LMFDB - Embedded newform 185.2.e.b.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [185,2,Mod(26,185)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(185, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("185.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 185 = 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	185.e (of order $3$, 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:	$1.47723243739$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} + 13 x^{12} - 16 x^{11} + 98 x^{10} - 116 x^{9} + 378 x^{8} - 264 x^{7} + 795 x^{6} + \cdots + 9 $ x^14 - 2x^13 + 13x^12 - 16x^11 + 98x^10 - 116x^9 + 378x^8 - 264x^7 + 795x^6 - 520x^5 + 927x^4 - 71x^3 + 94x^2 - 3*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.1
Root			$-1.24062 - 2.14882i$ of defining polynomial
Character	$\chi$	$=$	185.121
Dual form			185.2.e.b.26.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.24062 + 2.14882i) q^{2} +(-1.10207 - 1.90884i) q^{3} +(-2.07829 - 3.59971i) q^{4} +(0.500000 + 0.866025i) q^{5} +5.46902 q^{6} +(1.91357 + 3.31440i) q^{7} +5.35102 q^{8} +(-0.929125 + 1.60929i) q^{9} +O(q^{10})$	\(q+(-1.24062 + 2.14882i) q^{2} +(-1.10207 - 1.90884i) q^{3} +(-2.07829 - 3.59971i) q^{4} +(0.500000 + 0.866025i) q^{5} +5.46902 q^{6} +(1.91357 + 3.31440i) q^{7} +5.35102 q^{8} +(-0.929125 + 1.60929i) q^{9} -2.48125 q^{10} -4.82222 q^{11} +(-4.58086 + 7.93427i) q^{12} +(2.50742 + 4.34297i) q^{13} -9.49608 q^{14} +(1.10207 - 1.90884i) q^{15} +(-2.48202 + 4.29898i) q^{16} +(-2.38979 + 4.13924i) q^{17} +(-2.30539 - 3.99305i) q^{18} +(2.59596 + 4.49634i) q^{19} +(2.07829 - 3.59971i) q^{20} +(4.21778 - 7.30542i) q^{21} +(5.98255 - 10.3621i) q^{22} +0.630359 q^{23} +(-5.89721 - 10.2143i) q^{24} +(-0.500000 + 0.866025i) q^{25} -12.4430 q^{26} -2.51658 q^{27} +(7.95392 - 13.7766i) q^{28} +4.07392 q^{29} +(2.73451 + 4.73631i) q^{30} +1.59919 q^{31} +(-0.807472 - 1.39858i) q^{32} +(5.31443 + 9.20486i) q^{33} +(-5.92966 - 10.2705i) q^{34} +(-1.91357 + 3.31440i) q^{35} +7.72397 q^{36} +(6.03867 - 0.731052i) q^{37} -12.8824 q^{38} +(5.52671 - 9.57254i) q^{39} +(2.67551 + 4.63412i) q^{40} +(-0.00413940 - 0.00716965i) q^{41} +(10.4654 + 18.1265i) q^{42} -8.94210 q^{43} +(10.0220 + 17.3586i) q^{44} -1.85825 q^{45} +(-0.782038 + 1.35453i) q^{46} -2.48125 q^{47} +10.9414 q^{48} +(-3.82350 + 6.62250i) q^{49} +(-1.24062 - 2.14882i) q^{50} +10.5349 q^{51} +(10.4223 - 18.0519i) q^{52} +(0.157509 - 0.272813i) q^{53} +(3.12213 - 5.40769i) q^{54} +(-2.41111 - 4.17616i) q^{55} +(10.2396 + 17.7354i) q^{56} +(5.72187 - 9.91057i) q^{57} +(-5.05420 + 8.75413i) q^{58} +(7.51090 - 13.0093i) q^{59} -9.16171 q^{60} +(-1.80365 - 3.12402i) q^{61} +(-1.98399 + 3.43637i) q^{62} -7.11178 q^{63} -5.92099 q^{64} +(-2.50742 + 4.34297i) q^{65} -26.3728 q^{66} +(-4.62924 - 8.01808i) q^{67} +19.8667 q^{68} +(-0.694701 - 1.20326i) q^{69} +(-4.74804 - 8.22385i) q^{70} +(2.40006 + 4.15703i) q^{71} +(-4.97176 + 8.61135i) q^{72} +8.84627 q^{73} +(-5.92082 + 13.8830i) q^{74} +2.20414 q^{75} +(10.7903 - 18.6894i) q^{76} +(-9.22765 - 15.9828i) q^{77} +(13.7131 + 23.7518i) q^{78} +(-1.43498 - 2.48545i) q^{79} -4.96403 q^{80} +(5.56083 + 9.63164i) q^{81} +0.0205417 q^{82} +(2.38247 - 4.12657i) q^{83} -35.0632 q^{84} -4.77958 q^{85} +(11.0938 - 19.2150i) q^{86} +(-4.48975 - 7.77647i) q^{87} -25.8038 q^{88} +(-8.93544 + 15.4766i) q^{89} +(2.30539 - 3.99305i) q^{90} +(-9.59624 + 16.6212i) q^{91} +(-1.31007 - 2.26911i) q^{92} +(-1.76242 - 3.05260i) q^{93} +(3.07829 - 5.33176i) q^{94} +(-2.59596 + 4.49634i) q^{95} +(-1.77979 + 3.08268i) q^{96} +3.19533 q^{97} +(-9.48706 - 16.4321i) q^{98} +(4.48044 - 7.76035i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 2 q^{2} - 2 q^{3} - 8 q^{4} + 7 q^{5} + 4 q^{6} + 2 q^{7} - 6 q^{8} - 5 q^{9}+O(q^{10}) $ 14 * q + 2 * q^2 - 2 * q^3 - 8 * q^4 + 7 * q^5 + 4 * q^6 + 2 * q^7 - 6 * q^8 - 5 * q^9	\( 14 q + 2 q^{2} - 2 q^{3} - 8 q^{4} + 7 q^{5} + 4 q^{6} + 2 q^{7} - 6 q^{8} - 5 q^{9} + 4 q^{10} - 10 q^{11} - 8 q^{12} + 6 q^{13} - 36 q^{14} + 2 q^{15} - 14 q^{16} - q^{17} - 4 q^{18} + 6 q^{19} + 8 q^{20} + 13 q^{21} - q^{22} + 12 q^{23} - 21 q^{24} - 7 q^{25} + 2 q^{26} + 22 q^{27} + 13 q^{28} - 12 q^{29} + 2 q^{30} - 8 q^{31} + 18 q^{32} + q^{33} - 11 q^{34} - 2 q^{35} - 8 q^{36} + 12 q^{37} + 16 q^{38} + 23 q^{39} - 3 q^{40} - 3 q^{41} + 29 q^{42} - 38 q^{43} + 25 q^{44} - 10 q^{45} + 10 q^{46} + 4 q^{47} - 20 q^{48} - 7 q^{49} + 2 q^{50} - 14 q^{51} + 46 q^{52} - 2 q^{53} + 23 q^{54} - 5 q^{55} + 19 q^{56} + 22 q^{57} - 12 q^{58} - 18 q^{59} - 16 q^{60} - 20 q^{61} - 21 q^{62} + 46 q^{63} + 50 q^{64} - 6 q^{65} - 42 q^{66} - 20 q^{67} + 110 q^{68} + 17 q^{69} - 18 q^{70} - 11 q^{71} - 29 q^{72} - 36 q^{73} - 66 q^{74} + 4 q^{75} + 40 q^{76} - q^{77} + 6 q^{78} + 23 q^{79} - 28 q^{80} + 29 q^{81} - 24 q^{82} - 9 q^{83} + 8 q^{84} - 2 q^{85} - 3 q^{86} - 43 q^{87} - 116 q^{88} - 16 q^{89} + 4 q^{90} + 12 q^{91} - 33 q^{92} + 25 q^{93} + 22 q^{94} - 6 q^{95} - 67 q^{96} - 62 q^{97} - 24 q^{98} + 4 q^{99}+O(q^{100}) \) 14 * q + 2 * q^2 - 2 * q^3 - 8 * q^4 + 7 * q^5 + 4 * q^6 + 2 * q^7 - 6 * q^8 - 5 * q^9 + 4 * q^10 - 10 * q^11 - 8 * q^12 + 6 * q^13 - 36 * q^14 + 2 * q^15 - 14 * q^16 - q^17 - 4 * q^18 + 6 * q^19 + 8 * q^20 + 13 * q^21 - q^22 + 12 * q^23 - 21 * q^24 - 7 * q^25 + 2 * q^26 + 22 * q^27 + 13 * q^28 - 12 * q^29 + 2 * q^30 - 8 * q^31 + 18 * q^32 + q^33 - 11 * q^34 - 2 * q^35 - 8 * q^36 + 12 * q^37 + 16 * q^38 + 23 * q^39 - 3 * q^40 - 3 * q^41 + 29 * q^42 - 38 * q^43 + 25 * q^44 - 10 * q^45 + 10 * q^46 + 4 * q^47 - 20 * q^48 - 7 * q^49 + 2 * q^50 - 14 * q^51 + 46 * q^52 - 2 * q^53 + 23 * q^54 - 5 * q^55 + 19 * q^56 + 22 * q^57 - 12 * q^58 - 18 * q^59 - 16 * q^60 - 20 * q^61 - 21 * q^62 + 46 * q^63 + 50 * q^64 - 6 * q^65 - 42 * q^66 - 20 * q^67 + 110 * q^68 + 17 * q^69 - 18 * q^70 - 11 * q^71 - 29 * q^72 - 36 * q^73 - 66 * q^74 + 4 * q^75 + 40 * q^76 - q^77 + 6 * q^78 + 23 * q^79 - 28 * q^80 + 29 * q^81 - 24 * q^82 - 9 * q^83 + 8 * q^84 - 2 * q^85 - 3 * q^86 - 43 * q^87 - 116 * q^88 - 16 * q^89 + 4 * q^90 + 12 * q^91 - 33 * q^92 + 25 * q^93 + 22 * q^94 - 6 * q^95 - 67 * q^96 - 62 * q^97 - 24 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/185\mathbb{Z}\right)^\times$.

$n$	$76$	$112$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.24062	+	2.14882i	−0.877253	+	1.51945i	−0.0229102	+	0.999738i	$0.507293\pi$
$2$	−1.24062	+	2.14882i	−0.877253	+	1.51945i	−0.854343	+	0.519710i	$0.826040\pi$
$3$	−1.10207	−	1.90884i	−0.636281	−	1.10207i	−0.986242	−	0.165307i	$-0.947138\pi$
$3$	−1.10207	−	1.90884i	−0.636281	−	1.10207i	0.349961	−	0.936764i	$-0.386195\pi$
$4$	−2.07829	−	3.59971i	−1.03915	−	1.79985i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	5.46902			2.23272
$7$	1.91357	+	3.31440i	0.723262	+	1.25273i	0.959686	+	0.281076i	$0.0906913\pi$
$7$	1.91357	+	3.31440i	0.723262	+	1.25273i	−0.236424	+	0.971650i	$0.575975\pi$
$8$	5.35102			1.89187
$9$	−0.929125	+	1.60929i	−0.309708	+	0.536430i
$10$	−2.48125			−0.784639
$11$	−4.82222			−1.45395			−0.726976	−	0.686663i	$-0.759075\pi$
$11$	−4.82222			−1.45395			−0.726976	+	0.686663i	$0.759075\pi$
$12$	−4.58086	+	7.93427i	−1.32238	+	2.29043i
$13$	2.50742	+	4.34297i	0.695432	+	1.20452i	0.970035	+	0.242966i	$0.0781205\pi$
$13$	2.50742	+	4.34297i	0.695432	+	1.20452i	−0.274602	+	0.961558i	$0.588546\pi$
$14$	−9.49608			−2.53793
$15$	1.10207	−	1.90884i	0.284554	−	0.492862i
$16$	−2.48202	+	4.29898i	−0.620504	+	1.07474i
$17$	−2.38979	+	4.13924i	−0.579610	+	1.00391i	0.415914	+	0.909404i	$0.363462\pi$
$17$	−2.38979	+	4.13924i	−0.579610	+	1.00391i	−0.995524	+	0.0945094i	$0.969872\pi$
$18$	−2.30539	−	3.99305i	−0.543385	−	0.941170i
$19$	2.59596	+	4.49634i	0.595554	+	1.03153i	0.993468	+	0.114108i	$0.0364008\pi$
$19$	2.59596	+	4.49634i	0.595554	+	1.03153i	−0.397914	+	0.917423i	$0.630266\pi$
$20$	2.07829	−	3.59971i	0.464720	−	0.804919i
$21$	4.21778	−	7.30542i	0.920396	−	1.59417i
$22$	5.98255	−	10.3621i	1.27548	−	2.20920i
$23$	0.630359			0.131439			0.0657195	−	0.997838i	$-0.479066\pi$
$23$	0.630359			0.131439			0.0657195	+	0.997838i	$0.479066\pi$
$24$	−5.89721	−	10.2143i	−1.20376	−	2.08498i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−12.4430			−2.44028
$27$	−2.51658			−0.484317
$28$	7.95392	−	13.7766i	1.50315	−	2.60353i
$29$	4.07392			0.756507			0.378254	−	0.925702i	$-0.376525\pi$
$29$	4.07392			0.756507			0.378254	+	0.925702i	$0.376525\pi$
$30$	2.73451	+	4.73631i	0.499251	+	0.864729i
$31$	1.59919			0.287222			0.143611	−	0.989634i	$-0.454129\pi$
$31$	1.59919			0.287222			0.143611	+	0.989634i	$0.454129\pi$
$32$	−0.807472	−	1.39858i	−0.142742	−	0.247237i
$33$	5.31443	+	9.20486i	0.925123	+	1.60236i
$34$	−5.92966	−	10.2705i	−1.01693	−	1.76137i
$35$	−1.91357	+	3.31440i	−0.323452	+	0.560236i
$36$	7.72397			1.28733
$37$	6.03867	−	0.731052i	0.992752	−	0.120184i
$37$	6.03867	−	0.731052i	0.992752	−	0.120184i
$38$	−12.8824			−2.08981
$39$	5.52671	−	9.57254i	0.884982	−	1.53283i
$40$	2.67551	+	4.63412i	0.423035	+	0.732719i
$41$	−0.00413940	−	0.00716965i	−0.000646465	−	0.00111971i	0.865702	−	0.500560i	$-0.166872\pi$
$41$	−0.00413940	−	0.00716965i	−0.000646465	−	0.00111971i	−0.866348	+	0.499440i	$0.833539\pi$
$42$	10.4654	+	18.1265i	1.61484	+	2.79699i
$43$	−8.94210			−1.36366			−0.681829	−	0.731512i	$-0.738815\pi$
$43$	−8.94210			−1.36366			−0.681829	+	0.731512i	$0.738815\pi$
$44$	10.0220	+	17.3586i	1.51087	+	2.61690i
$45$	−1.85825			−0.277011
$46$	−0.782038	+	1.35453i	−0.115305	+	0.199714i
$47$	−2.48125			−0.361927			−0.180964	−	0.983490i	$-0.557922\pi$
$47$	−2.48125			−0.361927			−0.180964	+	0.983490i	$0.557922\pi$
$48$	10.9414			1.57926
$49$	−3.82350	+	6.62250i	−0.546215	+	0.946072i
$50$	−1.24062	−	2.14882i	−0.175451	−	0.303889i
$51$	10.5349			1.47518
$52$	10.4223	−	18.0519i	1.44531	−	2.50335i
$53$	0.157509	−	0.272813i	0.0216355	−	0.0374738i	−0.855005	−	0.518620i	$-0.826446\pi$
$53$	0.157509	−	0.272813i	0.0216355	−	0.0374738i	0.876640	+	0.481146i	$0.159779\pi$
$54$	3.12213	−	5.40769i	0.424868	−	0.735893i
$55$	−2.41111	−	4.17616i	−0.325114	−	0.563113i
$56$	10.2396	+	17.7354i	1.36832	+	2.37000i
$57$	5.72187	−	9.91057i	0.757880	−	1.31269i
$58$	−5.05420	+	8.75413i	−0.663649	+	1.14947i
$59$	7.51090	−	13.0093i	0.977835	−	1.69366i	0.307593	−	0.951518i	$-0.400476\pi$
$59$	7.51090	−	13.0093i	0.977835	−	1.69366i	0.670242	−	0.742143i	$-0.266190\pi$
$60$	−9.16171			−1.18277
$61$	−1.80365	−	3.12402i	−0.230934	−	0.399990i	0.727149	−	0.686479i	$-0.240845\pi$
$61$	−1.80365	−	3.12402i	−0.230934	−	0.399990i	−0.958083	+	0.286490i	$0.907511\pi$
$62$	−1.98399	+	3.43637i	−0.251967	+	0.436419i
$63$	−7.11178			−0.896000
$64$	−5.92099			−0.740123
$65$	−2.50742	+	4.34297i	−0.311007	+	0.538680i
$66$	−26.3728			−3.24627
$67$	−4.62924	−	8.01808i	−0.565552	−	0.979564i	−0.996998	−	0.0774259i	$-0.975330\pi$
$67$	−4.62924	−	8.01808i	−0.565552	−	0.979564i	0.431446	−	0.902139i	$-0.358003\pi$
$68$	19.8667			2.40920
$69$	−0.694701	−	1.20326i	−0.0836321	−	0.144855i
$70$	−4.74804	−	8.22385i	−0.567499	−	0.982938i
$71$	2.40006	+	4.15703i	0.284835	+	0.493349i	0.972569	−	0.232614i	$-0.0747279\pi$
$71$	2.40006	+	4.15703i	0.284835	+	0.493349i	−0.687734	+	0.725963i	$0.741395\pi$
$72$	−4.97176	+	8.61135i	−0.585928	+	1.01486i
$73$	8.84627			1.03538			0.517689	−	0.855569i	$-0.326793\pi$
$73$	8.84627			1.03538			0.517689	+	0.855569i	$0.326793\pi$
$74$	−5.92082	+	13.8830i	−0.688281	+	1.61387i
$75$	2.20414			0.254513
$76$	10.7903	−	18.6894i	1.23774	−	2.14382i
$77$	−9.22765	−	15.9828i	−1.05159	−	1.82140i
$78$	13.7131	+	23.7518i	1.55271	+	2.68937i
$79$	−1.43498	−	2.48545i	−0.161448	−	0.279635i	0.773940	−	0.633258i	$-0.218283\pi$
$79$	−1.43498	−	2.48545i	−0.161448	−	0.279635i	−0.935388	+	0.353623i	$0.884950\pi$
$80$	−4.96403			−0.554996
$81$	5.56083	+	9.63164i	0.617870	+	1.07018i
$82$	0.0205417			0.00226846
$83$	2.38247	−	4.12657i	0.261510	−	0.452949i	−0.705133	−	0.709075i	$-0.749113\pi$
$83$	2.38247	−	4.12657i	0.261510	−	0.452949i	0.966644	+	0.256126i	$0.0824461\pi$
$84$	−35.0632			−3.82570
$85$	−4.77958			−0.518419
$86$	11.0938	−	19.2150i	1.19627	−	2.07201i
$87$	−4.48975	−	7.77647i	−0.481352	−	0.833726i
$88$	−25.8038			−2.75069
$89$	−8.93544	+	15.4766i	−0.947155	+	1.64052i	−0.195777	+	0.980648i	$0.562723\pi$
$89$	−8.93544	+	15.4766i	−0.947155	+	1.64052i	−0.751378	+	0.659872i	$0.770610\pi$
$90$	2.30539	−	3.99305i	0.243009	−	0.420904i
$91$	−9.59624	+	16.6212i	−1.00596	+	1.74237i
$92$	−1.31007	−	2.26911i	−0.136584	−	0.236571i
$93$	−1.76242	−	3.05260i	−0.182754	−	0.316540i
$94$	3.07829	−	5.33176i	0.317502	−	0.549929i
$95$	−2.59596	+	4.49634i	−0.266340	+	0.461314i
$96$	−1.77979	+	3.08268i	−0.181649	+	0.314625i
$97$	3.19533			0.324436			0.162218	−	0.986755i	$-0.448135\pi$
$97$	3.19533			0.324436			0.162218	+	0.986755i	$0.448135\pi$
$98$	−9.48706	−	16.4321i	−0.958338	−	1.65989i
$99$	4.48044	−	7.76035i	0.450301	−	0.779944i
$100$	4.15659			0.415659
$101$	7.81980			0.778099			0.389050	−	0.921217i	$-0.372803\pi$
$101$	7.81980			0.778099			0.389050	+	0.921217i	$0.372803\pi$
$102$	−13.0698	+	22.6376i	−1.29411	+	2.24146i
$103$	−7.92893			−0.781261			−0.390630	−	0.920548i	$-0.627743\pi$
$103$	−7.92893			−0.781261			−0.390630	+	0.920548i	$0.627743\pi$
$104$	13.4172	+	23.2393i	1.31567	+	2.27881i
$105$	8.43557			0.823227
$106$	0.390818	+	0.676917i	0.0379596	+	0.0657480i
$107$	−0.150425	−	0.260544i	−0.0145421	−	0.0251877i	0.858663	−	0.512541i	$-0.171296\pi$
$107$	−0.150425	−	0.260544i	−0.0145421	−	0.0251877i	−0.873205	+	0.487353i	$0.837962\pi$
$108$	5.23020	+	9.05896i	0.503276	+	0.871699i
$109$	4.98368	−	8.63199i	0.477350	−	0.826794i	−0.522313	−	0.852754i	$-0.674931\pi$
$109$	4.98368	−	8.63199i	0.477350	−	0.826794i	0.999663	+	0.0259595i	$0.00826409\pi$
$110$	11.9651			1.14083
$111$	−8.05052	−	10.7212i	−0.764121	−	1.01761i
$112$	−18.9980			−1.79515
$113$	−3.77762	+	6.54303i	−0.355369	+	0.615517i	−0.987181	−	0.159605i	$-0.948978\pi$
$113$	−3.77762	+	6.54303i	−0.355369	+	0.615517i	0.631812	+	0.775122i	$0.282311\pi$
$114$	14.1974	+	24.5906i	1.32971	+	2.30312i
$115$	0.315179	+	0.545907i	0.0293906	+	0.0509061i
$116$	−8.46679	−	14.6649i	−0.786122	−	1.36160i
$117$	−9.31881			−0.861525
$118$	18.6364	+	32.2792i	1.71562	+	2.97154i
$119$	−18.2921			−1.67684
$120$	5.89721	−	10.2143i	0.538339	−	0.932431i
$121$	12.2538			1.11398
$122$	8.95061			0.810351
$123$	−0.00912383	+	0.0158029i	−0.000822668	+	0.00142490i
$124$	−3.32358	−	5.75660i	−0.298466	−	0.516958i
$125$	−1.00000			−0.0894427
$126$	8.82304	−	15.2820i	0.786019	−	1.36143i
$127$	−3.50350	+	6.06825i	−0.310886	+	0.538470i	−0.978554	−	0.205989i	$-0.933959\pi$
$127$	−3.50350	+	6.06825i	−0.310886	+	0.538470i	0.667669	+	0.744459i	$0.267292\pi$
$128$	8.96066	−	15.5203i	0.792018	−	1.37181i
$129$	9.85484	+	17.0691i	0.867670	+	1.50285i
$130$	−6.22152	−	10.7760i	−0.545663	−	0.945117i
$131$	7.16945	−	12.4179i	0.626398	−	1.08495i	−0.361871	−	0.932228i	$-0.617862\pi$
$131$	7.16945	−	12.4179i	0.626398	−	1.08495i	0.988269	−	0.152724i	$-0.0488047\pi$
$132$	22.0899	−	38.2608i	1.92268	−	3.33017i
$133$	−9.93511	+	17.2081i	−0.861483	+	1.49213i
$134$	22.9726			1.98453
$135$	−1.25829	−	2.17942i	−0.108296	−	0.187575i
$136$	−12.7878	+	22.1492i	−1.09655	+	1.89927i
$137$	−0.146102			−0.0124824			−0.00624119	−	0.999981i	$-0.501987\pi$
$137$	−0.146102			−0.0124824			−0.00624119	+	0.999981i	$0.501987\pi$
$138$	3.44745			0.293466
$139$	−0.102908	+	0.178242i	−0.00872854	+	0.0151183i	−0.870357	−	0.492422i	$-0.836112\pi$
$139$	−0.102908	+	0.178242i	−0.00872854	+	0.0151183i	0.861628	+	0.507540i	$0.169445\pi$
$140$	15.9078			1.34446
$141$	2.73451	+	4.73631i	0.230287	+	0.398870i
$142$	−11.9103			−0.999490
$143$	−12.0913	−	20.9428i	−1.01113	−	1.75132i
$144$	−4.61220	−	7.98857i	−0.384350	−	0.665714i
$145$	2.03696	+	3.52812i	0.169160	+	0.292994i
$146$	−10.9749	+	19.0091i	−0.908288	+	1.57320i
$147$	16.8551			1.39019
$148$	−15.1817	−	20.2181i	−1.24793	−	1.66192i
$149$	4.38047			0.358862			0.179431	−	0.983771i	$-0.442574\pi$
$149$	4.38047			0.358862			0.179431	+	0.983771i	$0.442574\pi$
$150$	−2.73451	+	4.73631i	−0.223272	+	0.386718i
$151$	6.77765	+	11.7392i	0.551558	+	0.955326i	0.998162	+	0.0605945i	$0.0192997\pi$
$151$	6.77765	+	11.7392i	0.551558	+	0.955326i	−0.446605	+	0.894731i	$0.647367\pi$
$152$	13.8910	+	24.0600i	1.12671	+	1.95152i
$153$	−4.44083	−	7.69174i	−0.359020	−	0.621840i
$154$	45.7921			3.69004
$155$	0.799593	+	1.38494i	0.0642248	+	0.111241i
$156$	−45.9445			−3.67850
$157$	10.0965	−	17.4876i	0.805787	−	1.39566i	−0.109971	−	0.993935i	$-0.535076\pi$
$157$	10.0965	−	17.4876i	0.805787	−	1.39566i	0.915758	−	0.401730i	$-0.131591\pi$
$158$	7.12107			0.566522
$159$	−0.694344			−0.0550651
$160$	0.807472	−	1.39858i	0.0638363	−	0.110568i
$161$	1.20624	+	2.08926i	0.0950647	+	0.164657i
$162$	−27.5956			−2.16811
$163$	1.26359	−	2.18861i	0.0989724	−	0.171425i	−0.812287	−	0.583258i	$-0.801778\pi$
$163$	1.26359	−	2.18861i	0.0989724	−	0.171425i	0.911260	+	0.411832i	$0.135111\pi$
$164$	−0.0172058	+	0.0298013i	−0.00134354	+	0.00232709i
$165$	−5.31443	+	9.20486i	−0.413728	+	0.716597i
$166$	5.91151	+	10.2390i	0.458822	+	0.794703i
$167$	11.3674	+	19.6890i	0.879638	+	1.52358i	0.851738	+	0.523967i	$0.175549\pi$
$167$	11.3674	+	19.6890i	0.879638	+	1.52358i	0.0278999	+	0.999611i	$0.491118\pi$
$168$	22.5694	−	39.0914i	1.74127	−	3.01597i
$169$	−6.07428	+	10.5210i	−0.467253	+	0.809305i
$170$	5.92966	−	10.2705i	0.454784	−	0.787710i
$171$	−9.64788			−0.737792
$172$	18.5843	+	32.1890i	1.41704	+	2.45438i
$173$	−7.18751	+	12.4491i	−0.546456	+	0.946490i	0.452058	+	0.891989i	$0.350690\pi$
$173$	−7.18751	+	12.4491i	−0.546456	+	0.946490i	−0.998514	+	0.0545009i	$0.982643\pi$
$174$	22.2804			1.68907
$175$	−3.82714			−0.289305
$176$	11.9688	−	20.7306i	0.902183	−	1.56263i
$177$	−33.1102			−2.48871
$178$	−22.1710	−	38.4014i	−1.66179	−	2.87830i
$179$	−16.1351			−1.20599			−0.602995	−	0.797745i	$-0.706026\pi$
$179$	−16.1351			−1.20599			−0.602995	+	0.797745i	$0.706026\pi$
$180$	3.86199	+	6.68916i	0.287855	+	0.498580i
$181$	−5.45954	−	9.45621i	−0.405805	−	0.702874i	0.588610	−	0.808417i	$-0.299675\pi$
$181$	−5.45954	−	9.45621i	−0.405805	−	0.702874i	−0.994415	+	0.105543i	$0.966342\pi$
$182$	−23.8106	−	41.2412i	−1.76496	−	3.05700i
$183$	−3.97551	+	6.88578i	−0.293878	+	0.509012i
$184$	3.37306			0.248666
$185$	3.65245	+	4.86412i	0.268533	+	0.357617i
$186$	8.74599			0.641287
$187$	11.5241	−	19.9603i	0.842725	−	1.45964i
$188$	5.15676	+	8.93176i	0.376095	+	0.651416i
$189$	−4.81566	−	8.34096i	−0.350288	−	0.606716i
$190$	−6.44122	−	11.1565i	−0.467295	−	0.809379i
$191$	18.5566			1.34271			0.671353	−	0.741138i	$-0.265714\pi$
$191$	18.5566			1.34271			0.671353	+	0.741138i	$0.265714\pi$
$192$	6.52535	+	11.3022i	0.470927	+	0.815669i
$193$	−18.1478			−1.30630			−0.653152	−	0.757227i	$-0.726554\pi$
$193$	−18.1478			−1.30630			−0.653152	+	0.757227i	$0.726554\pi$
$194$	−3.96420	+	6.86619i	−0.284613	+	0.492964i
$195$	11.0534			0.791552
$196$	31.7854			2.27039
$197$	−1.65489	+	2.86635i	−0.117906	+	0.204219i	−0.918938	−	0.394403i	$-0.870951\pi$
$197$	−1.65489	+	2.86635i	−0.117906	+	0.204219i	0.801032	+	0.598622i	$0.204285\pi$
$198$	11.1171	+	19.2553i	0.790056	+	1.36842i
$199$	19.0157			1.34799			0.673995	−	0.738736i	$-0.264577\pi$
$199$	19.0157			1.34799			0.673995	+	0.738736i	$0.264577\pi$
$200$	−2.67551	+	4.63412i	−0.189187	+	0.327682i
$201$	−10.2035	+	17.6730i	−0.719700	+	1.24656i
$202$	−9.70143	+	16.8034i	−0.682590	+	1.18228i
$203$	7.79573	+	13.5026i	0.547153	+	0.947697i
$204$	−21.8946	−	37.9225i	−1.53293	−	2.65511i
$205$	0.00413940	−	0.00716965i	0.000289108	−	0.000500750i
$206$	9.83682	−	17.0379i	0.685363	−	1.18708i
$207$	−0.585682	+	1.01443i	−0.0407077	+	0.0705078i
$208$	−24.8938			−1.72607
$209$	−12.5183	−	21.6823i	−0.865908	−	1.49980i
$210$	−10.4654	+	18.1265i	−0.722179	+	1.25085i
$211$	5.89530			0.405849			0.202925	−	0.979194i	$-0.434955\pi$
$211$	5.89530			0.405849			0.202925	+	0.979194i	$0.434955\pi$
$212$	−1.30940			−0.0899298
$213$	5.29008	−	9.16269i	0.362470	−	0.627817i
$214$	0.746482			0.0510285
$215$	−4.47105	−	7.74409i	−0.304923	−	0.528142i
$216$	−13.4663			−0.916265
$217$	3.06015	+	5.30034i	0.207737	+	0.359811i
$218$	12.3657	+	21.4181i	0.837514	+	1.45062i
$219$	−9.74922	−	16.8861i	−0.658791	−	1.14106i
$220$	−10.0220	+	17.3586i	−0.675681	+	1.17031i
$221$	−23.9688			−1.61232
$222$	33.0256	−	3.99814i	2.21654	−	0.268338i
$223$	17.8984			1.19857			0.599283	−	0.800537i	$-0.295452\pi$
$223$	17.8984			1.19857			0.599283	+	0.800537i	$0.295452\pi$
$224$	3.09031	−	5.35258i	0.206480	−	0.357634i
$225$	−0.929125	−	1.60929i	−0.0619416	−	0.107286i
$226$	−9.37321	−	16.2349i	−0.623497	−	1.07993i
$227$	−2.51156	−	4.35015i	−0.166698	−	0.288730i	0.770559	−	0.637369i	$-0.219977\pi$
$227$	−2.51156	−	4.35015i	−0.166698	−	0.288730i	−0.937257	+	0.348639i	$0.886644\pi$
$228$	−47.5669			−3.15019
$229$	−4.58575	−	7.94275i	−0.303035	−	0.524872i	0.673787	−	0.738926i	$-0.264666\pi$
$229$	−4.58575	−	7.94275i	−0.303035	−	0.524872i	−0.976822	+	0.214054i	$0.931333\pi$
$230$	−1.56408			−0.103132
$231$	−20.3391	+	35.2283i	−1.33821	+	2.31785i
$232$	21.7996			1.43121
$233$	22.9317			1.50231			0.751154	−	0.660127i	$-0.229497\pi$
$233$	22.9317			1.50231			0.751154	+	0.660127i	$0.229497\pi$
$234$	11.5611	−	20.0245i	0.755775	−	1.30904i
$235$	−1.24062	−	2.14882i	−0.0809293	−	0.140174i
$236$	−62.4394			−4.06446
$237$	−3.16290	+	5.47830i	−0.205452	+	0.355854i
$238$	22.6937	−	39.3066i	1.47101	−	2.54787i
$239$	10.2447	−	17.7443i	0.662674	−	1.14779i	−0.317236	−	0.948347i	$-0.602755\pi$
$239$	10.2447	−	17.7443i	0.662674	−	1.14779i	0.979910	−	0.199439i	$-0.0639119\pi$
$240$	5.47072	+	9.47556i	0.353133	+	0.611645i
$241$	2.83487	+	4.91014i	0.182610	+	0.316290i	0.942769	−	0.333448i	$-0.108212\pi$
$241$	2.83487	+	4.91014i	0.182610	+	0.316290i	−0.760158	+	0.649738i	$0.774879\pi$
$242$	−15.2023	+	26.3312i	−0.977241	+	1.69263i
$243$	8.48199	−	14.6912i	0.544120	−	0.942443i
$244$	−7.49704	+	12.9852i	−0.479949	+	0.831295i
$245$	−7.64701			−0.488549
$246$	−0.0226385	−	0.0392110i	−0.00144338	−	0.00250000i
$247$	−13.0183	+	22.5484i	−0.828335	+	1.43472i
$248$	8.55728			0.543388
$249$	−10.5026			−0.665577
$250$	1.24062	−	2.14882i	0.0784639	−	0.135903i
$251$	7.50644			0.473802			0.236901	−	0.971534i	$-0.423868\pi$
$251$	7.50644			0.473802			0.236901	+	0.971534i	$0.423868\pi$
$252$	14.7804	+	25.6003i	0.931075	+	1.61267i
$253$	−3.03973			−0.191106
$254$	−8.69306	−	15.0568i	−0.545451	−	0.944749i
$255$	5.26744	+	9.12348i	0.329860	+	0.571334i
$256$	16.3126	+	28.2543i	1.01954	+	1.76589i
$257$	12.7689	−	22.1164i	0.796502	−	1.37958i	−0.125379	−	0.992109i	$-0.540015\pi$
$257$	12.7689	−	22.1164i	0.796502	−	1.37958i	0.921881	−	0.387474i	$-0.126652\pi$
$258$	−48.9046			−3.04466
$259$	13.9784	+	18.6157i	0.868577	+	1.15672i
$260$	20.8446			1.29273
$261$	−3.78518	+	6.55612i	−0.234297	+	0.405814i
$262$	17.7892	+	30.8118i	1.09902	+	1.90356i
$263$	5.90966	+	10.2358i	0.364406	+	0.631169i	0.988681	−	0.150036i	$-0.0479389\pi$
$263$	5.90966	+	10.2358i	0.364406	+	0.631169i	−0.624275	+	0.781205i	$0.714606\pi$
$264$	28.4376	+	49.2554i	1.75021	+	3.03146i
$265$	0.315018			0.0193514
$266$	−24.6515	−	42.6976i	−1.51148	−	2.61796i
$267$	39.3900			2.41063
$268$	−19.2418	+	33.3278i	−1.17538	+	2.03582i
$269$	6.80069			0.414646			0.207323	−	0.978273i	$-0.433525\pi$
$269$	6.80069			0.414646			0.207323	+	0.978273i	$0.433525\pi$
$270$	6.24426			0.380014
$271$	−1.39915	+	2.42340i	−0.0849924	+	0.147211i	−0.905388	−	0.424585i	$-0.860420\pi$
$271$	−1.39915	+	2.42340i	−0.0849924	+	0.147211i	0.820396	+	0.571796i	$0.193753\pi$
$272$	−11.8630	−	20.5473i	−0.719300	−	1.24586i
$273$	42.3030			2.56029
$274$	0.181258	−	0.313948i	0.0109502	−	0.0189663i
$275$	2.41111	−	4.17616i	0.145395	−	0.251832i
$276$	−2.88758	+	5.00144i	−0.173812	+	0.301051i
$277$	10.6040	+	18.3667i	0.637134	+	1.10355i	0.986059	+	0.166398i	$0.0532137\pi$
$277$	10.6040	+	18.3667i	0.637134	+	1.10355i	−0.348924	+	0.937151i	$0.613453\pi$
$278$	−0.255340	−	0.442262i	−0.0153143	−	0.0265251i
$279$	−1.48584	+	2.57356i	−0.0889551	+	0.154075i
$280$	−10.2396	+	17.7354i	−0.611930	+	1.05989i
$281$	7.55007	−	13.0771i	0.450399	−	0.780115i	−0.548011	−	0.836471i	$-0.684615\pi$
$281$	7.55007	−	13.0771i	0.450399	−	0.780115i	0.998411	+	0.0563562i	$0.0179482\pi$
$282$	−13.5700			−0.808082
$283$	−1.95174	−	3.38052i	−0.116019	−	0.200951i	0.802168	−	0.597099i	$-0.203680\pi$
$283$	−1.95174	−	3.38052i	−0.116019	−	0.200951i	−0.918187	+	0.396148i	$0.870347\pi$
$284$	9.97606	−	17.2790i	0.591970	−	1.02532i
$285$	11.4437			0.677869
$286$	60.0030			3.54805
$287$	0.0158421	−	0.0274393i	0.000935127	−	0.00161969i
$288$	3.00097			0.176834
$289$	−2.92221	−	5.06141i	−0.171894	−	0.297730i
$290$	−10.1084			−0.593585
$291$	−3.52148	−	6.09938i	−0.206433	−	0.357552i
$292$	−18.3851	−	31.8440i	−1.07591	−	1.86353i
$293$	−5.60015	−	9.69975i	−0.327164	−	0.566665i	0.654784	−	0.755816i	$-0.272760\pi$
$293$	−5.60015	−	9.69975i	−0.327164	−	0.566665i	−0.981948	+	0.189151i	$0.939426\pi$
$294$	−20.9108	+	36.2186i	−1.21954	+	2.11231i
$295$	15.0218			0.874603
$296$	32.3131	−	3.91188i	1.87816	−	0.227373i
$297$	12.1355			0.704173
$298$	−5.43452	+	9.41286i	−0.314813	+	0.545272i
$299$	1.58057	+	2.73763i	0.0914069	+	0.158321i
$300$	−4.58086	−	7.93427i	−0.264476	−	0.458086i
$301$	−17.1113	−	29.6377i	−0.986281	−	1.70829i
$302$	−33.6341			−1.93542
$303$	−8.61798	−	14.9268i	−0.495090	−	0.857522i
$304$	−25.7729			−1.47817
$305$	1.80365	−	3.12402i	0.103277	−	0.178881i
$306$	22.0376			1.25980
$307$	−31.6714			−1.80758			−0.903792	−	0.427972i	$-0.859228\pi$
$307$	−31.6714			−1.80758			−0.903792	+	0.427972i	$0.859228\pi$
$308$	−38.3555	+	66.4337i	−2.18551	+	3.78541i
$309$	8.73825	+	15.1351i	0.497102	+	0.861005i
$310$	−3.96797			−0.225366
$311$	4.13838	−	7.16788i	0.234666	−	0.406453i	−0.724510	−	0.689265i	$-0.757934\pi$
$311$	4.13838	−	7.16788i	0.234666	−	0.406453i	0.959176	+	0.282812i	$0.0912671\pi$
$312$	29.5735	−	51.2228i	1.67427	−	2.89992i
$313$	−0.453299	+	0.785138i	−0.0256220	+	0.0443786i	−0.878552	−	0.477647i	$-0.841490\pi$
$313$	−0.453299	+	0.785138i	−0.0256220	+	0.0443786i	0.852930	+	0.522025i	$0.174823\pi$
$314$	25.0519	+	43.3911i	1.41376	+	2.44870i
$315$	−3.55589	−	6.15898i	−0.200352	−	0.347019i
$316$	−5.96461	+	10.3310i	−0.335535	+	0.581164i
$317$	−7.95023	+	13.7702i	−0.446530	+	0.773412i	−0.998157	−	0.0606786i	$-0.980674\pi$
$317$	−7.95023	+	13.7702i	−0.446530	+	0.773412i	0.551628	+	0.834090i	$0.314007\pi$
$318$	0.861420	−	1.49202i	0.0483060	−	0.0836685i
$319$	−19.6453			−1.09993
$320$	−2.96049	−	5.12772i	−0.165497	−	0.286648i
$321$	−0.331558	+	0.574275i	−0.0185058	+	0.0320529i
$322$	−5.98594			−0.333583
$323$	−24.8152			−1.38076
$324$	23.1141	−	40.0347i	1.28411	−	2.22415i
$325$	−5.01483			−0.278173
$326$	3.13529	+	5.43048i	0.173648	+	0.300767i
$327$	−21.9695			−1.21492
$328$	−0.0221500	−	0.0383649i	−0.00122303	−	0.00211835i
$329$	−4.74804	−	8.22385i	−0.261768	−	0.453395i
$330$	−13.1864	−	22.8395i	−0.725888	−	1.25727i
$331$	0.308611	−	0.534529i	0.0169628	−	0.0293804i	−0.857419	−	0.514618i	$-0.827934\pi$
$331$	0.308611	−	0.534529i	0.0169628	−	0.0293804i	0.874382	+	0.485238i	$0.161267\pi$
$332$	−19.8059			−1.08699
$333$	−4.43420	+	10.3972i	−0.242993	+	0.569764i
$334$	−56.4108			−3.08666
$335$	4.62924	−	8.01808i	0.252922	−	0.438075i
$336$	20.9372	+	36.2643i	1.14222	+	1.97838i
$337$	−5.98778	−	10.3711i	−0.326175	−	0.564952i	0.655574	−	0.755131i	$-0.272427\pi$
$337$	−5.98778	−	10.3711i	−0.326175	−	0.564952i	−0.981749	+	0.190179i	$0.939093\pi$
$338$	−15.0718	−	26.1051i	−0.819798	−	1.41993i
$339$	16.6528			0.904458
$340$	9.93337	+	17.2051i	0.538713	+	0.933078i
$341$	−7.71162			−0.417608
$342$	11.9694	−	20.7316i	0.647230	−	1.12104i
$343$	−2.47619			−0.133702
$344$	−47.8494			−2.57986
$345$	0.694701	−	1.20326i	0.0374014	−	0.0647812i
$346$	−17.8340	−	30.8894i	−0.958761	−	1.66062i
$347$	−3.92885			−0.210912			−0.105456	−	0.994424i	$-0.533630\pi$
$347$	−3.92885			−0.210912			−0.105456	+	0.994424i	$0.533630\pi$
$348$	−18.6620	+	32.3236i	−1.00039	+	1.73273i
$349$	−1.23341	+	2.13634i	−0.0660232	+	0.114356i	−0.897147	−	0.441731i	$-0.854364\pi$
$349$	−1.23341	+	2.13634i	−0.0660232	+	0.114356i	0.831124	+	0.556087i	$0.187698\pi$
$350$	4.74804	−	8.22385i	0.253793	−	0.439583i
$351$	−6.31012	−	10.9295i	−0.336809	−	0.583371i
$352$	3.89381	+	6.74427i	0.207541	+	0.359471i
$353$	13.2189	−	22.8957i	0.703568	−	1.21862i	−0.263637	−	0.964622i	$-0.584922\pi$
$353$	13.2189	−	22.8957i	0.703568	−	1.21862i	0.967206	−	0.253994i	$-0.0817445\pi$
$354$	41.0773	−	71.1479i	2.18323	−	3.78147i
$355$	−2.40006	+	4.15703i	−0.127382	+	0.220632i
$356$	74.2819			3.93693
$357$	20.1592	+	34.9168i	1.06694	+	1.84800i
$358$	20.0175	−	34.6714i	1.05796	−	1.83244i
$359$	−28.1301			−1.48465			−0.742324	−	0.670041i	$-0.766276\pi$
$359$	−28.1301			−1.48465			−0.742324	+	0.670041i	$0.766276\pi$
$360$	−9.94353			−0.524070
$361$	−3.97802	+	6.89014i	−0.209370	+	0.362639i
$362$	27.0929			1.42397
$363$	−13.5045	−	23.3905i	−0.708804	−	1.22768i
$364$	79.7752			4.18136
$365$	4.42313	+	7.66109i	0.231517	+	0.401000i
$366$	−9.86422	−	17.0853i	−0.515611	−	0.893064i
$367$	−11.1431	−	19.3005i	−0.581668	−	1.00748i	−0.995282	−	0.0970257i	$-0.969067\pi$
$367$	−11.1431	−	19.3005i	−0.581668	−	1.00748i	0.413614	−	0.910452i	$-0.364266\pi$
$368$	−1.56456	+	2.70990i	−0.0815584	+	0.141263i
$369$	0.0153841			0.000800863
$370$	−14.9834	+	1.81392i	−0.778952	+	0.0943013i
$371$	1.20562			0.0625925
$372$	−7.32564	+	12.6884i	−0.379817	+	0.657862i
$373$	−5.09320	−	8.82169i	−0.263716	−	0.456770i	0.703510	−	0.710685i	$-0.251615\pi$
$373$	−5.09320	−	8.82169i	−0.263716	−	0.456770i	−0.967226	+	0.253915i	$0.918282\pi$
$374$	28.5941	+	49.5264i	1.47857	+	2.56095i
$375$	1.10207	+	1.90884i	0.0569107	+	0.0985723i
$376$	−13.2772			−0.684719
$377$	10.2150	+	17.6929i	0.526100	+	0.911232i
$378$	23.8977			1.22916
$379$	−12.7325	+	22.0533i	−0.654025	+	1.13280i	0.328113	+	0.944639i	$0.393587\pi$
$379$	−12.7325	+	22.0533i	−0.654025	+	1.13280i	−0.982137	+	0.188165i	$0.939746\pi$
$380$	21.5807			1.10706
$381$	15.4444			0.791243
$382$	−23.0217	+	39.8748i	−1.17789	+	2.04017i
$383$	8.09860	+	14.0272i	0.413819	+	0.716756i	0.995304	−	0.0968017i	$-0.0308613\pi$
$383$	8.09860	+	14.0272i	0.413819	+	0.716756i	−0.581485	+	0.813557i	$0.697528\pi$
$384$	−39.5012			−2.01578
$385$	9.22765	−	15.9828i	0.470285	−	0.814557i
$386$	22.5145	−	38.9963i	1.14596	−	1.98486i
$387$	8.30833	−	14.3904i	0.422336	−	0.731507i
$388$	−6.64082	−	11.5022i	−0.337137	−	0.583938i
$389$	−3.10344	−	5.37532i	−0.157351	−	0.272540i	0.776562	−	0.630041i	$-0.216962\pi$
$389$	−3.10344	−	5.37532i	−0.157351	−	0.272540i	−0.933913	+	0.357502i	$0.883629\pi$
$390$	−13.7131	+	23.7518i	−0.694391	+	1.20272i
$391$	−1.50643	+	2.60921i	−0.0761833	+	0.131953i
$392$	−20.4596	+	35.4372i	−1.03337	+	1.78985i
$393$	−31.6050			−1.59426
$394$	−4.10619	−	7.11213i	−0.206867	−	0.358304i
$395$	1.43498	−	2.48545i	0.0722016	−	0.125057i
$396$	−37.2467			−1.87171
$397$	17.9400			0.900384			0.450192	−	0.892932i	$-0.351356\pi$
$397$	17.9400			0.900384			0.450192	+	0.892932i	$0.351356\pi$
$398$	−23.5914	+	40.8615i	−1.18253	+	2.04820i
$399$	43.7968			2.19258
$400$	−2.48202	−	4.29898i	−0.124101	−	0.214949i
$401$	−16.6023			−0.829079			−0.414539	−	0.910031i	$-0.636057\pi$
$401$	−16.6023			−0.829079			−0.414539	+	0.910031i	$0.636057\pi$
$402$	−25.3174	−	43.8511i	−1.26272	−	2.18709i
$403$	4.00983	+	6.94522i	0.199744	+	0.345966i
$404$	−16.2518	−	28.1490i	−0.808559	−	1.40047i
$405$	−5.56083	+	9.63164i	−0.276320	+	0.478600i
$406$	−38.6862			−1.91997
$407$	−29.1198	+	3.52529i	−1.44341	+	0.174742i
$408$	56.3724			2.79085
$409$	−14.2533	+	24.6874i	−0.704780	+	1.22071i	0.261991	+	0.965070i	$0.415621\pi$
$409$	−14.2533	+	24.6874i	−0.704780	+	1.22071i	−0.966771	+	0.255644i	$0.917713\pi$
$410$	0.0102709	+	0.0177897i	0.000507242	+	0.000878569i
$411$	0.161015	+	0.278887i	0.00794230	+	0.0137565i
$412$	16.4786	+	28.5418i	0.811844	+	1.40616i
$413$	57.4905			2.82892
$414$	−1.45322	−	2.51705i	−0.0714219	−	0.123706i
$415$	4.76495			0.233902
$416$	4.04934	−	7.01366i	0.198535	−	0.343873i
$417$	0.453648			0.0222152
$418$	62.1219			3.03848
$419$	6.22629	−	10.7843i	0.304174	−	0.526845i	−0.672903	−	0.739731i	$-0.734953\pi$
$419$	6.22629	−	10.7843i	0.304174	−	0.526845i	0.977077	+	0.212886i	$0.0682862\pi$
$420$	−17.5316	−	30.3656i	−0.855454	−	1.48169i
$421$	36.4761			1.77774			0.888868	−	0.458163i	$-0.151493\pi$
$421$	36.4761			1.77774			0.888868	+	0.458163i	$0.151493\pi$
$422$	−7.31385	+	12.6680i	−0.356032	+	0.616666i
$423$	2.30539	−	3.99305i	0.112092	−	0.194149i
$424$	0.842833	−	1.45983i	0.0409316	−	0.0708956i
$425$	−2.38979	−	4.13924i	−0.115922	−	0.200783i
$426$	13.1260	+	22.7349i	0.635957	+	1.10151i
$427$	6.90283	−	11.9561i	0.334051	−	0.578594i
$428$	−0.625254	+	1.08297i	−0.0302228	+	0.0523474i
$429$	−26.6510	+	46.1608i	−1.28672	+	2.22867i
$430$	22.1876			1.06998
$431$	17.6410	+	30.5551i	0.849737	+	1.47179i	0.881443	+	0.472291i	$0.156573\pi$
$431$	17.6410	+	30.5551i	0.849737	+	1.47179i	−0.0317053	+	0.999497i	$0.510094\pi$
$432$	6.24620	−	10.8187i	0.300520	−	0.520516i
$433$	−12.3488			−0.593445			−0.296723	−	0.954964i	$-0.595894\pi$
$433$	−12.3488			−0.593445			−0.296723	+	0.954964i	$0.595894\pi$
$434$	−15.1860			−0.728951
$435$	4.48975	−	7.77647i	0.215267	−	0.372853i
$436$	−41.4302			−1.98415
$437$	1.63639	+	2.83431i	0.0782790	+	0.135583i
$438$	48.3805			2.31171
$439$	7.59518	+	13.1552i	0.362498	+	0.627865i	0.988371	−	0.152059i	$-0.0485905\pi$
$439$	7.59518	+	13.1552i	0.362498	+	0.627865i	−0.625873	+	0.779925i	$0.715257\pi$
$440$	−12.9019	−	22.3467i	−0.615073	−	1.06534i
$441$	−7.10502	−	12.3063i	−0.338335	−	0.586013i
$442$	29.7363	−	51.5047i	1.41441	−	2.44983i
$443$	14.9083			0.708316			0.354158	−	0.935186i	$-0.384767\pi$
$443$	14.9083			0.708316			0.354158	+	0.935186i	$0.384767\pi$
$444$	−21.8619	+	51.2613i	−1.03752	+	2.43275i
$445$	−17.8709			−0.847161
$446$	−22.2052	+	38.4605i	−1.05145	+	1.82116i
$447$	−4.82760	−	8.36164i	−0.228337	−	0.395492i
$448$	−11.3302	−	19.6245i	−0.535303	−	0.927172i
$449$	−6.76422	−	11.7160i	−0.319223	−	0.552911i	0.661103	−	0.750295i	$-0.270089\pi$
$449$	−6.76422	−	11.7160i	−0.319223	−	0.552911i	−0.980326	+	0.197384i	$0.936755\pi$
$450$	4.61077			0.217354
$451$	0.0199611	+	0.0345736i	0.000939930	+	0.00162801i
$452$	31.4040			1.47712
$453$	14.9389	−	25.8750i	0.701892	−	1.21571i
$454$	12.4636			0.584946
$455$	−19.1925			−0.899757
$456$	30.6178	−	53.0317i	1.43381	−	2.48343i
$457$	−16.4789	−	28.5424i	−0.770852	−	1.33516i	−0.937096	−	0.349071i	$-0.886497\pi$
$457$	−16.4789	−	28.5424i	−0.770852	−	1.33516i	0.166244	−	0.986085i	$-0.446836\pi$
$458$	22.7567			1.06335
$459$	6.01411	−	10.4167i	0.280714	−	0.486212i
$460$	1.31007	−	2.26911i	0.0610823	−	0.105798i
$461$	−1.33483	+	2.31199i	−0.0621691	+	0.107680i	−0.895435	−	0.445193i	$-0.853135\pi$
$461$	−1.33483	+	2.31199i	−0.0621691	+	0.107680i	0.833266	+	0.552873i	$0.186468\pi$
$462$	−50.4662	−	87.4101i	−2.34790	−	4.06669i
$463$	−2.20210	−	3.81416i	−0.102340	−	0.177259i	0.810308	−	0.586004i	$-0.199300\pi$
$463$	−2.20210	−	3.81416i	−0.102340	−	0.177259i	−0.912648	+	0.408745i	$0.865966\pi$
$464$	−10.1115	+	17.5137i	−0.469416	+	0.813052i
$465$	1.76242	−	3.05260i	0.0817302	−	0.141561i
$466$	−28.4497	+	49.2763i	−1.31790	+	2.28268i
$467$	22.3129			1.03252			0.516259	−	0.856433i	$-0.327324\pi$
$467$	22.3129			1.03252			0.516259	+	0.856433i	$0.327324\pi$
$468$	19.3672	+	33.5450i	0.895250	+	1.55062i
$469$	17.7168	−	30.6863i	0.818084	−	1.41696i
$470$	6.15659			0.283982
$471$	−44.5082			−2.05083
$472$	40.1910	−	69.6128i	1.84994	−	3.20419i
$473$	43.1207			1.98269
$474$	−7.84793	−	13.5930i	−0.360467	−	0.624348i
$475$	−5.19192			−0.238222
$476$	38.0164	+	65.8464i	1.74248	+	3.01806i
$477$	0.292691	+	0.506955i	0.0134014	+	0.0232119i
$478$	25.4196	+	44.0281i	1.16267	+	2.01380i
$479$	−8.10536	+	14.0389i	−0.370343	+	0.641453i	−0.989618	−	0.143721i	$-0.954093\pi$
$479$	−8.10536	+	14.0389i	−0.370343	+	0.641453i	0.619275	+	0.785174i	$0.287427\pi$
$480$	−3.55957			−0.162471
$481$	18.3164	+	24.3927i	0.835157	+	1.11221i
$482$	−14.0680			−0.640782
$483$	2.65872	−	4.60503i	0.120976	−	0.209536i
$484$	−25.4669	−	44.1100i	−1.15759	−	2.00500i
$485$	1.59766	+	2.76723i	0.0725461	+	0.125654i
$486$	21.0459	+	36.4526i	0.954662	+	1.65352i
$487$	−4.89040			−0.221605			−0.110802	−	0.993842i	$-0.535342\pi$
$487$	−4.89040			−0.221605			−0.110802	+	0.993842i	$0.535342\pi$
$488$	−9.65138	−	16.7167i	−0.436898	−	0.756729i
$489$	−5.57029			−0.251897
$490$	9.48706	−	16.4321i	0.428582	−	0.742325i
$491$	−33.9430			−1.53183			−0.765914	−	0.642943i	$-0.777713\pi$
$491$	−33.9430			−1.53183			−0.765914	+	0.642943i	$0.777713\pi$
$492$	0.0758479			0.00341949
$493$	−9.73581	+	16.8629i	−0.438479	+	0.759468i
$494$	−32.3016	−	55.9481i	−1.45332	−	2.51722i
$495$	8.96088			0.402762
$496$	−3.96920	+	6.87486i	−0.178223	+	0.308690i
$497$	−9.18538	+	15.9095i	−0.412020	+	0.713640i
$498$	13.0298	−	22.5683i	0.583880	−	1.01131i
$499$	17.6317	+	30.5390i	0.789302	+	1.36711i	0.926395	+	0.376553i	$0.122891\pi$
$499$	17.6317	+	30.5390i	0.789302	+	1.36711i	−0.137093	+	0.990558i	$0.543776\pi$
$500$	2.07829	+	3.59971i	0.0929441	+	0.160984i
$501$	25.0555	−	43.3973i	1.11940	−	1.93885i
$502$	−9.31266	+	16.1300i	−0.415645	+	0.719917i
$503$	−9.15014	+	15.8485i	−0.407985	+	0.706650i	−0.994664	−	0.103169i	$-0.967102\pi$
$503$	−9.15014	+	15.8485i	−0.407985	+	0.706650i	0.586679	+	0.809819i	$0.300435\pi$
$504$	−38.0553			−1.69512
$505$	3.90990	+	6.77215i	0.173988	+	0.301357i
$506$	3.77116	−	6.53183i	0.167648	−	0.290375i
$507$	26.7772			1.18922
$508$	29.1252			1.29222
$509$	11.0657	−	19.1663i	0.490478	−	0.849532i	−0.509462	−	0.860493i	$-0.670156\pi$
$509$	11.0657	−	19.1663i	0.490478	−	0.849532i	0.999940	+	0.0109608i	$0.00348901\pi$
$510$	−26.1397			−1.15748
$511$	16.9280	+	29.3201i	0.748849	+	1.29704i
$512$	−45.1086			−1.99354
$513$	−6.53295	−	11.3154i	−0.288437	−	0.499587i
$514$	31.6828	+	54.8762i	1.39747	+	2.42049i
$515$	−3.96447	−	6.86666i	−0.174695	−	0.302581i
$516$	40.9625	−	70.9491i	1.80327	−	3.12336i
$517$	11.9651			0.526225
$518$	−57.3437	+	6.94213i	−2.51954	+	0.305020i
$519$	31.6846			1.39080
$520$	−13.4172	+	23.2393i	−0.588385	+	1.01911i
$521$	3.01739	+	5.22628i	0.132194	+	0.228967i	0.924522	−	0.381128i	$-0.124464\pi$
$521$	3.01739	+	5.22628i	0.132194	+	0.228967i	−0.792328	+	0.610096i	$0.791131\pi$
$522$	−9.39196	−	16.2673i	−0.411075	−	0.712002i
$523$	14.9409	+	25.8785i	0.653321	+	1.13159i	0.982312	+	0.187252i	$0.0599582\pi$
$523$	14.9409	+	25.8785i	0.653321	+	1.13159i	−0.328991	+	0.944333i	$0.606708\pi$
$524$	−59.6009			−2.60368
$525$	4.21778	+	7.30542i	0.184079	+	0.318835i
$526$	−29.3267			−1.27870
$527$	−3.82172	+	6.61941i	−0.166477	+	0.288346i
$528$	−52.7620			−2.29617
$529$	−22.6026			−0.982724
$530$	−0.390818	+	0.676917i	−0.0169761	+	0.0294034i
$531$	13.9571	+	24.1744i	0.605687	+	1.04908i
$532$	82.5922			3.58083
$533$	0.0207584	−	0.0359546i	0.000899146	−	0.00155737i
$534$	−48.8682	+	84.6421i	−2.11473	+	3.66282i
$535$	0.150425	−	0.260544i	0.00650343	−	0.0112643i
$536$	−24.7712	−	42.9049i	−1.06995	−	1.85321i
$537$	17.7820	+	30.7993i	0.767350	+	1.32909i
$538$	−8.43710	+	14.6135i	−0.363749	+	0.630032i
$539$	18.4378	−	31.9351i	0.794171	−	1.37554i
$540$	−5.23020	+	9.05896i	−0.225072	+	0.389836i
$541$	−27.5840			−1.18593			−0.592964	−	0.805229i	$-0.702042\pi$
$541$	−27.5840			−1.18593			−0.592964	+	0.805229i	$0.702042\pi$
$542$	−3.47164	−	6.01305i	−0.149120	−	0.258283i
$543$	−12.0336	+	20.8428i	−0.516412	+	0.894452i
$544$	7.71876			0.330939
$545$	9.96736			0.426955
$546$	−52.4821	+	90.9016i	−2.24603	+	3.89023i
$547$	−24.4954			−1.04735			−0.523674	−	0.851919i	$-0.675439\pi$
$547$	−24.4954			−1.04735			−0.523674	+	0.851919i	$0.675439\pi$
$548$	0.303644	+	0.525926i	0.0129710	+	0.0224664i
$549$	6.70327			0.286089
$550$	5.98255	+	10.3621i	0.255097	+	0.441841i
$551$	10.5757	+	18.3177i	0.450541	+	0.780360i
$552$	−3.71736	−	6.43865i	−0.158221	−	0.274047i
$553$	5.49186	−	9.51218i	0.233538	−	0.404499i
$554$	−52.6224			−2.23571
$555$	5.25959	−	12.3326i	0.223257	−	0.523488i
$556$	0.855492			0.0362809
$557$	6.29500	−	10.9033i	0.266728	−	0.461986i	−0.701287	−	0.712879i	$-0.747391\pi$
$557$	6.29500	−	10.9033i	0.266728	−	0.461986i	0.968015	+	0.250893i	$0.0807243\pi$
$558$	−3.68674	−	6.38563i	−0.156072	−	0.270325i
$559$	−22.4216	−	38.8353i	−0.948332	−	1.64256i
$560$	−9.49902	−	16.4528i	−0.401407	−	0.695257i
$561$	−50.8015			−2.14484
$562$	18.7336	+	32.4475i	0.790229	+	1.36872i
$563$	−1.69407			−0.0713964			−0.0356982	−	0.999363i	$-0.511365\pi$
$563$	−1.69407			−0.0713964			−0.0356982	+	0.999363i	$0.511365\pi$
$564$	11.3662	−	19.6869i	0.478605	−	0.828968i
$565$	−7.55525			−0.317852
$566$	9.68551			0.407113
$567$	−21.2821	+	36.8616i	−0.893763	+	1.54804i
$568$	12.8428	+	22.2444i	0.538871	+	0.933352i
$569$	20.9702			0.879118			0.439559	−	0.898214i	$-0.355135\pi$
$569$	20.9702			0.879118			0.439559	+	0.898214i	$0.355135\pi$
$570$	−14.1974	+	24.5906i	−0.594662	+	1.02999i
$571$	−16.2509	+	28.1474i	−0.680080	+	1.17793i	0.294876	+	0.955536i	$0.404722\pi$
$571$	−16.2509	+	28.1474i	−0.680080	+	1.17793i	−0.974956	+	0.222398i	$0.928612\pi$
$572$	−50.2585	+	87.0504i	−2.10142	+	3.63976i
$573$	−20.4507	−	35.4216i	−0.854339	−	1.47976i
$574$	0.0393081	+	0.0680836i	0.00164069	+	0.00284175i
$575$	−0.315179	+	0.545907i	−0.0131439	+	0.0227659i
$576$	5.50133	−	9.52859i	0.229222	−	0.397025i
$577$	17.3902	−	30.1207i	0.723963	−	1.25394i	−0.235436	−	0.971890i	$-0.575652\pi$
$577$	17.3902	−	30.1207i	0.723963	−	1.25394i	0.959399	−	0.282052i	$-0.0910149\pi$
$578$	14.5014			0.603180
$579$	20.0001	+	34.6412i	0.831177	+	1.43964i
$580$	8.46679	−	14.6649i	0.351564	−	0.608927i
$581$	18.2361			0.756562
$582$	17.4753			0.724375
$583$	−0.759541	+	1.31556i	−0.0314570	+	0.0544851i
$584$	47.3366			1.95880
$585$	−4.65941	−	8.07033i	−0.192643	−	0.333667i
$586$	27.7907			1.14802
$587$	8.37890	+	14.5127i	0.345834	+	0.599002i	0.985505	−	0.169647i	$-0.0542626\pi$
$587$	8.37890	+	14.5127i	0.345834	+	0.599002i	−0.639671	+	0.768649i	$0.720929\pi$
$588$	−35.0298	−	60.6735i	−1.44461	−	2.50213i
$589$	4.15142	+	7.19048i	0.171056	+	0.296278i
$590$	−18.6364	+	32.2792i	−0.767248	+	1.32891i
$591$	7.29523			0.300086
$592$	−11.8453	+	27.7746i	−0.486839	+	1.14153i
$593$	−19.9116			−0.817671			−0.408835	−	0.912608i	$-0.634065\pi$
$593$	−19.9116			−0.817671			−0.408835	+	0.912608i	$0.634065\pi$
$594$	−15.0556	+	26.0770i	−0.617738	+	1.06995i
$595$	−9.14607	−	15.8415i	−0.374952	−	0.649436i
$596$	−9.10390	−	15.7684i	−0.372910	−	0.645900i
$597$	−20.9567	−	36.2981i	−0.857701	−	1.48558i
$598$	−7.84358			−0.320748
$599$	−6.36052	−	11.0167i	−0.259884	−	0.450132i	0.706327	−	0.707886i	$-0.250351\pi$
$599$	−6.36052	−	11.0167i	−0.259884	−	0.450132i	−0.966211	+	0.257754i	$0.917018\pi$
$600$	11.7944			0.481505
$601$	15.2131	−	26.3499i	0.620556	−	1.07483i	−0.368827	−	0.929498i	$-0.620240\pi$
$601$	15.2131	−	26.3499i	0.620556	−	1.07483i	0.989382	−	0.145336i	$-0.0464263\pi$
$602$	84.9149			3.46087
$603$	17.2046			0.700624
$604$	28.1719	−	48.7952i	1.14630	−	1.98545i
$605$	6.12688	+	10.6121i	0.249093	+	0.431442i
$606$	42.7667			1.73728
$607$	11.4379	−	19.8110i	0.464250	−	0.804104i	−0.534918	−	0.844904i	$-0.679657\pi$
$607$	11.4379	−	19.8110i	0.464250	−	0.804104i	0.999167	+	0.0408001i	$0.0129907\pi$
$608$	4.19233	−	7.26133i	0.170022	−	0.294486i
$609$	17.1829	−	29.7617i	0.696286	−	1.20600i
$610$	4.47531	+	7.75146i	0.181200	+	0.313847i
$611$	−6.22152	−	10.7760i	−0.251696	−	0.435950i
$612$	−18.4587	+	31.9714i	−0.746148	+	1.29237i
$613$	−2.66181	+	4.61039i	−0.107510	+	0.186212i	−0.914761	−	0.403996i	$-0.867621\pi$
$613$	−2.66181	+	4.61039i	−0.107510	+	0.186212i	0.807251	+	0.590208i	$0.200954\pi$
$614$	39.2923	−	68.0563i	1.58571	−	2.74653i
$615$	−0.0182477			−0.000735817
$616$	−49.3773	−	85.5241i	−1.98947	−	3.44586i
$617$	3.69284	−	6.39618i	0.148668	−	0.257501i	−0.782067	−	0.623194i	$-0.785835\pi$
$617$	3.69284	−	6.39618i	0.148668	−	0.257501i	0.930735	+	0.365693i	$0.119168\pi$
$618$	−43.3635			−1.74434
$619$	18.6353			0.749014			0.374507	−	0.927224i	$-0.377812\pi$
$619$	18.6353			0.749014			0.374507	+	0.927224i	$0.377812\pi$
$620$	3.32358	−	5.75660i	0.133478	−	0.231191i
$621$	−1.58635			−0.0636580
$622$	10.2683	+	17.7853i	0.411723	+	0.713125i
$623$	−68.3944			−2.74016
$624$	27.4347	+	47.5184i	1.09827	+	1.90226i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−1.12475	−	1.94812i	−0.0449540	−	0.0778625i
$627$	−27.5921	+	47.7909i	−1.10192	+	1.90858i
$628$	−83.9338			−3.34932
$629$	−11.4052	+	26.7426i	−0.454754	+	1.06630i
$630$	17.6461			0.703037
$631$	−2.69748	+	4.67217i	−0.107385	+	0.185996i	−0.914710	−	0.404111i	$-0.867581\pi$
$631$	−2.69748	+	4.67217i	−0.107385	+	0.185996i	0.807325	+	0.590107i	$0.200914\pi$
$632$	−7.67859	−	13.2997i	−0.305438	−	0.529034i
$633$	−6.49704	−	11.2532i	−0.258234	−	0.447275i
$634$	−19.7265	−	34.1673i	−0.783439	−	1.35696i
$635$	−7.00701			−0.278065
$636$	1.44305	+	2.49944i	0.0572207	+	0.0991091i
$637$	−38.3485			−1.51942
$638$	24.3724	−	42.2143i	0.964914	−	1.67128i
$639$	−8.91983			−0.352863
$640$	17.9213			0.708402
$641$	15.3886	−	26.6538i	0.607812	−	1.05276i	−0.383788	−	0.923421i	$-0.625381\pi$
$641$	15.3886	−	26.6538i	0.607812	−	1.05276i	0.991600	−	0.129340i	$-0.0412859\pi$
$642$	−0.822677	−	1.42492i	−0.0324685	−	0.0562371i
$643$	−29.0572			−1.14591			−0.572953	−	0.819588i	$-0.694202\pi$
$643$	−29.0572			−1.14591			−0.572953	+	0.819588i	$0.694202\pi$
$644$	5.01382	−	8.68420i	0.197572	−	0.342205i
$645$	−9.85484	+	17.0691i	−0.388034	+	0.672094i
$646$	30.7863	−	53.3235i	1.21127	−	2.09799i
$647$	−15.6967	−	27.1874i	−0.617099	−	1.06885i	−0.990012	−	0.140981i	$-0.954974\pi$
$647$	−15.6967	−	27.1874i	−0.617099	−	1.06885i	0.372913	−	0.927866i	$-0.378359\pi$
$648$	29.7561	+	51.5391i	1.16893	+	2.02465i
$649$	−36.2192	+	62.7334i	−1.42173	+	2.46250i
$650$	6.22152	−	10.7760i	0.244028	−	0.422669i
$651$	6.74502	−	11.6827i	0.264358	−	0.457882i
$652$	−10.5045			−0.411387
$653$	8.62859	+	14.9452i	0.337663	+	0.584849i	0.983993	−	0.178209i	$-0.0570303\pi$
$653$	8.62859	+	14.9452i	0.337663	+	0.584849i	−0.646330	+	0.763058i	$0.723697\pi$
$654$	27.2559	−	47.2085i	1.06579	−	1.84600i
$655$	14.3389			0.560267
$656$	0.0410962			0.00160454
$657$	−8.21929	+	14.2362i	−0.320665	+	0.555408i
$658$	23.5621			0.918547
$659$	1.62802	+	2.81981i	0.0634185	+	0.109844i	0.895991	−	0.444071i	$-0.146466\pi$
$659$	1.62802	+	2.81981i	0.0634185	+	0.109844i	−0.832573	+	0.553916i	$0.813133\pi$
$660$	44.1797			1.71969
$661$	0.816096	+	1.41352i	0.0317425	+	0.0549795i	0.881460	−	0.472258i	$-0.156561\pi$
$661$	0.816096	+	1.41352i	0.0317425	+	0.0549795i	−0.849718	+	0.527238i	$0.823228\pi$
$662$	0.765739	+	1.32630i	0.0297613	+	0.0515481i
$663$	26.4154	+	45.7527i	1.02589	+	1.77689i
$664$	12.7487	−	22.0813i	0.494744	−	0.856922i
$665$	−19.8702			−0.770534
$666$	−16.8406	−	22.4274i	−0.652560	−	0.869042i
$667$	2.56803			0.0994345
$668$	47.2497	−	81.8389i	1.82815	−	3.16644i
$669$	−19.7253	−	34.1653i	−0.762626	−	1.32091i
$670$	11.4863	+	19.8948i	0.443754	+	0.768605i
$671$	8.69760	+	15.0647i	0.335767	+	0.581566i
$672$	−13.6230			−0.525518
$673$	4.72532	+	8.18449i	0.182148	+	0.315489i	0.942612	−	0.333891i	$-0.108362\pi$
$673$	4.72532	+	8.18449i	0.182148	+	0.315489i	−0.760464	+	0.649380i	$0.775028\pi$
$674$	29.7143			1.14455
$675$	1.25829	−	2.17942i	0.0484317	−	0.0838861i
$676$	50.4966			1.94218
$677$	−32.1871			−1.23705			−0.618526	−	0.785764i	$-0.712270\pi$
$677$	−32.1871			−1.23705			−0.618526	+	0.785764i	$0.712270\pi$
$678$	−20.6599	+	35.7840i	−0.793439	+	1.37428i
$679$	6.11448	+	10.5906i	0.234652	+	0.406430i
$680$	−25.5756			−0.980781
$681$	−5.53584	+	9.58836i	−0.212134	+	0.367427i
$682$	9.56721	−	16.5709i	0.366348	−	0.634533i
$683$	15.2232	−	26.3674i	0.582500	−	1.00892i	−0.412683	−	0.910875i	$-0.635408\pi$
$683$	15.2232	−	26.3674i	0.582500	−	1.00892i	0.995182	−	0.0980438i	$-0.0312585\pi$
$684$	20.0511	+	34.7296i	0.766674	+	1.32792i
$685$	−0.0730512	−	0.126528i	−0.00279114	−	0.00483440i
$686$	3.07203	−	5.32090i	0.117290	−	0.203153i
$687$	−10.1076	+	17.5070i	−0.385631	+	0.667932i
$688$	22.1944	−	38.4419i	0.846155	−	1.46558i
$689$	1.57976			0.0601841
$690$	1.72372	+	2.98558i	0.0656211	+	0.113659i
$691$	16.2043	−	28.0668i	0.616442	−	1.06771i	−0.373687	−	0.927555i	$-0.621907\pi$
$691$	16.2043	−	28.0668i	0.616442	−	1.06771i	0.990130	−	0.140155i	$-0.0447601\pi$
$692$	59.7510			2.27139
$693$	34.2945			1.30274
$694$	4.87423	−	8.44241i	0.185023	−	0.320470i
$695$	−0.205816			−0.00780705
$696$	−24.0247	−	41.6121i	−0.910655	−	1.57730i
$697$	0.0395692			0.00149879
$698$	−3.06041	−	5.30078i	−0.115838	−	0.200637i
$699$	−25.2724	−	43.7731i	−0.955891	−	1.65565i
$700$	7.95392	+	13.7766i	0.300630	+	0.520706i
$701$	−5.80078	+	10.0472i	−0.219092	+	0.379479i	−0.954531	−	0.298112i	$-0.903643\pi$
$701$	−5.80078	+	10.0472i	−0.219092	+	0.379479i	0.735438	+	0.677592i	$0.236976\pi$
$702$	31.3139			1.18187
$703$	18.9632	+	25.2541i	0.715211	+	0.952477i
$704$	28.5523			1.07610
$705$	−2.73451	+	4.73631i	−0.102988	+	0.178380i
$706$	32.7992	+	56.8099i	1.23442	+	2.13807i
$707$	14.9637	+	25.9180i	0.562770	+	0.974745i
$708$	68.8127	+	119.187i	2.58614	+	4.47932i
$709$	−6.33991			−0.238100			−0.119050	−	0.992888i	$-0.537985\pi$
$709$	−6.33991			−0.238100			−0.119050	+	0.992888i	$0.537985\pi$
$710$	−5.95515	−	10.3146i	−0.223493	−	0.387101i
$711$	5.33309			0.200007
$712$	−47.8137	+	82.8158i	−1.79190	+	3.10365i
$713$	1.00806			0.0377522
$714$	−100.040			−3.74391
$715$	12.0913	−	20.9428i	0.452189	−	0.783215i
$716$	33.5334	+	58.0815i	1.25320	+	2.17061i
$717$	−45.1616			−1.68659
$718$	34.8988	−	60.4465i	1.30241	−	2.25584i
$719$	−3.89180	+	6.74080i	−0.145140	+	0.251389i	−0.929425	−	0.369011i	$-0.879696\pi$
$719$	−3.89180	+	6.74080i	−0.145140	+	0.251389i	0.784285	+	0.620400i	$0.213030\pi$
$720$	4.61220	−	7.98857i	0.171887	−	0.297716i
$721$	−15.1726	−	26.2797i	−0.565056	−	0.978706i
$722$	−9.87046	−	17.0961i	−0.367340	−	0.636252i
$723$	6.24847	−	10.8227i	0.232383	−	0.402499i
$724$	−22.6931	+	39.3055i	−0.843381	+	1.46078i
$725$	−2.03696	+	3.52812i	−0.0756507	+	0.131031i
$726$	67.0161			2.48720
$727$	−25.9195	−	44.8939i	−0.961302	−	1.66502i	−0.719238	−	0.694764i	$-0.755509\pi$
$727$	−25.9195	−	44.8939i	−0.961302	−	1.66502i	−0.242065	−	0.970260i	$-0.577825\pi$
$728$	−51.3497	+	88.9402i	−1.90315	+	3.29634i
$729$	−4.02608			−0.149114
$730$	−21.9498			−0.812398
$731$	21.3698	−	37.0135i	0.790389	−	1.36899i
$732$	33.0491			1.22153
$733$	−9.61709	−	16.6573i	−0.355215	−	0.615251i	0.631940	−	0.775018i	$-0.282259\pi$
$733$	−9.61709	−	16.6573i	−0.355215	−	0.615251i	−0.987155	+	0.159767i	$0.948926\pi$
$734$	55.2978			2.04108
$735$	8.42755	+	14.5970i	0.310855	+	0.538417i
$736$	−0.508997	−	0.881609i	−0.0187619	−	0.0324966i
$737$	22.3232	+	38.6649i	0.822286	+	1.42424i
$738$	−0.0190858	+	0.0330576i	−0.000702559	+	0.00121687i
$739$	26.2900			0.967094			0.483547	−	0.875318i	$-0.339348\pi$
$739$	26.2900			0.967094			0.483547	+	0.875318i	$0.339348\pi$
$740$	9.91855	−	23.2568i	0.364613	−	0.854937i
$741$	57.3885			2.10822
$742$	−1.49572	+	2.59066i	−0.0549095	+	0.0951060i
$743$	6.45859	+	11.1866i	0.236943	+	0.410397i	0.959835	−	0.280563i	$-0.0905213\pi$
$743$	6.45859	+	11.1866i	0.236943	+	0.410397i	−0.722893	+	0.690960i	$0.757188\pi$
$744$	−9.43073	−	16.3345i	−0.345747	−	0.598852i
$745$	2.19024	+	3.79360i	0.0802440	+	0.138987i
$746$	25.2750			0.925383
$747$	4.42723	+	7.66819i	0.161984	+	0.280564i
$748$	−95.8017			−3.50286
$749$	0.575697	−	0.997137i	0.0210355	−	0.0364346i
$750$	−5.46902			−0.199701
$751$	−4.23561			−0.154560			−0.0772798	−	0.997009i	$-0.524623\pi$
$751$	−4.23561			−0.154560			−0.0772798	+	0.997009i	$0.524623\pi$
$752$	6.15849	−	10.6668i	0.224577	−	0.388979i
$753$	−8.27264	−	14.3286i	−0.301472	−	0.522164i
$754$	−50.6919			−1.84609
$755$	−6.77765	+	11.7392i	−0.246664	+	0.427235i
$756$	−20.0167	+	34.6699i	−0.728000	+	1.26093i
$757$	−16.8505	+	29.1860i	−0.612443	+	1.06078i	0.378384	+	0.925649i	$0.376480\pi$
$757$	−16.8505	+	29.1860i	−0.612443	+	1.06078i	−0.990827	+	0.135134i	$0.956854\pi$
$758$	−31.5925	−	54.7198i	−1.14749	−	1.98751i
$759$	3.35000	+	5.80236i	0.121597	+	0.210612i
$760$	−13.8910	+	24.0600i	−0.503881	+	0.872747i
$761$	−13.8817	+	24.0438i	−0.503210	+	0.871585i	0.496783	+	0.867875i	$0.334514\pi$
$761$	−13.8817	+	24.0438i	−0.503210	+	0.871585i	−0.999993	+	0.00371069i	$0.998819\pi$
$762$	−19.1607	+	33.1874i	−0.694121	+	1.20225i
$763$	38.1465			1.38100
$764$	−38.5660	−	66.7982i	−1.39527	−	2.41667i
$765$	4.44083	−	7.69174i	0.160558	−	0.278095i
$766$	−40.1892			−1.45210
$767$	75.3318			2.72007
$768$	35.9554	−	62.2765i	1.29743	−	2.24721i
$769$	−14.4316			−0.520417			−0.260209	−	0.965552i	$-0.583791\pi$
$769$	−14.4316			−0.520417			−0.260209	+	0.965552i	$0.583791\pi$
$770$	22.8961	+	39.6572i	0.825117	+	1.42914i
$771$	−56.2890			−2.02720
$772$	37.7163	+	65.3266i	1.35744	+	2.35116i
$773$	3.55511	+	6.15763i	0.127868	+	0.221475i	0.922851	−	0.385158i	$-0.125853\pi$
$773$	3.55511	+	6.15763i	0.127868	+	0.221475i	−0.794982	+	0.606633i	$0.792520\pi$
$774$	20.6150	+	35.7062i	0.740991	+	1.28343i
$775$	−0.799593	+	1.38494i	−0.0287222	+	0.0497484i
$776$	17.0983			0.613792
$777$	20.1292	−	47.1984i	0.722130	−	1.69323i
$778$	15.4008			0.552146
$779$	0.0214914	−	0.0372242i	0.000770010	−	0.00133370i
$780$	−22.9722	−	39.7891i	−0.822538	−	1.42468i
$781$	−11.5736	−	20.0461i	−0.414137	−	0.717306i
$782$	−3.73782	−	6.47409i	−0.133664	−	0.231513i
$783$	−10.2523			−0.366389
$784$	−18.9800	−	32.8743i	−0.677857	−	1.17408i
$785$	20.1930			0.720718
$786$	39.2099	−	67.9135i	1.39857	−	2.42240i
$787$	5.68459			0.202634			0.101317	−	0.994854i	$-0.467694\pi$
$787$	5.68459			0.202634			0.101317	+	0.994854i	$0.467694\pi$
$788$	13.7574			0.490086
$789$	13.0258	−	22.5613i	0.463729	−	0.803202i
$790$	3.56053	+	6.16703i	0.126678	+	0.219413i
$791$	−28.9150			−1.02810
$792$	23.9749	−	41.5258i	0.851912	−	1.47555i
$793$	9.04502	−	15.6664i	0.321198	−	0.556331i
$794$	−22.2568	+	38.5499i	−0.789865	+	1.36809i
$795$	−0.347172	−	0.601320i	−0.0123129	−	0.0213266i
$796$	−39.5203	−	68.4511i	−1.40076	−	2.42619i
$797$	−2.80836	+	4.86422i	−0.0994772	+	0.172300i	−0.911468	−	0.411370i	$-0.865050\pi$
$797$	−2.80836	+	4.86422i	−0.0994772	+	0.172300i	0.811991	+	0.583670i	$0.198384\pi$
$798$	−54.3353	+	94.1116i	−1.92345	+	3.33151i
$799$	5.92966	−	10.2705i	0.209776	−	0.363343i
$800$	1.61494			0.0570969
$801$	−16.6043	−	28.7595i	−0.586683	−	1.01617i
$802$	20.5972	−	35.6754i	0.727312	−	1.25974i
$803$	−42.6586			−1.50539
$804$	84.8235			2.99150
$805$	−1.20624	+	2.08926i	−0.0425142	+	0.0736368i
$806$	−19.8987			−0.700903
$807$	−7.49485	−	12.9815i	−0.263831	−	0.456969i
$808$	41.8439			1.47206
$809$	12.2303	+	21.1835i	0.429994	+	0.744772i	0.996872	−	0.0790300i	$-0.0251823\pi$
$809$	12.2303	+	21.1835i	0.429994	+	0.744772i	−0.566878	+	0.823802i	$0.691849\pi$
$810$	−13.7978	−	23.8985i	−0.484805	−	0.839707i
$811$	−17.0663	−	29.5597i	−0.599279	−	1.03798i	−0.992928	−	0.118720i	$-0.962121\pi$
$811$	−17.0663	−	29.5597i	−0.599279	−	1.03798i	0.393649	−	0.919261i	$-0.371212\pi$
$812$	32.4036	−	56.1247i	1.13714	−	1.96959i
$813$	6.16786			0.216316
$814$	28.5515	−	66.9468i	1.00073	−	2.34648i
$815$	2.52719			0.0885236
$816$	−26.1478	+	45.2892i	−0.915354	+	1.58544i
$817$	−23.2133	−	40.2067i	−0.812132	−	1.40665i
$818$	−35.3659	−	61.2556i	−1.23654	−	2.14175i
$819$	−17.8322	−	30.8863i	−0.623108	−	1.07925i
$820$	−0.0344115			−0.00120170
$821$	4.50674	+	7.80590i	0.157286	+	0.272428i	0.933889	−	0.357563i	$-0.116392\pi$
$821$	4.50674	+	7.80590i	0.157286	+	0.272428i	−0.776603	+	0.629990i	$0.783059\pi$
$822$	−0.799038			−0.0278696
$823$	−25.5771	+	44.3009i	−0.891563	+	1.54423i	−0.0535605	+	0.998565i	$0.517057\pi$
$823$	−25.5771	+	44.3009i	−0.891563	+	1.54423i	−0.838002	+	0.545667i	$0.816276\pi$
$824$	−42.4279			−1.47804
$825$	−10.6289			−0.370049
$826$	−71.3241	+	123.537i	−2.48168	+	4.29840i
$827$	9.67577	+	16.7589i	0.336459	+	0.582765i	0.983764	−	0.179467i	$-0.0574372\pi$
$827$	9.67577	+	16.7589i	0.336459	+	0.582765i	−0.647305	+	0.762231i	$0.724104\pi$
$828$	4.86887			0.169205
$829$	−9.55444	+	16.5488i	−0.331839	+	0.574763i	−0.982873	−	0.184287i	$-0.941003\pi$
$829$	−9.55444	+	16.5488i	−0.331839	+	0.574763i	0.651033	+	0.759049i	$0.274336\pi$
$830$	−5.91151	+	10.2390i	−0.205191	+	0.355402i
$831$	23.3728	−	40.4829i	0.810793	−	1.40434i
$832$	−14.8464	−	25.7147i	−0.514706	−	0.891496i
$833$	−18.2748	−	31.6528i	−0.633183	−	1.09670i
$834$	−0.562806	+	0.974809i	−0.0194884	+	0.0337549i
$835$	−11.3674	+	19.6890i	−0.393386	+	0.681365i
$836$	−52.0333	+	90.1243i	−1.79961	+	3.11701i
$837$	−4.02448			−0.139106
$838$	15.4490	+	26.7584i	0.533676	+	0.924353i
$839$	−10.5018	+	18.1896i	−0.362561	+	0.627975i	−0.988382	−	0.151992i	$-0.951431\pi$
$839$	−10.5018	+	18.1896i	−0.362561	+	0.627975i	0.625820	+	0.779967i	$0.284764\pi$
$840$	45.1389			1.55744
$841$	−12.4032			−0.427697
$842$	−45.2531	+	78.3807i	−1.55952	+	2.70118i
$843$	−33.2829			−1.14632
$844$	−12.2522	−	21.2214i	−0.421737	−	0.730469i
$845$	−12.1486			−0.417923
$846$	5.72024	+	9.90774i	0.196666	+	0.340635i
$847$	23.4484	+	40.6139i	0.805698	+	1.39551i
$848$	0.781879	+	1.35425i	0.0268498	+	0.0465053i
$849$	−4.30192	+	7.45115i	−0.147642	+	0.255723i
$850$	11.8593			0.406771
$851$	3.80653	−	0.460825i	0.130486	−	0.0157969i
$852$	−43.9774			−1.50664
$853$	25.2188	−	43.6803i	0.863477	−	1.49559i	−0.00507488	−	0.999987i	$-0.501615\pi$
$853$	25.2188	−	43.6803i	0.863477	−	1.49559i	0.868552	−	0.495599i	$-0.165051\pi$
$854$	17.1276	+	29.6659i	0.586095	+	1.01515i
$855$	−4.82394	−	8.35531i	−0.164975	−	0.285746i
$856$	−0.804927	−	1.39417i	−0.0275118	−	0.0476519i
$857$	39.3760			1.34506			0.672529	−	0.740071i	$-0.265208\pi$
$857$	39.3760			1.34506			0.672529	+	0.740071i	$0.265208\pi$
$858$	−66.1276	−	114.536i	−2.25756	−	3.91021i
$859$	45.9613			1.56818			0.784090	−	0.620647i	$-0.213130\pi$
$859$	45.9613			1.56818			0.784090	+	0.620647i	$0.213130\pi$
$860$	−18.5843	+	32.1890i	−0.633719	+	1.09763i
$861$	−0.0698364			−0.00238002
$862$	−87.5434			−2.98174
$863$	13.2567	−	22.9613i	0.451264	−	0.781612i	−0.547201	−	0.837001i	$-0.684307\pi$
$863$	13.2567	−	22.9613i	0.451264	−	0.781612i	0.998465	+	0.0553895i	$0.0176400\pi$
$864$	2.03207	+	3.51965i	0.0691325	+	0.119741i
$865$	−14.3750			−0.488765
$866$	15.3202	−	26.5354i	0.520602	−	0.901709i
$867$	−6.44096	+	11.1561i	−0.218747	+	0.378880i
$868$	12.7198	−	22.0313i	0.431738	−	0.747792i
$869$	6.91977	+	11.9854i	0.234737	+	0.406577i
$870$	11.1402	+	19.2954i	0.377687	+	0.654174i
$871$	23.2149	−	40.2093i	0.786606	−	1.36244i
$872$	26.6678	−	46.1899i	0.903085	−	1.56419i
$873$	−2.96886	+	5.14221i	−0.100481	+	0.174037i
$874$	−8.12056			−0.274682
$875$	−1.91357	−	3.31440i	−0.0646905	−	0.112047i
$876$	−40.5235	+	70.1887i	−1.36916	+	2.37146i
$877$	−38.0090			−1.28347			−0.641736	−	0.766926i	$-0.721785\pi$
$877$	−38.0090			−1.28347			−0.641736	+	0.766926i	$0.721785\pi$
$878$	−37.6910			−1.27201
$879$	−12.3435	+	21.3796i	−0.416337	+	0.721117i
$880$	23.9376			0.806937
$881$	−9.82834	−	17.0232i	−0.331125	−	0.573526i	0.651608	−	0.758556i	$-0.274095\pi$
$881$	−9.82834	−	17.0232i	−0.331125	−	0.573526i	−0.982733	+	0.185031i	$0.940762\pi$
$882$	35.2586			1.18722
$883$	8.25390	+	14.2962i	0.277766	+	0.481104i	0.970829	−	0.239772i	$-0.0770727\pi$
$883$	8.25390	+	14.2962i	0.277766	+	0.481104i	−0.693063	+	0.720877i	$0.743739\pi$
$884$	49.8142	+	86.2808i	1.67543	+	2.90194i
$885$	−16.5551	−	28.6743i	−0.556493	−	0.963875i
$886$	−18.4956	+	32.0354i	−0.621373	+	1.07625i
$887$	−5.97807			−0.200724			−0.100362	−	0.994951i	$-0.532000\pi$
$887$	−5.97807			−0.200724			−0.100362	+	0.994951i	$0.532000\pi$
$888$	−43.0785	−	57.3694i	−1.44562	−	1.92519i
$889$	−26.8168			−0.899407
$890$	22.1710	−	38.4014i	0.743175	−	1.28722i
$891$	−26.8155	−	46.4458i	−0.898353	−	1.55599i
$892$	−37.1982	−	64.4291i	−1.24549	−	2.15725i
$893$	−6.44122	−	11.1565i	−0.215547	−	0.373339i
$894$	23.9569			0.801239
$895$	−8.06753	−	13.9734i	−0.269668	−	0.467078i
$896$	68.5874			2.29134
$897$	3.48381	−	6.03414i	0.116321	−	0.201474i
$898$	33.5674			1.12016
$899$	6.51495			0.217286
$900$	−3.86199	+	6.68916i	−0.128733	+	0.222972i
$901$	0.752826	+	1.30393i	0.0250803	+	0.0434403i
$902$	−0.0990567			−0.00329823
$903$	−37.7158	+	65.3258i	−1.25510	+	2.17391i
$904$	−20.2141	+	35.0119i	−0.672312	+	1.16448i
$905$	5.45954	−	9.45621i	0.181481	−	0.314335i
$906$	37.0672	+	64.2022i	1.23147	+	2.13297i
$907$	13.1319	+	22.7451i	0.436038	+	0.755239i	0.997380	−	0.0723445i	$-0.0230481\pi$
$907$	13.1319	+	22.7451i	0.436038	+	0.755239i	−0.561342	+	0.827584i	$0.689715\pi$
$908$	−10.4395	+	18.0818i	−0.346448	+	0.600065i
$909$	−7.26557	+	12.5843i	−0.240984	+	0.417396i
$910$	23.8106	−	41.2412i	0.789315	−	1.36713i
$911$	−13.6704			−0.452920			−0.226460	−	0.974021i	$-0.572715\pi$
$911$	−13.6704			−0.452920			−0.226460	+	0.974021i	$0.572715\pi$
$912$	28.4035	+	49.1964i	0.940535	+	1.62905i
$913$	−11.4888	+	19.8992i	−0.380224	+	0.658567i
$914$	81.7766			2.70493
$915$	−7.95102			−0.262853
$916$	−19.0611	+	33.0147i	−0.629795	+	1.09084i
$917$	54.8770			1.81220
$918$	14.9225	+	25.8465i	0.492515	+	0.853062i
$919$	−19.0662			−0.628936			−0.314468	−	0.949268i	$-0.601826\pi$
$919$	−19.0662			−0.628936			−0.314468	+	0.949268i	$0.601826\pi$
$920$	1.68653	+	2.92116i	0.0556033	+	0.0963077i
$921$	34.9042	+	60.4558i	1.15013	+	1.99209i
$922$	−3.31203	−	5.73661i	−0.109076	−	0.188925i
$923$	−12.0359	+	20.8468i	−0.396167	+	0.686181i
$924$	169.082			5.56239
$925$	−2.38623	+	5.59517i	−0.0784586	+	0.183968i
$926$	10.9279			0.359114
$927$	7.36696	−	12.7600i	0.241963	−	0.419092i
$928$	−3.28958	−	5.69771i	−0.107986	−	0.187037i
$929$	0.482019	+	0.834881i	0.0158145	+	0.0273916i	0.873824	−	0.486242i	$-0.161633\pi$
$929$	0.482019	+	0.834881i	0.0158145	+	0.0273916i	−0.858010	+	0.513633i	$0.828299\pi$
$930$	4.37299	+	7.57425i	0.143396	+	0.248369i
$931$	−39.7027			−1.30120
$932$	−47.6589	−	82.5476i	−1.56112	−	2.70394i
$933$	−18.2432			−0.597254
$934$	−27.6819	+	47.9464i	−0.905779	+	1.56886i
$935$	23.0482			0.753756
$936$	−49.8652			−1.62989
$937$	23.3900	−	40.5126i	0.764117	−	1.32349i	−0.176596	−	0.984283i	$-0.556509\pi$
$937$	23.3900	−	40.5126i	0.764117	−	1.32349i	0.940712	−	0.339205i	$-0.110158\pi$
$938$	43.9597	+	76.1403i	1.43533	+	2.48607i
$939$	1.99827			0.0652112
$940$	−5.15676	+	8.93176i	−0.168195	+	0.291322i
$941$	15.2491	−	26.4122i	0.497107	−	0.861014i	−0.502888	−	0.864352i	$-0.667729\pi$
$941$	15.2491	−	26.4122i	0.497107	−	0.861014i	0.999994	+	0.00333761i	$0.00106240\pi$
$942$	55.2179	−	95.6402i	1.79910	−	3.11613i
$943$	−0.00260931	−	0.00451945i	−8.49707e−5	−	0.000147174i
$944$	37.2843	+	64.5783i	1.21350	+	2.10185i
$945$	4.81566	−	8.34096i	0.156653	−	0.271332i
$946$	−53.4966	+	92.6588i	−1.73932	+	3.01260i
$947$	2.94239	−	5.09637i	0.0956148	−	0.165610i	−0.814250	−	0.580514i	$-0.802852\pi$
$947$	2.94239	−	5.09637i	0.0956148	−	0.165610i	0.909865	+	0.414904i	$0.136185\pi$
$948$	26.2937			0.853980
$949$	22.1813	+	38.4191i	0.720035	+	1.24714i
$950$	6.44122	−	11.1565i	0.208981	−	0.361965i
$951$	35.0469			1.13647
$952$	−97.8816			−3.17236
$953$	−1.68491	+	2.91836i	−0.0545797	+	0.0945348i	−0.892024	−	0.451987i	$-0.850715\pi$
$953$	−1.68491	+	2.91836i	−0.0545797	+	0.0945348i	0.837445	+	0.546522i	$0.184049\pi$
$954$	−1.45248			−0.0470256
$955$	9.27828	+	16.0705i	0.300238	+	0.520028i
$956$	−85.1659			−2.75446
$957$	21.6505	+	37.4998i	0.699862	+	1.21220i
$958$	−20.1114	−	34.8340i	−0.649770	−	1.12543i
$959$	−0.279577	−	0.484242i	−0.00902802	−	0.0156370i
$960$	−6.52535	+	11.3022i	−0.210605	+	0.364778i
$961$	−28.4426			−0.917503
$962$	−75.1395	+	9.09651i	−2.42259	+	0.293283i
$963$	0.559054			0.0180153
$964$	11.7834	−	20.4094i	0.379517	−	0.657344i
$965$	−9.07388	−	15.7164i	−0.292098	−	0.505929i
$966$	6.59694	+	11.4262i	0.212253	+	0.367633i
$967$	−3.14762	−	5.45184i	−0.101221	−	0.175319i	0.810967	−	0.585092i	$-0.198941\pi$
$967$	−3.14762	−	5.45184i	−0.101221	−	0.175319i	−0.912188	+	0.409772i	$0.865608\pi$
$968$	65.5701			2.10750
$969$	27.3482	+	47.3684i	0.878549	+	1.52169i
$970$	−7.92839			−0.254565
$971$	11.4789	−	19.8820i	0.368376	−	0.638045i	−0.620936	−	0.783861i	$-0.713247\pi$
$971$	11.4789	−	19.8820i	0.368376	−	0.638045i	0.989312	+	0.145816i	$0.0465807\pi$
$972$	−70.5122			−2.26168
$973$	−0.787687			−0.0252521
$974$	6.06714	−	10.5086i	0.194404	−	0.336717i
$975$	5.52671	+	9.57254i	0.176996	+	0.306567i
$976$	17.9068			0.573182
$977$	18.0057	−	31.1869i	0.576055	−	0.997756i	−0.419871	−	0.907584i	$-0.637925\pi$
$977$	18.0057	−	31.1869i	0.576055	−	0.997756i	0.995926	−	0.0901725i	$-0.0287418\pi$
$978$	6.91063	−	11.9696i	0.220978	−	0.382744i
$979$	43.0886	−	74.6317i	1.37712	−	2.38524i
$980$	15.8927	+	27.5270i	0.507674	+	0.879318i
$981$	9.26092	+	16.0404i	0.295678	+	0.512130i
$982$	42.1105	−	72.9376i	1.34380	−	2.32753i
$983$	−2.27046	+	3.93256i	−0.0724165	+	0.125429i	−0.899960	−	0.435973i	$-0.856404\pi$
$983$	−2.27046	+	3.93256i	−0.0724165	+	0.125429i	0.827543	+	0.561402i	$0.189738\pi$
$984$	−0.0488218	+	0.0845618i	−0.00155638	+	0.00269573i
$985$	−3.30978			−0.105458
$986$	−24.1570	−	41.8411i	−0.769314	−	1.33249i
$987$	−10.4654	+	18.1265i	−0.333116	+	0.576974i
$988$	108.223			3.44305
$989$	−5.63673			−0.179238
$990$	−11.1171	+	19.2553i	−0.353324	+	0.611975i
$991$	−8.48245			−0.269454			−0.134727	−	0.990883i	$-0.543016\pi$
$991$	−8.48245			−0.269454			−0.134727	+	0.990883i	$0.543016\pi$
$992$	−1.29130	−	2.23659i	−0.0409988	−	0.0710119i
$993$	−1.36044			−0.0431724
$994$	−22.7912	−	39.4755i	−0.722893	−	1.25209i
$995$	9.50787	+	16.4681i	0.301420	+	0.522074i
$996$	21.8275	+	37.8064i	0.691632	+	1.19794i
$997$	−16.0716	+	27.8368i	−0.508992	+	0.881599i	0.490954	+	0.871185i	$0.336648\pi$
$997$	−16.0716	+	27.8368i	−0.508992	+	0.881599i	−0.999946	+	0.0104139i	$0.996685\pi$
$998$	−87.4971			−2.76967
$999$	−15.1968	+	1.83975i	−0.480806	+	0.0582072i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	185.2.e.b.121.1	yes	14
5.2	odd	4		925.2.o.c.824.2		28
5.3	odd	4		925.2.o.c.824.13		28
5.4	even	2		925.2.e.b.676.7		14
37.10	even	3		6845.2.a.j.1.7		7
37.26	even	3	inner	185.2.e.b.26.1	✓	14
37.27	even	6		6845.2.a.m.1.1		7
185.63	odd	12		925.2.o.c.174.2		28
185.137	odd	12		925.2.o.c.174.13		28
185.174	even	6		925.2.e.b.26.7		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.e.b.26.1	✓	14	37.26	even	3	inner
185.2.e.b.121.1	yes	14	1.1	even	1	trivial
925.2.e.b.26.7		14	185.174	even	6
925.2.e.b.676.7		14	5.4	even	2
925.2.o.c.174.2		28	185.63	odd	12
925.2.o.c.174.13		28	185.137	odd	12
925.2.o.c.824.2		28	5.2	odd	4
925.2.o.c.824.13		28	5.3	odd	4
6845.2.a.j.1.7		7	37.10	even	3
6845.2.a.m.1.1		7	37.27	even	6

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:	\( N \)	\(=\)	\( 185 = 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	185.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.24062 + 2.14882i) q^{2} +(-1.10207 - 1.90884i) q^{3} +(-2.07829 - 3.59971i) q^{4} +(0.500000 + 0.866025i) q^{5} +5.46902 q^{6} +(1.91357 + 3.31440i) q^{7} +5.35102 q^{8} +(-0.929125 + 1.60929i) q^{9} +O(q^{10})\)	\(q+(-1.24062 + 2.14882i) q^{2} +(-1.10207 - 1.90884i) q^{3} +(-2.07829 - 3.59971i) q^{4} +(0.500000 + 0.866025i) q^{5} +5.46902 q^{6} +(1.91357 + 3.31440i) q^{7} +5.35102 q^{8} +(-0.929125 + 1.60929i) q^{9} -2.48125 q^{10} -4.82222 q^{11} +(-4.58086 + 7.93427i) q^{12} +(2.50742 + 4.34297i) q^{13} -9.49608 q^{14} +(1.10207 - 1.90884i) q^{15} +(-2.48202 + 4.29898i) q^{16} +(-2.38979 + 4.13924i) q^{17} +(-2.30539 - 3.99305i) q^{18} +(2.59596 + 4.49634i) q^{19} +(2.07829 - 3.59971i) q^{20} +(4.21778 - 7.30542i) q^{21} +(5.98255 - 10.3621i) q^{22} +0.630359 q^{23} +(-5.89721 - 10.2143i) q^{24} +(-0.500000 + 0.866025i) q^{25} -12.4430 q^{26} -2.51658 q^{27} +(7.95392 - 13.7766i) q^{28} +4.07392 q^{29} +(2.73451 + 4.73631i) q^{30} +1.59919 q^{31} +(-0.807472 - 1.39858i) q^{32} +(5.31443 + 9.20486i) q^{33} +(-5.92966 - 10.2705i) q^{34} +(-1.91357 + 3.31440i) q^{35} +7.72397 q^{36} +(6.03867 - 0.731052i) q^{37} -12.8824 q^{38} +(5.52671 - 9.57254i) q^{39} +(2.67551 + 4.63412i) q^{40} +(-0.00413940 - 0.00716965i) q^{41} +(10.4654 + 18.1265i) q^{42} -8.94210 q^{43} +(10.0220 + 17.3586i) q^{44} -1.85825 q^{45} +(-0.782038 + 1.35453i) q^{46} -2.48125 q^{47} +10.9414 q^{48} +(-3.82350 + 6.62250i) q^{49} +(-1.24062 - 2.14882i) q^{50} +10.5349 q^{51} +(10.4223 - 18.0519i) q^{52} +(0.157509 - 0.272813i) q^{53} +(3.12213 - 5.40769i) q^{54} +(-2.41111 - 4.17616i) q^{55} +(10.2396 + 17.7354i) q^{56} +(5.72187 - 9.91057i) q^{57} +(-5.05420 + 8.75413i) q^{58} +(7.51090 - 13.0093i) q^{59} -9.16171 q^{60} +(-1.80365 - 3.12402i) q^{61} +(-1.98399 + 3.43637i) q^{62} -7.11178 q^{63} -5.92099 q^{64} +(-2.50742 + 4.34297i) q^{65} -26.3728 q^{66} +(-4.62924 - 8.01808i) q^{67} +19.8667 q^{68} +(-0.694701 - 1.20326i) q^{69} +(-4.74804 - 8.22385i) q^{70} +(2.40006 + 4.15703i) q^{71} +(-4.97176 + 8.61135i) q^{72} +8.84627 q^{73} +(-5.92082 + 13.8830i) q^{74} +2.20414 q^{75} +(10.7903 - 18.6894i) q^{76} +(-9.22765 - 15.9828i) q^{77} +(13.7131 + 23.7518i) q^{78} +(-1.43498 - 2.48545i) q^{79} -4.96403 q^{80} +(5.56083 + 9.63164i) q^{81} +0.0205417 q^{82} +(2.38247 - 4.12657i) q^{83} -35.0632 q^{84} -4.77958 q^{85} +(11.0938 - 19.2150i) q^{86} +(-4.48975 - 7.77647i) q^{87} -25.8038 q^{88} +(-8.93544 + 15.4766i) q^{89} +(2.30539 - 3.99305i) q^{90} +(-9.59624 + 16.6212i) q^{91} +(-1.31007 - 2.26911i) q^{92} +(-1.76242 - 3.05260i) q^{93} +(3.07829 - 5.33176i) q^{94} +(-2.59596 + 4.49634i) q^{95} +(-1.77979 + 3.08268i) q^{96} +3.19533 q^{97} +(-9.48706 - 16.4321i) q^{98} +(4.48044 - 7.76035i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 2 q^{2} - 2 q^{3} - 8 q^{4} + 7 q^{5} + 4 q^{6} + 2 q^{7} - 6 q^{8} - 5 q^{9}+O(q^{10}) \) 14 * q + 2 * q^2 - 2 * q^3 - 8 * q^4 + 7 * q^5 + 4 * q^6 + 2 * q^7 - 6 * q^8 - 5 * q^9	\( 14 q + 2 q^{2} - 2 q^{3} - 8 q^{4} + 7 q^{5} + 4 q^{6} + 2 q^{7} - 6 q^{8} - 5 q^{9} + 4 q^{10} - 10 q^{11} - 8 q^{12} + 6 q^{13} - 36 q^{14} + 2 q^{15} - 14 q^{16} - q^{17} - 4 q^{18} + 6 q^{19} + 8 q^{20} + 13 q^{21} - q^{22} + 12 q^{23} - 21 q^{24} - 7 q^{25} + 2 q^{26} + 22 q^{27} + 13 q^{28} - 12 q^{29} + 2 q^{30} - 8 q^{31} + 18 q^{32} + q^{33} - 11 q^{34} - 2 q^{35} - 8 q^{36} + 12 q^{37} + 16 q^{38} + 23 q^{39} - 3 q^{40} - 3 q^{41} + 29 q^{42} - 38 q^{43} + 25 q^{44} - 10 q^{45} + 10 q^{46} + 4 q^{47} - 20 q^{48} - 7 q^{49} + 2 q^{50} - 14 q^{51} + 46 q^{52} - 2 q^{53} + 23 q^{54} - 5 q^{55} + 19 q^{56} + 22 q^{57} - 12 q^{58} - 18 q^{59} - 16 q^{60} - 20 q^{61} - 21 q^{62} + 46 q^{63} + 50 q^{64} - 6 q^{65} - 42 q^{66} - 20 q^{67} + 110 q^{68} + 17 q^{69} - 18 q^{70} - 11 q^{71} - 29 q^{72} - 36 q^{73} - 66 q^{74} + 4 q^{75} + 40 q^{76} - q^{77} + 6 q^{78} + 23 q^{79} - 28 q^{80} + 29 q^{81} - 24 q^{82} - 9 q^{83} + 8 q^{84} - 2 q^{85} - 3 q^{86} - 43 q^{87} - 116 q^{88} - 16 q^{89} + 4 q^{90} + 12 q^{91} - 33 q^{92} + 25 q^{93} + 22 q^{94} - 6 q^{95} - 67 q^{96} - 62 q^{97} - 24 q^{98} + 4 q^{99}+O(q^{100}) \) 14 * q + 2 * q^2 - 2 * q^3 - 8 * q^4 + 7 * q^5 + 4 * q^6 + 2 * q^7 - 6 * q^8 - 5 * q^9 + 4 * q^10 - 10 * q^11 - 8 * q^12 + 6 * q^13 - 36 * q^14 + 2 * q^15 - 14 * q^16 - q^17 - 4 * q^18 + 6 * q^19 + 8 * q^20 + 13 * q^21 - q^22 + 12 * q^23 - 21 * q^24 - 7 * q^25 + 2 * q^26 + 22 * q^27 + 13 * q^28 - 12 * q^29 + 2 * q^30 - 8 * q^31 + 18 * q^32 + q^33 - 11 * q^34 - 2 * q^35 - 8 * q^36 + 12 * q^37 + 16 * q^38 + 23 * q^39 - 3 * q^40 - 3 * q^41 + 29 * q^42 - 38 * q^43 + 25 * q^44 - 10 * q^45 + 10 * q^46 + 4 * q^47 - 20 * q^48 - 7 * q^49 + 2 * q^50 - 14 * q^51 + 46 * q^52 - 2 * q^53 + 23 * q^54 - 5 * q^55 + 19 * q^56 + 22 * q^57 - 12 * q^58 - 18 * q^59 - 16 * q^60 - 20 * q^61 - 21 * q^62 + 46 * q^63 + 50 * q^64 - 6 * q^65 - 42 * q^66 - 20 * q^67 + 110 * q^68 + 17 * q^69 - 18 * q^70 - 11 * q^71 - 29 * q^72 - 36 * q^73 - 66 * q^74 + 4 * q^75 + 40 * q^76 - q^77 + 6 * q^78 + 23 * q^79 - 28 * q^80 + 29 * q^81 - 24 * q^82 - 9 * q^83 + 8 * q^84 - 2 * q^85 - 3 * q^86 - 43 * q^87 - 116 * q^88 - 16 * q^89 + 4 * q^90 + 12 * q^91 - 33 * q^92 + 25 * q^93 + 22 * q^94 - 6 * q^95 - 67 * q^96 - 62 * q^97 - 24 * q^98 + 4 * q^99

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