LMFDB - Embedded newform 671.2.bn.a.12.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [671,2,Mod(12,671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(671, base_ring=CyclotomicField(30))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("671.12");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 671 = 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	671.bn (of order $15$, degree $8$, 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:	$5.35796197563$
Analytic rank:	$0$
Dimension:	$208$
Relative dimension:	$26$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			12.3
Character	$\chi$	$=$	671.12
Dual form			671.2.bn.a.56.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.03902 - 0.907829i) q^{2} +(1.68678 - 1.22552i) q^{3} +(1.99518 + 2.21587i) q^{4} +(-2.26004 + 0.480387i) q^{5} +(-4.55193 + 0.967543i) q^{6} +(-0.0297354 + 0.282913i) q^{7} +(-0.677129 - 2.08399i) q^{8} +(0.416282 - 1.28118i) q^{9} +O(q^{10})$	\(q+(-2.03902 - 0.907829i) q^{2} +(1.68678 - 1.22552i) q^{3} +(1.99518 + 2.21587i) q^{4} +(-2.26004 + 0.480387i) q^{5} +(-4.55193 + 0.967543i) q^{6} +(-0.0297354 + 0.282913i) q^{7} +(-0.677129 - 2.08399i) q^{8} +(0.416282 - 1.28118i) q^{9} +(5.04437 + 1.07221i) q^{10} -1.00000 q^{11} +(6.08100 + 1.29256i) q^{12} +(-1.47991 - 2.56328i) q^{13} +(0.317468 - 0.549870i) q^{14} +(-3.22347 + 3.58003i) q^{15} +(0.112127 - 1.06682i) q^{16} +(-1.89459 - 2.10416i) q^{17} +(-2.01190 + 2.23444i) q^{18} +(-0.0603871 - 0.574545i) q^{19} +(-5.57365 - 4.04950i) q^{20} +(0.296558 + 0.513653i) q^{21} +(2.03902 + 0.907829i) q^{22} +(-2.66785 + 8.21078i) q^{23} +(-3.69613 - 2.68539i) q^{24} +(0.309291 - 0.137705i) q^{25} +(0.690544 + 6.57008i) q^{26} +(1.06494 + 3.27755i) q^{27} +(-0.686225 + 0.498572i) q^{28} +(-2.38678 + 4.13403i) q^{29} +(9.82276 - 4.37338i) q^{30} +(-3.57537 + 1.59186i) q^{31} +(-3.38835 + 5.86879i) q^{32} +(-1.68678 + 1.22552i) q^{33} +(1.95289 + 6.01038i) q^{34} +(-0.0687045 - 0.653680i) q^{35} +(3.66949 - 1.63376i) q^{36} +(2.36926 + 1.72137i) q^{37} +(-0.398458 + 1.22633i) q^{38} +(-5.63763 - 2.51004i) q^{39} +(2.53146 + 4.38462i) q^{40} +(-6.73159 - 4.89079i) q^{41} +(-0.138377 - 1.31657i) q^{42} +(0.235896 - 0.261989i) q^{43} +(-1.99518 - 2.21587i) q^{44} +(-0.325351 + 3.09551i) q^{45} +(12.8938 - 14.3200i) q^{46} +(-5.39652 + 9.34705i) q^{47} +(-1.11827 - 1.93690i) q^{48} +(6.76788 + 1.43856i) q^{49} -0.755663 q^{50} +(-5.77444 - 1.22739i) q^{51} +(2.72721 - 8.39349i) q^{52} +(-2.44063 - 7.51150i) q^{53} +(0.804022 - 7.64976i) q^{54} +(2.26004 - 0.480387i) q^{55} +(0.609722 - 0.129600i) q^{56} +(-0.805975 - 0.895125i) q^{57} +(8.61968 - 6.26256i) q^{58} +(-0.643479 - 0.286495i) q^{59} -14.3643 q^{60} +(-2.36656 + 7.44308i) q^{61} +8.73537 q^{62} +(0.350086 + 0.155868i) q^{63} +(10.5011 - 7.62950i) q^{64} +(4.57603 + 5.08220i) q^{65} +(4.55193 - 0.967543i) q^{66} +(-2.59278 + 0.551112i) q^{67} +(0.882489 - 8.39633i) q^{68} +(5.56239 + 17.1193i) q^{69} +(-0.453340 + 1.39524i) q^{70} +(5.63234 + 1.19719i) q^{71} -2.95185 q^{72} +(-0.596604 - 0.126812i) q^{73} +(-3.26826 - 5.66079i) q^{74} +(0.352946 - 0.611320i) q^{75} +(1.15263 - 1.28013i) q^{76} +(0.0297354 - 0.282913i) q^{77} +(9.21655 + 10.2360i) q^{78} +(4.02395 - 4.46905i) q^{79} +(0.259073 + 2.46491i) q^{80} +(9.08253 + 6.59885i) q^{81} +(9.28583 + 16.0835i) q^{82} +(-7.20951 - 3.20988i) q^{83} +(-0.546502 + 1.68196i) q^{84} +(5.29266 + 3.84535i) q^{85} +(-0.718836 + 0.320047i) q^{86} +(1.04035 + 9.89824i) q^{87} +(0.677129 + 2.08399i) q^{88} +(-3.37298 + 2.45061i) q^{89} +(3.47359 - 6.01643i) q^{90} +(0.769192 - 0.342466i) q^{91} +(-23.5168 + 10.4704i) q^{92} +(-4.08001 + 7.06678i) q^{93} +(19.4891 - 14.1597i) q^{94} +(0.412481 + 1.26949i) q^{95} +(1.47691 + 14.0518i) q^{96} +(-6.53865 + 2.91119i) q^{97} +(-12.4939 - 9.07732i) q^{98} +(-0.416282 + 1.28118i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 208 q - 2 q^{3} + 30 q^{4} - 10 q^{5} - 12 q^{6} - 10 q^{7} + 18 q^{8} - 60 q^{9}+O(q^{10}) $ 208 * q - 2 * q^3 + 30 * q^4 - 10 * q^5 - 12 * q^6 - 10 * q^7 + 18 * q^8 - 60 * q^9	\( 208 q - 2 q^{3} + 30 q^{4} - 10 q^{5} - 12 q^{6} - 10 q^{7} + 18 q^{8} - 60 q^{9} - 75 q^{10} - 208 q^{11} - 25 q^{12} - 17 q^{14} - 8 q^{15} + 42 q^{16} + 8 q^{17} - 5 q^{18} - 19 q^{19} - 26 q^{20} + 50 q^{21} + 18 q^{23} - 41 q^{24} - 6 q^{25} - 32 q^{26} - 8 q^{27} + 24 q^{28} + 40 q^{29} - 12 q^{30} - 13 q^{31} + 12 q^{32} + 2 q^{33} - 38 q^{34} + 40 q^{35} - 94 q^{36} + 66 q^{37} + 15 q^{38} - 58 q^{39} + 157 q^{40} + 20 q^{41} + 42 q^{42} - 3 q^{43} - 30 q^{44} - 25 q^{45} + 90 q^{46} - 34 q^{47} - 58 q^{48} + 56 q^{49} - 84 q^{50} + 37 q^{51} + 98 q^{52} + 18 q^{53} + 92 q^{54} + 10 q^{55} + 76 q^{56} + 16 q^{57} - 119 q^{58} - 7 q^{59} - 60 q^{60} - 7 q^{61} + 34 q^{62} + 30 q^{63} + 38 q^{64} - 95 q^{65} + 12 q^{66} - 43 q^{67} + 40 q^{68} + 100 q^{69} + 43 q^{70} - 46 q^{71} - 156 q^{72} - 28 q^{73} - 4 q^{74} - 47 q^{75} - 121 q^{76} + 10 q^{77} - 108 q^{78} + 38 q^{79} - 45 q^{80} - 78 q^{81} - 2 q^{82} - 62 q^{83} - 14 q^{84} + 54 q^{85} + 7 q^{86} + 23 q^{87} - 18 q^{88} + 6 q^{89} + 121 q^{90} + 32 q^{91} - 39 q^{92} + 70 q^{93} + 73 q^{94} - 74 q^{95} + 220 q^{96} - 49 q^{97} - 63 q^{98} + 60 q^{99}+O(q^{100}) \) 208 * q - 2 * q^3 + 30 * q^4 - 10 * q^5 - 12 * q^6 - 10 * q^7 + 18 * q^8 - 60 * q^9 - 75 * q^10 - 208 * q^11 - 25 * q^12 - 17 * q^14 - 8 * q^15 + 42 * q^16 + 8 * q^17 - 5 * q^18 - 19 * q^19 - 26 * q^20 + 50 * q^21 + 18 * q^23 - 41 * q^24 - 6 * q^25 - 32 * q^26 - 8 * q^27 + 24 * q^28 + 40 * q^29 - 12 * q^30 - 13 * q^31 + 12 * q^32 + 2 * q^33 - 38 * q^34 + 40 * q^35 - 94 * q^36 + 66 * q^37 + 15 * q^38 - 58 * q^39 + 157 * q^40 + 20 * q^41 + 42 * q^42 - 3 * q^43 - 30 * q^44 - 25 * q^45 + 90 * q^46 - 34 * q^47 - 58 * q^48 + 56 * q^49 - 84 * q^50 + 37 * q^51 + 98 * q^52 + 18 * q^53 + 92 * q^54 + 10 * q^55 + 76 * q^56 + 16 * q^57 - 119 * q^58 - 7 * q^59 - 60 * q^60 - 7 * q^61 + 34 * q^62 + 30 * q^63 + 38 * q^64 - 95 * q^65 + 12 * q^66 - 43 * q^67 + 40 * q^68 + 100 * q^69 + 43 * q^70 - 46 * q^71 - 156 * q^72 - 28 * q^73 - 4 * q^74 - 47 * q^75 - 121 * q^76 + 10 * q^77 - 108 * q^78 + 38 * q^79 - 45 * q^80 - 78 * q^81 - 2 * q^82 - 62 * q^83 - 14 * q^84 + 54 * q^85 + 7 * q^86 + 23 * q^87 - 18 * q^88 + 6 * q^89 + 121 * q^90 + 32 * q^91 - 39 * q^92 + 70 * q^93 + 73 * q^94 - 74 * q^95 + 220 * q^96 - 49 * q^97 - 63 * q^98 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/671\mathbb{Z}\right)^\times$.

$n$	$123$	$551$
$\chi(n)$	$1$	$e\left(\frac{2}{15}\right)$

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 $

$2$	−2.03902	−	0.907829i	−1.44180	−	0.641932i	−0.471070	−	0.882096i	$-0.656132\pi$
$2$	−2.03902	−	0.907829i	−1.44180	−	0.641932i	−0.970732	+	0.240164i	$0.922799\pi$
$3$	1.68678	−	1.22552i	0.973863	−	0.707553i	0.0175340	−	0.999846i	$-0.494418\pi$
$3$	1.68678	−	1.22552i	0.973863	−	0.707553i	0.956329	+	0.292294i	$0.0944185\pi$
$4$	1.99518	+	2.21587i	0.997588	+	1.10793i
$5$	−2.26004	+	0.480387i	−1.01072	+	0.214835i	−0.683374	−	0.730069i	$-0.739488\pi$
$5$	−2.26004	+	0.480387i	−1.01072	+	0.214835i	−0.327348	+	0.944904i	$0.606155\pi$
$6$	−4.55193	+	0.967543i	−1.85832	+	0.394998i
$7$	−0.0297354	+	0.282913i	−0.0112389	+	0.106931i	−0.998703	−	0.0509117i	$-0.983787\pi$
$7$	−0.0297354	+	0.282913i	−0.0112389	+	0.106931i	0.987464	+	0.157843i	$0.0504539\pi$
$8$	−0.677129	−	2.08399i	−0.239401	−	0.736801i
$9$	0.416282	−	1.28118i	0.138761	−	0.427061i
$10$	5.04437	+	1.07221i	1.59517	+	0.339064i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$	6.08100	+	1.29256i	1.75543	+	0.373129i
$13$	−1.47991	−	2.56328i	−0.410454	−	0.710927i	0.584486	−	0.811404i	$-0.301296\pi$
$13$	−1.47991	−	2.56328i	−0.410454	−	0.710927i	−0.994939	+	0.100477i	$0.967963\pi$
$14$	0.317468	−	0.549870i	0.0848468	−	0.146959i
$15$	−3.22347	+	3.58003i	−0.832296	+	0.924359i
$16$	0.112127	−	1.06682i	0.0280317	−	0.266704i
$17$	−1.89459	−	2.10416i	−0.459506	−	0.510333i	0.468211	−	0.883616i	$-0.344899\pi$
$17$	−1.89459	−	2.10416i	−0.459506	−	0.510333i	−0.927717	+	0.373283i	$0.878232\pi$
$18$	−2.01190	+	2.23444i	−0.474210	+	0.526663i
$19$	−0.0603871	−	0.574545i	−0.0138538	−	0.131810i	0.985409	−	0.170204i	$-0.0544425\pi$
$19$	−0.0603871	−	0.574545i	−0.0138538	−	0.131810i	−0.999263	+	0.0383939i	$0.987776\pi$
$20$	−5.57365	−	4.04950i	−1.24631	−	0.905495i
$21$	0.296558	+	0.513653i	0.0647142	+	0.112088i
$22$	2.03902	+	0.907829i	0.434720	+	0.193550i
$23$	−2.66785	+	8.21078i	−0.556284	+	1.71207i	0.136244	+	0.990675i	$0.456497\pi$
$23$	−2.66785	+	8.21078i	−0.556284	+	1.71207i	−0.692528	+	0.721391i	$0.743503\pi$
$24$	−3.69613	−	2.68539i	−0.754469	−	0.548154i
$25$	0.309291	−	0.137705i	0.0618582	−	0.0275411i
$26$	0.690544	+	6.57008i	0.135427	+	1.28850i
$27$	1.06494	+	3.27755i	0.204948	+	0.630764i
$28$	−0.686225	+	0.498572i	−0.129684	+	0.0942212i
$29$	−2.38678	+	4.13403i	−0.443214	+	0.767670i	−0.997926	−	0.0643730i	$-0.979495\pi$
$29$	−2.38678	+	4.13403i	−0.443214	+	0.767670i	0.554712	+	0.832043i	$0.312829\pi$
$30$	9.82276	−	4.37338i	1.79338	−	0.798465i
$31$	−3.57537	+	1.59186i	−0.642155	+	0.285906i	−0.701865	−	0.712310i	$-0.747649\pi$
$31$	−3.57537	+	1.59186i	−0.642155	+	0.285906i	0.0597101	+	0.998216i	$0.480982\pi$
$32$	−3.38835	+	5.86879i	−0.598981	+	1.03747i
$33$	−1.68678	+	1.22552i	−0.293631	+	0.213335i
$34$	1.95289	+	6.01038i	0.334918	+	1.03077i
$35$	−0.0687045	−	0.653680i	−0.0116132	−	0.110492i
$36$	3.66949	−	1.63376i	0.611582	−	0.272294i
$37$	2.36926	+	1.72137i	0.389505	+	0.282992i	0.765252	−	0.643730i	$-0.222614\pi$
$37$	2.36926	+	1.72137i	0.389505	+	0.282992i	−0.375748	+	0.926722i	$0.622614\pi$
$38$	−0.398458	+	1.22633i	−0.0646385	+	0.198937i
$39$	−5.63763	−	2.51004i	−0.902744	−	0.401927i
$40$	2.53146	+	4.38462i	0.400259	+	0.693269i
$41$	−6.73159	−	4.89079i	−1.05130	−	0.763813i	−0.0788391	−	0.996887i	$-0.525121\pi$
$41$	−6.73159	−	4.89079i	−1.05130	−	0.763813i	−0.972459	+	0.233075i	$0.925121\pi$
$42$	−0.138377	−	1.31657i	−0.0213521	−	0.203151i
$43$	0.235896	−	0.261989i	0.0359738	−	0.0399529i	−0.724889	−	0.688865i	$-0.758109\pi$
$43$	0.235896	−	0.261989i	0.0359738	−	0.0399529i	0.760863	+	0.648912i	$0.224776\pi$
$44$	−1.99518	−	2.21587i	−0.300784	−	0.334055i
$45$	−0.325351	+	3.09551i	−0.0485004	+	0.461451i
$46$	12.8938	−	14.3200i	1.90108	−	2.11137i
$47$	−5.39652	+	9.34705i	−0.787163	+	1.36341i	0.140535	+	0.990076i	$0.455118\pi$
$47$	−5.39652	+	9.34705i	−0.787163	+	1.36341i	−0.927698	+	0.373331i	$0.878216\pi$
$48$	−1.11827	−	1.93690i	−0.161408	−	0.279567i
$49$	6.76788	+	1.43856i	0.966840	+	0.205508i
$50$	−0.755663			−0.106867
$51$	−5.77444	−	1.22739i	−0.808583	−	0.171870i
$52$	2.72721	−	8.39349i	0.378196	−	1.16397i
$53$	−2.44063	−	7.51150i	−0.335247	−	1.03178i	−0.966600	−	0.256289i	$-0.917500\pi$
$53$	−2.44063	−	7.51150i	−0.335247	−	1.03178i	0.631353	−	0.775495i	$-0.282500\pi$
$54$	0.804022	−	7.64976i	0.109414	−	1.04100i
$55$	2.26004	−	0.480387i	0.304744	−	0.0647753i
$56$	0.609722	−	0.129600i	0.0814775	−	0.0173186i
$57$	−0.805975	−	0.895125i	−0.106754	−	0.118562i
$58$	8.61968	−	6.26256i	1.13182	−	0.822315i
$59$	−0.643479	−	0.286495i	−0.0837739	−	0.0372985i	0.364422	−	0.931234i	$-0.381267\pi$
$59$	−0.643479	−	0.286495i	−0.0837739	−	0.0372985i	−0.448196	+	0.893935i	$0.647933\pi$
$60$	−14.3643			−1.85442
$61$	−2.36656	+	7.44308i	−0.303007	+	0.952988i
$61$	−2.36656	+	7.44308i	−0.303007	+	0.952988i
$62$	8.73537			1.10939
$63$	0.350086	+	0.155868i	0.0441066	+	0.0196375i
$64$	10.5011	−	7.62950i	1.31264	−	0.953688i
$65$	4.57603	+	5.08220i	0.567587	+	0.630369i
$66$	4.55193	−	0.967543i	0.560304	−	0.119096i
$67$	−2.59278	+	0.551112i	−0.316758	+	0.0673290i	−0.363547	−	0.931576i	$-0.618434\pi$
$67$	−2.59278	+	0.551112i	−0.316758	+	0.0673290i	0.0467891	+	0.998905i	$0.485101\pi$
$68$	0.882489	−	8.39633i	0.107018	−	1.01820i
$69$	5.56239	+	17.1193i	0.669633	+	2.06092i
$70$	−0.453340	+	1.39524i	−0.0541845	+	0.166763i
$71$	5.63234	+	1.19719i	0.668436	+	0.142080i	0.529616	−	0.848237i	$-0.322336\pi$
$71$	5.63234	+	1.19719i	0.668436	+	0.142080i	0.138819	+	0.990318i	$0.455669\pi$
$72$	−2.95185			−0.347879
$73$	−0.596604	−	0.126812i	−0.0698272	−	0.0148422i	0.172866	−	0.984945i	$-0.444697\pi$
$73$	−0.596604	−	0.126812i	−0.0698272	−	0.0148422i	−0.242693	+	0.970103i	$0.578031\pi$
$74$	−3.26826	−	5.66079i	−0.379927	−	0.658054i
$75$	0.352946	−	0.611320i	0.0407547	−	0.0705892i
$76$	1.15263	−	1.28013i	0.132216	−	0.146841i
$77$	0.0297354	−	0.282913i	0.00338866	−	0.0322409i
$78$	9.21655	+	10.2360i	1.04357	+	1.15900i
$79$	4.02395	−	4.46905i	0.452730	−	0.502808i	−0.472963	−	0.881082i	$-0.656816\pi$
$79$	4.02395	−	4.46905i	0.452730	−	0.502808i	0.925694	+	0.378274i	$0.123482\pi$
$80$	0.259073	+	2.46491i	0.0289652	+	0.275586i
$81$	9.08253	+	6.59885i	1.00917	+	0.733205i
$82$	9.28583	+	16.0835i	1.02545	+	1.77613i
$83$	−7.20951	−	3.20988i	−0.791347	−	0.352330i	−0.0290666	−	0.999577i	$-0.509253\pi$
$83$	−7.20951	−	3.20988i	−0.791347	−	0.352330i	−0.762280	+	0.647247i	$0.775920\pi$
$84$	−0.546502	+	1.68196i	−0.0596283	+	0.183517i
$85$	5.29266	+	3.84535i	0.574070	+	0.417086i
$86$	−0.718836	+	0.320047i	−0.0775141	+	0.0345115i
$87$	1.04035	+	9.89824i	0.111537	+	1.06120i
$88$	0.677129	+	2.08399i	0.0721821	+	0.222154i
$89$	−3.37298	+	2.45061i	−0.357535	+	0.259765i	−0.752023	−	0.659137i	$-0.770922\pi$
$89$	−3.37298	+	2.45061i	−0.357535	+	0.259765i	0.394488	+	0.918901i	$0.370922\pi$
$90$	3.47359	−	6.01643i	0.366148	−	0.634187i
$91$	0.769192	−	0.342466i	0.0806332	−	0.0359002i
$92$	−23.5168	+	10.4704i	−2.45180	+	1.09161i
$93$	−4.08001	+	7.06678i	−0.423077	+	0.732791i
$94$	19.4891	−	14.1597i	2.01015	−	1.46046i
$95$	0.412481	+	1.26949i	0.0423197	+	0.130247i
$96$	1.47691	+	14.0518i	0.150736	+	1.43416i
$97$	−6.53865	+	2.91119i	−0.663899	+	0.295587i	−0.710885	−	0.703309i	$-0.751705\pi$
$97$	−6.53865	+	2.91119i	−0.663899	+	0.295587i	0.0469855	+	0.998896i	$0.485039\pi$
$98$	−12.4939	−	9.07732i	−1.26207	−	0.916947i
$99$	−0.416282	+	1.28118i	−0.0418379	+	0.128764i
$100$	0.922227	+	0.410602i	0.0922227	+	0.0410602i
$101$	2.58501	+	4.47738i	0.257219	+	0.445516i	0.965496	−	0.260419i	$-0.0838607\pi$
$101$	2.58501	+	4.47738i	0.257219	+	0.445516i	−0.708277	+	0.705934i	$0.750527\pi$
$102$	10.6599	+	7.74488i	1.05549	+	0.766857i
$103$	0.968748	+	9.21702i	0.0954536	+	0.908180i	0.932530	+	0.361094i	$0.117597\pi$
$103$	0.968748	+	9.21702i	0.0954536	+	0.908180i	−0.837076	+	0.547087i	$0.815737\pi$
$104$	−4.33976	+	4.81979i	−0.425548	+	0.472619i
$105$	−0.916985	−	1.01842i	−0.0894886	−	0.0993872i
$106$	−1.84266	+	17.5318i	−0.178975	+	1.70283i
$107$	4.07848	−	4.52961i	0.394282	−	0.437894i	−0.513019	−	0.858377i	$-0.671473\pi$
$107$	4.07848	−	4.52961i	0.394282	−	0.437894i	0.907300	+	0.420483i	$0.138140\pi$
$108$	−5.13787	+	8.89905i	−0.494392	+	0.856312i
$109$	−7.52740	−	13.0378i	−0.720994	−	1.24880i	−0.960602	−	0.277929i	$-0.910352\pi$
$109$	−7.52740	−	13.0378i	−0.720994	−	1.24880i	0.239608	−	0.970870i	$-0.422981\pi$
$110$	−5.04437	−	1.07221i	−0.480962	−	0.102232i
$111$	6.10599			0.579555
$112$	0.298482	+	0.0634443i	0.0282039	+	0.00599493i
$113$	−2.40268	+	7.39469i	−0.226025	+	0.695634i	0.772161	+	0.635427i	$0.219176\pi$
$113$	−2.40268	+	7.39469i	−0.226025	+	0.695634i	−0.998186	+	0.0602068i	$0.980824\pi$
$114$	0.830775	+	2.55686i	0.0778092	+	0.239472i
$115$	2.08509	−	19.8383i	0.194436	−	1.84993i
$116$	−13.9225	+	2.95932i	−1.29267	+	0.274766i
$117$	−3.90010	+	0.828992i	−0.360564	+	0.0766403i
$118$	1.05198	+	1.16834i	0.0968423	+	0.107554i
$119$	0.651630	−	0.473437i	0.0597348	−	0.0433999i
$120$	9.64343	+	4.29353i	0.880321	+	0.391944i
$121$	1.00000			0.0909091
$122$	11.5825	−	13.0281i	1.04863	−	1.17951i
$123$	−17.3485			−1.56426
$124$	−10.6608	−	4.74651i	−0.957371	−	0.426249i
$125$	8.71344	−	6.33069i	0.779354	−	0.566234i
$126$	−0.572329	−	0.635636i	−0.0509871	−	0.0566269i
$127$	−16.7515	+	3.56064i	−1.48646	+	0.315956i	−0.878396	−	0.477934i	$-0.841386\pi$
$127$	−16.7515	+	3.56064i	−1.48646	+	0.315956i	−0.608061	+	0.793890i	$0.708052\pi$
$128$	−15.0810	+	3.20556i	−1.33298	+	0.283335i
$129$	0.0768324	−	0.731012i	0.00676472	−	0.0643620i
$130$	−4.71684	−	14.5169i	−0.413694	−	1.27322i
$131$	3.18153	−	9.79175i	0.277972	−	0.855510i	−0.710446	−	0.703752i	$-0.751507\pi$
$131$	3.18153	−	9.79175i	0.277972	−	0.855510i	0.988418	−	0.151758i	$-0.0484933\pi$
$132$	−6.08100	−	1.29256i	−0.529284	−	0.112503i
$133$	0.164342			0.0142503
$134$	5.78703	+	1.23007i	0.499923	+	0.106262i
$135$	−3.98130	−	6.89581i	−0.342656	−	0.593497i
$136$	−3.10215	+	5.37309i	−0.266008	+	0.460739i
$137$	4.77167	−	5.29948i	0.407671	−	0.452765i	−0.503989	−	0.863710i	$-0.668135\pi$
$137$	4.77167	−	5.29948i	0.407671	−	0.452765i	0.911660	+	0.410945i	$0.134801\pi$
$138$	4.19956	−	39.9562i	0.357491	−	3.40130i
$139$	5.55849	+	6.17333i	0.471465	+	0.523615i	0.931233	−	0.364424i	$-0.118734\pi$
$139$	5.55849	+	6.17333i	0.471465	+	0.523615i	−0.459768	+	0.888039i	$0.652067\pi$
$140$	1.31139	−	1.45645i	0.110833	−	0.123092i
$141$	2.35223	+	22.3799i	0.198093	+	1.88473i
$142$	−10.3976	−	7.55429i	−0.872547	−	0.633942i
$143$	1.47991	+	2.56328i	0.123756	+	0.214353i
$144$	−1.32011	−	0.587752i	−0.110009	−	0.0489793i
$145$	3.40830	−	10.4897i	0.283044	−	0.871119i
$146$	1.10136	+	0.800186i	0.0911493	+	0.0662239i
$147$	13.1789	−	5.86762i	1.08698	−	0.483953i
$148$	0.912768	+	8.68441i	0.0750291	+	0.713854i
$149$	−5.16130	−	15.8848i	−0.422830	−	1.30134i	−0.905057	−	0.425290i	$-0.860172\pi$
$149$	−5.16130	−	15.8848i	−0.422830	−	1.30134i	0.482227	−	0.876046i	$-0.339828\pi$
$150$	−1.27464	+	0.926078i	−0.104074	+	0.0756139i
$151$	2.91761	−	5.05345i	0.237432	−	0.411244i	−0.722545	−	0.691324i	$-0.757028\pi$
$151$	2.91761	−	5.05345i	0.237432	−	0.411244i	0.959977	+	0.280080i	$0.0903611\pi$
$152$	−1.15645	+	0.514887i	−0.0938009	+	0.0417628i
$153$	−3.48450	+	1.55140i	−0.281705	+	0.125423i
$154$	−0.317468	+	0.549870i	−0.0255823	+	0.0443098i
$155$	7.31577	−	5.31522i	0.587617	−	0.426929i
$156$	−5.68616	−	17.5002i	−0.455257	−	1.40114i
$157$	1.20589	+	11.4733i	0.0962406	+	0.915668i	0.930992	+	0.365040i	$0.118945\pi$
$157$	1.20589	+	11.4733i	0.0962406	+	0.915668i	−0.834751	+	0.550627i	$0.814388\pi$
$158$	−12.2620	+	5.45941i	−0.975516	+	0.434328i
$159$	−13.3223	−	9.67921i	−1.05653	−	0.767611i
$160$	4.83852	−	14.8914i	0.382519	−	1.17727i
$161$	−2.24361	−	0.998919i	−0.176821	−	0.0787258i
$162$	−12.5288	−	21.7005i	−0.984357	−	1.70496i
$163$	−17.9168	−	13.0173i	−1.40335	−	1.01960i	−0.994247	−	0.107108i	$-0.965841\pi$
$163$	−17.9168	−	13.0173i	−1.40335	−	1.01960i	−0.409105	−	0.912487i	$-0.634159\pi$
$164$	−2.59337	−	24.6743i	−0.202508	−	1.92674i
$165$	3.22347	−	3.58003i	0.250947	−	0.278705i
$166$	11.7863	+	13.0900i	0.914794	+	1.01598i
$167$	−0.830582	+	7.90246i	−0.0642724	+	0.611511i	0.914219	+	0.405221i	$0.132806\pi$
$167$	−0.830582	+	7.90246i	−0.0642724	+	0.611511i	−0.978491	+	0.206289i	$0.933861\pi$
$168$	0.869639	−	0.965832i	0.0670941	−	0.0745156i
$169$	2.11972	−	3.67146i	0.163055	−	0.282420i
$170$	−7.30092	−	12.6456i	−0.559955	−	0.969870i
$171$	−0.761236	−	0.161806i	−0.0582132	−	0.0123736i
$172$	1.05119			0.0801522
$173$	−6.75327	−	1.43545i	−0.513442	−	0.109135i	−0.0560977	−	0.998425i	$-0.517866\pi$
$173$	−6.75327	−	1.43545i	−0.513442	−	0.109135i	−0.457344	+	0.889290i	$0.651199\pi$
$174$	6.86462	−	21.1271i	0.520406	−	1.60164i
$175$	0.0297618	+	0.0915973i	0.00224978	+	0.00692410i
$176$	−0.112127	+	1.06682i	−0.00845188	+	0.0804143i
$177$	−1.43651	+	0.305340i	−0.107975	+	0.0229508i
$178$	9.10230	−	1.93475i	0.682246	−	0.145016i
$179$	−10.4638	−	11.6212i	−0.782100	−	0.868610i	0.211979	−	0.977274i	$-0.432009\pi$
$179$	−10.4638	−	11.6212i	−0.782100	−	0.868610i	−0.994078	+	0.108665i	$0.965343\pi$
$180$	−7.50836	+	5.45515i	−0.559640	+	0.406603i
$181$	17.8061	+	7.92779i	1.32352	+	0.589268i	0.942161	−	0.335161i	$-0.108791\pi$
$181$	17.8061	+	7.92779i	1.32352	+	0.589268i	0.381356	+	0.924428i	$0.375457\pi$
$182$	−1.87930			−0.139303
$183$	5.12975	+	15.4551i	0.379202	+	1.14247i
$184$	18.9176			1.39463
$185$	−6.18156	−	2.75221i	−0.454477	−	0.202346i
$186$	14.7346	−	10.7053i	1.08040	−	0.784954i
$187$	1.89459	+	2.10416i	0.138546	+	0.153871i
$188$	−31.4788	+	6.69103i	−2.29583	+	0.487993i
$189$	−0.958928	+	0.203826i	−0.0697517	+	0.0148262i
$190$	0.311420	−	2.96297i	0.0225928	−	0.214956i
$191$	−2.76923	−	8.52281i	−0.200374	−	0.616689i	−0.999872	−	0.0160193i	$-0.994901\pi$
$191$	−2.76923	−	8.52281i	−0.200374	−	0.616689i	0.799497	−	0.600670i	$-0.205099\pi$
$192$	8.36297	−	25.7386i	0.603545	−	1.85752i
$193$	−15.4240	−	3.27848i	−1.11025	−	0.235990i	−0.383938	−	0.923359i	$-0.625432\pi$
$193$	−15.4240	−	3.27848i	−1.11025	−	0.235990i	−0.726309	+	0.687368i	$0.758766\pi$
$194$	15.9753			1.14696
$195$	13.9471	+	2.96454i	0.998771	+	0.212295i
$196$	10.3155	+	17.8669i	0.736818	+	1.27621i
$197$	−4.11645	+	7.12990i	−0.293285	+	0.507984i	−0.974584	−	0.224021i	$-0.928082\pi$
$197$	−4.11645	+	7.12990i	−0.293285	+	0.507984i	0.681300	+	0.732005i	$0.261415\pi$
$198$	2.01190	−	2.23444i	0.142980	−	0.158795i
$199$	1.74922	−	16.6428i	0.123999	−	1.17977i	−0.738692	−	0.674043i	$-0.764556\pi$
$199$	1.74922	−	16.6428i	0.123999	−	1.17977i	0.862691	−	0.505731i	$-0.168777\pi$
$200$	−0.496406	−	0.551315i	−0.0351012	−	0.0389838i
$201$	−3.69805	+	4.10710i	−0.260840	+	0.289692i
$202$	−1.20620	−	11.4762i	−0.0848677	−	0.807462i
$203$	−1.09860	−	0.798179i	−0.0771065	−	0.0560212i
$204$	−8.80127	−	15.2443i	−0.616212	−	1.06731i
$205$	17.5631	+	7.81962i	1.22666	+	0.546146i
$206$	6.39219	−	19.6731i	0.445365	−	1.37069i
$207$	9.40895	+	6.83600i	0.653967	+	0.475135i
$208$	−2.90049	+	1.29138i	−0.201113	+	0.0895412i
$209$	0.0603871	+	0.574545i	0.00417706	+	0.0397421i
$210$	0.945202	+	2.90903i	0.0652251	+	0.200742i
$211$	−1.55938	+	1.13296i	−0.107352	+	0.0779961i	−0.640166	−	0.768236i	$-0.721135\pi$
$211$	−1.55938	+	1.13296i	−0.107352	+	0.0779961i	0.532814	+	0.846232i	$0.321135\pi$
$212$	11.7750	−	20.3949i	0.808710	−	1.40073i
$213$	10.9677	−	4.88313i	0.751494	−	0.334587i
$214$	−12.4282	+	5.53339i	−0.849574	+	0.378255i
$215$	−0.407278	+	0.705427i	−0.0277762	+	0.0481097i
$216$	6.10927	−	4.43864i	0.415683	−	0.302011i
$217$	−0.344042	−	1.05885i	−0.0233551	−	0.0718796i
$218$	3.51237	+	33.4180i	0.237888	+	2.26335i
$219$	−1.16175	+	0.517244i	−0.0785037	+	0.0349521i
$220$	5.57365	+	4.04950i	0.375776	+	0.273017i
$221$	−2.58972	+	7.97034i	−0.174203	+	0.536143i
$222$	−12.4502	−	5.54320i	−0.835605	−	0.372035i
$223$	−5.87577	−	10.1771i	−0.393471	−	0.681511i	0.599434	−	0.800424i	$-0.295392\pi$
$223$	−5.87577	−	10.1771i	−0.393471	−	0.681511i	−0.992905	+	0.118913i	$0.962059\pi$
$224$	−1.55960	−	1.13312i	−0.104205	−	0.0757097i
$225$	−0.0476735	−	0.453583i	−0.00317824	−	0.0302389i
$226$	11.6122	−	12.8967i	0.772434	−	0.857874i
$227$	−3.88908	−	4.31926i	−0.258127	−	0.286679i	0.600126	−	0.799905i	$-0.295117\pi$
$227$	−3.88908	−	4.31926i	−0.258127	−	0.286679i	−0.858254	+	0.513226i	$0.828450\pi$
$228$	0.375418	−	3.57187i	0.0248627	−	0.236553i
$229$	−12.4548	+	13.8325i	−0.823037	+	0.914075i	−0.997506	−	0.0705873i	$-0.977513\pi$
$229$	−12.4548	+	13.8325i	−0.823037	+	0.914075i	0.174468	+	0.984663i	$0.444179\pi$
$230$	−22.2613	+	38.5577i	−1.46787	+	2.54242i
$231$	−0.296558	−	0.513653i	−0.0195121	−	0.0337959i
$232$	10.2314	+	2.17476i	0.671726	+	0.142780i
$233$	6.88627			0.451135			0.225567	−	0.974228i	$-0.427576\pi$
$233$	6.88627			0.451135			0.225567	+	0.974228i	$0.427576\pi$
$234$	8.70495	+	1.85029i	0.569060	+	0.120958i
$235$	7.70616	−	23.7171i	0.502695	−	1.54714i
$236$	−0.649019	−	1.99747i	−0.0422475	−	0.130024i
$237$	1.31062	−	12.4697i	0.0851340	−	0.809996i
$238$	−1.75848	+	0.373777i	−0.113986	+	0.0242284i
$239$	−8.27437	+	1.75877i	−0.535225	+	0.113765i	−0.467591	−	0.883945i	$-0.654878\pi$
$239$	−8.27437	+	1.75877i	−0.535225	+	0.113765i	−0.0676332	+	0.997710i	$0.521545\pi$
$240$	3.45779	+	3.84027i	0.223200	+	0.247888i
$241$	−10.6075	+	7.70682i	−0.683291	+	0.496440i	−0.874448	−	0.485119i	$-0.838776\pi$
$241$	−10.6075	+	7.70682i	−0.683291	+	0.496440i	0.191157	+	0.981560i	$0.438776\pi$
$242$	−2.03902	−	0.907829i	−0.131073	−	0.0583574i
$243$	13.0686			0.838349
$244$	−21.2146	+	9.60627i	−1.35812	+	0.614978i
$245$	−15.9868			−1.02136
$246$	35.3738	+	15.7494i	2.25535	+	1.00415i
$247$	−1.38335	+	1.00507i	−0.0880207	+	0.0639508i
$248$	5.73839	+	6.37313i	0.364388	+	0.404694i
$249$	−16.0946	+	3.42102i	−1.01996	+	0.216798i
$250$	−23.5140	+	4.99806i	−1.48716	+	0.316105i
$251$	−2.31861	+	22.0601i	−0.146349	+	1.39242i	0.637012	+	0.770854i	$0.280170\pi$
$251$	−2.31861	+	22.0601i	−0.146349	+	1.39242i	−0.783361	+	0.621567i	$0.786496\pi$
$252$	0.353099	+	1.08673i	0.0222432	+	0.0684574i
$253$	2.66785	−	8.21078i	0.167726	−	0.516207i
$254$	37.3891	+	7.94730i	2.34600	+	0.498658i
$255$	13.6401			0.854176
$256$	8.26764	+	1.75734i	0.516727	+	0.109834i
$257$	−7.08359	−	12.2691i	−0.441862	−	0.765328i	0.555965	−	0.831205i	$-0.312349\pi$
$257$	−7.08359	−	12.2691i	−0.441862	−	0.765328i	−0.997828	+	0.0658775i	$0.979015\pi$
$258$	−0.820296	+	1.42079i	−0.0510694	+	0.0884548i
$259$	−0.557449	+	0.619110i	−0.0346382	+	0.0384696i
$260$	−2.13149	+	20.2798i	−0.132189	+	1.25770i
$261$	4.30288	+	4.77883i	0.266341	+	0.295802i
$262$	−15.3764	+	17.0773i	−0.949960	+	1.05504i
$263$	0.109172	+	1.03870i	0.00673185	+	0.0640493i	0.997372	−	0.0724496i	$-0.0230817\pi$
$263$	0.109172	+	1.03870i	0.00673185	+	0.0640493i	−0.990640	+	0.136499i	$0.956415\pi$
$264$	3.69613	+	2.68539i	0.227481	+	0.165275i
$265$	9.12436	+	15.8039i	0.560505	+	0.970823i
$266$	−0.335096	−	0.149194i	−0.0205461	−	0.00914769i
$267$	−2.68621	+	8.26729i	−0.164393	+	0.505950i
$268$	−6.39424	−	4.64569i	−0.390590	−	0.283780i
$269$	12.3725	−	5.50858i	0.754363	−	0.335864i	0.00673079	−	0.999977i	$-0.497858\pi$
$269$	12.3725	−	5.50858i	0.754363	−	0.335864i	0.747632	+	0.664113i	$0.231191\pi$
$270$	1.85772	+	17.6750i	0.113057	+	1.07567i
$271$	2.49440	+	7.67698i	0.151524	+	0.466343i	0.997792	−	0.0664142i	$-0.0211559\pi$
$271$	2.49440	+	7.67698i	0.151524	+	0.466343i	−0.846268	+	0.532757i	$0.821156\pi$
$272$	−2.45718	+	1.78525i	−0.148989	+	0.108247i
$273$	0.877759	−	1.52032i	0.0531244	−	0.0920142i
$274$	−14.5405	+	6.47386i	−0.878426	+	0.391100i
$275$	−0.309291	+	0.137705i	−0.0186510	+	0.00830394i
$276$	−26.8361	+	46.4815i	−1.61534	+	2.79786i
$277$	−2.29010	+	1.66386i	−0.137599	+	0.0999716i	−0.654456	−	0.756101i	$-0.727102\pi$
$277$	−2.29010	+	1.66386i	−0.137599	+	0.0999716i	0.516856	+	0.856072i	$0.327102\pi$
$278$	−5.72953	−	17.6337i	−0.343635	−	1.05760i
$279$	0.551100	+	5.24337i	0.0329935	+	0.313912i
$280$	−1.31574	+	0.585805i	−0.0786304	+	0.0350085i
$281$	14.9647	+	10.8725i	0.892718	+	0.648598i	0.936585	−	0.350439i	$-0.113968\pi$
$281$	14.9647	+	10.8725i	0.892718	+	0.648598i	−0.0438669	+	0.999037i	$0.513968\pi$
$282$	15.5209	−	47.7685i	0.924257	−	2.84457i
$283$	19.1997	+	8.54828i	1.14131	+	0.508142i	0.888273	−	0.459315i	$-0.151905\pi$
$283$	19.1997	+	8.54828i	1.14131	+	0.508142i	0.253033	+	0.967458i	$0.418572\pi$
$284$	8.58469	+	14.8691i	0.509408	+	0.882320i
$285$	2.25154	+	1.63584i	0.133370	+	0.0968989i
$286$	−0.690544	−	6.57008i	−0.0408327	−	0.388497i
$287$	1.58383	−	1.75903i	0.0934908	−	0.103832i
$288$	6.10850	+	6.78417i	0.359947	+	0.399761i
$289$	0.938984	−	8.93384i	0.0552344	−	0.525520i
$290$	−16.4724	+	18.2944i	−0.967292	+	1.07429i
$291$	−7.46154	+	12.9238i	−0.437403	+	0.757605i
$292$	−0.909331	−	1.57501i	−0.0532145	−	0.0921703i
$293$	22.6348	+	4.81118i	1.32234	+	0.281072i	0.814392	−	0.580316i	$-0.197071\pi$
$293$	22.6348	+	4.81118i	1.32234	+	0.281072i	0.507948	+	0.861388i	$0.330404\pi$
$294$	−32.1988			−1.87787
$295$	1.59192	+	0.338373i	0.0926851	+	0.0197008i
$296$	1.98302	−	6.10310i	0.115261	−	0.354736i
$297$	−1.06494	−	3.27755i	−0.0617941	−	0.190183i
$298$	−3.89674	+	37.0750i	−0.225732	+	2.14770i
$299$	24.9947	−	5.31280i	1.44548	−	0.307247i
$300$	2.05879	−	0.437610i	0.118865	−	0.0252654i
$301$	0.0671056	+	0.0745283i	0.00386790	+	0.00429574i
$302$	−10.5367	+	7.65538i	−0.606320	+	0.440517i
$303$	9.84745	+	4.38437i	0.565721	+	0.251875i
$304$	−0.619705			−0.0355425
$305$	1.77297	−	17.9585i	0.101520	−	1.02830i
$306$	8.51335			0.486676
$307$	25.6598	+	11.4245i	1.46448	+	0.652029i	0.975447	−	0.220236i	$-0.0706827\pi$
$307$	25.6598	+	11.4245i	1.46448	+	0.652029i	0.489034	+	0.872265i	$0.337349\pi$
$308$	0.686225	−	0.498572i	0.0391013	−	0.0284088i
$309$	12.9297	+	14.3599i	0.735544	+	0.816904i
$310$	−19.7423	+	4.19635i	−1.12129	+	0.238337i
$311$	2.36169	−	0.501993i	0.133919	−	0.0284654i	−0.140464	−	0.990086i	$-0.544860\pi$
$311$	2.36169	−	0.501993i	0.133919	−	0.0284654i	0.274384	+	0.961620i	$0.411526\pi$
$312$	−1.41348	+	13.4484i	−0.0800226	+	0.761364i
$313$	−8.06993	−	24.8367i	−0.456139	−	1.40385i	−0.869792	−	0.493418i	$-0.835747\pi$
$313$	−8.06993	−	24.8367i	−0.456139	−	1.40385i	0.413653	−	0.910435i	$-0.364253\pi$
$314$	7.95695	−	24.4890i	0.449037	−	1.38199i
$315$	−0.866085	−	0.184092i	−0.0487984	−	0.0103724i
$316$	17.9313			1.00872
$317$	−7.74171	−	1.64555i	−0.434818	−	0.0924234i	−0.0146979	−	0.999892i	$-0.504679\pi$
$317$	−7.74171	−	1.64555i	−0.434818	−	0.0924234i	−0.420120	+	0.907469i	$0.638012\pi$
$318$	18.3773	+	31.8304i	1.03055	+	1.78496i
$319$	2.38678	−	4.13403i	0.133634	−	0.231461i
$320$	−20.0678	+	22.2876i	−1.12183	+	1.24591i
$321$	1.32838	−	12.6387i	0.0741430	−	0.705424i
$322$	3.66791	+	4.07363i	0.204405	+	0.227014i
$323$	−1.09452	+	1.21559i	−0.0609009	+	0.0676373i
$324$	3.49908	+	33.2915i	0.194393	+	1.84953i
$325$	−0.810702	−	0.589009i	−0.0449696	−	0.0326724i
$326$	24.7152	+	42.8079i	1.36885	+	2.37091i
$327$	−28.6752	−	12.7670i	−1.58574	−	0.706017i
$328$	−5.63419	+	17.3402i	−0.311096	+	0.957455i
$329$	−2.48393	−	1.80468i	−0.136944	−	0.0994954i
$330$	−9.82276	+	4.37338i	−0.540725	+	0.240746i
$331$	2.06138	+	19.6127i	0.113304	+	1.07801i	0.892443	+	0.451161i	$0.148990\pi$
$331$	2.06138	+	19.6127i	0.113304	+	1.07801i	−0.779139	+	0.626851i	$0.784343\pi$
$332$	−7.27157	−	22.3796i	−0.399079	−	1.22824i
$333$	3.19168	−	2.31889i	0.174903	−	0.127074i
$334$	8.86765	−	15.3592i	0.485216	−	0.840419i
$335$	5.59504	−	2.49107i	0.305690	−	0.136102i
$336$	0.581226	−	0.258778i	0.0317085	−	0.0141175i
$337$	−13.3266	+	23.0824i	−0.725948	+	1.25738i	0.232634	+	0.972564i	$0.425266\pi$
$337$	−13.3266	+	23.0824i	−0.725948	+	1.25738i	−0.958582	+	0.284815i	$0.908068\pi$
$338$	−7.65520	+	5.56183i	−0.416388	+	0.302524i
$339$	5.00953	+	15.4177i	0.272080	+	0.837377i
$340$	2.03902	+	19.4000i	0.110581	+	1.05211i
$341$	3.57537	−	1.59186i	0.193617	−	0.0862038i
$342$	1.40528	+	1.02100i	0.0759889	+	0.0552092i
$343$	−1.22358	+	3.76578i	−0.0660670	+	0.203333i
$344$	−0.705713	−	0.314204i	−0.0380495	−	0.0169407i
$345$	−20.7951	−	36.0182i	−1.11957	−	1.93915i
$346$	12.4669	+	9.05773i	0.670224	+	0.486946i
$347$	−2.58560	−	24.6003i	−0.138802	−	1.32061i	−0.813087	−	0.582143i	$-0.802215\pi$
$347$	−2.58560	−	24.6003i	−0.138802	−	1.32061i	0.674285	−	0.738472i	$-0.264452\pi$
$348$	−19.8575	+	22.0540i	−1.06447	+	1.18222i
$349$	−8.17445	−	9.07865i	−0.437569	−	0.485969i	0.483514	−	0.875337i	$-0.339360\pi$
$349$	−8.17445	−	9.07865i	−0.437569	−	0.485969i	−0.921082	+	0.389368i	$0.872694\pi$
$350$	0.0224699	−	0.213787i	0.00120107	−	0.0114274i
$351$	6.82527	−	7.58023i	0.364306	−	0.404603i
$352$	3.38835	−	5.86879i	0.180600	−	0.312808i
$353$	−15.9857	−	27.6881i	−0.850835	−	1.47369i	−0.880455	−	0.474129i	$-0.842763\pi$
$353$	−15.9857	−	27.6881i	−0.850835	−	1.47369i	0.0296201	−	0.999561i	$-0.490570\pi$
$354$	3.20627	+	0.681514i	0.170411	+	0.0362221i
$355$	−13.3044			−0.706126
$356$	−12.1599	−	2.58467i	−0.644475	−	0.136987i
$357$	0.518951	−	1.59717i	0.0274658	−	0.0845310i
$358$	10.7858	+	33.1952i	0.570045	+	1.75442i
$359$	0.663276	−	6.31065i	0.0350063	−	0.333063i	−0.962977	−	0.269584i	$-0.913114\pi$
$359$	0.663276	−	6.31065i	0.0350063	−	0.333063i	0.997983	−	0.0634790i	$-0.0202196\pi$
$360$	6.67130	−	1.41803i	0.351608	−	0.0747367i
$361$	18.2583	−	3.88093i	0.960966	−	0.204260i
$362$	−29.1099	−	32.3298i	−1.52998	−	1.69922i
$363$	1.68678	−	1.22552i	0.0885330	−	0.0643230i
$364$	2.29353	+	1.02115i	0.120214	+	0.0535226i
$365$	1.40927			0.0737645
$366$	3.57092	−	36.1701i	0.186655	−	1.89064i
$367$	−1.84173			−0.0961377			−0.0480689	−	0.998844i	$-0.515307\pi$
$367$	−1.84173			−0.0961377			−0.0480689	+	0.998844i	$0.515307\pi$
$368$	8.46026	+	3.76675i	0.441021	+	0.196355i
$369$	−9.06824	+	6.58846i	−0.472074	+	0.342982i
$370$	10.1058	+	11.2236i	0.525374	+	0.583487i
$371$	2.19768	−	0.467130i	0.114098	−	0.0242522i
$372$	−23.7994	+	5.05872i	−1.23394	+	0.262282i
$373$	2.13032	−	20.2687i	0.110304	−	1.04947i	−0.789671	−	0.613531i	$-0.789749\pi$
$373$	2.13032	−	20.2687i	0.110304	−	1.04947i	0.899975	−	0.435942i	$-0.143585\pi$
$374$	−1.95289	−	6.01038i	−0.100982	−	0.310789i
$375$	6.93929	−	21.3569i	0.358343	−	1.10287i
$376$	23.1333	+	4.91713i	1.19301	+	0.253581i
$377$	14.1289			0.727676
$378$	2.14031	+	0.454937i	0.110086	+	0.0233994i
$379$	−9.63232	−	16.6837i	−0.494779	−	0.856982i	0.505203	−	0.863001i	$-0.331418\pi$
$379$	−9.63232	−	16.6837i	−0.494779	−	0.856982i	−0.999982	+	0.00601826i	$0.998084\pi$
$380$	−1.99004	+	3.44685i	−0.102087	+	0.176820i
$381$	−23.8925	+	26.5353i	−1.22405	+	1.35944i
$382$	−2.09075	+	19.8921i	−0.106972	+	1.01777i
$383$	16.3766	+	18.1880i	0.836803	+	0.929364i	0.998345	−	0.0575022i	$-0.0183136\pi$
$383$	16.3766	+	18.1880i	0.836803	+	0.929364i	−0.161543	+	0.986866i	$0.551647\pi$
$384$	−21.5098	+	23.8891i	−1.09767	+	1.21909i
$385$	0.0687045	+	0.653680i	0.00350151	+	0.0333146i
$386$	28.4736	+	20.6873i	1.44927	+	1.05295i
$387$	−0.237457	−	0.411287i	−0.0120706	−	0.0209069i
$388$	−19.4966	−	8.68043i	−0.989788	−	0.440682i
$389$	−1.75241	+	5.39335i	−0.0888505	+	0.273454i	−0.985602	−	0.169080i	$-0.945920\pi$
$389$	−1.75241	+	5.39335i	−0.0888505	+	0.273454i	0.896752	+	0.442534i	$0.145920\pi$
$390$	−25.7470	−	18.7063i	−1.30375	−	0.947231i
$391$	22.3312	−	9.94251i	1.12934	−	0.502814i
$392$	−1.58479	−	15.0783i	−0.0800439	−	0.761567i
$393$	−6.63342	−	20.4156i	−0.334612	−	1.02983i
$394$	14.8662	−	10.8009i	0.748950	−	0.544144i
$395$	−6.94743	+	12.0333i	−0.349563	+	0.605461i
$396$	−3.66949	+	1.63376i	−0.184399	+	0.0820996i
$397$	−30.2735	+	13.4786i	−1.51938	+	0.676472i	−0.985591	−	0.169145i	$-0.945900\pi$
$397$	−30.2735	+	13.4786i	−1.51938	+	0.676472i	−0.533790	+	0.845617i	$0.679233\pi$
$398$	−18.6755	+	32.3469i	−0.936117	+	1.62140i
$399$	0.277209	−	0.201404i	0.0138778	−	0.0100828i
$400$	−0.112226	−	0.345397i	−0.00561132	−	0.0172699i
$401$	−0.974736	−	9.27399i	−0.0486760	−	0.463121i	−0.991526	−	0.129905i	$-0.958533\pi$
$401$	−0.974736	−	9.27399i	−0.0486760	−	0.463121i	0.942850	−	0.333216i	$-0.108134\pi$
$402$	11.2689	−	5.01725i	0.562043	−	0.250238i
$403$	9.37161	+	6.80887i	0.466833	+	0.339174i
$404$	−4.76371	+	14.6612i	−0.237004	+	0.729422i
$405$	−23.6969	−	10.5505i	−1.17751	−	0.524261i
$406$	1.51545	+	2.62484i	0.0752106	+	0.130269i
$407$	−2.36926	−	1.72137i	−0.117440	−	0.0853252i
$408$	1.35216	+	12.8650i	0.0669420	+	0.636910i
$409$	−18.6063	+	20.6643i	−0.920020	+	1.02179i	0.0796681	+	0.996821i	$0.474614\pi$
$409$	−18.6063	+	20.6643i	−0.920020	+	1.02179i	−0.999688	+	0.0249646i	$0.992053\pi$
$410$	−28.7127	−	31.8887i	−1.41802	−	1.57487i
$411$	1.55416	−	14.7868i	0.0766609	−	0.729380i
$412$	−18.4909	+	20.5362i	−0.910980	+	1.01175i
$413$	0.100187	−	0.173530i	0.00492990	−	0.00853884i
$414$	−12.9791	−	22.4804i	−0.637887	−	1.10485i
$415$	17.8358	+	3.79111i	0.875524	+	0.186098i
$416$	20.0578			0.983416
$417$	16.9415	+	3.60102i	0.829628	+	0.176343i
$418$	0.398458	−	1.22633i	0.0194892	−	0.0599817i
$419$	8.33275	+	25.6456i	0.407081	+	1.25287i	0.919145	+	0.393920i	$0.128881\pi$
$419$	8.33275	+	25.6456i	0.407081	+	1.25287i	−0.512063	+	0.858948i	$0.671119\pi$
$420$	0.427126	−	4.06384i	0.0208416	−	0.198295i
$421$	−5.31308	+	1.12933i	−0.258944	+	0.0550402i	−0.335554	−	0.942021i	$-0.608924\pi$
$421$	−5.31308	+	1.12933i	−0.258944	+	0.0550402i	0.0766105	+	0.997061i	$0.475590\pi$
$422$	4.20814	−	0.894469i	0.204849	−	0.0435421i
$423$	9.72881	+	10.8049i	0.473031	+	0.525354i
$424$	−14.0013	+	10.1725i	−0.679961	+	0.494020i
$425$	−0.875734	−	0.389902i	−0.0424793	−	0.0189130i
$426$	−26.7964			−1.29829
$427$	−2.03537	−	0.890853i	−0.0984986	−	0.0431114i
$428$	18.1743			0.878488
$429$	5.63763	+	2.51004i	0.272187	+	0.121186i
$430$	1.47085	−	1.06864i	0.0709309	−	0.0515343i
$431$	19.9155	+	22.1184i	0.959294	+	1.06540i	0.997810	+	0.0661456i	$0.0210702\pi$
$431$	19.9155	+	22.1184i	0.959294	+	1.06540i	−0.0385163	+	0.999258i	$0.512263\pi$
$432$	3.61595	−	0.768594i	0.173972	−	0.0369790i
$433$	5.46683	−	1.16201i	0.262719	−	0.0558427i	−0.0746687	−	0.997208i	$-0.523790\pi$
$433$	5.46683	−	1.16201i	0.262719	−	0.0558427i	0.337388	+	0.941366i	$0.390457\pi$
$434$	−0.259749	+	2.47135i	−0.0124684	+	0.118629i
$435$	−7.10621	−	21.8707i	−0.340717	−	1.04862i
$436$	13.8716	−	42.6925i	0.664331	−	2.04460i
$437$	4.87857	+	1.03697i	0.233374	+	0.0496051i
$438$	2.83840			0.135624
$439$	30.6815	+	6.52156i	1.46435	+	0.311257i	0.870041	−	0.492980i	$-0.164092\pi$
$439$	30.6815	+	6.52156i	1.46435	+	0.311257i	0.594308	+	0.804237i	$0.297426\pi$
$440$	−2.53146	−	4.38462i	−0.120683	−	0.209028i
$441$	4.66040	−	8.07205i	0.221924	−	0.384383i
$442$	12.5162	−	13.9006i	0.595334	−	0.661186i
$443$	3.68082	−	35.0206i	0.174881	−	1.66388i	−0.457490	−	0.889215i	$-0.651251\pi$
$443$	3.68082	−	35.0206i	0.174881	−	1.66388i	0.632371	−	0.774666i	$-0.282082\pi$
$444$	12.1825	+	13.5301i	0.578157	+	0.642109i
$445$	6.44584	−	7.15883i	0.305562	−	0.339361i
$446$	2.74170	+	26.0855i	0.129823	+	1.23519i
$447$	−28.1731	−	20.4690i	−1.33254	−	0.968148i
$448$	1.84623	+	3.19777i	0.0872263	+	0.151080i
$449$	−2.20769	−	0.982927i	−0.104187	−	0.0463872i	0.353981	−	0.935253i	$-0.384828\pi$
$449$	−2.20769	−	0.982927i	−0.104187	−	0.0463872i	−0.458168	+	0.888865i	$0.651494\pi$
$450$	−0.314569	+	0.968144i	−0.0148289	+	0.0456387i
$451$	6.73159	+	4.89079i	0.316978	+	0.230298i
$452$	−21.1794	+	9.42969i	−0.996196	+	0.443535i
$453$	−1.27172	−	12.0996i	−0.0597507	−	0.568490i
$454$	4.00875	+	12.3377i	0.188140	+	0.579035i
$455$	−1.57389	+	1.14350i	−0.0737851	+	0.0536080i
$456$	−1.31968	+	2.28576i	−0.0617998	+	0.107040i
$457$	−25.0974	+	11.1741i	−1.17401	+	0.522702i	−0.898661	−	0.438643i	$-0.855459\pi$
$457$	−25.0974	+	11.1741i	−1.17401	+	0.522702i	−0.275347	+	0.961345i	$0.588793\pi$
$458$	37.9531	−	16.8978i	1.77343	−	0.789583i
$459$	4.87885	−	8.45042i	0.227725	−	0.394432i
$460$	48.1192	−	34.9606i	2.24357	−	1.63005i
$461$	8.42372	+	25.9255i	0.392332	+	1.20747i	0.931020	+	0.364968i	$0.118920\pi$
$461$	8.42372	+	25.9255i	0.392332	+	1.20747i	−0.538689	+	0.842505i	$0.681080\pi$
$462$	0.138377	+	1.31657i	0.00643789	+	0.0612524i
$463$	−1.71171	+	0.762103i	−0.0795500	+	0.0354179i	−0.446126	−	0.894970i	$-0.647197\pi$
$463$	−1.71171	+	0.762103i	−0.0795500	+	0.0354179i	0.366576	+	0.930388i	$0.380530\pi$
$464$	4.14263	+	3.00979i	0.192317	+	0.139726i
$465$	5.82620	−	17.9312i	0.270184	−	0.831540i
$466$	−14.0412	−	6.25155i	−0.650447	−	0.289598i
$467$	−11.5393	−	19.9867i	−0.533975	−	0.924872i	−0.999212	−	0.0396861i	$-0.987364\pi$
$467$	−11.5393	−	19.9867i	−0.533975	−	0.924872i	0.465237	−	0.885186i	$-0.345969\pi$
$468$	−9.61832	−	6.98812i	−0.444607	−	0.323026i
$469$	−0.0788196	−	0.749918i	−0.00363955	−	0.0346280i
$470$	−37.2441	+	41.3638i	−1.71794	+	1.90797i
$471$	16.0948	+	17.8751i	0.741608	+	0.823639i
$472$	−0.161335	+	1.53500i	−0.00742603	+	0.0706540i
$473$	−0.235896	+	0.261989i	−0.0108465	+	0.0120463i
$474$	−13.9928	+	24.2362i	−0.642709	+	1.11320i
$475$	−0.0977951	−	0.169386i	−0.00448715	−	0.00777197i
$476$	2.34919	+	0.499336i	0.107675	+	0.0228870i
$477$	−10.6396			−0.487154
$478$	18.4682	+	3.92555i	0.844718	+	0.179550i
$479$	6.38411	−	19.6483i	0.291698	−	0.897753i	−0.692613	−	0.721309i	$-0.743541\pi$
$479$	6.38411	−	19.6483i	0.291698	−	0.897753i	0.984311	−	0.176444i	$-0.0564593\pi$
$480$	−10.0882	−	31.0483i	−0.460461	−	1.41715i
$481$	0.906059	−	8.62057i	0.0413127	−	0.393064i
$482$	28.6254	−	6.08452i	1.30385	−	0.277142i
$483$	−5.00867	+	1.06462i	−0.227902	+	0.0484421i
$484$	1.99518	+	2.21587i	0.0906898	+	0.100721i
$485$	13.3791	−	9.72050i	0.607515	−	0.441385i
$486$	−26.6470	−	11.8640i	−1.20873	−	0.538163i
$487$	−21.5669			−0.977291			−0.488646	−	0.872482i	$-0.662509\pi$
$487$	−21.5669			−0.977291			−0.488646	+	0.872482i	$0.662509\pi$
$488$	17.1137	−	0.108040i	0.774703	−	0.00489076i
$489$	−46.1747			−2.08809
$490$	32.5973	+	14.5132i	1.47259	+	0.655641i
$491$	5.58278	−	4.05613i	0.251947	−	0.183050i	−0.454642	−	0.890674i	$-0.650233\pi$
$491$	5.58278	−	4.05613i	0.251947	−	0.183050i	0.706589	+	0.707624i	$0.250233\pi$
$492$	−34.6132	−	38.4419i	−1.56048	−	1.73309i
$493$	13.2206	−	2.81013i	0.595427	−	0.126562i
$494$	3.73311	−	0.793497i	0.167961	−	0.0357011i
$495$	0.325351	−	3.09551i	0.0146234	−	0.139133i
$496$	1.29732	+	3.99275i	0.0582515	+	0.179280i
$497$	−0.506181	+	1.55786i	−0.0227053	+	0.0698797i
$498$	35.9229	+	7.63565i	1.60974	+	0.342162i
$499$	27.3195			1.22299			0.611494	−	0.791249i	$-0.290569\pi$
$499$	27.3195			1.22299			0.611494	+	0.791249i	$0.290569\pi$
$500$	31.4128	+	6.67700i	1.40482	+	0.298604i
$501$	8.28359	+	14.3476i	0.370084	+	0.641003i
$502$	24.7545	−	42.8760i	1.10485	−	1.91365i
$503$	−14.2655	+	15.8435i	−0.636069	+	0.706426i	−0.971873	−	0.235506i	$-0.924325\pi$
$503$	−14.2655	+	15.8435i	−0.636069	+	0.706426i	0.335804	+	0.941932i	$0.390992\pi$
$504$	0.0877743	−	0.835117i	0.00390978	−	0.0371991i
$505$	−7.99311	−	8.87725i	−0.355689	−	0.395032i
$506$	−12.8938	+	14.3200i	−0.573198	+	0.636601i
$507$	−0.923940	−	8.79070i	−0.0410336	−	0.390409i
$508$	−41.3121	−	30.0150i	−1.83293	−	1.33170i
$509$	19.1543	+	33.1763i	0.849001	+	1.47051i	0.882101	+	0.471060i	$0.156129\pi$
$509$	19.1543	+	33.1763i	0.849001	+	1.47051i	−0.0331003	+	0.999452i	$0.510538\pi$
$510$	−27.8124	−	12.3829i	−1.23155	−	0.548323i
$511$	0.0536170	−	0.165016i	0.00237188	−	0.00729989i
$512$	9.68422	+	7.03600i	0.427986	+	0.310950i
$513$	1.81879	−	0.809778i	0.0803016	−	0.0357526i
$514$	3.30528	+	31.4477i	0.145790	+	1.38710i
$515$	−6.61715	−	20.3655i	−0.291586	−	0.897411i
$516$	1.77312	−	1.28825i	0.0780572	−	0.0567119i
$517$	5.39652	−	9.34705i	0.237339	−	0.411083i
$518$	1.69869	−	0.756308i	0.0746364	−	0.0332303i
$519$	−13.1505	+	5.85496i	−0.577241	+	0.257004i
$520$	7.49267	−	12.9777i	0.328575	−	0.569109i
$521$	−3.83653	+	2.78740i	−0.168081	+	0.122118i	−0.668646	−	0.743581i	$-0.733126\pi$
$521$	−3.83653	+	2.78740i	−0.168081	+	0.122118i	0.500565	+	0.865699i	$0.333126\pi$
$522$	−4.43528	−	13.6504i	−0.194127	−	0.597461i
$523$	2.07185	+	19.7124i	0.0905959	+	0.861962i	0.941584	+	0.336778i	$0.109337\pi$
$523$	2.07185	+	19.7124i	0.0905959	+	0.861962i	−0.850988	+	0.525185i	$0.823996\pi$
$524$	28.0449	−	12.4864i	1.22515	−	0.545472i
$525$	0.162456	+	0.118031i	0.00709014	+	0.00515129i
$526$	0.720362	−	2.21705i	0.0314093	−	0.0966678i
$527$	10.1234	+	4.50722i	0.440981	+	0.196337i
$528$	1.11827	+	1.93690i	0.0486664	+	0.0842926i
$529$	−41.6922	−	30.2911i	−1.81270	−	1.31701i
$530$	−4.25753	−	40.5077i	−0.184935	−	1.75954i
$531$	−0.634922	+	0.705153i	−0.0275533	+	0.0306010i
$532$	0.327891	+	0.364160i	0.0142159	+	0.0157883i
$533$	−2.57431	+	24.4929i	−0.111506	+	1.06091i
$534$	12.9825	−	14.4185i	0.561808	−	0.623951i
$535$	−7.04157	+	12.1964i	−0.304434	+	0.527295i
$536$	2.90415	+	5.03014i	0.125440	+	0.217269i
$537$	−31.8921	−	6.77887i	−1.37624	−	0.292530i
$538$	−30.2285			−1.30324
$539$	−6.76788	−	1.43856i	−0.291513	−	0.0619630i
$540$	7.33681	−	22.5804i	0.315726	−	0.971705i
$541$	6.64826	+	20.4612i	0.285831	+	0.879697i	0.986148	+	0.165866i	$0.0530418\pi$
$541$	6.64826	+	20.4612i	0.285831	+	0.879697i	−0.700317	+	0.713832i	$0.746958\pi$
$542$	1.88325	−	17.9180i	0.0808927	−	0.769643i
$543$	39.7506	−	8.44925i	1.70586	−	0.362592i
$544$	18.7684	−	3.98935i	0.804688	−	0.171042i
$545$	23.2754	+	25.8500i	0.997010	+	1.10729i
$546$	−3.16996	+	2.30311i	−0.135662	+	0.0985640i
$547$	30.6324	+	13.6384i	1.30975	+	0.583137i	0.938462	−	0.345382i	$-0.112251\pi$
$547$	30.6324	+	13.6384i	1.30975	+	0.583137i	0.371285	+	0.928519i	$0.378917\pi$
$548$	21.2633			0.908321
$549$	8.55080	+	6.13042i	0.364939	+	0.261640i
$550$	0.755663			0.0322216
$551$	2.51932	+	1.12167i	0.107326	+	0.0477848i
$552$	31.9099	−	23.1839i	1.35817	−	0.986772i
$553$	1.14470	+	1.27132i	0.0486776	+	0.0540619i
$554$	6.18006	−	1.31361i	0.262566	−	0.0558101i
$555$	−13.7998	+	2.93324i	−0.585769	+	0.124509i
$556$	−2.58911	+	24.6338i	−0.109803	+	1.04470i
$557$	−11.2881	−	34.7412i	−0.478292	−	1.47203i	−0.841466	−	0.540311i	$-0.818307\pi$
$557$	−11.2881	−	34.7412i	−0.478292	−	1.47203i	0.363173	−	0.931722i	$-0.381693\pi$
$558$	3.63638	−	11.1916i	0.153940	−	0.473779i
$559$	−1.02066	−	0.216947i	−0.0431692	−	0.00917589i
$560$	−0.705060			−0.0297942
$561$	5.77444	+	1.22739i	0.243797	+	0.0518206i
$562$	−20.6429	−	35.7546i	−0.870768	−	1.50821i
$563$	−10.0697	+	17.4413i	−0.424388	+	0.735062i	−0.996363	−	0.0852094i	$-0.972844\pi$
$563$	−10.0697	+	17.4413i	−0.424388	+	0.735062i	0.571975	+	0.820271i	$0.306177\pi$
$564$	−44.8979	+	49.8641i	−1.89054	+	2.09966i
$565$	1.87785	−	17.8665i	0.0790017	−	0.751651i
$566$	−31.3882	−	34.8602i	−1.31935	−	1.46528i
$567$	−2.13697	+	2.37335i	−0.0897444	+	0.0996713i
$568$	−1.31889	−	12.5484i	−0.0553393	−	0.526518i
$569$	−9.77076	−	7.09887i	−0.409612	−	0.297600i	0.363833	−	0.931464i	$-0.381468\pi$
$569$	−9.77076	−	7.09887i	−0.409612	−	0.297600i	−0.773445	+	0.633864i	$0.781468\pi$
$570$	−3.10587	−	5.37952i	−0.130091	−	0.225323i
$571$	−9.86291	−	4.39125i	−0.412750	−	0.183768i	0.189847	−	0.981814i	$-0.439201\pi$
$571$	−9.86291	−	4.39125i	−0.412750	−	0.183768i	−0.602597	+	0.798045i	$0.705867\pi$
$572$	−2.72721	+	8.39349i	−0.114030	+	0.350949i
$573$	−15.1159	−	10.9824i	−0.631477	−	0.458795i
$574$	−4.82636	+	2.14883i	−0.201448	+	0.0896906i
$575$	0.305527	+	2.90690i	0.0127414	+	0.121226i
$576$	−5.40338	−	16.6299i	−0.225141	−	0.692912i
$577$	10.0784	−	7.32237i	0.419569	−	0.304834i	−0.357896	−	0.933762i	$-0.616506\pi$
$577$	10.0784	−	7.32237i	0.419569	−	0.304834i	0.777464	+	0.628927i	$0.216506\pi$
$578$	−10.0250	+	17.3638i	−0.416985	+	0.722239i
$579$	−30.0348	+	13.3724i	−1.24820	+	0.555736i
$580$	30.0438	−	13.3764i	1.24750	−	0.555424i
$581$	1.12250	−	1.94422i	0.0465689	−	0.0806598i
$582$	26.9468	−	19.5780i	1.11698	−	0.811533i
$583$	2.44063	+	7.51150i	0.101081	+	0.311095i
$584$	0.139703	+	1.32918i	0.00578094	+	0.0550020i
$585$	8.41615	−	3.74711i	0.347965	−	0.154924i
$586$	−41.7850	−	30.3586i	−1.72612	−	1.25410i
$587$	1.67483	−	5.15460i	0.0691277	−	0.212753i	−0.910525	−	0.413455i	$-0.864322\pi$
$587$	1.67483	−	5.15460i	0.0691277	−	0.212753i	0.979652	+	0.200701i	$0.0643221\pi$
$588$	39.2961	+	17.4957i	1.62054	+	0.721512i
$589$	1.13050	+	1.95808i	0.0465814	+	0.0806814i
$590$	−2.93877	−	2.13514i	−0.120987	−	0.0879022i
$591$	1.79427	+	17.0713i	0.0738064	+	0.702221i
$592$	2.10204	−	2.33456i	0.0863935	−	0.0959497i
$593$	−7.77882	−	8.63926i	−0.319438	−	0.354772i	0.561945	−	0.827175i	$-0.310053\pi$
$593$	−7.77882	−	8.63926i	−0.319438	−	0.354772i	−0.881383	+	0.472403i	$0.843387\pi$
$594$	−0.804022	+	7.64976i	−0.0329894	+	0.313873i
$595$	−1.24528	+	1.38302i	−0.0510514	+	0.0566984i
$596$	24.9010	−	43.1298i	1.01998	−	1.76666i
$597$	−17.4454	−	30.2164i	−0.713994	−	1.23667i
$598$	−55.7878	−	11.8581i	−2.28133	−	0.484912i
$599$	−1.36366			−0.0557175			−0.0278587	−	0.999612i	$-0.508869\pi$
$599$	−1.36366			−0.0557175			−0.0278587	+	0.999612i	$0.508869\pi$
$600$	−1.51297	−	0.321592i	−0.0617669	−	0.0131290i
$601$	−9.00460	+	27.7133i	−0.367305	+	1.13045i	0.581220	+	0.813747i	$0.302576\pi$
$601$	−9.00460	+	27.7133i	−0.367305	+	1.13045i	−0.948525	+	0.316703i	$0.897424\pi$
$602$	−0.0691705	−	0.212885i	−0.00281918	−	0.00867654i
$603$	−0.373251	+	3.55124i	−0.0151999	+	0.144618i
$604$	17.0189	−	3.61748i	0.692490	−	0.147193i
$605$	−2.26004	+	0.480387i	−0.0918838	+	0.0195305i
$606$	−16.0989	−	17.8796i	−0.653972	−	0.726309i
$607$	−20.5636	+	14.9404i	−0.834652	+	0.606410i	−0.920872	−	0.389866i	$-0.872521\pi$
$607$	−20.5636	+	14.9404i	−0.834652	+	0.606410i	0.0862194	+	0.996276i	$0.472521\pi$
$608$	3.57650	+	1.59236i	0.145046	+	0.0645787i
$609$	−2.83128			−0.114729
$610$	−19.9184	+	35.0082i	−0.806472	+	1.41744i
$611$	31.9455			1.29238
$612$	−10.3899	−	4.62587i	−0.419986	−	0.186990i
$613$	−6.09868	+	4.43095i	−0.246323	+	0.178964i	−0.704096	−	0.710105i	$-0.748647\pi$
$613$	−6.09868	+	4.43095i	−0.246323	+	0.178964i	0.457772	+	0.889069i	$0.348647\pi$
$614$	−41.9493	−	46.5894i	−1.69293	−	1.88019i
$615$	39.2082	−	8.33397i	1.58103	−	0.336058i
$616$	−0.609722	+	0.129600i	−0.0245664	+	0.00522175i
$617$	2.29778	−	21.8620i	0.0925053	−	0.880129i	−0.845609	−	0.533803i	$-0.820762\pi$
$617$	2.29778	−	21.8620i	0.0925053	−	0.880129i	0.938114	−	0.346326i	$-0.112571\pi$
$618$	−13.3275	−	41.0180i	−0.536112	−	1.64998i
$619$	−5.62369	+	17.3079i	−0.226035	+	0.695665i	0.772150	+	0.635441i	$0.219182\pi$
$619$	−5.62369	+	17.3079i	−0.226035	+	0.695665i	−0.998185	+	0.0602240i	$0.980818\pi$
$620$	26.3741	+	5.60598i	1.05921	+	0.225142i
$621$	−29.7523			−1.19392
$622$	−5.27125	−	1.12044i	−0.211358	−	0.0449255i
$623$	−0.593014	−	1.02713i	−0.0237586	−	0.0411511i
$624$	−3.30988	+	5.73288i	−0.132501	+	0.229499i
$625$	−17.7843	+	19.7514i	−0.711371	+	0.790058i
$626$	−6.09274	+	57.9685i	−0.243515	+	2.31689i
$627$	0.805975	+	0.895125i	0.0321875	+	0.0357479i
$628$	−23.0173	+	25.5633i	−0.918491	+	1.02009i
$629$	−0.866752	−	8.24660i	−0.0345597	−	0.328813i
$630$	1.59884	+	1.16162i	0.0636992	+	0.0462802i
$631$	4.33201	+	7.50326i	0.172455	+	0.298700i	0.939277	−	0.343159i	$-0.111497\pi$
$631$	4.33201	+	7.50326i	0.172455	+	0.298700i	−0.766823	+	0.641859i	$0.778164\pi$
$632$	−12.0382	−	5.35974i	−0.478853	−	0.213199i
$633$	−1.24188	+	3.82210i	−0.0493602	+	0.151915i
$634$	14.2916	+	10.3835i	0.567592	+	0.412380i
$635$	36.1486	−	16.0944i	1.43452	−	0.638687i
$636$	−5.13246	−	48.8321i	−0.203515	−	1.93632i
$637$	−6.32844	−	19.4769i	−0.250742	−	0.771704i
$638$	−8.61968	+	6.26256i	−0.341256	+	0.247937i
$639$	3.87846	−	6.71770i	0.153430	−	0.265748i
$640$	32.5438	−	14.4894i	1.28641	−	0.572745i
$641$	25.0649	−	11.1596i	0.990005	−	0.440779i	0.153150	−	0.988203i	$-0.451058\pi$
$641$	25.0649	−	11.1596i	0.990005	−	0.440779i	0.836855	+	0.547425i	$0.184392\pi$
$642$	−14.1824	+	24.5646i	−0.559734	+	0.969487i
$643$	9.40162	−	6.83068i	0.370764	−	0.269376i	−0.386764	−	0.922179i	$-0.626407\pi$
$643$	9.40162	−	6.83068i	0.370764	−	0.269376i	0.757528	+	0.652803i	$0.226407\pi$
$644$	−2.26292	−	6.96456i	−0.0891716	−	0.274442i
$645$	0.177524	+	1.68903i	0.00698999	+	0.0665053i
$646$	3.33530	−	1.48497i	0.131226	−	0.0584255i
$647$	35.7733	+	25.9908i	1.40639	+	1.02181i	0.993834	+	0.110875i	$0.0353655\pi$
$647$	35.7733	+	25.9908i	1.40639	+	1.02181i	0.412561	+	0.910930i	$0.364635\pi$
$648$	7.60187	−	23.3961i	0.298630	−	0.919087i
$649$	0.643479	+	0.286495i	0.0252588	+	0.0112459i
$650$	1.11831	+	1.93698i	0.0438639	+	0.0759745i
$651$	−1.87797	−	1.36442i	−0.0736033	−	0.0534759i
$652$	−6.90252	−	65.6731i	−0.270324	−	2.57196i
$653$	−31.9976	+	35.5369i	−1.25216	+	1.39067i	−0.363829	+	0.931466i	$0.618531\pi$
$653$	−31.9976	+	35.5369i	−1.25216	+	1.39067i	−0.888333	+	0.459200i	$0.848136\pi$
$654$	46.8789	+	52.0643i	1.83311	+	2.03587i
$655$	−2.48657	+	23.6581i	−0.0971584	+	0.924400i
$656$	−5.97236	+	6.63298i	−0.233182	+	0.258974i
$657$	−0.410825	+	0.711570i	−0.0160278	+	0.0277610i
$658$	3.42644	+	5.93477i	0.133577	+	0.231361i
$659$	0.685425	+	0.145692i	0.0267004	+	0.00567534i	0.221243	−	0.975219i	$-0.428989\pi$
$659$	0.685425	+	0.145692i	0.0267004	+	0.00567534i	−0.194542	+	0.980894i	$0.562322\pi$
$660$	14.3643			0.559128
$661$	−31.1091	−	6.61243i	−1.21000	−	0.257194i	−0.441630	−	0.897197i	$-0.645600\pi$
$661$	−31.1091	−	6.61243i	−1.21000	−	0.257194i	−0.768372	+	0.640003i	$0.778933\pi$
$662$	13.6018	−	41.8620i	0.528649	−	1.62701i
$663$	5.39950	+	16.6180i	0.209699	+	0.645388i
$664$	−1.80759	+	17.1980i	−0.0701479	+	0.667413i
$665$	−0.371420	+	0.0789477i	−0.0144030	+	0.00306146i
$666$	−8.61303	+	1.83076i	−0.333748	+	0.0709404i
$667$	−27.5760	−	30.6263i	−1.06775	−	1.18585i
$668$	−19.1680	+	13.9263i	−0.741631	+	0.538826i
$669$	−22.3834	−	9.96572i	−0.865391	−	0.385297i
$670$	−13.6698			−0.528112
$671$	2.36656	−	7.44308i	0.0913600	−	0.287337i
$672$	−4.01937			−0.155050
$673$	1.67152	+	0.744211i	0.0644325	+	0.0286872i	0.438700	−	0.898634i	$-0.355439\pi$
$673$	1.67152	+	0.744211i	0.0644325	+	0.0286872i	−0.374267	+	0.927321i	$0.622106\pi$
$674$	48.1281	−	34.9671i	1.85383	−	1.34688i
$675$	0.780713	+	0.867069i	0.0300496	+	0.0333735i
$676$	12.3647	−	2.62820i	0.475565	−	0.101084i
$677$	21.3902	−	4.54662i	0.822092	−	0.174741i	0.222383	−	0.974959i	$-0.428616\pi$
$677$	21.3902	−	4.54662i	0.822092	−	0.174741i	0.599709	+	0.800218i	$0.295283\pi$
$678$	3.78216	−	35.9848i	0.145253	−	1.38199i
$679$	−0.629186	−	1.93643i	−0.0241459	−	0.0743135i
$680$	4.42984	−	13.6336i	0.169877	−	0.522826i
$681$	−11.8533	−	2.51951i	−0.454221	−	0.0965477i
$682$	−8.73537			−0.334494
$683$	9.06719	+	1.92729i	0.346947	+	0.0737458i	0.378089	−	0.925769i	$-0.376581\pi$
$683$	9.06719	+	1.92729i	0.346947	+	0.0737458i	−0.0311426	+	0.999515i	$0.509915\pi$
$684$	−1.16026	−	2.00963i	−0.0443637	−	0.0768401i
$685$	−8.23838	+	14.2693i	−0.314772	+	0.545201i
$686$	5.91358	−	6.56770i	0.225782	−	0.250756i
$687$	−4.05659	+	38.5959i	−0.154769	+	1.47253i
$688$	−0.253044	−	0.281033i	−0.00964720	−	0.0107143i
$689$	−15.6422	+	17.3724i	−0.595920	+	0.661836i
$690$	9.70323	+	92.3201i	0.369396	+	3.51456i
$691$	27.3672	+	19.8834i	1.04110	+	0.756402i	0.970499	−	0.241103i	$-0.0775092\pi$
$691$	27.3672	+	19.8834i	1.04110	+	0.756402i	0.0705980	+	0.997505i	$0.477509\pi$
$692$	−10.2932	−	17.8283i	−0.391288	−	0.677731i
$693$	−0.350086	−	0.155868i	−0.0132987	−	0.00592094i
$694$	−17.0608	+	52.5077i	−0.647619	+	1.99317i
$695$	−15.5280	−	11.2818i	−0.589011	−	0.427942i
$696$	19.9233	−	8.87045i	0.755193	−	0.336233i
$697$	2.46263	+	23.4304i	0.0932788	+	0.887488i
$698$	8.42599	+	25.9325i	0.318928	+	0.981561i
$699$	11.6156	−	8.43924i	0.439343	−	0.319201i
$700$	−0.143587	+	0.248701i	−0.00542710	+	0.00940001i
$701$	−14.5416	+	6.47433i	−0.549228	+	0.244532i	−0.662539	−	0.749027i	$-0.730521\pi$
$701$	−14.5416	+	6.47433i	−0.549228	+	0.244532i	0.113311	+	0.993560i	$0.463854\pi$
$702$	−20.7984	+	9.26004i	−0.784984	+	0.349498i
$703$	0.845932	−	1.46520i	0.0319049	−	0.0552610i
$704$	−10.5011	+	7.62950i	−0.395775	+	0.287548i
$705$	−16.0672	−	49.4496i	−0.605124	−	1.86238i
$706$	7.45913	+	70.9689i	0.280728	+	2.67095i
$707$	−1.34357	+	0.598198i	−0.0505303	+	0.0224976i
$708$	−3.54269	−	2.57391i	−0.133142	−	0.0967336i
$709$	−2.14450	+	6.60011i	−0.0805386	+	0.247872i	−0.983216	−	0.182446i	$-0.941599\pi$
$709$	−2.14450	+	6.60011i	−0.0805386	+	0.247872i	0.902677	+	0.430318i	$0.141599\pi$
$710$	27.1280	+	12.0782i	1.01809	+	0.453285i
$711$	−4.05058	−	7.01581i	−0.151909	−	0.263114i
$712$	7.39099	+	5.36987i	0.276989	+	0.201244i
$713$	−3.53186	−	33.6034i	−0.132269	−	1.25846i
$714$	−2.50810	+	2.78553i	−0.0938634	+	0.104246i
$715$	−4.57603	−	5.08220i	−0.171134	−	0.190063i
$716$	4.87397	−	46.3727i	0.182149	−	1.73303i
$717$	−11.8016	+	13.1070i	−0.440740	+	0.489492i
$718$	−7.08142	+	12.2654i	−0.264276	+	0.457740i
$719$	17.5389	+	30.3783i	0.654092	+	1.13292i	0.982121	+	0.188253i	$0.0602824\pi$
$719$	17.5389	+	30.3783i	0.654092	+	1.13292i	−0.328029	+	0.944668i	$0.606384\pi$
$720$	3.26586	+	0.694179i	0.121711	+	0.0258705i
$721$	−2.63642			−0.0981855
$722$	−40.7523	−	8.66217i	−1.51664	−	0.322373i
$723$	−8.44772	+	25.9994i	−0.314174	+	0.966929i
$724$	17.9594	+	55.2733i	0.667455	+	2.05422i
$725$	−0.168933	+	1.60729i	−0.00627402	+	0.0596933i
$726$	−4.55193	+	0.967543i	−0.168938	+	0.0359089i
$727$	35.5193	−	7.54986i	1.31734	−	0.280009i	0.504961	−	0.863142i	$-0.331507\pi$
$727$	35.5193	−	7.54986i	1.31734	−	0.280009i	0.812376	+	0.583134i	$0.198174\pi$
$728$	−1.23454	−	1.37109i	−0.0457550	−	0.0508161i
$729$	−5.20380	+	3.78078i	−0.192733	+	0.140029i
$730$	−2.87352	−	1.27937i	−0.106354	−	0.0473518i
$731$	−0.998192			−0.0369194
$732$	−24.0117	+	42.2025i	−0.887497	+	1.55985i
$733$	38.9534			1.43878			0.719389	−	0.694607i	$-0.244422\pi$
$733$	38.9534			1.43878			0.719389	+	0.694607i	$0.244422\pi$
$734$	3.75533	+	1.67198i	0.138612	+	0.0617139i
$735$	−26.9661	+	19.5920i	−0.994660	+	0.722663i
$736$	−39.1478	−	43.4780i	−1.44301	−	1.60262i
$737$	2.59278	−	0.551112i	0.0955062	−	0.0203005i
$738$	24.4715	−	5.20158i	0.900808	−	0.191473i
$739$	0.658041	−	6.26084i	0.0242064	−	0.230309i	−0.975729	−	0.218980i	$-0.929727\pi$
$739$	0.658041	−	6.26084i	0.0242064	−	0.230309i	0.999936	−	0.0113290i	$-0.00360622\pi$
$740$	−6.23477	−	19.1887i	−0.229195	−	0.705389i
$741$	−1.10169	+	3.39065i	−0.0404715	+	0.124559i
$742$	−4.90517	−	1.04263i	−0.180075	−	0.0382760i
$743$	−17.1379			−0.628727			−0.314364	−	0.949303i	$-0.601791\pi$
$743$	−17.1379			−0.628727			−0.314364	+	0.949303i	$0.601791\pi$
$744$	17.4898	+	3.71757i	0.641206	+	0.136293i
$745$	19.2956	+	33.4210i	0.706936	+	1.22445i
$746$	−22.7443	+	39.3942i	−0.832727	+	1.44232i
$747$	−7.11364	+	7.90050i	−0.260274	+	0.289064i
$748$	−0.882489	+	8.39633i	−0.0322670	+	0.307000i
$749$	1.16021	+	1.28855i	0.0423932	+	0.0470824i
$750$	−33.5378	+	37.2475i	−1.22463	+	1.36009i
$751$	−2.63951	−	25.1133i	−0.0963173	−	0.916397i	−0.930841	−	0.365425i	$-0.880924\pi$
$751$	−2.63951	−	25.1133i	−0.0963173	−	0.916397i	0.834523	−	0.550972i	$-0.185743\pi$
$752$	9.36648	+	6.80515i	0.341561	+	0.248158i
$753$	23.1240	+	40.0520i	0.842687	+	1.45958i
$754$	−28.8091	−	12.8266i	−1.04917	−	0.467118i
$755$	−4.16631	+	12.8226i	−0.151628	+	0.466662i
$756$	−2.36488	−	1.71819i	−0.0860099	−	0.0624899i
$757$	31.1640	−	13.8751i	1.13267	−	0.504299i	0.247189	−	0.968967i	$-0.420493\pi$
$757$	31.1640	−	13.8751i	1.13267	−	0.504299i	0.885485	+	0.464668i	$0.153826\pi$
$758$	4.49455	+	42.7628i	0.163249	+	1.55321i
$759$	−5.56239	−	17.1193i	−0.201902	−	0.621390i
$760$	2.36629	−	1.71921i	0.0858344	−	0.0623624i
$761$	5.94456	−	10.2963i	0.215490	−	0.373240i	−0.737934	−	0.674873i	$-0.764198\pi$
$761$	5.94456	−	10.2963i	0.215490	−	0.373240i	0.953424	+	0.301633i	$0.0975317\pi$
$762$	72.8067	−	32.4156i	2.63751	−	1.17429i
$763$	3.91241	−	1.74192i	0.141639	−	0.0630616i
$764$	13.3603	−	23.1408i	0.483359	−	0.837203i
$765$	7.12984	−	5.18013i	0.257780	−	0.187288i
$766$	−16.8805	−	51.9528i	−0.609916	−	1.87713i
$767$	0.217924	+	2.07341i	0.00786878	+	0.0748664i
$768$	16.0993	−	7.16789i	0.580935	−	0.258649i
$769$	−19.7152	−	14.3240i	−0.710950	−	0.516535i	0.172530	−	0.985004i	$-0.444806\pi$
$769$	−19.7152	−	14.3240i	−0.710950	−	0.516535i	−0.883480	+	0.468469i	$0.844806\pi$
$770$	0.453340	−	1.39524i	0.0163372	−	0.0502808i
$771$	−26.9845	−	12.0143i	−0.971823	−	0.432683i
$772$	−23.5090	−	40.7188i	−0.846108	−	1.46550i
$773$	13.1226	+	9.53414i	0.471988	+	0.342919i	0.798216	−	0.602372i	$-0.205778\pi$
$773$	13.1226	+	9.53414i	0.471988	+	0.342919i	−0.326228	+	0.945291i	$0.605778\pi$
$774$	0.110800	+	1.05419i	0.00398262	+	0.0378921i
$775$	−0.886623	+	0.984694i	−0.0318484	+	0.0353713i
$776$	10.4944	+	11.6552i	0.376727	+	0.418398i
$777$	−0.181564	+	1.72747i	−0.00651357	+	0.0619725i
$778$	8.46942	−	9.40625i	0.303644	−	0.337230i
$779$	−2.40348	+	4.16294i	−0.0861135	+	0.149153i
$780$	21.2578	+	36.8196i	0.761153	+	1.31835i
$781$	−5.63234	−	1.19719i	−0.201541	−	0.0428389i
$782$	−54.5599			−1.95106
$783$	−16.0913	−	3.42030i	−0.575055	−	0.122232i
$784$	2.29354	−	7.05878i	0.0819120	−	0.252099i
$785$	−8.23698	−	25.3508i	−0.293990	−	0.904809i
$786$	−5.00818	+	47.6497i	−0.178636	+	1.69961i
$787$	−28.6746	+	6.09498i	−1.02214	+	0.217263i	−0.688346	−	0.725383i	$-0.741663\pi$
$787$	−28.6746	+	6.09498i	−1.02214	+	0.217263i	−0.333795	+	0.942646i	$0.608329\pi$
$788$	−24.0119	+	5.10390i	−0.855390	+	0.181819i
$789$	1.45710	+	1.61827i	0.0518741	+	0.0576120i
$790$	25.0901	−	18.2290i	0.892666	−	0.648560i
$791$	−2.02061	−	0.899634i	−0.0718447	−	0.0319873i
$792$	2.95185			0.104889
$793$	22.5810	−	4.94894i	0.801875	−	0.175742i
$794$	73.9644			2.62490
$795$	34.7587	+	15.4756i	1.23276	+	0.548862i
$796$	40.3681	−	29.3292i	1.43081	−	1.03955i
$797$	36.5557	+	40.5993i	1.29487	+	1.43810i	0.835136	+	0.550043i	$0.185389\pi$
$797$	36.5557	+	40.5993i	1.29487	+	1.43810i	0.459735	+	0.888056i	$0.347945\pi$
$798$	−0.748073	+	0.159008i	−0.0264815	+	0.00562882i
$799$	29.8918	−	6.35371i	1.05750	−	0.224778i
$800$	−0.239823	+	2.28176i	−0.00847901	+	0.0806724i
$801$	1.73558	+	5.34156i	0.0613236	+	0.188735i
$802$	−6.43170	+	19.7947i	−0.227111	+	0.698976i
$803$	0.596604	+	0.126812i	0.0210537	+	0.00447510i
$804$	−16.4790			−0.581171
$805$	5.55052	+	1.17980i	0.195630	+	0.0415824i
$806$	−12.9276	−	22.3912i	−0.455354	−	0.788697i
$807$	14.1188	−	24.4544i	0.497004	−	0.860836i
$808$	7.58041	−	8.41890i	0.266678	−	0.296176i
$809$	2.57044	−	24.4561i	0.0903720	−	0.859832i	−0.851612	−	0.524173i	$-0.824374\pi$
$809$	2.57044	−	24.4561i	0.0903720	−	0.859832i	0.941984	−	0.335659i	$-0.108959\pi$
$810$	38.7403	+	43.0255i	1.36120	+	1.51176i
$811$	34.8465	−	38.7009i	1.22363	−	1.35897i	0.310878	−	0.950450i	$-0.399377\pi$
$811$	34.8465	−	38.7009i	1.22363	−	1.35897i	0.912747	−	0.408524i	$-0.133956\pi$
$812$	−0.423240	−	4.02686i	−0.0148528	−	0.141315i
$813$	13.6158	+	9.89243i	0.477526	+	0.346943i
$814$	3.26826	+	5.66079i	0.114552	+	0.198411i
$815$	46.7461	+	20.8127i	1.63744	+	0.729037i
$816$	−1.95687	+	6.02264i	−0.0685043	+	0.210835i
$817$	−0.164769	−	0.119712i	−0.00576455	−	0.00418819i
$818$	56.6982	−	25.2436i	1.98240	−	0.882623i
$819$	−0.118562	−	1.12804i	−0.00414288	−	0.0394169i
$820$	17.7143	+	54.5191i	0.618611	+	1.90389i
$821$	13.1242	−	9.53532i	0.458039	−	0.332785i	−0.334722	−	0.942317i	$-0.608642\pi$
$821$	13.1242	−	9.53532i	0.458039	−	0.332785i	0.792762	+	0.609532i	$0.208642\pi$
$822$	−16.5928	+	28.7396i	−0.578742	+	1.00241i
$823$	−14.7172	+	6.55252i	−0.513009	+	0.228407i	−0.646879	−	0.762592i	$-0.723926\pi$
$823$	−14.7172	+	6.55252i	−0.513009	+	0.228407i	0.133870	+	0.990999i	$0.457260\pi$
$824$	18.5522	−	8.25997i	0.646296	−	0.287750i
$825$	−0.352946	+	0.611320i	−0.0122880	+	0.0212834i
$826$	−0.361819	+	0.262877i	−0.0125893	+	0.00914666i
$827$	10.6838	+	32.8813i	0.371512	+	1.14340i	0.945802	+	0.324744i	$0.105278\pi$
$827$	10.6838	+	32.8813i	0.371512	+	1.14340i	−0.574290	+	0.818652i	$0.694722\pi$
$828$	3.62484	+	34.4880i	0.125972	+	1.19854i
$829$	7.86029	−	3.49963i	0.272999	−	0.121547i	−0.265671	−	0.964064i	$-0.585594\pi$
$829$	7.86029	−	3.49963i	0.272999	−	0.121547i	0.538670	+	0.842517i	$0.318927\pi$
$830$	−32.9258	−	23.9220i	−1.14287	−	0.830344i
$831$	−1.82381	+	5.61312i	−0.0632674	+	0.194717i
$832$	−35.0973	−	15.6263i	−1.21678	−	0.541745i
$833$	−9.79541	−	16.9662i	−0.339391	−	0.587842i
$834$	−31.2749	−	22.7225i	−1.08296	−	0.786816i
$835$	−1.91909	−	18.2589i	−0.0664127	−	0.631875i
$836$	−1.15263	+	1.28013i	−0.0398646	+	0.0442742i
$837$	−9.02494	−	10.0232i	−0.311947	−	0.346453i
$838$	6.29117	−	59.8564i	0.217325	−	2.06771i
$839$	−4.57842	+	5.08485i	−0.158065	+	0.175549i	−0.816975	−	0.576673i	$-0.804351\pi$
$839$	−4.57842	+	5.08485i	−0.158065	+	0.175549i	0.658911	+	0.752221i	$0.271018\pi$
$840$	−1.50145	+	2.60058i	−0.0518049	+	0.0897287i
$841$	3.10654	+	5.38069i	0.107122	+	0.185541i
$842$	11.8587	+	2.52064i	0.408678	+	0.0868671i
$843$	38.5665			1.32830
$844$	−5.62173	−	1.19494i	−0.193508	−	0.0411314i
$845$	−3.02693	+	9.31594i	−0.104130	+	0.320478i
$846$	−10.0282	−	30.8636i	−0.344776	−	1.06111i
$847$	−0.0297354	+	0.282913i	−0.00102172	+	0.00972101i
$848$	−8.28705	+	1.76147i	−0.284579	+	0.0604890i
$849$	42.8618	−	9.11056i	1.47101	−	0.312673i
$850$	1.43167	+	1.59003i	0.0491060	+	0.0545377i
$851$	−20.4546	+	14.8612i	−0.701176	+	0.509434i
$852$	32.7028	+	14.5602i	1.12038	+	0.498826i
$853$	−45.2021			−1.54769			−0.773846	−	0.633374i	$-0.781669\pi$
$853$	−45.2021			−1.54769			−0.773846	+	0.633374i	$0.781669\pi$
$854$	3.34142	+	3.66424i	0.114341	+	0.125388i
$855$	1.79816			0.0614956
$856$	−12.2013	−	5.43237i	−0.417032	−	0.185675i
$857$	−39.9854	+	29.0511i	−1.36587	+	0.992366i	−0.367828	+	0.929894i	$0.619899\pi$
$857$	−39.9854	+	29.0511i	−1.36587	+	0.992366i	−0.998047	+	0.0624724i	$0.980101\pi$
$858$	−9.21655	−	10.2360i	−0.314648	−	0.349452i
$859$	46.6817	−	9.92250i	1.59276	−	0.338551i	0.675660	−	0.737213i	$-0.263859\pi$
$859$	46.6817	−	9.92250i	1.59276	−	0.338551i	0.917098	+	0.398662i	$0.130525\pi$
$860$	−2.37572	+	0.504976i	−0.0810115	+	0.0172195i
$861$	0.515863	−	4.90811i	0.0175806	−	0.167268i
$862$	−20.5283	−	63.1795i	−0.699196	−	2.15190i
$863$	7.84386	−	24.1409i	0.267008	−	0.821767i	−0.724216	−	0.689573i	$-0.757798\pi$
$863$	7.84386	−	24.1409i	0.267008	−	0.821767i	0.991224	−	0.132193i	$-0.0422019\pi$
$864$	−22.8436	−	4.85557i	−0.777156	−	0.165190i
$865$	15.9522			0.542393
$866$	−12.2019	−	2.59359i	−0.414637	−	0.0881337i
$867$	−9.36471	−	16.2202i	−0.318042	−	0.550865i
$868$	1.65985	−	2.87495i	0.0563391	−	0.0975821i
$869$	−4.02395	+	4.46905i	−0.136503	+	0.151602i
$870$	−5.36514	+	51.0459i	−0.181895	+	1.73062i
$871$	5.24974	+	5.83043i	0.177881	+	0.197556i
$872$	−22.0737	+	24.5153i	−0.747509	+	0.830193i
$873$	1.00785	+	9.58909i	0.0341107	+	0.324542i
$874$	−9.00609	−	6.54331i	−0.304636	−	0.221331i
$875$	1.53194	+	2.65339i	0.0517889	+	0.0897010i
$876$	−3.46404	−	1.54229i	−0.117039	−	0.0521091i
$877$	−14.7699	+	45.4572i	−0.498746	+	1.53498i	0.312291	+	0.949986i	$0.398904\pi$
$877$	−14.7699	+	45.4572i	−0.498746	+	1.53498i	−0.811037	+	0.584995i	$0.801096\pi$
$878$	−56.6397	−	41.1511i	−1.91150	−	1.38878i
$879$	44.0761	−	19.6239i	1.48665	−	0.661899i
$880$	−0.259073	−	2.46491i	−0.00873335	−	0.0830922i
$881$	−14.8455	−	45.6898i	−0.500159	−	1.53933i	−0.808760	−	0.588139i	$-0.799861\pi$
$881$	−14.8455	−	45.6898i	−0.500159	−	1.53933i	0.308602	−	0.951191i	$-0.400139\pi$
$882$	−16.8307	+	12.2282i	−0.566719	+	0.411745i
$883$	3.89326	−	6.74332i	0.131018	−	0.226931i	−0.793051	−	0.609155i	$-0.791509\pi$
$883$	3.89326	−	6.74332i	0.131018	−	0.226931i	0.924069	+	0.382225i	$0.124842\pi$
$884$	−22.8282	+	10.1638i	−0.767794	+	0.341844i
$885$	3.09990	−	1.38016i	0.104202	−	0.0463937i
$886$	−39.2980	+	68.0661i	−1.32024	+	2.28673i
$887$	−26.4741	+	19.2346i	−0.888914	+	0.645834i	−0.935595	−	0.353076i	$-0.885136\pi$
$887$	−26.4741	+	19.2346i	−0.888914	+	0.645834i	0.0466804	+	0.998910i	$0.485136\pi$
$888$	−4.13454	−	12.7248i	−0.138746	−	0.427017i
$889$	−0.509241	−	4.84510i	−0.0170794	−	0.162499i
$890$	−19.6422	+	8.74525i	−0.658407	+	0.293142i
$891$	−9.08253	−	6.59885i	−0.304276	−	0.221070i
$892$	10.8280	−	33.3251i	0.362548	−	1.11581i
$893$	5.69618	+	2.53610i	0.190615	+	0.0848674i
$894$	38.8631	+	67.3129i	1.29978	+	2.25128i
$895$	29.2313	+	21.2377i	0.977093	+	0.709900i
$896$	−0.458457	−	4.36193i	−0.0153160	−	0.145722i
$897$	35.6497	−	39.5930i	1.19031	−	1.32197i
$898$	3.60919	+	4.00841i	0.120440	+	0.133762i
$899$	1.95285	−	18.5801i	0.0651310	−	0.619680i
$900$	0.909963	−	1.01062i	0.0303321	−	0.0336872i
$901$	−11.1814	+	19.3667i	−0.372505	+	0.645198i
$902$	−9.28583	−	16.0835i	−0.309184	−	0.535523i
$903$	0.204528	+	0.0434738i	0.00680627	+	0.00144672i
$904$	17.0374			0.566654
$905$	−44.0509	−	9.36331i	−1.46430	−	0.311247i
$906$	−8.39133	+	25.8259i	−0.278783	+	0.858007i
$907$	8.96215	+	27.5827i	0.297583	+	0.915868i	0.982341	+	0.187097i	$0.0599079\pi$
$907$	8.96215	+	27.5827i	0.297583	+	0.915868i	−0.684758	+	0.728770i	$0.740092\pi$
$908$	1.81151	−	17.2354i	0.0601171	−	0.571976i
$909$	6.81244	−	1.44803i	0.225954	−	0.0480281i
$910$	4.24729	−	0.902789i	0.140796	−	0.0299272i
$911$	11.8647	+	13.1771i	0.393097	+	0.436578i	0.906910	−	0.421324i	$-0.138434\pi$
$911$	11.8647	+	13.1771i	0.393097	+	0.436578i	−0.513814	+	0.857902i	$0.671768\pi$
$912$	−1.04531	+	0.759459i	−0.0346135	+	0.0251482i
$913$	7.20951	+	3.20988i	0.238600	+	0.106232i
$914$	61.3182			2.02823
$915$	−19.0179	−	32.4649i	−0.628712	−	1.07326i
$916$	−55.5005			−1.83379
$917$	2.67561	+	1.19126i	0.0883565	+	0.0393388i
$918$	−17.6196	+	12.8014i	−0.581533	+	0.422509i
$919$	−23.3434	−	25.9255i	−0.770028	−	0.855203i	0.222786	−	0.974867i	$-0.428485\pi$
$919$	−23.3434	−	25.9255i	−0.770028	−	0.855203i	−0.992814	+	0.119664i	$0.961818\pi$
$920$	−42.7547	+	9.08778i	−1.40958	+	0.299615i
$921$	57.2833	−	12.1759i	1.88755	−	0.401211i
$922$	6.35985	−	60.5099i	0.209450	−	1.99279i
$923$	−5.26663	−	16.2090i	−0.173353	−	0.533526i
$924$	0.546502	−	1.68196i	0.0179786	−	0.0553325i
$925$	0.969835	+	0.206145i	0.0318880	+	0.00677800i
$926$	4.18207			0.137431
$927$	12.2120	+	2.59574i	0.401094	+	0.0852552i
$928$	−16.1745	−	28.0151i	−0.530954	−	0.919639i
$929$	2.27445	−	3.93946i	0.0746223	−	0.129250i	−0.826300	−	0.563231i	$-0.809558\pi$
$929$	2.27445	−	3.93946i	0.0746223	−	0.129250i	0.900922	+	0.433981i	$0.142892\pi$
$930$	−28.1582	+	31.2728i	−0.923344	+	1.02548i
$931$	0.417823	−	3.97532i	0.0136936	−	0.130286i
$932$	13.7393	+	15.2591i	0.450046	+	0.499827i
$933$	3.36845	−	3.74105i	0.110278	−	0.122476i
$934$	5.38437	+	51.2289i	0.176182	+	1.67626i
$935$	−5.29266	−	3.84535i	−0.173089	−	0.125756i
$936$	4.36848	+	7.56642i	0.142788	+	0.247316i
$937$	−54.3861	−	24.2143i	−1.77672	−	0.791045i	−0.983208	−	0.182487i	$-0.941585\pi$
$937$	−54.3861	−	24.2143i	−1.77672	−	0.791045i	−0.793509	−	0.608559i	$-0.791748\pi$
$938$	−0.520083	+	1.60065i	−0.0169813	+	0.0522631i
$939$	−44.0500	−	32.0042i	−1.43752	−	1.04442i
$940$	67.9292	−	30.2440i	2.21561	−	0.986451i
$941$	−3.33593	−	31.7392i	−0.108748	−	1.03467i	−0.903750	−	0.428061i	$-0.859197\pi$
$941$	−3.33593	−	31.7392i	−0.108748	−	1.03467i	0.795002	−	0.606607i	$-0.207470\pi$
$942$	−16.5900	−	51.0589i	−0.540532	−	1.66359i
$943$	58.1160	−	42.2238i	1.89252	−	1.37500i
$944$	−0.377789	+	0.654350i	−0.0122960	+	0.0212973i
$945$	2.06930	−	0.921312i	0.0673144	−	0.0299703i
$946$	0.718836	−	0.320047i	0.0233714	−	0.0104056i
$947$	19.4288	−	33.6516i	0.631350	−	1.09353i	−0.355926	−	0.934514i	$-0.615835\pi$
$947$	19.4288	−	33.6516i	0.631350	−	1.09353i	0.987276	−	0.159016i	$-0.0508321\pi$
$948$	30.2462	−	21.9751i	0.982350	−	0.713719i
$949$	0.557866	+	1.71693i	0.0181091	+	0.0557341i
$950$	0.0456323	+	0.434162i	0.00148051	+	0.0140861i
$951$	−15.0752	+	6.71192i	−0.488847	+	0.217649i
$952$	−1.42787	−	1.03741i	−0.0462776	−	0.0336227i
$953$	−15.1528	+	46.6355i	−0.490847	+	1.51067i	0.332484	+	0.943109i	$0.392113\pi$
$953$	−15.1528	+	46.6355i	−0.490847	+	1.51067i	−0.823331	+	0.567562i	$0.807887\pi$
$954$	21.6943	+	9.65895i	0.702380	+	0.312720i
$955$	10.3528	+	17.9316i	0.335009	+	0.580253i
$956$	−20.4060	−	14.8258i	−0.659978	−	0.479502i
$957$	−1.04035	−	9.89824i	−0.0336296	−	0.319965i
$958$	−30.8546	+	34.2675i	−0.996866	+	1.10713i
$959$	1.35740	+	1.50755i	0.0438329	+	0.0486813i
$960$	−6.53619	+	62.1877i	−0.210955	+	2.00710i
$961$	−10.4938	+	11.6546i	−0.338510	+	0.375953i
$962$	−9.67347	+	16.7549i	−0.311885	+	0.540201i
$963$	−4.10547	−	7.11088i	−0.132297	−	0.229145i
$964$	−38.2412	−	8.12841i	−1.23167	−	0.261799i
$965$	36.4339			1.17285
$966$	11.1793	+	2.37622i	0.359687	+	0.0764537i
$967$	−13.6348	+	41.9635i	−0.438465	+	1.34946i	0.451030	+	0.892509i	$0.351057\pi$
$967$	−13.6348	+	41.9635i	−0.438465	+	1.34946i	−0.889494	+	0.456946i	$0.848943\pi$
$968$	−0.677129	−	2.08399i	−0.0217637	−	0.0669819i
$969$	−0.356492	+	3.39179i	−0.0114522	+	0.108960i
$970$	−36.1048	+	7.67431i	−1.15926	+	0.246407i
$971$	−17.9875	+	3.82336i	−0.577246	+	0.122697i	−0.487277	−	0.873247i	$-0.662010\pi$
$971$	−17.9875	+	3.82336i	−0.577246	+	0.122697i	−0.0899684	+	0.995945i	$0.528677\pi$
$972$	26.0741	+	28.9582i	0.836327	+	0.928835i
$973$	−1.91180	+	1.38900i	−0.0612895	+	0.0445294i
$974$	43.9754	+	19.5791i	1.40906	+	0.627354i
$975$	−2.08932			−0.0669117
$976$	7.67504	+	3.35925i	0.245672	+	0.107527i
$977$	22.2497			0.711832			0.355916	−	0.934518i	$-0.384169\pi$
$977$	22.2497			0.711832			0.355916	+	0.934518i	$0.384169\pi$
$978$	94.1509	+	41.9187i	3.01061	+	1.34041i
$979$	3.37298	−	2.45061i	0.107801	−	0.0783220i
$980$	−31.8964	−	35.4245i	−1.01889	−	1.13159i
$981$	−19.8374	+	4.21657i	−0.633359	+	0.134625i
$982$	−15.0656	+	3.20230i	−0.480764	+	0.102190i
$983$	−2.36720	+	22.5224i	−0.0755021	+	0.718354i	0.889646	+	0.456651i	$0.150951\pi$
$983$	−2.36720	+	22.5224i	−0.0755021	+	0.718354i	−0.965148	+	0.261704i	$0.915716\pi$
$984$	11.7471	+	36.1540i	0.374485	+	1.15255i
$985$	5.87824	−	18.0914i	0.187296	−	0.576438i
$986$	−29.5082	−	6.27216i	−0.939732	−	0.199746i
$987$	−6.40152			−0.203763
$988$	−4.98713	−	1.06005i	−0.158662	−	0.0337246i
$989$	1.52180	+	2.63583i	0.0483904	+	0.0838147i
$990$	−3.47359	+	6.01643i	−0.110398	+	0.191215i
$991$	−21.8603	+	24.2783i	−0.694416	+	0.771227i	−0.982477	−	0.186385i	$-0.940323\pi$
$991$	−21.8603	+	24.2783i	−0.694416	+	0.771227i	0.288061	+	0.957612i	$0.406989\pi$
$992$	2.77232	−	26.3769i	0.0880212	−	0.837466i
$993$	27.5128	+	30.5561i	0.873093	+	0.969668i
$994$	2.44638	−	2.71699i	0.0775946	−	0.0861776i
$995$	4.04164	+	38.4536i	0.128129	+	1.21906i
$996$	−39.6921	−	28.8380i	−1.25769	−	0.913767i
$997$	19.8477	+	34.3772i	0.628583	+	1.08874i	0.987836	+	0.155497i	$0.0496979\pi$
$997$	19.8477	+	34.3772i	0.628583	+	1.08874i	−0.359254	+	0.933240i	$0.616969\pi$
$998$	−55.7049	−	24.8014i	−1.76331	−	0.785075i
$999$	−3.11875	+	9.59853i	−0.0986730	+	0.303684i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	671.2.bn.a.12.3	✓	208
61.56	even	15	inner	671.2.bn.a.56.3	yes	208

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.bn.a.12.3	✓	208	1.1	even	1	trivial
671.2.bn.a.56.3	yes	208	61.56	even	15	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.bn (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.03902 - 0.907829i) q^{2} +(1.68678 - 1.22552i) q^{3} +(1.99518 + 2.21587i) q^{4} +(-2.26004 + 0.480387i) q^{5} +(-4.55193 + 0.967543i) q^{6} +(-0.0297354 + 0.282913i) q^{7} +(-0.677129 - 2.08399i) q^{8} +(0.416282 - 1.28118i) q^{9} +O(q^{10})\)	\(q+(-2.03902 - 0.907829i) q^{2} +(1.68678 - 1.22552i) q^{3} +(1.99518 + 2.21587i) q^{4} +(-2.26004 + 0.480387i) q^{5} +(-4.55193 + 0.967543i) q^{6} +(-0.0297354 + 0.282913i) q^{7} +(-0.677129 - 2.08399i) q^{8} +(0.416282 - 1.28118i) q^{9} +(5.04437 + 1.07221i) q^{10} -1.00000 q^{11} +(6.08100 + 1.29256i) q^{12} +(-1.47991 - 2.56328i) q^{13} +(0.317468 - 0.549870i) q^{14} +(-3.22347 + 3.58003i) q^{15} +(0.112127 - 1.06682i) q^{16} +(-1.89459 - 2.10416i) q^{17} +(-2.01190 + 2.23444i) q^{18} +(-0.0603871 - 0.574545i) q^{19} +(-5.57365 - 4.04950i) q^{20} +(0.296558 + 0.513653i) q^{21} +(2.03902 + 0.907829i) q^{22} +(-2.66785 + 8.21078i) q^{23} +(-3.69613 - 2.68539i) q^{24} +(0.309291 - 0.137705i) q^{25} +(0.690544 + 6.57008i) q^{26} +(1.06494 + 3.27755i) q^{27} +(-0.686225 + 0.498572i) q^{28} +(-2.38678 + 4.13403i) q^{29} +(9.82276 - 4.37338i) q^{30} +(-3.57537 + 1.59186i) q^{31} +(-3.38835 + 5.86879i) q^{32} +(-1.68678 + 1.22552i) q^{33} +(1.95289 + 6.01038i) q^{34} +(-0.0687045 - 0.653680i) q^{35} +(3.66949 - 1.63376i) q^{36} +(2.36926 + 1.72137i) q^{37} +(-0.398458 + 1.22633i) q^{38} +(-5.63763 - 2.51004i) q^{39} +(2.53146 + 4.38462i) q^{40} +(-6.73159 - 4.89079i) q^{41} +(-0.138377 - 1.31657i) q^{42} +(0.235896 - 0.261989i) q^{43} +(-1.99518 - 2.21587i) q^{44} +(-0.325351 + 3.09551i) q^{45} +(12.8938 - 14.3200i) q^{46} +(-5.39652 + 9.34705i) q^{47} +(-1.11827 - 1.93690i) q^{48} +(6.76788 + 1.43856i) q^{49} -0.755663 q^{50} +(-5.77444 - 1.22739i) q^{51} +(2.72721 - 8.39349i) q^{52} +(-2.44063 - 7.51150i) q^{53} +(0.804022 - 7.64976i) q^{54} +(2.26004 - 0.480387i) q^{55} +(0.609722 - 0.129600i) q^{56} +(-0.805975 - 0.895125i) q^{57} +(8.61968 - 6.26256i) q^{58} +(-0.643479 - 0.286495i) q^{59} -14.3643 q^{60} +(-2.36656 + 7.44308i) q^{61} +8.73537 q^{62} +(0.350086 + 0.155868i) q^{63} +(10.5011 - 7.62950i) q^{64} +(4.57603 + 5.08220i) q^{65} +(4.55193 - 0.967543i) q^{66} +(-2.59278 + 0.551112i) q^{67} +(0.882489 - 8.39633i) q^{68} +(5.56239 + 17.1193i) q^{69} +(-0.453340 + 1.39524i) q^{70} +(5.63234 + 1.19719i) q^{71} -2.95185 q^{72} +(-0.596604 - 0.126812i) q^{73} +(-3.26826 - 5.66079i) q^{74} +(0.352946 - 0.611320i) q^{75} +(1.15263 - 1.28013i) q^{76} +(0.0297354 - 0.282913i) q^{77} +(9.21655 + 10.2360i) q^{78} +(4.02395 - 4.46905i) q^{79} +(0.259073 + 2.46491i) q^{80} +(9.08253 + 6.59885i) q^{81} +(9.28583 + 16.0835i) q^{82} +(-7.20951 - 3.20988i) q^{83} +(-0.546502 + 1.68196i) q^{84} +(5.29266 + 3.84535i) q^{85} +(-0.718836 + 0.320047i) q^{86} +(1.04035 + 9.89824i) q^{87} +(0.677129 + 2.08399i) q^{88} +(-3.37298 + 2.45061i) q^{89} +(3.47359 - 6.01643i) q^{90} +(0.769192 - 0.342466i) q^{91} +(-23.5168 + 10.4704i) q^{92} +(-4.08001 + 7.06678i) q^{93} +(19.4891 - 14.1597i) q^{94} +(0.412481 + 1.26949i) q^{95} +(1.47691 + 14.0518i) q^{96} +(-6.53865 + 2.91119i) q^{97} +(-12.4939 - 9.07732i) q^{98} +(-0.416282 + 1.28118i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 208 q - 2 q^{3} + 30 q^{4} - 10 q^{5} - 12 q^{6} - 10 q^{7} + 18 q^{8} - 60 q^{9}+O(q^{10}) \) 208 * q - 2 * q^3 + 30 * q^4 - 10 * q^5 - 12 * q^6 - 10 * q^7 + 18 * q^8 - 60 * q^9	\( 208 q - 2 q^{3} + 30 q^{4} - 10 q^{5} - 12 q^{6} - 10 q^{7} + 18 q^{8} - 60 q^{9} - 75 q^{10} - 208 q^{11} - 25 q^{12} - 17 q^{14} - 8 q^{15} + 42 q^{16} + 8 q^{17} - 5 q^{18} - 19 q^{19} - 26 q^{20} + 50 q^{21} + 18 q^{23} - 41 q^{24} - 6 q^{25} - 32 q^{26} - 8 q^{27} + 24 q^{28} + 40 q^{29} - 12 q^{30} - 13 q^{31} + 12 q^{32} + 2 q^{33} - 38 q^{34} + 40 q^{35} - 94 q^{36} + 66 q^{37} + 15 q^{38} - 58 q^{39} + 157 q^{40} + 20 q^{41} + 42 q^{42} - 3 q^{43} - 30 q^{44} - 25 q^{45} + 90 q^{46} - 34 q^{47} - 58 q^{48} + 56 q^{49} - 84 q^{50} + 37 q^{51} + 98 q^{52} + 18 q^{53} + 92 q^{54} + 10 q^{55} + 76 q^{56} + 16 q^{57} - 119 q^{58} - 7 q^{59} - 60 q^{60} - 7 q^{61} + 34 q^{62} + 30 q^{63} + 38 q^{64} - 95 q^{65} + 12 q^{66} - 43 q^{67} + 40 q^{68} + 100 q^{69} + 43 q^{70} - 46 q^{71} - 156 q^{72} - 28 q^{73} - 4 q^{74} - 47 q^{75} - 121 q^{76} + 10 q^{77} - 108 q^{78} + 38 q^{79} - 45 q^{80} - 78 q^{81} - 2 q^{82} - 62 q^{83} - 14 q^{84} + 54 q^{85} + 7 q^{86} + 23 q^{87} - 18 q^{88} + 6 q^{89} + 121 q^{90} + 32 q^{91} - 39 q^{92} + 70 q^{93} + 73 q^{94} - 74 q^{95} + 220 q^{96} - 49 q^{97} - 63 q^{98} + 60 q^{99}+O(q^{100}) \) 208 * q - 2 * q^3 + 30 * q^4 - 10 * q^5 - 12 * q^6 - 10 * q^7 + 18 * q^8 - 60 * q^9 - 75 * q^10 - 208 * q^11 - 25 * q^12 - 17 * q^14 - 8 * q^15 + 42 * q^16 + 8 * q^17 - 5 * q^18 - 19 * q^19 - 26 * q^20 + 50 * q^21 + 18 * q^23 - 41 * q^24 - 6 * q^25 - 32 * q^26 - 8 * q^27 + 24 * q^28 + 40 * q^29 - 12 * q^30 - 13 * q^31 + 12 * q^32 + 2 * q^33 - 38 * q^34 + 40 * q^35 - 94 * q^36 + 66 * q^37 + 15 * q^38 - 58 * q^39 + 157 * q^40 + 20 * q^41 + 42 * q^42 - 3 * q^43 - 30 * q^44 - 25 * q^45 + 90 * q^46 - 34 * q^47 - 58 * q^48 + 56 * q^49 - 84 * q^50 + 37 * q^51 + 98 * q^52 + 18 * q^53 + 92 * q^54 + 10 * q^55 + 76 * q^56 + 16 * q^57 - 119 * q^58 - 7 * q^59 - 60 * q^60 - 7 * q^61 + 34 * q^62 + 30 * q^63 + 38 * q^64 - 95 * q^65 + 12 * q^66 - 43 * q^67 + 40 * q^68 + 100 * q^69 + 43 * q^70 - 46 * q^71 - 156 * q^72 - 28 * q^73 - 4 * q^74 - 47 * q^75 - 121 * q^76 + 10 * q^77 - 108 * q^78 + 38 * q^79 - 45 * q^80 - 78 * q^81 - 2 * q^82 - 62 * q^83 - 14 * q^84 + 54 * q^85 + 7 * q^86 + 23 * q^87 - 18 * q^88 + 6 * q^89 + 121 * q^90 + 32 * q^91 - 39 * q^92 + 70 * q^93 + 73 * q^94 - 74 * q^95 + 220 * q^96 - 49 * q^97 - 63 * q^98 + 60 * q^99

Introduction

L-functions

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