) q^{77} +(40.6644 - 8.02931i) q^{78} +(-47.7434 + 82.6940i) q^{79} +(-16.1714 + 9.33658i) q^{80} +(-78.1210 - 21.4035i) q^{81} +(-8.26975 + 14.3236i) q^{82} +114.706i q^{83} +(66.0790 + 22.5343i) q^{84} +43.1623 q^{85} +(6.98322 + 4.03177i) q^{86} +(21.3631 + 24.4290i) q^{87} +(32.9605 + 57.0893i) q^{88} +(-45.2833 - 26.1443i) q^{89} +(-15.2982 + 6.28646i) q^{90} +117.680 q^{91} +67.7922i q^{92} +(45.8169 + 15.6245i) q^{93} +(-27.0548 - 46.8603i) q^{94} +(-25.4376 + 14.6864i) q^{95} +(-29.9614 + 87.8580i) q^{96} -40.1886 q^{97} +(-34.8756 - 20.1354i) q^{98} +(-37.4605 - 91.1609i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} + 12 q^{4} + 32 q^{6} + 56 q^{7} + 8 q^{9}+O(q^{10}) \) 8 * q - 4 * q^3 + 12 * q^4 + 32 * q^6 + 56 * q^7 + 8 * q^9	\( 8 q - 4 q^{3} + 12 q^{4} + 32 q^{6} + 56 q^{7} + 8 q^{9} - 20 q^{10} + 52 q^{12} + 8 q^{13} - 40 q^{15} - 84 q^{16} - 52 q^{18} + 36 q^{19} - 28 q^{21} - 72 q^{22} + 24 q^{24} + 20 q^{25} + 56 q^{27} + 84 q^{28} - 40 q^{30} + 24 q^{31} - 72 q^{33} - 304 q^{34} - 272 q^{36} - 12 q^{37} + 96 q^{39} + 60 q^{40} + 224 q^{42} + 48 q^{43} + 20 q^{45} - 148 q^{46} + 328 q^{48} + 392 q^{49} - 164 q^{51} - 388 q^{52} - 160 q^{54} + 120 q^{55} - 352 q^{57} - 200 q^{58} - 20 q^{60} + 264 q^{61} + 56 q^{63} - 88 q^{64} + 36 q^{66} + 288 q^{67} + 88 q^{69} - 140 q^{70} + 348 q^{72} - 288 q^{73} + 20 q^{75} + 1336 q^{76} - 168 q^{78} - 344 q^{79} - 28 q^{81} - 180 q^{82} + 364 q^{84} + 320 q^{85} + 140 q^{87} + 36 q^{88} + 80 q^{90} + 56 q^{91} + 164 q^{93} - 52 q^{94} - 320 q^{96} - 448 q^{97} - 72 q^{99}+O(q^{100}) \) 8 * q - 4 * q^3 + 12 * q^4 + 32 * q^6 + 56 * q^7 + 8 * q^9 - 20 * q^10 + 52 * q^12 + 8 * q^13 - 40 * q^15 - 84 * q^16 - 52 * q^18 + 36 * q^19 - 28 * q^21 - 72 * q^22 + 24 * q^24 + 20 * q^25 + 56 * q^27 + 84 * q^28 - 40 * q^30 + 24 * q^31 - 72 * q^33 - 304 * q^34 - 272 * q^36 - 12 * q^37 + 96 * q^39 + 60 * q^40 + 224 * q^42 + 48 * q^43 + 20 * q^45 - 148 * q^46 + 328 * q^48 + 392 * q^49 - 164 * q^51 - 388 * q^52 - 160 * q^54 + 120 * q^55 - 352 * q^57 - 200 * q^58 - 20 * q^60 + 264 * q^61 + 56 * q^63 - 88 * q^64 + 36 * q^66 + 288 * q^67 + 88 * q^69 - 140 * q^70 + 348 * q^72 - 288 * q^73 + 20 * q^75 + 1336 * q^76 - 168 * q^78 - 344 * q^79 - 28 * q^81 - 180 * q^82 + 364 * q^84 + 320 * q^85 + 140 * q^87 + 36 * q^88 + 80 * q^90 + 56 * q^91 + 164 * q^93 - 52 * q^94 - 320 * q^96 - 448 * q^97 - 72 * q^99

Introduction

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