LMFDB - Embedded newform 33.4.e.b.4.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,4,Mod(4,33)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("33.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	33.e (of order $5$, degree $4$, 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:	$1.94706303019$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.682515625.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} + 2x^{5} + 19x^{4} + 28x^{3} + 100x^{2} + 88x + 121 $ x^8 - 3x^7 + 5x^6 + 2x^5 + 19x^4 + 28x^3 + 100x^2 + 88*x + 121
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			4.2
Root			$-0.390899 - 1.20306i$ of defining polynomial
Character	$\chi$	$=$	33.4
Dual form			33.4.e.b.25.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.523388 + 0.380264i) q^{2} +(0.927051 - 2.85317i) q^{3} +(-2.34280 - 7.21040i) q^{4} +(9.01441 - 6.54935i) q^{5} +(1.57016 - 1.14079i) q^{6} +(8.07696 + 24.8583i) q^{7} +(3.11499 - 9.58696i) q^{8} +(-7.28115 - 5.29007i) q^{9} +O(q^{10})$	\(q+(0.523388 + 0.380264i) q^{2} +(0.927051 - 2.85317i) q^{3} +(-2.34280 - 7.21040i) q^{4} +(9.01441 - 6.54935i) q^{5} +(1.57016 - 1.14079i) q^{6} +(8.07696 + 24.8583i) q^{7} +(3.11499 - 9.58696i) q^{8} +(-7.28115 - 5.29007i) q^{9} +7.20851 q^{10} +(-36.0937 - 5.31471i) q^{11} -22.7444 q^{12} +(43.2976 + 31.4576i) q^{13} +(-5.22533 + 16.0819i) q^{14} +(-10.3296 - 31.7912i) q^{15} +(-43.7924 + 31.8170i) q^{16} +(-18.9494 + 13.7676i) q^{17} +(-1.79925 - 5.53752i) q^{18} +(-21.8916 + 67.3756i) q^{19} +(-68.3424 - 49.6537i) q^{20} +78.4128 q^{21} +(-16.8700 - 16.5068i) q^{22} +164.114 q^{23} +(-24.4655 - 17.7752i) q^{24} +(-0.261588 + 0.805085i) q^{25} +(10.6993 + 32.9290i) q^{26} +(-21.8435 + 15.8702i) q^{27} +(160.316 - 116.476i) q^{28} +(-67.5495 - 207.896i) q^{29} +(6.68266 - 20.5671i) q^{30} +(62.0698 + 45.0964i) q^{31} -115.662 q^{32} +(-48.6244 + 98.0544i) q^{33} -15.1532 q^{34} +(235.615 + 171.184i) q^{35} +(-21.0852 + 64.8936i) q^{36} +(-87.5569 - 269.472i) q^{37} +(-37.0783 + 26.9390i) q^{38} +(129.893 - 94.3727i) q^{39} +(-34.7085 - 106.822i) q^{40} +(1.50043 - 4.61784i) q^{41} +(41.0403 + 29.8175i) q^{42} -333.848 q^{43} +(46.2392 + 272.701i) q^{44} -100.282 q^{45} +(85.8951 + 62.4064i) q^{46} +(-121.601 + 374.250i) q^{47} +(50.1816 + 154.443i) q^{48} +(-275.206 + 199.949i) q^{49} +(-0.443057 + 0.321899i) q^{50} +(21.7141 + 66.8292i) q^{51} +(125.384 - 385.892i) q^{52} +(-123.029 - 89.3860i) q^{53} -17.4675 q^{54} +(-360.171 + 188.481i) q^{55} +263.475 q^{56} +(171.939 + 124.921i) q^{57} +(43.7007 - 134.497i) q^{58} +(-237.027 - 729.494i) q^{59} +(-205.027 + 148.961i) q^{60} +(287.741 - 209.056i) q^{61} +(15.3381 + 47.2058i) q^{62} +(72.6926 - 223.725i) q^{63} +(289.803 + 210.554i) q^{64} +596.329 q^{65} +(-62.7360 + 32.8304i) q^{66} +102.070 q^{67} +(143.665 + 104.378i) q^{68} +(152.142 - 468.244i) q^{69} +(58.2228 + 179.191i) q^{70} +(-504.157 + 366.292i) q^{71} +(-73.3964 + 53.3256i) q^{72} +(-95.7190 - 294.593i) q^{73} +(56.6443 - 174.333i) q^{74} +(2.05454 + 1.49271i) q^{75} +537.093 q^{76} +(-159.412 - 940.155i) q^{77} +103.871 q^{78} +(517.284 + 375.829i) q^{79} +(-186.381 + 573.623i) q^{80} +(25.0304 + 77.0356i) q^{81} +(2.54130 - 1.84636i) q^{82} +(-233.374 + 169.556i) q^{83} +(-183.706 - 565.387i) q^{84} +(-80.6493 + 248.213i) q^{85} +(-174.732 - 126.950i) q^{86} -655.784 q^{87} +(-163.383 + 329.473i) q^{88} +184.513 q^{89} +(-52.4863 - 38.1335i) q^{90} +(-432.269 + 1330.39i) q^{91} +(-384.486 - 1183.32i) q^{92} +(186.210 - 135.289i) q^{93} +(-205.958 + 149.637i) q^{94} +(243.926 + 750.727i) q^{95} +(-107.224 + 330.003i) q^{96} +(-515.522 - 374.549i) q^{97} -220.073 q^{98} +(234.688 + 229.635i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{2} - 6 q^{3} - 16 q^{4} + 9 q^{5} - 18 q^{6} + 3 q^{7} + 36 q^{8} - 18 q^{9}+O(q^{10}) $ 8 * q - 6 * q^2 - 6 * q^3 - 16 * q^4 + 9 * q^5 - 18 * q^6 + 3 * q^7 + 36 * q^8 - 18 * q^9	\( 8 q - 6 q^{2} - 6 q^{3} - 16 q^{4} + 9 q^{5} - 18 q^{6} + 3 q^{7} + 36 q^{8} - 18 q^{9} + 8 q^{10} - 87 q^{11} - 18 q^{12} + 171 q^{13} + 12 q^{14} - 63 q^{15} + 44 q^{16} + 36 q^{17} + 81 q^{18} + 324 q^{19} - 87 q^{20} - 66 q^{21} - 521 q^{22} - 84 q^{23} + 18 q^{24} + 263 q^{25} - 774 q^{26} - 54 q^{27} + 387 q^{28} + 393 q^{29} + 204 q^{30} + 15 q^{31} + 102 q^{32} - 216 q^{33} - 712 q^{34} + 1002 q^{35} - 144 q^{36} - 747 q^{37} - 36 q^{38} + 513 q^{39} + 41 q^{40} + 159 q^{41} + 396 q^{42} - 644 q^{43} + 219 q^{44} + 216 q^{45} + 753 q^{46} - 351 q^{47} - 423 q^{48} - 1967 q^{49} + 330 q^{50} + 63 q^{51} + 2871 q^{52} - 531 q^{53} - 162 q^{54} - 716 q^{55} + 1470 q^{56} - 453 q^{57} - 1205 q^{58} - 1002 q^{59} - 261 q^{60} + 1449 q^{61} + 99 q^{62} + 27 q^{63} - 1118 q^{64} - 954 q^{65} + 897 q^{66} - 518 q^{67} + 873 q^{68} + 693 q^{69} + 26 q^{70} + 429 q^{71} + 54 q^{72} + 2547 q^{73} + 468 q^{74} - 231 q^{75} - 2276 q^{76} - 2697 q^{77} + 1638 q^{78} + 2805 q^{79} - 1620 q^{80} - 162 q^{81} - 1631 q^{82} - 2553 q^{83} - 1509 q^{84} - 197 q^{85} - 1713 q^{86} - 3906 q^{87} + 2866 q^{88} + 1788 q^{89} - 648 q^{90} + 2885 q^{91} + 423 q^{92} + 45 q^{93} + 1159 q^{94} + 3009 q^{95} - 504 q^{96} + 9 q^{97} + 5550 q^{98} + 27 q^{99}+O(q^{100}) \) 8 * q - 6 * q^2 - 6 * q^3 - 16 * q^4 + 9 * q^5 - 18 * q^6 + 3 * q^7 + 36 * q^8 - 18 * q^9 + 8 * q^10 - 87 * q^11 - 18 * q^12 + 171 * q^13 + 12 * q^14 - 63 * q^15 + 44 * q^16 + 36 * q^17 + 81 * q^18 + 324 * q^19 - 87 * q^20 - 66 * q^21 - 521 * q^22 - 84 * q^23 + 18 * q^24 + 263 * q^25 - 774 * q^26 - 54 * q^27 + 387 * q^28 + 393 * q^29 + 204 * q^30 + 15 * q^31 + 102 * q^32 - 216 * q^33 - 712 * q^34 + 1002 * q^35 - 144 * q^36 - 747 * q^37 - 36 * q^38 + 513 * q^39 + 41 * q^40 + 159 * q^41 + 396 * q^42 - 644 * q^43 + 219 * q^44 + 216 * q^45 + 753 * q^46 - 351 * q^47 - 423 * q^48 - 1967 * q^49 + 330 * q^50 + 63 * q^51 + 2871 * q^52 - 531 * q^53 - 162 * q^54 - 716 * q^55 + 1470 * q^56 - 453 * q^57 - 1205 * q^58 - 1002 * q^59 - 261 * q^60 + 1449 * q^61 + 99 * q^62 + 27 * q^63 - 1118 * q^64 - 954 * q^65 + 897 * q^66 - 518 * q^67 + 873 * q^68 + 693 * q^69 + 26 * q^70 + 429 * q^71 + 54 * q^72 + 2547 * q^73 + 468 * q^74 - 231 * q^75 - 2276 * q^76 - 2697 * q^77 + 1638 * q^78 + 2805 * q^79 - 1620 * q^80 - 162 * q^81 - 1631 * q^82 - 2553 * q^83 - 1509 * q^84 - 197 * q^85 - 1713 * q^86 - 3906 * q^87 + 2866 * q^88 + 1788 * q^89 - 648 * q^90 + 2885 * q^91 + 423 * q^92 + 45 * q^93 + 1159 * q^94 + 3009 * q^95 - 504 * q^96 + 9 * q^97 + 5550 * q^98 + 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

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 $

$2$	0.523388	+	0.380264i	0.185046	+	0.134443i	0.676452	−	0.736487i	$-0.263517\pi$
$2$	0.523388	+	0.380264i	0.185046	+	0.134443i	−0.491406	+	0.870931i	$0.663517\pi$
$3$	0.927051	−	2.85317i	0.178411	−	0.549093i
$3$	0.927051	−	2.85317i	0.178411	−	0.549093i
$4$	−2.34280	−	7.21040i	−0.292850	−	0.901300i
$5$	9.01441	−	6.54935i	0.806273	−	0.585792i	−0.106475	−	0.994315i	$-0.533956\pi$
$5$	9.01441	−	6.54935i	0.806273	−	0.585792i	0.912748	+	0.408524i	$0.133956\pi$
$6$	1.57016	−	1.14079i	0.106836	−	0.0776210i
$7$	8.07696	+	24.8583i	0.436115	+	1.34222i	0.891940	+	0.452154i	$0.149344\pi$
$7$	8.07696	+	24.8583i	0.436115	+	1.34222i	−0.455825	+	0.890069i	$0.650656\pi$
$8$	3.11499	−	9.58696i	0.137664	−	0.423688i
$9$	−7.28115	−	5.29007i	−0.269672	−	0.195928i
$10$	7.20851			0.227953
$11$	−36.0937	−	5.31471i	−0.989332	−	0.145677i
$11$	−36.0937	−	5.31471i	−0.989332	−	0.145677i
$12$	−22.7444			−0.547145
$13$	43.2976	+	31.4576i	0.923738	+	0.671135i	0.944452	−	0.328650i	$-0.106594\pi$
$13$	43.2976	+	31.4576i	0.923738	+	0.671135i	−0.0207134	+	0.999785i	$0.506594\pi$
$14$	−5.22533	+	16.0819i	−0.0997521	+	0.307005i
$15$	−10.3296	−	31.7912i	−0.177806	−	0.547230i
$16$	−43.7924	+	31.8170i	−0.684255	+	0.497141i
$17$	−18.9494	+	13.7676i	−0.270348	+	0.196419i	−0.714697	−	0.699435i	$-0.753435\pi$
$17$	−18.9494	+	13.7676i	−0.270348	+	0.196419i	0.444349	+	0.895854i	$0.353435\pi$
$18$	−1.79925	−	5.53752i	−0.0235604	−	0.0725114i
$19$	−21.8916	+	67.3756i	−0.264331	+	0.813527i	0.727516	+	0.686091i	$0.240675\pi$
$19$	−21.8916	+	67.3756i	−0.264331	+	0.813527i	−0.991847	+	0.127436i	$0.959325\pi$
$20$	−68.3424	−	49.6537i	−0.764091	−	0.555145i
$21$	78.4128			0.814813
$22$	−16.8700	−	16.5068i	−0.163486	−	0.159966i
$23$	164.114			1.48783			0.743914	−	0.668275i	$-0.232967\pi$
$23$	164.114			1.48783			0.743914	+	0.668275i	$0.232967\pi$
$24$	−24.4655	−	17.7752i	−0.208083	−	0.151181i
$25$	−0.261588	+	0.805085i	−0.00209270	+	0.00644068i
$26$	10.6993	+	32.9290i	0.0807040	+	0.248381i
$27$	−21.8435	+	15.8702i	−0.155695	+	0.113119i
$28$	160.316	−	116.476i	1.08203	−	0.786141i
$29$	−67.5495	−	207.896i	−0.432539	−	1.33122i	−0.895588	−	0.444885i	$-0.853245\pi$
$29$	−67.5495	−	207.896i	−0.432539	−	1.33122i	0.463049	−	0.886333i	$-0.346755\pi$
$30$	6.68266	−	20.5671i	0.0406694	−	0.125167i
$31$	62.0698	+	45.0964i	0.359615	+	0.261276i	0.752892	−	0.658145i	$-0.228658\pi$
$31$	62.0698	+	45.0964i	0.359615	+	0.261276i	−0.393276	+	0.919420i	$0.628658\pi$
$32$	−115.662			−0.638947
$33$	−48.6244	+	98.0544i	−0.256498	+	0.517245i
$34$	−15.1532			−0.0764340
$35$	235.615	+	171.184i	1.13789	+	0.826726i
$36$	−21.0852	+	64.8936i	−0.0976167	+	0.300433i
$37$	−87.5569	−	269.472i	−0.389034	−	1.19732i	−0.933511	−	0.358548i	$-0.883272\pi$
$37$	−87.5569	−	269.472i	−0.389034	−	1.19732i	0.544477	−	0.838776i	$-0.316728\pi$
$38$	−37.0783	+	26.9390i	−0.158287	+	0.115002i
$39$	129.893	−	94.3727i	0.533321	−	0.387480i
$40$	−34.7085	−	106.822i	−0.137198	−	0.422251i
$41$	1.50043	−	4.61784i	0.00571530	−	0.0175899i	−0.948158	−	0.317799i	$-0.897056\pi$
$41$	1.50043	−	4.61784i	0.00571530	−	0.0175899i	0.953874	+	0.300209i	$0.0970564\pi$
$42$	41.0403	+	29.8175i	0.150778	+	0.109546i
$43$	−333.848			−1.18398			−0.591992	−	0.805944i	$-0.701658\pi$
$43$	−333.848			−1.18398			−0.591992	+	0.805944i	$0.701658\pi$
$44$	46.2392	+	272.701i	0.158428	+	0.934347i
$45$	−100.282			−0.332203
$46$	85.8951	+	62.4064i	0.275316	+	0.200029i
$47$	−121.601	+	374.250i	−0.377390	+	1.16149i	0.564461	+	0.825459i	$0.309084\pi$
$47$	−121.601	+	374.250i	−0.377390	+	1.16149i	−0.941852	+	0.336029i	$0.890916\pi$
$48$	50.1816	+	154.443i	0.150898	+	0.464415i
$49$	−275.206	+	199.949i	−0.802350	+	0.582941i
$50$	−0.443057	+	0.321899i	−0.00125315	+	0.000910469i
$51$	21.7141	+	66.8292i	0.0596193	+	0.183489i
$52$	125.384	−	385.892i	0.334377	−	1.02911i
$53$	−123.029	−	89.3860i	−0.318856	−	0.231663i	0.416831	−	0.908984i	$-0.363141\pi$
$53$	−123.029	−	89.3860i	−0.318856	−	0.231663i	−0.735687	+	0.677321i	$0.763141\pi$
$54$	−17.4675			−0.0440189
$55$	−360.171	+	188.481i	−0.883008	+	0.462087i
$56$	263.475			0.628721
$57$	171.939	+	124.921i	0.399542	+	0.290284i
$58$	43.7007	−	134.497i	0.0989341	−	0.304488i
$59$	−237.027	−	729.494i	−0.523021	−	1.60969i	−0.768195	−	0.640215i	$-0.778845\pi$
$59$	−237.027	−	729.494i	−0.523021	−	1.60969i	0.245174	−	0.969479i	$-0.421155\pi$
$60$	−205.027	+	148.961i	−0.441148	+	0.320513i
$61$	287.741	−	209.056i	0.603959	−	0.438802i	−0.243323	−	0.969945i	$-0.578237\pi$
$61$	287.741	−	209.056i	0.603959	−	0.438802i	0.847282	+	0.531143i	$0.178237\pi$
$62$	15.3381	+	47.2058i	0.0314184	+	0.0966959i
$63$	72.6926	−	223.725i	0.145372	−	0.447408i
$64$	289.803	+	210.554i	0.566021	+	0.411238i
$65$	596.329			1.13793
$66$	−62.7360	+	32.8304i	−0.117004	+	0.0612294i
$67$	102.070			0.186116			0.0930582	−	0.995661i	$-0.470336\pi$
$67$	102.070			0.186116			0.0930582	+	0.995661i	$0.470336\pi$
$68$	143.665	+	104.378i	0.256204	+	0.186143i
$69$	152.142	−	468.244i	0.265445	−	0.816956i
$70$	58.2228	+	179.191i	0.0994137	+	0.305964i
$71$	−504.157	+	366.292i	−0.842711	+	0.612265i	−0.923127	−	0.384496i	$-0.874375\pi$
$71$	−504.157	+	366.292i	−0.842711	+	0.612265i	0.0804159	+	0.996761i	$0.474375\pi$
$72$	−73.3964	+	53.3256i	−0.120137	+	0.0872844i
$73$	−95.7190	−	294.593i	−0.153467	−	0.472322i	0.844536	−	0.535499i	$-0.179877\pi$
$73$	−95.7190	−	294.593i	−0.153467	−	0.472322i	−0.998002	+	0.0631776i	$0.979877\pi$
$74$	56.6443	−	174.333i	0.0889834	−	0.273863i
$75$	2.05454	+	1.49271i	0.00316317	+	0.00229818i
$76$	537.093			0.810642
$77$	−159.412	−	940.155i	−0.235932	−	1.39144i
$78$	103.871			0.150783
$79$	517.284	+	375.829i	0.736697	+	0.535242i	0.891675	−	0.452676i	$-0.149531\pi$
$79$	517.284	+	375.829i	0.736697	+	0.535242i	−0.154978	+	0.987918i	$0.549531\pi$
$80$	−186.381	+	573.623i	−0.260476	+	0.801662i
$81$	25.0304	+	77.0356i	0.0343352	+	0.105673i
$82$	2.54130	−	1.84636i	0.00342244	−	0.00248655i
$83$	−233.374	+	169.556i	−0.308628	+	0.224232i	−0.731308	−	0.682048i	$-0.761090\pi$
$83$	−233.374	+	169.556i	−0.308628	+	0.224232i	0.422679	+	0.906279i	$0.361090\pi$
$84$	−183.706	−	565.387i	−0.238618	−	0.734391i
$85$	−80.6493	+	248.213i	−0.102913	+	0.316735i
$86$	−174.732	−	126.950i	−0.219091	−	0.159179i
$87$	−655.784			−0.808131
$88$	−163.383	+	329.473i	−0.197917	+	0.399113i
$89$	184.513			0.219756			0.109878	−	0.993945i	$-0.464954\pi$
$89$	184.513			0.219756			0.109878	+	0.993945i	$0.464954\pi$
$90$	−52.4863	−	38.1335i	−0.0614727	−	0.0446625i
$91$	−432.269	+	1330.39i	−0.497957	+	1.53255i
$92$	−384.486	−	1183.32i	−0.435711	−	1.34098i
$93$	186.210	−	135.289i	0.207624	−	0.150848i
$94$	−205.958	+	149.637i	−0.225989	+	0.164191i
$95$	243.926	+	750.727i	0.263434	+	0.810768i
$96$	−107.224	+	330.003i	−0.113995	+	0.350841i
$97$	−515.522	−	374.549i	−0.539622	−	0.392058i	0.284323	−	0.958729i	$-0.408231\pi$
$97$	−515.522	−	374.549i	−0.539622	−	0.392058i	−0.823945	+	0.566670i	$0.808231\pi$
$98$	−220.073			−0.226844
$99$	234.688	+	229.635i	0.238253	+	0.233123i
$100$	6.41783			0.00641783
$101$	621.680	+	451.677i	0.612470	+	0.444986i	0.850283	−	0.526325i	$-0.176431\pi$
$101$	621.680	+	451.677i	0.612470	+	0.444986i	−0.237813	+	0.971311i	$0.576431\pi$
$102$	−14.0478	+	43.2347i	−0.0136367	+	0.0419694i
$103$	354.197	+	1090.10i	0.338835	+	1.04283i	0.964802	+	0.262978i	$0.0847046\pi$
$103$	354.197	+	1090.10i	0.338835	+	1.04283i	−0.625967	+	0.779850i	$0.715295\pi$
$104$	436.454	−	317.102i	0.411518	−	0.298985i
$105$	706.844	−	513.553i	0.656961	−	0.477310i
$106$	−30.4018	−	93.5672i	−0.0278574	−	0.0857363i
$107$	−230.941	+	710.765i	−0.208654	+	0.642170i	0.790890	+	0.611959i	$0.209618\pi$
$107$	−230.941	+	710.765i	−0.208654	+	0.642170i	−0.999544	+	0.0302117i	$0.990382\pi$
$108$	165.605	+	120.319i	0.147550	+	0.107201i
$109$	−742.910			−0.652825			−0.326412	−	0.945227i	$-0.605840\pi$
$109$	−742.910			−0.652825			−0.326412	+	0.945227i	$0.605840\pi$
$110$	−260.182	−	38.3111i	−0.225521	−	0.0332075i
$111$	−850.020			−0.726850
$112$	−1144.63	−	831.620i	−0.965688	−	0.701613i
$113$	561.797	−	1729.03i	0.467694	−	1.43942i	−0.387868	−	0.921715i	$-0.626788\pi$
$113$	561.797	−	1729.03i	0.467694	−	1.43942i	0.855562	−	0.517700i	$-0.173212\pi$
$114$	42.4880	+	130.764i	0.0349067	+	0.107432i
$115$	1479.39	−	1074.84i	1.19960	−	0.871557i
$116$	−1340.76	+	974.118i	−1.07316	+	0.779694i
$117$	−148.844	−	458.095i	−0.117612	−	0.361973i
$118$	153.343	−	471.941i	0.119630	−	0.368184i
$119$	−495.293	−	359.851i	−0.381541	−	0.277206i
$120$	−336.957			−0.256332
$121$	1274.51	+	383.655i	0.957557	+	0.288245i
$122$	230.097			0.170754
$123$	−11.7845	−	8.56195i	−0.00863881	−	0.00627646i
$124$	179.746	−	553.200i	0.130175	−	0.400636i
$125$	433.314	+	1333.60i	0.310054	+	0.954250i
$126$	123.121	−	89.4526i	0.0870514	−	0.0632466i
$127$	1958.12	−	1422.66i	1.36815	−	0.994021i	0.370274	−	0.928923i	$-0.379264\pi$
$127$	1958.12	−	1422.66i	1.36815	−	0.994021i	0.997879	−	0.0650981i	$-0.0207360\pi$
$128$	357.545	+	1100.41i	0.246897	+	0.759871i
$129$	−309.494	+	952.524i	−0.211236	+	0.650117i
$130$	312.111	+	226.762i	0.210569	+	0.152987i
$131$	1878.36			1.25277			0.626386	−	0.779513i	$-0.284533\pi$
$131$	1878.36			1.25277			0.626386	+	0.779513i	$0.284533\pi$
$132$	820.929	+	120.880i	0.541308	+	0.0797063i
$133$	−1851.66			−1.20721
$134$	53.4221	+	38.8134i	0.0344400	+	0.0250222i
$135$	−92.9663	+	286.121i	−0.0592686	+	0.182410i
$136$	72.9618	+	224.553i	0.0460031	+	0.141583i
$137$	430.765	−	312.969i	0.268633	−	0.195174i	−0.445311	−	0.895376i	$-0.646907\pi$
$137$	430.765	−	312.969i	0.268633	−	0.195174i	0.713944	+	0.700202i	$0.246907\pi$
$138$	257.685	−	187.219i	0.158954	−	0.115487i
$139$	−516.215	−	1588.75i	−0.314999	−	0.969466i	−0.975755	−	0.218866i	$-0.929764\pi$
$139$	−516.215	−	1588.75i	−0.314999	−	0.969466i	0.660756	−	0.750601i	$-0.270236\pi$
$140$	682.308	−	2099.93i	0.411897	−	1.26769i
$141$	955.068	+	693.897i	0.570434	+	0.414445i
$142$	−403.157			−0.238255
$143$	−1395.58	−	1365.53i	−0.816115	−	0.798543i
$144$	487.173			0.281929
$145$	−1970.50	−	1431.65i	−1.12856	−	0.819947i
$146$	61.9248	−	190.585i	0.0351023	−	0.108034i
$147$	315.358	+	970.572i	0.176941	+	0.544568i
$148$	−1737.88	+	1262.64i	−0.965219	+	0.701273i
$149$	−2432.65	+	1767.42i	−1.33752	+	0.971763i	−0.337986	+	0.941151i	$0.609746\pi$
$149$	−2432.65	+	1767.42i	−1.33752	+	0.971763i	−0.999531	+	0.0306124i	$0.990254\pi$
$150$	0.507698	+	1.56253i	0.000276356	+	0.000850535i
$151$	−767.053	+	2360.75i	−0.413390	+	1.27228i	0.500293	+	0.865856i	$0.333226\pi$
$151$	−767.053	+	2360.75i	−0.413390	+	1.27228i	−0.913683	+	0.406428i	$0.866774\pi$
$152$	577.734	+	419.749i	0.308292	+	0.223988i
$153$	210.805			0.111389
$154$	274.072	−	552.685i	0.143411	−	0.289199i
$155$	854.875			0.443001
$156$	−984.778	−	715.483i	−0.505419	−	0.367208i
$157$	975.427	−	3002.06i	0.495844	−	1.52605i	−0.319792	−	0.947488i	$-0.603613\pi$
$157$	975.427	−	3002.06i	0.495844	−	1.52605i	0.815637	−	0.578564i	$-0.196387\pi$
$158$	127.826	+	393.409i	0.0643628	+	0.198088i
$159$	−369.088	+	268.158i	−0.184092	+	0.133750i
$160$	−1042.62	+	757.510i	−0.515166	+	0.374290i
$161$	1325.54	+	4079.59i	0.648864	+	1.99700i
$162$	−16.1932	+	49.8376i	−0.00785346	+	0.0241705i
$163$	667.571	+	485.019i	0.320787	+	0.233065i	0.736511	−	0.676425i	$-0.236472\pi$
$163$	667.571	+	485.019i	0.320787	+	0.233065i	−0.415724	+	0.909491i	$0.636472\pi$
$164$	−36.8117			−0.0175275
$165$	203.872	+	1202.36i	0.0961904	+	0.567295i
$166$	−186.621			−0.0872568
$167$	−2792.71	−	2029.02i	−1.29405	−	0.940184i	−0.294173	−	0.955752i	$-0.595044\pi$
$167$	−2792.71	−	2029.02i	−1.29405	−	0.940184i	−0.999879	+	0.0155686i	$0.995044\pi$
$168$	244.255	−	751.740i	0.112171	−	0.345226i
$169$	206.195	+	634.604i	0.0938531	+	0.288850i
$170$	−136.597	+	99.2437i	−0.0616267	+	0.0447744i
$171$	515.818	−	374.764i	0.230676	−	0.167596i
$172$	782.139	+	2407.17i	0.346730	+	1.06712i
$173$	−229.523	+	706.398i	−0.100869	+	0.310442i	−0.988739	−	0.149653i	$-0.952184\pi$
$173$	−229.523	+	706.398i	−0.100869	+	0.310442i	0.887870	+	0.460094i	$0.152184\pi$
$174$	−343.230	−	249.371i	−0.149541	−	0.108648i
$175$	−22.1259			−0.00955749
$176$	1749.73	−	915.649i	0.749378	−	0.392157i
$177$	−2301.10			−0.977184
$178$	96.5717	+	70.1635i	0.0406649	+	0.0295448i
$179$	−726.105	+	2234.72i	−0.303193	+	0.933133i	0.677152	+	0.735843i	$0.263214\pi$
$179$	−726.105	+	2234.72i	−0.303193	+	0.933133i	−0.980345	+	0.197290i	$0.936786\pi$
$180$	234.940	+	723.072i	0.0972856	+	0.299414i
$181$	2282.19	−	1658.11i	0.937202	−	0.680917i	−0.0105436	−	0.999944i	$-0.503356\pi$
$181$	2282.19	−	1658.11i	0.937202	−	0.680917i	0.947746	+	0.319027i	$0.103356\pi$
$182$	−732.142	+	531.933i	−0.298187	+	0.216645i
$183$	−329.722	−	1014.78i	−0.133190	−	0.409917i
$184$	511.212	−	1573.35i	0.204821	−	0.630374i
$185$	−2554.14	−	1855.69i	−1.01505	−	0.737477i
$186$	148.905			0.0587004
$187$	757.126	−	396.212i	0.296078	−	0.154941i
$188$	2983.38			1.15737
$189$	−570.935	−	414.809i	−0.219732	−	0.159645i
$190$	−157.806	+	485.678i	−0.0602551	+	0.185446i
$191$	−1144.94	−	3523.78i	−0.433745	−	1.33493i	−0.894367	−	0.447333i	$-0.852374\pi$
$191$	−1144.94	−	3523.78i	−0.433745	−	1.33493i	0.460622	−	0.887596i	$-0.347626\pi$
$192$	869.408	−	631.662i	0.326792	−	0.237429i
$193$	−2004.39	+	1456.28i	−0.747561	+	0.543135i	−0.895070	−	0.445926i	$-0.852875\pi$
$193$	−2004.39	+	1456.28i	−0.747561	+	0.543135i	0.147509	+	0.989061i	$0.452875\pi$
$194$	−127.391	−	392.069i	−0.0471450	−	0.145097i
$195$	552.827	−	1701.43i	0.203019	−	0.624829i
$196$	2086.47	+	1515.91i	0.760374	+	0.552444i
$197$	1713.08			0.619551			0.309775	−	0.950810i	$-0.399746\pi$
$197$	1713.08			0.619551			0.309775	+	0.950810i	$0.399746\pi$
$198$	35.5112	+	209.432i	0.0127458	+	0.0751700i
$199$	825.847			0.294185			0.147092	−	0.989123i	$-0.453009\pi$
$199$	825.847			0.294185			0.147092	+	0.989123i	$0.453009\pi$
$200$	6.90347	+	5.01566i	0.00244075	+	0.00177331i
$201$	94.6239	−	291.222i	0.0332052	−	0.102195i
$202$	153.624	+	472.805i	0.0535095	+	0.164685i
$203$	4622.35	−	3358.33i	1.59815	−	1.16113i
$204$	430.994	−	313.135i	0.147920	−	0.107470i
$205$	−16.7184	−	51.4539i	−0.00569592	−	0.0175302i
$206$	−229.145	+	705.236i	−0.0775014	+	0.238525i
$207$	−1194.94	−	868.172i	−0.401226	−	0.291508i
$208$	−2896.99			−0.965722
$209$	1148.23	−	2315.48i	0.380023	−	0.766342i
$210$	565.239			0.185739
$211$	2266.93	+	1647.02i	0.739629	+	0.537372i	0.892595	−	0.450860i	$-0.148883\pi$
$211$	2266.93	+	1647.02i	0.739629	+	0.537372i	−0.152966	+	0.988231i	$0.548883\pi$
$212$	−356.276	+	1096.50i	−0.115420	+	0.355228i
$213$	577.713	+	1778.02i	0.185841	+	0.571961i
$214$	−391.150	+	284.187i	−0.124946	+	0.0907787i
$215$	−3009.44	+	2186.48i	−0.954614	+	0.693567i
$216$	84.1047	+	258.848i	0.0264935	+	0.0815387i
$217$	−619.685	+	1907.19i	−0.193857	+	0.596630i
$218$	−388.830	−	282.502i	−0.120802	−	0.0877680i
$219$	−929.260			−0.286729
$220$	2202.83	+	2155.40i	0.675068	+	0.660533i
$221$	−1253.56			−0.381555
$222$	−444.890	−	323.232i	−0.134500	−	0.0977202i
$223$	682.251	−	2099.75i	0.204874	−	0.630538i	−0.794844	−	0.606813i	$-0.792448\pi$
$223$	682.251	−	2099.75i	0.204874	−	0.630538i	0.999719	−	0.0237244i	$-0.00755241\pi$
$224$	−934.196	−	2875.16i	−0.278654	−	0.857610i
$225$	6.16362	−	4.47813i	0.00182626	−	0.00132685i
$226$	951.527	−	691.325i	0.280065	−	0.203479i
$227$	−733.649	−	2257.94i	−0.214511	−	0.660197i	−0.999188	−	0.0402921i	$-0.987171\pi$
$227$	−733.649	−	2257.94i	−0.214511	−	0.660197i	0.784677	−	0.619905i	$-0.212829\pi$
$228$	497.912	−	1532.42i	0.144627	−	0.445117i
$229$	−346.279	−	251.587i	−0.0999248	−	0.0725996i	0.536701	−	0.843773i	$-0.319670\pi$
$229$	−346.279	−	251.587i	−0.0999248	−	0.0725996i	−0.636626	+	0.771173i	$0.719670\pi$
$230$	1183.01			0.339155
$231$	−2830.21	−	416.741i	−0.806120	−	0.118699i
$232$	−2203.50			−0.623565
$233$	2238.22	+	1626.16i	0.629316	+	0.457225i	0.856163	−	0.516705i	$-0.172842\pi$
$233$	2238.22	+	1626.16i	0.629316	+	0.457225i	−0.226847	+	0.973930i	$0.572842\pi$
$234$	96.2936	−	296.361i	0.0269013	−	0.0827937i
$235$	1354.93	+	4170.05i	0.376110	+	1.15755i
$236$	−4704.63	+	3418.12i	−1.29765	+	0.942799i
$237$	1551.85	−	1127.49i	0.425332	−	0.309022i
$238$	−122.392	−	376.684i	−0.0333340	−	0.102591i
$239$	−1066.04	+	3280.94i	−0.288521	+	0.887977i	0.696800	+	0.717265i	$0.254606\pi$
$239$	−1066.04	+	3280.94i	−0.288521	+	0.887977i	−0.985321	+	0.170711i	$0.945394\pi$
$240$	1463.86	+	1063.56i	0.393715	+	0.286051i
$241$	1453.69			0.388549			0.194274	−	0.980947i	$-0.437765\pi$
$241$	1453.69			0.388549			0.194274	+	0.980947i	$0.437765\pi$
$242$	521.172	+	685.449i	0.138439	+	0.182076i
$243$	243.000			0.0641500
$244$	−2181.50	−	1584.95i	−0.572362	−	0.415845i
$245$	−1171.28	+	3604.84i	−0.305431	+	0.940020i
$246$	−2.91207	−	8.96244i	−0.000754744	−	0.00232286i
$247$	−3067.33	+	2228.54i	−0.790159	+	0.574084i
$248$	625.684	−	454.586i	0.160206	−	0.116396i
$249$	267.423	+	823.044i	0.0680613	+	0.209471i
$250$	−280.330	+	862.766i	−0.0709184	+	0.218264i
$251$	−2346.81	−	1705.06i	−0.590158	−	0.428775i	0.252214	−	0.967671i	$-0.418841\pi$
$251$	−2346.81	−	1705.06i	−0.590158	−	0.428775i	−0.842372	+	0.538897i	$0.818841\pi$
$252$	−1783.45			−0.445821
$253$	−5923.46	−	872.215i	−1.47196	−	0.216742i
$254$	1565.84			0.386810
$255$	633.428	+	460.212i	0.155556	+	0.113018i
$256$	654.247	−	2013.57i	0.159728	−	0.491593i
$257$	971.414	+	2989.70i	0.235779	+	0.725652i	0.997017	+	0.0771801i	$0.0245917\pi$
$257$	971.414	+	2989.70i	0.235779	+	0.725652i	−0.761238	+	0.648472i	$0.775408\pi$
$258$	−524.195	+	380.850i	−0.126492	+	0.0919019i
$259$	5991.44	−	4353.03i	1.43741	−	1.04434i
$260$	−1397.08	−	4299.77i	−0.333243	−	1.02562i
$261$	−607.945	+	1871.06i	−0.144180	+	0.443739i
$262$	983.112	+	714.273i	0.231820	+	0.168427i
$263$	587.892			0.137836			0.0689182	−	0.997622i	$-0.478045\pi$
$263$	587.892			0.137836			0.0689182	+	0.997622i	$0.478045\pi$
$264$	788.578	+	771.599i	0.183840	+	0.179881i
$265$	−1694.46			−0.392791
$266$	−969.137	−	704.120i	−0.223390	−	0.162302i
$267$	171.053	−	526.446i	0.0392069	−	0.120667i
$268$	−239.129	−	735.964i	−0.0545042	−	0.167747i
$269$	1303.12	−	946.775i	0.295364	−	0.214594i	−0.430227	−	0.902721i	$-0.641567\pi$
$269$	1303.12	−	946.775i	0.295364	−	0.214594i	0.725591	+	0.688126i	$0.241567\pi$
$270$	−157.459	+	114.401i	−0.0354913	+	0.0257859i
$271$	−700.861	−	2157.03i	−0.157101	−	0.483506i	0.841267	−	0.540620i	$-0.181810\pi$
$271$	−700.861	−	2157.03i	−0.157101	−	0.483506i	−0.998368	+	0.0571137i	$0.981810\pi$
$272$	391.798	−	1205.83i	0.0873391	−	0.268802i
$273$	3395.09	+	2466.67i	0.752674	+	0.546849i
$274$	344.468			0.0759492
$275$	13.7205	−	27.6682i	0.00300864	−	0.00606711i
$276$	−3732.66			−0.814058
$277$	3930.39	+	2855.60i	0.852543	+	0.619409i	0.925846	−	0.377901i	$-0.123354\pi$
$277$	3930.39	+	2855.60i	0.852543	+	0.619409i	−0.0733031	+	0.997310i	$0.523354\pi$
$278$	333.962	−	1027.83i	0.0720493	−	0.221745i
$279$	−213.377	−	656.707i	−0.0457869	−	0.140918i
$280$	2375.07	−	1725.59i	0.506921	−	0.368299i
$281$	3948.13	−	2868.49i	0.838170	−	0.608966i	−0.0836886	−	0.996492i	$-0.526670\pi$
$281$	3948.13	−	2868.49i	0.838170	−	0.608966i	0.921859	+	0.387526i	$0.126670\pi$
$282$	236.007	+	726.355i	0.0498369	+	0.153382i
$283$	2061.42	−	6344.40i	0.432999	−	1.33264i	−0.462124	−	0.886816i	$-0.652912\pi$
$283$	2061.42	−	6344.40i	0.432999	−	1.33264i	0.895123	−	0.445819i	$-0.147088\pi$
$284$	3822.25	+	2777.03i	0.798623	+	0.580233i
$285$	2368.08			0.492186
$286$	−211.169	−	1245.39i	−0.0436597	−	0.257488i
$287$	126.911			0.0261021
$288$	842.151	+	611.859i	0.172306	+	0.125188i
$289$	−1348.67	+	4150.76i	−0.274510	+	0.844853i
$290$	−486.931	−	1498.62i	−0.0985986	−	0.303455i
$291$	−1546.57	+	1123.65i	−0.311551	+	0.226355i
$292$	−1899.88	+	1380.34i	−0.380761	+	0.276639i
$293$	1675.44	+	5156.47i	0.334062	+	1.02814i	0.967182	+	0.254084i	$0.0817740\pi$
$293$	1675.44	+	5156.47i	0.334062	+	1.02814i	−0.633120	+	0.774054i	$0.718226\pi$
$294$	−204.019	+	627.905i	−0.0404715	+	0.124558i
$295$	−6914.36	−	5023.58i	−1.36464	−	0.991472i
$296$	−2856.16			−0.560847
$297$	872.756	−	456.722i	0.170513	−	0.0892314i
$298$	−1945.30			−0.378149
$299$	7105.73	+	5162.61i	1.37436	+	0.998534i
$300$	5.94966	−	18.3112i	0.00114501	−	0.00352399i
$301$	−2696.47	−	8298.89i	−0.516353	−	1.58917i
$302$	−1299.17	+	943.904i	−0.247546	+	0.179853i
$303$	1865.04	−	1355.03i	0.353610	−	0.256913i
$304$	−1185.00	−	3647.06i	−0.223568	−	0.688070i
$305$	1224.63	−	3769.04i	0.229909	−	0.707588i
$306$	110.333	+	80.1616i	0.0206121	+	0.0149756i
$307$	4774.61			0.887627			0.443813	−	0.896119i	$-0.353625\pi$
$307$	4774.61			0.887627			0.443813	+	0.896119i	$0.353625\pi$
$308$	−6405.42	+	3352.02i	−1.18501	+	0.620128i
$309$	3438.61			0.633061
$310$	447.431	+	325.078i	0.0819754	+	0.0595586i
$311$	273.472	−	841.659i	0.0498622	−	0.153460i	−0.923025	−	0.384740i	$-0.874291\pi$
$311$	273.472	−	841.659i	0.0498622	−	0.153460i	0.972887	+	0.231280i	$0.0742912\pi$
$312$	−500.132	−	1539.25i	−0.0907512	−	0.279304i
$313$	−5381.54	+	3909.92i	−0.971829	+	0.706075i	−0.955868	−	0.293797i	$-0.905081\pi$
$313$	−5381.54	+	3909.92i	−0.971829	+	0.706075i	−0.0159614	+	0.999873i	$0.505081\pi$
$314$	1652.10	−	1200.32i	0.296922	−	0.215726i
$315$	−809.972	−	2492.84i	−0.144879	−	0.445890i
$316$	1497.98	−	4610.32i	0.266672	−	0.820731i
$317$	1246.50	+	905.636i	0.220853	+	0.160459i	0.692711	−	0.721216i	$-0.256416\pi$
$317$	1246.50	+	905.636i	0.220853	+	0.160459i	−0.471857	+	0.881675i	$0.656416\pi$
$318$	−295.147			−0.0520472
$319$	1333.20	+	7862.73i	0.233997	+	1.38003i
$320$	3991.39			0.697267
$321$	1813.84	+	1317.83i	0.315385	+	0.229141i
$322$	−857.548	+	2639.26i	−0.148414	+	0.456771i
$323$	−512.764	−	1578.12i	−0.0883311	−	0.271855i
$324$	496.816	−	360.958i	0.0851880	−	0.0618927i
$325$	−36.6521	+	26.6293i	−0.00625568	+	0.00454502i
$326$	164.964	+	507.706i	0.0280261	+	0.0862554i
$327$	−688.716	+	2119.65i	−0.116471	+	0.358461i
$328$	−39.5972	−	28.7691i	−0.00666583	−	0.00484301i
$329$	−10285.4			−1.72356
$330$	−350.510	+	706.826i	−0.0584695	+	0.117908i
$331$	3573.14			0.593346			0.296673	−	0.954979i	$-0.404123\pi$
$331$	3573.14			0.593346			0.296673	+	0.954979i	$0.404123\pi$
$332$	1769.32	+	1285.49i	0.292482	+	0.212501i
$333$	−788.012	+	2425.25i	−0.129678	+	0.399108i
$334$	−690.108	−	2123.93i	−0.113057	−	0.347954i
$335$	920.098	−	668.490i	0.150061	−	0.109025i
$336$	−3433.88	+	2494.86i	−0.557540	+	0.405077i
$337$	363.720	+	1119.42i	0.0587926	+	0.180945i	0.976140	−	0.217143i	$-0.0696738\pi$
$337$	363.720	+	1119.42i	0.0587926	+	0.180945i	−0.917347	+	0.398088i	$0.869674\pi$
$338$	−133.397	+	410.552i	−0.0214669	+	0.0660684i
$339$	−4412.41	−	3205.81i	−0.706931	−	0.513615i
$340$	1978.66			0.315612
$341$	−2000.66	−	1957.58i	−0.317717	−	0.310876i
$342$	412.482			0.0652177
$343$	59.7704	+	43.4257i	0.00940903	+	0.00683606i
$344$	−1039.93	+	3200.58i	−0.162992	+	0.501639i
$345$	−1695.23	−	5217.37i	−0.264545	−	0.814185i
$346$	−388.747	+	282.441i	−0.0604022	+	0.0438848i
$347$	−4623.91	+	3359.46i	−0.715344	+	0.519728i	−0.884893	−	0.465794i	$-0.845769\pi$
$347$	−4623.91	+	3359.46i	−0.715344	+	0.519728i	0.169549	+	0.985522i	$0.445769\pi$
$348$	1536.37	+	4728.47i	0.236661	+	0.728369i
$349$	−2843.25	+	8750.62i	−0.436091	+	1.34215i	0.455874	+	0.890044i	$0.349327\pi$
$349$	−2843.25	+	8750.62i	−0.436091	+	1.34215i	−0.891965	+	0.452105i	$0.850673\pi$
$350$	−11.5804	−	8.41367i	−0.00176857	−	0.00128494i
$351$	−1445.01			−0.219740
$352$	4174.66	+	614.709i	0.632131	+	0.0930798i
$353$	844.785			0.127375			0.0636875	−	0.997970i	$-0.479714\pi$
$353$	844.785			0.127375			0.0636875	+	0.997970i	$0.479714\pi$
$354$	−1204.37	−	875.026i	−0.180824	−	0.131376i
$355$	−2145.71	+	6603.80i	−0.320795	+	0.987306i
$356$	−432.277	−	1330.41i	−0.0643556	−	0.198066i
$357$	−1485.88	+	1079.55i	−0.220283	+	0.160045i
$358$	−1229.82	+	893.515i	−0.181558	+	0.131910i
$359$	−2857.69	−	8795.08i	−0.420121	−	1.29300i	−0.907590	−	0.419858i	$-0.862080\pi$
$359$	−2857.69	−	8795.08i	−0.420121	−	1.29300i	0.487469	−	0.873140i	$-0.337920\pi$
$360$	−312.377	+	961.397i	−0.0457325	+	0.140750i
$361$	1488.82	+	1081.69i	0.217061	+	0.157704i
$362$	1824.99			0.264970
$363$	2276.17	−	3280.72i	0.329112	−	0.474361i
$364$	10605.3			1.52712
$365$	−2792.24	−	2028.68i	−0.400418	−	0.290921i
$366$	213.312	−	656.505i	0.0304644	−	0.0937598i
$367$	1001.85	+	3083.37i	0.142496	+	0.438558i	0.996681	−	0.0814122i	$-0.0259430\pi$
$367$	1001.85	+	3083.37i	0.142496	+	0.438558i	−0.854184	+	0.519970i	$0.825943\pi$
$368$	−7186.92	+	5221.60i	−1.01805	+	0.739660i
$369$	−35.3535	+	25.6858i	−0.00498762	+	0.00362372i
$370$	−631.155	−	1942.49i	−0.0886815	−	0.272934i
$371$	1228.28	−	3780.27i	0.171885	−	0.529008i
$372$	−1411.74	−	1025.69i	−0.196762	−	0.142956i
$373$	−3319.48			−0.460794			−0.230397	−	0.973097i	$-0.574002\pi$
$373$	−3319.48			−0.460794			−0.230397	+	0.973097i	$0.574002\pi$
$374$	546.936	+	80.5349i	0.0756186	+	0.0111347i
$375$	4206.70			0.579289
$376$	3209.13	+	2331.57i	0.440155	+	0.319791i
$377$	3615.17	−	11126.3i	0.493874	−	1.51999i
$378$	−141.084	−	434.212i	−0.0191973	−	0.0590832i
$379$	−718.800	+	522.239i	−0.0974202	+	0.0707799i	−0.635429	−	0.772159i	$-0.719177\pi$
$379$	−718.800	+	522.239i	−0.0974202	+	0.0707799i	0.538009	+	0.842939i	$0.319177\pi$
$380$	4841.57	−	3517.61i	0.653598	−	0.474867i
$381$	−2243.81	−	6905.74i	−0.301716	−	0.928587i
$382$	740.714	−	2279.68i	0.0992100	−	0.305337i
$383$	2726.60	+	1980.99i	0.363767	+	0.264292i	0.754622	−	0.656160i	$-0.227820\pi$
$383$	2726.60	+	1980.99i	0.363767	+	0.264292i	−0.390854	+	0.920453i	$0.627820\pi$
$384$	3471.12			0.461289
$385$	−7594.41	−	7430.89i	−1.00532	−	0.983671i
$386$	−1602.84			−0.211354
$387$	2430.80	+	1766.08i	0.319287	+	0.231976i
$388$	−1492.88	+	4594.62i	−0.195334	+	0.601176i
$389$	1482.84	+	4563.71i	0.193272	+	0.594831i	0.999992	+	0.00389744i	$0.00124060\pi$
$389$	1482.84	+	4563.71i	0.193272	+	0.594831i	−0.806720	+	0.590934i	$0.798759\pi$
$390$	936.334	−	680.287i	0.121572	−	0.0883273i
$391$	−3109.86	+	2259.45i	−0.402231	+	0.292238i
$392$	1059.64	+	3261.23i	0.136530	+	0.420196i
$393$	1741.34	−	5359.28i	0.223508	−	0.687888i
$394$	896.603	+	651.420i	0.114645	+	0.0832946i
$395$	7124.45			0.907519
$396$	1105.93	−	2230.19i	0.140342	−	0.283008i
$397$	3560.10			0.450066			0.225033	−	0.974351i	$-0.427751\pi$
$397$	3560.10			0.450066			0.225033	+	0.974351i	$0.427751\pi$
$398$	432.238	+	314.040i	0.0544376	+	0.0395512i
$399$	−1716.58	+	5283.10i	−0.215380	+	0.662872i
$400$	−14.1598	−	43.5795i	−0.00176998	−	0.00544744i
$401$	−2926.55	+	2126.26i	−0.364451	+	0.264789i	−0.754906	−	0.655833i	$-0.772318\pi$
$401$	−2926.55	+	2126.26i	−0.364451	+	0.264789i	0.390455	+	0.920622i	$0.372318\pi$
$402$	160.266	−	116.440i	0.0198840	−	0.0144465i
$403$	1268.85	+	3905.13i	0.156839	+	0.482701i
$404$	1800.30	−	5540.75i	0.221704	−	0.682334i
$405$	730.167	+	530.497i	0.0895859	+	0.0650880i
$406$	3696.33			0.451837
$407$	1728.08	+	10191.6i	0.210462	+	1.24122i
$408$	708.328			0.0859497
$409$	−137.720	−	100.060i	−0.0166500	−	0.0120969i	0.579429	−	0.815023i	$-0.303276\pi$
$409$	−137.720	−	100.060i	−0.0166500	−	0.0120969i	−0.596079	+	0.802926i	$0.703276\pi$
$410$	10.8159	−	33.2878i	0.00130282	−	0.00400967i
$411$	−493.613	−	1519.19i	−0.0592412	−	0.182326i
$412$	7030.28	−	5107.80i	0.840673	−	0.610784i
$413$	16219.5	−	11784.2i	1.93247	−	1.40402i
$414$	−295.281	−	908.782i	−0.0350538	−	0.107884i
$415$	−993.247	+	3056.90i	−0.117486	+	0.361584i
$416$	−5007.88	−	3638.44i	−0.590220	−	0.428820i
$417$	−5011.52			−0.588526
$418$	1481.47	−	775.266i	0.173351	−	0.0907165i
$419$	−17029.2			−1.98552			−0.992759	−	0.120126i	$-0.961670\pi$
$419$	−17029.2			−1.98552			−0.992759	+	0.120126i	$0.961670\pi$
$420$	−5358.92	−	3893.48i	−0.622591	−	0.452339i
$421$	3297.86	−	10149.8i	0.381776	−	1.17499i	−0.557016	−	0.830502i	$-0.688054\pi$
$421$	3297.86	−	10149.8i	0.381776	−	1.17499i	0.938792	−	0.344484i	$-0.111946\pi$
$422$	560.181	+	1724.06i	0.0646189	+	0.198877i
$423$	2865.20	−	2081.69i	0.329340	−	0.239280i
$424$	−1240.18	+	901.040i	−0.142048	+	0.103204i
$425$	−6.12712	−	18.8573i	−0.000699316	−	0.00215227i
$426$	−373.747	+	1150.28i	−0.0425073	+	0.130824i
$427$	7520.86	+	5464.23i	0.852366	+	0.619280i
$428$	5665.95			0.639893
$429$	−5189.87	+	2715.92i	−0.584078	+	0.305654i
$430$	−2406.54			−0.269893
$431$	−13944.8	−	10131.5i	−1.55847	−	1.13229i	−0.937253	−	0.348649i	$-0.886641\pi$
$431$	−13944.8	−	10131.5i	−1.55847	−	1.13229i	−0.621212	−	0.783643i	$-0.713359\pi$
$432$	451.634	−	1389.99i	0.0502992	−	0.154805i
$433$	−2083.79	−	6413.24i	−0.231271	−	0.711780i	−0.997594	−	0.0693242i	$-0.977916\pi$
$433$	−2083.79	−	6413.24i	−0.231271	−	0.711780i	0.766323	−	0.642456i	$-0.222084\pi$
$434$	−1049.57	+	762.559i	−0.116085	+	0.0843410i
$435$	−5911.50	+	4294.96i	−0.651575	+	0.473397i
$436$	1740.49	+	5356.68i	0.191180	+	0.588391i
$437$	−3592.72	+	11057.2i	−0.393279	+	1.21039i
$438$	−486.363	−	353.364i	−0.0530579	−	0.0385488i
$439$	−10414.5			−1.13224			−0.566122	−	0.824321i	$-0.691557\pi$
$439$	−10414.5			−1.13224			−0.566122	+	0.824321i	$0.691557\pi$
$440$	685.032	+	4040.06i	0.0742218	+	0.437733i
$441$	3061.56			0.330586
$442$	−656.098	−	476.683i	−0.0706050	−	0.0512975i
$443$	1873.47	−	5765.94i	0.200928	−	0.618393i	−0.798928	−	0.601426i	$-0.794599\pi$
$443$	1873.47	−	5765.94i	0.200928	−	0.618393i	0.999856	−	0.0169660i	$-0.00540072\pi$
$444$	1991.43	+	6128.98i	0.212858	+	0.655110i
$445$	1663.27	−	1208.44i	0.177183	−	0.128731i
$446$	1155.54	−	839.550i	0.122683	−	0.0891342i
$447$	2787.56	+	8579.24i	0.294960	+	0.907795i
$448$	−2893.30	+	8904.65i	−0.305124	+	0.939074i
$449$	7622.53	+	5538.10i	0.801180	+	0.582091i	0.911260	−	0.411832i	$-0.135111\pi$
$449$	7622.53	+	5538.10i	0.801180	+	0.582091i	−0.110080	+	0.993923i	$0.535111\pi$
$450$	4.92883			0.000516327
$451$	−78.6984	+	158.701i	−0.00821677	+	0.0165697i
$452$	−13783.2			−1.43431
$453$	6024.51	+	4377.07i	0.624848	+	0.453979i
$454$	474.629	−	1460.76i	0.0490649	−	0.151006i
$455$	4816.52	+	14823.7i	0.496268	+	1.52736i
$456$	1733.20	−	1259.25i	0.177993	−	0.129319i
$457$	−933.726	+	678.392i	−0.0955752	+	0.0694394i	−0.634547	−	0.772885i	$-0.718813\pi$
$457$	−933.726	+	678.392i	−0.0955752	+	0.0694394i	0.538971	+	0.842324i	$0.318813\pi$
$458$	−85.5692	−	263.355i	−0.00873010	−	0.0268685i
$459$	195.427	−	601.463i	0.0198731	−	0.0611632i
$460$	−11215.9	−	8148.84i	−1.13684	−	0.825960i
$461$	−5162.80			−0.521595			−0.260798	−	0.965393i	$-0.583986\pi$
$461$	−5162.80			−0.521595			−0.260798	+	0.965393i	$0.583986\pi$
$462$	−1322.82	−	1294.34i	−0.133211	−	0.130342i
$463$	−7080.69			−0.710729			−0.355365	−	0.934728i	$-0.615643\pi$
$463$	−7080.69			−0.710729			−0.355365	+	0.934728i	$0.615643\pi$
$464$	9572.78	+	6955.03i	0.957769	+	0.695860i
$465$	792.512	−	2439.10i	0.0790363	−	0.243249i
$466$	553.087	+	1702.23i	0.0549813	+	0.169215i
$467$	8364.95	−	6077.49i	0.828873	−	0.602212i	−0.0903671	−	0.995909i	$-0.528804\pi$
$467$	8364.95	−	6077.49i	0.828873	−	0.602212i	0.919240	+	0.393697i	$0.128804\pi$
$468$	−2954.33	+	2146.45i	−0.291804	+	0.212008i
$469$	824.413	+	2537.28i	0.0811681	+	0.249810i
$470$	−876.563	+	2697.78i	−0.0860273	+	0.264765i
$471$	−7661.10	−	5566.12i	−0.749480	−	0.544529i
$472$	−7731.96			−0.754009
$473$	12049.8	+	1774.30i	1.17135	+	0.172479i
$474$	1240.96			0.120252
$475$	−48.5165	−	35.2493i	−0.00468650	−	0.00340494i
$476$	−1434.30	+	4414.32i	−0.138111	+	0.425063i
$477$	422.937	+	1301.67i	0.0405974	+	0.124946i
$478$	−1805.58	+	1311.83i	−0.172772	+	0.125526i
$479$	−4098.81	+	2977.96i	−0.390980	+	0.284064i	−0.765857	−	0.643011i	$-0.777685\pi$
$479$	−4098.81	+	2977.96i	−0.390980	+	0.284064i	0.374877	+	0.927075i	$0.377685\pi$
$480$	1194.74	+	3677.03i	0.113609	+	0.349651i
$481$	4685.94	−	14421.8i	0.444200	−	1.36711i
$482$	760.843	+	552.785i	0.0718993	+	0.0522379i
$483$	12868.6			1.21230
$484$	−219.615	−	10088.5i	−0.0206250	−	0.947459i
$485$	−7100.18			−0.664747
$486$	127.183	+	92.4041i	0.0118707	+	0.00862455i
$487$	1899.42	−	5845.80i	0.176737	−	0.543939i	−0.822972	−	0.568082i	$-0.807686\pi$
$487$	1899.42	−	5845.80i	0.176737	−	0.543939i	0.999709	+	0.0241426i	$0.00768559\pi$
$488$	−1107.90	−	3409.77i	−0.102771	−	0.316297i
$489$	2002.71	−	1455.06i	0.185206	−	0.134560i
$490$	−1983.83	+	1441.33i	−0.182898	+	0.132883i
$491$	489.927	+	1507.84i	0.0450307	+	0.138590i	0.971044	−	0.238901i	$-0.0767870\pi$
$491$	489.927	+	1507.84i	0.0450307	+	0.138590i	−0.926013	+	0.377491i	$0.876787\pi$
$492$	−34.1263	+	105.030i	−0.00312710	+	0.00962423i
$493$	4142.25	+	3009.52i	0.378413	+	0.274933i
$494$	−2452.84			−0.223397
$495$	3619.54	+	532.968i	0.328659	+	0.0483942i
$496$	−4153.02			−0.375960
$497$	−13177.5	−	9573.98i	−1.18931	−	0.864088i
$498$	−173.008	+	532.462i	−0.0155676	+	0.0479121i
$499$	324.409	+	998.427i	0.0291033	+	0.0895706i	0.964553	−	0.263889i	$-0.0850052\pi$
$499$	324.409	+	998.427i	0.0291033	+	0.0895706i	−0.935450	+	0.353459i	$0.885005\pi$
$500$	8600.65	−	6248.74i	0.769266	−	0.558904i
$501$	−8378.14	+	6087.07i	−0.747121	+	0.542815i
$502$	−579.922	−	1784.82i	−0.0515601	−	0.158686i
$503$	−2970.82	+	9143.24i	−0.263345	+	0.810491i	0.728726	+	0.684806i	$0.240113\pi$
$503$	−2970.82	+	9143.24i	−0.263345	+	0.810491i	−0.992070	+	0.125685i	$0.959887\pi$
$504$	−1918.40	−	1393.80i	−0.169549	−	0.123184i
$505$	8562.27			0.754487
$506$	−2768.60	−	2708.98i	−0.243240	−	0.238002i
$507$	2001.79			0.175350
$508$	−14845.4	−	10785.8i	−1.29657	−	0.942017i
$509$	482.077	−	1483.68i	0.0419798	−	0.129200i	−0.927870	−	0.372904i	$-0.878362\pi$
$509$	482.077	−	1483.68i	0.0419798	−	0.129200i	0.969850	+	0.243703i	$0.0783622\pi$
$510$	156.527	+	481.739i	0.0135904	+	0.0418270i
$511$	6549.96	−	4758.83i	0.567032	−	0.411973i
$512$	8596.63	−	6245.82i	0.742033	−	0.539119i
$513$	−591.075	−	1819.14i	−0.0508705	−	0.156563i
$514$	−628.449	+	1934.17i	−0.0539294	+	0.165978i
$515$	10332.3	+	7506.89i	0.884073	+	0.642317i
$516$	7593.16			0.647811
$517$	6378.06	−	12861.8i	0.542566	−	1.09412i
$518$	4791.15			0.406392
$519$	1802.69	+	1309.73i	0.152465	+	0.110773i
$520$	1857.56	−	5716.98i	0.156653	−	0.482127i
$521$	3668.79	+	11291.4i	0.308507	+	0.949488i	0.978345	+	0.206981i	$0.0663637\pi$
$521$	3668.79	+	11291.4i	0.308507	+	0.949488i	−0.669838	+	0.742508i	$0.733636\pi$
$522$	−1029.69	+	748.113i	−0.0863376	+	0.0627280i
$523$	−7071.20	+	5137.53i	−0.591209	+	0.429538i	−0.842748	−	0.538309i	$-0.819063\pi$
$523$	−7071.20	+	5137.53i	−0.591209	+	0.429538i	0.251539	+	0.967847i	$0.419063\pi$
$524$	−4400.63	−	13543.7i	−0.366875	−	1.12912i
$525$	−20.5118	+	63.1289i	−0.00170516	+	0.00524795i
$526$	307.696	+	223.554i	0.0255060	+	0.0185312i
$527$	−1797.06			−0.148541
$528$	−990.418	−	5841.12i	−0.0816334	−	0.481443i
$529$	14766.3			1.21363
$530$	−886.858	−	644.340i	−0.0726843	−	0.0528082i
$531$	−2133.24	+	6565.44i	−0.174340	+	0.536565i
$532$	4338.08	+	13351.2i	0.353533	+	1.08806i
$533$	210.231	−	152.742i	0.0170846	−	0.0124127i
$534$	289.715	−	210.490i	0.0234779	−	0.0170577i
$535$	2573.25	+	7919.64i	0.207946	+	0.639992i
$536$	317.946	−	978.538i	0.0256216	−	0.0788552i
$537$	5702.90	+	4143.40i	0.458284	+	0.332963i
$538$	1042.06			0.0835066
$539$	10995.9	−	5754.25i	0.878712	−	0.459839i
$540$	2280.85			0.181763
$541$	7589.57	+	5514.15i	0.603145	+	0.438210i	0.846994	−	0.531603i	$-0.178410\pi$
$541$	7589.57	+	5514.15i	0.603145	+	0.438210i	−0.243849	+	0.969813i	$0.578410\pi$
$542$	453.417	−	1395.48i	0.0359335	−	0.110592i
$543$	−2615.15	−	8048.61i	−0.206679	−	0.636094i
$544$	2191.73	−	1592.38i	0.172738	−	0.125502i
$545$	−6696.89	+	4865.58i	−0.526355	+	0.382419i
$546$	838.961	+	2582.06i	0.0657586	+	0.202384i
$547$	74.4993	−	229.285i	0.00582333	−	0.0179224i	−0.948103	−	0.317964i	$-0.897001\pi$
$547$	74.4993	−	229.285i	0.00582333	−	0.0179224i	0.953926	+	0.300042i	$0.0970007\pi$
$548$	−3265.83	−	2372.77i	−0.254579	−	0.184963i
$549$	−3201.01			−0.248845
$550$	17.7023	−	9.26382i	0.00137242	−	0.000718201i
$551$	15485.9			1.19731
$552$	−4015.11	−	2917.15i	−0.309592	−	0.224931i
$553$	−5164.40	+	15894.4i	−0.397129	+	1.22224i
$554$	971.240	+	2989.17i	0.0744838	+	0.229238i
$555$	−7662.42	+	5567.08i	−0.586039	+	0.425782i
$556$	−10246.1	+	7444.24i	−0.781533	+	0.567817i
$557$	−2796.81	−	8607.70i	−0.212755	−	0.654793i	−0.999305	−	0.0372668i	$-0.988135\pi$
$557$	−2796.81	−	8607.70i	−0.212755	−	0.654793i	0.786550	−	0.617526i	$-0.211865\pi$
$558$	138.043	−	424.852i	0.0104728	−	0.0322320i
$559$	−14454.8	−	10502.0i	−1.09369	−	0.794613i
$560$	−15764.7			−1.18961
$561$	−428.565	−	2527.52i	−0.0322532	−	0.190217i
$562$	3157.19			0.236971
$563$	−17478.7	−	12699.0i	−1.30842	−	0.950622i	−0.308420	−	0.951250i	$-0.599800\pi$
$563$	−17478.7	−	12699.0i	−1.30842	−	0.950622i	−1.00000		0.000627893i	$0.999800\pi$
$564$	2765.74	−	8512.08i	0.206487	−	0.635502i
$565$	−6259.78	−	19265.6i	−0.466108	−	1.43453i
$566$	3491.47	−	2536.70i	0.259289	−	0.188384i
$567$	−1712.81	+	1244.43i	−0.126863	+	0.0921711i
$568$	1941.18	+	5974.33i	0.143398	+	0.441333i
$569$	902.599	−	2777.92i	0.0665008	−	0.204668i	−0.912285	−	0.409557i	$-0.865683\pi$
$569$	902.599	−	2777.92i	0.0665008	−	0.204668i	0.978785	+	0.204889i	$0.0656833\pi$
$570$	1239.43	+	900.496i	0.0910769	+	0.0661713i
$571$	17676.0			1.29548			0.647741	−	0.761861i	$-0.275714\pi$
$571$	17676.0			1.29548			0.647741	+	0.761861i	$0.275714\pi$
$572$	−6576.47	+	13261.9i	−0.480727	+	0.969418i
$573$	−11115.4			−0.810385
$574$	66.4235	+	48.2595i	0.00483008	+	0.00350926i
$575$	−42.9301	+	132.125i	−0.00311358	+	0.00958262i
$576$	−996.253	−	3066.15i	−0.0720669	−	0.221799i
$577$	−3392.48	+	2464.78i	−0.244767	+	0.177834i	−0.703404	−	0.710790i	$-0.748338\pi$
$577$	−3392.48	+	2464.78i	−0.244767	+	0.177834i	0.458637	+	0.888624i	$0.348338\pi$
$578$	−2284.26	+	1659.61i	−0.164382	+	0.119430i
$579$	2296.83	+	7068.91i	0.164858	+	0.507382i
$580$	−5706.30	+	17562.2i	−0.408519	+	1.25729i
$581$	−6099.84	−	4431.79i	−0.435566	−	0.316457i
$582$	−1236.74			−0.0880831
$583$	3965.52	+	3880.14i	0.281707	+	0.275641i
$584$	−3122.41			−0.221244
$585$	−4341.96	−	3154.62i	−0.306868	−	0.222953i
$586$	−1083.91	+	3335.95i	−0.0764097	+	0.235165i
$587$	8165.92	+	25132.1i	0.574180	+	1.76714i	0.638955	+	0.769245i	$0.279367\pi$
$587$	8165.92	+	25132.1i	0.574180	+	1.76714i	−0.0647745	+	0.997900i	$0.520633\pi$
$588$	6259.40	−	4547.72i	0.439002	−	0.318954i
$589$	−4397.21	+	3194.76i	−0.307612	+	0.223493i
$590$	−1708.61	−	5258.56i	−0.119224	−	0.366935i
$591$	1588.11	−	4887.69i	0.110535	−	0.340191i
$592$	12408.1	+	9015.03i	0.861437	+	0.625871i
$593$	−13972.0			−0.967555			−0.483778	−	0.875191i	$-0.660736\pi$
$593$	−13972.0			−0.967555			−0.483778	+	0.875191i	$0.660736\pi$
$594$	630.465	+	92.8344i	0.0435493	+	0.00641253i
$595$	−6821.56			−0.470011
$596$	18443.0	+	13399.6i	1.26754	+	0.920924i
$597$	765.602	−	2356.28i	0.0524858	−	0.161535i
$598$	1755.90	+	5404.10i	0.120074	+	0.369549i
$599$	−1460.87	+	1061.38i	−0.0996486	+	0.0723989i	−0.636494	−	0.771282i	$-0.719616\pi$
$599$	−1460.87	+	1061.38i	−0.0996486	+	0.0723989i	0.536845	+	0.843681i	$0.319616\pi$
$600$	20.7104	−	15.0470i	0.00140916	−	0.00102382i
$601$	7977.94	+	24553.6i	0.541476	+	1.66649i	0.729224	+	0.684275i	$0.239881\pi$
$601$	7977.94	+	24553.6i	0.541476	+	1.66649i	−0.187748	+	0.982217i	$0.560119\pi$
$602$	1744.46	−	5368.91i	0.118105	−	0.363489i
$603$	−743.185	−	539.956i	−0.0501905	−	0.0364655i
$604$	18819.0			1.26777
$605$	14001.6	−	4888.78i	0.940904	−	0.328524i
$606$	1491.41			0.0999742
$607$	−21298.4	−	15474.2i	−1.42418	−	1.03473i	−0.991064	−	0.133388i	$-0.957414\pi$
$607$	−21298.4	−	15474.2i	−1.42418	−	1.03473i	−0.433115	−	0.901339i	$-0.642586\pi$
$608$	2532.03	−	7792.78i	0.168894	−	0.519801i
$609$	−5296.74	−	16301.7i	−0.352438	−	1.08469i
$610$	2074.19	−	1506.98i	0.137674	−	0.100026i
$611$	−17038.0	+	12378.8i	−1.12813	+	0.819631i
$612$	−493.875	−	1519.99i	−0.0326204	−	0.100395i
$613$	5780.29	−	17789.9i	0.380855	−	1.17215i	−0.558589	−	0.829445i	$-0.688657\pi$
$613$	5780.29	−	17789.9i	0.380855	−	1.17215i	0.939443	−	0.342705i	$-0.111343\pi$
$614$	2498.97	+	1815.61i	0.164251	+	0.119336i
$615$	−162.306			−0.0106419
$616$	−9509.79	−	1400.29i	−0.622014	−	0.0915900i
$617$	−14282.3			−0.931903			−0.465952	−	0.884810i	$-0.654288\pi$
$617$	−14282.3			−0.931903			−0.465952	+	0.884810i	$0.654288\pi$
$618$	1799.73	+	1307.58i	0.117145	+	0.0851109i
$619$	−2242.48	+	6901.65i	−0.145611	+	0.448143i	−0.997089	−	0.0762464i	$-0.975706\pi$
$619$	−2242.48	+	6901.65i	−0.145611	+	0.448143i	0.851478	+	0.524390i	$0.175706\pi$
$620$	−2002.80	−	6163.99i	−0.129733	−	0.399277i
$621$	−3584.81	+	2604.52i	−0.231648	+	0.168302i
$622$	463.184	−	336.523i	0.0298585	−	0.0216935i
$623$	1490.30	+	4586.67i	0.0958389	+	0.294962i
$624$	−2685.66	+	8265.60i	−0.172295	+	0.530271i
$625$	12554.7	+	9121.53i	0.803501	+	0.583778i
$626$	−4303.43			−0.274760
$627$	−5542.00	−	5422.67i	−0.352992	−	0.345392i
$628$	−23931.3			−1.52064
$629$	5369.14	+	3900.91i	0.340352	+	0.247280i
$630$	524.006	−	1612.72i	0.0331379	−	0.101988i
$631$	−46.7826	−	143.982i	−0.00295149	−	0.00908374i	0.949570	−	0.313555i	$-0.101520\pi$
$631$	−46.7826	−	143.982i	−0.00295149	−	0.00908374i	−0.952521	+	0.304472i	$0.901520\pi$
$632$	5214.39	−	3788.48i	0.328192	−	0.238446i
$633$	6800.78	−	4941.05i	0.427025	−	0.310252i
$634$	308.023	+	947.998i	0.0192952	+	0.0593846i
$635$	8333.82	−	25648.9i	0.520815	−	1.60290i
$636$	2798.23	+	2033.03i	0.174461	+	0.126753i
$637$	−18205.7			−1.13239
$638$	−2292.13	+	4622.23i	−0.142236	+	0.286827i
$639$	5608.55			0.347216
$640$	10430.0	+	7577.86i	0.644192	+	0.468033i
$641$	6323.77	−	19462.6i	0.389663	−	1.19926i	−0.543378	−	0.839488i	$-0.682855\pi$
$641$	6323.77	−	19462.6i	0.389663	−	1.19926i	0.933041	−	0.359771i	$-0.117145\pi$
$642$	448.218	+	1379.47i	0.0275541	+	0.0848029i
$643$	−1007.21	+	731.783i	−0.0617739	+	0.0448813i	−0.618244	−	0.785987i	$-0.712155\pi$
$643$	−1007.21	+	731.783i	−0.0617739	+	0.0448813i	0.556470	+	0.830868i	$0.312155\pi$
$644$	26310.0	−	19115.3i	1.60987	−	1.16964i
$645$	3448.51	+	10613.4i	0.210519	+	0.647911i
$646$	331.729	−	1020.96i	0.0202039	−	0.0621811i
$647$	272.538	+	198.010i	0.0165604	+	0.0120318i	0.596035	−	0.802959i	$-0.296742\pi$
$647$	272.538	+	198.010i	0.0165604	+	0.0120318i	−0.579474	+	0.814991i	$0.696742\pi$
$648$	816.506			0.0494991
$649$	4678.13	+	27589.8i	0.282947	+	1.66871i
$650$	−29.3095			−0.00176863
$651$	4867.07	+	3536.13i	0.293019	+	0.212891i
$652$	1933.19	−	5949.76i	0.116119	−	0.357378i
$653$	−4353.14	−	13397.6i	−0.260875	−	0.802892i	−0.992615	−	0.121308i	$-0.961291\pi$
$653$	−4353.14	−	13397.6i	−0.260875	−	0.802892i	0.731739	−	0.681584i	$-0.238709\pi$
$654$	−1166.49	+	847.505i	−0.0697453	+	0.0506729i
$655$	16932.3	−	12302.0i	1.01008	−	0.733864i
$656$	81.2186	+	249.965i	0.00483393	+	0.0148773i
$657$	−861.471	+	2651.34i	−0.0511555	+	0.157441i
$658$	−5383.25	−	3911.16i	−0.318938	−	0.231722i
$659$	4111.66			0.243046			0.121523	−	0.992589i	$-0.461222\pi$
$659$	4111.66			0.243046			0.121523	+	0.992589i	$0.461222\pi$
$660$	8191.87	−	4286.89i	0.483134	−	0.252829i
$661$	22986.9			1.35263			0.676314	−	0.736614i	$-0.263576\pi$
$661$	22986.9			1.35263			0.676314	+	0.736614i	$0.263576\pi$
$662$	1870.14	+	1358.73i	0.109796	+	0.0797715i
$663$	−1162.11	+	3576.62i	−0.0680736	+	0.209509i
$664$	898.570	+	2765.52i	0.0525170	+	0.161631i
$665$	−16691.6	+	12127.2i	−0.973344	+	0.707176i
$666$	−1334.67	+	969.695i	−0.0776538	+	0.0564188i
$667$	−11085.8	−	34118.5i	−0.643543	−	1.98062i
$668$	−8087.31	+	24890.2i	−0.468424	+	1.44166i
$669$	−5358.47	−	3893.16i	−0.309672	−	0.224990i
$670$	735.771			0.0424258
$671$	−11496.7	+	6016.35i	−0.661439	+	0.346138i
$672$	−9069.36			−0.520622
$673$	13127.9	+	9538.01i	0.751924	+	0.546305i	0.896423	−	0.443200i	$-0.146157\pi$
$673$	13127.9	+	9538.01i	0.751924	+	0.546305i	−0.144499	+	0.989505i	$0.546157\pi$
$674$	−235.306	+	724.198i	−0.0134476	+	0.0413873i
$675$	−7.06287	−	21.7373i	−0.000402741	−	0.00123951i
$676$	4092.67	−	2973.50i	0.232856	−	0.169180i
$677$	10994.8	−	7988.20i	0.624173	−	0.453488i	−0.230204	−	0.973142i	$-0.573939\pi$
$677$	10994.8	−	7988.20i	0.624173	−	0.453488i	0.854377	+	0.519654i	$0.173939\pi$
$678$	−1090.35	−	3355.76i	−0.0617622	−	0.190084i
$679$	5146.80	−	15840.2i	0.290893	−	0.895276i
$680$	2128.39	+	1546.36i	0.120029	+	0.0872063i
$681$	−7122.41			−0.400781
$682$	−302.723	−	1785.35i	−0.0169969	−	0.100241i
$683$	10864.9			0.608688			0.304344	−	0.952562i	$-0.401563\pi$
$683$	10864.9			0.608688			0.304344	+	0.952562i	$0.401563\pi$
$684$	−3910.65	−	2841.26i	−0.218608	−	0.158828i
$685$	1833.35	−	5642.47i	0.102261	−	0.314726i
$686$	14.7699	+	45.4570i	0.000822036	+	0.00252997i
$687$	−1038.84	+	754.760i	−0.0576916	+	0.0419154i
$688$	14620.0	−	10622.0i	0.810147	−	0.588606i
$689$	−2515.01	−	7740.41i	−0.139063	−	0.427991i
$690$	1096.71	−	3375.34i	0.0605090	−	0.186228i
$691$	−9632.06	−	6998.10i	−0.530276	−	0.385268i	0.290185	−	0.956971i	$-0.406283\pi$
$691$	−9632.06	−	6998.10i	−0.530276	−	0.385268i	−0.820461	+	0.571702i	$0.806283\pi$
$692$	5631.14			0.309341
$693$	−3812.78	+	7688.72i	−0.208998	+	0.421458i
$694$	−3697.58			−0.202245
$695$	−15058.6	−	10940.7i	−0.821880	−	0.597131i
$696$	−2042.76	+	6286.97i	−0.111251	+	0.342395i
$697$	35.1442	+	108.163i	0.00190987	+	0.00587799i
$698$	−4815.67	+	3498.79i	−0.261140	+	0.189729i
$699$	6714.66	−	4878.49i	0.363336	−	0.263979i
$700$	51.8366	+	159.537i	0.00279891	+	0.00861417i
$701$	−9510.30	+	29269.7i	−0.512410	+	1.57703i	0.275537	+	0.961291i	$0.411144\pi$
$701$	−9510.30	+	29269.7i	−0.512410	+	1.57703i	−0.787946	+	0.615744i	$0.788856\pi$
$702$	−756.300	−	549.484i	−0.0406620	−	0.0295426i
$703$	20072.6			1.07689
$704$	−9341.02	−	9139.89i	−0.500075	−	0.489308i
$705$	13153.9			0.702704
$706$	442.151	+	321.241i	0.0235702	+	0.0171247i
$707$	−6206.65	+	19102.1i	−0.330163	+	1.01614i
$708$	5391.03	+	16591.9i	0.286169	+	0.880736i
$709$	−18051.0	+	13114.8i	−0.956163	+	0.694693i	−0.952257	−	0.305299i	$-0.901244\pi$
$709$	−18051.0	+	13114.8i	−0.956163	+	0.694693i	−0.00390691	+	0.999992i	$0.501244\pi$
$710$	−3634.22	+	2640.42i	−0.192099	+	0.139568i
$711$	−1778.27	−	5472.94i	−0.0937977	−	0.288680i
$712$	574.755	−	1768.91i	0.0302526	−	0.0931080i
$713$	10186.5	+	7400.93i	0.535046	+	0.388733i
$714$	−1188.21			−0.0622794
$715$	−21523.7	−	3169.31i	−1.12579	−	0.165770i
$716$	17814.3			0.929823
$717$	8372.80	+	6083.20i	0.436106	+	0.316850i
$718$	1848.77	−	5689.91i	0.0960937	−	0.295746i
$719$	−288.595	−	888.205i	−0.0149691	−	0.0460702i	0.943293	−	0.331961i	$-0.107710\pi$
$719$	−288.595	−	888.205i	−0.0149691	−	0.0460702i	−0.958262	+	0.285891i	$0.907710\pi$
$720$	4391.57	−	3190.67i	0.227312	−	0.165151i
$721$	−24237.3	+	17609.5i	−1.25194	+	0.909585i
$722$	367.904	+	1132.29i	0.0189639	+	0.0583650i
$723$	1347.64	−	4147.62i	0.0693214	−	0.213349i
$724$	−17302.3	−	12570.9i	−0.888170	−	0.645294i
$725$	185.044			0.00947912
$726$	2438.86	−	851.546i	0.124676	−	0.0435315i
$727$	2130.84			0.108705			0.0543526	−	0.998522i	$-0.482691\pi$
$727$	2130.84			0.108705			0.0543526	+	0.998522i	$0.482691\pi$
$728$	11407.9	+	8288.29i	0.580774	+	0.421957i
$729$	225.273	−	693.320i	0.0114451	−	0.0352243i
$730$	−689.992	−	2123.58i	−0.0349832	−	0.107667i
$731$	6326.23	−	4596.27i	0.320087	−	0.232557i
$732$	−6544.50	+	4754.86i	−0.330453	+	0.240088i
$733$	−10219.1	−	31451.1i	−0.514939	−	1.58482i	−0.783393	−	0.621527i	$-0.786513\pi$
$733$	−10219.1	−	31451.1i	−0.514939	−	1.58482i	0.268454	−	0.963293i	$-0.413487\pi$
$734$	−648.139	+	1994.77i	−0.0325930	+	0.100311i
$735$	9199.38	+	6683.74i	0.461666	+	0.335420i
$736$	−18981.7			−0.950644
$737$	−3684.07	−	542.471i	−0.184131	−	0.0271128i
$738$	−28.2710			−0.00141012
$739$	−3698.98	−	2687.47i	−0.184126	−	0.133775i	0.491904	−	0.870649i	$-0.336301\pi$
$739$	−3698.98	−	2687.47i	−0.184126	−	0.133775i	−0.676030	+	0.736874i	$0.736301\pi$
$740$	−7396.44	+	22763.9i	−0.367431	+	1.13083i
$741$	3514.84	+	10817.6i	0.174252	+	0.536294i
$742$	2080.37	−	1511.48i	0.102928	−	0.0747817i
$743$	14937.1	−	10852.5i	0.737537	−	0.535852i	−0.154402	−	0.988008i	$-0.549345\pi$
$743$	14937.1	−	10852.5i	0.737537	−	0.535852i	0.891939	+	0.452156i	$0.149345\pi$
$744$	−716.970	−	2206.61i	−0.0353298	−	0.108734i
$745$	−10353.4	+	31864.5i	−0.509153	+	1.56701i
$746$	−1737.37	−	1262.28i	−0.0852678	−	0.0619507i
$747$	2596.20			0.127162
$748$	−4630.64	−	4530.94i	−0.226354	−	0.221481i
$749$	−19533.7			−0.952933
$750$	2201.74	+	1599.66i	0.107195	+	0.0778816i
$751$	−8719.88	+	26837.0i	−0.423692	+	1.30399i	0.480549	+	0.876968i	$0.340438\pi$
$751$	−8719.88	+	26837.0i	−0.423692	+	1.30399i	−0.904241	+	0.427023i	$0.859562\pi$
$752$	−6582.31	−	20258.3i	−0.319192	−	0.982371i
$753$	−7040.44	+	5115.18i	−0.340728	+	0.247553i
$754$	6123.08	−	4448.68i	0.295742	−	0.214869i
$755$	8546.83	+	26304.4i	0.411988	+	1.26797i
$756$	−1653.35	+	5088.49i	−0.0795393	+	0.244797i
$757$	−7135.09	−	5183.95i	−0.342575	−	0.248895i	0.403173	−	0.915124i	$-0.367907\pi$
$757$	−7135.09	−	5183.95i	−0.342575	−	0.248895i	−0.745747	+	0.666229i	$0.767907\pi$
$758$	−574.799			−0.0275431
$759$	−7979.93	+	16092.1i	−0.381625	+	0.769571i
$760$	7957.01			0.379778
$761$	23670.8	+	17197.8i	1.12755	+	0.819212i	0.985336	−	0.170624i	$-0.0545785\pi$
$761$	23670.8	+	17197.8i	1.12755	+	0.819212i	0.142212	+	0.989836i	$0.454579\pi$
$762$	1451.62	−	4467.62i	0.0690112	−	0.212395i
$763$	−6000.45	−	18467.5i	−0.284706	−	0.876236i
$764$	−22725.5	+	16511.0i	−1.07615	+	0.781869i
$765$	1900.28	−	1380.64i	0.0898103	−	0.0652510i
$766$	673.772	+	2073.66i	0.0317811	+	0.0978123i
$767$	12685.4	−	39041.6i	0.597188	−	1.83795i
$768$	−5138.52	−	3733.36i	−0.241433	−	0.175411i
$769$	−19322.0			−0.906074			−0.453037	−	0.891492i	$-0.649659\pi$
$769$	−19322.0			−0.906074			−0.453037	+	0.891492i	$0.649659\pi$
$770$	−1149.13	−	6777.12i	−0.0537814	−	0.317182i
$771$	9430.68			0.440516
$772$	15196.2	+	11040.7i	0.708451	+	0.514720i
$773$	−5164.93	+	15896.0i	−0.240323	+	0.739638i	0.756048	+	0.654517i	$0.227128\pi$
$773$	−5164.93	+	15896.0i	−0.240323	+	0.739638i	−0.996371	+	0.0851216i	$0.972872\pi$
$774$	600.674	+	1848.69i	0.0278951	+	0.0858523i
$775$	−52.5431	+	38.1748i	−0.00243536	+	0.00176939i
$776$	−5196.63	+	3775.57i	−0.240397	+	0.174659i
$777$	−6865.58	−	21130.1i	−0.316990	−	0.975595i
$778$	−959.313	+	2952.46i	−0.0442070	+	0.136055i
$779$	278.283	+	202.184i	0.0127991	+	0.00929911i
$780$	−13563.1			−0.622613
$781$	20143.6	−	10541.4i	0.922914	−	0.482970i
$782$	−2486.85			−0.113721
$783$	4774.86	+	3469.14i	0.217931	+	0.158336i
$784$	5690.14	−	17512.5i	0.259209	−	0.797762i
$785$	−10868.6	−	33450.2i	−0.494163	−	1.52088i
$786$	2949.34	−	2142.82i	0.133841	−	0.0972415i
$787$	14855.6	−	10793.2i	0.672865	−	0.488865i	−0.198118	−	0.980178i	$-0.563483\pi$
$787$	14855.6	−	10793.2i	0.672865	−	0.488865i	0.870983	+	0.491313i	$0.163483\pi$
$788$	−4013.39	−	12352.0i	−0.181436	−	0.558401i
$789$	545.006	−	1677.36i	0.0245916	−	0.0756850i
$790$	3728.85	+	2709.17i	0.167932	+	0.122010i
$791$	47518.5			2.13598
$792$	2932.55	−	1534.64i	0.131570	−	0.0688522i
$793$	19034.9			0.852396
$794$	1863.31	+	1353.78i	0.0832828	+	0.0605085i
$795$	−1570.85	+	4834.57i	−0.0700783	+	0.215679i
$796$	−1934.80	−	5954.69i	−0.0861520	−	0.265149i
$797$	10888.0	−	7910.57i	0.483904	−	0.351577i	−0.318931	−	0.947778i	$-0.603324\pi$
$797$	10888.0	−	7910.57i	0.483904	−	0.351577i	0.802835	+	0.596201i	$0.203324\pi$
$798$	−2907.41	+	2112.36i	−0.128974	+	0.0937051i
$799$	−2848.24	−	8765.98i	−0.126112	−	0.388133i
$800$	30.2557	−	93.1176i	0.00133713	−	0.00411525i
$801$	−1343.46	−	976.084i	−0.0592622	−	0.0430565i
$802$	−2340.26			−0.103039
$803$	1889.18	+	11141.7i	0.0830232	+	0.489640i
$804$	−2321.51			−0.101833
$805$	38667.6	+	28093.6i	1.69299	+	1.23003i
$806$	−820.877	+	2526.40i	−0.0358736	+	0.110408i
$807$	−1493.25	−	4595.74i	−0.0651361	−	0.200468i
$808$	6266.74	−	4553.05i	0.272850	−	0.198237i
$809$	−17140.3	+	12453.2i	−0.744898	+	0.541200i	−0.894241	−	0.447585i	$-0.852284\pi$
$809$	−17140.3	+	12453.2i	−0.744898	+	0.541200i	0.149343	+	0.988785i	$0.452284\pi$
$810$	180.432	+	555.312i	0.00782682	+	0.0240885i
$811$	4326.78	−	13316.5i	0.187341	−	0.576578i	−0.812639	−	0.582767i	$-0.801970\pi$
$811$	4326.78	−	13316.5i	0.187341	−	0.576578i	0.999981	+	0.00618924i	$0.00197011\pi$
$812$	−35044.2	−	25461.1i	−1.51454	−	1.10038i
$813$	−6804.10			−0.293518
$814$	−2971.03	+	5991.28i	−0.127930	+	0.257978i
$815$	9194.32			0.395169
$816$	−3077.22	−	2235.73i	−0.132015	−	0.0959145i
$817$	7308.47	−	22493.2i	0.312963	−	0.963202i
$818$	−34.0321	−	104.740i	−0.00145465	−	0.00447696i
$819$	10185.3	−	7400.02i	0.434556	−	0.315724i
$820$	−331.836	+	241.093i	−0.0141320	+	0.0102675i
$821$	10375.0	+	31931.0i	0.441036	+	1.35737i	0.886773	+	0.462205i	$0.152941\pi$
$821$	10375.0	+	31931.0i	0.441036	+	1.35737i	−0.445738	+	0.895164i	$0.647059\pi$
$822$	319.340	−	982.827i	0.0135502	−	0.0417032i
$823$	12079.5	+	8776.26i	0.511621	+	0.371715i	0.813438	−	0.581651i	$-0.197593\pi$
$823$	12079.5	+	8776.26i	0.511621	+	0.371715i	−0.301817	+	0.953366i	$0.597593\pi$
$824$	11554.1			0.488479
$825$	−66.2225	−	64.7967i	−0.00279463	−	0.00273446i
$826$	12970.2			0.546357
$827$	−7429.44	−	5397.80i	−0.312390	−	0.226965i	0.420531	−	0.907278i	$-0.361844\pi$
$827$	−7429.44	−	5397.80i	−0.312390	−	0.226965i	−0.732921	+	0.680313i	$0.761844\pi$
$828$	−3460.37	+	10649.9i	−0.145237	+	0.446993i
$829$	5484.93	+	16880.9i	0.229794	+	0.707234i	0.997769	+	0.0667543i	$0.0212644\pi$
$829$	5484.93	+	16880.9i	0.229794	+	0.707234i	−0.767975	+	0.640480i	$0.778736\pi$
$830$	−1682.28	+	1222.25i	−0.0703528	+	0.0511143i
$831$	11791.2	−	8566.79i	0.492216	−	0.357616i
$832$	5924.25	+	18233.0i	0.246859	+	0.759753i
$833$	2462.19	−	7577.84i	0.102413	−	0.315194i
$834$	−2622.97	−	1905.70i	−0.108904	−	0.0791235i
$835$	−38463.4			−1.59411
$836$	−19385.7	−	2854.49i	−0.801994	−	0.118092i
$837$	−2071.51			−0.0855458
$838$	−8912.89	−	6475.59i	−0.367411	−	0.266940i
$839$	3114.36	−	9585.01i	0.128152	−	0.394412i	−0.866310	−	0.499507i	$-0.833515\pi$
$839$	3114.36	−	9585.01i	0.128152	−	0.394412i	0.994462	+	0.105095i	$0.0335147\pi$
$840$	−2721.59	−	8376.20i	−0.111790	−	0.344055i
$841$	−18926.7	+	13751.0i	−0.776033	+	0.563821i
$842$	5585.65	−	4058.21i	0.228615	−	0.166099i
$843$	−4524.16	−	13923.9i	−0.184840	−	0.568880i
$844$	6564.70	−	20204.1i	0.267733	−	0.823997i
$845$	6014.97	+	4370.13i	0.244877	+	0.177914i
$846$	2291.20			0.0931126
$847$	757.136	+	34780.9i	0.0307149	+	1.41096i
$848$	8231.74			0.333348
$849$	−16190.6	−	11763.2i	−0.654488	−	0.475514i
$850$	3.96390	−	12.1996i	0.000159954	−	0.000492287i
$851$	−14369.3	−	44224.1i	−0.578816	−	1.78141i
$852$	11466.7	−	8331.08i	0.461085	−	0.334998i
$853$	5770.57	−	4192.57i	0.231630	−	0.168289i	−0.465916	−	0.884829i	$-0.654275\pi$
$853$	5770.57	−	4192.57i	0.231630	−	0.168289i	0.697546	+	0.716540i	$0.254275\pi$
$854$	1858.48	+	5719.82i	0.0744684	+	0.229190i
$855$	2195.33	−	6756.54i	0.0878115	−	0.270256i
$856$	6094.69	+	4428.05i	0.243355	+	0.176808i
$857$	11652.5			0.464458			0.232229	−	0.972661i	$-0.425398\pi$
$857$	11652.5			0.464458			0.232229	+	0.972661i	$0.425398\pi$
$858$	−3749.08	−	552.043i	−0.149174	−	0.0219655i
$859$	−38407.9			−1.52557			−0.762783	−	0.646655i	$-0.776167\pi$
$859$	−38407.9			−1.52557			−0.762783	+	0.646655i	$0.776167\pi$
$860$	22815.9	+	16576.8i	0.904671	+	0.657282i
$861$	117.653	−	362.098i	0.00465690	−	0.0143325i
$862$	−3445.91	−	10605.4i	−0.136158	−	0.419051i
$863$	1891.32	−	1374.12i	0.0746017	−	0.0542013i	−0.549859	−	0.835257i	$-0.685319\pi$
$863$	1891.32	−	1374.12i	0.0746017	−	0.0542013i	0.624461	+	0.781056i	$0.285319\pi$
$864$	2526.45	−	1835.58i	0.0994811	−	0.0722773i
$865$	2557.44	+	7870.98i	0.100527	+	0.309389i
$866$	1348.09	−	4149.00i	0.0528984	−	0.162805i
$867$	10592.6	+	7695.94i	0.414927	+	0.301462i
$868$	15203.4			0.594514
$869$	−16673.3	−	16314.3i	−0.650866	−	0.636851i
$870$	−4727.23			−0.184216
$871$	4419.38	+	3210.87i	0.171923	+	0.124909i
$872$	−2314.16	+	7122.25i	−0.0898707	+	0.276594i
$873$	1772.21	+	5454.29i	0.0687058	+	0.211455i
$874$	−6085.05	+	4421.05i	−0.235503	+	0.171103i
$875$	−29651.3	+	21542.9i	−1.14560	+	0.832325i
$876$	2177.07	+	6700.34i	0.0839685	+	0.258428i
$877$	−6096.23	+	18762.3i	−0.234726	+	0.722413i	0.762431	+	0.647069i	$0.224006\pi$
$877$	−6096.23	+	18762.3i	−0.234726	+	0.722413i	−0.997158	+	0.0753442i	$0.975994\pi$
$878$	−5450.81	−	3960.24i	−0.209517	−	0.152223i
$879$	16265.5			0.624144
$880$	9775.83	−	19713.6i	0.374481	−	0.755165i
$881$	10669.9			0.408036			0.204018	−	0.978967i	$-0.434600\pi$
$881$	10669.9			0.408036			0.204018	+	0.978967i	$0.434600\pi$
$882$	1602.38	+	1164.20i	0.0611736	+	0.0444452i
$883$	−9947.39	+	30614.9i	−0.379112	+	1.16679i	0.561549	+	0.827443i	$0.310205\pi$
$883$	−9947.39	+	30614.9i	−0.379112	+	1.16679i	−0.940662	+	0.339345i	$0.889795\pi$
$884$	2936.84	+	9038.67i	0.111738	+	0.343895i
$885$	−20743.1	+	15070.7i	−0.787877	+	0.572426i
$886$	3173.13	−	2305.41i	0.120320	−	0.0874174i
$887$	193.766	+	596.350i	0.00733486	+	0.0225744i	0.954657	−	0.297708i	$-0.0962222\pi$
$887$	193.766	+	596.350i	0.00733486	+	0.0225744i	−0.947322	+	0.320282i	$0.896222\pi$
$888$	−2647.80	+	8149.10i	−0.100061	+	0.307957i
$889$	51180.6	+	37184.9i	1.93087	+	1.40286i
$890$	1330.06			0.0500941
$891$	−494.017	−	2913.53i	−0.0185749	−	0.109547i
$892$	−16738.4			−0.628301
$893$	−22553.2	−	16385.9i	−0.845146	−	0.614035i
$894$	−1803.40	+	5550.28i	−0.0674660	+	0.207639i
$895$	8090.56	+	24900.2i	0.302165	+	0.929968i
$896$	−24466.5	+	17775.9i	−0.912241	+	0.662782i
$897$	21317.2	−	15487.8i	0.793489	−	0.576504i
$898$	1883.61	+	5797.15i	0.0699964	+	0.215427i
$899$	5182.57	−	15950.3i	0.192267	−	0.591738i
$900$	−46.7292	−	33.9508i	−0.00173071	−	0.00125744i
$901$	3561.97			0.131705
$902$	−101.538	+	53.1358i	−0.00374816	+	0.00196145i
$903$	−26177.9			−0.964724
$904$	−14826.2	−	10771.9i	−0.545477	−	0.396313i
$905$	9713.04	−	29893.7i	0.356765	−	1.09801i
$906$	1488.72	+	4581.81i	0.0545909	+	0.168014i
$907$	−37985.9	+	27598.4i	−1.39063	+	1.01035i	−0.394835	+	0.918752i	$0.629198\pi$
$907$	−37985.9	+	27598.4i	−1.39063	+	1.01035i	−0.995796	+	0.0916008i	$0.970802\pi$
$908$	−14561.9	+	10579.8i	−0.532216	+	0.386678i
$909$	−2137.15	−	6577.46i	−0.0779809	−	0.240001i
$910$	−3116.02	+	9590.11i	−0.113511	+	0.349351i
$911$	−8224.34	−	5975.33i	−0.299105	−	0.217312i	0.428103	−	0.903730i	$-0.359182\pi$
$911$	−8224.34	−	5975.33i	−0.299105	−	0.217312i	−0.727208	+	0.686418i	$0.759182\pi$
$912$	−11504.2			−0.417701
$913$	9324.48	−	4879.60i	0.338001	−	0.176880i
$914$	−746.669			−0.0270215
$915$	−9618.40	−	6988.18i	−0.347513	−	0.252483i
$916$	−1002.78	+	3086.23i	−0.0361710	+	0.111323i
$917$	15171.4	+	46692.9i	0.546353	+	1.68150i
$918$	330.999	−	240.485i	0.0119004	−	0.00864616i
$919$	18876.9	−	13714.9i	0.677576	−	0.492287i	−0.194977	−	0.980808i	$-0.562463\pi$
$919$	18876.9	−	13714.9i	0.677576	−	0.492287i	0.872552	+	0.488520i	$0.162463\pi$
$920$	−5696.14	−	17530.9i	−0.204126	−	0.628236i
$921$	4426.31	−	13622.8i	0.158362	−	0.487389i
$922$	−2702.15	−	1963.22i	−0.0965189	−	0.0701251i
$923$	−33351.4			−1.18936
$924$	3625.74	+	21383.3i	0.129089	+	0.761318i
$925$	239.852			0.00852571
$926$	−3705.95	−	2692.53i	−0.131517	−	0.0955529i
$927$	3187.77	−	9810.94i	0.112945	−	0.347609i
$928$	7812.90	+	24045.6i	0.276369	+	0.850578i
$929$	24108.2	−	17515.6i	0.851415	−	0.618589i	−0.0741212	−	0.997249i	$-0.523615\pi$
$929$	24108.2	−	17515.6i	0.851415	−	0.618589i	0.925536	+	0.378660i	$0.123615\pi$
$930$	1342.29	−	975.233i	0.0473285	−	0.0343862i
$931$	−7446.96	−	22919.4i	−0.262153	−	0.806823i
$932$	6481.58	−	19948.2i	0.227802	−	0.701101i
$933$	−2147.87	−	1560.52i	−0.0753679	−	0.0547580i
$934$	6689.16			0.234343
$935$	4230.11	−	8530.30i	0.147957	−	0.298364i
$936$	−4855.38			−0.169555
$937$	−29762.2	−	21623.5i	−1.03766	−	0.753904i	−0.0678330	−	0.997697i	$-0.521608\pi$
$937$	−29762.2	−	21623.5i	−1.03766	−	0.753904i	−0.969827	+	0.243792i	$0.921608\pi$
$938$	−533.348	+	1641.48i	−0.0185655	+	0.0571387i
$939$	6166.69	+	18979.1i	0.214316	+	0.659596i
$940$	26893.4	−	19539.2i	0.933155	−	0.677977i
$941$	−34764.8	+	25258.1i	−1.20436	+	0.875018i	−0.994706	−	0.102758i	$-0.967233\pi$
$941$	−34764.8	+	25258.1i	−1.20436	+	0.875018i	−0.209652	+	0.977776i	$0.567233\pi$
$942$	−1893.14	−	5826.48i	−0.0654796	−	0.201525i
$943$	246.241	−	757.851i	0.00850339	−	0.0261707i
$944$	33590.3	+	24404.8i	1.15812	+	0.841427i
$945$	−7863.37			−0.270683
$946$	5632.01	+	5510.74i	0.193565	+	0.189397i
$947$	12592.4			0.432099			0.216049	−	0.976382i	$-0.430683\pi$
$947$	12592.4			0.432099			0.216049	+	0.976382i	$0.430683\pi$
$948$	−11765.3	−	8548.01i	−0.403080	−	0.292855i
$949$	5122.77	−	15766.3i	0.175229	−	0.539298i
$950$	−11.9889	−	36.8981i	−0.000409444	−	0.00126014i
$951$	3739.50	−	2716.91i	0.127510	−	0.0926412i
$952$	−4992.71	+	3627.42i	−0.169973	+	0.123493i
$953$	−507.019	−	1560.44i	−0.0172340	−	0.0530407i	0.942070	−	0.335417i	$-0.108877\pi$
$953$	−507.019	−	1560.44i	−0.0172340	−	0.0530407i	−0.959304	+	0.282376i	$0.908877\pi$
$954$	−273.616	+	842.104i	−0.00928580	+	0.0285788i
$955$	−33399.4	−	24266.1i	−1.13171	−	0.822233i
$956$	26154.4			0.884827
$957$	23669.7	+	3485.30i	0.799510	+	0.117726i
$958$	−3277.68			−0.110540
$959$	11259.2	+	8180.26i	0.379121	+	0.275448i
$960$	3700.22	−	11388.1i	0.124400	−	0.382865i
$961$	−7386.94	−	22734.7i	−0.247959	−	0.763139i
$962$	7936.66	−	5766.32i	0.265996	−	0.193258i
$963$	5441.51	−	3953.49i	0.182088	−	0.132294i
$964$	−3405.70	−	10481.7i	−0.113787	−	0.350199i
$965$	−8530.74	+	26254.9i	−0.284574	+	0.875830i
$966$	6735.27	+	4893.46i	0.224331	+	0.162986i
$967$	13354.3			0.444100			0.222050	−	0.975035i	$-0.428725\pi$
$967$	13354.3			0.444100			0.222050	+	0.975035i	$0.428725\pi$
$968$	7648.16	−	11023.6i	0.253947	−	0.366024i
$969$	−4978.02			−0.165033
$970$	−3716.15	−	2699.94i	−0.123009	−	0.0893709i
$971$	−4498.14	+	13843.8i	−0.148663	+	0.457539i	−0.997464	−	0.0711746i	$-0.977325\pi$
$971$	−4498.14	+	13843.8i	−0.148663	+	0.457539i	0.848801	+	0.528713i	$0.177325\pi$
$972$	−569.301	−	1752.13i	−0.0187863	−	0.0578184i
$973$	35324.1	−	25664.5i	1.16386	−	0.845597i
$974$	3217.08	−	2337.34i	0.105833	−	0.0768925i
$975$	41.9996	+	129.262i	0.00137955	+	0.00424583i
$976$	−5949.32	+	18310.1i	−0.195116	+	0.600505i
$977$	−14858.3	−	10795.2i	−0.486549	−	0.353498i	0.317307	−	0.948323i	$-0.397222\pi$
$977$	−14858.3	−	10795.2i	−0.486549	−	0.353498i	−0.803856	+	0.594825i	$0.797222\pi$
$978$	1601.50			0.0523624
$979$	−6659.74	−	980.631i	−0.217412	−	0.0320134i
$980$	28736.4			0.936686
$981$	5409.24	+	3930.04i	0.176049	+	0.127907i
$982$	−316.955	+	975.486i	−0.0102998	+	0.0316996i
$983$	6560.07	+	20189.8i	0.212852	+	0.655092i	0.999299	+	0.0374338i	$0.0119183\pi$
$983$	6560.07	+	20189.8i	0.212852	+	0.655092i	−0.786447	+	0.617658i	$0.788082\pi$
$984$	−118.792	+	86.3072i	−0.00384852	+	0.00279611i
$985$	15442.4	−	11219.5i	0.499527	−	0.362928i
$986$	1023.59	+	3150.29i	0.0330607	+	0.101750i
$987$	−9535.08	+	29346.0i	−0.307502	+	0.946395i
$988$	23254.8	+	16895.6i	0.748821	+	0.544050i
$989$	−54788.9			−1.76156
$990$	1691.75	+	1655.33i	0.0543106	+	0.0531412i
$991$	−11835.8			−0.379391			−0.189695	−	0.981843i	$-0.560750\pi$
$991$	−11835.8			−0.379391			−0.189695	+	0.981843i	$0.560750\pi$
$992$	−7179.11	−	5215.93i	−0.229775	−	0.166941i
$993$	3312.48	−	10194.8i	0.105859	−	0.325802i
$994$	−3256.28	−	10021.8i	−0.103906	−	0.319791i
$995$	7444.52	−	5408.76i	0.237193	−	0.172331i
$996$	5307.96	−	3856.46i	0.168864	−	0.122687i
$997$	−4218.71	−	12983.9i	−0.134010	−	0.412441i	0.861425	−	0.507885i	$-0.169573\pi$
$997$	−4218.71	−	12983.9i	−0.134010	−	0.412441i	−0.995435	+	0.0954448i	$0.969573\pi$
$998$	−209.874	+	645.926i	−0.00665676	+	0.0204874i
$999$	6189.13	+	4496.66i	0.196011	+	0.142411i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.4.e.b.4.2	✓	8
3.2	odd	2		99.4.f.b.37.1		8
11.3	even	5	inner	33.4.e.b.25.2	yes	8
11.5	even	5		363.4.a.p.1.2		4
11.6	odd	10		363.4.a.t.1.3		4
33.5	odd	10		1089.4.a.bg.1.3		4
33.14	odd	10		99.4.f.b.91.1		8
33.17	even	10		1089.4.a.z.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.4.e.b.4.2	✓	8	1.1	even	1	trivial
33.4.e.b.25.2	yes	8	11.3	even	5	inner
99.4.f.b.37.1		8	3.2	odd	2
99.4.f.b.91.1		8	33.14	odd	10
363.4.a.p.1.2		4	11.5	even	5
363.4.a.t.1.3		4	11.6	odd	10
1089.4.a.z.1.2		4	33.17	even	10
1089.4.a.bg.1.3		4	33.5	odd	10

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:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	33.e (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.523388 + 0.380264i) q^{2} +(0.927051 - 2.85317i) q^{3} +(-2.34280 - 7.21040i) q^{4} +(9.01441 - 6.54935i) q^{5} +(1.57016 - 1.14079i) q^{6} +(8.07696 + 24.8583i) q^{7} +(3.11499 - 9.58696i) q^{8} +(-7.28115 - 5.29007i) q^{9} +O(q^{10})\)	\(q+(0.523388 + 0.380264i) q^{2} +(0.927051 - 2.85317i) q^{3} +(-2.34280 - 7.21040i) q^{4} +(9.01441 - 6.54935i) q^{5} +(1.57016 - 1.14079i) q^{6} +(8.07696 + 24.8583i) q^{7} +(3.11499 - 9.58696i) q^{8} +(-7.28115 - 5.29007i) q^{9} +7.20851 q^{10} +(-36.0937 - 5.31471i) q^{11} -22.7444 q^{12} +(43.2976 + 31.4576i) q^{13} +(-5.22533 + 16.0819i) q^{14} +(-10.3296 - 31.7912i) q^{15} +(-43.7924 + 31.8170i) q^{16} +(-18.9494 + 13.7676i) q^{17} +(-1.79925 - 5.53752i) q^{18} +(-21.8916 + 67.3756i) q^{19} +(-68.3424 - 49.6537i) q^{20} +78.4128 q^{21} +(-16.8700 - 16.5068i) q^{22} +164.114 q^{23} +(-24.4655 - 17.7752i) q^{24} +(-0.261588 + 0.805085i) q^{25} +(10.6993 + 32.9290i) q^{26} +(-21.8435 + 15.8702i) q^{27} +(160.316 - 116.476i) q^{28} +(-67.5495 - 207.896i) q^{29} +(6.68266 - 20.5671i) q^{30} +(62.0698 + 45.0964i) q^{31} -115.662 q^{32} +(-48.6244 + 98.0544i) q^{33} -15.1532 q^{34} +(235.615 + 171.184i) q^{35} +(-21.0852 + 64.8936i) q^{36} +(-87.5569 - 269.472i) q^{37} +(-37.0783 + 26.9390i) q^{38} +(129.893 - 94.3727i) q^{39} +(-34.7085 - 106.822i) q^{40} +(1.50043 - 4.61784i) q^{41} +(41.0403 + 29.8175i) q^{42} -333.848 q^{43} +(46.2392 + 272.701i) q^{44} -100.282 q^{45} +(85.8951 + 62.4064i) q^{46} +(-121.601 + 374.250i) q^{47} +(50.1816 + 154.443i) q^{48} +(-275.206 + 199.949i) q^{49} +(-0.443057 + 0.321899i) q^{50} +(21.7141 + 66.8292i) q^{51} +(125.384 - 385.892i) q^{52} +(-123.029 - 89.3860i) q^{53} -17.4675 q^{54} +(-360.171 + 188.481i) q^{55} +263.475 q^{56} +(171.939 + 124.921i) q^{57} +(43.7007 - 134.497i) q^{58} +(-237.027 - 729.494i) q^{59} +(-205.027 + 148.961i) q^{60} +(287.741 - 209.056i) q^{61} +(15.3381 + 47.2058i) q^{62} +(72.6926 - 223.725i) q^{63} +(289.803 + 210.554i) q^{64} +596.329 q^{65} +(-62.7360 + 32.8304i) q^{66} +102.070 q^{67} +(143.665 + 104.378i) q^{68} +(152.142 - 468.244i) q^{69} +(58.2228 + 179.191i) q^{70} +(-504.157 + 366.292i) q^{71} +(-73.3964 + 53.3256i) q^{72} +(-95.7190 - 294.593i) q^{73} +(56.6443 - 174.333i) q^{74} +(2.05454 + 1.49271i) q^{75} +537.093 q^{76} +(-159.412 - 940.155i) q^{77} +103.871 q^{78} +(517.284 + 375.829i) q^{79} +(-186.381 + 573.623i) q^{80} +(25.0304 + 77.0356i) q^{81} +(2.54130 - 1.84636i) q^{82} +(-233.374 + 169.556i) q^{83} +(-183.706 - 565.387i) q^{84} +(-80.6493 + 248.213i) q^{85} +(-174.732 - 126.950i) q^{86} -655.784 q^{87} +(-163.383 + 329.473i) q^{88} +184.513 q^{89} +(-52.4863 - 38.1335i) q^{90} +(-432.269 + 1330.39i) q^{91} +(-384.486 - 1183.32i) q^{92} +(186.210 - 135.289i) q^{93} +(-205.958 + 149.637i) q^{94} +(243.926 + 750.727i) q^{95} +(-107.224 + 330.003i) q^{96} +(-515.522 - 374.549i) q^{97} -220.073 q^{98} +(234.688 + 229.635i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{2} - 6 q^{3} - 16 q^{4} + 9 q^{5} - 18 q^{6} + 3 q^{7} + 36 q^{8} - 18 q^{9}+O(q^{10}) \) 8 * q - 6 * q^2 - 6 * q^3 - 16 * q^4 + 9 * q^5 - 18 * q^6 + 3 * q^7 + 36 * q^8 - 18 * q^9	\( 8 q - 6 q^{2} - 6 q^{3} - 16 q^{4} + 9 q^{5} - 18 q^{6} + 3 q^{7} + 36 q^{8} - 18 q^{9} + 8 q^{10} - 87 q^{11} - 18 q^{12} + 171 q^{13} + 12 q^{14} - 63 q^{15} + 44 q^{16} + 36 q^{17} + 81 q^{18} + 324 q^{19} - 87 q^{20} - 66 q^{21} - 521 q^{22} - 84 q^{23} + 18 q^{24} + 263 q^{25} - 774 q^{26} - 54 q^{27} + 387 q^{28} + 393 q^{29} + 204 q^{30} + 15 q^{31} + 102 q^{32} - 216 q^{33} - 712 q^{34} + 1002 q^{35} - 144 q^{36} - 747 q^{37} - 36 q^{38} + 513 q^{39} + 41 q^{40} + 159 q^{41} + 396 q^{42} - 644 q^{43} + 219 q^{44} + 216 q^{45} + 753 q^{46} - 351 q^{47} - 423 q^{48} - 1967 q^{49} + 330 q^{50} + 63 q^{51} + 2871 q^{52} - 531 q^{53} - 162 q^{54} - 716 q^{55} + 1470 q^{56} - 453 q^{57} - 1205 q^{58} - 1002 q^{59} - 261 q^{60} + 1449 q^{61} + 99 q^{62} + 27 q^{63} - 1118 q^{64} - 954 q^{65} + 897 q^{66} - 518 q^{67} + 873 q^{68} + 693 q^{69} + 26 q^{70} + 429 q^{71} + 54 q^{72} + 2547 q^{73} + 468 q^{74} - 231 q^{75} - 2276 q^{76} - 2697 q^{77} + 1638 q^{78} + 2805 q^{79} - 1620 q^{80} - 162 q^{81} - 1631 q^{82} - 2553 q^{83} - 1509 q^{84} - 197 q^{85} - 1713 q^{86} - 3906 q^{87} + 2866 q^{88} + 1788 q^{89} - 648 q^{90} + 2885 q^{91} + 423 q^{92} + 45 q^{93} + 1159 q^{94} + 3009 q^{95} - 504 q^{96} + 9 q^{97} + 5550 q^{98} + 27 q^{99}+O(q^{100}) \) 8 * q - 6 * q^2 - 6 * q^3 - 16 * q^4 + 9 * q^5 - 18 * q^6 + 3 * q^7 + 36 * q^8 - 18 * q^9 + 8 * q^10 - 87 * q^11 - 18 * q^12 + 171 * q^13 + 12 * q^14 - 63 * q^15 + 44 * q^16 + 36 * q^17 + 81 * q^18 + 324 * q^19 - 87 * q^20 - 66 * q^21 - 521 * q^22 - 84 * q^23 + 18 * q^24 + 263 * q^25 - 774 * q^26 - 54 * q^27 + 387 * q^28 + 393 * q^29 + 204 * q^30 + 15 * q^31 + 102 * q^32 - 216 * q^33 - 712 * q^34 + 1002 * q^35 - 144 * q^36 - 747 * q^37 - 36 * q^38 + 513 * q^39 + 41 * q^40 + 159 * q^41 + 396 * q^42 - 644 * q^43 + 219 * q^44 + 216 * q^45 + 753 * q^46 - 351 * q^47 - 423 * q^48 - 1967 * q^49 + 330 * q^50 + 63 * q^51 + 2871 * q^52 - 531 * q^53 - 162 * q^54 - 716 * q^55 + 1470 * q^56 - 453 * q^57 - 1205 * q^58 - 1002 * q^59 - 261 * q^60 + 1449 * q^61 + 99 * q^62 + 27 * q^63 - 1118 * q^64 - 954 * q^65 + 897 * q^66 - 518 * q^67 + 873 * q^68 + 693 * q^69 + 26 * q^70 + 429 * q^71 + 54 * q^72 + 2547 * q^73 + 468 * q^74 - 231 * q^75 - 2276 * q^76 - 2697 * q^77 + 1638 * q^78 + 2805 * q^79 - 1620 * q^80 - 162 * q^81 - 1631 * q^82 - 2553 * q^83 - 1509 * q^84 - 197 * q^85 - 1713 * q^86 - 3906 * q^87 + 2866 * q^88 + 1788 * q^89 - 648 * q^90 + 2885 * q^91 + 423 * q^92 + 45 * q^93 + 1159 * q^94 + 3009 * q^95 - 504 * q^96 + 9 * q^97 + 5550 * q^98 + 27 * q^99

Introduction

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