LMFDB - Embedded newform 170.3.e.b.13.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,3,Mod(13,170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(170, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("170.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	170.e (of order $4$, 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:	$4.63216449413$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 80 x^{14} + 2532 x^{12} + 40532 x^{10} + 346464 x^{8} + 1518752 x^{6} + 2895224 x^{4} + \cdots + 148996 $ x^16 + 80x^14 + 2532x^12 + 40532x^10 + 346464x^8 + 1518752x^6 + 2895224x^4 + 1253728*x^2 + 148996
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2\cdot 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.4
Root			$0.574749i$ of defining polynomial
Character	$\chi$	$=$	170.13
Dual form			170.3.e.b.157.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} -0.574749i q^{3} +2.00000i q^{4} +(-4.36413 + 2.44015i) q^{5} +(0.574749 - 0.574749i) q^{6} +5.24832i q^{7} +(-2.00000 + 2.00000i) q^{8} +8.66966 q^{9} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{2} -0.574749i q^{3} +2.00000i q^{4} +(-4.36413 + 2.44015i) q^{5} +(0.574749 - 0.574749i) q^{6} +5.24832i q^{7} +(-2.00000 + 2.00000i) q^{8} +8.66966 q^{9} +(-6.80428 - 1.92398i) q^{10} +(-12.9078 + 12.9078i) q^{11} +1.14950 q^{12} +(2.34417 + 2.34417i) q^{13} +(-5.24832 + 5.24832i) q^{14} +(1.40247 + 2.50828i) q^{15} -4.00000 q^{16} +(-15.4156 + 7.16645i) q^{17} +(8.66966 + 8.66966i) q^{18} +17.5328 q^{19} +(-4.88030 - 8.72827i) q^{20} +3.01647 q^{21} -25.8156 q^{22} +15.0470 q^{23} +(1.14950 + 1.14950i) q^{24} +(13.0913 - 21.2983i) q^{25} +4.68834i q^{26} -10.1556i q^{27} -10.4966 q^{28} +(10.9063 - 10.9063i) q^{29} +(-1.10581 + 3.91076i) q^{30} +(5.76255 + 5.76255i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(7.41876 + 7.41876i) q^{33} +(-22.5821 - 8.24920i) q^{34} +(-12.8067 - 22.9044i) q^{35} +17.3393i q^{36} -14.0439 q^{37} +(17.5328 + 17.5328i) q^{38} +(1.34731 - 1.34731i) q^{39} +(3.84797 - 13.6086i) q^{40} +(1.12248 - 1.12248i) q^{41} +(3.01647 + 3.01647i) q^{42} +(12.5385 - 12.5385i) q^{43} +(-25.8156 - 25.8156i) q^{44} +(-37.8356 + 21.1553i) q^{45} +(15.0470 + 15.0470i) q^{46} +(30.4179 - 30.4179i) q^{47} +2.29900i q^{48} +21.4552 q^{49} +(34.3896 - 8.20695i) q^{50} +(4.11891 + 8.86013i) q^{51} +(-4.68834 + 4.68834i) q^{52} +(-15.8536 + 15.8536i) q^{53} +(10.1556 - 10.1556i) q^{54} +(24.8344 - 87.8285i) q^{55} +(-10.4966 - 10.4966i) q^{56} -10.0770i q^{57} +21.8126 q^{58} +15.1006 q^{59} +(-5.01657 + 2.80495i) q^{60} +(50.5922 - 50.5922i) q^{61} +11.5251i q^{62} +45.5011i q^{63} -8.00000i q^{64} +(-15.9504 - 4.51014i) q^{65} +14.8375i q^{66} +(-43.5594 + 43.5594i) q^{67} +(-14.3329 - 30.8313i) q^{68} -8.64827i q^{69} +(10.0977 - 35.7110i) q^{70} +(87.6553 + 87.6553i) q^{71} +(-17.3393 + 17.3393i) q^{72} -16.6705i q^{73} +(-14.0439 - 14.0439i) q^{74} +(-12.2412 - 7.52423i) q^{75} +35.0657i q^{76} +(-67.7443 - 67.7443i) q^{77} +2.69462 q^{78} +(98.0638 + 98.0638i) q^{79} +(17.4565 - 9.76060i) q^{80} +72.1900 q^{81} +2.24497 q^{82} +(-79.2698 + 79.2698i) q^{83} +6.03293i q^{84} +(49.7887 - 68.8918i) q^{85} +25.0770 q^{86} +(-6.26839 - 6.26839i) q^{87} -51.6313i q^{88} -168.113i q^{89} +(-58.9909 - 16.6803i) q^{90} +(-12.3029 + 12.3029i) q^{91} +30.0941i q^{92} +(3.31202 - 3.31202i) q^{93} +60.8358 q^{94} +(-76.5157 + 42.7828i) q^{95} +(-2.29900 + 2.29900i) q^{96} -192.258 q^{97} +(21.4552 + 21.4552i) q^{98} +(-111.906 + 111.906i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} - 2 q^{5} - 32 q^{8} - 16 q^{9}+O(q^{10}) $ 16 * q + 16 * q^2 - 2 * q^5 - 32 * q^8 - 16 * q^9	$ 16 q + 16 q^{2} - 2 q^{5} - 32 q^{8} - 16 q^{9} - 4 q^{10} + 20 q^{11} + 4 q^{13} - 12 q^{14} + 12 q^{15} - 64 q^{16} + 36 q^{17} - 16 q^{18} - 16 q^{19} - 4 q^{20} + 40 q^{22} + 16 q^{23} + 44 q^{25} - 24 q^{28} - 20 q^{29} + 12 q^{30} + 92 q^{31} - 64 q^{32} - 60 q^{33} + 24 q^{34} - 124 q^{35} + 32 q^{37} - 16 q^{38} - 140 q^{39} - 60 q^{41} + 52 q^{43} + 40 q^{44} + 198 q^{45} + 16 q^{46} + 112 q^{47} + 136 q^{49} - 4 q^{50} - 140 q^{51} - 8 q^{52} + 48 q^{53} + 108 q^{54} + 40 q^{55} - 24 q^{56} - 40 q^{58} + 76 q^{61} - 40 q^{65} + 116 q^{67} - 24 q^{68} - 124 q^{70} - 268 q^{71} + 32 q^{72} + 32 q^{74} + 136 q^{75} - 116 q^{77} - 280 q^{78} - 88 q^{79} + 8 q^{80} - 352 q^{81} - 120 q^{82} - 160 q^{83} + 310 q^{85} + 104 q^{86} + 236 q^{87} + 260 q^{90} - 168 q^{91} + 48 q^{93} + 224 q^{94} + 264 q^{95} - 256 q^{97} + 136 q^{98} - 348 q^{99}+O(q^{100}) $ 16 * q + 16 * q^2 - 2 * q^5 - 32 * q^8 - 16 * q^9 - 4 * q^10 + 20 * q^11 + 4 * q^13 - 12 * q^14 + 12 * q^15 - 64 * q^16 + 36 * q^17 - 16 * q^18 - 16 * q^19 - 4 * q^20 + 40 * q^22 + 16 * q^23 + 44 * q^25 - 24 * q^28 - 20 * q^29 + 12 * q^30 + 92 * q^31 - 64 * q^32 - 60 * q^33 + 24 * q^34 - 124 * q^35 + 32 * q^37 - 16 * q^38 - 140 * q^39 - 60 * q^41 + 52 * q^43 + 40 * q^44 + 198 * q^45 + 16 * q^46 + 112 * q^47 + 136 * q^49 - 4 * q^50 - 140 * q^51 - 8 * q^52 + 48 * q^53 + 108 * q^54 + 40 * q^55 - 24 * q^56 - 40 * q^58 + 76 * q^61 - 40 * q^65 + 116 * q^67 - 24 * q^68 - 124 * q^70 - 268 * q^71 + 32 * q^72 + 32 * q^74 + 136 * q^75 - 116 * q^77 - 280 * q^78 - 88 * q^79 + 8 * q^80 - 352 * q^81 - 120 * q^82 - 160 * q^83 + 310 * q^85 + 104 * q^86 + 236 * q^87 + 260 * q^90 - 168 * q^91 + 48 * q^93 + 224 * q^94 + 264 * q^95 - 256 * q^97 + 136 * q^98 - 348 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/170\mathbb{Z}\right)^\times$.

$n$	$71$	$137$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$3$		−	0.574749i		−	0.191583i	−0.995401	−	0.0957915i	$-0.969462\pi$
$3$		−	0.574749i		−	0.191583i	0.995401	−	0.0957915i	$-0.0305382\pi$
$4$			2.00000i			0.500000i
$5$	−4.36413	+	2.44015i	−0.872827	+	0.488030i
$5$	−4.36413	+	2.44015i	−0.872827	+	0.488030i
$6$	0.574749	−	0.574749i	0.0957915	−	0.0957915i
$7$			5.24832i			0.749760i	0.927073	+	0.374880i	$0.122316\pi$
$7$			5.24832i			0.749760i	−0.927073	+	0.374880i	$0.877684\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$	8.66966			0.963296
$10$	−6.80428	−	1.92398i	−0.680428	−	0.192398i
$11$	−12.9078	+	12.9078i	−1.17344	+	1.17344i	−0.192053	+	0.981384i	$0.561515\pi$
$11$	−12.9078	+	12.9078i	−1.17344	+	1.17344i	−0.981384	+	0.192053i	$0.938485\pi$
$12$	1.14950			0.0957915
$13$	2.34417	+	2.34417i	0.180321	+	0.180321i	0.791496	−	0.611175i	$-0.209303\pi$
$13$	2.34417	+	2.34417i	0.180321	+	0.180321i	−0.611175	+	0.791496i	$0.709303\pi$
$14$	−5.24832	+	5.24832i	−0.374880	+	0.374880i
$15$	1.40247	+	2.50828i	0.0934983	+	0.167219i
$16$	−4.00000			−0.250000
$17$	−15.4156	+	7.16645i	−0.906803	+	0.421556i
$17$	−15.4156	+	7.16645i	−0.906803	+	0.421556i
$18$	8.66966	+	8.66966i	0.481648	+	0.481648i
$19$	17.5328			0.922781			0.461391	−	0.887197i	$-0.347351\pi$
$19$	17.5328			0.922781			0.461391	+	0.887197i	$0.347351\pi$
$20$	−4.88030	−	8.72827i	−0.244015	−	0.436413i
$21$	3.01647			0.143641
$22$	−25.8156			−1.17344
$23$	15.0470			0.654219			0.327110	−	0.944986i	$-0.393925\pi$
$23$	15.0470			0.654219			0.327110	+	0.944986i	$0.393925\pi$
$24$	1.14950	+	1.14950i	0.0478958	+	0.0478958i
$25$	13.0913	−	21.2983i	0.523653	−	0.851931i
$26$			4.68834i			0.180321i
$27$		−	10.1556i		−	0.376134i
$28$	−10.4966			−0.374880
$29$	10.9063	−	10.9063i	0.376079	−	0.376079i	−0.493606	−	0.869686i	$-0.664322\pi$
$29$	10.9063	−	10.9063i	0.376079	−	0.376079i	0.869686	+	0.493606i	$0.164322\pi$
$30$	−1.10581	+	3.91076i	−0.0368603	+	0.130359i
$31$	5.76255	+	5.76255i	0.185889	+	0.185889i	0.793916	−	0.608027i	$-0.208039\pi$
$31$	5.76255	+	5.76255i	0.185889	+	0.185889i	−0.608027	+	0.793916i	$0.708039\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	7.41876	+	7.41876i	0.224811	+	0.224811i
$34$	−22.5821	−	8.24920i	−0.664179	−	0.242623i
$35$	−12.8067	−	22.9044i	−0.365905	−	0.654410i
$36$			17.3393i			0.481648i
$37$	−14.0439			−0.379564			−0.189782	−	0.981826i	$-0.560778\pi$
$37$	−14.0439			−0.379564			−0.189782	+	0.981826i	$0.560778\pi$
$38$	17.5328	+	17.5328i	0.461391	+	0.461391i
$39$	1.34731	−	1.34731i	0.0345464	−	0.0345464i
$40$	3.84797	−	13.6086i	0.0961992	−	0.340214i
$41$	1.12248	−	1.12248i	0.0273777	−	0.0273777i	−0.693285	−	0.720663i	$-0.743837\pi$
$41$	1.12248	−	1.12248i	0.0273777	−	0.0273777i	0.720663	+	0.693285i	$0.243837\pi$
$42$	3.01647	+	3.01647i	0.0718206	+	0.0718206i
$43$	12.5385	−	12.5385i	0.291593	−	0.291593i	−0.546117	−	0.837709i	$-0.683894\pi$
$43$	12.5385	−	12.5385i	0.291593	−	0.291593i	0.837709	+	0.546117i	$0.183894\pi$
$44$	−25.8156	−	25.8156i	−0.586719	−	0.586719i
$45$	−37.8356	+	21.1553i	−0.840791	+	0.470117i
$46$	15.0470	+	15.0470i	0.327110	+	0.327110i
$47$	30.4179	−	30.4179i	0.647190	−	0.647190i	−0.305123	−	0.952313i	$-0.598698\pi$
$47$	30.4179	−	30.4179i	0.647190	−	0.647190i	0.952313	+	0.305123i	$0.0986976\pi$
$48$			2.29900i			0.0478958i
$49$	21.4552			0.437861
$50$	34.3896	−	8.20695i	0.687792	−	0.164139i
$51$	4.11891	+	8.86013i	0.0807629	+	0.173728i
$52$	−4.68834	+	4.68834i	−0.0901604	+	0.0901604i
$53$	−15.8536	+	15.8536i	−0.299124	+	0.299124i	−0.840671	−	0.541546i	$-0.817839\pi$
$53$	−15.8536	+	15.8536i	−0.299124	+	0.299124i	0.541546	+	0.840671i	$0.317839\pi$
$54$	10.1556	−	10.1556i	0.188067	−	0.188067i
$55$	24.8344	−	87.8285i	0.451535	−	1.59688i
$56$	−10.4966	−	10.4966i	−0.187440	−	0.187440i
$57$		−	10.0770i		−	0.176789i
$58$	21.8126			0.376079
$59$	15.1006			0.255943			0.127972	−	0.991778i	$-0.459153\pi$
$59$	15.1006			0.255943			0.127972	+	0.991778i	$0.459153\pi$
$60$	−5.01657	+	2.80495i	−0.0836094	+	0.0467491i
$61$	50.5922	−	50.5922i	0.829380	−	0.829380i	−0.158051	−	0.987431i	$-0.550521\pi$
$61$	50.5922	−	50.5922i	0.829380	−	0.829380i	0.987431	+	0.158051i	$0.0505211\pi$
$62$			11.5251i			0.185889i
$63$			45.5011i			0.722240i
$64$		−	8.00000i		−	0.125000i
$65$	−15.9504	−	4.51014i	−0.245391	−	0.0693868i
$66$			14.8375i			0.224811i
$67$	−43.5594	+	43.5594i	−0.650140	+	0.650140i	−0.953027	−	0.302887i	$-0.902050\pi$
$67$	−43.5594	+	43.5594i	−0.650140	+	0.650140i	0.302887	+	0.953027i	$0.402050\pi$
$68$	−14.3329	−	30.8313i	−0.210778	−	0.453401i
$69$		−	8.64827i		−	0.125337i
$70$	10.0977	−	35.7110i	0.144253	−	0.510158i
$71$	87.6553	+	87.6553i	1.23458	+	1.23458i	0.962185	+	0.272397i	$0.0878165\pi$
$71$	87.6553	+	87.6553i	1.23458	+	1.23458i	0.272397	+	0.962185i	$0.412184\pi$
$72$	−17.3393	+	17.3393i	−0.240824	+	0.240824i
$73$		−	16.6705i		−	0.228363i	−0.993460	−	0.114182i	$-0.963575\pi$
$73$		−	16.6705i		−	0.228363i	0.993460	−	0.114182i	$-0.0364246\pi$
$74$	−14.0439	−	14.0439i	−0.189782	−	0.189782i
$75$	−12.2412	−	7.52423i	−0.163216	−	0.100323i
$76$			35.0657i			0.461391i
$77$	−67.7443	−	67.7443i	−0.879796	−	0.879796i
$78$	2.69462			0.0345464
$79$	98.0638	+	98.0638i	1.24131	+	1.24131i	0.959456	+	0.281857i	$0.0909505\pi$
$79$	98.0638	+	98.0638i	1.24131	+	1.24131i	0.281857	+	0.959456i	$0.409049\pi$
$80$	17.4565	−	9.76060i	0.218207	−	0.122008i
$81$	72.1900			0.891235
$82$	2.24497			0.0273777
$83$	−79.2698	+	79.2698i	−0.955058	+	0.955058i	−0.999033	−	0.0439748i	$-0.985998\pi$
$83$	−79.2698	+	79.2698i	−0.955058	+	0.955058i	0.0439748	+	0.999033i	$0.485998\pi$
$84$			6.03293i			0.0718206i
$85$	49.7887	−	68.8918i	0.585750	−	0.810492i
$86$	25.0770			0.291593
$87$	−6.26839	−	6.26839i	−0.0720504	−	0.0720504i
$88$		−	51.6313i		−	0.586719i
$89$		−	168.113i		−	1.88891i	−0.328642	−	0.944455i	$-0.606591\pi$
$89$		−	168.113i		−	1.88891i	0.328642	−	0.944455i	$-0.393409\pi$
$90$	−58.9909	−	16.6803i	−0.655454	−	0.185337i
$91$	−12.3029	+	12.3029i	−0.135197	+	0.135197i
$92$			30.0941i			0.327110i
$93$	3.31202	−	3.31202i	0.0356131	−	0.0356131i
$94$	60.8358			0.647190
$95$	−76.5157	+	42.7828i	−0.805428	+	0.450345i
$96$	−2.29900	+	2.29900i	−0.0239479	+	0.0239479i
$97$	−192.258			−1.98205			−0.991023	−	0.133694i	$-0.957316\pi$
$97$	−192.258			−1.98205			−0.991023	+	0.133694i	$0.957316\pi$
$98$	21.4552	+	21.4552i	0.218930	+	0.218930i
$99$	−111.906	+	111.906i	−1.13037	+	1.13037i
$100$	42.5966	+	26.1827i	0.425966	+	0.261827i
$101$	−109.363			−1.08280			−0.541400	−	0.840765i	$-0.682106\pi$
$101$	−109.363			−1.08280			−0.541400	+	0.840765i	$0.682106\pi$
$102$	−4.74122	+	12.9790i	−0.0464825	+	0.127245i
$103$	33.2314	+	33.2314i	0.322635	+	0.322635i	0.849777	−	0.527142i	$-0.176736\pi$
$103$	33.2314	+	33.2314i	0.322635	+	0.322635i	−0.527142	+	0.849777i	$0.676736\pi$
$104$	−9.37668			−0.0901604
$105$	−13.1643	+	7.36063i	−0.125374	+	0.0701012i
$106$	−31.7072			−0.299124
$107$	−126.469			−1.18195			−0.590975	−	0.806690i	$-0.701257\pi$
$107$	−126.469			−1.18195			−0.590975	+	0.806690i	$0.701257\pi$
$108$	20.3112			0.188067
$109$	22.7934	+	22.7934i	0.209114	+	0.209114i	0.803891	−	0.594777i	$-0.202760\pi$
$109$	22.7934	+	22.7934i	0.209114	+	0.209114i	−0.594777	+	0.803891i	$0.702760\pi$
$110$	112.663	−	62.9940i	1.02421	−	0.572673i
$111$			8.07170i			0.0727180i
$112$		−	20.9933i		−	0.187440i
$113$	49.3329			0.436574			0.218287	−	0.975885i	$-0.429953\pi$
$113$	49.3329			0.436574			0.218287	+	0.975885i	$0.429953\pi$
$114$	10.0770	−	10.0770i	0.0883946	−	0.0883946i
$115$	−65.6673	+	36.7170i	−0.571020	+	0.319279i
$116$	21.8126	+	21.8126i	0.188040	+	0.188040i
$117$	20.3232	+	20.3232i	0.173702	+	0.173702i
$118$	15.1006	+	15.1006i	0.127972	+	0.127972i
$119$	−37.6118	−	80.9062i	−0.316065	−	0.679884i
$120$	−7.82151	−	2.21162i	−0.0651793	−	0.0184301i
$121$		−	212.223i		−	1.75391i
$122$	101.184			0.829380
$123$	−0.645147	−	0.645147i	−0.00524510	−	0.00524510i
$124$	−11.5251	+	11.5251i	−0.0929444	+	0.0929444i
$125$	−5.16132	+	124.893i	−0.0412906	+	0.999147i
$126$	−45.5011	+	45.5011i	−0.361120	+	0.361120i
$127$	142.511	+	142.511i	1.12213	+	1.12213i	0.991420	+	0.130713i	$0.0417267\pi$
$127$	142.511	+	142.511i	1.12213	+	1.12213i	0.130713	+	0.991420i	$0.458273\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$	−7.20648	−	7.20648i	−0.0558642	−	0.0558642i
$130$	−11.4403	−	20.4605i	−0.0880019	−	0.157389i
$131$	76.1083	+	76.1083i	0.580979	+	0.580979i	0.935172	−	0.354193i	$-0.115244\pi$
$131$	76.1083	+	76.1083i	0.580979	+	0.580979i	−0.354193	+	0.935172i	$0.615244\pi$
$132$	−14.8375	+	14.8375i	−0.112405	+	0.112405i
$133$			92.0179i			0.691864i
$134$	−87.1188			−0.650140
$135$	24.7812	+	44.3205i	0.183565	+	0.328300i
$136$	16.4984	−	45.1642i	0.121312	−	0.332090i
$137$	−46.4830	+	46.4830i	−0.339292	+	0.339292i	−0.856101	−	0.516809i	$-0.827120\pi$
$137$	−46.4830	+	46.4830i	−0.339292	+	0.339292i	0.516809	+	0.856101i	$0.327120\pi$
$138$	8.64827	−	8.64827i	0.0626686	−	0.0626686i
$139$	28.1682	−	28.1682i	0.202649	−	0.202649i	−0.598485	−	0.801134i	$-0.704230\pi$
$139$	28.1682	−	28.1682i	0.202649	−	0.202649i	0.801134	+	0.598485i	$0.204230\pi$
$140$	45.8087	−	25.6134i	0.327205	−	0.182953i
$141$	−17.4827	−	17.4827i	−0.123991	−	0.123991i
$142$			175.311i			1.23458i
$143$	−60.5162			−0.423190
$144$	−34.6787			−0.240824
$145$	−20.9835	+	74.2096i	−0.144714	+	0.511790i
$146$	16.6705	−	16.6705i	0.114182	−	0.114182i
$147$		−	12.3313i		−	0.0838867i
$148$		−	28.0877i		−	0.189782i
$149$			265.320i			1.78067i	0.455303	+	0.890336i	$0.349531\pi$
$149$			265.320i			1.78067i	−0.455303	+	0.890336i	$0.650469\pi$
$150$	−4.71694	−	19.7654i	−0.0314463	−	0.131769i
$151$		−	119.231i		−	0.789609i	−0.918765	−	0.394805i	$-0.870812\pi$
$151$		−	119.231i		−	0.789609i	0.918765	−	0.394805i	$-0.129188\pi$
$152$	−35.0657	+	35.0657i	−0.230695	+	0.230695i
$153$	−133.648	+	62.1307i	−0.873519	+	0.406083i
$154$		−	135.489i		−	0.879796i
$155$	−39.2100	−	11.0871i	−0.252968	−	0.0715294i
$156$	2.69462	+	2.69462i	0.0172732	+	0.0172732i
$157$	138.033	−	138.033i	0.879191	−	0.879191i	−0.114260	−	0.993451i	$-0.536450\pi$
$157$	138.033	−	138.033i	0.879191	−	0.879191i	0.993451	+	0.114260i	$0.0364498\pi$
$158$			196.128i			1.24131i
$159$	9.11184	+	9.11184i	0.0573072	+	0.0573072i
$160$	27.2171	+	7.69594i	0.170107	+	0.0480996i
$161$			78.9716i			0.490507i
$162$	72.1900	+	72.1900i	0.445617	+	0.445617i
$163$	−259.022			−1.58909			−0.794546	−	0.607204i	$-0.792291\pi$
$163$	−259.022			−1.58909			−0.794546	+	0.607204i	$0.792291\pi$
$164$	2.24497	+	2.24497i	0.0136888	+	0.0136888i
$165$	−50.4793	−	14.2736i	−0.305935	−	0.0865065i
$166$	−158.540			−0.955058
$167$	3.43597			0.0205747			0.0102873	−	0.999947i	$-0.496725\pi$
$167$	3.43597			0.0205747			0.0102873	+	0.999947i	$0.496725\pi$
$168$	−6.03293	+	6.03293i	−0.0359103	+	0.0359103i
$169$		−	158.010i		−	0.934969i
$170$	118.681	−	19.1031i	0.698121	−	0.112371i
$171$	152.004			0.888911
$172$	25.0770	+	25.0770i	0.145796	+	0.145796i
$173$		−	135.662i		−	0.784176i	−0.919928	−	0.392088i	$-0.871753\pi$
$173$		−	135.662i		−	0.784176i	0.919928	−	0.392088i	$-0.128247\pi$
$174$		−	12.5368i		−	0.0720504i
$175$	111.780	+	68.7075i	0.638744	+	0.392614i
$176$	51.6313	−	51.6313i	0.293359	−	0.293359i
$177$		−	8.67909i		−	0.0490344i
$178$	168.113	−	168.113i	0.944455	−	0.944455i
$179$	199.538			1.11474			0.557369	−	0.830265i	$-0.311811\pi$
$179$	199.538			1.11474			0.557369	+	0.830265i	$0.311811\pi$
$180$	−42.3106	−	75.6711i	−0.235059	−	0.420395i
$181$	176.293	−	176.293i	0.973993	−	0.973993i	−0.0256776	−	0.999670i	$-0.508174\pi$
$181$	176.293	−	176.293i	0.973993	−	0.973993i	0.999670	+	0.0256776i	$0.00817433\pi$
$182$	−24.6059			−0.135197
$183$	−29.0778	−	29.0778i	−0.158895	−	0.158895i
$184$	−30.0941	+	30.0941i	−0.163555	+	0.163555i
$185$	61.2893	−	34.2691i	0.331294	−	0.185239i
$186$	6.62404			0.0356131
$187$	106.479	−	291.485i	0.569407	−	1.55875i
$188$	60.8358	+	60.8358i	0.323595	+	0.323595i
$189$	53.2999			0.282010
$190$	−119.298	−	33.7329i	−0.627886	−	0.177542i
$191$	−140.941			−0.737911			−0.368955	−	0.929447i	$-0.620284\pi$
$191$	−140.941			−0.737911			−0.368955	+	0.929447i	$0.620284\pi$
$192$	−4.59799			−0.0239479
$193$	123.427			0.639518			0.319759	−	0.947499i	$-0.396398\pi$
$193$	123.427			0.639518			0.319759	+	0.947499i	$0.396398\pi$
$194$	−192.258	−	192.258i	−0.991023	−	0.991023i
$195$	−2.59220	+	9.16748i	−0.0132933	+	0.0470127i
$196$			42.9103i			0.218930i
$197$		−	212.768i		−	1.08004i	−0.841652	−	0.540021i	$-0.818416\pi$
$197$		−	212.768i		−	1.08004i	0.841652	−	0.540021i	$-0.181584\pi$
$198$	−223.813			−1.13037
$199$	127.501	−	127.501i	0.640708	−	0.640708i	−0.310021	−	0.950730i	$-0.600336\pi$
$199$	127.501	−	127.501i	0.640708	−	0.640708i	0.950730	+	0.310021i	$0.100336\pi$
$200$	16.4139	+	68.7792i	0.0820695	+	0.343896i
$201$	25.0357	+	25.0357i	0.124556	+	0.124556i
$202$	−109.363	−	109.363i	−0.541400	−	0.541400i
$203$	57.2397	+	57.2397i	0.281969	+	0.281969i
$204$	−17.7203	+	8.23782i	−0.0868640	+	0.0403815i
$205$	−2.15964	+	7.63770i	−0.0105348	+	0.0372571i
$206$			66.4628i			0.322635i
$207$	130.453			0.630207
$208$	−9.37668	−	9.37668i	−0.0450802	−	0.0450802i
$209$	−226.311	+	226.311i	−1.08283	+	1.08283i
$210$	−20.5249	−	5.80363i	−0.0977376	−	0.0276363i
$211$	−62.0539	+	62.0539i	−0.294094	+	0.294094i	−0.838695	−	0.544601i	$-0.816681\pi$
$211$	−62.0539	+	62.0539i	−0.294094	+	0.294094i	0.544601	+	0.838695i	$0.316681\pi$
$212$	−31.7072	−	31.7072i	−0.149562	−	0.149562i
$213$	50.3798	−	50.3798i	0.236525	−	0.236525i
$214$	−126.469	−	126.469i	−0.590975	−	0.590975i
$215$	−24.1238	+	85.3154i	−0.112204	+	0.396816i
$216$	20.3112	+	20.3112i	0.0940336	+	0.0940336i
$217$	−30.2437	+	30.2437i	−0.139372	+	0.139372i
$218$			45.5869i			0.209114i
$219$	−9.58137			−0.0437506
$220$	175.657	+	49.6689i	0.798441	+	0.225768i
$221$	−52.9363	−	19.3375i	−0.239531	−	0.0875001i
$222$	−8.07170	+	8.07170i	−0.0363590	+	0.0363590i
$223$	185.784	−	185.784i	0.833113	−	0.833113i	−0.154828	−	0.987941i	$-0.549482\pi$
$223$	185.784	−	185.784i	0.833113	−	0.833113i	0.987941	+	0.154828i	$0.0494824\pi$
$224$	20.9933	−	20.9933i	0.0937199	−	0.0937199i
$225$	113.497	−	184.649i	0.504433	−	0.820662i
$226$	49.3329	+	49.3329i	0.218287	+	0.218287i
$227$		−	61.7400i		−	0.271983i	−0.990710	−	0.135991i	$-0.956578\pi$
$227$		−	61.7400i		−	0.271983i	0.990710	−	0.135991i	$-0.0434219\pi$
$228$	20.1540			0.0883946
$229$	165.553			0.722940			0.361470	−	0.932384i	$-0.382275\pi$
$229$	165.553			0.722940			0.361470	+	0.932384i	$0.382275\pi$
$230$	−102.384	−	28.9503i	−0.445149	−	0.125871i
$231$	−38.9360	+	38.9360i	−0.168554	+	0.168554i
$232$			43.6252i			0.188040i
$233$		−	214.841i		−	0.922065i	−0.887383	−	0.461033i	$-0.847479\pi$
$233$		−	214.841i		−	0.922065i	0.887383	−	0.461033i	$-0.152521\pi$
$234$			40.6463i			0.173702i
$235$	−58.5236	+	206.972i	−0.249037	+	0.880733i
$236$			30.2013i			0.127972i
$237$	56.3621	−	56.3621i	0.237815	−	0.237815i
$238$	43.2944	−	118.518i	0.181909	−	0.497975i
$239$			29.8241i			0.124787i	0.998052	+	0.0623935i	$0.0198734\pi$
$239$			29.8241i			0.124787i	−0.998052	+	0.0623935i	$0.980127\pi$
$240$	−5.60990	−	10.0331i	−0.0233746	−	0.0418047i
$241$	−245.980	−	245.980i	−1.02067	−	1.02067i	−0.999782	−	0.0208834i	$-0.993352\pi$
$241$	−245.980	−	245.980i	−1.02067	−	1.02067i	−0.0208834	−	0.999782i	$-0.506648\pi$
$242$	212.223	−	212.223i	0.876957	−	0.876957i
$243$		−	132.892i		−	0.546880i
$244$	101.184	+	101.184i	0.414690	+	0.414690i
$245$	−93.6332	+	52.3538i	−0.382176	+	0.213689i
$246$		−	1.29029i		−	0.00524510i
$247$	41.1000	+	41.1000i	0.166397	+	0.166397i
$248$	−23.0502			−0.0929444
$249$	45.5603	+	45.5603i	0.182973	+	0.182973i
$250$	−130.055	+	119.732i	−0.520219	+	0.478928i
$251$	−61.2489			−0.244020			−0.122010	−	0.992529i	$-0.538934\pi$
$251$	−61.2489			−0.244020			−0.122010	+	0.992529i	$0.538934\pi$
$252$	−91.0023			−0.361120
$253$	−194.224	+	194.224i	−0.767685	+	0.767685i
$254$			285.022i			1.12213i
$255$	−39.5955	−	28.6160i	−0.155277	−	0.112220i
$256$	16.0000			0.0625000
$257$	306.355	+	306.355i	1.19204	+	1.19204i	0.976493	+	0.215549i	$0.0691540\pi$
$257$	306.355	+	306.355i	1.19204	+	1.19204i	0.215549	+	0.976493i	$0.430846\pi$
$258$		−	14.4130i		−	0.0558642i
$259$		−	73.7067i		−	0.284582i
$260$	9.02029	−	31.9008i	0.0346934	−	0.122695i
$261$	94.5539	−	94.5539i	0.362276	−	0.362276i
$262$			152.217i			0.580979i
$263$	229.501	−	229.501i	0.872627	−	0.872627i	−0.120131	−	0.992758i	$-0.538332\pi$
$263$	229.501	−	229.501i	0.872627	−	0.872627i	0.992758	+	0.120131i	$0.0383315\pi$
$264$	−29.6750			−0.112405
$265$	30.5021	−	107.872i	0.115102	−	0.407066i
$266$	−92.0179	+	92.0179i	−0.345932	+	0.345932i
$267$	−96.6228			−0.361883
$268$	−87.1188	−	87.1188i	−0.325070	−	0.325070i
$269$	−295.364	+	295.364i	−1.09801	+	1.09801i	−0.103362	+	0.994644i	$0.532960\pi$
$269$	−295.364	+	295.364i	−1.09801	+	1.09801i	−0.994644	+	0.103362i	$0.967040\pi$
$270$	−19.5393	+	69.1018i	−0.0723676	+	0.255932i
$271$	−312.139			−1.15180			−0.575902	−	0.817519i	$-0.695349\pi$
$271$	−312.139			−1.15180			−0.575902	+	0.817519i	$0.695349\pi$
$272$	61.6626	−	28.6658i	0.226701	−	0.105389i
$273$	7.07111	+	7.07111i	0.0259015	+	0.0259015i
$274$	−92.9660			−0.339292
$275$	105.934	+	443.895i	0.385214	+	1.61416i
$276$	17.2965			0.0626686
$277$	213.540			0.770904			0.385452	−	0.922728i	$-0.374045\pi$
$277$	213.540			0.770904			0.385452	+	0.922728i	$0.374045\pi$
$278$	56.3365			0.202649
$279$	49.9594	+	49.9594i	0.179066	+	0.179066i
$280$	71.4221	+	20.1954i	0.255079	+	0.0721263i
$281$			289.369i			1.02978i	0.857255	+	0.514892i	$0.172168\pi$
$281$			289.369i			1.02978i	−0.857255	+	0.514892i	$0.827832\pi$
$282$		−	34.9654i		−	0.123991i
$283$	503.475			1.77906			0.889532	−	0.456872i	$-0.151030\pi$
$283$	503.475			1.77906			0.889532	+	0.456872i	$0.151030\pi$
$284$	−175.311	+	175.311i	−0.617291	+	0.617291i
$285$	24.5894	+	43.9773i	0.0862785	+	0.154306i
$286$	−60.5162	−	60.5162i	−0.211595	−	0.211595i
$287$	5.89116	+	5.89116i	0.0205267	+	0.0205267i
$288$	−34.6787	−	34.6787i	−0.120412	−	0.120412i
$289$	186.284	−	220.951i	0.644582	−	0.764535i
$290$	−95.1931	+	53.2260i	−0.328252	+	0.183538i
$291$			110.500i			0.379726i
$292$	33.3411			0.114182
$293$	−308.280	−	308.280i	−1.05215	−	1.05215i	−0.998563	−	0.0535887i	$-0.982934\pi$
$293$	−308.280	−	308.280i	−1.05215	−	1.05215i	−0.0535887	−	0.998563i	$-0.517066\pi$
$294$	12.3313	−	12.3313i	0.0419433	−	0.0419433i
$295$	−65.9013	+	36.8479i	−0.223394	+	0.124908i
$296$	28.0877	−	28.0877i	0.0948910	−	0.0948910i
$297$	131.087	+	131.087i	0.441370	+	0.441370i
$298$	−265.320	+	265.320i	−0.890336	+	0.890336i
$299$	35.2728	+	35.2728i	0.117969	+	0.117969i
$300$	15.0485	−	24.4823i	0.0501616	−	0.0816078i
$301$	65.8059	+	65.8059i	0.218624	+	0.218624i
$302$	119.231	−	119.231i	0.394805	−	0.394805i
$303$			62.8562i			0.207446i
$304$	−70.1314			−0.230695
$305$	−97.3385	+	344.243i	−0.319143	+	1.12867i
$306$	−195.779	−	71.5178i	−0.639801	−	0.233718i
$307$	−209.141	+	209.141i	−0.681243	+	0.681243i	−0.960280	−	0.279038i	$-0.909985\pi$
$307$	−209.141	+	209.141i	−0.681243	+	0.681243i	0.279038	+	0.960280i	$0.409985\pi$
$308$	135.489	−	135.489i	0.439898	−	0.439898i
$309$	19.0997	−	19.0997i	0.0618114	−	0.0618114i
$310$	−28.1230	−	50.2971i	−0.0907193	−	0.162249i
$311$	−188.092	−	188.092i	−0.604798	−	0.604798i	0.336784	−	0.941582i	$-0.390661\pi$
$311$	−188.092	−	188.092i	−0.604798	−	0.604798i	−0.941582	+	0.336784i	$0.890661\pi$
$312$			5.38924i			0.0172732i
$313$	−231.073			−0.738252			−0.369126	−	0.929379i	$-0.620343\pi$
$313$	−231.073			−0.738252			−0.369126	+	0.929379i	$0.620343\pi$
$314$	276.066			0.879191
$315$	−111.030	−	198.573i	−0.352475	−	0.630391i
$316$	−196.128	+	196.128i	−0.620657	+	0.620657i
$317$			89.1781i			0.281319i	0.990058	+	0.140659i	$0.0449223\pi$
$317$			89.1781i			0.281319i	−0.990058	+	0.140659i	$0.955078\pi$
$318$			18.2237i			0.0573072i
$319$			281.553i			0.882611i
$320$	19.5212	+	34.9131i	0.0610038	+	0.109103i
$321$			72.6878i			0.226442i
$322$	−78.9716	+	78.9716i	−0.245254	+	0.245254i
$323$	−270.280	+	125.648i	−0.836780	+	0.389004i
$324$			144.380i			0.445617i
$325$	80.6151	−	19.2385i	0.248046	−	0.0591954i
$326$	−259.022	−	259.022i	−0.794546	−	0.794546i
$327$	13.1005	−	13.1005i	0.0400627	−	0.0400627i
$328$			4.48994i			0.0136888i
$329$	159.643	+	159.643i	0.485237	+	0.485237i
$330$	−36.2058	−	64.7529i	−0.109714	−	0.196221i
$331$			115.403i			0.348650i	0.984688	+	0.174325i	$0.0557744\pi$
$331$			115.403i			0.348650i	−0.984688	+	0.174325i	$0.944226\pi$
$332$	−158.540	−	158.540i	−0.477529	−	0.477529i
$333$	−121.756			−0.365632
$334$	3.43597	+	3.43597i	0.0102873	+	0.0102873i
$335$	83.8075	−	296.390i	0.250172	−	0.884747i
$336$	−12.0659			−0.0359103
$337$	−166.064			−0.492772			−0.246386	−	0.969172i	$-0.579243\pi$
$337$	−166.064			−0.492772			−0.246386	+	0.969172i	$0.579243\pi$
$338$	158.010	−	158.010i	0.467484	−	0.467484i
$339$		−	28.3540i		−	0.0836402i
$340$	137.784	+	99.5775i	0.405246	+	0.292875i
$341$	−148.764			−0.436258
$342$	152.004	+	152.004i	0.444456	+	0.444456i
$343$			369.771i			1.07805i
$344$			50.1539i			0.145796i
$345$	21.1031	+	37.7422i	0.0611684	+	0.109398i
$346$	135.662	−	135.662i	0.392088	−	0.392088i
$347$		−	412.331i		−	1.18827i	−0.804364	−	0.594136i	$-0.797494\pi$
$347$		−	412.331i		−	1.18827i	0.804364	−	0.594136i	$-0.202506\pi$
$348$	12.5368	−	12.5368i	0.0360252	−	0.0360252i
$349$	−140.292			−0.401982			−0.200991	−	0.979593i	$-0.564416\pi$
$349$	−140.292			−0.401982			−0.200991	+	0.979593i	$0.564416\pi$
$350$	43.0727	+	180.488i	0.123065	+	0.515679i
$351$	23.8065	−	23.8065i	0.0678248	−	0.0678248i
$352$	103.263			0.293359
$353$	323.896	+	323.896i	0.917552	+	0.917552i	0.996851	−	0.0792988i	$-0.0252681\pi$
$353$	323.896	+	323.896i	0.917552	+	0.917552i	−0.0792988	+	0.996851i	$0.525268\pi$
$354$	8.67909	−	8.67909i	0.0245172	−	0.0245172i
$355$	−596.432	−	168.647i	−1.68009	−	0.475063i
$356$	336.226			0.944455
$357$	−46.5008	+	21.6173i	−0.130254	+	0.0605528i
$358$	199.538	+	199.538i	0.557369	+	0.557369i
$359$	259.039			0.721556			0.360778	−	0.932652i	$-0.382511\pi$
$359$	259.039			0.721556			0.360778	+	0.932652i	$0.382511\pi$
$360$	33.3606	−	117.982i	0.0926683	−	0.327727i
$361$	−53.5995			−0.148475
$362$	352.585			0.973993
$363$	−121.975			−0.336020
$364$	−24.6059	−	24.6059i	−0.0675986	−	0.0675986i
$365$	40.6786	+	72.7524i	0.111448	+	0.199322i
$366$		−	58.1556i		−	0.158895i
$367$		−	295.835i		−	0.806089i	−0.915180	−	0.403045i	$-0.867952\pi$
$367$		−	295.835i		−	0.806089i	0.915180	−	0.403045i	$-0.132048\pi$
$368$	−60.1882			−0.163555
$369$	9.73156	−	9.73156i	0.0263728	−	0.0263728i
$370$	95.5585	+	27.0202i	0.258266	+	0.0730275i
$371$	−83.2047	−	83.2047i	−0.224271	−	0.224271i
$372$	6.62404	+	6.62404i	0.0178066	+	0.0178066i
$373$	−290.339	−	290.339i	−0.778389	−	0.778389i	0.201168	−	0.979557i	$-0.435526\pi$
$373$	−290.339	−	290.339i	−0.778389	−	0.778389i	−0.979557	+	0.201168i	$0.935526\pi$
$374$	397.965	−	185.006i	1.06408	−	0.494669i
$375$	71.7824	+	2.96646i	0.191420	+	0.00791057i
$376$			121.672i			0.323595i
$377$	51.1324			0.135630
$378$	53.2999	+	53.2999i	0.141005	+	0.141005i
$379$	−385.744	+	385.744i	−1.01779	+	1.01779i	−0.0179549	+	0.999839i	$0.505716\pi$
$379$	−385.744	+	385.744i	−1.01779	+	1.01779i	−0.999839	+	0.0179549i	$0.994284\pi$
$380$	−85.5655	−	153.031i	−0.225172	−	0.402714i
$381$	81.9081	−	81.9081i	0.214982	−	0.214982i
$382$	−140.941	−	140.941i	−0.368955	−	0.368955i
$383$	502.097	−	502.097i	1.31096	−	1.31096i	0.390249	−	0.920709i	$-0.372389\pi$
$383$	502.097	−	502.097i	1.31096	−	1.31096i	0.920709	−	0.390249i	$-0.127611\pi$
$384$	−4.59799	−	4.59799i	−0.0119739	−	0.0119739i
$385$	460.952	+	130.339i	1.19728	+	0.338543i
$386$	123.427	+	123.427i	0.319759	+	0.319759i
$387$	108.704	−	108.704i	0.280890	−	0.280890i
$388$		−	384.517i		−	0.991023i
$389$	−268.339			−0.689819			−0.344909	−	0.938636i	$-0.612090\pi$
$389$	−268.339			−0.689819			−0.344909	+	0.938636i	$0.612090\pi$
$390$	−11.7597	+	6.57528i	−0.0301530	+	0.0168597i
$391$	−231.960	+	107.834i	−0.593248	+	0.275790i
$392$	−42.9103	+	42.9103i	−0.109465	+	0.109465i
$393$	43.7432	−	43.7432i	0.111306	−	0.111306i
$394$	212.768	−	212.768i	0.540021	−	0.540021i
$395$	−667.254	−	188.673i	−1.68925	−	0.477654i
$396$	−223.813	−	223.813i	−0.565184	−	0.565184i
$397$		−	96.6764i		−	0.243517i	−0.992560	−	0.121759i	$-0.961147\pi$
$397$		−	96.6764i		−	0.243517i	0.992560	−	0.121759i	$-0.0388534\pi$
$398$	255.002			0.640708
$399$	52.8872			0.132549
$400$	−52.3653	+	85.1931i	−0.130913	+	0.212983i
$401$	469.176	−	469.176i	1.17001	−	1.17001i	0.187809	−	0.982206i	$-0.439861\pi$
$401$	469.176	−	469.176i	1.17001	−	1.17001i	0.982206	−	0.187809i	$-0.0601386\pi$
$402$			50.0714i			0.124556i
$403$			27.0168i			0.0670392i
$404$		−	218.726i		−	0.541400i
$405$	−315.047	+	176.155i	−0.777894	+	0.434949i
$406$			114.479i			0.281969i
$407$	181.276	−	181.276i	0.445395	−	0.445395i
$408$	−25.9581	−	9.48244i	−0.0636227	−	0.0232413i
$409$		−	372.062i		−	0.909688i	−0.890571	−	0.454844i	$-0.849695\pi$
$409$		−	372.062i		−	0.909688i	0.890571	−	0.454844i	$-0.150305\pi$
$410$	−9.79735	+	5.47806i	−0.0238960	+	0.0133611i
$411$	26.7161	+	26.7161i	0.0650026	+	0.0650026i
$412$	−66.4628	+	66.4628i	−0.161317	+	0.161317i
$413$			79.2530i			0.191896i
$414$	130.453	+	130.453i	0.315103	+	0.315103i
$415$	152.514	−	539.374i	0.367503	−	1.29970i
$416$		−	18.7534i		−	0.0450802i
$417$	−16.1897	−	16.1897i	−0.0388242	−	0.0388242i
$418$	−452.621			−1.08283
$419$	−540.057	−	540.057i	−1.28892	−	1.28892i	−0.935443	−	0.353477i	$-0.884999\pi$
$419$	−540.057	−	540.057i	−1.28892	−	1.28892i	−0.353477	−	0.935443i	$-0.615001\pi$
$420$	−14.7213	−	26.3285i	−0.0350506	−	0.0626870i
$421$	434.929			1.03308			0.516542	−	0.856262i	$-0.327219\pi$
$421$	434.929			1.03308			0.516542	+	0.856262i	$0.327219\pi$
$422$	−124.108			−0.294094
$423$	263.713	−	263.713i	0.623435	−	0.623435i
$424$		−	63.4144i		−	0.149562i
$425$	−49.1783	+	422.145i	−0.115714	+	0.993283i
$426$	100.760			0.236525
$427$	265.524	+	265.524i	0.621835	+	0.621835i
$428$		−	252.937i		−	0.590975i
$429$			34.7817i			0.0810761i
$430$	−109.439	+	61.1916i	−0.254510	+	0.142306i
$431$	−292.074	+	292.074i	−0.677667	+	0.677667i	−0.959472	−	0.281805i	$-0.909067\pi$
$431$	−292.074	+	292.074i	−0.677667	+	0.677667i	0.281805	+	0.959472i	$0.409067\pi$
$432$			40.6225i			0.0940336i
$433$	−567.368	+	567.368i	−1.31032	+	1.31032i	−0.389141	+	0.921178i	$0.627228\pi$
$433$	−567.368	+	567.368i	−1.31032	+	1.31032i	−0.921178	+	0.389141i	$0.872772\pi$
$434$	−60.4874			−0.139372
$435$	42.6519	+	12.0603i	0.0980503	+	0.0277248i
$436$	−45.5869	+	45.5869i	−0.104557	+	0.104557i
$437$	263.817			0.603701
$438$	−9.58137	−	9.58137i	−0.0218753	−	0.0218753i
$439$	10.2750	−	10.2750i	0.0234055	−	0.0234055i	−0.695307	−	0.718713i	$-0.744732\pi$
$439$	10.2750	−	10.2750i	0.0234055	−	0.0234055i	0.718713	+	0.695307i	$0.244732\pi$
$440$	125.988	+	225.326i	0.286336	+	0.512104i
$441$	186.009			0.421789
$442$	−33.5987	−	72.2738i	−0.0760152	−	0.163515i
$443$	105.663	+	105.663i	0.238516	+	0.238516i	0.816235	−	0.577719i	$-0.196057\pi$
$443$	105.663	+	105.663i	0.238516	+	0.238516i	−0.577719	+	0.816235i	$0.696057\pi$
$444$	−16.1434			−0.0363590
$445$	410.221	+	733.667i	0.921845	+	1.64869i
$446$	371.568			0.833113
$447$	152.493			0.341147
$448$	41.9865			0.0937199
$449$	−604.148	−	604.148i	−1.34554	−	1.34554i	−0.890439	−	0.455102i	$-0.849603\pi$
$449$	−604.148	−	604.148i	−1.34554	−	1.34554i	−0.455102	−	0.890439i	$-0.650397\pi$
$450$	298.146	−	71.1515i	0.662548	−	0.158114i
$451$			28.9777i			0.0642520i
$452$			98.6658i			0.218287i
$453$	−68.5279			−0.151276
$454$	61.7400	−	61.7400i	0.135991	−	0.135991i
$455$	23.6707	−	83.7127i	0.0520235	−	0.183984i
$456$	20.1540	+	20.1540i	0.0441973	+	0.0441973i
$457$	119.959	+	119.959i	0.262493	+	0.262493i	0.826066	−	0.563573i	$-0.190574\pi$
$457$	119.959	+	119.959i	0.262493	+	0.262493i	−0.563573	+	0.826066i	$0.690574\pi$
$458$	165.553	+	165.553i	0.361470	+	0.361470i
$459$	72.7797	+	156.555i	0.158562	+	0.341079i
$460$	−73.4341	−	131.335i	−0.159639	−	0.285510i
$461$			489.295i			1.06138i	0.847567	+	0.530689i	$0.178067\pi$
$461$			489.295i			1.06138i	−0.847567	+	0.530689i	$0.821933\pi$
$462$	−77.8720			−0.168554
$463$	176.939	+	176.939i	0.382157	+	0.382157i	0.871879	−	0.489722i	$-0.162902\pi$
$463$	176.939	+	176.939i	0.382157	+	0.382157i	−0.489722	+	0.871879i	$0.662902\pi$
$464$	−43.6252	+	43.6252i	−0.0940198	+	0.0940198i
$465$	−6.37228	+	22.5359i	−0.0137038	+	0.0484644i
$466$	214.841	−	214.841i	0.461033	−	0.461033i
$467$	−502.175	−	502.175i	−1.07532	−	1.07532i	−0.996922	−	0.0783999i	$-0.975019\pi$
$467$	−502.175	−	502.175i	−1.07532	−	1.07532i	−0.0783999	−	0.996922i	$-0.524981\pi$
$468$	−40.6463	+	40.6463i	−0.0868511	+	0.0868511i
$469$	−228.613	−	228.613i	−0.487449	−	0.487449i
$470$	−265.496	+	148.449i	−0.564885	+	0.315848i
$471$	−79.3343	−	79.3343i	−0.168438	−	0.168438i
$472$	−30.2013	+	30.2013i	−0.0639858	+	0.0639858i
$473$			323.689i			0.684332i
$474$	112.724			0.237815
$475$	229.528	−	373.419i	0.483217	−	0.786146i
$476$	161.812	−	75.2236i	0.339942	−	0.158033i
$477$	−137.445	+	137.445i	−0.288145	+	0.288145i
$478$	−29.8241	+	29.8241i	−0.0623935	+	0.0623935i
$479$	215.836	−	215.836i	0.450597	−	0.450597i	−0.444955	−	0.895553i	$-0.646780\pi$
$479$	215.836	−	215.836i	0.450597	−	0.450597i	0.895553	+	0.444955i	$0.146780\pi$
$480$	4.42323	−	15.6430i	0.00921507	−	0.0325896i
$481$	−32.9212	−	32.9212i	−0.0684433	−	0.0684433i
$482$		−	491.961i		−	1.02067i
$483$	45.3889			0.0939728
$484$	424.447			0.876957
$485$	839.041	−	469.139i	1.72998	−	0.967298i
$486$	132.892	−	132.892i	0.273440	−	0.273440i
$487$			476.790i			0.979034i	0.871994	+	0.489517i	$0.162827\pi$
$487$			476.790i			0.979034i	−0.871994	+	0.489517i	$0.837173\pi$
$488$			202.369i			0.414690i
$489$			148.873i			0.304443i
$490$	−145.987	−	41.2794i	−0.297933	−	0.0842437i
$491$		−	154.218i		−	0.314090i	−0.987591	−	0.157045i	$-0.949803\pi$
$491$		−	154.218i		−	0.314090i	0.987591	−	0.157045i	$-0.0501968\pi$
$492$	1.29029	−	1.29029i	0.00262255	−	0.00262255i
$493$	−89.9682	+	246.287i	−0.182491	+	0.499568i
$494$			82.1999i			0.166397i
$495$	215.306	−	761.443i	0.434962	−	1.53827i
$496$	−23.0502	−	23.0502i	−0.0464722	−	0.0464722i
$497$	−460.043	+	460.043i	−0.925640	+	0.925640i
$498$			91.1205i			0.182973i
$499$	488.476	+	488.476i	0.978911	+	0.978911i	0.999782	−	0.0208717i	$-0.00664414\pi$
$499$	488.476	+	488.476i	0.978911	+	0.978911i	−0.0208717	+	0.999782i	$0.506644\pi$
$500$	−249.787	−	10.3226i	−0.499574	−	0.0206453i
$501$		−	1.97482i		−	0.00394176i
$502$	−61.2489	−	61.2489i	−0.122010	−	0.122010i
$503$	−260.464			−0.517820			−0.258910	−	0.965901i	$-0.583363\pi$
$503$	−260.464			−0.517820			−0.258910	+	0.965901i	$0.583363\pi$
$504$	−91.0023	−	91.0023i	−0.180560	−	0.180560i
$505$	477.274	−	266.862i	0.945097	−	0.528439i
$506$	−388.449			−0.767685
$507$	−90.8160			−0.179124
$508$	−285.022	+	285.022i	−0.561067	+	0.561067i
$509$		−	516.198i		−	1.01414i	−0.861904	−	0.507071i	$-0.830728\pi$
$509$		−	516.198i		−	1.01414i	0.861904	−	0.507071i	$-0.169272\pi$
$510$	−10.9795	−	68.2115i	−0.0215284	−	0.133748i
$511$	87.4922			0.171218
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$		−	178.057i		−	0.347090i
$514$			612.709i			1.19204i
$515$	−226.116	−	63.9367i	−0.439060	−	0.124149i
$516$	14.4130	−	14.4130i	0.0279321	−	0.0279321i
$517$			785.258i			1.51887i
$518$	73.7067	−	73.7067i	0.142291	−	0.142291i
$519$	−77.9719			−0.150235
$520$	40.9211	−	22.8805i	0.0786944	−	0.0440010i
$521$	−18.7611	+	18.7611i	−0.0360097	+	0.0360097i	−0.724882	−	0.688873i	$-0.758106\pi$
$521$	−18.7611	+	18.7611i	−0.0360097	+	0.0360097i	0.688873	+	0.724882i	$0.258106\pi$
$522$	189.108			0.362276
$523$	166.619	+	166.619i	0.318582	+	0.318582i	0.848223	−	0.529640i	$-0.177673\pi$
$523$	166.619	+	166.619i	0.318582	+	0.318582i	−0.529640	+	0.848223i	$0.677673\pi$
$524$	−152.217	+	152.217i	−0.290490	+	0.290490i
$525$	39.4896	−	64.2456i	0.0752182	−	0.122372i
$526$	459.002			0.872627
$527$	−130.130	−	47.5364i	−0.246927	−	0.0902020i
$528$	−29.6750	−	29.6750i	−0.0562027	−	0.0562027i
$529$	−302.587			−0.571997
$530$	138.374	−	77.3703i	0.261084	−	0.145982i
$531$	130.918			0.246549
$532$	−184.036			−0.345932
$533$	5.26259			0.00987353
$534$	−96.6228	−	96.6228i	−0.180942	−	0.180942i
$535$	551.926	−	308.603i	1.03164	−	0.576827i
$536$		−	174.238i		−	0.325070i
$537$		−	114.684i		−	0.213565i
$538$	−590.727			−1.09801
$539$	−276.939	+	276.939i	−0.513802	+	0.513802i
$540$	−88.6410	+	49.5625i	−0.164150	+	0.0917824i
$541$	414.064	+	414.064i	0.765369	+	0.765369i	0.977287	−	0.211919i	$-0.0679712\pi$
$541$	414.064	+	414.064i	0.765369	+	0.765369i	−0.211919	+	0.977287i	$0.567971\pi$
$542$	−312.139	−	312.139i	−0.575902	−	0.575902i
$543$	−101.324	−	101.324i	−0.186601	−	0.186601i
$544$	90.3284	+	32.9968i	0.166045	+	0.0606559i
$545$	−155.093	−	43.8542i	−0.284574	−	0.0804665i
$546$			14.1422i			0.0259015i
$547$	−795.932			−1.45509			−0.727543	−	0.686062i	$-0.759338\pi$
$547$	−795.932			−1.45509			−0.727543	+	0.686062i	$0.759338\pi$
$548$	−92.9660	−	92.9660i	−0.169646	−	0.169646i
$549$	438.617	−	438.617i	0.798938	−	0.798938i
$550$	−337.961	+	549.829i	−0.614475	+	0.999689i
$551$	191.218	−	191.218i	0.347039	−	0.347039i
$552$	17.2965	+	17.2965i	0.0313343	+	0.0313343i
$553$	−514.670	+	514.670i	−0.930687	+	0.930687i
$554$	213.540	+	213.540i	0.385452	+	0.385452i
$555$	−19.6962	−	35.2260i	−0.0354886	−	0.0634703i
$556$	56.3365	+	56.3365i	0.101325	+	0.101325i
$557$	−592.276	+	592.276i	−1.06333	+	1.06333i	−0.0654775	+	0.997854i	$0.520857\pi$
$557$	−592.276	+	592.276i	−1.06333	+	1.06333i	−0.997854	+	0.0654775i	$0.979143\pi$
$558$			99.9188i			0.179066i
$559$	58.7847			0.105160
$560$	51.2267	+	91.6174i	0.0914763	+	0.163603i
$561$	−167.531	−	61.1988i	−0.298629	−	0.109089i
$562$	−289.369	+	289.369i	−0.514892	+	0.514892i
$563$	418.457	−	418.457i	0.743264	−	0.743264i	−0.229941	−	0.973205i	$-0.573853\pi$
$563$	418.457	−	418.457i	0.743264	−	0.743264i	0.973205	+	0.229941i	$0.0738533\pi$
$564$	34.9654	−	34.9654i	0.0619953	−	0.0619953i
$565$	−215.295	+	120.380i	−0.381054	+	0.213061i
$566$	503.475	+	503.475i	0.889532	+	0.889532i
$567$			378.876i			0.668212i
$568$	−350.621			−0.617291
$569$	−497.904			−0.875051			−0.437526	−	0.899206i	$-0.644145\pi$
$569$	−497.904			−0.875051			−0.437526	+	0.899206i	$0.644145\pi$
$570$	−19.3880	+	68.5667i	−0.0340140	+	0.120292i
$571$	−463.161	+	463.161i	−0.811140	+	0.811140i	−0.984805	−	0.173665i	$-0.944439\pi$
$571$	−463.161	+	463.161i	−0.811140	+	0.811140i	0.173665	+	0.984805i	$0.444439\pi$
$572$		−	121.032i		−	0.211595i
$573$			81.0057i			0.141371i
$574$			11.7823i			0.0205267i
$575$	196.986	−	320.476i	0.342584	−	0.557350i
$576$		−	69.3573i		−	0.120412i
$577$	−343.864	+	343.864i	−0.595952	+	0.595952i	−0.939233	−	0.343281i	$-0.888462\pi$
$577$	−343.864	+	343.864i	−0.595952	+	0.595952i	0.343281	+	0.939233i	$0.388462\pi$
$578$	407.235	−	34.6666i	0.704559	−	0.0599769i
$579$		−	70.9396i		−	0.122521i
$580$	−148.419	−	41.9671i	−0.255895	−	0.0723571i
$581$	−416.033	−	416.033i	−0.716064	−	0.716064i
$582$	−110.500	+	110.500i	−0.189863	+	0.189863i
$583$		−	409.271i		−	0.702008i
$584$	33.3411	+	33.3411i	0.0570908	+	0.0570908i
$585$	−138.285	−	39.1014i	−0.236384	−	0.0668401i
$586$		−	616.561i		−	1.05215i
$587$	−32.0640	−	32.0640i	−0.0546235	−	0.0546235i	0.679267	−	0.733891i	$-0.262298\pi$
$587$	−32.0640	−	32.0640i	−0.0546235	−	0.0546235i	−0.733891	+	0.679267i	$0.762298\pi$
$588$	24.6627			0.0419433
$589$	101.034	+	101.034i	0.171535	+	0.171535i
$590$	−102.749	−	29.0534i	−0.174151	−	0.0492431i
$591$	−122.288			−0.206918
$592$	56.1755			0.0948910
$593$	533.068	−	533.068i	0.898934	−	0.898934i	−0.0964076	−	0.995342i	$-0.530735\pi$
$593$	533.068	−	533.068i	0.898934	−	0.898934i	0.995342	+	0.0964076i	$0.0307352\pi$
$594$			262.174i			0.441370i
$595$	361.566	+	261.307i	0.607674	+	0.439172i
$596$	−530.640			−0.890336
$597$	−73.2811	−	73.2811i	−0.122749	−	0.122749i
$598$			70.5456i			0.117969i
$599$		−	665.756i		−	1.11145i	−0.831368	−	0.555723i	$-0.812442\pi$
$599$		−	665.756i		−	1.11145i	0.831368	−	0.555723i	$-0.187558\pi$
$600$	39.5308	−	9.43388i	0.0658847	−	0.0157231i
$601$	354.228	−	354.228i	0.589398	−	0.589398i	−0.348070	−	0.937468i	$-0.613163\pi$
$601$	354.228	−	354.228i	0.589398	−	0.589398i	0.937468	+	0.348070i	$0.113163\pi$
$602$			131.612i			0.218624i
$603$	−377.645	+	377.645i	−0.626277	+	0.626277i
$604$	238.462			0.394805
$605$	517.857	+	926.172i	0.855962	+	1.53086i
$606$	−62.8562	+	62.8562i	−0.103723	+	0.103723i
$607$	−388.073			−0.639330			−0.319665	−	0.947531i	$-0.603570\pi$
$607$	−388.073			−0.639330			−0.319665	+	0.947531i	$0.603570\pi$
$608$	−70.1314	−	70.1314i	−0.115348	−	0.115348i
$609$	32.8985	−	32.8985i	0.0540205	−	0.0540205i
$610$	−441.582	+	246.905i	−0.723905	+	0.404762i
$611$	142.610			0.233404
$612$	−124.261	−	267.297i	−0.203041	−	0.436760i
$613$	334.081	+	334.081i	0.544993	+	0.544993i	0.924989	−	0.379995i	$-0.124074\pi$
$613$	334.081	+	334.081i	0.544993	+	0.544993i	−0.379995	+	0.924989i	$0.624074\pi$
$614$	−418.283			−0.681243
$615$	4.38976	+	1.24125i	0.00713783	+	0.00201830i
$616$	270.977			0.439898
$617$	1053.98			1.70823			0.854115	−	0.520084i	$-0.174099\pi$
$617$	1053.98			1.70823			0.854115	+	0.520084i	$0.174099\pi$
$618$	38.1994			0.0618114
$619$	159.005	+	159.005i	0.256873	+	0.256873i	0.823781	−	0.566908i	$-0.191860\pi$
$619$	159.005	+	159.005i	0.256873	+	0.256873i	−0.566908	+	0.823781i	$0.691860\pi$
$620$	22.1741	−	78.4201i	0.0357647	−	0.126484i
$621$		−	152.812i		−	0.246074i
$622$		−	376.184i		−	0.604798i
$623$	882.310			1.41623
$624$	−5.38924	+	5.38924i	−0.00863660	+	0.00863660i
$625$	−282.234	−	557.646i	−0.451574	−	0.892234i
$626$	−231.073	−	231.073i	−0.369126	−	0.369126i
$627$	130.072	+	130.072i	0.207451	+	0.207451i
$628$	276.066	+	276.066i	0.439595	+	0.439595i
$629$	216.495	−	100.645i	0.344190	−	0.160007i
$630$	87.5435	−	309.603i	0.138958	−	0.491433i
$631$			686.287i			1.08762i	0.839209	+	0.543809i	$0.183019\pi$
$631$			686.287i			1.08762i	−0.839209	+	0.543809i	$0.816981\pi$
$632$	−392.255			−0.620657
$633$	35.6654	+	35.6654i	0.0563435	+	0.0563435i
$634$	−89.1781	+	89.1781i	−0.140659	+	0.140659i
$635$	−969.685	−	274.189i	−1.52706	−	0.431793i
$636$	−18.2237	+	18.2237i	−0.0286536	+	0.0286536i
$637$	50.2946	+	50.2946i	0.0789553	+	0.0789553i
$638$	−281.553	+	281.553i	−0.441306	+	0.441306i
$639$	759.942	+	759.942i	1.18927	+	1.18927i
$640$	−15.3919	+	54.4343i	−0.0240498	+	0.0850536i
$641$	458.486	+	458.486i	0.715267	+	0.715267i	0.967632	−	0.252365i	$-0.0812085\pi$
$641$	458.486	+	458.486i	0.715267	+	0.715267i	−0.252365	+	0.967632i	$0.581208\pi$
$642$	−72.6878	+	72.6878i	−0.113221	+	0.113221i
$643$		−	267.670i		−	0.416282i	−0.978099	−	0.208141i	$-0.933259\pi$
$643$		−	267.670i		−	0.416282i	0.978099	−	0.208141i	$-0.0667414\pi$
$644$	−157.943			−0.245254
$645$	49.0350	+	13.8652i	0.0760232	+	0.0214964i
$646$	−395.928	−	144.632i	−0.612892	−	0.223888i
$647$	−653.020	+	653.020i	−1.00931	+	1.00931i	−0.00934880	+	0.999956i	$0.502976\pi$
$647$	−653.020	+	653.020i	−1.00931	+	1.00931i	−0.999956	+	0.00934880i	$0.997024\pi$
$648$	−144.380	+	144.380i	−0.222809	+	0.222809i
$649$	−194.916	+	194.916i	−0.300333	+	0.300333i
$650$	99.8536	+	61.3766i	0.153621	+	0.0944256i
$651$	17.3825	+	17.3825i	0.0267013	+	0.0267013i
$652$		−	518.044i		−	0.794546i
$653$	1042.04			1.59578			0.797888	−	0.602805i	$-0.205950\pi$
$653$	1042.04			1.59578			0.797888	+	0.602805i	$0.205950\pi$
$654$	26.2010			0.0400627
$655$	−517.862	−	146.431i	−0.790630	−	0.223559i
$656$	−4.48994	+	4.48994i	−0.00684442	+	0.00684442i
$657$		−	144.528i		−	0.219981i
$658$			319.286i			0.485237i
$659$			20.9603i			0.0318062i	0.999874	+	0.0159031i	$0.00506232\pi$
$659$			20.9603i			0.0318062i	−0.999874	+	0.0159031i	$0.994938\pi$
$660$	28.5471	−	100.959i	0.0432532	−	0.152968i
$661$		−	275.237i		−	0.416394i	−0.978087	−	0.208197i	$-0.933240\pi$
$661$		−	275.237i		−	0.416394i	0.978087	−	0.208197i	$-0.0667595\pi$
$662$	−115.403	+	115.403i	−0.174325	+	0.174325i
$663$	−11.1142	+	30.4251i	−0.0167635	+	0.0458900i
$664$		−	317.079i		−	0.477529i
$665$	−224.538	−	401.578i	−0.337650	−	0.603877i
$666$	−121.756	−	121.756i	−0.182816	−	0.182816i
$667$	164.108	−	164.108i	0.246038	−	0.246038i
$668$			6.87194i			0.0102873i
$669$	−106.779	−	106.779i	−0.159610	−	0.159610i
$670$	380.198	−	212.583i	0.567460	−	0.317288i
$671$			1306.07i			1.94645i
$672$	−12.0659	−	12.0659i	−0.0179552	−	0.0179552i
$673$	75.4628			0.112129			0.0560645	−	0.998427i	$-0.482145\pi$
$673$	75.4628			0.112129			0.0560645	+	0.998427i	$0.482145\pi$
$674$	−166.064	−	166.064i	−0.246386	−	0.246386i
$675$	−216.297	−	132.951i	−0.320441	−	0.196964i
$676$	316.019			0.467484
$677$	612.921			0.905348			0.452674	−	0.891676i	$-0.350470\pi$
$677$	612.921			0.905348			0.452674	+	0.891676i	$0.350470\pi$
$678$	28.3540	−	28.3540i	0.0418201	−	0.0418201i
$679$		−	1009.03i		−	1.48606i
$680$	38.2062	+	237.361i	0.0561855	+	0.349060i
$681$	−35.4850			−0.0521072
$682$	−148.764	−	148.764i	−0.218129	−	0.218129i
$683$			369.424i			0.540884i	0.962736	+	0.270442i	$0.0871699\pi$
$683$			369.424i			0.540884i	−0.962736	+	0.270442i	$0.912830\pi$
$684$			304.008i			0.444456i
$685$	89.4325	−	316.284i	0.130558	−	0.461728i
$686$	−369.771	+	369.771i	−0.539025	+	0.539025i
$687$		−	95.1516i		−	0.138503i
$688$	−50.1539	+	50.1539i	−0.0728982	+	0.0728982i
$689$	−74.3270			−0.107877
$690$	−16.6391	+	58.8453i	−0.0241147	+	0.0852831i
$691$	444.040	−	444.040i	0.642604	−	0.642604i	−0.308591	−	0.951195i	$-0.599857\pi$
$691$	444.040	−	444.040i	0.642604	−	0.642604i	0.951195	+	0.308591i	$0.0998573\pi$
$692$	271.325			0.392088
$693$	−587.320	−	587.320i	−0.847504	−	0.847504i
$694$	412.331	−	412.331i	0.594136	−	0.594136i
$695$	−54.1952	+	191.665i	−0.0779788	+	0.275777i
$696$	25.0735			0.0360252
$697$	−9.25960	+	25.3480i	−0.0132849	+	0.0363674i
$698$	−140.292	−	140.292i	−0.200991	−	0.200991i
$699$	−123.480			−0.176652
$700$	−137.415	+	223.560i	−0.196307	+	0.319372i
$701$	259.919			0.370783			0.185392	−	0.982665i	$-0.440645\pi$
$701$	259.919			0.370783			0.185392	+	0.982665i	$0.440645\pi$
$702$	47.6130			0.0678248
$703$	−246.229			−0.350254
$704$	103.263	+	103.263i	0.146680	+	0.146680i
$705$	118.957	+	33.6364i	0.168733	+	0.0477112i
$706$			647.792i			0.917552i
$707$		−	573.971i		−	0.811840i
$708$	17.3582			0.0245172
$709$	−40.1572	+	40.1572i	−0.0566391	+	0.0566391i	−0.734859	−	0.678220i	$-0.762752\pi$
$709$	−40.1572	+	40.1572i	−0.0566391	+	0.0566391i	0.678220	+	0.734859i	$0.262752\pi$
$710$	−427.784	−	765.079i	−0.602513	−	1.07758i
$711$	850.180	+	850.180i	1.19575	+	1.19575i
$712$	336.226	+	336.226i	0.472227	+	0.472227i
$713$	86.7094	+	86.7094i	0.121612	+	0.121612i
$714$	−68.1181	−	24.8834i	−0.0954035	−	0.0348507i
$715$	264.101	−	147.669i	0.369372	−	0.206530i
$716$			399.076i			0.557369i
$717$	17.1414			0.0239071
$718$	259.039	+	259.039i	0.360778	+	0.360778i
$719$	466.846	−	466.846i	0.649299	−	0.649299i	−0.303524	−	0.952824i	$-0.598163\pi$
$719$	466.846	−	466.846i	0.649299	−	0.649299i	0.952824	+	0.303524i	$0.0981634\pi$
$720$	151.342	−	84.6211i	0.210198	−	0.117529i
$721$	−174.409	+	174.409i	−0.241899	+	0.241899i
$722$	−53.5995	−	53.5995i	−0.0742376	−	0.0742376i
$723$	−141.377	+	141.377i	−0.195542	+	0.195542i
$724$	352.585	+	352.585i	0.486996	+	0.486996i
$725$	−89.5075	−	375.063i	−0.123459	−	0.517329i
$726$	−121.975	−	121.975i	−0.168010	−	0.168010i
$727$	553.017	−	553.017i	0.760684	−	0.760684i	−0.215762	−	0.976446i	$-0.569223\pi$
$727$	553.017	−	553.017i	0.760684	−	0.760684i	0.976446	+	0.215762i	$0.0692235\pi$
$728$		−	49.2118i		−	0.0675986i
$729$	573.331			0.786462
$730$	−32.0738	+	113.431i	−0.0439367	+	0.155385i
$731$	−103.432	+	283.145i	−0.141494	+	0.387340i
$732$	58.1556	−	58.1556i	0.0794475	−	0.0794475i
$733$	−513.816	+	513.816i	−0.700977	+	0.700977i	−0.964620	−	0.263644i	$-0.915076\pi$
$733$	−513.816	+	513.816i	−0.700977	+	0.700977i	0.263644	+	0.964620i	$0.415076\pi$
$734$	295.835	−	295.835i	0.403045	−	0.403045i
$735$	30.0903	+	53.8156i	0.0409392	+	0.0732185i
$736$	−60.1882	−	60.1882i	−0.0817774	−	0.0817774i
$737$		−	1124.51i		−	1.52580i
$738$	19.4631			0.0263728
$739$	−1121.66			−1.51781			−0.758905	−	0.651202i	$-0.774265\pi$
$739$	−1121.66			−1.51781			−0.758905	+	0.651202i	$0.774265\pi$
$740$	68.5383	+	122.579i	0.0926193	+	0.165647i
$741$	23.6222	−	23.6222i	0.0318788	−	0.0318788i
$742$		−	166.409i		−	0.224271i
$743$		−	171.197i		−	0.230413i	−0.993342	−	0.115206i	$-0.963247\pi$
$743$		−	171.197i		−	0.230413i	0.993342	−	0.115206i	$-0.0367529\pi$
$744$			13.2481i			0.0178066i
$745$	−647.421	−	1157.89i	−0.869022	−	1.55422i
$746$		−	580.678i		−	0.778389i
$747$	−687.242	+	687.242i	−0.920003	+	0.920003i
$748$	582.971	+	212.958i	0.779373	+	0.284704i
$749$		−	663.748i		−	0.886179i
$750$	68.8159	+	74.7488i	0.0917546	+	0.0996651i
$751$	−1.94582	−	1.94582i	−0.00259097	−	0.00259097i	0.705810	−	0.708401i	$-0.250583\pi$
$751$	−1.94582	−	1.94582i	−0.00259097	−	0.00259097i	−0.708401	+	0.705810i	$0.750583\pi$
$752$	−121.672	+	121.672i	−0.161797	+	0.161797i
$753$			35.2028i			0.0467500i
$754$	51.1324	+	51.1324i	0.0678149	+	0.0678149i
$755$	290.941	+	520.340i	0.385353	+	0.689192i
$756$			106.600i			0.141005i
$757$	−531.955	−	531.955i	−0.702715	−	0.702715i	0.262277	−	0.964993i	$-0.415526\pi$
$757$	−531.955	−	531.955i	−0.702715	−	0.702715i	−0.964993	+	0.262277i	$0.915526\pi$
$758$	−771.488			−1.01779
$759$	111.630	+	111.630i	0.147076	+	0.147076i
$760$	67.4658	−	238.597i	0.0887708	−	0.313943i
$761$	729.875			0.959099			0.479550	−	0.877515i	$-0.340800\pi$
$761$	729.875			0.959099			0.479550	+	0.877515i	$0.340800\pi$
$762$	163.816			0.214982
$763$	−119.627	+	119.627i	−0.156785	+	0.156785i
$764$		−	281.882i		−	0.368955i
$765$	431.652	−	597.269i	0.564250	−	0.780744i
$766$	1004.19			1.31096
$767$	35.3985	+	35.3985i	0.0461519	+	0.0461519i
$768$		−	9.19599i		−	0.0119739i
$769$			329.686i			0.428721i	0.976755	+	0.214360i	$0.0687667\pi$
$769$			329.686i			0.428721i	−0.976755	+	0.214360i	$0.931233\pi$
$770$	330.613	+	591.291i	0.429367	+	0.767910i
$771$	176.077	−	176.077i	0.228375	−	0.228375i
$772$			246.854i			0.319759i
$773$	266.134	−	266.134i	0.344287	−	0.344287i	−0.513689	−	0.857976i	$-0.671722\pi$
$773$	266.134	−	266.134i	0.344287	−	0.344287i	0.857976	+	0.513689i	$0.171722\pi$
$774$	217.409			0.280890
$775$	198.172	−	47.2930i	0.255706	−	0.0610232i
$776$	384.517	−	384.517i	0.495511	−	0.495511i
$777$	−42.3629			−0.0545210
$778$	−268.339	−	268.339i	−0.344909	−	0.344909i
$779$	19.6803	−	19.6803i	0.0252636	−	0.0252636i
$780$	−18.3350	−	5.18440i	−0.0235064	−	0.00664667i
$781$	−2262.88			−2.89741
$782$	−339.794	−	124.126i	−0.434519	−	0.158729i
$783$	−110.760	−	110.760i	−0.141456	−	0.141456i
$784$	−85.8207			−0.109465
$785$	−265.573	+	939.215i	−0.338310	+	1.19645i
$786$	87.4863			0.111306
$787$	88.7070			0.112715			0.0563577	−	0.998411i	$-0.482051\pi$
$787$	88.7070			0.112715			0.0563577	+	0.998411i	$0.482051\pi$
$788$	425.537			0.540021
$789$	−131.905	−	131.905i	−0.167181	−	0.167181i
$790$	−478.581	−	855.927i	−0.605798	−	1.08345i
$791$			258.915i			0.327326i
$792$		−	447.626i		−	0.565184i
$793$	237.193			0.299109
$794$	96.6764	−	96.6764i	0.121759	−	0.121759i
$795$	−61.9996	−	17.5310i	−0.0779869	−	0.0220516i
$796$	255.002	+	255.002i	0.320354	+	0.320354i
$797$	−79.2747	−	79.2747i	−0.0994664	−	0.0994664i	0.655622	−	0.755089i	$-0.272406\pi$
$797$	−79.2747	−	79.2747i	−0.0994664	−	0.0994664i	−0.755089	+	0.655622i	$0.772406\pi$
$798$	52.8872	+	52.8872i	0.0662747	+	0.0662747i
$799$	−250.923	+	686.900i	−0.314047	+	0.859700i
$800$	−137.558	+	32.8278i	−0.171948	+	0.0410348i
$801$		−	1457.48i		−	1.81958i
$802$	938.352			1.17001
$803$	215.180	+	215.180i	0.267970	+	0.267970i
$804$	−50.0714	+	50.0714i	−0.0622779	+	0.0622779i
$805$	−192.703	−	344.643i	−0.239382	−	0.428128i
$806$	−27.0168	+	27.0168i	−0.0335196	+	0.0335196i
$807$	169.760	+	169.760i	0.210359	+	0.210359i
$808$	218.726	−	218.726i	0.270700	−	0.270700i
$809$	658.421	+	658.421i	0.813870	+	0.813870i	0.985212	−	0.171342i	$-0.0548102\pi$
$809$	658.421	+	658.421i	0.813870	+	0.813870i	−0.171342	+	0.985212i	$0.554810\pi$
$810$	−491.202	−	138.892i	−0.606422	−	0.171472i
$811$	−757.445	−	757.445i	−0.933965	−	0.933965i	0.0639859	−	0.997951i	$-0.479619\pi$
$811$	−757.445	−	757.445i	−0.933965	−	0.933965i	−0.997951	+	0.0639859i	$0.979619\pi$
$812$	−114.479	+	114.479i	−0.140985	+	0.140985i
$813$			179.401i			0.220666i
$814$	362.551			0.445395
$815$	1130.41	−	632.053i	1.38700	−	0.775525i
$816$	−16.4756	−	35.4405i	−0.0201907	−	0.0434320i
$817$	219.835	−	219.835i	0.269076	−	0.269076i
$818$	372.062	−	372.062i	0.454844	−	0.454844i
$819$	−106.662	+	106.662i	−0.130235	+	0.130235i
$820$	−15.2754	−	4.31928i	−0.0186285	−	0.00526742i
$821$	−286.591	−	286.591i	−0.349075	−	0.349075i	0.510690	−	0.859765i	$-0.329390\pi$
$821$	−286.591	−	286.591i	−0.349075	−	0.349075i	−0.859765	+	0.510690i	$0.829390\pi$
$822$			53.4321i			0.0650026i
$823$	455.322			0.553246			0.276623	−	0.960978i	$-0.410785\pi$
$823$	455.322			0.553246			0.276623	+	0.960978i	$0.410785\pi$
$824$	−132.926			−0.161317
$825$	255.128	−	60.8854i	0.309246	−	0.0738005i
$826$	−79.2530	+	79.2530i	−0.0959479	+	0.0959479i
$827$		−	1057.49i		−	1.27871i	−0.768912	−	0.639355i	$-0.779201\pi$
$827$		−	1057.49i		−	1.27871i	0.768912	−	0.639355i	$-0.220799\pi$
$828$			260.906i			0.315103i
$829$			101.348i			0.122254i	0.998130	+	0.0611270i	$0.0194695\pi$
$829$			101.348i			0.122254i	−0.998130	+	0.0611270i	$0.980531\pi$
$830$	691.888	−	386.860i	0.833600	−	0.466097i
$831$		−	122.732i		−	0.147692i
$832$	18.7534	−	18.7534i	0.0225401	−	0.0225401i
$833$	−330.745	+	153.757i	−0.397053	+	0.184583i
$834$		−	32.3793i		−	0.0388242i
$835$	−14.9950	+	8.38428i	−0.0179581	+	0.0100411i
$836$	−452.621	−	452.621i	−0.541413	−	0.541413i
$837$	58.5223	−	58.5223i	0.0699191	−	0.0699191i
$838$		−	1080.11i		−	1.28892i
$839$	352.624	+	352.624i	0.420291	+	0.420291i	0.885304	−	0.465013i	$-0.153950\pi$
$839$	352.624	+	352.624i	0.420291	+	0.420291i	−0.465013	+	0.885304i	$0.653950\pi$
$840$	11.6073	−	41.0498i	0.0138182	−	0.0488688i
$841$			603.105i			0.717129i
$842$	434.929	+	434.929i	0.516542	+	0.516542i
$843$	166.315			0.197289
$844$	−124.108	−	124.108i	−0.147047	−	0.147047i
$845$	385.567	+	689.576i	0.456293	+	0.816066i
$846$	527.426			0.623435
$847$	1113.82			1.31501
$848$	63.4144	−	63.4144i	0.0747811	−	0.0747811i
$849$		−	289.372i		−	0.340839i
$850$	−471.323	+	372.967i	−0.554498	+	0.438784i
$851$	−211.319			−0.248318
$852$	100.760	+	100.760i	0.118263	+	0.118263i
$853$			446.871i			0.523881i	0.965084	+	0.261941i	$0.0843625\pi$
$853$			446.871i			0.523881i	−0.965084	+	0.261941i	$0.915638\pi$
$854$			531.047i			0.621835i
$855$	−663.365	+	370.912i	−0.775866	+	0.433815i
$856$	252.937	−	252.937i	0.295488	−	0.295488i
$857$			1518.51i			1.77189i	0.463788	+	0.885946i	$0.346490\pi$
$857$			1518.51i			1.77189i	−0.463788	+	0.885946i	$0.653510\pi$
$858$	−34.7817	+	34.7817i	−0.0405381	+	0.0405381i
$859$	737.422			0.858465			0.429233	−	0.903194i	$-0.358784\pi$
$859$	737.422			0.858465			0.429233	+	0.903194i	$0.358784\pi$
$860$	−170.631	−	48.2477i	−0.198408	−	0.0561020i
$861$	3.38594	−	3.38594i	0.00393256	−	0.00393256i
$862$	−584.149			−0.677667
$863$	−4.76036	−	4.76036i	−0.00551606	−	0.00551606i	0.704343	−	0.709859i	$-0.251242\pi$
$863$	−4.76036	−	4.76036i	−0.00551606	−	0.00551606i	−0.709859	+	0.704343i	$0.751242\pi$
$864$	−40.6225	+	40.6225i	−0.0470168	+	0.0470168i
$865$	331.037	+	592.049i	0.382701	+	0.684450i
$866$	−1134.74			−1.31032
$867$	−126.991	−	107.067i	−0.146472	−	0.123491i
$868$	−60.4874	−	60.4874i	−0.0696860	−	0.0696860i
$869$	−2531.58			−2.91321
$870$	30.5916	+	54.7122i	0.0351628	+	0.0628875i
$871$	−204.221			−0.234467
$872$	−91.1738			−0.104557
$873$	−1666.82			−1.90930
$874$	263.817	+	263.817i	0.301850	+	0.301850i
$875$	−655.480	−	27.0882i	−0.749120	−	0.0309580i
$876$		−	19.1627i		−	0.0218753i
$877$		−	897.670i		−	1.02357i	−0.859114	−	0.511785i	$-0.828985\pi$
$877$		−	897.670i		−	1.02357i	0.859114	−	0.511785i	$-0.171015\pi$
$878$	20.5501			0.0234055
$879$	−177.184	+	177.184i	−0.201574	+	0.201574i
$880$	−99.3377	+	351.314i	−0.112884	+	0.399220i
$881$	−416.364	−	416.364i	−0.472604	−	0.472604i	0.430152	−	0.902756i	$-0.358460\pi$
$881$	−416.364	−	416.364i	−0.472604	−	0.472604i	−0.902756	+	0.430152i	$0.858460\pi$
$882$	186.009	+	186.009i	0.210895	+	0.210895i
$883$	320.476	+	320.476i	0.362940	+	0.362940i	0.864894	−	0.501954i	$-0.167385\pi$
$883$	320.476	+	320.476i	0.362940	+	0.362940i	−0.501954	+	0.864894i	$0.667385\pi$
$884$	38.6750	−	105.873i	0.0437500	−	0.119765i
$885$	21.1783	+	37.8767i	0.0239303	+	0.0427985i
$886$			211.325i			0.238516i
$887$	254.485			0.286905			0.143452	−	0.989657i	$-0.454180\pi$
$887$	254.485			0.286905			0.143452	+	0.989657i	$0.454180\pi$
$888$	−16.1434	−	16.1434i	−0.0181795	−	0.0181795i
$889$	−747.943	+	747.943i	−0.841330	+	0.841330i
$890$	−323.447	+	1143.89i	−0.363423	+	1.28527i
$891$	−931.816	+	931.816i	−1.04581	+	1.04581i
$892$	371.568	+	371.568i	0.416557	+	0.416557i
$893$	533.313	−	533.313i	0.597215	−	0.597215i
$894$	152.493	+	152.493i	0.170573	+	0.170573i
$895$	−870.811	+	486.903i	−0.972973	+	0.544026i
$896$	41.9865	+	41.9865i	0.0468600	+	0.0468600i
$897$	20.2730	−	20.2730i	0.0226009	−	0.0226009i
$898$		−	1208.30i		−	1.34554i
$899$	125.696			0.139818
$900$	369.298	+	226.995i	0.410331	+	0.252217i
$901$	130.779	−	358.007i	0.145149	−	0.397344i
$902$	−28.9777	+	28.9777i	−0.0321260	+	0.0321260i
$903$	37.8219	−	37.8219i	0.0418847	−	0.0418847i
$904$	−98.6658	+	98.6658i	−0.109144	+	0.109144i
$905$	−339.184	+	1199.55i	−0.374789	+	1.32546i
$906$	−68.5279	−	68.5279i	−0.0756379	−	0.0756379i
$907$			106.997i			0.117968i	0.998259	+	0.0589838i	$0.0187860\pi$
$907$			106.997i			0.117968i	−0.998259	+	0.0589838i	$0.981214\pi$
$908$	123.480			0.135991
$909$	−948.139			−1.04306
$910$	107.383	−	60.0421i	0.118004	−	0.0659803i
$911$	−255.464	+	255.464i	−0.280421	+	0.280421i	−0.833277	−	0.552856i	$-0.813538\pi$
$911$	−255.464	+	255.464i	−0.280421	+	0.280421i	0.552856	+	0.833277i	$0.313538\pi$
$912$			40.3079i			0.0441973i
$913$		−	2046.40i		−	2.24140i
$914$			239.918i			0.262493i
$915$	197.854	+	55.9452i	0.216233	+	0.0611423i
$916$			331.107i			0.361470i
$917$	−399.440	+	399.440i	−0.435595	+	0.435595i
$918$	−83.7758	+	229.335i	−0.0912590	+	0.249820i
$919$		−	1133.15i		−	1.23303i	−0.787343	−	0.616515i	$-0.788544\pi$
$919$		−	1133.15i		−	1.23303i	0.787343	−	0.616515i	$-0.211456\pi$
$920$	57.9005	−	204.769i	0.0629353	−	0.222575i
$921$	120.204	+	120.204i	0.130515	+	0.130515i
$922$	−489.295	+	489.295i	−0.530689	+	0.530689i
$923$			410.958i			0.445242i
$924$	−77.8720	−	77.8720i	−0.0842770	−	0.0842770i
$925$	−183.853	+	299.110i	−0.198760	+	0.323363i
$926$			353.877i			0.382157i
$927$	288.105	+	288.105i	0.310793	+	0.310793i
$928$	−87.2504			−0.0940198
$929$	1023.70	+	1023.70i	1.10194	+	1.10194i	0.994177	+	0.107763i	$0.0343686\pi$
$929$	1023.70	+	1023.70i	1.10194	+	1.10194i	0.107763	+	0.994177i	$0.465631\pi$
$930$	−28.9082	+	16.1637i	−0.0310841	+	0.0173803i
$931$	376.170			0.404049
$932$	429.682			0.461033
$933$	−108.106	+	108.106i	−0.115869	+	0.115869i
$934$		−	1004.35i		−	1.07532i
$935$	246.579	+	1531.91i	0.263721	+	1.63840i
$936$	−81.2927			−0.0868511
$937$	528.642	+	528.642i	0.564185	+	0.564185i	0.930494	−	0.366308i	$-0.119378\pi$
$937$	528.642	+	528.642i	0.564185	+	0.564185i	−0.366308	+	0.930494i	$0.619378\pi$
$938$		−	457.227i		−	0.487449i
$939$			132.809i			0.141437i
$940$	−413.944	−	117.047i	−0.440366	−	0.124518i
$941$	726.683	−	726.683i	0.772246	−	0.772246i	−0.206253	−	0.978499i	$-0.566127\pi$
$941$	726.683	−	726.683i	0.772246	−	0.772246i	0.978499	+	0.206253i	$0.0661270\pi$
$942$		−	158.669i		−	0.168438i
$943$	16.8901	−	16.8901i	0.0179110	−	0.0179110i
$944$	−60.4026			−0.0639858
$945$	−232.608	+	130.060i	−0.246146	+	0.137629i
$946$	−323.689	+	323.689i	−0.342166	+	0.342166i
$947$	−738.345			−0.779667			−0.389834	−	0.920885i	$-0.627468\pi$
$947$	−738.345			−0.779667			−0.389834	+	0.920885i	$0.627468\pi$
$948$	112.724	+	112.724i	0.118907	+	0.118907i
$949$	39.0785	−	39.0785i	0.0411787	−	0.0411787i
$950$	602.948	−	143.891i	0.634682	−	0.151464i
$951$	51.2550			0.0538959
$952$	237.036	+	86.5888i	0.248987	+	0.0909546i
$953$	655.875	+	655.875i	0.688221	+	0.688221i	0.961839	−	0.273617i	$-0.0882202\pi$
$953$	655.875	+	655.875i	0.688221	+	0.688221i	−0.273617	+	0.961839i	$0.588220\pi$
$954$	−274.891			−0.288145
$955$	615.085	−	343.917i	0.644068	−	0.360123i
$956$	−59.6482			−0.0623935
$957$	161.822			0.169093
$958$	431.672			0.450597
$959$	−243.958	−	243.958i	−0.254387	−	0.254387i
$960$	20.0663	−	11.2198i	0.0209024	−	0.0116873i
$961$		−	894.586i		−	0.930891i
$962$		−	65.8424i		−	0.0684433i
$963$	−1096.44			−1.13857
$964$	491.961	−	491.961i	0.510333	−	0.510333i
$965$	−538.652	+	301.180i	−0.558189	+	0.312104i
$966$	45.3889	+	45.3889i	0.0469864	+	0.0469864i
$967$	807.852	+	807.852i	0.835421	+	0.835421i	0.988252	−	0.152832i	$-0.0488392\pi$
$967$	807.852	+	807.852i	0.835421	+	0.835421i	−0.152832	+	0.988252i	$0.548839\pi$
$968$	424.447	+	424.447i	0.438478	+	0.438478i
$969$	72.2162	+	155.343i	0.0745265	+	0.160313i
$970$	1308.18	+	369.902i	1.34864	+	0.381342i
$971$			1275.04i			1.31312i	0.754275	+	0.656559i	$0.227989\pi$
$971$			1275.04i			1.31312i	−0.754275	+	0.656559i	$0.772011\pi$
$972$	265.784			0.273440
$973$	147.836	+	147.836i	0.151938	+	0.151938i
$974$	−476.790	+	476.790i	−0.489517	+	0.489517i
$975$	−11.0573	−	46.3335i	−0.0113408	−	0.0475215i
$976$	−202.369	+	202.369i	−0.207345	+	0.207345i
$977$	−1306.24	−	1306.24i	−1.33699	−	1.33699i	−0.898956	−	0.438038i	$-0.855673\pi$
$977$	−1306.24	−	1306.24i	−1.33699	−	1.33699i	−0.438038	−	0.898956i	$-0.644327\pi$
$978$	−148.873	+	148.873i	−0.152222	+	0.152222i
$979$	2169.97	+	2169.97i	2.21652	+	2.21652i
$980$	−104.708	−	187.266i	−0.106845	−	0.191088i
$981$	197.612	+	197.612i	0.201439	+	0.201439i
$982$	154.218	−	154.218i	0.157045	−	0.157045i
$983$		−	1486.67i		−	1.51238i	−0.654350	−	0.756192i	$-0.727058\pi$
$983$		−	1486.67i		−	1.51238i	0.654350	−	0.756192i	$-0.272942\pi$
$984$	2.58059			0.00262255
$985$	519.187	+	928.549i	0.527093	+	0.942690i
$986$	−336.255	+	156.319i	−0.341030	+	0.158538i
$987$	91.7546	−	91.7546i	0.0929632	−	0.0929632i
$988$	−82.1999	+	82.1999i	−0.0831983	+	0.0831983i
$989$	188.667	−	188.667i	0.190765	−	0.190765i
$990$	976.749	−	546.137i	0.986616	−	0.551654i
$991$	−333.182	−	333.182i	−0.336207	−	0.336207i	0.518730	−	0.854938i	$-0.326405\pi$
$991$	−333.182	−	333.182i	−0.336207	−	0.336207i	−0.854938	+	0.518730i	$0.826405\pi$
$992$		−	46.1004i		−	0.0464722i
$993$	66.3279			0.0667955
$994$	−920.086			−0.925640
$995$	−245.310	+	867.553i	−0.246543	+	0.871913i
$996$	−91.1205	+	91.1205i	−0.0914865	+	0.0914865i
$997$		−	90.8688i		−	0.0911422i	−0.998961	−	0.0455711i	$-0.985489\pi$
$997$		−	90.8688i		−	0.0911422i	0.998961	−	0.0455711i	$-0.0145108\pi$
$998$			976.953i			0.978911i
$999$			142.624i			0.142767i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.3.e.b.13.4	✓	16
5.2	odd	4		170.3.j.b.47.4	yes	16
17.4	even	4		170.3.j.b.123.4	yes	16
85.72	odd	4	inner	170.3.e.b.157.5	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.3.e.b.13.4	✓	16	1.1	even	1	trivial
170.3.e.b.157.5	yes	16	85.72	odd	4	inner
170.3.j.b.47.4	yes	16	5.2	odd	4
170.3.j.b.123.4	yes	16	17.4	even	4

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:	\( N \)	\(=\)	\( 170 = 2 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	170.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} -0.574749i q^{3} +2.00000i q^{4} +(-4.36413 + 2.44015i) q^{5} +(0.574749 - 0.574749i) q^{6} +5.24832i q^{7} +(-2.00000 + 2.00000i) q^{8} +8.66966 q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.00000i) q^{2} -0.574749i q^{3} +2.00000i q^{4} +(-4.36413 + 2.44015i) q^{5} +(0.574749 - 0.574749i) q^{6} +5.24832i q^{7} +(-2.00000 + 2.00000i) q^{8} +8.66966 q^{9} +(-6.80428 - 1.92398i) q^{10} +(-12.9078 + 12.9078i) q^{11} +1.14950 q^{12} +(2.34417 + 2.34417i) q^{13} +(-5.24832 + 5.24832i) q^{14} +(1.40247 + 2.50828i) q^{15} -4.00000 q^{16} +(-15.4156 + 7.16645i) q^{17} +(8.66966 + 8.66966i) q^{18} +17.5328 q^{19} +(-4.88030 - 8.72827i) q^{20} +3.01647 q^{21} -25.8156 q^{22} +15.0470 q^{23} +(1.14950 + 1.14950i) q^{24} +(13.0913 - 21.2983i) q^{25} +4.68834i q^{26} -10.1556i q^{27} -10.4966 q^{28} +(10.9063 - 10.9063i) q^{29} +(-1.10581 + 3.91076i) q^{30} +(5.76255 + 5.76255i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(7.41876 + 7.41876i) q^{33} +(-22.5821 - 8.24920i) q^{34} +(-12.8067 - 22.9044i) q^{35} +17.3393i q^{36} -14.0439 q^{37} +(17.5328 + 17.5328i) q^{38} +(1.34731 - 1.34731i) q^{39} +(3.84797 - 13.6086i) q^{40} +(1.12248 - 1.12248i) q^{41} +(3.01647 + 3.01647i) q^{42} +(12.5385 - 12.5385i) q^{43} +(-25.8156 - 25.8156i) q^{44} +(-37.8356 + 21.1553i) q^{45} +(15.0470 + 15.0470i) q^{46} +(30.4179 - 30.4179i) q^{47} +2.29900i q^{48} +21.4552 q^{49} +(34.3896 - 8.20695i) q^{50} +(4.11891 + 8.86013i) q^{51} +(-4.68834 + 4.68834i) q^{52} +(-15.8536 + 15.8536i) q^{53} +(10.1556 - 10.1556i) q^{54} +(24.8344 - 87.8285i) q^{55} +(-10.4966 - 10.4966i) q^{56} -10.0770i q^{57} +21.8126 q^{58} +15.1006 q^{59} +(-5.01657 + 2.80495i) q^{60} +(50.5922 - 50.5922i) q^{61} +11.5251i q^{62} +45.5011i q^{63} -8.00000i q^{64} +(-15.9504 - 4.51014i) q^{65} +14.8375i q^{66} +(-43.5594 + 43.5594i) q^{67} +(-14.3329 - 30.8313i) q^{68} -8.64827i q^{69} +(10.0977 - 35.7110i) q^{70} +(87.6553 + 87.6553i) q^{71} +(-17.3393 + 17.3393i) q^{72} -16.6705i q^{73} +(-14.0439 - 14.0439i) q^{74} +(-12.2412 - 7.52423i) q^{75} +35.0657i q^{76} +(-67.7443 - 67.7443i) q^{77} +2.69462 q^{78} +(98.0638 + 98.0638i) q^{79} +(17.4565 - 9.76060i) q^{80} +72.1900 q^{81} +2.24497 q^{82} +(-79.2698 + 79.2698i) q^{83} +6.03293i q^{84} +(49.7887 - 68.8918i) q^{85} +25.0770 q^{86} +(-6.26839 - 6.26839i) q^{87} -51.6313i q^{88} -168.113i q^{89} +(-58.9909 - 16.6803i) q^{90} +(-12.3029 + 12.3029i) q^{91} +30.0941i q^{92} +(3.31202 - 3.31202i) q^{93} +60.8358 q^{94} +(-76.5157 + 42.7828i) q^{95} +(-2.29900 + 2.29900i) q^{96} -192.258 q^{97} +(21.4552 + 21.4552i) q^{98} +(-111.906 + 111.906i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} - 2 q^{5} - 32 q^{8} - 16 q^{9}+O(q^{10}) \) 16 * q + 16 * q^2 - 2 * q^5 - 32 * q^8 - 16 * q^9	\( 16 q + 16 q^{2} - 2 q^{5} - 32 q^{8} - 16 q^{9} - 4 q^{10} + 20 q^{11} + 4 q^{13} - 12 q^{14} + 12 q^{15} - 64 q^{16} + 36 q^{17} - 16 q^{18} - 16 q^{19} - 4 q^{20} + 40 q^{22} + 16 q^{23} + 44 q^{25} - 24 q^{28} - 20 q^{29} + 12 q^{30} + 92 q^{31} - 64 q^{32} - 60 q^{33} + 24 q^{34} - 124 q^{35} + 32 q^{37} - 16 q^{38} - 140 q^{39} - 60 q^{41} + 52 q^{43} + 40 q^{44} + 198 q^{45} + 16 q^{46} + 112 q^{47} + 136 q^{49} - 4 q^{50} - 140 q^{51} - 8 q^{52} + 48 q^{53} + 108 q^{54} + 40 q^{55} - 24 q^{56} - 40 q^{58} + 76 q^{61} - 40 q^{65} + 116 q^{67} - 24 q^{68} - 124 q^{70} - 268 q^{71} + 32 q^{72} + 32 q^{74} + 136 q^{75} - 116 q^{77} - 280 q^{78} - 88 q^{79} + 8 q^{80} - 352 q^{81} - 120 q^{82} - 160 q^{83} + 310 q^{85} + 104 q^{86} + 236 q^{87} + 260 q^{90} - 168 q^{91} + 48 q^{93} + 224 q^{94} + 264 q^{95} - 256 q^{97} + 136 q^{98} - 348 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 - 2 * q^5 - 32 * q^8 - 16 * q^9 - 4 * q^10 + 20 * q^11 + 4 * q^13 - 12 * q^14 + 12 * q^15 - 64 * q^16 + 36 * q^17 - 16 * q^18 - 16 * q^19 - 4 * q^20 + 40 * q^22 + 16 * q^23 + 44 * q^25 - 24 * q^28 - 20 * q^29 + 12 * q^30 + 92 * q^31 - 64 * q^32 - 60 * q^33 + 24 * q^34 - 124 * q^35 + 32 * q^37 - 16 * q^38 - 140 * q^39 - 60 * q^41 + 52 * q^43 + 40 * q^44 + 198 * q^45 + 16 * q^46 + 112 * q^47 + 136 * q^49 - 4 * q^50 - 140 * q^51 - 8 * q^52 + 48 * q^53 + 108 * q^54 + 40 * q^55 - 24 * q^56 - 40 * q^58 + 76 * q^61 - 40 * q^65 + 116 * q^67 - 24 * q^68 - 124 * q^70 - 268 * q^71 + 32 * q^72 + 32 * q^74 + 136 * q^75 - 116 * q^77 - 280 * q^78 - 88 * q^79 + 8 * q^80 - 352 * q^81 - 120 * q^82 - 160 * q^83 + 310 * q^85 + 104 * q^86 + 236 * q^87 + 260 * q^90 - 168 * q^91 + 48 * q^93 + 224 * q^94 + 264 * q^95 - 256 * q^97 + 136 * q^98 - 348 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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