LMFDB - Embedded newform 120.4.b.b.11.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [120,4,Mod(11,120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(120, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))

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

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

chi := DirichletCharacter("120.11");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 120 = 2^{3} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	120.b (of order $2$, degree $1$, 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:	$7.08022920069$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.1
Character	$\chi$	$=$	120.11
Dual form			120.4.b.b.11.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.81366 - 0.288693i) q^{2} +(-3.93281 + 3.39603i) q^{3} +(7.83331 + 1.62457i) q^{4} -5.00000 q^{5} +(12.0460 - 8.41989i) q^{6} -20.9207i q^{7} +(-21.5712 - 6.83239i) q^{8} +(3.93395 - 26.7119i) q^{9} +O(q^{10})$	\(q+(-2.81366 - 0.288693i) q^{2} +(-3.93281 + 3.39603i) q^{3} +(7.83331 + 1.62457i) q^{4} -5.00000 q^{5} +(12.0460 - 8.41989i) q^{6} -20.9207i q^{7} +(-21.5712 - 6.83239i) q^{8} +(3.93395 - 26.7119i) q^{9} +(14.0683 + 1.44347i) q^{10} +46.5638i q^{11} +(-36.3240 + 20.2131i) q^{12} -14.8028i q^{13} +(-6.03968 + 58.8638i) q^{14} +(19.6640 - 16.9802i) q^{15} +(58.7216 + 25.4515i) q^{16} +19.4688i q^{17} +(-18.7803 + 74.0223i) q^{18} +120.209 q^{19} +(-39.1666 - 8.12283i) q^{20} +(71.0475 + 82.2773i) q^{21} +(13.4427 - 131.015i) q^{22} +89.5152 q^{23} +(108.039 - 46.3861i) q^{24} +25.0000 q^{25} +(-4.27346 + 41.6499i) q^{26} +(75.2429 + 118.412i) q^{27} +(33.9871 - 163.879i) q^{28} +150.385 q^{29} +(-60.2299 + 42.0994i) q^{30} +332.983i q^{31} +(-157.875 - 88.5642i) q^{32} +(-158.132 - 183.126i) q^{33} +(5.62051 - 54.7785i) q^{34} +104.604i q^{35} +(74.2110 - 202.851i) q^{36} +119.283i q^{37} +(-338.226 - 34.7035i) q^{38} +(50.2707 + 58.2165i) q^{39} +(107.856 + 34.1620i) q^{40} -516.650i q^{41} +(-176.150 - 252.011i) q^{42} +35.5262 q^{43} +(-75.6460 + 364.749i) q^{44} +(-19.6697 + 133.559i) q^{45} +(-251.865 - 25.8424i) q^{46} +288.892 q^{47} +(-317.375 + 99.3245i) q^{48} -94.6777 q^{49} +(-70.3414 - 7.21733i) q^{50} +(-66.1166 - 76.5670i) q^{51} +(24.0481 - 115.955i) q^{52} -249.034 q^{53} +(-177.523 - 354.894i) q^{54} -232.819i q^{55} +(-142.939 + 451.286i) q^{56} +(-472.758 + 408.233i) q^{57} +(-423.131 - 43.4150i) q^{58} +9.27078i q^{59} +(181.620 - 101.065i) q^{60} -184.845i q^{61} +(96.1300 - 936.900i) q^{62} +(-558.832 - 82.3011i) q^{63} +(418.637 + 294.766i) q^{64} +74.0139i q^{65} +(392.062 + 560.907i) q^{66} +822.813 q^{67} +(-31.6283 + 152.505i) q^{68} +(-352.046 + 303.996i) q^{69} +(30.1984 - 294.319i) q^{70} +578.587 q^{71} +(-267.366 + 549.330i) q^{72} -381.638 q^{73} +(34.4361 - 335.620i) q^{74} +(-98.3202 + 84.9008i) q^{75} +(941.633 + 195.287i) q^{76} +974.150 q^{77} +(-124.638 - 178.314i) q^{78} -991.394i q^{79} +(-293.608 - 127.257i) q^{80} +(-698.048 - 210.166i) q^{81} +(-149.153 + 1453.67i) q^{82} -227.546i q^{83} +(422.872 + 759.925i) q^{84} -97.3439i q^{85} +(-99.9586 - 10.2562i) q^{86} +(-591.434 + 510.711i) q^{87} +(318.142 - 1004.44i) q^{88} -401.965i q^{89} +(93.9015 - 370.111i) q^{90} -309.685 q^{91} +(701.201 + 145.423i) q^{92} +(-1130.82 - 1309.56i) q^{93} +(-812.843 - 83.4012i) q^{94} -601.044 q^{95} +(921.657 - 187.841i) q^{96} +1459.93 q^{97} +(266.390 + 27.3328i) q^{98} +(1243.81 + 183.180i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{2} - 3 q^{4} - 120 q^{5} + 11 q^{6} - 21 q^{8}+O(q^{10}) $ 24 * q + 3 * q^2 - 3 * q^4 - 120 * q^5 + 11 * q^6 - 21 * q^8	$ 24 q + 3 q^{2} - 3 q^{4} - 120 q^{5} + 11 q^{6} - 21 q^{8} - 15 q^{10} - 33 q^{12} + 54 q^{14} + 153 q^{16} + 59 q^{18} + 12 q^{19} + 15 q^{20} + 4 q^{21} - 102 q^{22} - 228 q^{23} - 27 q^{24} + 600 q^{25} - 336 q^{26} + 132 q^{27} - 186 q^{28} - 55 q^{30} - 177 q^{32} + 116 q^{33} + 408 q^{34} + 641 q^{36} - 312 q^{38} + 656 q^{39} + 105 q^{40} - 1042 q^{42} + 450 q^{44} - 1104 q^{46} + 924 q^{47} - 717 q^{48} - 816 q^{49} + 75 q^{50} - 700 q^{51} - 1548 q^{52} - 528 q^{53} + 987 q^{54} + 390 q^{56} - 172 q^{57} + 1410 q^{58} + 165 q^{60} + 978 q^{62} - 476 q^{63} + 1137 q^{64} - 582 q^{66} + 1632 q^{67} + 1608 q^{68} - 980 q^{69} - 270 q^{70} - 216 q^{71} - 589 q^{72} - 216 q^{73} - 768 q^{74} - 1812 q^{76} - 324 q^{78} - 765 q^{80} + 152 q^{81} + 2244 q^{82} - 134 q^{84} + 2808 q^{86} - 252 q^{87} + 2622 q^{88} - 295 q^{90} - 1800 q^{91} + 1836 q^{92} - 1968 q^{94} - 60 q^{95} + 1445 q^{96} + 792 q^{97} - 4851 q^{98} - 1328 q^{99}+O(q^{100}) $ 24 * q + 3 * q^2 - 3 * q^4 - 120 * q^5 + 11 * q^6 - 21 * q^8 - 15 * q^10 - 33 * q^12 + 54 * q^14 + 153 * q^16 + 59 * q^18 + 12 * q^19 + 15 * q^20 + 4 * q^21 - 102 * q^22 - 228 * q^23 - 27 * q^24 + 600 * q^25 - 336 * q^26 + 132 * q^27 - 186 * q^28 - 55 * q^30 - 177 * q^32 + 116 * q^33 + 408 * q^34 + 641 * q^36 - 312 * q^38 + 656 * q^39 + 105 * q^40 - 1042 * q^42 + 450 * q^44 - 1104 * q^46 + 924 * q^47 - 717 * q^48 - 816 * q^49 + 75 * q^50 - 700 * q^51 - 1548 * q^52 - 528 * q^53 + 987 * q^54 + 390 * q^56 - 172 * q^57 + 1410 * q^58 + 165 * q^60 + 978 * q^62 - 476 * q^63 + 1137 * q^64 - 582 * q^66 + 1632 * q^67 + 1608 * q^68 - 980 * q^69 - 270 * q^70 - 216 * q^71 - 589 * q^72 - 216 * q^73 - 768 * q^74 - 1812 * q^76 - 324 * q^78 - 765 * q^80 + 152 * q^81 + 2244 * q^82 - 134 * q^84 + 2808 * q^86 - 252 * q^87 + 2622 * q^88 - 295 * q^90 - 1800 * q^91 + 1836 * q^92 - 1968 * q^94 - 60 * q^95 + 1445 * q^96 + 792 * q^97 - 4851 * q^98 - 1328 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$.

$n$	$31$	$41$	$61$	$97$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

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 $

$2$	−2.81366	−	0.288693i	−0.994777	−	0.102068i
$2$	−2.81366	−	0.288693i	−0.994777	−	0.102068i
$3$	−3.93281	+	3.39603i	−0.756869	+	0.653566i
$3$	−3.93281	+	3.39603i	−0.756869	+	0.653566i
$4$	7.83331	+	1.62457i	0.979164	+	0.203071i
$5$	−5.00000			−0.447214
$5$	−5.00000			−0.447214
$6$	12.0460	−	8.41989i	0.819625	−	0.572901i
$7$		−	20.9207i		−	1.12961i	−0.825223	−	0.564807i	$-0.808951\pi$
$7$		−	20.9207i		−	1.12961i	0.825223	−	0.564807i	$-0.191049\pi$
$8$	−21.5712	−	6.83239i	−0.953323	−	0.301952i
$9$	3.93395	−	26.7119i	0.145702	−	0.989329i
$10$	14.0683	+	1.44347i	0.444878	+	0.0456464i
$11$			46.5638i			1.27632i	0.769904	+	0.638160i	$0.220304\pi$
$11$			46.5638i			1.27632i	−0.769904	+	0.638160i	$0.779696\pi$
$12$	−36.3240	+	20.2131i	−0.873819	+	0.486251i
$13$		−	14.8028i		−	0.315812i	−0.987454	−	0.157906i	$-0.949526\pi$
$13$		−	14.8028i		−	0.315812i	0.987454	−	0.157906i	$-0.0504743\pi$
$14$	−6.03968	+	58.8638i	−0.115298	+	1.12371i
$15$	19.6640	−	16.9802i	0.338482	−	0.292284i
$16$	58.7216	+	25.4515i	0.917524	+	0.397679i
$17$			19.4688i			0.277757i	0.990309	+	0.138879i	$0.0443498\pi$
$17$			19.4688i			0.277757i	−0.990309	+	0.138879i	$0.955650\pi$
$18$	−18.7803	+	74.0223i	−0.245920	+	0.969290i
$19$	120.209			1.45146			0.725731	−	0.687978i	$-0.241502\pi$
$19$	120.209			1.45146			0.725731	+	0.687978i	$0.241502\pi$
$20$	−39.1666	−	8.12283i	−0.437895	−	0.0908160i
$21$	71.0475	+	82.2773i	0.738278	+	0.854970i
$22$	13.4427	−	131.015i	0.130272	−	1.26965i
$23$	89.5152			0.811531			0.405765	−	0.913977i	$-0.367005\pi$
$23$	89.5152			0.811531			0.405765	+	0.913977i	$0.367005\pi$
$24$	108.039	−	46.3861i	0.918887	−	0.394522i
$25$	25.0000			0.200000
$26$	−4.27346	+	41.6499i	−0.0322344	+	0.314162i
$27$	75.2429	+	118.412i	0.536315	+	0.844018i
$28$	33.9871	−	163.879i	0.229392	−	1.10608i
$29$	150.385			0.962956			0.481478	−	0.876458i	$-0.340100\pi$
$29$	150.385			0.962956			0.481478	+	0.876458i	$0.340100\pi$
$30$	−60.2299	+	42.0994i	−0.366547	+	0.256209i
$31$			332.983i			1.92921i	0.263695	+	0.964606i	$0.415059\pi$
$31$			332.983i			1.92921i	−0.263695	+	0.964606i	$0.584941\pi$
$32$	−157.875	−	88.5642i	−0.872142	−	0.489253i
$33$	−158.132	−	183.126i	−0.834160	−	0.966007i
$34$	5.62051	−	54.7785i	0.0283503	−	0.276307i
$35$			104.604i			0.505179i
$36$	74.2110	−	202.851i	0.343570	−	0.939127i
$37$			119.283i			0.529998i	0.964249	+	0.264999i	$0.0853716\pi$
$37$			119.283i			0.529998i	−0.964249	+	0.264999i	$0.914628\pi$
$38$	−338.226	−	34.7035i	−1.44388	−	0.148149i
$39$	50.2707	+	58.2165i	0.206404	+	0.239028i
$40$	107.856	+	34.1620i	0.426339	+	0.135037i
$41$		−	516.650i		−	1.96798i	−0.178228	−	0.983989i	$-0.557036\pi$
$41$		−	516.650i		−	1.96798i	0.178228	−	0.983989i	$-0.442964\pi$
$42$	−176.150	−	252.011i	−0.647157	−	0.925860i
$43$	35.5262			0.125993			0.0629965	−	0.998014i	$-0.479934\pi$
$43$	35.5262			0.125993			0.0629965	+	0.998014i	$0.479934\pi$
$44$	−75.6460	+	364.749i	−0.259183	+	1.24973i
$45$	−19.6697	+	133.559i	−0.0651598	+	0.442441i
$46$	−251.865	−	25.8424i	−0.807293	−	0.0828317i
$47$	288.892			0.896580			0.448290	−	0.893888i	$-0.352033\pi$
$47$	288.892			0.896580			0.448290	+	0.893888i	$0.352033\pi$
$48$	−317.375	+	99.3245i	−0.954356	+	0.298672i
$49$	−94.6777			−0.276028
$50$	−70.3414	−	7.21733i	−0.198955	−	0.0204137i
$51$	−66.1166	−	76.5670i	−0.181533	−	0.210226i
$52$	24.0481	−	115.955i	0.0641321	−	0.309231i
$53$	−249.034			−0.645423			−0.322712	−	0.946497i	$-0.604594\pi$
$53$	−249.034			−0.645423			−0.322712	+	0.946497i	$0.604594\pi$
$54$	−177.523	−	354.894i	−0.447366	−	0.894351i
$55$		−	232.819i		−	0.570788i
$56$	−142.939	+	451.286i	−0.341089	+	1.07689i
$57$	−472.758	+	408.233i	−1.09857	+	0.948627i
$58$	−423.131	−	43.4150i	−0.957927	−	0.0982875i
$59$			9.27078i			0.0204568i	0.999948	+	0.0102284i	$0.00325586\pi$
$59$			9.27078i			0.0204568i	−0.999948	+	0.0102284i	$0.996744\pi$
$60$	181.620	−	101.065i	0.390784	−	0.217458i
$61$		−	184.845i		−	0.387983i	−0.981003	−	0.193991i	$-0.937857\pi$
$61$		−	184.845i		−	0.387983i	0.981003	−	0.193991i	$-0.0621434\pi$
$62$	96.1300	−	936.900i	0.196912	−	1.91914i
$63$	−558.832	−	82.3011i	−1.11756	−	0.164587i
$64$	418.637	+	294.766i	0.817650	+	0.575716i
$65$			74.0139i			0.141235i
$66$	392.062	+	560.907i	0.731204	+	1.04610i
$67$	822.813			1.50034			0.750168	−	0.661247i	$-0.229972\pi$
$67$	822.813			1.50034			0.750168	+	0.661247i	$0.229972\pi$
$68$	−31.6283	+	152.505i	−0.0564044	+	0.271970i
$69$	−352.046	+	303.996i	−0.614223	+	0.530389i
$70$	30.1984	−	294.319i	0.0515628	−	0.502540i
$71$	578.587			0.967122			0.483561	−	0.875311i	$-0.339343\pi$
$71$	578.587			0.967122			0.483561	+	0.875311i	$0.339343\pi$
$72$	−267.366	+	549.330i	−0.437631	+	0.899155i
$73$	−381.638			−0.611882			−0.305941	−	0.952050i	$-0.598971\pi$
$73$	−381.638			−0.611882			−0.305941	+	0.952050i	$0.598971\pi$
$74$	34.4361	−	335.620i	0.0540961	−	0.527230i
$75$	−98.3202	+	84.9008i	−0.151374	+	0.130713i
$76$	941.633	+	195.287i	1.42122	+	0.294750i
$77$	974.150			1.44175
$78$	−124.638	−	178.314i	−0.180929	−	0.258847i
$79$		−	991.394i		−	1.41191i	−0.708259	−	0.705953i	$-0.750519\pi$
$79$		−	991.394i		−	1.41191i	0.708259	−	0.705953i	$-0.249481\pi$
$80$	−293.608	−	127.257i	−0.410329	−	0.177848i
$81$	−698.048	−	210.166i	−0.957542	−	0.288294i
$82$	−149.153	+	1453.67i	−0.200869	+	1.95770i
$83$		−	227.546i		−	0.300920i	−0.988616	−	0.150460i	$-0.951924\pi$
$83$		−	227.546i		−	0.300920i	0.988616	−	0.150460i	$-0.0480755\pi$
$84$	422.872	+	759.925i	0.549276	+	0.987079i
$85$		−	97.3439i		−	0.124217i
$86$	−99.9586	−	10.2562i	−0.125335	−	0.0128599i
$87$	−591.434	+	510.711i	−0.728832	+	0.629356i
$88$	318.142	−	1004.44i	0.385387	−	1.21675i
$89$		−	401.965i		−	0.478744i	−0.970928	−	0.239372i	$-0.923058\pi$
$89$		−	401.965i		−	0.478744i	0.970928	−	0.239372i	$-0.0769415\pi$
$90$	93.9015	−	370.111i	0.109979	−	0.433480i
$91$	−309.685			−0.356745
$92$	701.201	+	145.423i	0.794622	+	0.164798i
$93$	−1130.82	−	1309.56i	−1.26087	−	1.46016i
$94$	−812.843	−	83.4012i	−0.891897	−	0.0915125i
$95$	−601.044			−0.649114
$96$	921.657	−	187.841i	0.979857	−	0.199703i
$97$	1459.93			1.52818			0.764088	−	0.645112i	$-0.223189\pi$
$97$	1459.93			1.52818			0.764088	+	0.645112i	$0.223189\pi$
$98$	266.390	+	27.3328i	0.274587	+	0.0281738i
$99$	1243.81	+	183.180i	1.26270	+	0.185962i
$100$	195.833	+	40.6142i	0.195833	+	0.0406142i
$101$	323.987			0.319188			0.159594	−	0.987183i	$-0.448982\pi$
$101$	323.987			0.319188			0.159594	+	0.987183i	$0.448982\pi$
$102$	163.925	+	234.521i	0.159127	+	0.227657i
$103$			860.647i			0.823321i	0.911337	+	0.411660i	$0.135051\pi$
$103$			860.647i			0.823321i	−0.911337	+	0.411660i	$0.864949\pi$
$104$	−101.138	+	319.314i	−0.0953600	+	0.301071i
$105$	−355.238	−	411.386i	−0.330168	−	0.382354i
$106$	700.696	+	71.8944i	0.642053	+	0.0658774i
$107$			1735.68i			1.56817i	0.620654	+	0.784084i	$0.286867\pi$
$107$			1735.68i			1.56817i	−0.620654	+	0.784084i	$0.713133\pi$
$108$	397.032	+	1049.80i	0.353745	+	0.935342i
$109$			1098.55i			0.965335i	0.875804	+	0.482668i	$0.160332\pi$
$109$			1098.55i			0.965335i	−0.875804	+	0.482668i	$0.839668\pi$
$110$	−67.2133	+	655.073i	−0.0582594	+	0.567807i
$111$	−405.087	−	469.115i	−0.346389	−	0.401139i
$112$	532.464	−	1228.50i	0.449224	−	1.03645i
$113$			603.137i			0.502110i	0.967973	+	0.251055i	$0.0807775\pi$
$113$			603.137i			0.502110i	−0.967973	+	0.251055i	$0.919223\pi$
$114$	1448.03	−	1012.14i	1.18965	−	0.831544i
$115$	−447.576			−0.362928
$116$	1178.01	+	244.310i	0.942892	+	0.195548i
$117$	−395.410	−	58.2333i	−0.312442	−	0.0460143i
$118$	2.67641	−	26.0848i	0.00208800	−	0.0203500i
$119$	407.302			0.313759
$120$	−540.193	+	231.931i	−0.410939	+	0.176436i
$121$	−837.188			−0.628992
$122$	−53.3635	+	520.090i	−0.0396008	+	0.385957i
$123$	1754.56	+	2031.88i	1.28620	+	1.48950i
$124$	−540.954	+	2608.36i	−0.391767	+	1.88902i
$125$	−125.000			−0.0894427
$126$	1548.60	+	392.898i	1.09492	+	0.277795i
$127$		−	1806.25i		−	1.26204i	−0.775768	−	0.631018i	$-0.782638\pi$
$127$		−	1806.25i		−	1.26204i	0.775768	−	0.631018i	$-0.217362\pi$
$128$	−1092.80	−	950.229i	−0.754617	−	0.656165i
$129$	−139.718	+	120.648i	−0.0953602	+	0.0823448i
$130$	21.3673	−	208.250i	0.0144157	−	0.140498i
$131$		−	777.056i		−	0.518257i	−0.965843	−	0.259129i	$-0.916565\pi$
$131$		−	777.056i		−	0.518257i	0.965843	−	0.259129i	$-0.0834353\pi$
$132$	−941.197	−	1691.38i	−0.620611	−	1.11527i
$133$		−	2514.86i		−	1.63959i
$134$	−2315.11	−	237.540i	−1.49250	−	0.153137i
$135$	−376.214	−	592.062i	−0.239847	−	0.377456i
$136$	133.018	−	419.966i	0.0838694	−	0.264793i
$137$		−	423.773i		−	0.264273i	−0.991232	−	0.132136i	$-0.957816\pi$
$137$		−	423.773i		−	0.264273i	0.991232	−	0.132136i	$-0.0421837\pi$
$138$	1078.30	−	753.708i	0.665151	−	0.464927i
$139$	−2112.08			−1.28880			−0.644402	−	0.764687i	$-0.722894\pi$
$139$	−2112.08			−1.28880			−0.644402	+	0.764687i	$0.722894\pi$
$140$	−169.936	+	819.394i	−0.102587	+	0.494653i
$141$	−1136.16	+	981.087i	−0.678594	+	0.585975i
$142$	−1627.95	−	167.034i	−0.962071	−	0.0987127i
$143$	689.274			0.403077
$144$	910.864	−	1468.44i	0.527120	−	0.849791i
$145$	−751.923			−0.430647
$146$	1073.80	+	110.176i	0.608686	+	0.0624539i
$147$	372.349	−	321.528i	0.208917	−	0.180403i
$148$	−193.782	+	934.377i	−0.107627	+	0.518955i
$149$	−1905.97			−1.04794			−0.523970	−	0.851737i	$-0.675550\pi$
$149$	−1905.97			−1.04794			−0.523970	+	0.851737i	$0.675550\pi$
$150$	301.149	−	210.497i	0.163925	−	0.114580i
$151$			2510.92i			1.35322i	0.736342	+	0.676610i	$0.236551\pi$
$151$			2510.92i			1.35322i	−0.736342	+	0.676610i	$0.763449\pi$
$152$	−2593.05	−	821.314i	−1.38371	−	0.438272i
$153$	520.048	+	76.5892i	0.274793	+	0.0404697i
$154$	−2740.92	−	281.230i	−1.43422	−	0.147157i
$155$		−	1664.92i		−	0.862770i
$156$	299.210	+	537.696i	0.153564	+	0.275962i
$157$			1107.81i			0.563142i	0.959540	+	0.281571i	$0.0908554\pi$
$157$			1107.81i			0.563142i	−0.959540	+	0.281571i	$0.909145\pi$
$158$	−286.209	+	2789.44i	−0.144111	+	1.40453i
$159$	979.402	−	845.727i	0.488501	−	0.421827i
$160$	789.373	+	442.821i	0.390034	+	0.218800i
$161$		−	1872.73i		−	0.916717i
$162$	1903.39	+	792.857i	0.923115	+	0.384523i
$163$	−2646.60			−1.27177			−0.635884	−	0.771785i	$-0.719364\pi$
$163$	−2646.60			−1.27177			−0.635884	+	0.771785i	$0.719364\pi$
$164$	839.332	−	4047.08i	0.399639	−	1.92697i
$165$	790.661	+	915.632i	0.373048	+	0.432011i
$166$	−65.6909	+	640.236i	−0.0307145	+	0.299349i
$167$	−1591.16			−0.737294			−0.368647	−	0.929570i	$-0.620179\pi$
$167$	−1591.16			−0.737294			−0.368647	+	0.929570i	$0.620179\pi$
$168$	−970.432	−	2260.25i	−0.445657	−	1.03799i
$169$	1977.88			0.900263
$170$	−28.1025	+	273.892i	−0.0126786	+	0.123568i
$171$	472.895	−	3211.00i	0.211481	−	1.43597i
$172$	278.288	+	57.7147i	0.123368	+	0.0255855i
$173$	2314.87			1.01732			0.508659	−	0.860968i	$-0.330141\pi$
$173$	2314.87			1.01732			0.508659	+	0.860968i	$0.330141\pi$
$174$	1811.53	−	1266.22i	0.789263	−	0.551678i
$175$		−	523.019i		−	0.225923i
$176$	−1185.12	+	2734.30i	−0.507566	+	1.17105i
$177$	−31.4838	−	36.4602i	−0.0133699	−	0.0154831i
$178$	−116.045	+	1130.99i	−0.0488647	+	0.476244i
$179$			2141.25i			0.894104i	0.894508	+	0.447052i	$0.147526\pi$
$179$			2141.25i			0.894104i	−0.894508	+	0.447052i	$0.852474\pi$
$180$	−371.055	+	1014.26i	−0.153649	+	0.419990i
$181$		−	602.074i		−	0.247248i	−0.992329	−	0.123624i	$-0.960548\pi$
$181$		−	602.074i		−	0.247248i	0.992329	−	0.123624i	$-0.0394516\pi$
$182$	871.347	+	89.4040i	0.354882	+	0.0364125i
$183$	627.739	+	726.959i	0.253573	+	0.293652i
$184$	−1930.95	−	611.603i	−0.773651	−	0.245043i
$185$		−	596.413i		−	0.237022i
$186$	2803.68	+	4011.11i	1.10525	+	1.58123i
$187$	−906.541			−0.354507
$188$	2262.98	+	469.325i	0.877899	+	0.182069i
$189$	2477.28	−	1574.14i	0.953415	−	0.605829i
$190$	1691.13	+	173.517i	0.645724	+	0.0662540i
$191$	1751.02			0.663349			0.331675	−	0.943394i	$-0.392386\pi$
$191$	1751.02			0.663349			0.331675	+	0.943394i	$0.392386\pi$
$192$	−2647.45	+	262.444i	−0.995122	+	0.0986471i
$193$	1873.55			0.698761			0.349381	−	0.936981i	$-0.386392\pi$
$193$	1873.55			0.698761			0.349381	+	0.936981i	$0.386392\pi$
$194$	−4107.73	−	421.471i	−1.52020	−	0.155979i
$195$	−251.353	−	291.082i	−0.0923066	−	0.106897i
$196$	−741.640	−	153.810i	−0.270277	−	0.0560533i
$197$	2672.17			0.966418			0.483209	−	0.875505i	$-0.339471\pi$
$197$	2672.17			0.966418			0.483209	+	0.875505i	$0.339471\pi$
$198$	−3446.76	−	874.483i	−1.23712	−	0.313873i
$199$			3676.97i			1.30982i	0.755708	+	0.654909i	$0.227293\pi$
$199$			3676.97i			1.30982i	−0.755708	+	0.654909i	$0.772707\pi$
$200$	−539.281	−	170.810i	−0.190665	−	0.0603904i
$201$	−3235.96	+	2794.30i	−1.13556	+	0.980570i
$202$	−911.589	−	93.5329i	−0.317521	−	0.0325790i
$203$		−	3146.16i		−	1.08777i
$204$	−393.524	−	707.184i	−0.135060	−	0.242710i
$205$			2583.25i			0.880107i
$206$	248.463	−	2421.56i	0.0840351	−	0.819021i
$207$	352.148	−	2391.12i	0.118241	−	0.802871i
$208$	376.753	−	869.242i	0.125592	−	0.289765i
$209$			5597.38i			1.85253i
$210$	880.752	+	1260.05i	0.289417	+	0.414057i
$211$	−5638.61			−1.83971			−0.919853	−	0.392263i	$-0.871692\pi$
$211$	−5638.61			−1.83971			−0.919853	+	0.392263i	$0.871692\pi$
$212$	−1950.76	−	404.572i	−0.631975	−	0.131067i
$213$	−2275.47	+	1964.90i	−0.731985	+	0.632079i
$214$	501.078	−	4883.59i	0.160061	−	1.55998i
$215$	−177.631			−0.0563458
$216$	−814.042	−	3068.39i	−0.256428	−	0.966563i
$217$	6966.26			2.17927
$218$	317.143	−	3090.93i	0.0985303	−	0.960294i
$219$	1500.91	−	1296.06i	0.463115	−	0.399906i
$220$	378.230	−	1823.74i	0.115910	−	0.558895i
$221$	288.192			0.0877190
$222$	1004.35	+	1436.87i	0.303636	+	0.434400i
$223$			3171.93i			0.952503i	0.879309	+	0.476252i	$0.158005\pi$
$223$			3171.93i			0.952503i	−0.879309	+	0.476252i	$0.841995\pi$
$224$	−1852.83	+	3302.85i	−0.552667	+	0.985184i
$225$	98.3487	−	667.797i	0.0291403	−	0.197866i
$226$	174.122	−	1697.02i	0.0512496	−	0.499487i
$227$		−	2573.31i		−	0.752407i	−0.926537	−	0.376203i	$-0.877229\pi$
$227$		−	2573.31i		−	0.752407i	0.926537	−	0.376203i	$-0.122771\pi$
$228$	−4366.46	+	2429.79i	−1.26832	+	0.705775i
$229$		−	3743.34i		−	1.08021i	−0.841599	−	0.540103i	$-0.818385\pi$
$229$		−	3743.34i		−	1.08021i	0.841599	−	0.540103i	$-0.181615\pi$
$230$	1259.32	+	129.212i	0.361032	+	0.0370435i
$231$	−3831.14	+	3308.24i	−1.09122	+	0.942279i
$232$	−3243.98	−	1027.49i	−0.918008	−	0.290767i
$233$			3023.43i			0.850093i	0.905171	+	0.425047i	$0.139742\pi$
$233$			3023.43i			0.850093i	−0.905171	+	0.425047i	$0.860258\pi$
$234$	1095.74	+	278.001i	0.306113	+	0.0776644i
$235$	−1444.46			−0.400963
$236$	−15.0610	+	72.6209i	−0.00415418	+	0.0200306i
$237$	3366.81	+	3898.96i	0.922775	+	1.06863i
$238$	−1146.01	−	117.585i	−0.312120	−	0.0320249i
$239$	746.235			0.201966			0.100983	−	0.994888i	$-0.467801\pi$
$239$	746.235			0.201966			0.100983	+	0.994888i	$0.467801\pi$
$240$	1586.87	−	496.623i	0.426801	−	0.133570i
$241$	2814.72			0.752333			0.376167	−	0.926552i	$-0.377242\pi$
$241$	2814.72			0.752333			0.376167	+	0.926552i	$0.377242\pi$
$242$	2355.56	+	241.691i	0.625707	+	0.0642003i
$243$	3459.02	−	1544.05i	0.913153	−	0.407617i
$244$	300.293	−	1447.95i	0.0787880	−	0.379899i
$245$	473.389			0.123444
$246$	−4350.13	−	6223.55i	−1.12746	−	1.61300i
$247$		−	1779.42i		−	0.458389i
$248$	2275.07	−	7182.86i	0.582530	−	1.83916i
$249$	772.753	+	894.894i	0.196672	+	0.227757i
$250$	351.707	+	36.0867i	0.0889756	+	0.00912928i
$251$		−	3132.37i		−	0.787702i	−0.919174	−	0.393851i	$-0.871143\pi$
$251$		−	3132.37i		−	0.787702i	0.919174	−	0.393851i	$-0.128857\pi$
$252$	−4243.80	−	1552.55i	−1.06085	−	0.388101i
$253$			4168.17i			1.03577i
$254$	−521.451	+	5082.16i	−0.128814	+	1.25544i
$255$	330.583	+	382.835i	0.0811840	+	0.0940159i
$256$	2800.44	+	2989.10i	0.683702	+	0.729761i
$257$			3930.23i			0.953934i	0.878921	+	0.476967i	$0.158264\pi$
$257$			3930.23i			0.953934i	−0.878921	+	0.476967i	$0.841736\pi$
$258$	427.948	−	299.127i	0.103267	−	0.0721815i
$259$	2495.48			0.598693
$260$	−120.240	+	579.774i	−0.0286808	+	0.138293i
$261$	591.605	−	4017.06i	0.140304	−	0.952680i
$262$	−224.331	+	2186.37i	−0.0528977	+	0.515550i
$263$	7609.98			1.78423			0.892113	−	0.451812i	$-0.149222\pi$
$263$	7609.98			1.78423			0.892113	+	0.451812i	$0.149222\pi$
$264$	2159.91	+	5030.69i	0.503536	+	1.17279i
$265$	1245.17			0.288642
$266$	−726.022	+	7075.94i	−0.167351	+	1.63103i
$267$	1365.09	+	1580.85i	0.312891	+	0.362347i
$268$	6445.35	+	1336.71i	1.46908	+	0.304675i
$269$	−6800.04			−1.54128			−0.770642	−	0.637268i	$-0.780064\pi$
$269$	−6800.04			−1.54128			−0.770642	+	0.637268i	$0.780064\pi$
$270$	887.613	+	1774.47i	0.200068	+	0.399966i
$271$		−	8455.73i		−	1.89538i	−0.319186	−	0.947692i	$-0.603410\pi$
$271$		−	8455.73i		−	1.89538i	0.319186	−	0.947692i	$-0.396590\pi$
$272$	−495.509	+	1143.24i	−0.110458	+	0.254849i
$273$	1217.93	−	1051.70i	0.270010	−	0.233157i
$274$	−122.340	+	1192.35i	−0.0269739	+	0.262893i
$275$			1164.10i			0.255264i
$276$	−3251.55	+	1809.38i	−0.709131	+	0.394608i
$277$		−	216.045i		−	0.0468625i	−0.999725	−	0.0234312i	$-0.992541\pi$
$277$		−	216.045i		−	0.0468625i	0.999725	−	0.0234312i	$-0.00745907\pi$
$278$	5942.65	+	609.742i	1.28207	+	0.131546i
$279$	8894.61	+	1309.94i	1.90862	+	0.281090i
$280$	714.694	−	2256.43i	0.152540	−	0.481599i
$281$		−	2697.76i		−	0.572722i	−0.958122	−	0.286361i	$-0.907554\pi$
$281$		−	2697.76i		−	0.572722i	0.958122	−	0.286361i	$-0.0924456\pi$
$282$	3479.99	−	2432.44i	0.734859	−	0.513651i
$283$	−5281.35			−1.10934			−0.554671	−	0.832070i	$-0.687156\pi$
$283$	−5281.35			−1.10934			−0.554671	+	0.832070i	$0.687156\pi$
$284$	4532.25	+	939.954i	0.946971	+	0.196394i
$285$	2363.79	−	2041.16i	0.491294	−	0.424239i
$286$	−1939.38	−	198.989i	−0.400972	−	0.0411414i
$287$	−10808.7			−2.22306
$288$	−2986.79	+	3868.72i	−0.611104	+	0.791550i
$289$	4533.97			0.922851
$290$	2115.65	+	217.075i	0.428398	+	0.0439555i
$291$	−5741.61	+	4957.96i	−1.15663	+	0.998765i
$292$	−2989.49	−	619.997i	−0.599133	−	0.124255i
$293$	−2085.85			−0.415893			−0.207947	−	0.978140i	$-0.566678\pi$
$293$	−2085.85			−0.415893			−0.207947	+	0.978140i	$0.566678\pi$
$294$	−1140.49	+	797.175i	−0.226240	+	0.158137i
$295$		−	46.3539i		−	0.00914857i
$296$	814.985	−	2573.07i	0.160034	−	0.505259i
$297$	−5513.73	+	3503.60i	−1.07724	+	0.684509i
$298$	5362.74	+	550.240i	1.04247	+	0.106962i
$299$		−	1325.07i		−	0.256291i
$300$	−908.100	+	505.327i	−0.174764	+	0.0972502i
$301$		−	743.235i		−	0.142324i
$302$	724.887	−	7064.87i	0.138121	−	1.34615i
$303$	−1274.18	+	1100.27i	−0.241583	+	0.208610i
$304$	7058.85	+	3059.49i	1.33175	+	0.577216i
$305$			924.224i			0.173511i
$306$	−1441.12	−	365.630i	−0.269227	−	0.0683061i
$307$	1905.22			0.354190			0.177095	−	0.984194i	$-0.443330\pi$
$307$	1905.22			0.354190			0.177095	+	0.984194i	$0.443330\pi$
$308$	7630.82	+	1582.57i	1.41171	+	0.292777i
$309$	−2922.78	−	3384.76i	−0.538095	−	0.623146i
$310$	−480.650	+	4684.50i	−0.0880616	+	0.858264i
$311$	−2855.85			−0.520709			−0.260354	−	0.965513i	$-0.583839\pi$
$311$	−2855.85			−0.520709			−0.260354	+	0.965513i	$0.583839\pi$
$312$	−686.643	−	1599.27i	−0.124595	−	0.290195i
$313$	−3991.11			−0.720737			−0.360369	−	0.932810i	$-0.617349\pi$
$313$	−3991.11			−0.720737			−0.360369	+	0.932810i	$0.617349\pi$
$314$	319.819	−	3117.01i	0.0574790	−	0.560200i
$315$	2794.16	+	411.506i	0.499788	+	0.0736054i
$316$	1610.59	−	7765.90i	0.286717	−	1.38249i
$317$	6525.22			1.15613			0.578065	−	0.815991i	$-0.303808\pi$
$317$	6525.22			1.15613			0.578065	+	0.815991i	$0.303808\pi$
$318$	−2999.86	+	2096.84i	−0.529005	+	0.369763i
$319$			7002.48i			1.22904i
$320$	−2093.18	−	1473.83i	−0.365664	−	0.257468i
$321$	−5894.41	−	6826.08i	−1.02490	−	1.18690i
$322$	−540.643	+	5269.20i	−0.0935679	+	0.911929i
$323$			2340.32i			0.403154i
$324$	−5126.60	−	2780.32i	−0.879047	−	0.476736i
$325$		−	370.069i		−	0.0631623i
$326$	7446.63	+	764.057i	1.26513	+	0.129807i
$327$	−3730.69	−	4320.37i	−0.630911	−	0.730632i
$328$	−3529.95	+	11144.8i	−0.594235	+	1.87612i
$329$		−	6043.84i		−	1.01279i
$330$	−1960.31	−	2804.53i	−0.327005	−	0.467832i
$331$	4440.15			0.737319			0.368660	−	0.929564i	$-0.379817\pi$
$331$	4440.15			0.737319			0.368660	+	0.929564i	$0.379817\pi$
$332$	369.663	−	1782.44i	0.0611082	−	0.294651i
$333$	3186.26	+	469.251i	0.524342	+	0.0772216i
$334$	4476.99	+	459.359i	0.733443	+	0.0752544i
$335$	−4114.06			−0.670971
$336$	2077.94	+	6639.71i	0.337384	+	1.07805i
$337$	−4075.64			−0.658796			−0.329398	−	0.944191i	$-0.606846\pi$
$337$	−4075.64			−0.658796			−0.329398	+	0.944191i	$0.606846\pi$
$338$	−5565.07	−	571.000i	−0.895561	−	0.0918885i
$339$	−2048.27	−	2372.02i	−0.328162	−	0.380031i
$340$	158.142	−	762.526i	0.0252248	−	0.121629i
$341$	−15505.0			−2.46229
$342$	−2257.56	+	8898.13i	−0.356944	+	1.40689i
$343$		−	5195.09i		−	0.817809i
$344$	−766.345	−	242.729i	−0.120112	−	0.0380439i
$345$	1760.23	−	1519.98i	0.274689	−	0.237197i
$346$	−6513.24	−	668.287i	−1.01201	−	0.103836i
$347$			10427.6i			1.61320i	0.591095	+	0.806602i	$0.298696\pi$
$347$			10427.6i			1.61320i	−0.591095	+	0.806602i	$0.701304\pi$
$348$	−5462.57	+	3039.73i	−0.841450	+	0.468238i
$349$		−	11110.6i		−	1.70411i	−0.523449	−	0.852057i	$-0.675355\pi$
$349$		−	11110.6i		−	1.70411i	0.523449	−	0.852057i	$-0.324645\pi$
$350$	−150.992	+	1471.59i	−0.0230596	+	0.224743i
$351$	1752.83	−	1113.80i	0.266551	−	0.169375i
$352$	4123.89	−	7351.24i	0.624443	−	1.11313i
$353$		−	10301.5i		−	1.55324i	−0.629972	−	0.776618i	$-0.716934\pi$
$353$		−	10301.5i		−	1.55324i	0.629972	−	0.776618i	$-0.283066\pi$
$354$	78.0589	+	111.676i	0.0117197	+	0.0167669i
$355$	−2892.94			−0.432510
$356$	653.019	−	3148.72i	0.0972189	−	0.468769i
$357$	−1601.84	+	1383.21i	−0.237474	+	0.205062i
$358$	618.164	−	6024.74i	0.0912598	−	0.889434i
$359$	−5240.94			−0.770490			−0.385245	−	0.922814i	$-0.625883\pi$
$359$	−5240.94			−0.770490			−0.385245	+	0.922814i	$0.625883\pi$
$360$	1336.83	−	2746.65i	0.195714	−	0.402114i
$361$	7591.15			1.10674
$362$	−173.815	+	1694.03i	−0.0252362	+	0.245956i
$363$	3292.50	−	2843.12i	0.476065	−	0.411088i
$364$	−2425.86	−	503.104i	−0.349312	−	0.0724446i
$365$	1908.19			0.273642
$366$	−1556.37	−	2226.64i	−0.222276	−	0.318000i
$367$		−	7753.30i		−	1.10278i	−0.834249	−	0.551388i	$-0.814098\pi$
$367$		−	7753.30i		−	1.10278i	0.834249	−	0.551388i	$-0.185902\pi$
$368$	5256.47	+	2278.29i	0.744600	+	0.322729i
$369$	−13800.7	−	2032.47i	−1.94698	−	0.286738i
$370$	−172.180	+	1678.10i	−0.0241925	+	0.235784i
$371$			5209.98i			0.729079i
$372$	−6730.61	−	12095.3i	−0.938081	−	1.68578i
$373$		−	1873.76i		−	0.260106i	−0.991507	−	0.130053i	$-0.958485\pi$
$373$		−	1873.76i		−	0.260106i	0.991507	−	0.130053i	$-0.0415147\pi$
$374$	2550.69	+	261.712i	0.352656	+	0.0361840i
$375$	491.601	−	424.504i	0.0676964	−	0.0584568i
$376$	−6231.76	−	1973.83i	−0.854730	−	0.270724i
$377$		−	2226.11i		−	0.304113i
$378$	−7424.65	+	3713.91i	−1.01027	+	0.505351i
$379$	2988.52			0.405039			0.202520	−	0.979278i	$-0.435087\pi$
$379$	2988.52			0.405039			0.202520	+	0.979278i	$0.435087\pi$
$380$	−4708.16	−	976.436i	−0.635589	−	0.131816i
$381$	6134.07	+	7103.62i	0.824824	+	0.955196i
$382$	−4926.78	−	505.509i	−0.659885	−	0.0677070i
$383$	−3869.52			−0.516249			−0.258124	−	0.966112i	$-0.583104\pi$
$383$	−3869.52			−0.516249			−0.258124	+	0.966112i	$0.583104\pi$
$384$	7524.79	+	25.8756i	0.999994	+	0.00343870i
$385$	−4870.75			−0.644770
$386$	−5271.52	−	540.881i	−0.695112	−	0.0713215i
$387$	139.758	−	948.972i	0.0183574	−	0.124649i
$388$	11436.1	+	2371.75i	1.49634	+	0.310328i
$389$	−11363.7			−1.48113			−0.740566	−	0.671984i	$-0.765443\pi$
$389$	−11363.7			−1.48113			−0.740566	+	0.671984i	$0.765443\pi$
$390$	623.189	+	891.570i	0.0809138	+	0.115760i
$391$			1742.75i			0.225409i
$392$	2042.32	+	646.875i	0.263144	+	0.0833473i
$393$	2638.91	+	3056.01i	0.338715	+	0.392253i
$394$	−7518.57	−	771.438i	−0.961371	−	0.0986409i
$395$			4956.97i			0.631424i
$396$	9445.54	+	3455.55i	1.19863	+	0.438505i
$397$			10805.7i			1.36606i	0.730392	+	0.683028i	$0.239337\pi$
$397$			10805.7i			1.36606i	−0.730392	+	0.683028i	$0.760663\pi$
$398$	1061.52	−	10345.7i	0.133691	−	1.30298i
$399$	8540.53	+	9890.45i	1.07158	+	1.24096i
$400$	1468.04	+	636.287i	0.183505	+	0.0795359i
$401$			9819.59i			1.22286i	0.791298	+	0.611430i	$0.209405\pi$
$401$			9819.59i			1.22286i	−0.791298	+	0.611430i	$0.790595\pi$
$402$	9911.58	−	6927.99i	1.22971	−	0.859544i
$403$	4929.08			0.609268
$404$	2537.89	+	526.339i	0.312537	+	0.0648177i
$405$	3490.24	+	1050.83i	0.428226	+	0.128929i
$406$	−908.275	+	8852.21i	−0.111027	+	1.08209i
$407$	−5554.25			−0.676447
$408$	903.081	+	2103.38i	0.109581	+	0.255227i
$409$	−8057.47			−0.974123			−0.487062	−	0.873368i	$-0.661931\pi$
$409$	−8057.47			−0.974123			−0.487062	+	0.873368i	$0.661931\pi$
$410$	745.766	−	7268.37i	0.0898312	−	0.875510i
$411$	1439.15	+	1666.62i	0.172720	+	0.200020i
$412$	−1398.18	+	6741.72i	−0.167192	+	0.806166i
$413$	193.952			0.0231083
$414$	−1681.12	+	6626.12i	−0.199572	+	0.786609i
$415$			1137.73i			0.134576i
$416$	−1311.00	+	2336.98i	−0.154512	+	0.275433i
$417$	8306.38	−	7172.67i	0.975457	−	0.842320i
$418$	1615.93	−	15749.1i	0.189085	−	1.84285i
$419$		−	1433.96i		−	0.167192i	−0.996500	−	0.0835961i	$-0.973359\pi$
$419$		−	1433.96i		−	0.167192i	0.996500	−	0.0835961i	$-0.0266406\pi$
$420$	−2114.36	−	3799.62i	−0.245644	−	0.441435i
$421$			5243.76i			0.607043i	0.952825	+	0.303522i	$0.0981625\pi$
$421$			5243.76i			0.607043i	−0.952825	+	0.303522i	$0.901838\pi$
$422$	15865.1	+	1627.83i	1.83010	+	0.187776i
$423$	1136.49	−	7716.85i	0.130633	−	0.887012i
$424$	5371.97	+	1701.50i	0.615297	+	0.194887i
$425$			486.720i			0.0555515i
$426$	6969.65	−	4871.64i	0.792677	−	0.554065i
$427$	−3867.09			−0.438271
$428$	−2819.72	+	13596.1i	−0.318449	+	1.53549i
$429$	−2710.78	+	2340.80i	−0.305076	+	0.263437i
$430$	499.793	+	51.2809i	0.0560515	+	0.00575113i
$431$	10959.4			1.22481			0.612406	−	0.790544i	$-0.290202\pi$
$431$	10959.4			1.22481			0.612406	+	0.790544i	$0.290202\pi$
$432$	1404.61	+	8868.41i	0.156434	+	0.987688i
$433$	−5297.16			−0.587911			−0.293955	−	0.955819i	$-0.594972\pi$
$433$	−5297.16			−0.587911			−0.293955	+	0.955819i	$0.594972\pi$
$434$	−19600.7	−	2011.11i	−2.16788	−	0.222434i
$435$	2957.17	−	2553.55i	0.325943	−	0.281457i
$436$	−1784.66	+	8605.25i	−0.196031	+	0.945222i
$437$	10760.5			1.17791
$438$	−4597.21	+	3213.35i	−0.501514	+	0.350548i
$439$			5766.45i			0.626920i	0.949601	+	0.313460i	$0.101488\pi$
$439$			5766.45i			0.626920i	−0.949601	+	0.313460i	$0.898512\pi$
$440$	−1590.71	+	5022.20i	−0.172350	+	0.544145i
$441$	−372.457	+	2529.02i	−0.0402178	+	0.273083i
$442$	−810.873	−	83.1991i	−0.0872609	−	0.00895335i
$443$			4964.92i			0.532484i	0.963906	+	0.266242i	$0.0857820\pi$
$443$			4964.92i			0.532484i	−0.963906	+	0.266242i	$0.914218\pi$
$444$	−2411.07	−	4332.82i	−0.257712	−	0.463123i
$445$			2009.83i			0.214101i
$446$	915.715	−	8924.72i	0.0972206	−	0.947529i
$447$	7495.81	−	6472.73i	0.793154	−	0.684899i
$448$	6166.73	−	8758.19i	0.650337	−	0.923629i
$449$		−	1021.53i		−	0.107370i	−0.998558	−	0.0536848i	$-0.982903\pi$
$449$		−	1021.53i		−	0.107370i	0.998558	−	0.0536848i	$-0.0170966\pi$
$450$	−469.508	+	1850.56i	−0.0491840	+	0.193858i
$451$	24057.2			2.51177
$452$	−979.837	+	4724.56i	−0.101964	+	0.491648i
$453$	−8527.17	−	9874.98i	−0.884419	−	1.02421i
$454$	−742.896	+	7240.40i	−0.0767970	+	0.748477i
$455$	1548.43			0.159541
$456$	12987.2	−	5576.02i	1.33373	−	0.572634i
$457$	−8540.31			−0.874177			−0.437088	−	0.899419i	$-0.643990\pi$
$457$	−8540.31			−0.874177			−0.437088	+	0.899419i	$0.643990\pi$
$458$	−1080.68	+	10532.5i	−0.110255	+	1.07456i
$459$	−2305.35	+	1464.89i	−0.234432	+	0.148965i
$460$	−3506.00	−	727.117i	−0.355366	−	0.0737000i
$461$	14876.5			1.50297			0.751484	−	0.659751i	$-0.229338\pi$
$461$	14876.5			1.50297			0.751484	+	0.659751i	$0.229338\pi$
$462$	11734.6	−	8202.23i	1.18169	−	0.825979i
$463$			10935.8i			1.09769i	0.835924	+	0.548846i	$0.184932\pi$
$463$			10935.8i			1.09769i	−0.835924	+	0.548846i	$0.815068\pi$
$464$	8830.82	+	3827.51i	0.883536	+	0.382948i
$465$	5654.11	+	6547.80i	0.563877	+	0.653004i
$466$	872.845	−	8506.90i	0.0867677	−	0.845654i
$467$		−	12924.0i		−	1.28062i	−0.768116	−	0.640311i	$-0.778805\pi$
$467$		−	12924.0i		−	1.28062i	0.768116	−	0.640311i	$-0.221195\pi$
$468$	−3002.77	−	1098.53i	−0.296587	−	0.108503i
$469$		−	17213.9i		−	1.69480i
$470$	4064.21	+	417.006i	0.398869	+	0.0409257i
$471$	−3762.17	−	4356.82i	−0.368050	−	0.426224i
$472$	63.3416	−	199.982i	0.00617698	−	0.0195020i
$473$			1654.24i			0.160807i
$474$	−8347.43	−	11942.3i	−0.808882	−	1.15723i
$475$	3005.22			0.290292
$476$	3190.52	+	661.689i	0.307221	+	0.0637152i
$477$	−979.686	+	6652.16i	−0.0940393	+	0.638536i
$478$	−2099.65	−	215.433i	−0.200911	−	0.0206144i
$479$	9728.21			0.927961			0.463981	−	0.885845i	$-0.346421\pi$
$479$	9728.21			0.927961			0.463981	+	0.885845i	$0.346421\pi$
$480$	−4608.29	+	939.205i	−0.438205	+	0.0893097i
$481$	1765.71			0.167380
$482$	−7919.66	−	812.592i	−0.748404	−	0.0767895i
$483$	6359.83	+	7365.07i	0.599135	+	0.693835i
$484$	−6557.96	−	1360.07i	−0.615886	−	0.127730i
$485$	−7299.63			−0.683421
$486$	−10178.2	+	3345.83i	−0.949989	+	0.312284i
$487$		−	2611.97i		−	0.243038i	−0.992589	−	0.121519i	$-0.961223\pi$
$487$		−	2611.97i		−	0.243038i	0.992589	−	0.121519i	$-0.0387766\pi$
$488$	−1262.93	+	3987.33i	−0.117152	+	0.369873i
$489$	10408.6	−	8987.95i	0.962561	−	0.831184i
$490$	−1331.95	−	136.664i	−0.122799	−	0.0125997i
$491$		−	578.318i		−	0.0531550i	−0.999647	−	0.0265775i	$-0.991539\pi$
$491$		−	578.318i		−	0.0531550i	0.999647	−	0.0265775i	$-0.00846088\pi$
$492$	10443.1	+	18766.8i	0.956931	+	1.71966i
$493$			2927.81i			0.267468i
$494$	−513.708	+	5006.69i	−0.0467870	+	0.455995i
$495$	−6219.03	−	915.898i	−0.564696	−	0.0831647i
$496$	−8474.92	+	19553.3i	−0.767208	+	1.77010i
$497$		−	12104.5i		−	1.09248i
$498$	−1915.91	−	2741.01i	−0.172398	−	0.246642i
$499$	−1254.36			−0.112531			−0.0562653	−	0.998416i	$-0.517919\pi$
$499$	−1254.36			−0.112531			−0.0562653	+	0.998416i	$0.517919\pi$
$500$	−979.164	−	203.071i	−0.0875791	−	0.0181632i
$501$	6257.74	−	5403.64i	0.558035	−	0.481870i
$502$	−904.293	+	8813.40i	−0.0803996	+	0.783588i
$503$	2512.08			0.222680			0.111340	−	0.993782i	$-0.464486\pi$
$503$	2512.08			0.222680			0.111340	+	0.993782i	$0.464486\pi$
$504$	11492.4	+	5593.50i	1.01570	+	0.494354i
$505$	−1619.94			−0.142745
$506$	1203.32	−	11727.8i	0.105720	−	1.03036i
$507$	−7778.61	+	6716.93i	−0.681381	+	0.588382i
$508$	2934.37	−	14148.9i	0.256283	−	1.23574i
$509$	12045.9			1.04897			0.524483	−	0.851421i	$-0.324259\pi$
$509$	12045.9			1.04897			0.524483	+	0.851421i	$0.324259\pi$
$510$	−819.625	−	1172.60i	−0.0711639	−	0.101811i
$511$			7984.16i			0.691191i
$512$	−7016.55	−	9218.77i	−0.605646	−	0.795734i
$513$	9044.85	+	14234.2i	0.778441	+	1.22506i
$514$	1134.63	−	11058.3i	0.0973666	−	0.948952i
$515$		−	4303.23i		−	0.368200i
$516$	−1290.45	+	718.094i	−0.110095	+	0.0612642i
$517$			13451.9i			1.14432i
$518$	−7021.42	−	720.428i	−0.595567	−	0.0611077i
$519$	−9103.93	+	7861.36i	−0.769977	+	0.664885i
$520$	505.692	−	1596.57i	0.0426463	−	0.134643i
$521$			11331.2i			0.952838i	0.879218	+	0.476419i	$0.158065\pi$
$521$			11331.2i			0.952838i	−0.879218	+	0.476419i	$0.841935\pi$
$522$	−2824.27	+	11131.8i	−0.236810	+	0.933384i
$523$	−13124.2			−1.09729			−0.548645	−	0.836056i	$-0.684856\pi$
$523$	−13124.2			−1.09729			−0.548645	+	0.836056i	$0.684856\pi$
$524$	1262.38	−	6086.92i	0.105243	−	0.507459i
$525$	1776.19	+	2056.93i	0.147656	+	0.170994i
$526$	−21411.9	−	2196.95i	−1.77491	−	0.182113i
$527$	−6482.78			−0.535853
$528$	−4624.93	−	14778.2i	−0.381201	−	1.21806i
$529$	−4154.03			−0.341418
$530$	−3503.48	−	359.472i	−0.287135	−	0.0294613i
$531$	247.640	+	36.4707i	0.0202385	+	0.00298059i
$532$	4085.55	−	19699.7i	0.332953	−	1.60543i
$533$	−7647.85			−0.621511
$534$	−3384.50	−	4842.06i	−0.274273	−	0.392390i
$535$		−	8678.38i		−	0.701306i
$536$	−17749.1	−	5621.78i	−1.43031	−	0.453030i
$537$	−7271.75	−	8421.12i	−0.584356	−	0.676719i
$538$	19133.0	+	1963.12i	1.53323	+	0.157317i
$539$		−	4408.55i		−	0.352300i
$540$	−1985.16	−	5248.99i	−0.158199	−	0.418298i
$541$		−	5447.57i		−	0.432919i	−0.976292	−	0.216460i	$-0.930549\pi$
$541$		−	5447.57i		−	0.432919i	0.976292	−	0.216460i	$-0.0694510\pi$
$542$	−2441.11	+	23791.5i	−0.193459	+	1.88549i
$543$	2044.66	+	2367.84i	0.161593	+	0.187134i
$544$	1724.24	−	3073.63i	0.135894	−	0.242244i
$545$		−	5492.73i		−	0.431711i
$546$	−3730.46	+	2607.51i	−0.292397	+	0.204380i
$547$	−5182.35			−0.405085			−0.202542	−	0.979274i	$-0.564920\pi$
$547$	−5182.35			−0.405085			−0.202542	+	0.979274i	$0.564920\pi$
$548$	688.447	−	3319.55i	0.0536661	−	0.258766i
$549$	−4937.55	−	727.170i	−0.383843	−	0.0565298i
$550$	336.066	−	3275.36i	0.0260544	−	0.253931i
$551$	18077.6			1.39769
$552$	9671.09	−	4152.26i	0.745705	−	0.320167i
$553$	−20740.7			−1.59491
$554$	−62.3708	+	607.877i	−0.00478318	+	0.0466177i
$555$	2025.44	+	2345.58i	0.154910	+	0.179395i
$556$	−16544.5	−	3431.21i	−1.26195	−	0.261719i
$557$	19645.2			1.49443			0.747213	−	0.664584i	$-0.231391\pi$
$557$	19645.2			1.49443			0.747213	+	0.664584i	$0.231391\pi$
$558$	−24648.2	−	6253.53i	−1.86997	−	0.474432i
$559$		−	525.887i		−	0.0397901i
$560$	−2662.32	+	6142.50i	−0.200899	+	0.463514i
$561$	3565.25	−	3078.64i	0.268316	−	0.231694i
$562$	−778.825	+	7590.57i	−0.0584568	+	0.569731i
$563$			5590.35i			0.418482i	0.977864	+	0.209241i	$0.0670993\pi$
$563$			5590.35i			0.418482i	−0.977864	+	0.209241i	$0.932901\pi$
$564$	−10493.7	+	5839.40i	−0.783449	+	0.435963i
$565$		−	3015.69i		−	0.224550i
$566$	14859.9	+	1524.69i	1.10355	+	0.113229i
$567$	−4396.83	+	14603.7i	−0.325661	+	1.08165i
$568$	−12480.8	−	3953.14i	−0.921980	−	0.292025i
$569$			5117.62i			0.377051i	0.982068	+	0.188525i	$0.0603708\pi$
$569$			5117.62i			0.377051i	−0.982068	+	0.188525i	$0.939629\pi$
$570$	−7240.16	+	5060.72i	−0.532030	+	0.371878i
$571$	10240.2			0.750506			0.375253	−	0.926922i	$-0.377556\pi$
$571$	10240.2			0.750506			0.375253	+	0.926922i	$0.377556\pi$
$572$	5399.30	+	1119.77i	0.394678	+	0.0818531i
$573$	−6886.44	+	5946.53i	−0.502069	+	0.433543i
$574$	30411.9	+	3120.40i	2.21145	+	0.226904i
$575$	2237.88			0.162306
$576$	9520.66	−	10023.0i	0.688705	−	0.725042i
$577$	−3988.23			−0.287750			−0.143875	−	0.989596i	$-0.545956\pi$
$577$	−3988.23			−0.287750			−0.143875	+	0.989596i	$0.545956\pi$
$578$	−12757.0	−	1308.93i	−0.918031	−	0.0941940i
$579$	−7368.30	+	6362.63i	−0.528871	+	0.456687i
$580$	−5890.05	−	1221.55i	−0.421674	−	0.0874519i
$581$	−4760.43			−0.339924
$582$	17586.2	−	12292.4i	1.25253	−	0.875493i
$583$		−	11596.0i		−	0.823767i
$584$	8232.41	+	2607.50i	0.583321	+	0.184759i
$585$	1977.05	+	291.167i	0.139728	+	0.0205782i
$586$	5868.86	+	602.171i	0.413721	+	0.0424496i
$587$		−	9381.45i		−	0.659649i	−0.944042	−	0.329824i	$-0.893010\pi$
$587$		−	9381.45i		−	0.659649i	0.944042	−	0.329824i	$-0.106990\pi$
$588$	3439.07	−	1913.73i	0.241199	−	0.134219i
$589$			40027.5i			2.80018i
$590$	−13.3821	+	130.424i	−0.000933780	+	0.00910079i
$591$	−10509.1	+	9074.78i	−0.731452	+	0.631619i
$592$	−3035.92	+	7004.46i	−0.210769	+	0.486286i
$593$		−	8375.60i		−	0.580008i	−0.957025	−	0.290004i	$-0.906343\pi$
$593$		−	8375.60i		−	0.580008i	0.957025	−	0.290004i	$-0.0936566\pi$
$594$	16525.2	−	8266.13i	1.14148	−	0.570982i
$595$	−2036.51			−0.140317
$596$	−14930.1	−	3096.37i	−1.02611	−	0.212806i
$597$	−12487.1	−	14460.8i	−0.856053	−	0.991361i
$598$	−382.540	+	3728.30i	−0.0261592	+	0.254952i
$599$	21970.8			1.49867			0.749334	−	0.662193i	$-0.230374\pi$
$599$	21970.8			1.49867			0.749334	+	0.662193i	$0.230374\pi$
$600$	2700.96	−	1159.65i	0.183777	−	0.0789044i
$601$	11220.4			0.761549			0.380775	−	0.924668i	$-0.375657\pi$
$601$	11220.4			0.761549			0.380775	+	0.924668i	$0.375657\pi$
$602$	−214.567	+	2091.21i	−0.0145267	+	0.141580i
$603$	3236.90	−	21978.9i	0.218602	−	1.48433i
$604$	−4079.16	+	19668.8i	−0.274799	+	1.32502i
$605$	4185.94			0.281294
$606$	3902.74	−	2727.94i	0.261614	−	0.182863i
$607$			6046.34i			0.404305i	0.979354	+	0.202153i	$0.0647937\pi$
$607$			6046.34i			0.404305i	−0.979354	+	0.202153i	$0.935206\pi$
$608$	−18977.9	−	10646.2i	−1.26588	−	0.710132i
$609$	10684.5	+	12373.2i	0.710929	+	0.823299i
$610$	266.817	−	2600.45i	0.0177100	−	0.172605i
$611$		−	4276.41i		−	0.283150i
$612$	3949.27	+	1444.80i	0.260849	+	0.0954290i
$613$		−	1249.20i		−	0.0823076i	−0.999153	−	0.0411538i	$-0.986897\pi$
$613$		−	1249.20i		−	0.0823076i	0.999153	−	0.0411538i	$-0.0131034\pi$
$614$	−5360.62	−	550.023i	−0.352340	−	0.0361516i
$615$	−8772.79	−	10159.4i	−0.575208	−	0.666126i
$616$	−21013.6	−	6655.78i	−1.37445	−	0.435339i
$617$		−	18950.5i		−	1.23650i	−0.785982	−	0.618250i	$-0.787842\pi$
$617$		−	18950.5i		−	1.23650i	0.785982	−	0.618250i	$-0.212158\pi$
$618$	7246.55	+	10367.3i	0.471681	+	0.674814i
$619$	6024.98			0.391218			0.195609	−	0.980682i	$-0.437332\pi$
$619$	6024.98			0.391218			0.195609	+	0.980682i	$0.437332\pi$
$620$	2704.77	−	13041.8i	0.175203	−	0.844793i
$621$	6735.38	+	10599.7i	0.435236	+	0.684947i
$622$	8035.38	+	824.465i	0.517989	+	0.0531480i
$623$	−8409.41			−0.540796
$624$	1470.28	+	4698.03i	0.0943241	+	0.301397i
$625$	625.000			0.0400000
$626$	11229.6	+	1152.21i	0.716973	+	0.0735645i
$627$	−19008.9	−	22013.4i	−1.21075	−	1.40212i
$628$	−1799.72	+	8677.86i	−0.114358	+	0.551408i
$629$	−2322.29			−0.147211
$630$	−7743.01	−	1964.49i	−0.489665	−	0.124234i
$631$			4056.01i			0.255891i	0.991781	+	0.127945i	$0.0408383\pi$
$631$			4056.01i			0.255891i	−0.991781	+	0.127945i	$0.959162\pi$
$632$	−6773.60	+	21385.6i	−0.426328	+	1.34600i
$633$	22175.6	−	19148.9i	1.39242	−	1.20237i
$634$	−18359.7	−	1883.79i	−1.15009	−	0.118004i
$635$			9031.23i			0.564399i
$636$	9045.90	−	5033.74i	0.563983	−	0.313838i
$637$			1401.49i			0.0871730i
$638$	2021.57	−	19702.6i	0.125446	−	1.22262i
$639$	2276.13	−	15455.1i	0.140911	−	0.956802i
$640$	5464.01	+	4751.14i	0.337475	+	0.293446i
$641$			2201.51i			0.135654i	0.997697	+	0.0678271i	$0.0216066\pi$
$641$			2201.51i			0.135654i	−0.997697	+	0.0678271i	$0.978393\pi$
$642$	14614.2	+	20907.9i	0.898405	+	1.28531i
$643$	−17477.9			−1.07195			−0.535974	−	0.844234i	$-0.680056\pi$
$643$	−17477.9			−1.07195			−0.535974	+	0.844234i	$0.680056\pi$
$644$	3042.37	−	14669.6i	0.186158	−	0.897616i
$645$	698.589	−	603.241i	0.0426464	−	0.0368257i
$646$	675.634	−	6584.85i	0.0411493	−	0.401049i
$647$	−20761.6			−1.26155			−0.630774	−	0.775966i	$-0.717263\pi$
$647$	−20761.6			−1.26155			−0.630774	+	0.775966i	$0.717263\pi$
$648$	13621.8	+	9302.88i	0.825796	+	0.563969i
$649$	−431.683			−0.0261094
$650$	−106.837	+	1041.25i	−0.00644688	+	0.0628325i
$651$	−27397.0	+	23657.6i	−1.64942	+	1.42429i
$652$	−20731.7	−	4299.59i	−1.24527	−	0.258259i
$653$	1894.01			0.113504			0.0567522	−	0.998388i	$-0.481925\pi$
$653$	1894.01			0.113504			0.0567522	+	0.998388i	$0.481925\pi$
$654$	9249.62	+	13233.0i	0.553041	+	0.791213i
$655$			3885.28i			0.231772i
$656$	13149.5	−	30338.5i	0.782624	−	1.80567i
$657$	−1501.34	+	10194.3i	−0.0891523	+	0.605352i
$658$	−1744.82	+	17005.3i	−0.103374	+	1.00750i
$659$			19300.8i			1.14090i	0.821333	+	0.570449i	$0.193231\pi$
$659$			19300.8i			1.14090i	−0.821333	+	0.570449i	$0.806769\pi$
$660$	4705.99	+	8456.92i	0.277546	+	0.498765i
$661$		−	30514.2i		−	1.79556i	−0.440443	−	0.897781i	$-0.645179\pi$
$661$		−	30514.2i		−	1.79556i	0.440443	−	0.897781i	$-0.354821\pi$
$662$	−12493.1	−	1281.84i	−0.733469	−	0.0752571i
$663$	−1133.40	+	978.710i	−0.0663918	+	0.0573302i
$664$	−1554.68	+	4908.45i	−0.0908636	+	0.286874i
$665$			12574.3i			0.733248i
$666$	−8829.57	−	2240.16i	−0.513722	−	0.130337i
$667$	13461.7			0.781469
$668$	−12464.1	−	2584.95i	−0.721931	−	0.149723i
$669$	−10772.0	−	12474.6i	−0.622524	−	0.720920i
$670$	11575.6	+	1187.70i	0.667467	+	0.0684850i
$671$	8607.08			0.495190
$672$	−3929.78	−	19281.8i	−0.225587	−	1.10686i
$673$	−13462.1			−0.771063			−0.385532	−	0.922695i	$-0.625982\pi$
$673$	−13462.1			−0.771063			−0.385532	+	0.922695i	$0.625982\pi$
$674$	11467.4	+	1176.61i	0.655356	+	0.0672423i
$675$	1881.07	+	2960.31i	0.107263	+	0.168804i
$676$	15493.3	+	3213.19i	0.881505	+	0.182817i
$677$	−10835.4			−0.615123			−0.307561	−	0.951528i	$-0.599513\pi$
$677$	−10835.4			−0.615123			−0.307561	+	0.951528i	$0.599513\pi$
$678$	5078.35	+	7265.38i	0.287659	+	0.411542i
$679$		−	30542.8i		−	1.72625i
$680$	−665.092	+	2099.83i	−0.0375075	+	0.118419i
$681$	8739.03	+	10120.3i	0.491748	+	0.569474i
$682$	43625.7	+	4476.18i	2.44943	+	0.251322i
$683$		−	5702.28i		−	0.319461i	−0.987161	−	0.159730i	$-0.948938\pi$
$683$		−	5702.28i		−	0.319461i	0.987161	−	0.159730i	$-0.0510624\pi$
$684$	8920.82	−	24384.5i	0.498678	−	1.36311i
$685$			2118.86i			0.118186i
$686$	−1499.79	+	14617.2i	−0.0834725	+	0.813538i
$687$	12712.5	+	14721.8i	0.705986	+	0.817574i
$688$	2086.16	+	904.195i	0.115602	+	0.0501048i
$689$			3686.39i			0.203832i
$690$	−5391.49	+	3768.54i	−0.297465	+	0.207922i
$691$	10946.3			0.602627			0.301313	−	0.953525i	$-0.402575\pi$
$691$	10946.3			0.602627			0.301313	+	0.953525i	$0.402575\pi$
$692$	18133.1	+	3760.66i	0.996122	+	0.206588i
$693$	3832.25	−	26021.4i	0.210065	−	1.42636i
$694$	3010.37	−	29339.6i	0.164657	−	1.60478i
$695$	10560.4			0.576371
$696$	16247.3	−	6975.76i	0.884848	−	0.379907i
$697$	10058.5			0.546621
$698$	−3207.55	+	31261.3i	−0.173936	+	1.69521i
$699$	−10267.7	−	11890.6i	−0.555592	−	0.643409i
$700$	849.679	−	4096.97i	0.0458783	−	0.221216i
$701$	−28180.5			−1.51835			−0.759174	−	0.650888i	$-0.774397\pi$
$701$	−28180.5			−1.51835			−0.759174	+	0.650888i	$0.774397\pi$
$702$	−5253.42	+	2627.83i	−0.282446	+	0.141283i
$703$			14338.8i			0.769272i
$704$	−13725.4	+	19493.3i	−0.734797	+	1.04358i
$705$	5680.79	−	4905.43i	0.303476	−	0.262056i
$706$	−2973.97	+	28984.8i	−0.158536	+	1.54512i
$707$		−	6778.06i		−	0.360559i
$708$	−187.391	−	336.752i	−0.00994714	−	0.0178756i
$709$		−	6517.20i		−	0.345216i	−0.984991	−	0.172608i	$-0.944781\pi$
$709$		−	6517.20i		−	0.345216i	0.984991	−	0.172608i	$-0.0552194\pi$
$710$	8139.73	+	835.171i	0.430251	+	0.0441457i
$711$	−26482.0	−	3900.09i	−1.39684	−	0.205717i
$712$	−2746.38	+	8670.89i	−0.144558	+	0.456398i
$713$			29807.1i			1.56562i
$714$	4906.35	−	3429.43i	0.257164	−	0.179753i
$715$	−3446.37			−0.180261
$716$	−3478.60	+	16773.1i	−0.181566	+	0.875474i
$717$	−2934.80	+	2534.24i	−0.152862	+	0.131998i
$718$	14746.2	+	1513.02i	0.766466	+	0.0786428i
$719$	−36949.3			−1.91652			−0.958258	−	0.285903i	$-0.907706\pi$
$719$	−36949.3			−1.91652			−0.958258	+	0.285903i	$0.907706\pi$
$720$	−4554.32	+	7342.19i	−0.235735	+	0.380038i
$721$	18005.4			0.930035
$722$	−21358.9	−	2191.51i	−1.10096	−	0.112964i
$723$	−11069.8	+	9558.89i	−0.569418	+	0.491700i
$724$	978.110	−	4716.24i	0.0502088	−	0.242096i
$725$	3759.62			0.192591
$726$	−10084.8	+	7049.03i	−0.515537	+	0.360350i
$727$		−	20155.9i		−	1.02825i	−0.857714	−	0.514126i	$-0.828116\pi$
$727$		−	20155.9i		−	1.02825i	0.857714	−	0.514126i	$-0.171884\pi$
$728$	6680.29	+	2115.89i	0.340094	+	0.107720i
$729$	−8360.02	+	17819.4i	−0.424733	+	0.905319i
$730$	−5368.99	−	550.882i	−0.272213	−	0.0279302i
$731$			691.653i			0.0349955i
$732$	3736.28	+	6714.30i	0.188657	+	0.339027i
$733$		−	33594.3i		−	1.69282i	−0.532535	−	0.846408i	$-0.678761\pi$
$733$		−	33594.3i		−	1.69282i	0.532535	−	0.846408i	$-0.321239\pi$
$734$	−2238.33	+	21815.1i	−0.112559	+	1.09702i
$735$	−1861.75	+	1607.64i	−0.0934307	+	0.0806786i
$736$	−14132.2	−	7927.84i	−0.707770	−	0.397044i
$737$			38313.3i			1.91491i
$738$	38243.6	+	9702.84i	1.90754	+	0.483965i
$739$	3183.11			0.158447			0.0792237	−	0.996857i	$-0.474756\pi$
$739$	3183.11			0.158447			0.0792237	+	0.996857i	$0.474756\pi$
$740$	968.912	−	4671.89i	0.0481323	−	0.232084i
$741$	6042.98	+	6998.13i	0.299588	+	0.346940i
$742$	1504.08	−	14659.1i	0.0744160	−	0.725272i
$743$	2499.08			0.123395			0.0616975	−	0.998095i	$-0.480349\pi$
$743$	2499.08			0.123395			0.0616975	+	0.998095i	$0.480349\pi$
$744$	15445.8	+	35975.0i	0.761116	+	1.77273i
$745$	9529.85			0.468653
$746$	−540.941	+	5272.10i	−0.0265486	+	0.258747i
$747$	−6078.17	−	895.153i	−0.297709	−	0.0438446i
$748$	−7101.22	−	1472.74i	−0.347121	−	0.0719901i
$749$	36311.6			1.77143
$750$	−1505.75	+	1052.49i	−0.0733095	+	0.0512418i
$751$		−	11193.8i		−	0.543900i	−0.962311	−	0.271950i	$-0.912331\pi$
$751$		−	11193.8i		−	0.543900i	0.962311	−	0.271950i	$-0.0876686\pi$
$752$	16964.2	+	7352.73i	0.822634	+	0.356551i
$753$	10637.6	+	12319.0i	0.514816	+	0.596187i
$754$	−642.663	+	6263.51i	−0.0310403	+	0.302525i
$755$		−	12554.6i		−	0.605178i
$756$	21962.6	−	8306.21i	1.05658	−	0.399595i
$757$		−	34868.9i		−	1.67415i	−0.547089	−	0.837074i	$-0.684264\pi$
$757$		−	34868.9i		−	1.67415i	0.547089	−	0.837074i	$-0.315736\pi$
$758$	−8408.66	−	862.765i	−0.402924	−	0.0413417i
$759$	−14155.2	−	16392.6i	−0.676946	−	0.783945i
$760$	12965.3	+	4106.57i	0.618815	+	0.196001i
$761$		−	8865.50i		−	0.422305i	−0.977453	−	0.211153i	$-0.932278\pi$
$761$		−	8865.50i		−	0.422305i	0.977453	−	0.211153i	$-0.0677217\pi$
$762$	−15208.4	−	21758.0i	−0.723021	−	1.03440i
$763$	22982.4			1.09046
$764$	13716.3	+	2844.66i	0.649528	+	0.134707i
$765$	−2600.24	−	382.946i	−0.122891	−	0.0180986i
$766$	10887.5	+	1117.10i	0.513552	+	0.0526927i
$767$	137.233			0.00646050
$768$	−21164.7	−	2245.16i	−0.994421	−	0.105489i
$769$	9493.12			0.445164			0.222582	−	0.974914i	$-0.428552\pi$
$769$	9493.12			0.445164			0.222582	+	0.974914i	$0.428552\pi$
$770$	13704.6	+	1406.15i	0.641402	+	0.0658107i
$771$	−13347.2	−	15456.8i	−0.623459	−	0.722003i
$772$	14676.1	+	3043.70i	0.684202	+	0.141898i
$773$	−8672.21			−0.403516			−0.201758	−	0.979435i	$-0.564665\pi$
$773$	−8672.21			−0.403516			−0.201758	+	0.979435i	$0.564665\pi$
$774$	−667.194	+	2629.73i	−0.0309842	+	0.122124i
$775$			8324.58i			0.385842i
$776$	−31492.4	−	9974.80i	−1.45685	−	0.461436i
$777$	−9814.24	+	8474.73i	−0.453132	+	0.391286i
$778$	31973.4	+	3280.61i	1.47340	+	0.151177i
$779$		−	62105.8i		−	2.85645i
$780$	−1496.05	−	2688.48i	−0.0686758	−	0.123414i
$781$			26941.2i			1.23436i
$782$	503.121	−	4903.51i	0.0230071	−	0.224231i
$783$	11315.4	+	17807.4i	0.516448	+	0.812752i
$784$	−5559.62	−	2409.69i	−0.253263	−	0.109771i
$785$		−	5539.07i		−	0.251845i
$786$	−6542.72	−	9360.39i	−0.296910	−	0.424776i
$787$	7442.47			0.337097			0.168548	−	0.985693i	$-0.446092\pi$
$787$	7442.47			0.337097			0.168548	+	0.985693i	$0.446092\pi$
$788$	20932.0	+	4341.12i	0.946282	+	0.196251i
$789$	−29928.6	+	25843.7i	−1.35043	+	1.16611i
$790$	1431.04	−	13947.2i	0.0644484	−	0.628126i
$791$	12618.1			0.567190
$792$	−25578.9	−	12449.6i	−1.14761	−	0.558557i
$793$	−2736.22			−0.122530
$794$	3119.54	−	30403.6i	0.139431	−	1.35892i
$795$	−4897.01	+	4228.63i	−0.218464	+	0.188647i
$796$	−5973.49	+	28802.9i	−0.265986	+	1.28253i
$797$	13284.2			0.590404			0.295202	−	0.955435i	$-0.404613\pi$
$797$	13284.2			0.590404			0.295202	+	0.955435i	$0.404613\pi$
$798$	−21174.8	−	30293.9i	−0.939324	−	1.34385i
$799$			5624.38i			0.249032i
$800$	−3946.86	−	2214.10i	−0.174428	−	0.0978505i
$801$	−10737.2	−	1581.31i	−0.473635	−	0.0697538i
$802$	2834.85	−	27628.9i	0.124815	−	1.21647i
$803$		−	17770.5i		−	0.780957i
$804$	−29887.8	+	16631.6i	−1.31102	+	0.729540i
$805$			9363.63i			0.409968i
$806$	−13868.7	−	1422.99i	−0.606086	−	0.0621870i
$807$	26743.2	−	23093.1i	1.16655	−	1.00733i
$808$	−6988.81	−	2213.61i	−0.304289	−	0.0963793i
$809$		−	16361.0i		−	0.711027i	−0.934671	−	0.355513i	$-0.884306\pi$
$809$		−	16361.0i		−	0.711027i	0.934671	−	0.355513i	$-0.115694\pi$
$810$	−9516.97	−	3964.28i	−0.412830	−	0.171964i
$811$	−7135.50			−0.308954			−0.154477	−	0.987996i	$-0.549369\pi$
$811$	−7135.50			−0.308954			−0.154477	+	0.987996i	$0.549369\pi$
$812$	5111.15	−	24644.9i	0.220894	−	1.06510i
$813$	28715.9	+	33254.8i	1.23876	+	1.43456i
$814$	15627.7	+	1603.47i	0.672914	+	0.0690439i
$815$	13233.0			0.568752
$816$	−1933.73	−	6178.90i	−0.0829584	−	0.265079i
$817$	4270.57			0.182874
$818$	22671.0	+	2326.14i	0.969036	+	0.0994273i
$819$	−1218.29	+	8272.27i	−0.0519784	+	0.352938i
$820$	−4196.66	+	20235.4i	−0.178724	+	0.861769i
$821$	−19570.8			−0.831945			−0.415972	−	0.909377i	$-0.636559\pi$
$821$	−19570.8			−0.831945			−0.415972	+	0.909377i	$0.636559\pi$
$822$	−3568.12	−	5104.76i	−0.151402	−	0.216604i
$823$			36147.1i			1.53099i	0.643440	+	0.765496i	$0.277506\pi$
$823$			36147.1i			1.53099i	−0.643440	+	0.765496i	$0.722494\pi$
$824$	5880.28	−	18565.2i	0.248603	−	0.784891i
$825$	−3953.30	−	4578.16i	−0.166832	−	0.193201i
$826$	−545.713	−	55.9925i	−0.0229876	−	0.00235863i
$827$			26853.3i			1.12912i	0.825392	+	0.564559i	$0.190954\pi$
$827$			26853.3i			1.12912i	−0.825392	+	0.564559i	$0.809046\pi$
$828$	6643.02	−	18158.3i	0.278817	−	0.762131i
$829$			22721.2i			0.951918i	0.879468	+	0.475959i	$0.157899\pi$
$829$			22721.2i			0.951918i	−0.879468	+	0.475959i	$0.842101\pi$
$830$	328.455	−	3201.18i	0.0137359	−	0.133873i
$831$	733.696	+	849.664i	0.0306277	+	0.0354687i
$832$	4363.36	−	6196.99i	0.181818	−	0.258223i
$833$		−	1843.26i		−	0.0766689i
$834$	−25442.0	+	17783.4i	−1.05634	+	0.738357i
$835$	7955.82			0.329728
$836$	−9093.31	+	43846.0i	−0.376195	+	1.81393i
$837$	−39429.4	+	25054.6i	−1.62829	+	1.03467i
$838$	−413.975	+	4034.67i	−0.0170651	+	0.166319i
$839$	−7891.14			−0.324711			−0.162355	−	0.986732i	$-0.551909\pi$
$839$	−7891.14			−0.324711			−0.162355	+	0.986732i	$0.551909\pi$
$840$	4852.16	+	11301.2i	0.199304	+	0.464202i
$841$	−1773.45			−0.0727153
$842$	1513.84	−	14754.1i	0.0619600	−	0.603873i
$843$	9161.68	+	10609.8i	0.374312	+	0.433476i
$844$	−44169.0	−	9160.30i	−1.80137	−	0.373591i
$845$	−9889.39			−0.402610
$846$	−5425.48	+	21384.5i	−0.220487	+	0.869046i
$847$			17514.6i			0.710518i
$848$	−14623.7	−	6338.28i	−0.592192	−	0.256672i
$849$	20770.5	−	17935.6i	0.839626	−	0.725028i
$850$	140.513	−	1369.46i	0.00567005	−	0.0552613i
$851$			10677.6i			0.430110i
$852$	−21016.6	+	11695.0i	−0.845090	+	0.470264i
$853$			29197.3i			1.17198i	0.810320	+	0.585988i	$0.199293\pi$
$853$			29197.3i			1.17198i	−0.810320	+	0.585988i	$0.800707\pi$
$854$	10880.7	+	1116.40i	0.435982	+	0.0447337i
$855$	−2364.47	+	16055.0i	−0.0945770	+	0.642187i
$856$	11858.8	−	37440.7i	0.473512	−	1.49497i
$857$			16417.1i			0.654372i	0.944960	+	0.327186i	$0.106100\pi$
$857$			16417.1i			0.654372i	−0.944960	+	0.327186i	$0.893900\pi$
$858$	8302.97	−	5803.61i	0.330372	−	0.230923i
$859$	−24884.1			−0.988398			−0.494199	−	0.869349i	$-0.664538\pi$
$859$	−24884.1			−0.988398			−0.494199	+	0.869349i	$0.664538\pi$
$860$	−1391.44	−	288.574i	−0.0551718	−	0.0114422i
$861$	42508.5	−	36706.7i	1.68256	−	1.45292i
$862$	−30835.9	−	3163.89i	−1.21841	−	0.125015i
$863$	−18704.2			−0.737771			−0.368886	−	0.929475i	$-0.620261\pi$
$863$	−18704.2			−0.737771			−0.368886	+	0.929475i	$0.620261\pi$
$864$	−1391.84	−	25358.1i	−0.0548047	−	0.998497i
$865$	−11574.3			−0.454959
$866$	14904.4	+	1529.25i	0.584840	+	0.0600071i
$867$	−17831.2	+	15397.5i	−0.698477	+	0.603144i
$868$	54568.9	+	11317.2i	2.13386	+	0.442545i
$869$	46163.1			1.80204
$870$	−9057.65	+	6331.11i	−0.352969	+	0.246718i
$871$		−	12179.9i		−	0.473824i
$872$	7505.69	−	23697.0i	0.291485	−	0.920276i
$873$	5743.27	−	38997.4i	0.222658	−	1.51187i
$874$	−30276.4	−	3106.49i	−1.17175	−	0.120227i
$875$			2615.09i			0.101036i
$876$	13862.6	−	7714.08i	0.534674	−	0.297528i
$877$		−	12917.5i		−	0.497369i	−0.968585	−	0.248684i	$-0.920002\pi$
$877$		−	12917.5i		−	0.497369i	0.968585	−	0.248684i	$-0.0799982\pi$
$878$	1664.74	−	16224.8i	0.0639887	−	0.623646i
$879$	8203.25	−	7083.61i	0.314777	−	0.271814i
$880$	5925.59	−	13671.5i	0.226990	−	0.523712i
$881$		−	9627.73i		−	0.368180i	−0.982909	−	0.184090i	$-0.941066\pi$
$881$		−	9627.73i		−	0.368180i	0.982909	−	0.184090i	$-0.0589338\pi$
$882$	1778.08	−	7008.26i	0.0678809	−	0.267552i
$883$	−11382.8			−0.433818			−0.216909	−	0.976192i	$-0.569598\pi$
$883$	−11382.8			−0.433818			−0.216909	+	0.976192i	$0.569598\pi$
$884$	2257.50	+	468.187i	0.0858913	+	0.0178132i
$885$	157.419	+	182.301i	0.00597920	+	0.00692427i
$886$	1433.34	−	13969.6i	0.0543498	−	0.529703i
$887$	30347.9			1.14880			0.574399	−	0.818576i	$-0.305236\pi$
$887$	30347.9			1.14880			0.574399	+	0.818576i	$0.305236\pi$
$888$	5533.05	+	12887.1i	0.209096	+	0.487008i
$889$	−37788.0			−1.42561
$890$	580.223	−	5654.96i	0.0218529	−	0.212983i
$891$	9786.14	−	32503.8i	0.367955	−	1.22213i
$892$	−5153.01	+	24846.7i	−0.193426	+	0.932657i
$893$	34727.4			1.30135
$894$	−22959.3	+	16048.0i	−0.858918	+	0.600366i
$895$		−	10706.2i		−	0.399855i
$896$	−19879.5	+	22862.2i	−0.741214	+	0.852426i
$897$	4499.99	+	5211.26i	0.167503	+	0.193979i
$898$	−294.909	+	2874.23i	−0.0109591	+	0.106809i
$899$			50075.6i			1.85775i
$900$	1855.28	−	5071.29i	0.0687139	−	0.187825i
$901$		−	4848.39i		−	0.179271i
$902$	−67688.6	−	6945.14i	−2.49865	−	0.256373i
$903$	2524.05	+	2923.00i	0.0930179	+	0.107720i
$904$	4120.87	−	13010.4i	0.151613	−	0.478673i
$905$			3010.37i			0.110573i
$906$	21141.7	+	30246.5i	0.775260	+	1.10913i
$907$	51376.4			1.88084			0.940422	−	0.340008i	$-0.110430\pi$
$907$	51376.4			1.88084			0.940422	+	0.340008i	$0.110430\pi$
$908$	4180.51	−	20157.5i	0.152792	−	0.736730i
$909$	1274.55	−	8654.31i	0.0465062	−	0.315781i
$910$	−4356.74	−	447.020i	−0.158708	−	0.0162841i
$911$	−8045.96			−0.292617			−0.146309	−	0.989239i	$-0.546739\pi$
$911$	−8045.96			−0.292617			−0.146309	+	0.989239i	$0.546739\pi$
$912$	−38151.2	+	11939.7i	−1.38521	+	0.433511i
$913$	10595.4			0.384071
$914$	24029.5	+	2465.53i	0.869611	+	0.0892259i
$915$	−3138.69	−	3634.80i	−0.113401	−	0.131325i
$916$	6081.31	−	29322.8i	0.219358	−	1.05770i
$917$	−16256.6			−0.585431
$918$	6909.36	−	3456.15i	0.248413	−	0.124259i
$919$			22359.0i			0.802565i	0.915954	+	0.401282i	$0.131435\pi$
$919$			22359.0i			0.802565i	−0.915954	+	0.401282i	$0.868565\pi$
$920$	9654.77	+	3058.02i	0.345987	+	0.109587i
$921$	−7492.84	+	6470.17i	−0.268076	+	0.231487i
$922$	−41857.4	−	4294.75i	−1.49512	−	0.153406i
$923$		−	8564.70i		−	0.305429i
$924$	−35385.0	+	19690.6i	−1.25983	+	0.701052i
$925$			2982.06i			0.106000i
$926$	3157.10	−	30769.6i	0.112040	−	1.09196i
$927$	22989.5	+	3385.74i	0.814535	+	0.119959i
$928$	−23741.9	−	13318.7i	−0.839835	−	0.471129i
$929$		−	46843.5i		−	1.65434i	−0.561949	−	0.827172i	$-0.689948\pi$
$929$		−	46843.5i		−	1.65434i	0.561949	−	0.827172i	$-0.310052\pi$
$930$	−14018.4	−	20055.5i	−0.494281	−	0.707148i
$931$	−11381.1			−0.400645
$932$	−4911.77	+	23683.5i	−0.172629	+	0.832381i
$933$	11231.5	−	9698.56i	0.394108	−	0.340318i
$934$	−3731.07	+	36363.6i	−0.130711	+	1.27393i
$935$	4532.71			0.158540
$936$	8131.61	+	3957.76i	0.283964	+	0.138209i
$937$	−300.096			−0.0104629			−0.00523143	−	0.999986i	$-0.501665\pi$
$937$	−300.096			−0.0104629			−0.00523143	+	0.999986i	$0.501665\pi$
$938$	−4969.52	+	48433.9i	−0.172986	+	1.68595i
$939$	15696.3	−	13553.9i	0.545504	−	0.471050i
$940$	−11314.9	−	2346.62i	−0.392608	−	0.0814238i
$941$	−45810.8			−1.58702			−0.793512	−	0.608554i	$-0.791750\pi$
$941$	−45810.8			−1.58702			−0.793512	+	0.608554i	$0.791750\pi$
$942$	9327.67	+	13344.7i	0.322624	+	0.461565i
$943$		−	46248.0i		−	1.59708i
$944$	−235.955	+	544.395i	−0.00813525	+	0.0187696i
$945$	−12386.4	+	7870.69i	−0.426380	+	0.270935i
$946$	477.567	−	4654.45i	0.0164134	−	0.159968i
$947$			11023.9i			0.378277i	0.981950	+	0.189138i	$0.0605695\pi$
$947$			11023.9i			0.378277i	−0.981950	+	0.189138i	$0.939431\pi$
$948$	20039.1	+	36011.4i	0.686540	+	1.23375i
$949$			5649.31i			0.193240i
$950$	−8455.65	−	867.586i	−0.288776	−	0.0296297i
$951$	−25662.4	+	22159.9i	−0.875038	+	0.755607i
$952$	−8786.00	−	2782.85i	−0.299113	−	0.0947401i
$953$		−	22044.9i		−	0.749321i	−0.927162	−	0.374660i	$-0.877759\pi$
$953$		−	22044.9i		−	0.749321i	0.927162	−	0.374660i	$-0.122241\pi$
$954$	4676.93	−	18434.1i	0.158723	−	0.625602i
$955$	−8755.12			−0.296659
$956$	5845.49	+	1212.31i	0.197758	+	0.0410134i
$957$	−23780.6	−	27539.4i	−0.803259	−	0.930222i
$958$	−27371.8	−	2808.47i	−0.923115	−	0.0947156i
$959$	−8865.65			−0.298526
$960$	13237.3	−	1312.22i	0.445032	−	0.0441163i
$961$	−81086.9			−2.72186
$962$	−4968.11	−	509.749i	−0.166505	−	0.0170842i
$963$	46363.1	+	6828.05i	1.55143	+	0.228485i
$964$	22048.6	+	4572.71i	0.736658	+	0.152777i
$965$	−9367.74			−0.312496
$966$	−15768.1	−	22558.8i	−0.525188	−	0.751364i
$967$			45315.7i			1.50699i	0.657456	+	0.753493i	$0.271633\pi$
$967$			45315.7i			1.50699i	−0.657456	+	0.753493i	$0.728367\pi$
$968$	18059.2	+	5720.00i	0.599633	+	0.189925i
$969$	−7947.80	−	9204.02i	−0.263488	−	0.305135i
$970$	20538.7	+	2107.36i	0.679852	+	0.0697558i
$971$			28977.6i			0.957709i	0.877894	+	0.478855i	$0.158948\pi$
$971$			28977.6i			0.957709i	−0.877894	+	0.478855i	$0.841052\pi$
$972$	29604.0	−	6475.62i	0.976902	−	0.213689i
$973$			44186.2i			1.45585i
$974$	−754.058	+	7349.19i	−0.0248066	+	0.241769i
$975$	1256.77	+	1455.41i	0.0412808	+	0.0478056i
$976$	4704.57	−	10854.4i	0.154293	−	0.355984i
$977$		−	37060.4i		−	1.21358i	−0.794863	−	0.606790i	$-0.792457\pi$
$977$		−	37060.4i		−	1.21358i	0.794863	−	0.606790i	$-0.207543\pi$
$978$	−31880.9	+	22284.1i	−1.04237	+	0.728596i
$979$	18717.0			0.611030
$980$	3708.20	+	769.051i	0.120872	+	0.0250678i
$981$	29344.2	+	4321.62i	0.955034	+	0.140651i
$982$	−166.956	+	1627.19i	−0.00542545	+	0.0528774i
$983$	1665.39			0.0540365			0.0270182	−	0.999635i	$-0.491399\pi$
$983$	1665.39			0.0540365			0.0270182	+	0.999635i	$0.491399\pi$
$984$	−23965.4	−	55818.1i	−0.776411	−	1.80835i
$985$	−13360.9			−0.432195
$986$	845.238	−	8237.84i	0.0273001	−	0.266071i
$987$	20525.1	+	23769.3i	0.661925	+	0.766549i
$988$	2890.79	−	13938.8i	0.0930854	−	0.448838i
$989$	3180.14			0.102247
$990$	17233.8	+	4372.41i	0.553259	+	0.140368i
$991$		−	19316.6i		−	0.619184i	−0.950869	−	0.309592i	$-0.899808\pi$
$991$		−	19316.6i		−	0.619184i	0.950869	−	0.309592i	$-0.100192\pi$
$992$	29490.4	−	52569.6i	0.943872	−	1.68255i
$993$	−17462.3	+	15078.9i	−0.558054	+	0.481887i
$994$	−3494.48	+	34057.8i	−0.111507	+	1.08677i
$995$		−	18384.9i		−	0.585768i
$996$	4599.40	+	8265.37i	0.146323	+	0.262950i
$997$		−	29267.3i		−	0.929694i	−0.885391	−	0.464847i	$-0.846109\pi$
$997$		−	29267.3i		−	0.929694i	0.885391	−	0.464847i	$-0.153891\pi$
$998$	3529.33	+	362.125i	0.111943	+	0.0114858i
$999$	−14124.5	+	8975.16i	−0.447328	+	0.284246i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	120.4.b.b.11.1	yes	24
3.2	odd	2		120.4.b.a.11.24	yes	24
4.3	odd	2		480.4.b.a.431.19		24
8.3	odd	2		120.4.b.a.11.23	✓	24
8.5	even	2		480.4.b.b.431.19		24
12.11	even	2		480.4.b.b.431.20		24
24.5	odd	2		480.4.b.a.431.20		24
24.11	even	2	inner	120.4.b.b.11.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.4.b.a.11.23	✓	24	8.3	odd	2
120.4.b.a.11.24	yes	24	3.2	odd	2
120.4.b.b.11.1	yes	24	1.1	even	1	trivial
120.4.b.b.11.2	yes	24	24.11	even	2	inner
480.4.b.a.431.19		24	4.3	odd	2
480.4.b.a.431.20		24	24.5	odd	2
480.4.b.b.431.19		24	8.5	even	2
480.4.b.b.431.20		24	12.11	even	2

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:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	120.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.81366 - 0.288693i) q^{2} +(-3.93281 + 3.39603i) q^{3} +(7.83331 + 1.62457i) q^{4} -5.00000 q^{5} +(12.0460 - 8.41989i) q^{6} -20.9207i q^{7} +(-21.5712 - 6.83239i) q^{8} +(3.93395 - 26.7119i) q^{9} +O(q^{10})\)	\(q+(-2.81366 - 0.288693i) q^{2} +(-3.93281 + 3.39603i) q^{3} +(7.83331 + 1.62457i) q^{4} -5.00000 q^{5} +(12.0460 - 8.41989i) q^{6} -20.9207i q^{7} +(-21.5712 - 6.83239i) q^{8} +(3.93395 - 26.7119i) q^{9} +(14.0683 + 1.44347i) q^{10} +46.5638i q^{11} +(-36.3240 + 20.2131i) q^{12} -14.8028i q^{13} +(-6.03968 + 58.8638i) q^{14} +(19.6640 - 16.9802i) q^{15} +(58.7216 + 25.4515i) q^{16} +19.4688i q^{17} +(-18.7803 + 74.0223i) q^{18} +120.209 q^{19} +(-39.1666 - 8.12283i) q^{20} +(71.0475 + 82.2773i) q^{21} +(13.4427 - 131.015i) q^{22} +89.5152 q^{23} +(108.039 - 46.3861i) q^{24} +25.0000 q^{25} +(-4.27346 + 41.6499i) q^{26} +(75.2429 + 118.412i) q^{27} +(33.9871 - 163.879i) q^{28} +150.385 q^{29} +(-60.2299 + 42.0994i) q^{30} +332.983i q^{31} +(-157.875 - 88.5642i) q^{32} +(-158.132 - 183.126i) q^{33} +(5.62051 - 54.7785i) q^{34} +104.604i q^{35} +(74.2110 - 202.851i) q^{36} +119.283i q^{37} +(-338.226 - 34.7035i) q^{38} +(50.2707 + 58.2165i) q^{39} +(107.856 + 34.1620i) q^{40} -516.650i q^{41} +(-176.150 - 252.011i) q^{42} +35.5262 q^{43} +(-75.6460 + 364.749i) q^{44} +(-19.6697 + 133.559i) q^{45} +(-251.865 - 25.8424i) q^{46} +288.892 q^{47} +(-317.375 + 99.3245i) q^{48} -94.6777 q^{49} +(-70.3414 - 7.21733i) q^{50} +(-66.1166 - 76.5670i) q^{51} +(24.0481 - 115.955i) q^{52} -249.034 q^{53} +(-177.523 - 354.894i) q^{54} -232.819i q^{55} +(-142.939 + 451.286i) q^{56} +(-472.758 + 408.233i) q^{57} +(-423.131 - 43.4150i) q^{58} +9.27078i q^{59} +(181.620 - 101.065i) q^{60} -184.845i q^{61} +(96.1300 - 936.900i) q^{62} +(-558.832 - 82.3011i) q^{63} +(418.637 + 294.766i) q^{64} +74.0139i q^{65} +(392.062 + 560.907i) q^{66} +822.813 q^{67} +(-31.6283 + 152.505i) q^{68} +(-352.046 + 303.996i) q^{69} +(30.1984 - 294.319i) q^{70} +578.587 q^{71} +(-267.366 + 549.330i) q^{72} -381.638 q^{73} +(34.4361 - 335.620i) q^{74} +(-98.3202 + 84.9008i) q^{75} +(941.633 + 195.287i) q^{76} +974.150 q^{77} +(-124.638 - 178.314i) q^{78} -991.394i q^{79} +(-293.608 - 127.257i) q^{80} +(-698.048 - 210.166i) q^{81} +(-149.153 + 1453.67i) q^{82} -227.546i q^{83} +(422.872 + 759.925i) q^{84} -97.3439i q^{85} +(-99.9586 - 10.2562i) q^{86} +(-591.434 + 510.711i) q^{87} +(318.142 - 1004.44i) q^{88} -401.965i q^{89} +(93.9015 - 370.111i) q^{90} -309.685 q^{91} +(701.201 + 145.423i) q^{92} +(-1130.82 - 1309.56i) q^{93} +(-812.843 - 83.4012i) q^{94} -601.044 q^{95} +(921.657 - 187.841i) q^{96} +1459.93 q^{97} +(266.390 + 27.3328i) q^{98} +(1243.81 + 183.180i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{2} - 3 q^{4} - 120 q^{5} + 11 q^{6} - 21 q^{8}+O(q^{10}) \) 24 * q + 3 * q^2 - 3 * q^4 - 120 * q^5 + 11 * q^6 - 21 * q^8	\( 24 q + 3 q^{2} - 3 q^{4} - 120 q^{5} + 11 q^{6} - 21 q^{8} - 15 q^{10} - 33 q^{12} + 54 q^{14} + 153 q^{16} + 59 q^{18} + 12 q^{19} + 15 q^{20} + 4 q^{21} - 102 q^{22} - 228 q^{23} - 27 q^{24} + 600 q^{25} - 336 q^{26} + 132 q^{27} - 186 q^{28} - 55 q^{30} - 177 q^{32} + 116 q^{33} + 408 q^{34} + 641 q^{36} - 312 q^{38} + 656 q^{39} + 105 q^{40} - 1042 q^{42} + 450 q^{44} - 1104 q^{46} + 924 q^{47} - 717 q^{48} - 816 q^{49} + 75 q^{50} - 700 q^{51} - 1548 q^{52} - 528 q^{53} + 987 q^{54} + 390 q^{56} - 172 q^{57} + 1410 q^{58} + 165 q^{60} + 978 q^{62} - 476 q^{63} + 1137 q^{64} - 582 q^{66} + 1632 q^{67} + 1608 q^{68} - 980 q^{69} - 270 q^{70} - 216 q^{71} - 589 q^{72} - 216 q^{73} - 768 q^{74} - 1812 q^{76} - 324 q^{78} - 765 q^{80} + 152 q^{81} + 2244 q^{82} - 134 q^{84} + 2808 q^{86} - 252 q^{87} + 2622 q^{88} - 295 q^{90} - 1800 q^{91} + 1836 q^{92} - 1968 q^{94} - 60 q^{95} + 1445 q^{96} + 792 q^{97} - 4851 q^{98} - 1328 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 3 * q^4 - 120 * q^5 + 11 * q^6 - 21 * q^8 - 15 * q^10 - 33 * q^12 + 54 * q^14 + 153 * q^16 + 59 * q^18 + 12 * q^19 + 15 * q^20 + 4 * q^21 - 102 * q^22 - 228 * q^23 - 27 * q^24 + 600 * q^25 - 336 * q^26 + 132 * q^27 - 186 * q^28 - 55 * q^30 - 177 * q^32 + 116 * q^33 + 408 * q^34 + 641 * q^36 - 312 * q^38 + 656 * q^39 + 105 * q^40 - 1042 * q^42 + 450 * q^44 - 1104 * q^46 + 924 * q^47 - 717 * q^48 - 816 * q^49 + 75 * q^50 - 700 * q^51 - 1548 * q^52 - 528 * q^53 + 987 * q^54 + 390 * q^56 - 172 * q^57 + 1410 * q^58 + 165 * q^60 + 978 * q^62 - 476 * q^63 + 1137 * q^64 - 582 * q^66 + 1632 * q^67 + 1608 * q^68 - 980 * q^69 - 270 * q^70 - 216 * q^71 - 589 * q^72 - 216 * q^73 - 768 * q^74 - 1812 * q^76 - 324 * q^78 - 765 * q^80 + 152 * q^81 + 2244 * q^82 - 134 * q^84 + 2808 * q^86 - 252 * q^87 + 2622 * q^88 - 295 * q^90 - 1800 * q^91 + 1836 * q^92 - 1968 * q^94 - 60 * q^95 + 1445 * q^96 + 792 * q^97 - 4851 * q^98 - 1328 * q^99

Introduction

L-functions

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