LMFDB - Embedded newform 201.3.h.b.97.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,3,Mod(97,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("201.97");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	201.h (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.47685331364$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			97.12
Character	$\chi$	$=$	201.97
Dual form			201.3.h.b.172.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.30938 - 1.91067i) q^{2} +1.73205i q^{3} +(5.30134 - 9.18219i) q^{4} +8.30841i q^{5} +(3.30938 + 5.73202i) q^{6} +(8.95628 + 5.17091i) q^{7} -25.2311i q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(3.30938 - 1.91067i) q^{2} +1.73205i q^{3} +(5.30134 - 9.18219i) q^{4} +8.30841i q^{5} +(3.30938 + 5.73202i) q^{6} +(8.95628 + 5.17091i) q^{7} -25.2311i q^{8} -3.00000 q^{9} +(15.8747 + 27.4957i) q^{10} +(-14.8510 - 8.57426i) q^{11} +(15.9040 + 9.18219i) q^{12} +(1.88096 - 1.08597i) q^{13} +39.5197 q^{14} -14.3906 q^{15} +(-27.0030 - 46.7706i) q^{16} +(-10.0662 - 17.4352i) q^{17} +(-9.92814 + 5.73202i) q^{18} +(1.53452 + 2.65787i) q^{19} +(76.2894 + 44.0457i) q^{20} +(-8.95628 + 15.5127i) q^{21} -65.5304 q^{22} +(-5.78443 - 10.0189i) q^{23} +43.7015 q^{24} -44.0297 q^{25} +(4.14987 - 7.18778i) q^{26} -5.19615i q^{27} +(94.9606 - 54.8255i) q^{28} +(16.3994 - 28.4046i) q^{29} +(-47.6240 + 27.4957i) q^{30} +(-6.11044 - 3.52786i) q^{31} +(-91.3234 - 52.7256i) q^{32} +(14.8510 - 25.7228i) q^{33} +(-66.6258 - 38.4664i) q^{34} +(-42.9621 + 74.4125i) q^{35} +(-15.9040 + 27.5466i) q^{36} +(25.3056 + 43.8306i) q^{37} +(10.1567 + 5.86395i) q^{38} +(1.88096 + 3.25791i) q^{39} +209.630 q^{40} +(-4.41637 - 2.54979i) q^{41} +68.4501i q^{42} +57.4331i q^{43} +(-157.461 + 90.9101i) q^{44} -24.9252i q^{45} +(-38.2857 - 22.1043i) q^{46} +(-13.6043 + 23.5633i) q^{47} +(81.0090 - 46.7706i) q^{48} +(28.9767 + 50.1891i) q^{49} +(-145.711 + 84.1264i) q^{50} +(30.1986 - 17.4352i) q^{51} -23.0284i q^{52} -2.48057i q^{53} +(-9.92814 - 17.1961i) q^{54} +(71.2385 - 123.389i) q^{55} +(130.468 - 225.977i) q^{56} +(-4.60357 + 2.65787i) q^{57} -125.335i q^{58} +40.6725 q^{59} +(-76.2894 + 132.137i) q^{60} +(-3.67716 + 2.12301i) q^{61} -26.9624 q^{62} +(-26.8689 - 15.5127i) q^{63} -186.941 q^{64} +(9.02269 + 15.6278i) q^{65} -113.502i q^{66} +(-64.0894 + 19.5334i) q^{67} -213.457 q^{68} +(17.3533 - 10.0189i) q^{69} +328.346i q^{70} +(46.5863 - 80.6898i) q^{71} +75.6933i q^{72} +(25.2091 + 43.6634i) q^{73} +(167.492 + 96.7015i) q^{74} -76.2617i q^{75} +32.5401 q^{76} +(-88.6735 - 153.587i) q^{77} +(12.4496 + 7.18778i) q^{78} +(-60.8440 - 35.1283i) q^{79} +(388.589 - 224.352i) q^{80} +9.00000 q^{81} -19.4873 q^{82} +(63.1050 + 109.301i) q^{83} +(94.9606 + 164.477i) q^{84} +(144.859 - 83.6342i) q^{85} +(109.736 + 190.068i) q^{86} +(49.1981 + 28.4046i) q^{87} +(-216.338 + 374.708i) q^{88} -87.5161 q^{89} +(-47.6240 - 82.4871i) q^{90} +22.4618 q^{91} -122.661 q^{92} +(6.11044 - 10.5836i) q^{93} +103.973i q^{94} +(-22.0827 + 12.7495i) q^{95} +(91.3234 - 158.177i) q^{96} +(89.0515 - 51.4139i) q^{97} +(191.790 + 110.730i) q^{98} +(44.5531 + 25.7228i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 34 q^{4} + 21 q^{7} - 72 q^{9}+O(q^{10}) $ 24 * q + 34 * q^4 + 21 * q^7 - 72 * q^9	$ 24 q + 34 q^{4} + 21 q^{7} - 72 q^{9} + 30 q^{10} + 12 q^{11} + 102 q^{12} + 30 q^{13} + 6 q^{14} - 6 q^{15} - 98 q^{16} + 4 q^{17} + 39 q^{19} + 108 q^{20} - 21 q^{21} - 82 q^{22} - 13 q^{23} - 36 q^{24} - 222 q^{25} + 29 q^{26} + 189 q^{28} - 90 q^{30} - 93 q^{31} - 33 q^{32} - 12 q^{33} + 72 q^{34} - 93 q^{35} - 102 q^{36} - 33 q^{37} - 210 q^{38} + 30 q^{39} + 274 q^{40} - 15 q^{41} - 9 q^{44} - 228 q^{46} - 131 q^{47} + 294 q^{48} + 295 q^{49} - 423 q^{50} - 12 q^{51} - 56 q^{55} + 349 q^{56} - 117 q^{57} - 116 q^{59} - 108 q^{60} + 120 q^{61} + 282 q^{62} - 63 q^{63} - 276 q^{64} + 136 q^{65} - 25 q^{67} + 10 q^{68} + 39 q^{69} + 169 q^{71} + 187 q^{73} + 849 q^{74} + 386 q^{76} - 348 q^{77} + 87 q^{78} + 51 q^{80} + 216 q^{81} - 14 q^{82} + 104 q^{83} + 189 q^{84} - 243 q^{85} + 641 q^{86} - 766 q^{88} + 152 q^{89} - 90 q^{90} + 32 q^{91} - 216 q^{92} + 93 q^{93} + 762 q^{95} + 33 q^{96} - 84 q^{97} - 1086 q^{98} - 36 q^{99}+O(q^{100}) $ 24 * q + 34 * q^4 + 21 * q^7 - 72 * q^9 + 30 * q^10 + 12 * q^11 + 102 * q^12 + 30 * q^13 + 6 * q^14 - 6 * q^15 - 98 * q^16 + 4 * q^17 + 39 * q^19 + 108 * q^20 - 21 * q^21 - 82 * q^22 - 13 * q^23 - 36 * q^24 - 222 * q^25 + 29 * q^26 + 189 * q^28 - 90 * q^30 - 93 * q^31 - 33 * q^32 - 12 * q^33 + 72 * q^34 - 93 * q^35 - 102 * q^36 - 33 * q^37 - 210 * q^38 + 30 * q^39 + 274 * q^40 - 15 * q^41 - 9 * q^44 - 228 * q^46 - 131 * q^47 + 294 * q^48 + 295 * q^49 - 423 * q^50 - 12 * q^51 - 56 * q^55 + 349 * q^56 - 117 * q^57 - 116 * q^59 - 108 * q^60 + 120 * q^61 + 282 * q^62 - 63 * q^63 - 276 * q^64 + 136 * q^65 - 25 * q^67 + 10 * q^68 + 39 * q^69 + 169 * q^71 + 187 * q^73 + 849 * q^74 + 386 * q^76 - 348 * q^77 + 87 * q^78 + 51 * q^80 + 216 * q^81 - 14 * q^82 + 104 * q^83 + 189 * q^84 - 243 * q^85 + 641 * q^86 - 766 * q^88 + 152 * q^89 - 90 * q^90 + 32 * q^91 - 216 * q^92 + 93 * q^93 + 762 * q^95 + 33 * q^96 - 84 * q^97 - 1086 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	3.30938	−	1.91067i	1.65469	−	0.955336i	0.679585	−	0.733597i	$-0.262160\pi$
$2$	3.30938	−	1.91067i	1.65469	−	0.955336i	0.975106	−	0.221739i	$-0.0711733\pi$
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	5.30134	−	9.18219i	1.32533	−	2.29555i
$5$			8.30841i			1.66168i	0.556509	+	0.830841i	$0.312140\pi$
$5$			8.30841i			1.66168i	−0.556509	+	0.830841i	$0.687860\pi$
$6$	3.30938	+	5.73202i	0.551564	+	0.955336i
$7$	8.95628	+	5.17091i	1.27947	+	0.738702i	0.976751	−	0.214378i	$-0.0687725\pi$
$7$	8.95628	+	5.17091i	1.27947	+	0.738702i	0.302718	+	0.953080i	$0.402106\pi$
$8$		−	25.2311i		−	3.15389i
$9$	−3.00000			−0.333333
$10$	15.8747	+	27.4957i	1.58747	+	2.74957i
$11$	−14.8510	−	8.57426i	−1.35010	−	0.779478i	−0.361833	−	0.932243i	$-0.617849\pi$
$11$	−14.8510	−	8.57426i	−1.35010	−	0.779478i	−0.988263	+	0.152765i	$0.951182\pi$
$12$	15.9040	+	9.18219i	1.32533	+	0.765182i
$13$	1.88096	−	1.08597i	0.144689	−	0.0835362i	−0.425908	−	0.904767i	$-0.640045\pi$
$13$	1.88096	−	1.08597i	0.144689	−	0.0835362i	0.570597	+	0.821230i	$0.306712\pi$
$14$	39.5197			2.82283
$15$	−14.3906			−0.959373
$16$	−27.0030	−	46.7706i	−1.68769	−	2.92316i
$17$	−10.0662	−	17.4352i	−0.592130	−	1.02560i	−0.993945	−	0.109878i	$-0.964954\pi$
$17$	−10.0662	−	17.4352i	−0.592130	−	1.02560i	0.401816	−	0.915721i	$-0.368379\pi$
$18$	−9.92814	+	5.73202i	−0.551564	+	0.318445i
$19$	1.53452	+	2.65787i	0.0807645	+	0.139888i	0.903579	−	0.428423i	$-0.140931\pi$
$19$	1.53452	+	2.65787i	0.0807645	+	0.139888i	−0.822814	+	0.568311i	$0.807597\pi$
$20$	76.2894	+	44.0457i	3.81447	+	2.20228i
$21$	−8.95628	+	15.5127i	−0.426490	+	0.738702i
$22$	−65.5304			−2.97865
$23$	−5.78443	−	10.0189i	−0.251497	−	0.435605i	0.712441	−	0.701732i	$-0.247589\pi$
$23$	−5.78443	−	10.0189i	−0.251497	−	0.435605i	−0.963938	+	0.266126i	$0.914256\pi$
$24$	43.7015			1.82090
$25$	−44.0297			−1.76119
$26$	4.14987	−	7.18778i	0.159610	−	0.276453i
$27$		−	5.19615i		−	0.192450i
$28$	94.9606	−	54.8255i	3.39145	−	1.95805i
$29$	16.3994	−	28.4046i	0.565496	−	0.979468i	−0.431507	−	0.902109i	$-0.642018\pi$
$29$	16.3994	−	28.4046i	0.565496	−	0.979468i	0.997003	−	0.0773583i	$-0.0246486\pi$
$30$	−47.6240	+	27.4957i	−1.58747	+	0.916524i
$31$	−6.11044	−	3.52786i	−0.197111	−	0.113802i	0.398196	−	0.917300i	$-0.369636\pi$
$31$	−6.11044	−	3.52786i	−0.197111	−	0.113802i	−0.595307	+	0.803498i	$0.702970\pi$
$32$	−91.3234	−	52.7256i	−2.85386	−	1.64767i
$33$	14.8510	−	25.7228i	0.450032	−	0.779478i
$34$	−66.6258	−	38.4664i	−1.95958	−	1.13137i
$35$	−42.9621	+	74.4125i	−1.22749	+	2.12607i
$36$	−15.9040	+	27.5466i	−0.441778	+	0.765182i
$37$	25.3056	+	43.8306i	0.683935	+	1.18461i	0.973770	+	0.227534i	$0.0730663\pi$
$37$	25.3056	+	43.8306i	0.683935	+	1.18461i	−0.289835	+	0.957077i	$0.593600\pi$
$38$	10.1567	+	5.86395i	0.267280	+	0.154314i
$39$	1.88096	+	3.25791i	0.0482296	+	0.0835362i
$40$	209.630			5.24076
$41$	−4.41637	−	2.54979i	−0.107716	−	0.0621900i	0.445174	−	0.895444i	$-0.353142\pi$
$41$	−4.41637	−	2.54979i	−0.107716	−	0.0621900i	−0.552890	+	0.833254i	$0.686475\pi$
$42$			68.4501i			1.62976i
$43$			57.4331i			1.33565i	0.744316	+	0.667827i	$0.232776\pi$
$43$			57.4331i			1.33565i	−0.744316	+	0.667827i	$0.767224\pi$
$44$	−157.461	+	90.9101i	−3.57866	+	2.06614i
$45$		−	24.9252i		−	0.553894i
$46$	−38.2857	−	22.1043i	−0.832299	−	0.480528i
$47$	−13.6043	+	23.5633i	−0.289453	+	0.501347i	−0.973679	−	0.227923i	$-0.926807\pi$
$47$	−13.6043	+	23.5633i	−0.289453	+	0.501347i	0.684226	+	0.729270i	$0.260140\pi$
$48$	81.0090	−	46.7706i	1.68769	−	0.974387i
$49$	28.9767	+	50.1891i	0.591361	+	1.02427i
$50$	−145.711	+	84.1264i	−2.91422	+	1.68253i
$51$	30.1986	−	17.4352i	0.592130	−	0.341866i
$52$		−	23.0284i		−	0.442853i
$53$		−	2.48057i		−	0.0468032i	−0.999726	−	0.0234016i	$-0.992550\pi$
$53$		−	2.48057i		−	0.0468032i	0.999726	−	0.0234016i	$-0.00744964\pi$
$54$	−9.92814	−	17.1961i	−0.183855	−	0.318445i
$55$	71.2385	−	123.389i	1.29524	−	2.24343i
$56$	130.468	−	225.977i	2.32978	−	4.03530i
$57$	−4.60357	+	2.65787i	−0.0807645	+	0.0466294i
$58$		−	125.335i		−	2.16095i
$59$	40.6725			0.689365			0.344682	−	0.938719i	$-0.387987\pi$
$59$	40.6725			0.689365			0.344682	+	0.938719i	$0.387987\pi$
$60$	−76.2894	+	132.137i	−1.27149	+	2.20228i
$61$	−3.67716	+	2.12301i	−0.0602813	+	0.0348034i	−0.529838	−	0.848099i	$-0.677747\pi$
$61$	−3.67716	+	2.12301i	−0.0602813	+	0.0348034i	0.469556	+	0.882902i	$0.344414\pi$
$62$	−26.9624			−0.434877
$63$	−26.8689	−	15.5127i	−0.426490	−	0.246234i
$64$	−186.941			−2.92096
$65$	9.02269	+	15.6278i	0.138811	+	0.240427i
$66$		−	113.502i		−	1.71973i
$67$	−64.0894	+	19.5334i	−0.956558	+	0.291543i
$67$	−64.0894	+	19.5334i	−0.956558	+	0.291543i
$68$	−213.457			−3.13908
$69$	17.3533	−	10.0189i	0.251497	−	0.145202i
$70$			328.346i			4.69065i
$71$	46.5863	−	80.6898i	0.656145	−	1.13648i	−0.325460	−	0.945556i	$-0.605519\pi$
$71$	46.5863	−	80.6898i	0.656145	−	1.13648i	0.981605	−	0.190921i	$-0.0611474\pi$
$72$			75.6933i			1.05130i
$73$	25.2091	+	43.6634i	0.345330	+	0.598129i	0.985414	−	0.170176i	$-0.0544337\pi$
$73$	25.2091	+	43.6634i	0.345330	+	0.598129i	−0.640084	+	0.768305i	$0.721100\pi$
$74$	167.492	+	96.7015i	2.26340	+	1.30678i
$75$		−	76.2617i		−	1.01682i
$76$	32.5401			0.428160
$77$	−88.6735	−	153.587i	−1.15160	−	1.99464i
$78$	12.4496	+	7.18778i	0.159610	+	0.0921510i
$79$	−60.8440	−	35.1283i	−0.770177	−	0.444662i	0.0627610	−	0.998029i	$-0.480009\pi$
$79$	−60.8440	−	35.1283i	−0.770177	−	0.444662i	−0.832938	+	0.553367i	$0.813343\pi$
$80$	388.589	−	224.352i	4.85737	−	2.80440i
$81$	9.00000			0.111111
$82$	−19.4873			−0.237649
$83$	63.1050	+	109.301i	0.760301	+	1.31688i	0.942695	+	0.333655i	$0.108282\pi$
$83$	63.1050	+	109.301i	0.760301	+	1.31688i	−0.182394	+	0.983226i	$0.558385\pi$
$84$	94.9606	+	164.477i	1.13048	+	1.95805i
$85$	144.859	−	83.6342i	1.70422	−	0.983931i
$86$	109.736	+	190.068i	1.27600	+	2.21010i
$87$	49.1981	+	28.4046i	0.565496	+	0.326489i
$88$	−216.338	+	374.708i	−2.45839	+	4.25805i
$89$	−87.5161			−0.983327			−0.491664	−	0.870785i	$-0.663611\pi$
$89$	−87.5161			−0.983327			−0.491664	+	0.870785i	$0.663611\pi$
$90$	−47.6240	−	82.4871i	−0.529155	−	0.916524i
$91$	22.4618			0.246833
$92$	−122.661			−1.33327
$93$	6.11044	−	10.5836i	0.0657036	−	0.113802i
$94$			103.973i			1.10610i
$95$	−22.0827	+	12.7495i	−0.232450	+	0.134205i
$96$	91.3234	−	158.177i	0.951285	−	1.64767i
$97$	89.0515	−	51.4139i	0.918057	−	0.530040i	0.0350423	−	0.999386i	$-0.488843\pi$
$97$	89.0515	−	51.4139i	0.918057	−	0.530040i	0.883015	+	0.469345i	$0.155510\pi$
$98$	191.790	+	110.730i	1.95704	+	1.12990i
$99$	44.5531	+	25.7228i	0.450032	+	0.259826i
$100$	−233.416	+	404.289i	−2.33416	+	4.04289i
$101$	−58.4549	−	33.7490i	−0.578761	−	0.334148i	0.181880	−	0.983321i	$-0.441782\pi$
$101$	−58.4549	−	33.7490i	−0.578761	−	0.334148i	−0.760641	+	0.649173i	$0.775115\pi$
$102$	66.6258	−	115.399i	0.653194	−	1.13137i
$103$	−44.6910	+	77.4071i	−0.433894	+	0.751526i	−0.997205	−	0.0747192i	$-0.976194\pi$
$103$	−44.6910	+	77.4071i	−0.433894	+	0.751526i	0.563311	+	0.826245i	$0.309527\pi$
$104$	−27.4002	−	47.4586i	−0.263464	−	0.456332i
$105$	−128.886	−	74.4125i	−1.22749	−	0.708690i
$106$	−4.73955	−	8.20915i	−0.0447128	−	0.0774448i
$107$	−123.213			−1.15152			−0.575762	−	0.817618i	$-0.695294\pi$
$107$	−123.213			−1.15152			−0.575762	+	0.817618i	$0.695294\pi$
$108$	−47.7120	−	27.5466i	−0.441778	−	0.255061i
$109$			45.8482i			0.420625i	0.977634	+	0.210313i	$0.0674482\pi$
$109$			45.8482i			0.420625i	−0.977634	+	0.210313i	$0.932552\pi$
$110$		−	544.453i		−	4.94958i
$111$	−75.9168	+	43.8306i	−0.683935	+	0.394870i
$112$		−	558.521i		−	4.98679i
$113$	39.8163	+	22.9879i	0.352357	+	0.203433i	0.665723	−	0.746199i	$-0.268123\pi$
$113$	39.8163	+	22.9879i	0.352357	+	0.203433i	−0.313366	+	0.949632i	$0.601457\pi$
$114$	−10.1567	+	17.5918i	−0.0890935	+	0.154314i
$115$	83.2413	−	48.0594i	0.723838	−	0.417908i
$116$	−173.877	−	301.164i	−1.49894	−	2.59624i
$117$	−5.64287	+	3.25791i	−0.0482296	+	0.0278454i
$118$	134.601	−	77.7119i	1.14069	−	0.658575i
$119$		−	208.206i		−	1.74963i
$120$			363.090i			3.02575i
$121$	86.5358	+	149.884i	0.715172	+	1.23871i
$122$	−8.11275	+	14.0517i	−0.0664979	+	0.115178i
$123$	4.41637	−	7.64937i	0.0359054	−	0.0621900i
$124$	−64.7870	+	37.4048i	−0.522476	+	0.301651i
$125$		−	158.107i		−	1.26485i
$126$	−118.559			−0.940945
$127$	47.9485	−	83.0492i	0.377547	−	0.653931i	−0.613158	−	0.789961i	$-0.710101\pi$
$127$	47.9485	−	83.0492i	0.377547	−	0.653931i	0.990705	+	0.136030i	$0.0434343\pi$
$128$	−253.366	+	146.281i	−1.97942	+	1.14282i
$129$	−99.4771			−0.771141
$130$	59.7190	+	34.4788i	0.459377	+	0.265222i
$131$	−27.8216			−0.212378			−0.106189	−	0.994346i	$-0.533865\pi$
$131$	−27.8216			−0.212378			−0.106189	+	0.994346i	$0.533865\pi$
$132$	−157.461	−	272.730i	−1.19289	−	2.06614i
$133$			31.7396i			0.238643i
$134$	−174.774	+	187.097i	−1.30429	+	1.39625i
$135$	43.1718			0.319791
$136$	−439.908	+	253.981i	−3.23462	+	1.86751i
$137$			143.011i			1.04388i	0.852982	+	0.521940i	$0.174791\pi$
$137$			143.011i			1.04388i	−0.852982	+	0.521940i	$0.825209\pi$
$138$	38.2857	−	66.3129i	0.277433	−	0.480528i
$139$		−	191.055i		−	1.37450i	−0.726422	−	0.687249i	$-0.758818\pi$
$139$		−	191.055i		−	1.37450i	0.726422	−	0.687249i	$-0.241182\pi$
$140$	455.513	+	788.972i	3.25366	+	5.63551i
$141$	−40.8129	−	23.5633i	−0.289453	−	0.167116i
$142$		−	356.045i		−	2.50736i
$143$	−37.2456			−0.260458
$144$	81.0090	+	140.312i	0.562563	+	0.974387i
$145$	235.997	+	136.253i	1.62756	+	0.939675i
$146$	166.853	+	96.3326i	1.14283	+	0.659812i
$147$	−86.9300	+	50.1891i	−0.591361	+	0.341422i
$148$	536.614			3.62577
$149$	232.047			1.55736			0.778681	−	0.627420i	$-0.215889\pi$
$149$	232.047			1.55736			0.778681	+	0.627420i	$0.215889\pi$
$150$	−145.711	−	252.379i	−0.971408	−	1.68253i
$151$	−80.2794	−	139.048i	−0.531652	−	0.920847i	−0.999317	−	0.0369421i	$-0.988238\pi$
$151$	−80.2794	−	139.048i	−0.531652	−	0.920847i	0.467666	−	0.883905i	$-0.345095\pi$
$152$	67.0611	−	38.7177i	0.441191	−	0.254722i
$153$	30.1986	+	52.3055i	0.197377	+	0.341866i
$154$	−586.909	−	338.852i	−3.81110	−	2.20034i
$155$	29.3109	−	50.7680i	0.189103	−	0.327536i
$156$	39.8863			0.255682
$157$	124.851	+	216.248i	0.795227	+	1.37737i	0.922695	+	0.385531i	$0.125982\pi$
$157$	124.851	+	216.248i	0.795227	+	1.37737i	−0.127468	+	0.991843i	$0.540685\pi$
$158$	−268.474			−1.69921
$159$	4.29647			0.0270218
$160$	438.066	−	758.753i	2.73791	−	4.74220i
$161$		−	119.643i		−	0.743125i
$162$	29.7844	−	17.1961i	0.183855	−	0.106148i
$163$	95.4846	−	165.384i	0.585795	−	1.01463i	−0.408980	−	0.912543i	$-0.634116\pi$
$163$	95.4846	−	165.384i	0.585795	−	1.01463i	0.994776	−	0.102084i	$-0.0325511\pi$
$164$	−46.8253	+	27.0346i	−0.285520	+	0.164845i
$165$	213.715	+	123.389i	1.29524	+	0.747810i
$166$	417.677	+	241.146i	2.51613	+	1.45269i
$167$	−61.5596	+	106.624i	−0.368620	+	0.638469i	−0.989350	−	0.145556i	$-0.953503\pi$
$167$	−61.5596	+	106.624i	−0.368620	+	0.638469i	0.620730	+	0.784024i	$0.286836\pi$
$168$	391.403	+	225.977i	2.32978	+	1.34510i
$169$	−82.1413	+	142.273i	−0.486043	+	0.841852i
$170$	319.595	−	553.555i	1.87997	−	3.25620i
$171$	−4.60357	−	7.97362i	−0.0269215	−	0.0466294i
$172$	527.362	+	304.472i	3.06606	+	1.77019i
$173$	83.1192	+	143.967i	0.480458	+	0.832177i	0.999749	−	0.0224204i	$-0.00713723\pi$
$173$	83.1192	+	143.967i	0.480458	+	0.832177i	−0.519291	+	0.854598i	$0.673804\pi$
$174$	217.087			1.24763
$175$	−394.343	−	227.674i	−2.25339	−	1.30099i
$176$			926.123i			5.26206i
$177$			70.4469i			0.398005i
$178$	−289.624	+	167.215i	−1.62710	+	0.939408i
$179$		−	349.570i		−	1.95290i	−0.215737	−	0.976452i	$-0.569215\pi$
$179$		−	349.570i		−	1.95290i	0.215737	−	0.976452i	$-0.430785\pi$
$180$	−228.868	−	132.137i	−1.27149	−	0.734095i
$181$	104.930	−	181.744i	0.579722	−	1.00411i	−0.415789	−	0.909461i	$-0.636494\pi$
$181$	104.930	−	181.744i	0.579722	−	1.00411i	0.995511	−	0.0946468i	$-0.0301722\pi$
$182$	74.3348	−	42.9172i	0.408433	−	0.235809i
$183$	−3.67716	−	6.36903i	−0.0200938	−	0.0348034i
$184$	−252.788	+	145.947i	−1.37385	+	0.793192i
$185$	−364.163	+	210.249i	−1.96845	+	1.13648i
$186$		−	46.7002i		−	0.251076i
$187$			345.241i			1.84621i
$188$	144.242	+	249.834i	0.767244	+	1.32891i
$189$	26.8689	−	46.5382i	0.142163	−	0.246234i
$190$	−48.7201	+	84.3857i	−0.256422	+	0.444135i
$191$	−102.864	+	59.3887i	−0.538556	+	0.310936i	−0.744494	−	0.667630i	$-0.767309\pi$
$191$	−102.864	+	59.3887i	−0.538556	+	0.310936i	0.205937	+	0.978565i	$0.433976\pi$
$192$		−	323.792i		−	1.68642i
$193$	50.2393			0.260307			0.130154	−	0.991494i	$-0.458453\pi$
$193$	50.2393			0.260307			0.130154	+	0.991494i	$0.458453\pi$
$194$	196.470	−	340.297i	1.01273	−	1.75411i
$195$	−27.0681	+	15.6278i	−0.138811	+	0.0801423i
$196$	614.461			3.13500
$197$	−26.7832	−	15.4633i	−0.135956	−	0.0784940i	0.430480	−	0.902600i	$-0.358344\pi$
$197$	−26.7832	−	15.4633i	−0.135956	−	0.0784940i	−0.566435	+	0.824106i	$0.691678\pi$
$198$	196.591			0.992885
$199$	−69.2819	−	120.000i	−0.348150	−	0.603014i	0.637770	−	0.770226i	$-0.279857\pi$
$199$	−69.2819	−	120.000i	−0.348150	−	0.603014i	−0.985921	+	0.167212i	$0.946524\pi$
$200$			1110.92i			5.55459i
$201$	−33.8328	−	111.006i	−0.168323	−	0.552269i
$202$	−257.933			−1.27689
$203$	293.755	−	169.600i	1.44707	−	0.835466i
$204$		−	369.719i		−	1.81235i
$205$	21.1847	−	36.6930i	0.103340	−	0.178990i
$206$			341.560i			1.65806i
$207$	17.3533	+	30.0568i	0.0838323	+	0.145202i
$208$	−101.583	−	58.6489i	−0.488379	−	0.281966i
$209$		−	52.6296i		−	0.251816i
$210$	−568.712			−2.70815
$211$	89.7098	+	155.382i	0.425165	+	0.736407i	0.996436	−	0.0843544i	$-0.0268828\pi$
$211$	89.7098	+	155.382i	0.425165	+	0.736407i	−0.571271	+	0.820762i	$0.693549\pi$
$212$	−22.7770	−	13.1503i	−0.107439	−	0.0620299i
$213$	139.759	+	80.6898i	0.656145	+	0.378826i
$214$	−407.759	+	235.420i	−1.90541	+	1.10009i
$215$	−477.178			−2.21943
$216$	−131.105			−0.606966
$217$	−36.4845	−	63.1931i	−0.168132	−	0.291212i
$218$	87.6008	+	151.729i	0.401839	+	0.696005i
$219$	−75.6272	+	43.6634i	−0.345330	+	0.199376i
$220$	−755.318	−	1308.25i	−3.43326	−	5.94659i
$221$	−37.8682	−	21.8632i	−0.171349	−	0.0989285i
$222$	−167.492	+	290.104i	−0.754468	+	1.30678i
$223$	269.388			1.20802			0.604008	−	0.796978i	$-0.293569\pi$
$223$	269.388			1.20802			0.604008	+	0.796978i	$0.293569\pi$
$224$	−545.279	−	944.451i	−2.43428	−	4.21630i
$225$	132.089			0.587063
$226$	175.690			0.777388
$227$	−157.672	+	273.096i	−0.694591	+	1.20307i	0.275728	+	0.961236i	$0.411081\pi$
$227$	−157.672	+	273.096i	−0.694591	+	1.20307i	−0.970318	+	0.241831i	$0.922252\pi$
$228$			56.3612i			0.247198i
$229$	−93.5037	+	53.9844i	−0.408313	+	0.235740i	−0.690065	−	0.723748i	$-0.742418\pi$
$229$	−93.5037	+	53.9844i	−0.408313	+	0.235740i	0.281752	+	0.959487i	$0.409085\pi$
$230$	183.652	−	318.094i	0.798485	−	1.38302i
$231$	266.020	−	153.587i	1.15160	−	0.664879i
$232$	−716.678	−	413.774i	−3.08913	−	1.78351i
$233$	108.508	+	62.6468i	0.465697	+	0.268871i	0.714437	−	0.699700i	$-0.246683\pi$
$233$	108.508	+	62.6468i	0.465697	+	0.268871i	−0.248739	+	0.968570i	$0.580016\pi$
$234$	−12.4496	+	21.5633i	−0.0532034	+	0.0921510i
$235$	−195.774	−	113.030i	−0.833080	−	0.480979i
$236$	215.619	−	373.463i	0.913639	−	1.58247i
$237$	60.8440	−	105.385i	0.256726	−	0.444662i
$238$	−397.813	−	689.032i	−1.67148	−	2.89509i
$239$	24.2950	+	14.0268i	0.101653	+	0.0586893i	0.549965	−	0.835188i	$-0.314641\pi$
$239$	24.2950	+	14.0268i	0.101653	+	0.0586893i	−0.448312	+	0.893877i	$0.647975\pi$
$240$	388.589	+	673.056i	1.61912	+	2.80440i
$241$	161.925			0.671889			0.335945	−	0.941882i	$-0.390944\pi$
$241$	161.925			0.671889			0.335945	+	0.941882i	$0.390944\pi$
$242$	572.760	+	330.683i	2.36678	+	1.36646i
$243$			15.5885i			0.0641500i
$244$			45.0191i			0.184505i
$245$	−416.992	+	240.750i	−1.70201	+	0.982654i
$246$		−	33.7529i		−	0.137207i
$247$	5.77275	+	3.33290i	0.0233714	+	0.0134935i
$248$	−89.0118	+	154.173i	−0.358919	+	0.621665i
$249$	−189.315	+	109.301i	−0.760301	+	0.438960i
$250$	−302.090	−	523.236i	−1.20836	−	2.09294i
$251$	−149.728	+	86.4457i	−0.596527	+	0.344405i	−0.767674	−	0.640840i	$-0.778586\pi$
$251$	−149.728	+	86.4457i	−0.596527	+	0.344405i	0.171147	+	0.985246i	$0.445253\pi$
$252$	−284.882	+	164.477i	−1.13048	+	0.652685i
$253$			198.389i			0.784145i
$254$		−	366.455i		−	1.44274i
$255$	144.859	+	250.902i	0.568073	+	0.983931i
$256$	−185.108	+	320.617i	−0.723079	+	1.25241i
$257$	−30.2670	+	52.4239i	−0.117770	+	0.203984i	−0.918884	−	0.394528i	$-0.870908\pi$
$257$	−30.2670	+	52.4239i	−0.117770	+	0.203984i	0.801113	+	0.598513i	$0.204241\pi$
$258$	−329.208	+	190.068i	−1.27600	+	0.736698i
$259$			523.412i			2.02090i
$260$	191.329			0.735882
$261$	−49.1981	+	85.2137i	−0.188499	+	0.326489i
$262$	−92.0722	+	53.1579i	−0.351420	+	0.202893i
$263$	−191.875			−0.729564			−0.364782	−	0.931093i	$-0.618856\pi$
$263$	−191.875			−0.729564			−0.364782	+	0.931093i	$0.618856\pi$
$264$	−649.014	−	374.708i	−2.45839	−	1.41935i
$265$	20.6096			0.0777720
$266$	60.6439	+	105.038i	0.227985	+	0.394881i
$267$		−	151.582i		−	0.567724i
$268$	−160.400	+	692.034i	−0.598507	+	2.58221i
$269$	424.280			1.57725			0.788624	−	0.614875i	$-0.210794\pi$
$269$	424.280			1.57725			0.788624	+	0.614875i	$0.210794\pi$
$270$	142.872	−	82.4871i	0.529155	−	0.305508i
$271$		−	282.968i		−	1.04416i	−0.852895	−	0.522082i	$-0.825156\pi$
$271$		−	282.968i		−	1.04416i	0.852895	−	0.522082i	$-0.174844\pi$
$272$	−543.635	+	941.604i	−1.99866	+	3.46178i
$273$			38.9050i			0.142509i
$274$	273.248	+	473.280i	0.997256	+	1.72730i
$275$	653.888	+	377.522i	2.37777	+	1.37281i
$276$		−	212.455i		−	0.769763i
$277$	323.006			1.16609			0.583043	−	0.812441i	$-0.301862\pi$
$277$	323.006			1.16609			0.583043	+	0.812441i	$0.301862\pi$
$278$	−365.044	−	632.275i	−1.31311	−	2.27437i
$279$	18.3313	+	10.5836i	0.0657036	+	0.0379340i
$280$	1877.51	+	1083.98i	6.70539	+	3.87136i
$281$	−389.155	+	224.679i	−1.38489	+	0.799568i	−0.992734	−	0.120329i	$-0.961605\pi$
$281$	−389.155	+	224.679i	−1.38489	+	0.799568i	−0.392159	+	0.919897i	$0.628272\pi$
$282$	−180.087			−0.638607
$283$	−179.388			−0.633881			−0.316940	−	0.948445i	$-0.602655\pi$
$283$	−179.388			−0.633881			−0.316940	+	0.948445i	$0.602655\pi$
$284$	−493.939	−	855.528i	−1.73922	−	3.01242i
$285$	−22.0827	−	38.2484i	−0.0774832	−	0.134205i
$286$	−123.260	+	71.1640i	−0.430978	+	0.248825i
$287$	−26.3695	−	45.6733i	−0.0918797	−	0.159140i
$288$	273.970	+	158.177i	0.951285	+	0.549225i
$289$	−58.1568	+	100.731i	−0.201235	+	0.348549i
$290$	1041.34			3.59082
$291$	89.0515	+	154.242i	0.306019	+	0.530040i
$292$	534.567			1.83071
$293$	117.219			0.400064			0.200032	−	0.979789i	$-0.435895\pi$
$293$	117.219			0.400064			0.200032	+	0.979789i	$0.435895\pi$
$294$	−191.790	+	332.190i	−0.652346	+	1.12990i
$295$			337.924i			1.14551i
$296$	1105.89	−	638.488i	3.73613	−	2.15705i
$297$	−44.5531	+	77.1683i	−0.150011	+	0.259826i
$298$	767.932	−	443.366i	2.57695	−	1.48780i
$299$	−21.7605	−	12.5634i	−0.0727776	−	0.0420182i
$300$	−700.249	−	404.289i	−2.33416	−	1.34763i
$301$	−296.982	+	514.388i	−0.986650	+	1.70893i
$302$	−531.350	−	306.775i	−1.75944	−	1.01581i
$303$	58.4549	−	101.247i	0.192920	−	0.334148i
$304$	82.8736	−	143.541i	0.272610	−	0.472175i
$305$	−17.6388	−	30.5514i	−0.0578322	−	0.100168i
$306$	199.877	+	115.399i	0.653194	+	0.377122i
$307$	−200.795	−	347.787i	−0.654056	−	1.13286i	−0.982130	−	0.188206i	$-0.939733\pi$
$307$	−200.795	−	347.787i	−0.654056	−	1.13286i	0.328074	−	0.944652i	$-0.393601\pi$
$308$	−1880.35			−6.10504
$309$	−134.073	−	77.4071i	−0.433894	−	0.250509i
$310$		−	224.014i		−	0.722627i
$311$			380.260i			1.22270i	0.791360	+	0.611351i	$0.209373\pi$
$311$			380.260i			1.22270i	−0.791360	+	0.611351i	$0.790627\pi$
$312$	82.2007	−	47.4586i	0.263464	−	0.152111i
$313$		−	401.777i		−	1.28363i	−0.766858	−	0.641817i	$-0.778181\pi$
$313$		−	401.777i		−	1.28363i	0.766858	−	0.641817i	$-0.221819\pi$
$314$	826.357	+	477.097i	2.63171	+	1.51942i
$315$	128.886	−	223.238i	0.409163	−	0.708690i
$316$	−645.109	+	372.454i	−2.04148	+	1.17865i
$317$	72.9111	+	126.286i	0.230004	+	0.398378i	0.957809	−	0.287406i	$-0.0927929\pi$
$317$	72.9111	+	126.286i	0.230004	+	0.398378i	−0.727805	+	0.685784i	$0.759460\pi$
$318$	14.2187	−	8.20915i	0.0447128	−	0.0258149i
$319$	−487.096	+	281.225i	−1.52695	+	0.881583i
$320$		−	1553.19i		−	4.85370i
$321$		−	213.411i		−	0.664832i
$322$	−228.599	−	395.944i	−0.709934	−	1.22964i
$323$	30.8937	−	53.5094i	0.0956460	−	0.165664i
$324$	47.7120	−	82.6397i	0.147259	−	0.255061i
$325$	−82.8180	+	47.8150i	−0.254824	+	0.147123i
$326$		−	729.759i		−	2.23853i
$327$	−79.4114			−0.242848
$328$	−64.3340	+	111.430i	−0.196140	+	0.339725i
$329$	−243.688	+	140.693i	−0.740692	+	0.427639i
$330$	943.021			2.85764
$331$	−139.048	−	80.2793i	−0.420084	−	0.242536i	0.275029	−	0.961436i	$-0.411312\pi$
$331$	−139.048	−	80.2793i	−0.420084	−	0.242536i	−0.695113	+	0.718900i	$0.744646\pi$
$332$	1338.16			4.03061
$333$	−75.9168	−	131.492i	−0.227978	−	0.394870i
$334$			470.481i			1.40862i
$335$	−162.292	−	532.481i	−0.484452	−	1.58950i
$336$	967.386			2.87913
$337$	−304.292	+	175.683i	−0.902942	+	0.521314i	−0.878154	−	0.478379i	$-0.841225\pi$
$337$	−304.292	+	175.683i	−0.902942	+	0.521314i	−0.0247886	+	0.999693i	$0.507891\pi$
$338$			627.781i			1.85734i
$339$	−39.8163	+	68.9638i	−0.117452	+	0.203433i
$340$		−	1773.49i		−	5.21615i
$341$	60.4976	+	104.785i	0.177412	+	0.307287i
$342$	−30.4700	−	17.5918i	−0.0890935	−	0.0514381i
$343$			92.5940i			0.269953i
$344$	1449.10			4.21250
$345$	83.2413	+	144.178i	0.241279	+	0.417908i
$346$	550.146	+	317.627i	1.59002	+	0.917997i
$347$	−514.759	−	297.196i	−1.48345	−	0.856473i	−0.483631	−	0.875272i	$-0.660682\pi$
$347$	−514.759	−	297.196i	−1.48345	−	0.856473i	−0.999823	+	0.0187996i	$0.994016\pi$
$348$	521.632	−	301.164i	1.49894	−	0.865415i
$349$	−89.4550			−0.256318			−0.128159	−	0.991754i	$-0.540907\pi$
$349$	−89.4550			−0.256318			−0.128159	+	0.991754i	$0.540907\pi$
$350$	−1740.04			−4.97154
$351$	−5.64287	−	9.77373i	−0.0160765	−	0.0278454i
$352$	904.166	+	1566.06i	2.56865	+	4.44904i
$353$	−133.999	+	77.3645i	−0.379601	+	0.219163i	−0.677645	−	0.735389i	$-0.736999\pi$
$353$	−133.999	+	77.3645i	−0.379601	+	0.219163i	0.298044	+	0.954552i	$0.403666\pi$
$354$	134.601	+	233.136i	0.380229	+	0.658575i
$355$	670.404	+	387.058i	1.88846	+	1.09030i
$356$	−463.953	+	803.589i	−1.30324	+	2.25727i
$357$	360.623			1.01015
$358$	−667.913	−	1156.86i	−1.86568	−	3.23145i
$359$	−28.0743			−0.0782013			−0.0391007	−	0.999235i	$-0.512449\pi$
$359$	−28.0743			−0.0782013			−0.0391007	+	0.999235i	$0.512449\pi$
$360$	−628.891			−1.74692
$361$	175.790	−	304.478i	0.486954	−	0.843429i
$362$		−	801.945i		−	2.21532i
$363$	−259.607	+	149.884i	−0.715172	+	0.412905i
$364$	119.078	−	206.249i	0.327137	−	0.566617i
$365$	−362.774	+	209.447i	−0.993900	+	0.573828i
$366$	−24.3382	−	14.0517i	−0.0664979	−	0.0383926i
$367$	−248.508	−	143.476i	−0.677132	−	0.390943i	0.121641	−	0.992574i	$-0.461184\pi$
$367$	−248.508	−	143.476i	−0.677132	−	0.390943i	−0.798774	+	0.601632i	$0.794518\pi$
$368$	−312.394	+	541.082i	−0.848896	+	1.47033i
$369$	13.2491	+	7.64937i	0.0359054	+	0.0207300i
$370$	−803.436	+	1391.59i	−2.17145	+	3.76106i
$371$	12.8268	−	22.2167i	0.0345736	−	0.0598832i
$372$	−64.7870	−	112.214i	−0.174159	−	0.301651i
$373$	−259.160	−	149.626i	−0.694800	−	0.401143i	0.110608	−	0.993864i	$-0.464720\pi$
$373$	−259.160	−	149.626i	−0.694800	−	0.401143i	−0.805408	+	0.592721i	$0.798054\pi$
$374$	659.642	+	1142.53i	1.76375	+	3.05490i
$375$	273.849			0.730264
$376$	594.528	+	343.251i	1.58119	+	0.912902i
$377$		−	71.2370i		−	0.188957i
$378$		−	205.350i		−	0.543255i
$379$	204.585	−	118.117i	0.539801	−	0.311654i	−0.205197	−	0.978721i	$-0.565784\pi$
$379$	204.585	−	118.117i	0.539801	−	0.311654i	0.744998	+	0.667066i	$0.232450\pi$
$380$			270.357i			0.711465i
$381$	143.845	+	83.0492i	0.377547	+	0.217977i
$382$	−226.945	+	393.080i	−0.594096	+	1.02900i
$383$	507.495	−	293.002i	1.32505	−	0.765019i	0.340522	−	0.940237i	$-0.389396\pi$
$383$	507.495	−	293.002i	1.32505	−	0.765019i	0.984530	+	0.175218i	$0.0560629\pi$
$384$	−253.366	−	438.843i	−0.659808	−	1.14282i
$385$	1276.06	−	736.736i	3.31445	−	1.91360i
$386$	166.261	−	95.9908i	0.430728	−	0.248681i
$387$		−	172.299i		−	0.445218i
$388$		−	1090.25i		−	2.80992i
$389$	191.586	+	331.836i	0.492508	+	0.853049i	0.999963	−	0.00862955i	$-0.00274690\pi$
$389$	191.586	+	331.836i	0.492508	+	0.853049i	−0.507455	+	0.861678i	$0.669414\pi$
$390$	−59.7190	+	103.436i	−0.153126	+	0.265222i
$391$	−116.454	+	201.705i	−0.297837	+	0.515869i
$392$	1266.33	−	731.113i	3.23042	−	1.86508i
$393$		−	48.1884i		−	0.122617i
$394$	−118.181			−0.299953
$395$	291.860	−	505.517i	0.738887	−	1.27979i
$396$	472.383	−	272.730i	1.19289	−	0.688713i
$397$	−227.226			−0.572357			−0.286178	−	0.958176i	$-0.592385\pi$
$397$	−227.226			−0.572357			−0.286178	+	0.958176i	$0.592385\pi$
$398$	−458.561	−	264.750i	−1.15216	−	0.665201i
$399$	−54.9746			−0.137781
$400$	1188.93	+	2059.30i	2.97234	+	5.14824i
$401$		−	651.510i		−	1.62471i	−0.583160	−	0.812357i	$-0.698184\pi$
$401$		−	651.510i		−	1.62471i	0.583160	−	0.812357i	$-0.301816\pi$
$402$	−324.062	−	302.718i	−0.806124	−	0.753029i
$403$	−15.3246			−0.0380263
$404$	−619.778	+	357.829i	−1.53410	+	0.885716i
$405$			74.7757i			0.184631i
$406$	648.098	−	1122.54i	1.59630	−	2.76488i
$407$		−	867.907i		−	2.13245i
$408$	−439.908	−	761.944i	−1.07821	−	1.86751i
$409$	−213.057	−	123.009i	−0.520922	−	0.300754i	0.216390	−	0.976307i	$-0.430572\pi$
$409$	−213.057	−	123.009i	−0.520922	−	0.300754i	−0.737312	+	0.675553i	$0.763905\pi$
$410$		−	161.908i		−	0.394898i
$411$	−247.703			−0.602684
$412$	473.845	+	820.723i	1.15011	+	1.99205i
$413$	364.275	+	210.314i	0.882021	+	0.509235i
$414$	114.857	+	66.3129i	0.277433	+	0.160176i
$415$	−908.119	+	524.303i	−2.18824	+	1.26338i
$416$	−229.034			−0.550562
$417$	330.917			0.793567
$418$	−100.558	−	174.172i	−0.240569	−	0.416678i
$419$	346.436	+	600.044i	0.826815	+	1.43209i	0.900524	+	0.434806i	$0.143183\pi$
$419$	346.436	+	600.044i	0.826815	+	1.43209i	−0.0737089	+	0.997280i	$0.523484\pi$
$420$	−1366.54	+	788.972i	−3.25366	+	1.87850i
$421$	−20.2533	−	35.0797i	−0.0481076	−	0.0833248i	0.840969	−	0.541083i	$-0.181986\pi$
$421$	−20.2533	−	35.0797i	−0.0481076	−	0.0833248i	−0.889076	+	0.457759i	$0.848652\pi$
$422$	593.768	+	342.812i	1.40703	+	0.812351i
$423$	40.8129	−	70.6900i	0.0964843	−	0.167116i
$424$	−62.5874			−0.147612
$425$	443.212	+	767.666i	1.04285	+	1.80627i
$426$	616.687			1.44762
$427$	−43.9116			−0.102837
$428$	−653.194	+	1131.36i	−1.52615	+	2.64337i
$429$		−	64.5112i		−	0.150376i
$430$	−1579.17	+	911.731i	−3.67248	+	2.12031i
$431$	146.412	−	253.593i	0.339702	−	0.588382i	−0.644674	−	0.764457i	$-0.723007\pi$
$431$	146.412	−	253.593i	0.339702	−	0.588382i	0.984377	+	0.176076i	$0.0563403\pi$
$432$	−243.027	+	140.312i	−0.562563	+	0.324796i
$433$	140.788	+	81.2843i	0.325147	+	0.187723i	0.653684	−	0.756767i	$-0.273222\pi$
$433$	140.788	+	81.2843i	0.325147	+	0.187723i	−0.328538	+	0.944491i	$0.606556\pi$
$434$	−241.483	−	139.420i	−0.556411	−	0.321244i
$435$	−235.997	+	408.759i	−0.542521	+	0.939675i
$436$	420.986	+	243.057i	0.965565	+	0.557469i
$437$	17.7527	−	30.7486i	0.0406240	−	0.0703628i
$438$	−166.853	+	288.998i	−0.380943	+	0.659812i
$439$	−16.1550	−	27.9813i	−0.0367996	−	0.0637388i	0.847039	−	0.531531i	$-0.178383\pi$
$439$	−16.1550	−	27.9813i	−0.0367996	−	0.0637388i	−0.883839	+	0.467792i	$0.845050\pi$
$440$	−3113.23	−	1797.42i	−7.07552	−	4.08506i
$441$	−86.9300	−	150.567i	−0.197120	−	0.341422i
$442$	−167.094			−0.378040
$443$	275.346	+	158.971i	0.621547	+	0.358851i	0.777471	−	0.628918i	$-0.216502\pi$
$443$	275.346	+	158.971i	0.621547	+	0.358851i	−0.155924	+	0.987769i	$0.549835\pi$
$444$			929.443i			2.09334i
$445$		−	727.120i		−	1.63398i
$446$	891.507	−	514.712i	1.99889	−	1.15406i
$447$			401.917i			0.899143i
$448$	−1674.30	−	966.657i	−3.73727	−	2.15772i
$449$	−239.333	+	414.537i	−0.533036	+	0.923245i	0.466220	+	0.884669i	$0.345615\pi$
$449$	−239.333	+	414.537i	−0.533036	+	0.923245i	−0.999256	+	0.0385759i	$0.987718\pi$
$450$	437.133	−	252.379i	0.971408	−	0.560842i
$451$	43.7251	+	75.7341i	0.0969515	+	0.167925i
$452$	422.159	−	243.734i	0.933981	−	0.539234i
$453$	240.838	−	139.048i	0.531652	−	0.306949i
$454$			1205.04i			2.65427i
$455$			186.622i			0.410159i
$456$	67.0611	+	116.153i	0.147064	+	0.254722i
$457$	404.554	−	700.707i	0.885238	−	1.53328i	0.0397966	−	0.999208i	$-0.487329\pi$
$457$	404.554	−	700.707i	0.885238	−	1.53328i	0.845441	−	0.534069i	$-0.179338\pi$
$458$	−206.293	+	357.310i	−0.450421	+	0.780153i
$459$	−90.5958	+	52.3055i	−0.197377	+	0.113955i
$460$		−	1019.12i		−	2.21547i
$461$	383.786			0.832508			0.416254	−	0.909248i	$-0.363343\pi$
$461$	383.786			0.832508			0.416254	+	0.909248i	$0.363343\pi$
$462$	586.909	−	1016.56i	1.27037	−	2.20034i
$463$	29.6981	−	17.1462i	0.0641428	−	0.0370328i	−0.467586	−	0.883948i	$-0.654876\pi$
$463$	29.6981	−	17.1462i	0.0641428	−	0.0370328i	0.531728	+	0.846915i	$0.321543\pi$
$464$	−1771.33			−3.81752
$465$	87.9328	+	50.7680i	0.189103	+	0.109179i
$466$	478.790			1.02745
$467$	205.622	+	356.147i	0.440303	+	0.762627i	0.997712	−	0.0676109i	$-0.0215376\pi$
$467$	205.622	+	356.147i	0.440303	+	0.762627i	−0.557409	+	0.830238i	$0.688204\pi$
$468$			69.0851i			0.147618i
$469$	−675.008	−	156.454i	−1.43925	−	0.333590i
$470$	−863.853			−1.83799
$471$	−374.552	+	216.248i	−0.795227	+	0.459124i
$472$		−	1026.21i		−	2.17418i
$473$	492.447	−	852.943i	1.04111	−	1.80326i
$474$		−	465.011i		−	0.981037i
$475$	−67.5647	−	117.025i	−0.142241	−	0.246369i
$476$	−1911.78	−	1103.77i	−4.01635	−	2.31884i
$477$			7.44170i			0.0156011i
$478$	107.202			0.224272
$479$	−281.384	−	487.372i	−0.587441	−	1.01748i	−0.994566	−	0.104106i	$-0.966802\pi$
$479$	−281.384	−	487.372i	−0.587441	−	1.01748i	0.407125	−	0.913372i	$-0.366531\pi$
$480$	1314.20	+	758.753i	2.73791	+	1.58073i
$481$	95.1975	+	54.9623i	0.197916	+	0.114267i
$482$	535.873	−	309.386i	1.11177	−	0.641880i
$483$	207.228			0.429043
$484$	1835.02			3.79137
$485$	427.168	+	739.877i	0.880759	+	1.52552i
$486$	29.7844	+	51.5882i	0.0612848	+	0.106148i
$487$	−361.541	+	208.736i	−0.742384	+	0.428616i	−0.822936	−	0.568135i	$-0.807665\pi$
$487$	−361.541	+	208.736i	−0.742384	+	0.428616i	0.0805512	+	0.996750i	$0.474332\pi$
$488$	53.5658	+	92.7788i	0.109766	+	0.190120i
$489$	286.454	+	165.384i	0.585795	+	0.338209i
$490$	−919.989	+	1593.47i	−1.87753	+	3.25198i
$491$	461.749			0.940426			0.470213	−	0.882553i	$-0.344177\pi$
$491$	461.749			0.940426			0.470213	+	0.882553i	$0.344177\pi$
$492$	−46.8253	−	81.1038i	−0.0951734	−	0.164845i
$493$	−660.318			−1.33939
$494$	25.4723			0.0515633
$495$	−213.715	+	370.166i	−0.431748	+	0.747810i
$496$			381.052i			0.768249i
$497$	834.480	−	481.787i	1.67903	−	0.969391i
$498$	−417.677	+	723.438i	−0.838709	+	1.45269i
$499$	−147.803	+	85.3338i	−0.296198	+	0.171010i	−0.640733	−	0.767763i	$-0.721370\pi$
$499$	−147.803	+	85.3338i	−0.296198	+	0.171010i	0.344536	+	0.938773i	$0.388036\pi$
$500$	−1451.77	−	838.177i	−2.90353	−	1.67635i
$501$	−184.679	−	106.624i	−0.368620	−	0.212823i
$502$	−330.339	+	572.164i	−0.658046	+	1.13977i
$503$	−795.911	−	459.519i	−1.58233	−	0.913557i	−0.994519	−	0.104557i	$-0.966658\pi$
$503$	−795.911	−	459.519i	−1.58233	−	0.913557i	−0.587808	−	0.809000i	$-0.700009\pi$
$504$	−391.403	+	677.930i	−0.776594	+	1.34510i
$505$	280.400	−	485.667i	0.555248	−	0.961718i
$506$	379.056	+	656.544i	0.749122	+	1.29752i
$507$	−246.424	−	142.273i	−0.486043	−	0.280617i
$508$	−508.382	−	880.543i	−1.00075	−	1.73335i
$509$	522.414			1.02635			0.513177	−	0.858283i	$-0.328468\pi$
$509$	522.414			1.02635			0.513177	+	0.858283i	$0.328468\pi$
$510$	958.785	+	553.555i	1.87997	+	1.08540i
$511$			521.416i			1.02038i
$512$			244.475i			0.477490i
$513$	13.8107	−	7.97362i	0.0269215	−	0.0155431i
$514$			231.321i			0.450041i
$515$	−643.131	−	371.312i	−1.24880	−	0.720993i
$516$	−527.362	+	913.417i	−1.02202	+	1.77019i
$517$	404.076	−	233.293i	0.781578	−	0.451244i
$518$	1000.07	+	1732.17i	1.93064	+	3.34396i
$519$	−249.358	+	143.967i	−0.480458	+	0.277392i
$520$	394.305	−	227.652i	0.758280	−	0.437793i
$521$		−	690.769i		−	1.32585i	−0.748685	−	0.662926i	$-0.769315\pi$
$521$		−	690.769i		−	1.32585i	0.748685	−	0.662926i	$-0.230685\pi$
$522$			376.006i			0.720318i
$523$	−263.102	−	455.706i	−0.503063	−	0.871331i	−0.999994	−	0.00354090i	$-0.998873\pi$
$523$	−263.102	−	455.706i	−0.503063	−	0.871331i	0.496930	−	0.867790i	$-0.334460\pi$
$524$	−147.491	+	255.463i	−0.281472	+	0.487524i
$525$	394.343	−	683.022i	0.751129	−	1.30099i
$526$	−634.989	+	366.611i	−1.20720	+	0.696979i
$527$			142.049i			0.269542i
$528$	−1604.09			−3.03805
$529$	197.581	−	342.220i	0.373499	−	0.646919i
$530$	68.2050	−	39.3782i	0.128689	−	0.0742984i
$531$	−122.018			−0.229788
$532$	291.439	+	168.262i	0.547817	+	0.316282i
$533$	−11.0760			−0.0207805
$534$	−289.624	−	501.644i	−0.542368	−	0.939408i
$535$		−	1023.70i		−	1.91347i
$536$	492.849	+	1617.04i	0.919495	+	3.01687i
$537$	605.472			1.12751
$538$	1404.10	−	810.660i	2.60986	−	1.50680i
$539$		−	993.814i		−	1.84381i
$540$	228.868	−	396.411i	0.423830	−	0.734095i
$541$			740.777i			1.36927i	0.728884	+	0.684637i	$0.240039\pi$
$541$			740.777i			1.36927i	−0.728884	+	0.684637i	$0.759961\pi$
$542$	−540.660	−	936.450i	−0.997527	−	1.72777i
$543$	314.789	+	181.744i	0.579722	+	0.334703i
$544$			2122.99i			3.90255i
$545$	−380.925			−0.698946
$546$	74.3348	+	128.752i	0.136144	+	0.235809i
$547$	−692.816	−	399.997i	−1.26657	−	0.731257i	−0.292235	−	0.956346i	$-0.594399\pi$
$547$	−692.816	−	399.997i	−1.26657	−	0.731257i	−0.974338	+	0.225090i	$0.927732\pi$
$548$	1313.16	+	758.152i	2.39627	+	1.38349i
$549$	11.0315	−	6.36903i	0.0200938	−	0.0116011i
$550$	2885.28			5.24597
$551$	100.661			0.182688
$552$	−252.788	−	437.842i	−0.457950	−	0.793192i
$553$	−363.290	−	629.238i	−0.656945	−	1.13786i
$554$	1068.95	−	617.158i	1.92951	−	1.11400i
$555$	−364.163	−	630.748i	−0.656149	−	1.13648i
$556$	−1754.30	−	1012.85i	−3.15522	−	1.82167i
$557$	−157.032	+	271.988i	−0.281925	+	0.488309i	−0.971859	−	0.235564i	$-0.924306\pi$
$557$	−157.032	+	271.988i	−0.281925	+	0.488309i	0.689934	+	0.723873i	$0.257640\pi$
$558$	80.8871			0.144959
$559$	62.3707	+	108.029i	0.111575	+	0.193254i
$560$	4640.42			8.28646
$561$	−597.975			−1.06591
$562$	−858.575	+	1487.10i	−1.52771	+	2.64608i
$563$		−	60.6565i		−	0.107738i	−0.998548	−	0.0538690i	$-0.982845\pi$
$563$		−	60.6565i		−	0.107738i	0.998548	−	0.0538690i	$-0.0171553\pi$
$564$	−432.726	+	249.834i	−0.767244	+	0.442968i
$565$	−190.993	+	330.810i	−0.338041	+	0.585505i
$566$	−593.664	+	342.752i	−1.04888	+	0.605569i
$567$	80.6066	+	46.5382i	0.142163	+	0.0820780i
$568$	−2035.89	−	1175.42i	−3.58432	−	2.06941i
$569$	−268.226	+	464.581i	−0.471399	+	0.816487i	−0.999465	−	0.0327168i	$-0.989584\pi$
$569$	−268.226	+	464.581i	−0.471399	+	0.816487i	0.528066	+	0.849203i	$0.322917\pi$
$570$	−146.160	−	84.3857i	−0.256422	−	0.148045i
$571$	404.461	−	700.547i	0.708338	−	1.22688i	−0.257136	−	0.966375i	$-0.582779\pi$
$571$	404.461	−	700.547i	0.708338	−	1.22688i	0.965473	−	0.260501i	$-0.0838879\pi$
$572$	−197.451	+	341.996i	−0.345194	+	0.597894i
$573$	−102.864	−	178.166i	−0.179519	−	0.310936i
$574$	−174.533	−	100.767i	−0.304065	−	0.175552i
$575$	254.687	+	441.130i	0.442933	+	0.767183i
$576$	560.824			0.973652
$577$	303.386	+	175.160i	0.525799	+	0.303570i	0.739304	−	0.673372i	$-0.235155\pi$
$577$	303.386	+	175.160i	0.525799	+	0.303570i	−0.213505	+	0.976942i	$0.568488\pi$
$578$			444.475i			0.768987i
$579$			87.0170i			0.150288i
$580$	2502.20	−	1444.64i	4.31413	−	2.49077i
$581$			1305.24i			2.24654i
$582$	589.411	+	340.297i	1.01273	+	0.584702i
$583$	−21.2690	+	36.8390i	−0.0364820	+	0.0631887i
$584$	1101.68	−	636.052i	1.88643	−	1.08913i
$585$	−27.0681	−	46.8833i	−0.0462702	−	0.0801423i
$586$	387.921	−	223.966i	0.661982	−	0.382195i
$587$	−169.813	+	98.0418i	−0.289290	+	0.167022i	−0.637622	−	0.770350i	$-0.720082\pi$
$587$	−169.813	+	98.0418i	−0.289290	+	0.167022i	0.348331	+	0.937371i	$0.386748\pi$
$588$			1064.28i			1.80999i
$589$		−	21.6544i		−	0.0367646i
$590$	645.662	+	1118.32i	1.09434	+	1.89546i
$591$	26.7832	−	46.3899i	0.0453185	−	0.0784940i
$592$	1366.65	−	2367.12i	2.30854	−	3.99851i
$593$	−698.357	+	403.196i	−1.17767	+	0.679927i	−0.955474	−	0.295076i	$-0.904655\pi$
$593$	−698.357	+	403.196i	−1.17767	+	0.679927i	−0.222194	+	0.975003i	$0.571322\pi$
$594$			340.506i			0.573242i
$595$	1729.86			2.90733
$596$	1230.16	−	2130.70i	2.06402	−	3.57500i
$597$	207.846	−	120.000i	0.348150	−	0.201005i
$598$	−96.0184			−0.160566
$599$	−626.711	−	361.832i	−1.04626	−	0.604060i	−0.124662	−	0.992199i	$-0.539785\pi$
$599$	−626.711	−	361.832i	−1.04626	−	0.604060i	−0.921601	+	0.388139i	$0.873118\pi$
$600$	−1924.17			−3.20694
$601$	53.9906	+	93.5145i	0.0898347	+	0.155598i	0.907441	−	0.420179i	$-0.138033\pi$
$601$	53.9906	+	93.5145i	0.0898347	+	0.155598i	−0.817606	+	0.575777i	$0.804699\pi$
$602$			2269.74i			3.77033i
$603$	192.268	−	58.6002i	0.318853	−	0.0971811i
$604$	−1702.35			−2.81846
$605$	−1245.30	+	718.975i	−2.05835	+	1.18839i
$606$		−	446.753i		−	0.737216i
$607$	−246.169	+	426.377i	−0.405550	+	0.702433i	−0.994385	−	0.105820i	$-0.966253\pi$
$607$	−246.169	+	426.377i	−0.405550	+	0.702433i	0.588835	+	0.808253i	$0.299587\pi$
$608$		−	323.635i		−	0.532294i
$609$	293.755	+	508.799i	0.482356	+	0.835466i
$610$	−116.747	−	67.4041i	−0.191389	−	0.110498i
$611$			59.0954i			0.0967192i
$612$	640.372			1.04636
$613$	−184.339	−	319.285i	−0.300717	−	0.520857i	0.675582	−	0.737285i	$-0.263893\pi$
$613$	−184.339	−	319.285i	−0.300717	−	0.520857i	−0.976299	+	0.216428i	$0.930559\pi$
$614$	−1329.02	−	767.308i	−2.16452	−	1.24969i
$615$	63.5541	+	36.6930i	0.103340	+	0.0596634i
$616$	−3875.17	+	2237.33i	−6.29086	+	3.63203i
$617$	224.281			0.363502			0.181751	−	0.983345i	$-0.441823\pi$
$617$	224.281			0.363502			0.181751	+	0.983345i	$0.441823\pi$
$618$	−591.599			−0.957280
$619$	344.444	+	596.594i	0.556452	+	0.963803i	0.997789	+	0.0664614i	$0.0211709\pi$
$619$	344.444	+	596.594i	0.556452	+	0.963803i	−0.441337	+	0.897341i	$0.645496\pi$
$620$	−310.774	−	538.277i	−0.501249	−	0.868189i
$621$	−52.0598	+	30.0568i	−0.0838323	+	0.0484006i
$622$	726.552	+	1258.43i	1.16809	+	2.02319i
$623$	−783.819	−	452.538i	−1.25814	−	0.726386i
$624$	101.583	−	175.947i	0.162793	−	0.281966i
$625$	212.873			0.340597
$626$	−767.665	−	1329.63i	−1.22630	−	2.12402i
$627$	91.1572			0.145386
$628$	2647.50			4.21577
$629$	509.463	−	882.415i	0.809957	−	1.40289i
$630$		−	985.037i		−	1.56355i
$631$	496.730	−	286.787i	0.787210	−	0.454496i	−0.0517692	−	0.998659i	$-0.516486\pi$
$631$	496.730	−	286.787i	0.787210	−	0.454496i	0.838980	+	0.544163i	$0.183153\pi$
$632$	−886.325	+	1535.16i	−1.40241	+	2.42905i
$633$	−269.129	+	155.382i	−0.425165	+	0.245469i
$634$	482.581	+	278.618i	0.761169	+	0.439461i
$635$	690.007	+	398.376i	1.08663	+	0.627363i
$636$	22.7770	−	39.4510i	0.0358130	−	0.0620299i
$637$	109.008	+	62.9356i	0.171127	+	0.0988000i
$638$	−1074.66	+	1861.36i	−1.68442	+	2.91750i
$639$	−139.759	+	242.070i	−0.218715	+	0.378826i
$640$	−1215.36	−	2105.07i	−1.89901	−	3.28918i
$641$	−529.558	−	305.740i	−0.826143	−	0.476974i	0.0263874	−	0.999652i	$-0.491600\pi$
$641$	−529.558	−	305.740i	−0.826143	−	0.476974i	−0.852530	+	0.522678i	$0.824933\pi$
$642$	−407.759	−	706.259i	−0.635138	−	1.10009i
$643$	686.855			1.06820			0.534102	−	0.845420i	$-0.320650\pi$
$643$	686.855			1.06820			0.534102	+	0.845420i	$0.320650\pi$
$644$	−1098.58	−	634.268i	−1.70588	−	0.984888i
$645$		−	826.497i		−	1.28139i
$646$		−	236.111i		−	0.365496i
$647$	−953.003	+	550.217i	−1.47296	+	0.850412i	−0.999537	−	0.0304243i	$-0.990314\pi$
$647$	−953.003	+	550.217i	−1.47296	+	0.850412i	−0.473420	+	0.880837i	$0.656981\pi$
$648$		−	227.080i		−	0.350432i
$649$	−604.030	−	348.737i	−0.930708	−	0.537345i
$650$	−182.717	+	316.476i	−0.281104	+	0.486886i
$651$	109.454	−	63.1931i	0.168132	−	0.0970708i
$652$	−1012.39	−	1753.52i	−1.55275	−	2.68944i
$653$	362.280	−	209.162i	0.554793	−	0.320310i	−0.196260	−	0.980552i	$-0.562880\pi$
$653$	362.280	−	209.162i	0.554793	−	0.320310i	0.751053	+	0.660242i	$0.229546\pi$
$654$	−262.802	+	151.729i	−0.401839	+	0.232002i
$655$		−	231.153i		−	0.352905i
$656$			275.408i			0.419829i
$657$	−75.6272	−	130.990i	−0.115110	−	0.199376i
$658$	−537.637	+	931.215i	−0.817078	+	1.41522i
$659$	−511.360	+	885.702i	−0.775964	+	1.34401i	0.158288	+	0.987393i	$0.449403\pi$
$659$	−511.360	+	885.702i	−0.775964	+	1.34401i	−0.934251	+	0.356616i	$0.883931\pi$
$660$	2265.95	−	1308.25i	3.43326	−	1.98220i
$661$			256.798i			0.388499i	0.980952	+	0.194249i	$0.0622271\pi$
$661$			256.798i			0.388499i	−0.980952	+	0.194249i	$0.937773\pi$
$662$	−613.550			−0.926812
$663$	37.8682	−	65.5896i	0.0571164	−	0.0989285i
$664$	2757.79	−	1592.21i	4.15329	−	2.39790i
$665$	−263.705			−0.396550
$666$	−502.476	−	290.104i	−0.754468	−	0.435592i
$667$	−379.444			−0.568882
$668$	652.696	+	1130.50i	0.977090	+	1.69237i
$669$			466.593i			0.697449i
$670$	−1554.48	−	1452.10i	−2.32012	−	2.16731i
$671$	72.8129			0.108514
$672$	1635.84	−	944.451i	2.43428	−	1.40543i
$673$		−	141.416i		−	0.210128i	−0.994465	−	0.105064i	$-0.966495\pi$
$673$		−	141.416i		−	0.210128i	0.994465	−	0.105064i	$-0.0335047\pi$
$674$	−671.344	+	1162.80i	−0.996060	+	1.72523i
$675$			228.785i			0.338941i
$676$	870.918	+	1508.47i	1.28834	+	2.23147i
$677$	−154.126	−	88.9845i	−0.227660	−	0.131440i	0.381832	−	0.924232i	$-0.375293\pi$
$677$	−154.126	−	88.9845i	−0.227660	−	0.131440i	−0.609492	+	0.792792i	$0.708627\pi$
$678$			304.304i			0.448825i
$679$	1063.43			1.56617
$680$	−2110.18	−	3654.94i	−3.10321	−	5.37491i
$681$	−473.016	−	273.096i	−0.694591	−	0.401022i
$682$	400.419	+	231.182i	0.587125	+	0.338977i
$683$	1088.14	−	628.240i	1.59318	−	0.919824i	0.600426	−	0.799681i	$-0.294998\pi$
$683$	1088.14	−	628.240i	1.59318	−	0.919824i	0.992757	−	0.120144i	$-0.0383355\pi$
$684$	−97.6204			−0.142720
$685$	−1188.20			−1.73460
$686$	176.917	+	306.429i	0.257896	+	0.446689i
$687$	−93.5037	−	161.953i	−0.136104	−	0.235740i
$688$	2686.18	−	1550.87i	3.90433	−	2.25417i
$689$	−2.69382	−	4.66584i	−0.00390976	−	0.00677190i
$690$	550.955	+	318.094i	0.798485	+	0.461005i
$691$	97.4066	−	168.713i	0.140965	−	0.244158i	−0.786895	−	0.617086i	$-0.788313\pi$
$691$	97.4066	−	168.713i	0.140965	−	0.244158i	0.927860	+	0.372928i	$0.121646\pi$
$692$	1762.57			2.54707
$693$	266.020	+	460.761i	0.383868	+	0.664879i
$694$	−2271.38			−3.27288
$695$	1587.37			2.28398
$696$	716.678	−	1241.32i	1.02971	−	1.78351i
$697$			102.667i			0.147298i
$698$	−296.041	+	170.919i	−0.424127	+	0.244870i
$699$	−108.508	+	187.941i	−0.155232	+	0.268871i
$700$	−4181.09	+	2413.95i	−5.97298	+	3.44850i
$701$	379.721	+	219.232i	0.541685	+	0.312742i	0.745762	−	0.666213i	$-0.232086\pi$
$701$	379.721	+	219.232i	0.541685	+	0.312742i	−0.204077	+	0.978955i	$0.565419\pi$
$702$	−37.3488	−	21.5633i	−0.0532034	−	0.0307170i
$703$	−77.6642	+	134.518i	−0.110475	+	0.191349i
$704$	2776.27	+	1602.88i	3.94357	+	2.27682i
$705$	195.774	−	339.090i	0.277693	−	0.480979i
$706$	−295.636	+	512.057i	−0.418748	+	0.725293i
$707$	−349.026	−	604.530i	−0.493672	−	0.855064i
$708$	646.856	+	373.463i	0.913639	+	0.527490i
$709$	−2.61614	−	4.53128i	−0.00368989	−	0.00639108i	0.864175	−	0.503192i	$-0.167841\pi$
$709$	−2.61614	−	4.53128i	−0.00368989	−	0.00639108i	−0.867864	+	0.496801i	$0.834508\pi$
$710$	2958.17			4.16643
$711$	182.532	+	105.385i	0.256726	+	0.148221i
$712$			2208.13i			3.10130i
$713$			81.6267i			0.114483i
$714$	1193.44	−	689.032i	1.67148	−	0.965031i
$715$		−	309.451i		−	0.432799i
$716$	−3209.81	−	1853.19i	−4.48298	−	2.58825i
$717$	−24.2950	+	42.0803i	−0.0338843	+	0.0586893i
$718$	−92.9085	+	53.6407i	−0.129399	+	0.0747086i
$719$	384.311	+	665.646i	0.534507	+	0.925794i	0.999187	+	0.0403150i	$0.0128361\pi$
$719$	384.311	+	665.646i	0.534507	+	0.925794i	−0.464680	+	0.885479i	$0.653831\pi$
$720$	−1165.77	+	673.056i	−1.61912	+	0.934800i
$721$	−800.531	+	462.187i	−1.11031	+	0.641036i
$722$		−	1343.51i		−	1.86082i
$723$			280.463i			0.387916i
$724$	−1112.54	−	1926.97i	−1.53665	−	2.66156i
$725$	−722.060	+	1250.65i	−0.995945	+	1.72503i
$726$	−572.760	+	992.049i	−0.788925	+	1.36646i
$727$	−529.012	+	305.425i	−0.727665	+	0.420117i	−0.817567	−	0.575833i	$-0.804678\pi$
$727$	−529.012	+	305.425i	−0.727665	+	0.420117i	0.0899025	+	0.995951i	$0.471344\pi$
$728$		−	566.737i		−	0.778484i
$729$	−27.0000			−0.0370370
$730$	−800.371	+	1386.28i	−1.09640	+	1.89902i
$731$	1001.36	−	578.134i	1.36985	−	0.790881i
$732$	−77.9754			−0.106524
$733$	492.779	+	284.506i	0.672277	+	0.388139i	0.796939	−	0.604060i	$-0.206451\pi$
$733$	492.779	+	284.506i	0.672277	+	0.388139i	−0.124662	+	0.992199i	$0.539785\pi$
$734$	−1096.54			−1.49393
$735$	−416.992	−	722.251i	−0.567335	−	0.982654i
$736$			1219.95i			1.65754i
$737$	1119.28	+	259.427i	1.51870	+	0.352004i
$738$	58.4618			0.0792165
$739$	−567.916	+	327.886i	−0.768492	+	0.443689i	−0.832336	−	0.554271i	$-0.812997\pi$
$739$	−567.916	+	327.886i	−0.768492	+	0.443689i	0.0638444	+	0.997960i	$0.479664\pi$
$740$			4458.41i			6.02488i
$741$	−5.77275	+	9.99869i	−0.00779048	+	0.0134935i
$742$		−	98.0313i		−	0.132118i
$743$	344.185	+	596.146i	0.463237	+	0.802350i	0.999120	−	0.0419420i	$-0.0133545\pi$
$743$	344.185	+	596.146i	0.463237	+	0.802350i	−0.535883	+	0.844292i	$0.680021\pi$
$744$	−267.036	−	154.173i	−0.358919	−	0.207222i
$745$			1927.94i			2.58784i
$746$	−1143.55			−1.53291
$747$	−189.315	−	327.903i	−0.253434	−	0.438960i
$748$	3170.07	+	1830.24i	4.23805	+	2.44684i
$749$	−1103.53	−	637.124i	−1.47334	−	0.850632i
$750$	906.271	−	523.236i	1.20836	−	0.697648i
$751$	−354.355			−0.471844			−0.235922	−	0.971772i	$-0.575811\pi$
$751$	−354.355			−0.471844			−0.235922	+	0.971772i	$0.575811\pi$
$752$	1469.43			1.95402
$753$	−149.728	−	259.337i	−0.198842	−	0.344405i
$754$	−136.111	−	235.750i	−0.180518	−	0.312666i
$755$	1155.27	−	666.994i	1.53016	−	0.883436i
$756$	−284.882	−	493.430i	−0.376828	−	0.652685i
$757$	859.015	+	495.952i	1.13476	+	0.655155i	0.945128	−	0.326700i	$-0.105937\pi$
$757$	859.015	+	495.952i	1.13476	+	0.655155i	0.189634	+	0.981855i	$0.439270\pi$
$758$	451.366	−	781.788i	0.595469	−	1.03138i
$759$	−343.619			−0.452726
$760$	321.683	+	557.171i	0.423267	+	0.733120i
$761$	−774.137			−1.01726			−0.508632	−	0.860984i	$-0.669848\pi$
$761$	−774.137			−1.01726			−0.508632	+	0.860984i	$0.669848\pi$
$762$	634.719			0.832965
$763$	−237.077	+	410.629i	−0.310717	+	0.538177i
$764$			1259.36i			1.64837i
$765$	−434.576	+	250.902i	−0.568073	+	0.327977i
$766$	1119.66	−	1939.31i	1.46170	−	2.53174i
$767$	76.5032	−	44.1692i	0.0997435	−	0.0575869i
$768$	−555.324	−	320.617i	−0.723079	−	0.417470i
$769$	653.060	+	377.044i	0.849233	+	0.490305i	0.860392	−	0.509633i	$-0.170219\pi$
$769$	653.060	+	377.044i	0.849233	+	0.490305i	−0.0111593	+	0.999938i	$0.503552\pi$
$770$	2815.32	−	4876.28i	3.65626	−	6.33283i
$771$	−90.8009	−	52.4239i	−0.117770	−	0.0679947i
$772$	266.335	−	461.306i	0.344994	−	0.597547i
$773$	416.646	−	721.653i	0.538999	−	0.933574i	−0.459959	−	0.887940i	$-0.652136\pi$
$773$	416.646	−	721.653i	0.538999	−	0.933574i	0.998958	−	0.0456338i	$-0.0145307\pi$
$774$	−329.208	−	570.205i	−0.425333	−	0.736698i
$775$	269.041	+	155.331i	0.347150	+	0.200427i
$776$	−1297.23	−	2246.87i	−1.67169	−	2.89545i
$777$	−906.577			−1.16677
$778$	1268.06	+	732.115i	1.62990	+	0.941021i
$779$		−	15.6509i		−	0.0200910i
$780$			331.392i			0.424862i
$781$	−1383.71	+	798.886i	−1.77172	+	1.02290i
$782$			890.025i			1.13814i
$783$	−147.594	−	85.2137i	−0.188499	−	0.108830i
$784$	1564.91	−	2710.51i	1.99606	−	3.45729i
$785$	−1796.67	+	1037.31i	−2.28876	+	1.32141i
$786$	−92.0722	−	159.474i	−0.117140	−	0.202893i
$787$	770.728	−	444.980i	0.979324	−	0.565413i	0.0772578	−	0.997011i	$-0.475384\pi$
$787$	770.728	−	444.980i	0.979324	−	0.565413i	0.902066	+	0.431598i	$0.142050\pi$
$788$	−283.974	+	163.952i	−0.360373	+	0.208062i
$789$		−	332.338i		−	0.421214i
$790$		−	2230.60i		−	2.82354i
$791$	237.737	+	411.773i	0.300553	+	0.520573i
$792$	649.014	−	1124.12i	0.819462	−	1.41935i
$793$	−4.61105	+	7.98657i	−0.00581469	+	0.0100713i
$794$	−751.976	+	434.154i	−0.947073	+	0.546793i
$795$			35.6968i			0.0449017i
$796$	−1469.15			−1.84566
$797$	245.194	−	424.689i	0.307647	−	0.532860i	−0.670200	−	0.742180i	$-0.733792\pi$
$797$	245.194	−	424.689i	0.307647	−	0.532860i	0.977847	+	0.209320i	$0.0671252\pi$
$798$	−181.932	+	105.038i	−0.227985	+	0.131627i
$799$	547.774			0.685575
$800$	4020.94	+	2321.49i	5.02618	+	2.90187i
$801$	262.548			0.327776
$802$	−1244.82	−	2156.10i	−1.55215	−	2.68840i
$803$		−	864.596i		−	1.07671i
$804$	−1198.64	−	277.821i	−1.49084	−	0.345548i
$805$	994.044			1.23484
$806$	−50.7150	+	29.2803i	−0.0629218	+	0.0363279i
$807$			734.874i			0.910625i
$808$	−851.523	+	1474.88i	−1.05387	+	1.82535i
$809$		−	21.2576i		−	0.0262764i	−0.999914	−	0.0131382i	$-0.995818\pi$
$809$		−	21.2576i		−	0.0262764i	0.999914	−	0.0131382i	$-0.00418214\pi$
$810$	142.872	+	247.461i	0.176385	+	0.305508i
$811$	−164.281	−	94.8479i	−0.202567	−	0.116952i	0.395286	−	0.918558i	$-0.370646\pi$
$811$	−164.281	−	94.8479i	−0.202567	−	0.116952i	−0.597852	+	0.801606i	$0.703979\pi$
$812$		−	3596.42i		−	4.42909i
$813$	490.116			0.602848
$814$	−1658.29	−	2872.24i	−2.03721	−	3.52855i
$815$	1374.08	+	793.326i	1.68599	+	0.973406i
$816$	−1630.91	−	941.604i	−1.99866	−	1.15393i
$817$	−152.650	+	88.1326i	−0.186842	+	0.107873i
$818$	−940.116			−1.14929
$819$	−67.3855			−0.0822778
$820$	−224.615	−	389.044i	−0.273920	−	0.474444i
$821$	−318.328	−	551.361i	−0.387732	−	0.671572i	0.604412	−	0.796672i	$-0.293408\pi$
$821$	−318.328	−	551.361i	−0.387732	−	0.671572i	−0.992144	+	0.125100i	$0.960075\pi$
$822$	−819.744	+	473.280i	−0.997256	+	0.575766i
$823$	585.900	+	1014.81i	0.711908	+	1.23306i	0.964140	+	0.265394i	$0.0855021\pi$
$823$	585.900	+	1014.81i	0.711908	+	1.23306i	−0.252232	+	0.967667i	$0.581165\pi$
$824$	1953.07	+	1127.60i	2.37023	+	1.36845i
$825$	−653.888	+	1132.57i	−0.792591	+	1.37281i
$826$	1607.37			1.94596
$827$	−250.747	−	434.306i	−0.303200	−	0.525159i	0.673659	−	0.739043i	$-0.264722\pi$
$827$	−250.747	−	434.306i	−0.303200	−	0.525159i	−0.976859	+	0.213884i	$0.931389\pi$
$828$	367.982			0.444423
$829$	−1138.01			−1.37274			−0.686372	−	0.727250i	$-0.740798\pi$
$829$	−1138.01			−1.37274			−0.686372	+	0.727250i	$0.740798\pi$
$830$	−2003.54	+	3470.23i	−2.41390	+	4.18101i
$831$			559.462i			0.673240i
$832$	−351.628	+	203.013i	−0.422630	+	0.244006i
$833$	583.370	−	1010.43i	0.700324	−	1.21300i
$834$	1095.13	−	632.275i	1.31311	−	0.758123i
$835$	−885.878	−	511.462i	−1.06093	−	0.612530i
$836$	−483.255	−	279.007i	−0.578056	−	0.333741i
$837$	−18.3313	+	31.7508i	−0.0219012	+	0.0379340i
$838$	2292.97	+	1323.85i	2.73625	+	1.57977i
$839$	117.284	−	203.142i	0.139790	−	0.242124i	−0.787627	−	0.616153i	$-0.788690\pi$
$839$	117.284	−	203.142i	0.139790	−	0.242124i	0.927417	+	0.374029i	$0.122024\pi$
$840$	−1877.51	+	3251.94i	−2.23513	+	3.87136i
$841$	−117.380	−	203.307i	−0.139571	−	0.241745i
$842$	−134.052	−	77.3948i	−0.159206	−	0.0919178i
$843$	−389.155	−	674.036i	−0.461631	−	0.799568i
$844$	1902.33			2.25394
$845$	−1182.06	−	682.464i	−1.39889	−	0.807650i
$846$		−	311.920i		−	0.368700i
$847$			1789.88i			2.11319i
$848$	−116.018	+	66.9828i	−0.136813	+	0.0789891i
$849$		−	310.709i		−	0.365971i
$850$	2933.52	+	1693.67i	3.45119	+	1.99255i
$851$	292.757	−	507.070i	0.344015	−	0.595852i
$852$	1481.82	−	855.528i	1.73922	−	1.00414i
$853$	−184.486	−	319.539i	−0.216279	−	0.374606i	0.737389	−	0.675469i	$-0.236059\pi$
$853$	−184.486	−	319.539i	−0.216279	−	0.374606i	−0.953667	+	0.300863i	$0.902725\pi$
$854$	−145.320	+	83.9006i	−0.170164	+	0.0982443i
$855$	66.2482	−	38.2484i	0.0774832	−	0.0447350i
$856$			3108.80i			3.63177i
$857$		−	1020.88i		−	1.19123i	−0.803272	−	0.595613i	$-0.796909\pi$
$857$		−	1020.88i		−	1.19123i	0.803272	−	0.595613i	$-0.203091\pi$
$858$	−123.260	−	213.492i	−0.143659	−	0.248825i
$859$	−459.864	+	796.508i	−0.535348	+	0.927250i	0.463798	+	0.885941i	$0.346486\pi$
$859$	−459.864	+	796.508i	−0.535348	+	0.927250i	−0.999146	+	0.0413094i	$0.986847\pi$
$860$	−2529.68	+	4381.54i	−2.94149	+	5.09481i
$861$	79.1085	−	45.6733i	0.0918797	−	0.0530468i
$862$		−	1118.98i		−	1.29812i
$863$	−524.535			−0.607804			−0.303902	−	0.952703i	$-0.598290\pi$
$863$	−524.535			−0.607804			−0.303902	+	0.952703i	$0.598290\pi$
$864$	−273.970	+	474.530i	−0.317095	+	0.549225i
$865$	−1196.13	+	690.588i	−1.38281	+	0.798368i
$866$	621.230			0.717356
$867$	−174.470	−	100.731i	−0.201235	−	0.116183i
$868$	−773.667			−0.891322
$869$	602.398	+	1043.38i	0.693208	+	1.20067i
$870$			1803.65i			2.07316i
$871$	−99.3366	+	106.341i	−0.114049	+	0.122090i
$872$	1156.80			1.32660
$873$	−267.155	+	154.242i	−0.306019	+	0.176680i
$874$		−	135.678i		−	0.155238i
$875$	817.556	−	1416.05i	0.934350	−	1.61834i
$876$			925.898i			1.05696i
$877$	489.321	+	847.529i	0.557949	+	0.966395i	0.997668	+	0.0682600i	$0.0217447\pi$
$877$	489.321	+	847.529i	0.557949	+	0.966395i	−0.439719	+	0.898135i	$0.644922\pi$
$878$	−106.926	−	61.7339i	−0.121784	−	0.0703120i
$879$			203.029i			0.230977i
$880$	−7694.61			−8.74388
$881$	106.661	+	184.743i	0.121068	+	0.209697i	0.920189	−	0.391474i	$-0.128035\pi$
$881$	106.661	+	184.743i	0.121068	+	0.209697i	−0.799121	+	0.601170i	$0.794701\pi$
$882$	−575.369	−	332.190i	−0.652346	−	0.376632i
$883$	−236.064	−	136.292i	−0.267343	−	0.154351i	0.360336	−	0.932822i	$-0.382662\pi$
$883$	−236.064	−	136.292i	−0.267343	−	0.154351i	−0.627680	+	0.778472i	$0.715995\pi$
$884$	−401.504	+	231.808i	−0.454190	+	0.262227i
$885$	−585.302			−0.661358
$886$	1214.96			1.37129
$887$	311.326	+	539.232i	0.350988	+	0.607928i	0.986423	−	0.164226i	$-0.0525126\pi$
$887$	311.326	+	539.232i	0.350988	+	0.607928i	−0.635435	+	0.772154i	$0.719179\pi$
$888$	1105.89	+	1915.46i	1.24538	+	2.15705i
$889$	858.880	−	495.875i	0.966119	−	0.557789i
$890$	−1389.29	−	2406.32i	−1.56100	−	2.70373i
$891$	−133.659	−	77.1683i	−0.150011	−	0.0866087i
$892$	1428.12	−	2473.57i	1.60103	−	2.77306i
$893$	−83.5045			−0.0935100
$894$	767.932	+	1330.10i	0.858984	+	1.48780i
$895$	2904.37			3.24511
$896$	−3025.63			−3.37682
$897$	21.7605	−	37.6903i	0.0242592	−	0.0420182i
$898$			1829.15i			2.03691i
$899$	−200.415	+	115.710i	−0.222931	+	0.128709i
$900$	700.249	−	1212.87i	0.778055	−	1.34763i
$901$	−43.2491	+	24.9699i	−0.0480013	+	0.0277135i
$902$	289.406	+	167.089i	0.320849	+	0.185242i
$903$	−890.945	−	514.388i	−0.986650	−	0.569643i
$904$	580.011	−	1004.61i	0.641605	−	1.11129i
$905$	1510.00	+	871.799i	1.66851	+	0.963314i
$906$	531.350	−	920.326i	0.586479	−	1.01581i
$907$	−465.601	+	806.445i	−0.513342	+	0.889134i	0.486538	+	0.873659i	$0.338259\pi$
$907$	−465.601	+	806.445i	−0.513342	+	0.889134i	−0.999880	+	0.0154750i	$0.995074\pi$
$908$	1671.75	+	2895.55i	1.84113	+	3.18893i
$909$	175.365	+	101.247i	0.192920	+	0.111383i
$910$	356.574	+	617.604i	0.391839	+	0.678686i
$911$	415.102			0.455656			0.227828	−	0.973701i	$-0.426838\pi$
$911$	415.102			0.455656			0.227828	+	0.973701i	$0.426838\pi$
$912$	248.621	+	143.541i	0.272610	+	0.157392i
$913$		−	2164.31i		−	2.37055i
$914$		−	3091.88i		−	3.38280i
$915$	52.9165	−	30.5514i	0.0578322	−	0.0333895i
$916$			1144.76i			1.24974i
$917$	−249.178	−	143.863i	−0.271732	−	0.156884i
$918$	−199.877	+	346.198i	−0.217731	+	0.377122i
$919$	148.614	−	85.8022i	0.161712	−	0.0933647i	−0.416960	−	0.908925i	$-0.636904\pi$
$919$	148.614	−	85.8022i	0.161712	−	0.0933647i	0.578672	+	0.815560i	$0.303571\pi$
$920$	−1212.59	−	2100.27i	−1.31803	−	2.28290i
$921$	602.386	−	347.787i	0.654056	−	0.377619i
$922$	1270.09	−	733.289i	1.37754	−	0.795325i
$923$		−	202.365i		−	0.219247i
$924$		−	3256.87i		−	3.52475i
$925$	−1114.20	−	1929.85i	−1.20454	−	2.08632i
$926$	65.5215	−	113.487i	0.0707576	−	0.122556i
$927$	134.073	−	232.221i	0.144631	−	0.250509i
$928$	−2995.29	+	1729.33i	−3.22769	+	1.86351i
$929$			715.918i			0.770633i	0.922784	+	0.385317i	$0.125908\pi$
$929$			715.918i			0.770633i	−0.922784	+	0.385317i	$0.874092\pi$
$930$	388.004			0.417209
$931$	−88.9309	+	154.033i	−0.0955219	+	0.165449i
$932$	1150.47	−	664.224i	1.23441	−	0.712687i
$933$	−658.630			−0.705927
$934$	1360.96	+	785.751i	1.45713	+	0.841275i
$935$	−2868.40			−3.06781
$936$	82.2007	+	142.376i	0.0878212	+	0.152111i
$937$			1746.17i			1.86357i	0.363006	+	0.931787i	$0.381751\pi$
$937$			1746.17i			1.86357i	−0.363006	+	0.931787i	$0.618249\pi$
$938$	−2532.79	+	771.954i	−2.70020	+	0.822979i
$939$	695.899			0.741107
$940$	−2075.73	+	1198.42i	−2.20822	+	1.27492i
$941$		−	926.800i		−	0.984910i	−0.870338	−	0.492455i	$-0.836100\pi$
$941$		−	926.800i		−	0.984910i	0.870338	−	0.492455i	$-0.163900\pi$
$942$	−826.357	+	1431.29i	−0.877236	+	1.51942i
$943$			58.9963i			0.0625623i
$944$	−1098.28	−	1902.28i	−1.16343	−	2.01512i
$945$	386.659	+	223.238i	0.409163	+	0.236230i
$946$		−	3763.62i		−	3.97845i
$947$	529.463			0.559095			0.279547	−	0.960132i	$-0.409816\pi$
$947$	529.463			0.559095			0.279547	+	0.960132i	$0.409816\pi$
$948$	−645.109	−	1117.36i	−0.680494	−	1.17865i
$949$	94.8343	+	54.7526i	0.0999308	+	0.0576951i
$950$	−447.195	−	258.188i	−0.470731	−	0.271777i
$951$	−218.733	+	126.286i	−0.230004	+	0.132793i
$952$	−5253.26			−5.51813
$953$	−1709.51			−1.79382			−0.896910	−	0.442214i	$-0.854193\pi$
$953$	−1709.51			−1.79382			−0.896910	+	0.442214i	$0.854193\pi$
$954$	14.2187	+	24.6274i	0.0149043	+	0.0258149i
$955$	−493.426	−	854.639i	−0.516676	−	0.894910i
$956$	257.592	−	148.721i	0.269448	−	0.155566i
$957$	−487.096	−	843.675i	−0.508982	−	0.881583i
$958$	−1862.42	−	1075.27i	−1.94407	−	1.12241i
$959$	−739.500	+	1280.85i	−0.771116	+	1.33561i
$960$	2690.20			2.80229
$961$	−455.608	−	789.137i	−0.474098	−	0.821162i
$962$	420.060			0.436652
$963$	369.639			0.383841
$964$	858.421	−	1486.83i	0.890478	−	1.54235i
$965$			417.409i			0.432548i
$966$	685.796	−	395.944i	0.709934	−	0.409880i
$967$	−683.469	+	1183.80i	−0.706793	+	1.22420i	0.259247	+	0.965811i	$0.416526\pi$
$967$	−683.469	+	1183.80i	−0.706793	+	1.22420i	−0.966040	+	0.258391i	$0.916808\pi$
$968$	3781.75	−	2183.39i	3.90676	−	2.25557i
$969$	92.6810	+	53.5094i	0.0956460	+	0.0552213i
$970$	2827.32	+	1632.36i	2.91477	+	1.68284i
$971$	448.254	−	776.398i	0.461641	−	0.799586i	−0.537402	−	0.843326i	$-0.680594\pi$
$971$	448.254	−	776.398i	0.461641	−	0.799586i	0.999043	+	0.0437403i	$0.0139274\pi$
$972$	143.136	+	82.6397i	0.147259	+	0.0850202i
$973$	987.930	−	1711.15i	1.01534	−	1.75863i
$974$	−797.652	+	1381.57i	−0.818944	+	1.41845i
$975$	−82.8180	−	143.445i	−0.0849415	−	0.147123i
$976$	198.589	+	114.655i	0.203472	+	0.117475i
$977$	843.979	+	1461.81i	0.863847	+	1.49623i	0.868187	+	0.496237i	$0.165285\pi$
$977$	843.979	+	1461.81i	0.863847	+	1.49623i	−0.00433994	+	0.999991i	$0.501381\pi$
$978$	1263.98			1.29241
$979$	1299.71	+	750.386i	1.32759	+	0.766482i
$980$			5105.19i			5.20938i
$981$		−	137.544i		−	0.140208i
$982$	1528.10	−	882.251i	1.55611	−	0.898423i
$983$		−	1396.73i		−	1.42089i	−0.703755	−	0.710443i	$-0.748495\pi$
$983$		−	1396.73i		−	1.42089i	0.703755	−	0.710443i	$-0.251505\pi$
$984$	−193.002	−	111.430i	−0.196140	−	0.113242i
$985$	128.476	−	222.526i	0.130432	−	0.225915i
$986$	−2185.24	+	1261.65i	−2.21627	+	1.27957i
$987$	−243.688	−	422.080i	−0.246897	−	0.427639i
$988$	61.2065	−	35.3376i	0.0619499	−	0.0357668i
$989$	575.418	−	332.218i	0.581818	−	0.335913i
$990$			1633.36i			1.64986i
$991$			403.312i			0.406975i	0.979078	+	0.203488i	$0.0652277\pi$
$991$			403.312i			0.406975i	−0.979078	+	0.203488i	$0.934772\pi$
$992$	372.017	+	644.353i	0.375017	+	0.649549i
$993$	139.048	−	240.838i	0.140028	−	0.242536i
$994$	1841.08	−	3188.84i	1.85219	−	3.20809i
$995$	997.008	−	575.623i	1.00202	−	0.578516i
$996$			2317.77i			2.32708i
$997$	1389.70			1.39388			0.696942	−	0.717128i	$-0.254544\pi$
$997$	1389.70			1.39388			0.696942	+	0.717128i	$0.254544\pi$
$998$	−326.090	+	564.804i	−0.326744	+	0.565936i
$999$	227.750	−	131.492i	0.227978	−	0.131623i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.h.b.97.12	✓	24
67.38	odd	6	inner	201.3.h.b.172.12	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.h.b.97.12	✓	24	1.1	even	1	trivial
201.3.h.b.172.12	yes	24	67.38	odd	6	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:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	201.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.30938 - 1.91067i) q^{2} +1.73205i q^{3} +(5.30134 - 9.18219i) q^{4} +8.30841i q^{5} +(3.30938 + 5.73202i) q^{6} +(8.95628 + 5.17091i) q^{7} -25.2311i q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(3.30938 - 1.91067i) q^{2} +1.73205i q^{3} +(5.30134 - 9.18219i) q^{4} +8.30841i q^{5} +(3.30938 + 5.73202i) q^{6} +(8.95628 + 5.17091i) q^{7} -25.2311i q^{8} -3.00000 q^{9} +(15.8747 + 27.4957i) q^{10} +(-14.8510 - 8.57426i) q^{11} +(15.9040 + 9.18219i) q^{12} +(1.88096 - 1.08597i) q^{13} +39.5197 q^{14} -14.3906 q^{15} +(-27.0030 - 46.7706i) q^{16} +(-10.0662 - 17.4352i) q^{17} +(-9.92814 + 5.73202i) q^{18} +(1.53452 + 2.65787i) q^{19} +(76.2894 + 44.0457i) q^{20} +(-8.95628 + 15.5127i) q^{21} -65.5304 q^{22} +(-5.78443 - 10.0189i) q^{23} +43.7015 q^{24} -44.0297 q^{25} +(4.14987 - 7.18778i) q^{26} -5.19615i q^{27} +(94.9606 - 54.8255i) q^{28} +(16.3994 - 28.4046i) q^{29} +(-47.6240 + 27.4957i) q^{30} +(-6.11044 - 3.52786i) q^{31} +(-91.3234 - 52.7256i) q^{32} +(14.8510 - 25.7228i) q^{33} +(-66.6258 - 38.4664i) q^{34} +(-42.9621 + 74.4125i) q^{35} +(-15.9040 + 27.5466i) q^{36} +(25.3056 + 43.8306i) q^{37} +(10.1567 + 5.86395i) q^{38} +(1.88096 + 3.25791i) q^{39} +209.630 q^{40} +(-4.41637 - 2.54979i) q^{41} +68.4501i q^{42} +57.4331i q^{43} +(-157.461 + 90.9101i) q^{44} -24.9252i q^{45} +(-38.2857 - 22.1043i) q^{46} +(-13.6043 + 23.5633i) q^{47} +(81.0090 - 46.7706i) q^{48} +(28.9767 + 50.1891i) q^{49} +(-145.711 + 84.1264i) q^{50} +(30.1986 - 17.4352i) q^{51} -23.0284i q^{52} -2.48057i q^{53} +(-9.92814 - 17.1961i) q^{54} +(71.2385 - 123.389i) q^{55} +(130.468 - 225.977i) q^{56} +(-4.60357 + 2.65787i) q^{57} -125.335i q^{58} +40.6725 q^{59} +(-76.2894 + 132.137i) q^{60} +(-3.67716 + 2.12301i) q^{61} -26.9624 q^{62} +(-26.8689 - 15.5127i) q^{63} -186.941 q^{64} +(9.02269 + 15.6278i) q^{65} -113.502i q^{66} +(-64.0894 + 19.5334i) q^{67} -213.457 q^{68} +(17.3533 - 10.0189i) q^{69} +328.346i q^{70} +(46.5863 - 80.6898i) q^{71} +75.6933i q^{72} +(25.2091 + 43.6634i) q^{73} +(167.492 + 96.7015i) q^{74} -76.2617i q^{75} +32.5401 q^{76} +(-88.6735 - 153.587i) q^{77} +(12.4496 + 7.18778i) q^{78} +(-60.8440 - 35.1283i) q^{79} +(388.589 - 224.352i) q^{80} +9.00000 q^{81} -19.4873 q^{82} +(63.1050 + 109.301i) q^{83} +(94.9606 + 164.477i) q^{84} +(144.859 - 83.6342i) q^{85} +(109.736 + 190.068i) q^{86} +(49.1981 + 28.4046i) q^{87} +(-216.338 + 374.708i) q^{88} -87.5161 q^{89} +(-47.6240 - 82.4871i) q^{90} +22.4618 q^{91} -122.661 q^{92} +(6.11044 - 10.5836i) q^{93} +103.973i q^{94} +(-22.0827 + 12.7495i) q^{95} +(91.3234 - 158.177i) q^{96} +(89.0515 - 51.4139i) q^{97} +(191.790 + 110.730i) q^{98} +(44.5531 + 25.7228i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 34 q^{4} + 21 q^{7} - 72 q^{9}+O(q^{10}) \) 24 * q + 34 * q^4 + 21 * q^7 - 72 * q^9	\( 24 q + 34 q^{4} + 21 q^{7} - 72 q^{9} + 30 q^{10} + 12 q^{11} + 102 q^{12} + 30 q^{13} + 6 q^{14} - 6 q^{15} - 98 q^{16} + 4 q^{17} + 39 q^{19} + 108 q^{20} - 21 q^{21} - 82 q^{22} - 13 q^{23} - 36 q^{24} - 222 q^{25} + 29 q^{26} + 189 q^{28} - 90 q^{30} - 93 q^{31} - 33 q^{32} - 12 q^{33} + 72 q^{34} - 93 q^{35} - 102 q^{36} - 33 q^{37} - 210 q^{38} + 30 q^{39} + 274 q^{40} - 15 q^{41} - 9 q^{44} - 228 q^{46} - 131 q^{47} + 294 q^{48} + 295 q^{49} - 423 q^{50} - 12 q^{51} - 56 q^{55} + 349 q^{56} - 117 q^{57} - 116 q^{59} - 108 q^{60} + 120 q^{61} + 282 q^{62} - 63 q^{63} - 276 q^{64} + 136 q^{65} - 25 q^{67} + 10 q^{68} + 39 q^{69} + 169 q^{71} + 187 q^{73} + 849 q^{74} + 386 q^{76} - 348 q^{77} + 87 q^{78} + 51 q^{80} + 216 q^{81} - 14 q^{82} + 104 q^{83} + 189 q^{84} - 243 q^{85} + 641 q^{86} - 766 q^{88} + 152 q^{89} - 90 q^{90} + 32 q^{91} - 216 q^{92} + 93 q^{93} + 762 q^{95} + 33 q^{96} - 84 q^{97} - 1086 q^{98} - 36 q^{99}+O(q^{100}) \) 24 * q + 34 * q^4 + 21 * q^7 - 72 * q^9 + 30 * q^10 + 12 * q^11 + 102 * q^12 + 30 * q^13 + 6 * q^14 - 6 * q^15 - 98 * q^16 + 4 * q^17 + 39 * q^19 + 108 * q^20 - 21 * q^21 - 82 * q^22 - 13 * q^23 - 36 * q^24 - 222 * q^25 + 29 * q^26 + 189 * q^28 - 90 * q^30 - 93 * q^31 - 33 * q^32 - 12 * q^33 + 72 * q^34 - 93 * q^35 - 102 * q^36 - 33 * q^37 - 210 * q^38 + 30 * q^39 + 274 * q^40 - 15 * q^41 - 9 * q^44 - 228 * q^46 - 131 * q^47 + 294 * q^48 + 295 * q^49 - 423 * q^50 - 12 * q^51 - 56 * q^55 + 349 * q^56 - 117 * q^57 - 116 * q^59 - 108 * q^60 + 120 * q^61 + 282 * q^62 - 63 * q^63 - 276 * q^64 + 136 * q^65 - 25 * q^67 + 10 * q^68 + 39 * q^69 + 169 * q^71 + 187 * q^73 + 849 * q^74 + 386 * q^76 - 348 * q^77 + 87 * q^78 + 51 * q^80 + 216 * q^81 - 14 * q^82 + 104 * q^83 + 189 * q^84 - 243 * q^85 + 641 * q^86 - 766 * q^88 + 152 * q^89 - 90 * q^90 + 32 * q^91 - 216 * q^92 + 93 * q^93 + 762 * q^95 + 33 * q^96 - 84 * q^97 - 1086 * q^98 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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