LMFDB - Embedded newform 74.3.g.b.45.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,3,Mod(23,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("74.23");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	74.g (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.01635395627$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 82x^{10} + 2505x^{8} + 34456x^{6} + 196096x^{4} + 262464x^{2} + 69696 $ x^12 + 82x^10 + 2505x^8 + 34456x^6 + 196096x^4 + 262464*x^2 + 69696
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			45.1
Root			$4.36026i$ of defining polynomial
Character	$\chi$	$=$	74.45
Dual form			74.3.g.b.51.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36603 - 0.366025i) q^{2} +(-3.77609 - 2.18013i) q^{3} +(1.73205 + 1.00000i) q^{4} +(0.866025 - 0.232051i) q^{5} +(4.36026 + 4.36026i) q^{6} +(-5.10188 + 8.83671i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(5.00591 + 8.67050i) q^{9} +O(q^{10})$	\(q+(-1.36603 - 0.366025i) q^{2} +(-3.77609 - 2.18013i) q^{3} +(1.73205 + 1.00000i) q^{4} +(0.866025 - 0.232051i) q^{5} +(4.36026 + 4.36026i) q^{6} +(-5.10188 + 8.83671i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(5.00591 + 8.67050i) q^{9} -1.26795 q^{10} +17.7559i q^{11} +(-4.36026 - 7.55218i) q^{12} +(-8.58823 + 2.30121i) q^{13} +(10.2038 - 10.2038i) q^{14} +(-3.77609 - 1.01180i) q^{15} +(2.00000 + 3.46410i) q^{16} +(6.79433 - 25.3568i) q^{17} +(-3.66458 - 13.6764i) q^{18} +(-20.4467 + 5.47869i) q^{19} +(1.73205 + 0.464102i) q^{20} +(38.5303 - 22.2455i) q^{21} +(6.49913 - 24.2551i) q^{22} +(-2.06993 - 2.06993i) q^{23} +(3.19193 + 11.9124i) q^{24} +(-20.9545 + 12.0981i) q^{25} +12.5740 q^{26} -4.41183i q^{27} +(-17.6734 + 10.2038i) q^{28} +(-11.3391 + 11.3391i) q^{29} +(4.78789 + 2.76429i) q^{30} +(12.3224 - 12.3224i) q^{31} +(-1.46410 - 5.46410i) q^{32} +(38.7102 - 67.0481i) q^{33} +(-18.5625 + 32.1511i) q^{34} +(-2.36779 + 8.83671i) q^{35} +20.0237i q^{36} +(-34.4233 + 13.5659i) q^{37} +29.9361 q^{38} +(37.4469 + 10.0339i) q^{39} +(-2.19615 - 1.26795i) q^{40} +(36.8085 + 21.2514i) q^{41} +(-60.7758 + 16.2848i) q^{42} +(-26.4125 - 26.4125i) q^{43} +(-17.7559 + 30.7542i) q^{44} +(6.34725 + 6.34725i) q^{45} +(2.06993 + 3.58523i) q^{46} -19.4657 q^{47} -17.4410i q^{48} +(-27.5583 - 47.7324i) q^{49} +(33.0526 - 8.85641i) q^{50} +(-80.9371 + 80.9371i) q^{51} +(-17.1765 - 4.60242i) q^{52} +(18.8493 + 32.6479i) q^{53} +(-1.61484 + 6.02667i) q^{54} +(4.12028 + 15.3771i) q^{55} +(27.8772 - 7.46967i) q^{56} +(89.1530 + 23.8885i) q^{57} +(19.6398 - 11.3391i) q^{58} +(20.4083 - 76.1648i) q^{59} +(-5.52858 - 5.52858i) q^{60} +(26.6673 + 99.5236i) q^{61} +(-21.3430 + 12.3224i) q^{62} -102.158 q^{63} +8.00000i q^{64} +(-6.90363 + 3.98581i) q^{65} +(-77.4204 + 77.4204i) q^{66} +(60.8125 + 35.1101i) q^{67} +(37.1249 - 37.1249i) q^{68} +(3.30354 + 12.3290i) q^{69} +(6.46892 - 11.2045i) q^{70} +(38.7519 - 67.1203i) q^{71} +(7.32917 - 27.3528i) q^{72} -39.1385i q^{73} +(51.9886 - 5.93160i) q^{74} +105.501 q^{75} +(-40.8935 - 10.9574i) q^{76} +(-156.904 - 90.5887i) q^{77} +(-47.4807 - 27.4130i) q^{78} +(-38.9698 + 10.4419i) q^{79} +(2.53590 + 2.53590i) q^{80} +(35.4349 - 61.3750i) q^{81} +(-42.5028 - 42.5028i) q^{82} +(-56.1474 - 97.2502i) q^{83} +88.9820 q^{84} -23.5363i q^{85} +(26.4125 + 45.7478i) q^{86} +(67.5379 - 18.0967i) q^{87} +(35.5119 - 35.5119i) q^{88} +(58.1258 + 15.5748i) q^{89} +(-6.34725 - 10.9938i) q^{90} +(23.4810 - 87.6322i) q^{91} +(-1.51530 - 5.65516i) q^{92} +(-73.3948 + 19.6661i) q^{93} +(26.5906 + 7.12493i) q^{94} +(-16.4361 + 9.48936i) q^{95} +(-6.38386 + 23.8249i) q^{96} +(73.8639 + 73.8639i) q^{97} +(20.1741 + 75.2908i) q^{98} +(-153.953 + 88.8847i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} + 4 q^{6} - 8 q^{7} - 24 q^{8} + 28 q^{9}+O(q^{10}) $ 12 * q - 6 * q^2 + 4 * q^6 - 8 * q^7 - 24 * q^8 + 28 * q^9	\( 12 q - 6 q^{2} + 4 q^{6} - 8 q^{7} - 24 q^{8} + 28 q^{9} - 36 q^{10} - 4 q^{12} + 16 q^{13} + 16 q^{14} + 24 q^{16} + 40 q^{17} + 28 q^{18} - 26 q^{19} + 66 q^{21} + 4 q^{22} - 80 q^{23} - 4 q^{24} - 54 q^{25} - 124 q^{26} - 12 q^{28} + 16 q^{29} - 6 q^{30} - 32 q^{31} + 24 q^{32} - 20 q^{33} - 10 q^{34} + 12 q^{35} - 148 q^{37} + 92 q^{38} + 216 q^{39} + 36 q^{40} + 66 q^{41} - 46 q^{42} + 152 q^{43} - 16 q^{44} + 84 q^{45} + 80 q^{46} - 112 q^{47} - 160 q^{49} + 168 q^{50} - 446 q^{51} + 32 q^{52} + 74 q^{53} + 230 q^{54} + 28 q^{56} + 50 q^{57} + 84 q^{58} - 114 q^{59} - 12 q^{60} + 448 q^{61} - 204 q^{62} - 784 q^{63} - 138 q^{65} + 40 q^{66} + 468 q^{67} + 20 q^{68} - 278 q^{69} + 18 q^{70} + 116 q^{71} - 56 q^{72} - 2 q^{74} + 76 q^{75} - 52 q^{76} + 60 q^{77} - 366 q^{78} + 114 q^{79} + 72 q^{80} + 14 q^{81} + 128 q^{82} - 20 q^{83} - 80 q^{84} - 152 q^{86} + 770 q^{87} + 32 q^{88} + 340 q^{89} - 84 q^{90} + 792 q^{91} + 68 q^{92} - 498 q^{93} + 20 q^{94} + 60 q^{95} + 8 q^{96} - 356 q^{97} - 160 q^{98} - 348 q^{99}+O(q^{100}) \) 12 * q - 6 * q^2 + 4 * q^6 - 8 * q^7 - 24 * q^8 + 28 * q^9 - 36 * q^10 - 4 * q^12 + 16 * q^13 + 16 * q^14 + 24 * q^16 + 40 * q^17 + 28 * q^18 - 26 * q^19 + 66 * q^21 + 4 * q^22 - 80 * q^23 - 4 * q^24 - 54 * q^25 - 124 * q^26 - 12 * q^28 + 16 * q^29 - 6 * q^30 - 32 * q^31 + 24 * q^32 - 20 * q^33 - 10 * q^34 + 12 * q^35 - 148 * q^37 + 92 * q^38 + 216 * q^39 + 36 * q^40 + 66 * q^41 - 46 * q^42 + 152 * q^43 - 16 * q^44 + 84 * q^45 + 80 * q^46 - 112 * q^47 - 160 * q^49 + 168 * q^50 - 446 * q^51 + 32 * q^52 + 74 * q^53 + 230 * q^54 + 28 * q^56 + 50 * q^57 + 84 * q^58 - 114 * q^59 - 12 * q^60 + 448 * q^61 - 204 * q^62 - 784 * q^63 - 138 * q^65 + 40 * q^66 + 468 * q^67 + 20 * q^68 - 278 * q^69 + 18 * q^70 + 116 * q^71 - 56 * q^72 - 2 * q^74 + 76 * q^75 - 52 * q^76 + 60 * q^77 - 366 * q^78 + 114 * q^79 + 72 * q^80 + 14 * q^81 + 128 * q^82 - 20 * q^83 - 80 * q^84 - 152 * q^86 + 770 * q^87 + 32 * q^88 + 340 * q^89 - 84 * q^90 + 792 * q^91 + 68 * q^92 - 498 * q^93 + 20 * q^94 + 60 * q^95 + 8 * q^96 - 356 * q^97 - 160 * q^98 - 348 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{1}{12}\right)$

Coefficient data

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

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

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

$2$	−1.36603	−	0.366025i	−0.683013	−	0.183013i
$2$	−1.36603	−	0.366025i	−0.683013	−	0.183013i
$3$	−3.77609	−	2.18013i	−1.25870	−	0.726709i	−0.285876	−	0.958267i	$-0.592285\pi$
$3$	−3.77609	−	2.18013i	−1.25870	−	0.726709i	−0.972821	+	0.231557i	$0.925618\pi$
$4$	1.73205	+	1.00000i	0.433013	+	0.250000i
$5$	0.866025	−	0.232051i	0.173205	−	0.0464102i	−0.171174	−	0.985241i	$-0.554756\pi$
$5$	0.866025	−	0.232051i	0.173205	−	0.0464102i	0.344379	+	0.938831i	$0.388089\pi$
$6$	4.36026	+	4.36026i	0.726709	+	0.726709i
$7$	−5.10188	+	8.83671i	−0.728840	+	1.26239i	0.228534	+	0.973536i	$0.426607\pi$
$7$	−5.10188	+	8.83671i	−0.728840	+	1.26239i	−0.957374	+	0.288852i	$0.906727\pi$
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$	5.00591	+	8.67050i	0.556213	+	0.963389i
$10$	−1.26795			−0.126795
$11$			17.7559i			1.61418i	0.590431	+	0.807088i	$0.298958\pi$
$11$			17.7559i			1.61418i	−0.590431	+	0.807088i	$0.701042\pi$
$12$	−4.36026	−	7.55218i	−0.363355	−	0.629349i
$13$	−8.58823	+	2.30121i	−0.660633	+	0.177016i	−0.573532	−	0.819183i	$-0.694427\pi$
$13$	−8.58823	+	2.30121i	−0.660633	+	0.177016i	−0.0871012	+	0.996199i	$0.527760\pi$
$14$	10.2038	−	10.2038i	0.728840	−	0.728840i
$15$	−3.77609	−	1.01180i	−0.251739	−	0.0674534i
$16$	2.00000	+	3.46410i	0.125000	+	0.216506i
$17$	6.79433	−	25.3568i	0.399667	−	1.49158i	−0.414017	−	0.910269i	$-0.635875\pi$
$17$	6.79433	−	25.3568i	0.399667	−	1.49158i	0.813684	−	0.581308i	$-0.197459\pi$
$18$	−3.66458	−	13.6764i	−0.203588	−	0.759801i
$19$	−20.4467	+	5.47869i	−1.07614	+	0.288352i	−0.753015	−	0.658003i	$-0.771401\pi$
$19$	−20.4467	+	5.47869i	−1.07614	+	0.288352i	−0.323129	+	0.946355i	$0.604735\pi$
$20$	1.73205	+	0.464102i	0.0866025	+	0.0232051i
$21$	38.5303	−	22.2455i	1.83478	−	1.05931i
$22$	6.49913	−	24.2551i	0.295415	−	1.10250i
$23$	−2.06993	−	2.06993i	−0.0899970	−	0.0899970i	0.660675	−	0.750672i	$-0.270270\pi$
$23$	−2.06993	−	2.06993i	−0.0899970	−	0.0899970i	−0.750672	+	0.660675i	$0.770270\pi$
$24$	3.19193	+	11.9124i	0.132997	+	0.496352i
$25$	−20.9545	+	12.0981i	−0.838179	+	0.483923i
$26$	12.5740			0.483617
$27$		−	4.41183i		−	0.163401i
$28$	−17.6734	+	10.2038i	−0.631194	+	0.364420i
$29$	−11.3391	+	11.3391i	−0.391002	+	0.391002i	−0.875044	−	0.484043i	$-0.839168\pi$
$29$	−11.3391	+	11.3391i	−0.391002	+	0.391002i	0.484043	+	0.875044i	$0.339168\pi$
$30$	4.78789	+	2.76429i	0.159596	+	0.0921430i
$31$	12.3224	−	12.3224i	0.397496	−	0.397496i	−0.479853	−	0.877349i	$-0.659310\pi$
$31$	12.3224	−	12.3224i	0.397496	−	0.397496i	0.877349	+	0.479853i	$0.159310\pi$
$32$	−1.46410	−	5.46410i	−0.0457532	−	0.170753i
$33$	38.7102	−	67.0481i	1.17304	−	2.03176i
$34$	−18.5625	+	32.1511i	−0.545955	+	0.945622i
$35$	−2.36779	+	8.83671i	−0.0676511	+	0.252478i
$36$			20.0237i			0.556213i
$37$	−34.4233	+	13.5659i	−0.930360	+	0.366647i
$37$	−34.4233	+	13.5659i	−0.930360	+	0.366647i
$38$	29.9361			0.787792
$39$	37.4469	+	10.0339i	0.960176	+	0.257278i
$40$	−2.19615	−	1.26795i	−0.0549038	−	0.0316987i
$41$	36.8085	+	21.2514i	0.897769	+	0.518327i	0.876476	−	0.481446i	$-0.159888\pi$
$41$	36.8085	+	21.2514i	0.897769	+	0.518327i	0.0212932	+	0.999773i	$0.493222\pi$
$42$	−60.7758	+	16.2848i	−1.44704	+	0.387734i
$43$	−26.4125	−	26.4125i	−0.614244	−	0.614244i	0.329805	−	0.944049i	$-0.393017\pi$
$43$	−26.4125	−	26.4125i	−0.614244	−	0.614244i	−0.944049	+	0.329805i	$0.893017\pi$
$44$	−17.7559	+	30.7542i	−0.403544	+	0.698959i
$45$	6.34725	+	6.34725i	0.141050	+	0.141050i
$46$	2.06993	+	3.58523i	0.0449985	+	0.0779397i
$47$	−19.4657			−0.414163			−0.207082	−	0.978324i	$-0.566397\pi$
$47$	−19.4657			−0.414163			−0.207082	+	0.978324i	$0.566397\pi$
$48$		−	17.4410i		−	0.363355i
$49$	−27.5583	−	47.7324i	−0.562415	−	0.974131i
$50$	33.0526	−	8.85641i	0.661051	−	0.177128i
$51$	−80.9371	+	80.9371i	−1.58700	+	1.58700i
$52$	−17.1765	−	4.60242i	−0.330316	−	0.0885080i
$53$	18.8493	+	32.6479i	0.355647	+	0.615999i	0.987228	−	0.159311i	$-0.0509272\pi$
$53$	18.8493	+	32.6479i	0.355647	+	0.615999i	−0.631581	+	0.775310i	$0.717594\pi$
$54$	−1.61484	+	6.02667i	−0.0299045	+	0.111605i
$55$	4.12028	+	15.3771i	0.0749142	+	0.279584i
$56$	27.8772	−	7.46967i	0.497807	−	0.133387i
$57$	89.1530	+	23.8885i	1.56409	+	0.419096i
$58$	19.6398	−	11.3391i	0.338617	−	0.195501i
$59$	20.4083	−	76.1648i	0.345903	−	1.29093i	−0.545650	−	0.838013i	$-0.683717\pi$
$59$	20.4083	−	76.1648i	0.345903	−	1.29093i	0.891553	−	0.452916i	$-0.149616\pi$
$60$	−5.52858	−	5.52858i	−0.0921430	−	0.0921430i
$61$	26.6673	+	99.5236i	0.437168	+	1.63153i	0.735823	+	0.677173i	$0.236795\pi$
$61$	26.6673	+	99.5236i	0.437168	+	1.63153i	−0.298655	+	0.954361i	$0.596538\pi$
$62$	−21.3430	+	12.3224i	−0.344242	+	0.198748i
$63$	−102.158			−1.62156
$64$			8.00000i			0.125000i
$65$	−6.90363	+	3.98581i	−0.106210	+	0.0613202i
$66$	−77.4204	+	77.4204i	−1.17304	+	1.17304i
$67$	60.8125	+	35.1101i	0.907649	+	0.524031i	0.879674	−	0.475577i	$-0.157761\pi$
$67$	60.8125	+	35.1101i	0.907649	+	0.524031i	0.0279750	+	0.999609i	$0.491094\pi$
$68$	37.1249	−	37.1249i	0.545955	−	0.545955i
$69$	3.30354	+	12.3290i	0.0478774	+	0.178681i
$70$	6.46892	−	11.2045i	0.0924132	−	0.160064i
$71$	38.7519	−	67.1203i	0.545801	−	0.945356i	−0.452755	−	0.891635i	$-0.649559\pi$
$71$	38.7519	−	67.1203i	0.545801	−	0.945356i	0.998556	−	0.0537207i	$-0.0171081\pi$
$72$	7.32917	−	27.3528i	0.101794	−	0.379900i
$73$		−	39.1385i		−	0.536144i	−0.963399	−	0.268072i	$-0.913613\pi$
$73$		−	39.1385i		−	0.536144i	0.963399	−	0.268072i	$-0.0863865\pi$
$74$	51.9886	−	5.93160i	0.702549	−	0.0801568i
$75$	105.501			1.40669
$76$	−40.8935	−	10.9574i	−0.538072	−	0.144176i
$77$	−156.904	−	90.5887i	−2.03772	−	1.17648i
$78$	−47.4807	−	27.4130i	−0.608727	−	0.351449i
$79$	−38.9698	+	10.4419i	−0.493288	+	0.132176i	−0.496883	−	0.867817i	$-0.665522\pi$
$79$	−38.9698	+	10.4419i	−0.493288	+	0.132176i	0.00359504	+	0.999994i	$0.498856\pi$
$80$	2.53590	+	2.53590i	0.0316987	+	0.0316987i
$81$	35.4349	−	61.3750i	0.437468	−	0.757716i
$82$	−42.5028	−	42.5028i	−0.518327	−	0.518327i
$83$	−56.1474	−	97.2502i	−0.676475	−	1.17169i	−0.976035	−	0.217612i	$-0.930173\pi$
$83$	−56.1474	−	97.2502i	−0.676475	−	1.17169i	0.299561	−	0.954077i	$-0.403160\pi$
$84$	88.9820			1.05931
$85$		−	23.5363i		−	0.276897i
$86$	26.4125	+	45.7478i	0.307122	+	0.531951i
$87$	67.5379	−	18.0967i	0.776298	−	0.208008i
$88$	35.5119	−	35.5119i	0.403544	−	0.403544i
$89$	58.1258	+	15.5748i	0.653099	+	0.174997i	0.570130	−	0.821555i	$-0.306893\pi$
$89$	58.1258	+	15.5748i	0.653099	+	0.174997i	0.0829694	+	0.996552i	$0.473560\pi$
$90$	−6.34725	−	10.9938i	−0.0705249	−	0.122153i
$91$	23.4810	−	87.6322i	0.258033	−	0.962991i
$92$	−1.51530	−	5.65516i	−0.0164706	−	0.0614691i
$93$	−73.3948	+	19.6661i	−0.789191	+	0.211463i
$94$	26.5906	+	7.12493i	0.282879	+	0.0757972i
$95$	−16.4361	+	9.48936i	−0.173011	+	0.0998880i
$96$	−6.38386	+	23.8249i	−0.0664985	+	0.248176i
$97$	73.8639	+	73.8639i	0.761483	+	0.761483i	0.976590	−	0.215107i	$-0.0690100\pi$
$97$	73.8639	+	73.8639i	0.761483	+	0.761483i	−0.215107	+	0.976590i	$0.569010\pi$
$98$	20.1741	+	75.2908i	0.205858	+	0.768273i
$99$	−153.953	+	88.8847i	−1.55508	+	0.897825i
$100$	−48.3923			−0.483923
$101$			142.906i			1.41492i	0.706756	+	0.707458i	$0.250158\pi$
$101$			142.906i			1.41492i	−0.706756	+	0.707458i	$0.749842\pi$
$102$	140.187	−	80.9371i	1.37438	−	0.793501i
$103$	−83.2756	+	83.2756i	−0.808501	+	0.808501i	−0.984407	−	0.175906i	$-0.943714\pi$
$103$	−83.2756	+	83.2756i	−0.808501	+	0.808501i	0.175906	+	0.984407i	$0.443714\pi$
$104$	21.7789	+	12.5740i	0.209412	+	0.120904i
$105$	28.2062	−	28.2062i	0.268630	−	0.268630i
$106$	−13.7986	−	51.4972i	−0.130176	−	0.485823i
$107$	−79.0074	+	136.845i	−0.738387	+	1.27892i	0.214834	+	0.976651i	$0.431079\pi$
$107$	−79.0074	+	136.845i	−0.738387	+	1.27892i	−0.953221	+	0.302274i	$0.902254\pi$
$108$	4.41183	−	7.64152i	0.0408503	−	0.0707548i
$109$	41.0734	−	153.288i	0.376820	−	1.40631i	−0.473847	−	0.880607i	$-0.657135\pi$
$109$	41.0734	−	153.288i	0.376820	−	1.40631i	0.850667	−	0.525705i	$-0.176198\pi$
$110$		−	22.5136i		−	0.204669i
$111$	159.561	+	23.8210i	1.43749	+	0.214604i
$112$	−40.8150			−0.364420
$113$	87.0753	+	23.3317i	0.770578	+	0.206476i	0.622627	−	0.782519i	$-0.286066\pi$
$113$	87.0753	+	23.3317i	0.770578	+	0.206476i	0.147951	+	0.988995i	$0.452732\pi$
$114$	−113.041	−	65.2645i	−0.991592	−	0.572496i
$115$	−2.27294	−	1.31228i	−0.0197647	−	0.0114112i
$116$	−30.9789	+	8.30076i	−0.267059	+	0.0715583i
$117$	−62.9446	−	62.9446i	−0.537988	−	0.537988i
$118$	−55.7565	+	96.5731i	−0.472513	+	0.818416i
$119$	189.407	+	189.407i	1.59165	+	1.59165i
$120$	5.52858	+	9.57579i	0.0460715	+	0.0797982i
$121$	−194.273			−1.60557
$122$		−	145.713i		−	1.19437i
$123$	−92.6616	−	160.495i	−0.753346	−	1.30483i
$124$	33.6653	−	9.02060i	0.271495	−	0.0727468i
$125$	−31.1891	+	31.1891i	−0.249513	+	0.249513i
$126$	139.551	+	37.3925i	1.10755	+	0.296766i
$127$	99.5825	+	172.482i	0.784115	+	1.35813i	0.929527	+	0.368755i	$0.120216\pi$
$127$	99.5825	+	172.482i	0.784115	+	1.35813i	−0.145412	+	0.989371i	$0.546451\pi$
$128$	2.92820	−	10.9282i	0.0228766	−	0.0853766i
$129$	42.1534	+	157.319i	0.326771	+	1.21952i
$130$	10.8894	−	2.91782i	0.0837649	−	0.0224447i
$131$	−214.119	−	57.3729i	−1.63449	−	0.437961i	−0.679280	−	0.733879i	$-0.737708\pi$
$131$	−214.119	−	57.3729i	−1.63449	−	0.437961i	−0.955213	+	0.295918i	$0.904375\pi$
$132$	134.096	−	77.4204i	1.01588	−	0.586519i
$133$	55.9032	−	208.634i	0.420325	−	1.56867i
$134$	−70.2202	−	70.2202i	−0.524031	−	0.524031i
$135$	−1.02377	−	3.82076i	−0.00758348	−	0.0283019i
$136$	−64.3023	+	37.1249i	−0.472811	+	0.272977i
$137$	−167.999			−1.22627			−0.613134	−	0.789979i	$-0.710091\pi$
$137$	−167.999			−1.22627			−0.613134	+	0.789979i	$0.710091\pi$
$138$		−	18.0509i		−	0.130803i
$139$	−10.2404	+	5.91228i	−0.0736718	+	0.0425344i	−0.536383	−	0.843974i	$-0.680210\pi$
$139$	−10.2404	+	5.91228i	−0.0736718	+	0.0425344i	0.462712	+	0.886509i	$0.346877\pi$
$140$	−12.9378	+	12.9378i	−0.0924132	+	0.0924132i
$141$	73.5042	+	42.4377i	0.521306	+	0.300976i
$142$	−77.5038	+	77.5038i	−0.545801	+	0.545801i
$143$	−40.8601	−	152.492i	−0.285735	−	1.06638i
$144$	−20.0237	+	34.6820i	−0.139053	+	0.240847i
$145$	−7.18867	+	12.4511i	−0.0495770	+	0.0858700i
$146$	−14.3257	+	53.4642i	−0.0981212	+	0.366193i
$147$			240.323i			1.63485i
$148$	−73.1889	−	10.9264i	−0.494520	−	0.0738273i
$149$	−115.269			−0.773616			−0.386808	−	0.922160i	$-0.626422\pi$
$149$	−115.269			−0.773616			−0.386808	+	0.922160i	$0.626422\pi$
$150$	−144.118	−	38.6162i	−0.960784	−	0.257441i
$151$	115.092	+	66.4484i	0.762198	+	0.440055i	0.830084	−	0.557638i	$-0.188292\pi$
$151$	115.092	+	66.4484i	0.762198	+	0.440055i	−0.0678862	+	0.997693i	$0.521625\pi$
$152$	51.8508	+	29.9361i	0.341124	+	0.196948i
$153$	253.868	−	68.0237i	1.65927	−	0.444599i
$154$	181.177	+	181.177i	1.17648	+	1.17648i
$155$	7.81207	−	13.5309i	0.0504005	−	0.0872962i
$156$	54.8260	+	54.8260i	0.351449	+	0.351449i
$157$	61.2844	+	106.148i	0.390346	+	0.676100i	0.992495	−	0.122284i	$-0.0390220\pi$
$157$	61.2844	+	106.148i	0.390346	+	0.676100i	−0.602149	+	0.798384i	$0.705689\pi$
$158$	57.0557			0.361112
$159$		−	164.375i		−	1.03381i
$160$	−2.53590	−	4.39230i	−0.0158494	−	0.0274519i
$161$	28.8519	−	7.73085i	0.179205	−	0.0480177i
$162$	−70.8697	+	70.8697i	−0.437468	+	0.437468i
$163$	60.9494	+	16.3313i	0.373923	+	0.100192i	0.440886	−	0.897563i	$-0.354664\pi$
$163$	60.9494	+	16.3313i	0.373923	+	0.100192i	−0.0669632	+	0.997755i	$0.521331\pi$
$164$	42.5028	+	73.6170i	0.259164	+	0.448884i
$165$	17.9655	−	67.0481i	0.108882	−	0.406352i
$166$	41.1028	+	153.398i	0.247607	+	0.924082i
$167$	87.3862	−	23.4151i	0.523271	−	0.140210i	0.0124917	−	0.999922i	$-0.496024\pi$
$167$	87.3862	−	23.4151i	0.523271	−	0.140210i	0.510779	+	0.859712i	$0.329357\pi$
$168$	−121.552	−	32.5697i	−0.723522	−	0.193867i
$169$	−77.8962	+	44.9734i	−0.460924	+	0.266115i
$170$	−8.61487	+	32.1511i	−0.0506757	+	0.189124i
$171$	−149.858	−	149.858i	−0.876360	−	0.876360i
$172$	−19.3353	−	72.1603i	−0.112414	−	0.419536i
$173$	13.4352	−	7.75682i	0.0776602	−	0.0448371i	−0.460667	−	0.887573i	$-0.652390\pi$
$173$	13.4352	−	7.75682i	0.0776602	−	0.0448371i	0.538327	+	0.842736i	$0.319056\pi$
$174$	−98.8823			−0.568289
$175$		−	246.892i		−	1.41081i
$176$	−61.5084	+	35.5119i	−0.349479	+	0.201772i
$177$	−243.113	+	243.113i	−1.37352	+	1.37352i
$178$	−73.7006	−	42.5511i	−0.414048	−	0.239051i
$179$	−17.8979	+	17.8979i	−0.0999880	+	0.0999880i	−0.755331	−	0.655343i	$-0.772524\pi$
$179$	−17.8979	+	17.8979i	−0.0999880	+	0.0999880i	0.655343	+	0.755331i	$0.272524\pi$
$180$	4.64651	+	17.3410i	0.0258139	+	0.0963389i
$181$	121.298	−	210.094i	0.670154	−	1.16074i	−0.307706	−	0.951481i	$-0.599561\pi$
$181$	121.298	−	210.094i	0.670154	−	1.16074i	0.977860	−	0.209259i	$-0.0671053\pi$
$182$	−64.1512	+	111.113i	−0.352479	+	0.610512i
$183$	116.276	−	433.948i	0.635389	−	2.37130i
$184$			8.27973i			0.0449985i
$185$	−26.6635	+	19.7364i	−0.144127	+	0.106683i
$186$	107.457			0.577728
$187$	450.234	+	120.640i	2.40767	+	0.645133i
$188$	−33.7155	−	19.4657i	−0.179338	−	0.103541i
$189$	38.9861	+	22.5086i	0.206276	+	0.119093i
$190$	25.9254	−	6.94670i	0.136450	−	0.0365616i
$191$	−32.1356	−	32.1356i	−0.168249	−	0.168249i	0.617960	−	0.786209i	$-0.287959\pi$
$191$	−32.1356	−	32.1356i	−0.168249	−	0.168249i	−0.786209	+	0.617960i	$0.787959\pi$
$192$	17.4410	−	30.2087i	0.0908387	−	0.157337i
$193$	−1.51233	−	1.51233i	−0.00783590	−	0.00783590i	0.703178	−	0.711014i	$-0.251764\pi$
$193$	−1.51233	−	1.51233i	−0.00783590	−	0.00783590i	−0.711014	+	0.703178i	$0.751764\pi$
$194$	−73.8639	−	127.936i	−0.380742	−	0.659464i
$195$	34.7583			0.178248
$196$		−	110.233i		−	0.562415i
$197$	49.4741	+	85.6916i	0.251137	+	0.434983i	0.963839	−	0.266484i	$-0.0858620\pi$
$197$	49.4741	+	85.6916i	0.251137	+	0.434983i	−0.712702	+	0.701467i	$0.752529\pi$
$198$	242.838	−	65.0681i	1.22645	−	0.328627i
$199$	85.7924	−	85.7924i	0.431117	−	0.431117i	−0.457891	−	0.889008i	$-0.651395\pi$
$199$	85.7924	−	85.7924i	0.431117	−	0.431117i	0.889008	+	0.457891i	$0.151395\pi$
$200$	66.1051	+	17.7128i	0.330526	+	0.0885641i
$201$	−153.089	−	265.158i	−0.761637	−	1.31919i
$202$	52.3074	−	195.214i	0.258947	−	0.966405i
$203$	−42.3495	−	158.050i	−0.208618	−	0.778574i
$204$	−221.124	+	59.2501i	−1.08394	+	0.290442i
$205$	36.8085	+	9.86281i	0.179554	+	0.0481113i
$206$	144.237	−	83.2756i	0.700182	−	0.404250i
$207$	7.58544	−	28.3092i	0.0366446	−	0.136760i
$208$	−25.1481	−	25.1481i	−0.120904	−	0.120904i
$209$	−97.2792	−	363.051i	−0.465451	−	1.73709i
$210$	−48.8545	+	28.2062i	−0.232640	+	0.134315i
$211$	−295.441			−1.40020			−0.700098	−	0.714046i	$-0.746861\pi$
$211$	−295.441			−1.40020			−0.700098	+	0.714046i	$0.746861\pi$
$212$			75.3972i			0.355647i
$213$	−292.662	+	168.968i	−1.37400	+	0.793278i
$214$	158.015	−	158.015i	0.738387	−	0.738387i
$215$	−29.0029	−	16.7449i	−0.134897	−	0.0778830i
$216$	−8.82366	+	8.82366i	−0.0408503	+	0.0408503i
$217$	46.0220	+	171.757i	0.212083	+	0.791505i
$218$	−112.215	+	194.361i	−0.514746	+	0.891566i
$219$	−85.3270	+	147.791i	−0.389621	+	0.674843i
$220$	−8.24056	+	30.7542i	−0.0374571	+	0.139792i
$221$			233.405i			1.05613i
$222$	−209.245	−	90.9435i	−0.942547	−	0.409656i
$223$	366.144			1.64190			0.820950	−	0.571000i	$-0.193444\pi$
$223$	366.144			1.64190			0.820950	+	0.571000i	$0.193444\pi$
$224$	55.7544	+	14.9393i	0.248903	+	0.0666935i
$225$	−209.793	−	121.124i	−0.932412	−	0.538328i
$226$	−110.407	−	63.7435i	−0.488527	−	0.282051i
$227$	267.918	−	71.7884i	1.18026	−	0.316248i	0.385228	−	0.922822i	$-0.374123\pi$
$227$	267.918	−	71.7884i	1.18026	−	0.316248i	0.795028	+	0.606573i	$0.207456\pi$
$228$	130.529	+	130.529i	0.572496	+	0.572496i
$229$	−94.9999	+	164.545i	−0.414847	+	0.718536i	−0.995412	−	0.0956778i	$-0.969498\pi$
$229$	−94.9999	+	164.545i	−0.414847	+	0.718536i	0.580566	+	0.814214i	$0.302831\pi$
$230$	2.62457	+	2.62457i	0.0114112	+	0.0114112i
$231$	394.990	+	684.142i	1.70991	+	2.96165i
$232$	45.3562			0.195501
$233$			103.968i			0.446214i	0.974794	+	0.223107i	$0.0716200\pi$
$233$			103.968i			0.446214i	−0.974794	+	0.223107i	$0.928380\pi$
$234$	62.9446	+	109.023i	0.268994	+	0.465911i
$235$	−16.8578	+	4.51703i	−0.0717352	+	0.0192214i
$236$	111.513	−	111.513i	0.472513	−	0.472513i
$237$	169.918	+	45.5294i	0.716954	+	0.192107i
$238$	−189.407	−	328.062i	−0.795827	−	1.37841i
$239$	−81.8060	+	305.304i	−0.342284	+	1.27742i	0.553468	+	0.832870i	$0.313304\pi$
$239$	−81.8060	+	305.304i	−0.342284	+	1.27742i	−0.895753	+	0.444553i	$0.853363\pi$
$240$	−4.04720	−	15.1044i	−0.0168633	−	0.0629349i
$241$	−356.512	+	95.5271i	−1.47930	+	0.396378i	−0.906110	−	0.423043i	$-0.860962\pi$
$241$	−356.512	+	95.5271i	−1.47930	+	0.396378i	−0.573193	+	0.819421i	$0.694295\pi$
$242$	265.382	+	71.1090i	1.09662	+	0.293839i
$243$	−301.998	+	174.358i	−1.24279	+	0.717524i
$244$	−53.3345	+	199.047i	−0.218584	+	0.815767i
$245$	−34.9426	−	34.9426i	−0.142623	−	0.142623i
$246$	67.8330	+	253.156i	0.275744	+	1.02909i
$247$	162.994	−	94.1044i	0.659893	−	0.380989i
$248$	−49.2895			−0.198748
$249$			489.634i			1.96640i
$250$	54.0211	−	31.1891i	0.216084	−	0.124756i
$251$	19.1836	−	19.1836i	0.0764288	−	0.0764288i	−0.667859	−	0.744288i	$-0.732789\pi$
$251$	19.1836	−	19.1836i	0.0764288	−	0.0764288i	0.744288	+	0.667859i	$0.232789\pi$
$252$	−176.943	−	102.158i	−0.702156	−	0.405390i
$253$	36.7536	−	36.7536i	0.145271	−	0.145271i
$254$	−72.8995	−	272.065i	−0.287006	−	1.07112i
$255$	−51.3121	+	88.8751i	−0.201224	+	0.348530i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	23.4065	−	87.3541i	0.0910757	−	0.339899i	−0.905320	−	0.424731i	$-0.860369\pi$
$257$	23.4065	−	87.3541i	0.0910757	−	0.339899i	0.996395	+	0.0848319i	$0.0270353\pi$
$258$		−	230.330i		−	0.892754i
$259$	55.7453	−	373.401i	0.215233	−	1.44170i
$260$	−15.9432			−0.0613202
$261$	−155.078	−	41.5529i	−0.594167	−	0.159207i
$262$	271.492	+	156.746i	1.03623	+	0.598266i
$263$	−89.6337	−	51.7500i	−0.340812	−	0.196768i	0.319819	−	0.947479i	$-0.396378\pi$
$263$	−89.6337	−	51.7500i	−0.340812	−	0.196768i	−0.660631	+	0.750711i	$0.729711\pi$
$264$	−211.517	+	56.6757i	−0.801199	+	0.214681i
$265$	23.9000	+	23.9000i	0.0901885	+	0.0901885i
$266$	−152.730	+	264.537i	−0.574174	+	0.994499i
$267$	−185.533	−	185.533i	−0.694882	−	0.694882i
$268$	70.2202	+	121.625i	0.262016	+	0.453824i
$269$	258.578			0.961257			0.480628	−	0.876924i	$-0.340409\pi$
$269$	258.578			0.961257			0.480628	+	0.876924i	$0.340409\pi$
$270$			5.59398i			0.0207184i
$271$	−84.7205	−	146.740i	−0.312622	−	0.541477i	0.666307	−	0.745677i	$-0.267874\pi$
$271$	−84.7205	−	146.740i	−0.312622	−	0.541477i	−0.978929	+	0.204200i	$0.934541\pi$
$272$	101.427	−	27.1773i	0.372894	−	0.0999167i
$273$	−279.716	+	279.716i	−1.02460	+	1.02460i
$274$	229.490	+	61.4918i	0.837556	+	0.224422i
$275$	−214.813	−	372.067i	−0.781137	−	1.35297i
$276$	−6.60708	+	24.6579i	−0.0239387	+	0.0893404i
$277$	92.8979	+	346.700i	0.335371	+	1.25162i	0.903466	+	0.428660i	$0.141014\pi$
$277$	92.8979	+	346.700i	0.335371	+	1.25162i	−0.568095	+	0.822963i	$0.692319\pi$
$278$	16.1527	−	4.32809i	0.0581031	−	0.0155687i
$279$	168.526	+	45.1564i	0.604035	+	0.161851i
$280$	22.4090	−	12.9378i	0.0800322	−	0.0462066i
$281$	87.4414	−	326.336i	0.311180	−	1.16134i	−0.616315	−	0.787500i	$-0.711375\pi$
$281$	87.4414	−	326.336i	0.311180	−	1.16134i	0.927494	−	0.373838i	$-0.121958\pi$
$282$	−84.8753	−	84.8753i	−0.300976	−	0.300976i
$283$	51.2248	+	191.173i	0.181006	+	0.675524i	0.995450	+	0.0952823i	$0.0303754\pi$
$283$	51.2248	+	191.173i	0.181006	+	0.675524i	−0.814444	+	0.580242i	$0.802958\pi$
$284$	134.241	−	77.5038i	0.472678	−	0.272901i
$285$	82.7521			0.290358
$286$			223.264i			0.780643i
$287$	−375.585	+	216.844i	−1.30866	+	0.755555i
$288$	40.0473	−	40.0473i	0.139053	−	0.139053i
$289$	−346.523	−	200.065i	−1.19904	−	0.692267i
$290$	14.3773	−	14.3773i	0.0495770	−	0.0495770i
$291$	−117.884	−	439.950i	−0.405100	−	1.51185i
$292$	39.1385	−	67.7899i	0.134036	−	0.232157i
$293$	−123.242	+	213.461i	−0.420621	+	0.728537i	−0.996000	−	0.0893499i	$-0.971521\pi$
$293$	−123.242	+	213.461i	−0.420621	+	0.728537i	0.575379	+	0.817887i	$0.304854\pi$
$294$	87.9642	−	328.287i	0.299198	−	1.11662i
$295$		−	70.6964i		−	0.239649i
$296$	95.9785	+	41.7148i	0.324252	+	0.140928i
$297$	78.3362			0.263758
$298$	157.460	+	42.1913i	0.528390	+	0.141582i
$299$	22.5404	+	13.0137i	0.0753859	+	0.0435241i
$300$	182.734	+	105.501i	0.609113	+	0.351671i
$301$	368.153	−	98.6463i	1.22310	−	0.327729i
$302$	−132.897	−	132.897i	−0.440055	−	0.440055i
$303$	311.554	−	539.628i	1.02823	−	1.78095i
$304$	−59.8722	−	59.8722i	−0.196948	−	0.196948i
$305$	46.1891	+	80.0018i	0.151440	+	0.262301i
$306$	−371.688			−1.21467
$307$			146.117i			0.475951i	0.971271	+	0.237976i	$0.0764838\pi$
$307$			146.117i			0.475951i	−0.971271	+	0.237976i	$0.923516\pi$
$308$	−181.177	−	313.808i	−0.588238	−	1.01886i
$309$	496.008	−	132.905i	1.60520	−	0.430113i
$310$	−15.6241	+	15.6241i	−0.0504005	+	0.0504005i
$311$	229.430	+	61.4755i	0.737716	+	0.197670i	0.608063	−	0.793889i	$-0.291947\pi$
$311$	229.430	+	61.4755i	0.737716	+	0.197670i	0.129653	+	0.991559i	$0.458614\pi$
$312$	−54.8260	−	94.9614i	−0.175724	−	0.304364i
$313$	−57.4541	+	214.421i	−0.183559	+	0.685053i	0.811375	+	0.584526i	$0.198719\pi$
$313$	−57.4541	+	214.421i	−0.183559	+	0.685053i	−0.994934	+	0.100527i	$0.967947\pi$
$314$	−44.8633	−	167.432i	−0.142877	−	0.533223i
$315$	−88.4717	+	23.7059i	−0.280862	+	0.0752569i
$316$	−77.9396	−	20.8838i	−0.246644	−	0.0660881i
$317$	134.190	−	77.4748i	0.423313	−	0.244400i	−0.273181	−	0.961963i	$-0.588076\pi$
$317$	134.190	−	77.4748i	0.423313	−	0.244400i	0.696494	+	0.717563i	$0.254742\pi$
$318$	−60.1656	+	224.541i	−0.189200	+	0.706104i
$319$	−201.336	−	201.336i	−0.631146	−	0.631146i
$320$	1.85641	+	6.92820i	0.00580127	+	0.0216506i
$321$	596.679	−	344.493i	1.85881	−	1.07319i
$322$	−42.2422			−0.131187
$323$			555.688i			1.72040i
$324$	122.750	−	70.8697i	0.378858	−	0.218734i
$325$	152.122	−	152.122i	0.468067	−	0.468067i
$326$	−77.2807	−	44.6181i	−0.237057	−	0.136865i
$327$	−489.284	+	489.284i	−1.49628	+	1.49628i
$328$	−31.1142	−	116.120i	−0.0948604	−	0.354024i
$329$	99.3115	−	172.013i	0.301859	−	0.522835i
$330$	−49.0826	+	85.0135i	−0.148735	+	0.257617i
$331$	−141.982	+	529.885i	−0.428950	+	1.60086i	0.326194	+	0.945303i	$0.394234\pi$
$331$	−141.982	+	529.885i	−0.428950	+	1.60086i	−0.755144	+	0.655559i	$0.772433\pi$
$332$		−	224.590i		−	0.676475i
$333$	−289.944	−	230.557i	−0.870702	−	0.692365i
$334$	−127.942			−0.383061
$335$	60.8125	+	16.2947i	0.181530	+	0.0486408i
$336$	154.121	+	88.9820i	0.458694	+	0.264827i
$337$	−331.651	−	191.479i	−0.984128	−	0.568187i	−0.0806143	−	0.996745i	$-0.525688\pi$
$337$	−331.651	−	191.479i	−0.984128	−	0.568187i	−0.903514	+	0.428559i	$0.859022\pi$
$338$	122.870	−	32.9228i	0.363520	−	0.0974048i
$339$	−277.938	−	277.938i	−0.819876	−	0.819876i
$340$	23.5363	−	40.7660i	0.0692243	−	0.119900i
$341$	218.795	+	218.795i	0.641629	+	0.641629i
$342$	149.858	+	259.561i	0.438180	+	0.758950i
$343$	62.4130			0.181962
$344$			105.650i			0.307122i
$345$	5.72190	+	9.91061i	0.0165852	+	0.0287264i
$346$	−21.1920	+	5.67839i	−0.0612487	+	0.0164115i
$347$	−100.877	+	100.877i	−0.290711	+	0.290711i	−0.837361	−	0.546650i	$-0.815903\pi$
$347$	−100.877	+	100.877i	−0.290711	+	0.290711i	0.546650	+	0.837361i	$0.315903\pi$
$348$	135.076	+	36.1934i	0.388149	+	0.104004i
$349$	−41.6647	−	72.1654i	−0.119383	−	0.206778i	0.800140	−	0.599813i	$-0.204758\pi$
$349$	−41.6647	−	72.1654i	−0.119383	−	0.206778i	−0.919523	+	0.393035i	$0.871425\pi$
$350$	−90.3686	+	337.260i	−0.258196	+	0.963601i
$351$	10.1525	+	37.8898i	0.0289246	+	0.107948i
$352$	97.0203	−	25.9965i	0.275626	−	0.0738537i
$353$	58.1372	+	15.5778i	0.164695	+	0.0441298i	0.340224	−	0.940344i	$-0.389497\pi$
$353$	58.1372	+	15.5778i	0.164695	+	0.0441298i	−0.175529	+	0.984474i	$0.556164\pi$
$354$	421.083	−	243.113i	1.18950	−	0.686759i
$355$	17.9848	−	67.1203i	0.0506615	−	0.189071i
$356$	85.1021	+	85.1021i	0.239051	+	0.239051i
$357$	−302.287	−	1128.15i	−0.846741	−	3.16008i
$358$	31.0000	−	17.8979i	0.0865922	−	0.0499940i
$359$	469.508			1.30782			0.653911	−	0.756572i	$-0.273127\pi$
$359$	469.508			1.30782			0.653911	+	0.756572i	$0.273127\pi$
$360$		−	25.3890i		−	0.0705249i
$361$	75.4178	−	43.5425i	0.208914	−	0.120616i
$362$	−242.596	+	242.596i	−0.670154	+	0.670154i
$363$	733.594	+	423.541i	2.02092	+	1.16678i
$364$	128.302	−	128.302i	0.352479	−	0.352479i
$365$	−9.08213	−	33.8950i	−0.0248825	−	0.0928629i
$366$	−317.672	+	550.224i	−0.867957	+	1.50335i
$367$	−85.2906	+	147.728i	−0.232399	+	0.402528i	−0.958514	−	0.285046i	$-0.907991\pi$
$367$	−85.2906	+	147.728i	−0.232399	+	0.402528i	0.726114	+	0.687574i	$0.241324\pi$
$368$	3.03059	−	11.3103i	0.00823530	−	0.0307346i
$369$			425.531i			1.15320i
$370$	43.6470	−	17.2009i	0.117965	−	0.0464890i
$371$	−384.667			−1.03684
$372$	−146.790	−	39.3321i	−0.394595	−	0.105732i
$373$	−281.954	−	162.786i	−0.755910	−	0.436425i	0.0719154	−	0.997411i	$-0.477089\pi$
$373$	−281.954	−	162.786i	−0.755910	−	0.436425i	−0.827825	+	0.560986i	$0.810422\pi$
$374$	−570.874	−	329.594i	−1.52640	−	0.881268i
$375$	185.769	−	49.7767i	0.495385	−	0.132738i
$376$	38.9314	+	38.9314i	0.103541	+	0.103541i
$377$	71.2888	−	123.476i	0.189095	−	0.327522i
$378$	−45.0173	−	45.0173i	−0.119093	−	0.119093i
$379$	116.085	+	201.066i	0.306294	+	0.530516i	0.977548	−	0.210711i	$-0.0675778\pi$
$379$	116.085	+	201.066i	0.306294	+	0.530516i	−0.671255	+	0.741227i	$0.734244\pi$
$380$	−37.9575			−0.0998880
$381$		−	868.411i		−	2.27929i
$382$	32.1356	+	55.6604i	0.0841245	+	0.145708i
$383$	−367.978	+	98.5994i	−0.960778	+	0.257440i	−0.704930	−	0.709277i	$-0.749021\pi$
$383$	−367.978	+	98.5994i	−0.960778	+	0.257440i	−0.255848	+	0.966717i	$0.582355\pi$
$384$	−34.8820	+	34.8820i	−0.0908387	+	0.0908387i
$385$	−156.904	−	42.0423i	−0.407543	−	0.109201i
$386$	1.51233	+	2.61943i	0.00391795	+	0.00678609i
$387$	96.7908	−	361.228i	0.250105	−	0.933406i
$388$	54.0721	+	201.800i	0.139361	+	0.520103i
$389$	19.2029	−	5.14540i	0.0493648	−	0.0132273i	−0.234052	−	0.972224i	$-0.575199\pi$
$389$	19.2029	−	5.14540i	0.0493648	−	0.0132273i	0.283417	+	0.958997i	$0.408532\pi$
$390$	−47.4807	−	12.7224i	−0.121745	−	0.0326216i
$391$	−66.5507	+	38.4230i	−0.170206	+	0.0982687i
$392$	−40.3482	+	150.582i	−0.102929	+	0.384137i
$393$	683.452	+	683.452i	1.73906	+	1.73906i
$394$	−36.2175	−	135.166i	−0.0919227	−	0.343060i
$395$	−31.3258	+	18.0859i	−0.0793057	+	0.0457872i
$396$	−355.539			−0.897825
$397$		−	398.530i		−	1.00385i	−0.864910	−	0.501927i	$-0.832625\pi$
$397$		−	398.530i		−	1.00385i	0.864910	−	0.501927i	$-0.167375\pi$
$398$	−148.597	+	85.7924i	−0.373359	+	0.215559i
$399$	−665.943	+	665.943i	−1.66903	+	1.66903i
$400$	−83.8179	−	48.3923i	−0.209545	−	0.120981i
$401$	180.274	−	180.274i	0.449560	−	0.449560i	−0.445648	−	0.895208i	$-0.647027\pi$
$401$	180.274	−	180.274i	0.449560	−	0.449560i	0.895208	+	0.445648i	$0.147027\pi$
$402$	112.069	+	418.247i	0.278778	+	1.04042i
$403$	−77.4710	+	134.184i	−0.192236	+	0.332962i
$404$	−142.906	+	247.521i	−0.353729	+	0.612676i
$405$	16.4454	−	61.3750i	0.0406059	−	0.151543i
$406$			231.402i			0.569955i
$407$	−240.876	−	611.219i	−0.591833	−	1.50177i
$408$	323.748			0.793501
$409$	350.616	+	93.9474i	0.857253	+	0.229700i	0.660568	−	0.750767i	$-0.270316\pi$
$409$	350.616	+	93.9474i	0.857253	+	0.229700i	0.196685	+	0.980467i	$0.436982\pi$
$410$	−46.6713	−	26.9457i	−0.113833	−	0.0657212i
$411$	634.378	+	366.258i	1.54350	+	0.891140i
$412$	−227.513	+	60.9619i	−0.552216	+	0.147966i
$413$	568.926	+	568.926i	1.37754	+	1.37754i
$414$	−20.7238	+	35.8947i	−0.0500575	+	0.0867021i
$415$	−71.1921	−	71.1921i	−0.171547	−	0.171547i
$416$	25.1481	+	43.5577i	0.0604521	+	0.104706i
$417$	51.5581			0.123641
$418$			531.544i			1.27164i
$419$	−307.868	−	533.243i	−0.734769	−	1.27266i	−0.954825	−	0.297169i	$-0.903957\pi$
$419$	−307.868	−	533.243i	−0.734769	−	1.27266i	0.220056	−	0.975487i	$-0.429376\pi$
$420$	77.0607	−	20.6483i	0.183478	−	0.0491627i
$421$	−110.483	+	110.483i	−0.262430	+	0.262430i	−0.826041	−	0.563611i	$-0.809412\pi$
$421$	−110.483	+	110.483i	−0.262430	+	0.262430i	0.563611	+	0.826041i	$0.309412\pi$
$422$	403.581	+	108.139i	0.956352	+	0.256254i
$423$	−97.4435	−	168.777i	−0.230363	−	0.399000i
$424$	27.5973	−	102.994i	0.0650879	−	0.242911i
$425$	164.397	+	613.537i	0.386816	+	1.44362i
$426$	461.630	−	123.693i	1.08364	−	0.290360i
$427$	−1015.51	−	272.106i	−2.37825	−	0.637251i
$428$	−273.690	+	158.015i	−0.639462	+	0.369194i
$429$	−178.161	+	664.904i	−0.415293	+	1.54989i
$430$	33.4897	+	33.4897i	0.0778830	+	0.0778830i
$431$	68.9204	+	257.215i	0.159908	+	0.596786i	0.998635	+	0.0522330i	$0.0166339\pi$
$431$	68.9204	+	257.215i	0.159908	+	0.596786i	−0.838727	+	0.544553i	$0.816699\pi$
$432$	15.2830	−	8.82366i	0.0353774	−	0.0204251i
$433$	−152.503			−0.352200			−0.176100	−	0.984372i	$-0.556348\pi$
$433$	−152.503			−0.352200			−0.176100	+	0.984372i	$0.556348\pi$
$434$		−	251.469i		−	0.579422i
$435$	54.2902	−	31.3444i	0.124805	−	0.0720562i
$436$	224.429	−	224.429i	0.514746	−	0.514746i
$437$	53.6639	+	30.9828i	0.122801	+	0.0708990i
$438$	170.654	−	170.654i	0.389621	−	0.389621i
$439$	−26.6777	−	99.5626i	−0.0607693	−	0.226794i	0.928862	−	0.370426i	$-0.120788\pi$
$439$	−26.6777	−	99.5626i	−0.0607693	−	0.226794i	−0.989631	+	0.143632i	$0.954122\pi$
$440$	22.5136	−	38.9948i	0.0511673	−	0.0886244i
$441$	275.909	−	477.889i	0.625645	−	1.08365i
$442$	85.4322	−	318.837i	0.193286	−	0.721351i
$443$		−	242.351i		−	0.547067i	−0.961862	−	0.273534i	$-0.911807\pi$
$443$		−	242.351i		−	0.547067i	0.961862	−	0.273534i	$-0.0881925\pi$
$444$	252.547	+	200.820i	0.568799	+	0.452298i
$445$	53.9526			0.121242
$446$	−500.162	−	134.018i	−1.12144	−	0.300489i
$447$	435.266	+	251.301i	0.973749	+	0.562194i
$448$	−70.6937	−	40.8150i	−0.157798	−	0.0911050i
$449$	134.918	−	36.1512i	0.300486	−	0.0805149i	−0.105426	−	0.994427i	$-0.533621\pi$
$449$	134.918	−	36.1512i	0.300486	−	0.0805149i	0.405912	+	0.913912i	$0.366954\pi$
$450$	242.248	+	242.248i	0.538328	+	0.538328i
$451$	−377.339	+	653.570i	−0.836671	+	1.44916i
$452$	127.487	+	127.487i	0.282051	+	0.282051i
$453$	−289.732	−	501.830i	−0.639585	−	1.10779i
$454$	−392.259			−0.864007
$455$		−	81.3405i		−	0.178770i
$456$	−130.529	−	226.083i	−0.286248	−	0.495796i
$457$	−312.193	+	83.6519i	−0.683136	+	0.183046i	−0.583665	−	0.811995i	$-0.698382\pi$
$457$	−312.193	+	83.6519i	−0.683136	+	0.183046i	−0.0994711	+	0.995040i	$0.531715\pi$
$458$	190.000	−	190.000i	0.414847	−	0.414847i
$459$	−111.870	−	29.9755i	−0.243725	−	0.0653060i
$460$	−2.62457	−	4.54589i	−0.00570558	−	0.00988236i
$461$	−149.162	+	556.679i	−0.323561	+	1.20755i	0.592189	+	0.805799i	$0.298264\pi$
$461$	−149.162	+	556.679i	−0.323561	+	1.20755i	−0.915750	+	0.401748i	$0.868403\pi$
$462$	−289.153	−	1079.13i	−0.625871	−	2.33578i
$463$	275.720	−	73.8789i	0.595507	−	0.159566i	0.0515381	−	0.998671i	$-0.483588\pi$
$463$	275.720	−	73.8789i	0.595507	−	0.159566i	0.543969	+	0.839105i	$0.316921\pi$
$464$	−61.9577	−	16.6015i	−0.133530	−	0.0357791i
$465$	−58.9982	+	34.0626i	−0.126878	+	0.0732530i
$466$	38.0549	−	142.023i	0.0816629	−	0.304770i
$467$	4.80739	+	4.80739i	0.0102942	+	0.0102942i	0.712235	−	0.701941i	$-0.247683\pi$
$467$	4.80739	+	4.80739i	0.0102942	+	0.0102942i	−0.701941	+	0.712235i	$0.747683\pi$
$468$	−46.0786	−	171.968i	−0.0984586	−	0.367452i
$469$	−620.516	+	358.255i	−1.32306	+	0.763870i
$470$	24.6815			0.0525138
$471$		−	534.431i		−	1.13467i
$472$	−193.146	+	111.513i	−0.409208	+	0.236256i
$473$	468.979	−	468.979i	0.991498	−	0.991498i
$474$	−215.448	−	124.389i	−0.454531	−	0.262424i
$475$	362.169	−	362.169i	0.762461	−	0.762461i
$476$	138.655	+	517.469i	0.291293	+	1.08712i
$477$	−188.716	+	326.866i	−0.395631	+	0.685253i
$478$	223.498	−	387.110i	0.467569	−	0.809854i
$479$	32.0261	−	119.523i	0.0668603	−	0.249526i	−0.924404	−	0.381414i	$-0.875437\pi$
$479$	32.0261	−	119.523i	0.0668603	−	0.249526i	0.991265	+	0.131888i	$0.0421039\pi$
$480$			22.1143i			0.0460715i
$481$	264.417	−	195.723i	0.549724	−	0.406908i
$482$	521.970			1.08292
$483$	−125.802	−	33.7085i	−0.260459	−	0.0697898i
$484$	−336.492	−	194.273i	−0.695230	−	0.401391i
$485$	81.1082	+	46.8278i	0.167233	+	0.0965522i
$486$	476.356	−	127.639i	0.980156	−	0.262632i
$487$	−45.5548	−	45.5548i	−0.0935417	−	0.0935417i	0.658787	−	0.752329i	$-0.271070\pi$
$487$	−45.5548	−	45.5548i	−0.0935417	−	0.0935417i	−0.752329	+	0.658787i	$0.771070\pi$
$488$	145.713	−	252.382i	0.298592	−	0.517176i
$489$	−194.546	−	194.546i	−0.397845	−	0.397845i
$490$	34.9426	+	60.5223i	0.0713114	+	0.123515i
$491$	−227.098			−0.462521			−0.231260	−	0.972892i	$-0.574285\pi$
$491$	−227.098			−0.462521			−0.231260	+	0.972892i	$0.574285\pi$
$492$		−	370.646i		−	0.753346i
$493$	210.481	+	364.563i	0.426939	+	0.739480i
$494$	−257.098	+	68.8892i	−0.520441	+	0.139452i
$495$	−112.701	+	112.701i	−0.227679	+	0.227679i
$496$	67.3307	+	18.0412i	0.135747	+	0.0363734i
$497$	395.415	+	684.879i	0.795604	+	1.37803i
$498$	179.219	−	668.853i	0.359877	−	1.34308i
$499$	120.640	+	450.234i	0.241763	+	0.902273i	0.974983	+	0.222281i	$0.0713501\pi$
$499$	120.640	+	450.234i	0.241763	+	0.902273i	−0.733219	+	0.679992i	$0.761983\pi$
$500$	−85.2102	+	22.8320i	−0.170420	+	0.0456640i
$501$	−381.026	−	102.096i	−0.760531	−	0.203784i
$502$	−33.2270	+	19.1836i	−0.0661893	+	0.0382144i
$503$	46.9206	−	175.110i	0.0932815	−	0.348131i	−0.903472	−	0.428648i	$-0.858990\pi$
$503$	46.9206	−	175.110i	0.0932815	−	0.348131i	0.996753	+	0.0805162i	$0.0256569\pi$
$504$	204.317	+	204.317i	0.405390	+	0.405390i
$505$	33.1616	+	123.761i	0.0656664	+	0.245071i
$506$	−63.6591	+	36.7536i	−0.125808	+	0.0726356i
$507$	392.191			0.773552
$508$			398.330i			0.784115i
$509$	633.066	−	365.501i	1.24374	−	0.718076i	0.273890	−	0.961761i	$-0.411690\pi$
$509$	633.066	−	365.501i	1.24374	−	0.718076i	0.969854	+	0.243685i	$0.0783563\pi$
$510$	102.624	−	102.624i	0.201224	−	0.201224i
$511$	345.856	+	199.680i	0.676822	+	0.390763i
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$	24.1710	+	90.2076i	0.0471170	+	0.175843i
$514$	−63.9476	+	110.761i	−0.124412	+	0.215487i
$515$	−52.7946	+	91.4429i	−0.102514	+	0.177559i
$516$	−84.3068	+	314.637i	−0.163385	+	0.609762i
$517$		−	345.631i		−	0.668533i
$518$	−212.824	+	489.671i	−0.410857	+	0.945310i
$519$	−67.6435			−0.130334
$520$	21.7789	+	5.83563i	0.0418824	+	0.0112224i
$521$	−273.990	−	158.188i	−0.525893	−	0.303625i	0.213449	−	0.976954i	$-0.431530\pi$
$521$	−273.990	−	158.188i	−0.525893	−	0.303625i	−0.739343	+	0.673329i	$0.764864\pi$
$522$	196.630	+	113.525i	0.376687	+	0.217480i
$523$	−644.176	+	172.606i	−1.23169	+	0.330031i	−0.815239	−	0.579125i	$-0.803394\pi$
$523$	−644.176	+	172.606i	−1.23169	+	0.330031i	−0.416455	+	0.909156i	$0.636728\pi$
$524$	−313.491	−	313.491i	−0.598266	−	0.598266i
$525$	−538.255	+	932.286i	−1.02525	+	1.77578i
$526$	103.500	+	103.500i	0.196768	+	0.196768i
$527$	−228.734	−	396.178i	−0.434030	−	0.751761i
$528$	309.682			0.586519
$529$		−	520.431i		−	0.983801i
$530$	−23.9000	−	41.3959i	−0.0450942	−	0.0781055i
$531$	762.549	−	204.324i	1.43606	−	0.384792i
$532$	305.461	−	305.461i	0.574174	−	0.574174i
$533$	−365.024	−	97.8078i	−0.684848	−	0.183504i
$534$	185.533	+	321.353i	0.347441	+	0.601785i
$535$	−36.6675	+	136.845i	−0.0685374	+	0.255785i
$536$	−51.4048	−	191.845i	−0.0959044	−	0.357920i
$537$	106.604	−	28.5643i	0.198517	−	0.0531925i
$538$	−353.224	−	94.6461i	−0.656550	−	0.175922i
$539$	847.534	−	489.324i	1.57242	−	0.907837i
$540$	2.04754	−	7.64152i	0.00379174	−	0.0141510i
$541$	−337.793	−	337.793i	−0.624387	−	0.624387i	0.322263	−	0.946650i	$-0.395556\pi$
$541$	−337.793	−	337.793i	−0.624387	−	0.624387i	−0.946650	+	0.322263i	$0.895556\pi$
$542$	62.0197	+	231.461i	0.114428	+	0.427049i
$543$	−916.064	+	528.890i	−1.68704	+	0.974014i
$544$	−148.500			−0.272977
$545$		−	142.282i		−	0.261069i
$546$	484.482	−	279.716i	0.887329	−	0.512300i
$547$	325.968	−	325.968i	0.595920	−	0.595920i	−0.343304	−	0.939224i	$-0.611546\pi$
$547$	325.968	−	325.968i	0.595920	−	0.595920i	0.939224	+	0.343304i	$0.111546\pi$
$548$	−290.982	−	167.999i	−0.530989	−	0.306567i
$549$	−729.425	+	729.425i	−1.32864	+	1.32864i
$550$	157.254	+	586.879i	0.285916	+	1.06705i
$551$	169.723	−	293.970i	0.308028	−	0.533520i
$552$	18.0509	−	31.2650i	0.0327008	−	0.0566395i
$553$	106.547	−	397.638i	0.192671	−	0.719056i
$554$		−	507.603i		−	0.916251i
$555$	143.712	−	16.3967i	0.258940	−	0.0295436i
$556$	−23.6491			−0.0425344
$557$	838.852	+	224.770i	1.50602	+	0.403537i	0.915111	−	0.403202i	$-0.132103\pi$
$557$	838.852	+	224.770i	1.50602	+	0.403537i	0.590908	+	0.806739i	$0.298770\pi$
$558$	−213.682	−	123.369i	−0.382943	−	0.221092i
$559$	287.617	+	166.056i	0.514521	+	0.297059i
$560$	−35.3469	+	9.47116i	−0.0631194	+	0.0169128i
$561$	−1437.11	−	1437.11i	−2.56170	−	2.56170i
$562$	−238.894	+	413.777i	−0.425079	+	0.736259i
$563$	−439.575	−	439.575i	−0.780773	−	0.780773i	0.199188	−	0.979961i	$-0.436170\pi$
$563$	−439.575	−	439.575i	−0.780773	−	0.780773i	−0.979961	+	0.199188i	$0.936170\pi$
$564$	84.8753	+	147.008i	0.150488	+	0.260653i
$565$	80.8235			0.143051
$566$		−	279.897i		−	0.494518i
$567$	361.569	+	626.256i	0.637688	+	1.10451i
$568$	−211.744	+	56.7367i	−0.372789	+	0.0998886i
$569$	−282.278	+	282.278i	−0.496095	+	0.496095i	−0.910220	−	0.414125i	$-0.864088\pi$
$569$	−282.278	+	282.278i	−0.496095	+	0.496095i	0.414125	+	0.910220i	$0.364088\pi$
$570$	−113.041	−	30.2894i	−0.198318	−	0.0531392i
$571$	360.262	+	623.993i	0.630933	+	1.09281i	0.987361	+	0.158485i	$0.0506609\pi$
$571$	360.262	+	623.993i	0.630933	+	1.09281i	−0.356429	+	0.934322i	$0.616006\pi$
$572$	81.7202	−	304.984i	0.142868	−	0.533189i
$573$	51.2872	+	191.407i	0.0895065	+	0.334043i
$574$	592.429	−	158.741i	1.03211	−	0.276552i
$575$	68.4166	+	18.3322i	0.118985	+	0.0318820i
$576$	−69.3640	+	40.0473i	−0.120424	+	0.0695266i
$577$	93.5238	−	349.036i	0.162086	−	0.604914i	−0.836308	−	0.548261i	$-0.815290\pi$
$577$	93.5238	−	349.036i	0.162086	−	0.604914i	0.998394	−	0.0566538i	$-0.0180431\pi$
$578$	400.130	+	400.130i	0.692267	+	0.692267i
$579$	2.41362	+	9.00777i	0.00416861	+	0.0155575i
$580$	−24.9023	+	14.3773i	−0.0429350	+	0.0247885i
$581$	1145.83			1.97217
$582$			644.131i			1.10675i
$583$	−579.695	+	334.687i	−0.994331	+	0.574077i
$584$	−78.2770	+	78.2770i	−0.134036	+	0.134036i
$585$	−69.1179	−	39.9052i	−0.118150	−	0.0682141i
$586$	246.484	−	246.484i	0.420621	−	0.420621i
$587$	−23.8827	−	89.1315i	−0.0406861	−	0.151842i	0.942594	−	0.333940i	$-0.108378\pi$
$587$	−23.8827	−	89.1315i	−0.0406861	−	0.151842i	−0.983281	+	0.182097i	$0.941711\pi$
$588$	−240.323	+	416.251i	−0.408712	+	0.707910i
$589$	−184.442	+	319.463i	−0.313144	+	0.542381i
$590$	−25.8767	+	96.5731i	−0.0438588	+	0.163683i
$591$		−	431.439i		−	0.730016i
$592$	−115.840	−	92.1140i	−0.195676	−	0.155598i
$593$	458.245			0.772757			0.386378	−	0.922340i	$-0.373726\pi$
$593$	458.245			0.772757			0.386378	+	0.922340i	$0.373726\pi$
$594$	−107.009	−	28.6730i	−0.180150	−	0.0482711i
$595$	207.983	+	120.079i	0.349552	+	0.201814i
$596$	−199.651	−	115.269i	−0.334986	−	0.193404i
$597$	−510.998	+	136.922i	−0.855944	+	0.229349i
$598$	−26.0274	−	26.0274i	−0.0435241	−	0.0435241i
$599$	556.180	−	963.332i	0.928514	−	1.60823i	0.142705	−	0.989765i	$-0.454420\pi$
$599$	556.180	−	963.332i	0.928514	−	1.60823i	0.785809	−	0.618469i	$-0.212247\pi$
$600$	−211.003	−	211.003i	−0.351671	−	0.351671i
$601$	−140.938	−	244.112i	−0.234506	−	0.406176i	0.724623	−	0.689146i	$-0.242014\pi$
$601$	−140.938	−	244.112i	−0.234506	−	0.406176i	−0.959129	+	0.282969i	$0.908681\pi$
$602$	−539.013			−0.895371
$603$			703.033i			1.16589i
$604$	132.897	+	230.184i	0.220028	+	0.381099i
$605$	−168.246	+	45.0813i	−0.278092	+	0.0745146i
$606$	−623.109	+	623.109i	−1.02823	+	1.02823i
$607$	−372.513	−	99.8145i	−0.613695	−	0.164439i	−0.0614349	−	0.998111i	$-0.519568\pi$
$607$	−372.513	−	99.8145i	−0.613695	−	0.164439i	−0.552260	+	0.833672i	$0.686234\pi$
$608$	59.8722	+	103.702i	0.0984740	+	0.170562i
$609$	−184.655	+	689.140i	−0.303209	+	1.13159i
$610$	−33.8127	−	126.191i	−0.0554307	−	0.206870i
$611$	167.176	−	44.7946i	0.273610	−	0.0733136i
$612$	507.736	+	136.047i	0.829634	+	0.222300i
$613$	−775.488	+	447.728i	−1.26507	+	0.730388i	−0.974051	−	0.226329i	$-0.927327\pi$
$613$	−775.488	+	447.728i	−1.26507	+	0.730388i	−0.291019	+	0.956717i	$0.593994\pi$
$614$	53.4825	−	199.599i	0.0871051	−	0.325081i
$615$	−117.490	−	117.490i	−0.191041	−	0.191041i
$616$	132.631	+	494.986i	0.215310	+	0.803548i
$617$	−255.734	+	147.648i	−0.414479	+	0.239300i	−0.692713	−	0.721214i	$-0.743585\pi$
$617$	−255.734	+	147.648i	−0.414479	+	0.239300i	0.278233	+	0.960514i	$0.410251\pi$
$618$	−726.205			−1.17509
$619$		−	769.926i		−	1.24382i	−0.783088	−	0.621912i	$-0.786356\pi$
$619$		−	769.926i		−	1.24382i	0.783088	−	0.621912i	$-0.213644\pi$
$620$	27.0618	−	15.6241i	0.0436481	−	0.0252002i
$621$	−9.13219	+	9.13219i	−0.0147056	+	0.0147056i
$622$	−290.905	−	167.954i	−0.467693	−	0.270023i
$623$	−434.181	+	434.181i	−0.696919	+	0.696919i
$624$	40.1354	+	149.787i	0.0643196	+	0.240044i
$625$	282.679	−	489.614i	0.452286	−	0.783382i
$626$	156.967	−	271.876i	0.250747	−	0.434306i
$627$	−424.162	+	1583.00i	−0.676495	+	2.52471i
$628$			245.137i			0.390346i
$629$	110.105	+	965.037i	0.175048	+	1.53424i
$630$	129.531			0.205606
$631$	−652.695	−	174.889i	−1.03438	−	0.277162i	−0.298598	−	0.954379i	$-0.596519\pi$
$631$	−652.695	−	174.889i	−1.03438	−	0.277162i	−0.735783	+	0.677217i	$0.763186\pi$
$632$	98.8234	+	57.0557i	0.156366	+	0.0902780i
$633$	1115.61	+	644.100i	1.76242	+	1.01754i
$634$	−211.665	+	56.7155i	−0.333857	+	0.0894566i
$635$	126.266	+	126.266i	0.198843	+	0.198843i
$636$	164.375	−	284.707i	0.258452	−	0.447652i
$637$	346.519	+	346.519i	0.543987	+	0.543987i
$638$	201.336	+	348.723i	0.315573	+	0.546588i
$639$	775.955			1.21433
$640$		−	10.1436i		−	0.0158494i
$641$	−83.1767	−	144.066i	−0.129761	−	0.224752i	0.793823	−	0.608149i	$-0.208088\pi$
$641$	−83.1767	−	144.066i	−0.129761	−	0.224752i	−0.923584	+	0.383397i	$0.874754\pi$
$642$	−941.171	+	252.186i	−1.46600	+	0.392813i
$643$	435.803	−	435.803i	0.677766	−	0.677766i	−0.281729	−	0.959494i	$-0.590908\pi$
$643$	435.803	−	435.803i	0.677766	−	0.677766i	0.959494	+	0.281729i	$0.0909078\pi$
$644$	57.7039	+	15.4617i	0.0896023	+	0.0240089i
$645$	73.0118	+	126.460i	0.113197	+	0.196062i
$646$	203.396	−	759.084i	0.314854	−	1.17505i
$647$	173.713	+	648.304i	0.268489	+	1.00202i	0.960080	+	0.279726i	$0.0902437\pi$
$647$	173.713	+	648.304i	0.268489	+	1.00202i	−0.691590	+	0.722290i	$0.743090\pi$
$648$	−193.620	+	51.8803i	−0.298796	+	0.0800621i
$649$	1352.38	+	362.369i	2.08379	+	0.558349i
$650$	−263.482	+	152.122i	−0.405358	+	0.234033i
$651$	200.668	−	748.902i	0.308245	−	1.15039i
$652$	89.2361	+	89.2361i	0.136865	+	0.136865i
$653$	150.432	+	561.420i	0.230371	+	0.859755i	0.980181	+	0.198102i	$0.0634778\pi$
$653$	150.432	+	561.420i	0.230371	+	0.859755i	−0.749811	+	0.661652i	$0.769856\pi$
$654$	847.465	−	489.284i	1.29582	−	0.748141i
$655$	−198.746			−0.303428
$656$			170.011i			0.259164i
$657$	339.350	−	195.924i	0.516515	−	0.298210i
$658$	−198.623	+	198.623i	−0.301859	+	0.301859i
$659$	941.556	+	543.608i	1.42877	+	0.824898i	0.997023	−	0.0770991i	$-0.0245658\pi$
$659$	941.556	+	543.608i	1.42877	+	0.824898i	0.431742	+	0.901997i	$0.357899\pi$
$660$	98.1652	−	98.1652i	0.148735	−	0.148735i
$661$	−169.898	−	634.068i	−0.257032	−	0.959256i	−0.966949	−	0.254971i	$-0.917934\pi$
$661$	−169.898	−	634.068i	−0.257032	−	0.959256i	0.709917	−	0.704285i	$-0.248732\pi$
$662$	387.903	−	671.868i	0.585956	−	1.01491i
$663$	508.853	−	881.359i	0.767501	−	1.32935i
$664$	−82.2055	+	306.795i	−0.123803	+	0.462041i
$665$		−	193.654i		−	0.291209i
$666$	311.681	+	421.074i	0.467989	+	0.632243i
$667$	46.9421			0.0703780
$668$	174.772	+	46.8301i	0.261635	+	0.0701050i
$669$	−1382.59	−	798.240i	−2.06666	−	1.19318i
$670$	−77.1071	−	44.5178i	−0.115085	−	0.0664445i
$671$	−1767.14	+	473.502i	−2.63358	+	0.705667i
$672$	−177.964	−	177.964i	−0.264827	−	0.264827i
$673$	−511.101	+	885.252i	−0.759436	+	1.31538i	0.183702	+	0.982982i	$0.441192\pi$
$673$	−511.101	+	885.252i	−0.759436	+	1.31538i	−0.943138	+	0.332400i	$0.892142\pi$
$674$	382.958	+	382.958i	0.568187	+	0.568187i
$675$	53.3747	+	92.4477i	0.0790736	+	0.136959i
$676$	−179.894			−0.266115
$677$		−	1015.58i		−	1.50012i	−0.661367	−	0.750062i	$-0.730023\pi$
$677$		−	1015.58i		−	1.50012i	0.661367	−	0.750062i	$-0.269977\pi$
$678$	277.938	+	481.403i	0.409938	+	0.710034i
$679$	−1029.56	+	275.869i	−1.51629	+	0.406288i
$680$	−47.0725	+	47.0725i	−0.0692243	+	0.0692243i
$681$	−1168.19	−	313.016i	−1.71540	−	0.459641i
$682$	−218.795	−	378.965i	−0.320814	−	0.555667i
$683$	172.380	−	643.332i	0.252387	−	0.941921i	−0.717138	−	0.696931i	$-0.754548\pi$
$683$	172.380	−	643.332i	0.252387	−	0.941921i	0.969525	−	0.244990i	$-0.0787848\pi$
$684$	−109.703	−	409.418i	−0.160385	−	0.598565i
$685$	−145.491	+	38.9842i	−0.212396	+	0.0569113i
$686$	−85.2577	−	22.8447i	−0.124282	−	0.0333013i
$687$	717.457	−	414.224i	1.04433	−	0.602946i
$688$	38.6706	−	144.321i	0.0562072	−	0.209768i
$689$	−237.012	−	237.012i	−0.343994	−	0.343994i
$690$	−4.18872	−	15.6325i	−0.00607061	−	0.0226558i
$691$	930.012	−	536.943i	1.34589	−	0.777051i	0.358228	−	0.933634i	$-0.383381\pi$
$691$	930.012	−	536.943i	1.34589	−	0.777051i	0.987665	+	0.156583i	$0.0500478\pi$
$692$	31.0273			0.0448371
$693$		−	1813.92i		−	2.61748i
$694$	174.724	−	100.877i	0.251763	−	0.145356i
$695$	−7.49648	+	7.49648i	−0.0107863	+	0.0107863i
$696$	−171.269	−	98.8823i	−0.246076	−	0.142072i
$697$	788.957	−	788.957i	1.13193	−	1.13193i
$698$	30.5007	+	113.830i	0.0436973	+	0.163080i
$699$	226.663	−	392.593i	0.324268	−	0.561649i
$700$	246.892	−	427.629i	0.352702	−	0.610898i
$701$	−47.7242	+	178.109i	−0.0680802	+	0.254079i	−0.991575	−	0.129531i	$-0.958653\pi$
$701$	−47.7242	+	178.109i	−0.0680802	+	0.254079i	0.923495	+	0.383610i	$0.125319\pi$
$702$		−	55.4745i		−	0.0790236i
$703$	629.521	−	465.974i	0.895478	−	0.662836i
$704$	−142.048			−0.201772
$705$	73.5042	+	19.6954i	0.104261	+	0.0279367i
$706$	−73.7150	−	42.5594i	−0.104412	−	0.0602824i
$707$	−1262.82	−	729.091i	−1.78617	−	1.03125i
$708$	−664.196	+	177.971i	−0.938130	+	0.251371i
$709$	590.027	+	590.027i	0.832197	+	0.832197i	0.987817	−	0.155620i	$-0.0497376\pi$
$709$	590.027	+	590.027i	0.832197	+	0.832197i	−0.155620	+	0.987817i	$0.549738\pi$
$710$	−49.1354	+	85.1051i	−0.0692049	+	0.119866i
$711$	−285.616	−	285.616i	−0.401710	−	0.401710i
$712$	−85.1021	−	147.401i	−0.119525	−	0.207024i
$713$	−51.0129			−0.0715469
$714$			1651.73i			2.31334i
$715$	−70.7718	−	122.580i	−0.0989816	−	0.171441i
$716$	−48.8979	+	13.1021i	−0.0682931	+	0.0182991i
$717$	974.509	−	974.509i	1.35915	−	1.35915i
$718$	−641.360	−	171.852i	−0.893259	−	0.239348i
$719$	−106.377	−	184.250i	−0.147951	−	0.256259i	0.782519	−	0.622627i	$-0.213934\pi$
$719$	−106.377	−	184.250i	−0.147951	−	0.256259i	−0.930470	+	0.366368i	$0.880601\pi$
$720$	−9.29301	+	34.6820i	−0.0129070	+	0.0481694i
$721$	−311.020	−	1160.74i	−0.431374	−	1.60991i
$722$	−118.960	+	31.8753i	−0.164765	+	0.0441486i
$723$	1554.48	+	416.522i	2.15005	+	0.576103i
$724$	420.188	−	242.596i	0.580370	−	0.335077i
$725$	100.423	−	374.785i	0.138515	−	0.516944i
$726$	−847.082	−	847.082i	−1.16678	−	1.16678i
$727$	58.8388	+	219.590i	0.0809337	+	0.302049i	0.994513	−	0.104611i	$-0.0333599\pi$
$727$	58.8388	+	219.590i	0.0809337	+	0.302049i	−0.913579	+	0.406660i	$0.866693\pi$
$728$	−222.226	+	128.302i	−0.305256	+	0.176240i
$729$	882.666			1.21079
$730$			49.6257i			0.0679803i
$731$	−849.192	+	490.281i	−1.16168	+	0.670699i
$732$	635.344	−	635.344i	0.867957	−	0.867957i
$733$	795.024	+	459.007i	1.08462	+	0.626204i	0.932138	−	0.362103i	$-0.117941\pi$
$733$	795.024	+	459.007i	1.08462	+	0.626204i	0.152478	+	0.988307i	$0.451275\pi$
$734$	170.581	−	170.581i	0.232399	−	0.232399i
$735$	55.7671	+	208.126i	0.0758736	+	0.283164i
$736$	−8.27973	+	14.3409i	−0.0112496	+	0.0194849i
$737$	−623.413	+	1079.78i	−0.845879	+	1.46511i
$738$	155.755	−	581.286i	0.211050	−	0.787651i
$739$		−	249.208i		−	0.337223i	−0.985683	−	0.168612i	$-0.946072\pi$
$739$		−	249.208i		−	0.337223i	0.985683	−	0.168612i	$-0.0539283\pi$
$740$	−65.9189	+	7.52097i	−0.0890796	+	0.0101635i
$741$	−820.638			−1.10747
$742$	525.465	+	140.798i	0.708174	+	0.189755i
$743$	495.417	+	286.029i	0.666780	+	0.384965i	0.794855	−	0.606799i	$-0.207547\pi$
$743$	495.417	+	286.029i	0.666780	+	0.384965i	−0.128076	+	0.991764i	$0.540880\pi$
$744$	186.122	+	107.457i	0.250164	+	0.144432i
$745$	−99.8257	+	26.7482i	−0.133994	+	0.0359037i
$746$	325.573	+	325.573i	0.436425	+	0.436425i
$747$	562.138	−	973.652i	0.752528	−	1.30342i
$748$	659.188	+	659.188i	0.881268	+	0.881268i
$749$	−806.173	−	1396.33i	−1.07633	−	1.86426i
$750$	−271.985			−0.362647
$751$			584.336i			0.778077i	0.921221	+	0.389039i	$0.127193\pi$
$751$			584.336i			0.778077i	−0.921221	+	0.389039i	$0.872807\pi$
$752$	−38.9314	−	67.4311i	−0.0517704	−	0.0896690i
$753$	−114.262	+	30.6164i	−0.151742	+	0.0406592i
$754$	−142.578	+	142.578i	−0.189095	+	0.189095i
$755$	115.092	+	30.8388i	0.152440	+	0.0408461i
$756$	45.0173	+	77.9722i	0.0595466	+	0.103138i
$757$	−245.936	+	917.845i	−0.324882	+	1.21248i	0.589548	+	0.807734i	$0.299306\pi$
$757$	−245.936	+	917.845i	−0.324882	+	1.21248i	−0.914430	+	0.404744i	$0.867361\pi$
$758$	−84.9803	−	317.151i	−0.112111	−	0.418405i
$759$	−218.912	+	58.6574i	−0.288422	+	0.0772825i
$760$	51.8508	+	13.8934i	0.0682248	+	0.0182808i
$761$	−515.200	+	297.451i	−0.677004	+	0.390869i	−0.798725	−	0.601696i	$-0.794492\pi$
$761$	−515.200	+	297.451i	−0.677004	+	0.390869i	0.121721	+	0.992564i	$0.461159\pi$
$762$	−317.860	+	1186.27i	−0.417140	+	1.55679i
$763$	1145.01	+	1145.01i	1.50067	+	1.50067i
$764$	−23.5249	−	87.7960i	−0.0307917	−	0.114916i
$765$	204.071	−	117.821i	0.266760	−	0.154014i
$766$	538.757			0.703338
$767$			701.084i			0.914060i
$768$	60.4175	−	34.8820i	0.0786686	−	0.0454193i
$769$	−603.563	+	603.563i	−0.784868	+	0.784868i	−0.980648	−	0.195780i	$-0.937276\pi$
$769$	−603.563	+	603.563i	−0.784868	+	0.784868i	0.195780	+	0.980648i	$0.437276\pi$
$770$	198.947	+	114.862i	0.258372	+	0.149171i
$771$	−278.828	+	278.828i	−0.361645	+	0.361645i
$772$	−1.10710	−	4.13176i	−0.00143407	−	0.00535202i
$773$	−207.262	+	358.988i	−0.268126	+	0.464408i	−0.968378	−	0.249488i	$-0.919738\pi$
$773$	−207.262	+	358.988i	−0.268126	+	0.464408i	0.700252	+	0.713896i	$0.253071\pi$
$774$	−264.437	+	458.019i	−0.341650	+	0.591756i
$775$	−109.132	+	407.286i	−0.140815	+	0.525530i
$776$		−	295.456i		−	0.380742i
$777$	−1024.56	+	1288.46i	−1.31861	+	1.65825i
$778$	−28.1150			−0.0361375
$779$	−869.044	−	232.860i	−1.11559	−	0.298921i
$780$	60.2031	+	34.7583i	0.0771835	+	0.0445619i
$781$	1191.78	+	688.077i	1.52597	+	0.881020i
$782$	104.974	−	28.1276i	0.134237	−	0.0359688i
$783$	50.0260	+	50.0260i	0.0638902	+	0.0638902i
$784$	110.233	−	190.930i	0.140604	−	0.243533i
$785$	77.7055	+	77.7055i	0.0989879	+	0.0989879i
$786$	−683.452	−	1183.77i	−0.869531	−	1.50607i
$787$	119.985			0.152458			0.0762291	−	0.997090i	$-0.475712\pi$
$787$	119.985			0.152458			0.0762291	+	0.997090i	$0.475712\pi$
$788$			197.896i			0.251137i
$789$	225.643	+	390.826i	0.285987	+	0.495343i
$790$	49.4117	−	13.2398i	0.0625465	−	0.0167593i
$791$	−650.423	+	650.423i	−0.822280	+	0.822280i
$792$	485.675	+	130.136i	0.613226	+	0.164313i
$793$	−458.049	−	793.364i	−0.577616	−	1.00046i
$794$	−145.872	+	544.402i	−0.183718	+	0.685644i
$795$	−38.1435	−	142.353i	−0.0479792	−	0.179061i
$796$	234.389	−	62.8044i	0.294459	−	0.0789000i
$797$	−1010.42	−	270.742i	−1.26778	−	0.339702i	−0.438603	−	0.898681i	$-0.644526\pi$
$797$	−1010.42	−	270.742i	−1.26778	−	0.339702i	−0.829182	+	0.558979i	$0.811193\pi$
$798$	1153.45	−	665.943i	1.44542	−	0.834515i
$799$	−132.256	+	493.587i	−0.165527	+	0.617756i
$800$	96.7846	+	96.7846i	0.120981	+	0.120981i
$801$	155.932	+	581.946i	0.194672	+	0.726524i
$802$	−312.243	+	180.274i	−0.389330	+	0.224780i
$803$	694.941			0.865431
$804$		−	612.356i		−	0.761637i
$805$	23.1926	−	13.3902i	0.0288106	−	0.0166338i
$806$	154.942	−	154.942i	0.192236	−	0.192236i
$807$	−976.414	−	563.733i	−1.20993	−	0.698554i
$808$	285.813	−	285.813i	0.353729	−	0.353729i
$809$	149.092	+	556.420i	0.184292	+	0.687787i	0.994781	+	0.102033i	$0.0325348\pi$
$809$	149.092	+	556.420i	0.184292	+	0.687787i	−0.810489	+	0.585754i	$0.800799\pi$
$810$	−44.9296	+	77.8204i	−0.0554687	+	0.0960745i
$811$	530.585	−	919.000i	0.654235	−	1.13317i	−0.327850	−	0.944730i	$-0.606324\pi$
$811$	530.585	−	919.000i	0.654235	−	1.13317i	0.982085	−	0.188439i	$-0.0603426\pi$
$812$	84.6990	−	316.101i	0.104309	−	0.389287i
$813$			738.806i			0.908741i
$814$	105.321	+	923.107i	0.129387	+	1.13404i
$815$	56.5734			0.0694152
$816$	−442.249	−	118.500i	−0.541971	−	0.145221i
$817$	684.755	+	395.343i	0.838133	+	0.483897i
$818$	−444.564	−	256.669i	−0.543476	−	0.313776i
$819$	877.358	−	235.087i	1.07126	−	0.287042i
$820$	53.8914	+	53.8914i	0.0657212	+	0.0657212i
$821$	−176.031	+	304.894i	−0.214410	+	0.371369i	−0.953090	−	0.302687i	$-0.902116\pi$
$821$	−176.031	+	304.894i	−0.214410	+	0.371369i	0.738680	+	0.674056i	$0.235450\pi$
$822$	−732.517	−	732.517i	−0.891140	−	0.891140i
$823$	−90.7239	−	157.138i	−0.110236	−	0.190934i	0.805630	−	0.592420i	$-0.201827\pi$
$823$	−90.7239	−	157.138i	−0.110236	−	0.190934i	−0.915865	+	0.401486i	$0.868494\pi$
$824$	333.102			0.404250
$825$			1873.28i			2.27064i
$826$	−568.926	−	985.408i	−0.688772	−	1.19299i
$827$	−589.583	+	157.978i	−0.712918	+	0.191026i	−0.597010	−	0.802234i	$-0.703645\pi$
$827$	−589.583	+	157.978i	−0.712918	+	0.191026i	−0.115909	+	0.993260i	$0.536978\pi$
$828$	41.4476	−	41.4476i	0.0500575	−	0.0500575i
$829$	−356.791	−	95.6018i	−0.430387	−	0.115322i	0.0371209	−	0.999311i	$-0.488181\pi$
$829$	−356.791	−	95.6018i	−0.430387	−	0.115322i	−0.467508	+	0.883989i	$0.654848\pi$
$830$	71.1921	+	123.308i	0.0857736	+	0.148564i
$831$	405.058	−	1511.70i	0.487435	−	1.81913i
$832$	−18.4097	−	68.7058i	−0.0221270	−	0.0825791i
$833$	−1397.58	+	374.481i	−1.67777	+	0.449557i
$834$	−70.4297	−	18.8716i	−0.0844481	−	0.0226278i
$835$	70.2452	−	40.5561i	0.0841260	−	0.0485702i
$836$	194.558	−	726.102i	0.232725	−	0.868543i
$837$	−54.3642	−	54.3642i	−0.0649513	−	0.0649513i
$838$	225.375	+	841.111i	0.268944	+	1.00371i
$839$	−266.118	+	153.644i	−0.317185	+	0.183127i	−0.650137	−	0.759817i	$-0.725289\pi$
$839$	−266.118	+	153.644i	−0.317185	+	0.183127i	0.332952	+	0.942944i	$0.391955\pi$
$840$	−112.825			−0.134315
$841$			583.852i			0.694235i
$842$	191.362	−	110.483i	0.227271	−	0.131215i
$843$	−1041.64	+	1041.64i	−1.23564	+	1.23564i
$844$	−511.720	−	295.441i	−0.606303	−	0.350049i
$845$	−57.0240	+	57.0240i	−0.0674840	+	0.0674840i
$846$	71.3336	+	266.221i	0.0843187	+	0.314682i
$847$	991.160	−	1716.74i	1.17020	−	2.02685i
$848$	−75.3972	+	130.592i	−0.0889118	+	0.154000i
$849$	223.353	−	833.565i	0.263078	−	0.981820i
$850$		−	898.281i		−	1.05680i
$851$	99.3345	+	43.1734i	0.116727	+	0.0507325i
$852$	−675.873			−0.793278
$853$	−1533.19	−	410.817i	−1.79741	−	0.481614i	−0.803841	−	0.594845i	$-0.797214\pi$
$853$	−1533.19	−	410.817i	−1.79741	−	0.481614i	−0.993569	+	0.113230i	$0.963880\pi$
$854$	1287.62	+	743.408i	1.50775	+	0.870502i
$855$	−164.555	−	95.0059i	−0.192462	−	0.111118i
$856$	431.705	−	115.675i	0.504328	−	0.135134i
$857$	170.418	+	170.418i	0.198854	+	0.198854i	0.799508	−	0.600655i	$-0.205093\pi$
$857$	170.418	+	170.418i	0.198854	+	0.198854i	−0.600655	+	0.799508i	$0.705093\pi$
$858$	486.744	−	843.065i	0.567300	−	0.982593i
$859$	447.526	+	447.526i	0.520985	+	0.520985i	0.917869	−	0.396884i	$-0.129908\pi$
$859$	447.526	+	447.526i	0.520985	+	0.520985i	−0.396884	+	0.917869i	$0.629908\pi$
$860$	−33.4897	−	58.0059i	−0.0389415	−	0.0674487i
$861$	1890.99			2.19627
$862$		−	376.588i		−	0.436877i
$863$	401.084	+	694.697i	0.464755	+	0.804979i	0.999190	−	0.0402301i	$-0.0128091\pi$
$863$	401.084	+	694.697i	0.464755	+	0.804979i	−0.534435	+	0.845209i	$0.679476\pi$
$864$	−24.1067	+	6.45937i	−0.0279013	+	0.00747612i
$865$	9.83526	−	9.83526i	0.0113702	−	0.0113702i
$866$	208.322	+	55.8198i	0.240557	+	0.0644571i
$867$	872.335	+	1510.93i	1.00615	+	1.74271i
$868$	−92.0440	+	343.513i	−0.106042	+	0.395752i
$869$	−185.406	−	691.945i	−0.213356	−	0.796254i
$870$	−85.6346	+	22.9457i	−0.0984306	+	0.0263744i
$871$	−603.067	−	161.591i	−0.692385	−	0.185524i
$872$	−388.723	+	224.429i	−0.445783	+	0.257373i
$873$	−270.680	+	1010.19i	−0.310058	+	1.15715i
$874$	−61.9657	−	61.9657i	−0.0708990	−	0.0708990i
$875$	−116.486	−	434.732i	−0.133127	−	0.496837i
$876$	−295.581	+	170.654i	−0.337422	+	0.194810i
$877$	252.641			0.288074			0.144037	−	0.989572i	$-0.453992\pi$
$877$	252.641			0.288074			0.144037	+	0.989572i	$0.453992\pi$
$878$			145.770i			0.166025i
$879$	930.746	−	537.366i	1.05887	−	0.611338i
$880$	−45.0273	+	45.0273i	−0.0511673	+	0.0511673i
$881$	−807.829	−	466.400i	−0.916946	−	0.529399i	−0.0342863	−	0.999412i	$-0.510916\pi$
$881$	−807.829	−	466.400i	−0.916946	−	0.529399i	−0.882659	+	0.470013i	$0.844249\pi$
$882$	−551.819	+	551.819i	−0.625645	+	0.625645i
$883$	−265.752	−	991.799i	−0.300965	−	1.12322i	−0.936364	−	0.351031i	$-0.885831\pi$
$883$	−265.752	−	991.799i	−0.300965	−	1.12322i	0.635399	−	0.772184i	$-0.280836\pi$
$884$	−233.405	+	404.270i	−0.264033	+	0.457319i
$885$	−154.127	+	266.956i	−0.174155	+	0.301645i
$886$	−88.7066	+	331.057i	−0.100120	+	0.373654i
$887$			1117.85i			1.26026i	0.776490	+	0.630130i	$0.216998\pi$
$887$			1117.85i			1.26026i	−0.776490	+	0.630130i	$0.783002\pi$
$888$	−271.480	−	366.764i	−0.305721	−	0.413023i
$889$	−2032.23			−2.28598
$890$	−73.7006	−	19.7480i	−0.0828097	−	0.0221888i
$891$	1089.77	+	629.180i	1.22309	+	0.706150i
$892$	634.180	+	366.144i	0.710964	+	0.410475i
$893$	398.010	−	106.646i	0.445699	−	0.119425i
$894$	−502.602	−	502.602i	−0.562194	−	0.562194i
$895$	−11.3468	+	19.6532i	−0.0126780	+	0.0219589i
$896$	81.6301	+	81.6301i	0.0911050	+	0.0911050i
$897$	−56.7431	−	98.2819i	−0.0632587	−	0.109567i
$898$	−197.534			−0.219971
$899$			279.448i			0.310843i
$900$	−242.248	−	419.585i	−0.269164	−	0.466206i
$901$	955.916	−	256.137i	1.06095	−	0.284281i
$902$	754.678	−	754.678i	0.836671	−	0.836671i
$903$	−1605.24	−	430.123i	−1.77768	−	0.476327i
$904$	−127.487	−	220.814i	−0.141025	−	0.244263i
$905$	56.2945	−	210.094i	0.0622039	−	0.232148i
$906$	212.098	+	791.562i	0.234104	+	0.873689i
$907$	104.238	−	27.9305i	0.114926	−	0.0307944i	−0.200898	−	0.979612i	$-0.564386\pi$
$907$	104.238	−	27.9305i	0.114926	−	0.0307944i	0.315824	+	0.948818i	$0.397719\pi$
$908$	535.836	+	143.577i	0.590128	+	0.158124i
$909$	−1239.07	+	715.377i	−1.36311	+	0.786994i
$910$	−29.7727	+	111.113i	−0.0327172	+	0.122102i
$911$	−927.879	−	927.879i	−1.01853	−	1.01853i	−0.999825	−	0.0187028i	$-0.994046\pi$
$911$	−927.879	−	927.879i	−1.01853	−	1.01853i	−0.0187028	−	0.999825i	$-0.505954\pi$
$912$	95.5539	+	356.612i	0.104774	+	0.391022i
$913$	1726.77	−	996.950i	1.89131	−	1.09195i
$914$	457.082			0.500090
$915$		−	402.792i		−	0.440210i
$916$	−329.089	+	190.000i	−0.359268	+	0.207423i
$917$	1599.40	−	1599.40i	1.74416	−	1.74416i
$918$	141.845	+	81.8945i	0.154516	+	0.0892097i
$919$	−53.1519	+	53.1519i	−0.0578367	+	0.0578367i	−0.735434	−	0.677597i	$-0.763021\pi$
$919$	−53.1519	+	53.1519i	−0.0578367	+	0.0578367i	0.677597	+	0.735434i	$0.263021\pi$
$920$	1.92132	+	7.17046i	0.00208839	+	0.00779397i
$921$	318.554	−	551.751i	0.345878	−	0.599078i
$922$	407.517	−	705.841i	0.441993	−	0.765554i
$923$	−178.352	+	665.620i	−0.193231	+	0.721149i
$924$			1579.96i			1.70991i
$925$	557.201	−	700.723i	0.602380	−	0.757539i
$926$	−403.682			−0.435941
$927$	−1138.91	−	305.170i	−1.22860	−	0.329202i
$928$	78.5593	+	45.3562i	0.0846544	+	0.0488752i
$929$	−273.259	−	157.766i	−0.294143	−	0.169824i	0.345666	−	0.938358i	$-0.387653\pi$
$929$	−273.259	−	157.766i	−0.294143	−	0.169824i	−0.639809	+	0.768534i	$0.720986\pi$
$930$	93.0608	−	24.9356i	0.100065	−	0.0268124i
$931$	824.989	+	824.989i	0.886132	+	0.886132i
$932$	−103.968	+	180.078i	−0.111554	+	0.193217i
$933$	−732.323	−	732.323i	−0.784912	−	0.784912i
$934$	−4.80739	−	8.32665i	−0.00514710	−	0.00891504i
$935$	417.909			0.446961
$936$			251.778i			0.268994i
$937$	355.117	+	615.081i	0.378994	+	0.656436i	0.990916	−	0.134481i	$-0.0429369\pi$
$937$	355.117	+	615.081i	0.378994	+	0.656436i	−0.611922	+	0.790918i	$0.709604\pi$
$938$	978.771	−	262.261i	1.04347	−	0.279596i
$939$	684.418	−	684.418i	0.728880	−	0.728880i
$940$	−33.7155	−	9.03405i	−0.0358676	−	0.00961069i
$941$	422.082	+	731.067i	0.448546	+	0.776904i	0.998292	−	0.0584277i	$-0.0186087\pi$
$941$	422.082	+	731.067i	0.448546	+	0.776904i	−0.549746	+	0.835332i	$0.685275\pi$
$942$	−195.615	+	730.046i	−0.207660	+	0.774996i
$943$	−32.2022	−	120.180i	−0.0341486	−	0.127444i
$944$	304.659	−	81.6332i	0.322732	−	0.0864758i
$945$	38.9861	+	10.4463i	0.0412551	+	0.0110543i
$946$	−812.295	+	468.979i	−0.858663	+	0.495749i
$947$	213.076	−	795.212i	0.225002	−	0.839717i	−0.757402	−	0.652948i	$-0.773532\pi$
$947$	213.076	−	795.212i	0.225002	−	0.839717i	0.982404	−	0.186769i	$-0.0598015\pi$
$948$	248.778	+	248.778i	0.262424	+	0.262424i
$949$	90.0659	+	336.130i	0.0949061	+	0.354194i
$950$	−627.295	+	362.169i	−0.660311	+	0.381231i
$951$	−675.620			−0.710431
$952$		−	757.628i		−	0.795827i
$953$	314.439	−	181.542i	0.329947	−	0.190495i	−0.325871	−	0.945414i	$-0.605657\pi$
$953$	314.439	−	181.542i	0.329947	−	0.190495i	0.655818	+	0.754919i	$0.272324\pi$
$954$	377.432	−	377.432i	0.395631	−	0.395631i
$955$	−35.2873	−	20.3731i	−0.0369501	−	0.0213331i
$956$	−446.996	+	446.996i	−0.467569	+	0.467569i
$957$	321.324	+	1199.20i	0.335762	+	1.25308i
$958$	−87.4969	+	151.549i	−0.0913328	+	0.158193i
$959$	857.109	−	1484.56i	0.893752	−	1.54802i
$960$	8.09441	−	30.2087i	0.00843167	−	0.0314674i
$961$			657.318i			0.683994i
$962$	−432.840	+	170.579i	−0.449938	+	0.177317i
$963$	−1582.02			−1.64280
$964$	−713.024	−	191.054i	−0.739651	−	0.198189i
$965$	−1.66065	−	0.958778i	−0.00172088	−	0.000993553i
$966$	159.510	+	92.0933i	0.165125	+	0.0953347i
$967$	1343.74	−	360.055i	1.38960	−	0.372342i	0.515001	−	0.857189i	$-0.327791\pi$
$967$	1343.74	−	360.055i	1.38960	−	0.372342i	0.874599	+	0.484847i	$0.161125\pi$
$968$	388.547	+	388.547i	0.401391	+	0.401391i
$969$	1211.47	−	2098.33i	1.25023	−	2.16546i
$970$	−93.6557	−	93.6557i	−0.0965522	−	0.0965522i
$971$	−285.080	−	493.774i	−0.293595	−	0.508521i	0.681062	−	0.732225i	$-0.261518\pi$
$971$	−285.080	−	493.774i	−0.293595	−	0.508521i	−0.974657	+	0.223705i	$0.928185\pi$
$972$	−697.433			−0.717524
$973$		−	120.655i		−	0.124003i
$974$	45.5548	+	78.9033i	0.0467709	+	0.0810095i
$975$	−906.070	+	242.781i	−0.929303	+	0.249006i
$976$	−291.425	+	291.425i	−0.298592	+	0.298592i
$977$	−818.846	−	219.409i	−0.838123	−	0.224574i	−0.185869	−	0.982575i	$-0.559510\pi$
$977$	−818.846	−	219.409i	−0.838123	−	0.224574i	−0.652254	+	0.758000i	$0.726177\pi$
$978$	194.546	+	336.964i	0.198922	+	0.344544i
$979$	−276.545	+	1032.08i	−0.282477	+	1.05422i
$980$	−25.5797	−	95.4649i	−0.0261018	−	0.0974131i
$981$	1534.69	−	411.220i	1.56442	−	0.419184i
$982$	310.221	+	83.1235i	0.315908	+	0.0846472i
$983$	−1174.42	+	678.052i	−1.19473	+	0.689779i	−0.959376	−	0.282131i	$-0.908959\pi$
$983$	−1174.42	+	678.052i	−1.19473	+	0.689779i	−0.235356	+	0.971909i	$0.575625\pi$
$984$	−135.666	+	506.312i	−0.137872	+	0.514545i
$985$	62.7306	+	62.7306i	0.0636859	+	0.0636859i
$986$	−154.083	−	575.044i	−0.156270	−	0.583209i
$987$	−750.019	+	433.024i	−0.759898	+	0.438727i
$988$	376.418			0.380989
$989$			109.344i			0.110560i
$990$	195.204	−	112.701i	0.197176	−	0.113840i
$991$	513.184	−	513.184i	0.517844	−	0.517844i	−0.399074	−	0.916919i	$-0.630668\pi$
$991$	513.184	−	513.184i	0.517844	−	0.517844i	0.916919	+	0.399074i	$0.130668\pi$
$992$	−85.3719	−	49.2895i	−0.0860604	−	0.0496870i
$993$	1691.36	−	1691.36i	1.70328	−	1.70328i
$994$	−289.464	−	1080.29i	−0.291211	−	1.08681i
$995$	54.3902	−	94.2066i	0.0546635	−	0.0946800i
$996$	−489.634	+	848.071i	−0.491601	+	0.851477i
$997$	191.337	−	714.081i	0.191913	−	0.716229i	−0.801131	−	0.598489i	$-0.795768\pi$
$997$	191.337	−	714.081i	0.191913	−	0.716229i	0.993044	−	0.117741i	$-0.0375652\pi$
$998$		−	659.188i		−	0.660510i
$999$	59.8506	+	151.870i	0.0599105	+	0.152022i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.3.g.b.45.1	✓	12
37.14	odd	12	inner	74.3.g.b.51.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.3.g.b.45.1	✓	12	1.1	even	1	trivial
74.3.g.b.51.1	yes	12	37.14	odd	12	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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	74.g (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36603 - 0.366025i) q^{2} +(-3.77609 - 2.18013i) q^{3} +(1.73205 + 1.00000i) q^{4} +(0.866025 - 0.232051i) q^{5} +(4.36026 + 4.36026i) q^{6} +(-5.10188 + 8.83671i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(5.00591 + 8.67050i) q^{9} +O(q^{10})\)	\(q+(-1.36603 - 0.366025i) q^{2} +(-3.77609 - 2.18013i) q^{3} +(1.73205 + 1.00000i) q^{4} +(0.866025 - 0.232051i) q^{5} +(4.36026 + 4.36026i) q^{6} +(-5.10188 + 8.83671i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(5.00591 + 8.67050i) q^{9} -1.26795 q^{10} +17.7559i q^{11} +(-4.36026 - 7.55218i) q^{12} +(-8.58823 + 2.30121i) q^{13} +(10.2038 - 10.2038i) q^{14} +(-3.77609 - 1.01180i) q^{15} +(2.00000 + 3.46410i) q^{16} +(6.79433 - 25.3568i) q^{17} +(-3.66458 - 13.6764i) q^{18} +(-20.4467 + 5.47869i) q^{19} +(1.73205 + 0.464102i) q^{20} +(38.5303 - 22.2455i) q^{21} +(6.49913 - 24.2551i) q^{22} +(-2.06993 - 2.06993i) q^{23} +(3.19193 + 11.9124i) q^{24} +(-20.9545 + 12.0981i) q^{25} +12.5740 q^{26} -4.41183i q^{27} +(-17.6734 + 10.2038i) q^{28} +(-11.3391 + 11.3391i) q^{29} +(4.78789 + 2.76429i) q^{30} +(12.3224 - 12.3224i) q^{31} +(-1.46410 - 5.46410i) q^{32} +(38.7102 - 67.0481i) q^{33} +(-18.5625 + 32.1511i) q^{34} +(-2.36779 + 8.83671i) q^{35} +20.0237i q^{36} +(-34.4233 + 13.5659i) q^{37} +29.9361 q^{38} +(37.4469 + 10.0339i) q^{39} +(-2.19615 - 1.26795i) q^{40} +(36.8085 + 21.2514i) q^{41} +(-60.7758 + 16.2848i) q^{42} +(-26.4125 - 26.4125i) q^{43} +(-17.7559 + 30.7542i) q^{44} +(6.34725 + 6.34725i) q^{45} +(2.06993 + 3.58523i) q^{46} -19.4657 q^{47} -17.4410i q^{48} +(-27.5583 - 47.7324i) q^{49} +(33.0526 - 8.85641i) q^{50} +(-80.9371 + 80.9371i) q^{51} +(-17.1765 - 4.60242i) q^{52} +(18.8493 + 32.6479i) q^{53} +(-1.61484 + 6.02667i) q^{54} +(4.12028 + 15.3771i) q^{55} +(27.8772 - 7.46967i) q^{56} +(89.1530 + 23.8885i) q^{57} +(19.6398 - 11.3391i) q^{58} +(20.4083 - 76.1648i) q^{59} +(-5.52858 - 5.52858i) q^{60} +(26.6673 + 99.5236i) q^{61} +(-21.3430 + 12.3224i) q^{62} -102.158 q^{63} +8.00000i q^{64} +(-6.90363 + 3.98581i) q^{65} +(-77.4204 + 77.4204i) q^{66} +(60.8125 + 35.1101i) q^{67} +(37.1249 - 37.1249i) q^{68} +(3.30354 + 12.3290i) q^{69} +(6.46892 - 11.2045i) q^{70} +(38.7519 - 67.1203i) q^{71} +(7.32917 - 27.3528i) q^{72} -39.1385i q^{73} +(51.9886 - 5.93160i) q^{74} +105.501 q^{75} +(-40.8935 - 10.9574i) q^{76} +(-156.904 - 90.5887i) q^{77} +(-47.4807 - 27.4130i) q^{78} +(-38.9698 + 10.4419i) q^{79} +(2.53590 + 2.53590i) q^{80} +(35.4349 - 61.3750i) q^{81} +(-42.5028 - 42.5028i) q^{82} +(-56.1474 - 97.2502i) q^{83} +88.9820 q^{84} -23.5363i q^{85} +(26.4125 + 45.7478i) q^{86} +(67.5379 - 18.0967i) q^{87} +(35.5119 - 35.5119i) q^{88} +(58.1258 + 15.5748i) q^{89} +(-6.34725 - 10.9938i) q^{90} +(23.4810 - 87.6322i) q^{91} +(-1.51530 - 5.65516i) q^{92} +(-73.3948 + 19.6661i) q^{93} +(26.5906 + 7.12493i) q^{94} +(-16.4361 + 9.48936i) q^{95} +(-6.38386 + 23.8249i) q^{96} +(73.8639 + 73.8639i) q^{97} +(20.1741 + 75.2908i) q^{98} +(-153.953 + 88.8847i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} + 4 q^{6} - 8 q^{7} - 24 q^{8} + 28 q^{9}+O(q^{10}) \) 12 * q - 6 * q^2 + 4 * q^6 - 8 * q^7 - 24 * q^8 + 28 * q^9	\( 12 q - 6 q^{2} + 4 q^{6} - 8 q^{7} - 24 q^{8} + 28 q^{9} - 36 q^{10} - 4 q^{12} + 16 q^{13} + 16 q^{14} + 24 q^{16} + 40 q^{17} + 28 q^{18} - 26 q^{19} + 66 q^{21} + 4 q^{22} - 80 q^{23} - 4 q^{24} - 54 q^{25} - 124 q^{26} - 12 q^{28} + 16 q^{29} - 6 q^{30} - 32 q^{31} + 24 q^{32} - 20 q^{33} - 10 q^{34} + 12 q^{35} - 148 q^{37} + 92 q^{38} + 216 q^{39} + 36 q^{40} + 66 q^{41} - 46 q^{42} + 152 q^{43} - 16 q^{44} + 84 q^{45} + 80 q^{46} - 112 q^{47} - 160 q^{49} + 168 q^{50} - 446 q^{51} + 32 q^{52} + 74 q^{53} + 230 q^{54} + 28 q^{56} + 50 q^{57} + 84 q^{58} - 114 q^{59} - 12 q^{60} + 448 q^{61} - 204 q^{62} - 784 q^{63} - 138 q^{65} + 40 q^{66} + 468 q^{67} + 20 q^{68} - 278 q^{69} + 18 q^{70} + 116 q^{71} - 56 q^{72} - 2 q^{74} + 76 q^{75} - 52 q^{76} + 60 q^{77} - 366 q^{78} + 114 q^{79} + 72 q^{80} + 14 q^{81} + 128 q^{82} - 20 q^{83} - 80 q^{84} - 152 q^{86} + 770 q^{87} + 32 q^{88} + 340 q^{89} - 84 q^{90} + 792 q^{91} + 68 q^{92} - 498 q^{93} + 20 q^{94} + 60 q^{95} + 8 q^{96} - 356 q^{97} - 160 q^{98} - 348 q^{99}+O(q^{100}) \) 12 * q - 6 * q^2 + 4 * q^6 - 8 * q^7 - 24 * q^8 + 28 * q^9 - 36 * q^10 - 4 * q^12 + 16 * q^13 + 16 * q^14 + 24 * q^16 + 40 * q^17 + 28 * q^18 - 26 * q^19 + 66 * q^21 + 4 * q^22 - 80 * q^23 - 4 * q^24 - 54 * q^25 - 124 * q^26 - 12 * q^28 + 16 * q^29 - 6 * q^30 - 32 * q^31 + 24 * q^32 - 20 * q^33 - 10 * q^34 + 12 * q^35 - 148 * q^37 + 92 * q^38 + 216 * q^39 + 36 * q^40 + 66 * q^41 - 46 * q^42 + 152 * q^43 - 16 * q^44 + 84 * q^45 + 80 * q^46 - 112 * q^47 - 160 * q^49 + 168 * q^50 - 446 * q^51 + 32 * q^52 + 74 * q^53 + 230 * q^54 + 28 * q^56 + 50 * q^57 + 84 * q^58 - 114 * q^59 - 12 * q^60 + 448 * q^61 - 204 * q^62 - 784 * q^63 - 138 * q^65 + 40 * q^66 + 468 * q^67 + 20 * q^68 - 278 * q^69 + 18 * q^70 + 116 * q^71 - 56 * q^72 - 2 * q^74 + 76 * q^75 - 52 * q^76 + 60 * q^77 - 366 * q^78 + 114 * q^79 + 72 * q^80 + 14 * q^81 + 128 * q^82 - 20 * q^83 - 80 * q^84 - 152 * q^86 + 770 * q^87 + 32 * q^88 + 340 * q^89 - 84 * q^90 + 792 * q^91 + 68 * q^92 - 498 * q^93 + 20 * q^94 + 60 * q^95 + 8 * q^96 - 356 * q^97 - 160 * q^98 - 348 * q^99

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