LMFDB - Embedded newform 35.3.l.a.2.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,3,Mod(2,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("35.2");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	35.l (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.953680925261$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			2.1
Character	$\chi$	$=$	35.2
Dual form			35.3.l.a.18.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.54535 + 0.949975i) q^{2} +(-1.41502 - 0.379154i) q^{3} +(8.20298 - 4.73599i) q^{4} +(0.551807 - 4.96946i) q^{5} +5.37694 q^{6} +(3.87123 - 5.83212i) q^{7} +(-14.2019 + 14.2019i) q^{8} +(-5.93570 - 3.42698i) q^{9} +O(q^{10})$	\(q+(-3.54535 + 0.949975i) q^{2} +(-1.41502 - 0.379154i) q^{3} +(8.20298 - 4.73599i) q^{4} +(0.551807 - 4.96946i) q^{5} +5.37694 q^{6} +(3.87123 - 5.83212i) q^{7} +(-14.2019 + 14.2019i) q^{8} +(-5.93570 - 3.42698i) q^{9} +(2.76451 + 18.1427i) q^{10} +(-0.586967 - 1.01666i) q^{11} +(-13.4031 + 3.59134i) q^{12} +(2.48387 - 2.48387i) q^{13} +(-8.18451 + 24.3545i) q^{14} +(-2.66501 + 6.82267i) q^{15} +(17.9153 - 31.0302i) q^{16} +(4.20137 - 15.6797i) q^{17} +(24.2997 + 6.51109i) q^{18} +(2.54557 + 1.46969i) q^{19} +(-19.0089 - 43.3777i) q^{20} +(-7.68914 + 6.78478i) q^{21} +(3.04681 + 3.04681i) q^{22} +(7.62508 + 28.4572i) q^{23} +(25.4807 - 14.7113i) q^{24} +(-24.3910 - 5.48436i) q^{25} +(-6.44658 + 11.1658i) q^{26} +(16.4226 + 16.4226i) q^{27} +(4.13475 - 66.1749i) q^{28} -11.3707i q^{29} +(2.96703 - 26.7205i) q^{30} +(15.6227 + 27.0593i) q^{31} +(-13.2451 + 49.4315i) q^{32} +(0.445102 + 1.66114i) q^{33} +59.5814i q^{34} +(-26.8463 - 22.4561i) q^{35} -64.9206 q^{36} +(-37.0160 + 9.91842i) q^{37} +(-10.4211 - 2.79233i) q^{38} +(-4.45650 + 2.57296i) q^{39} +(62.7389 + 78.4123i) q^{40} +59.3486 q^{41} +(20.8154 - 31.3589i) q^{42} +(18.7104 - 18.7104i) q^{43} +(-9.62976 - 5.55975i) q^{44} +(-20.3056 + 27.6062i) q^{45} +(-54.0672 - 93.6472i) q^{46} +(66.3850 - 17.7878i) q^{47} +(-37.1157 + 37.1157i) q^{48} +(-19.0272 - 45.1549i) q^{49} +(91.6848 - 3.72685i) q^{50} +(-11.8901 + 20.5942i) q^{51} +(8.61155 - 32.1387i) q^{52} +(-7.25898 - 1.94504i) q^{53} +(-73.8250 - 42.6229i) q^{54} +(-5.37613 + 2.35591i) q^{55} +(27.8483 + 137.806i) q^{56} +(-3.04480 - 3.04480i) q^{57} +(10.8019 + 40.3131i) q^{58} +(5.15171 - 2.97434i) q^{59} +(10.4511 + 68.5877i) q^{60} +(0.00821757 - 0.0142333i) q^{61} +(-81.0937 - 81.0937i) q^{62} +(-42.9650 + 21.3511i) q^{63} -44.5126i q^{64} +(-10.9729 - 13.7141i) q^{65} +(-3.15609 - 5.46650i) q^{66} +(-10.8655 + 40.5504i) q^{67} +(-39.7953 - 148.518i) q^{68} -43.1586i q^{69} +(116.512 + 54.1116i) q^{70} -15.7230 q^{71} +(132.968 - 35.6286i) q^{72} +(35.8263 + 9.59964i) q^{73} +(121.813 - 70.3286i) q^{74} +(32.4344 + 17.0084i) q^{75} +27.8417 q^{76} +(-8.20155 - 0.512451i) q^{77} +(13.3556 - 13.3556i) q^{78} +(60.3579 + 34.8477i) q^{79} +(-144.317 - 106.152i) q^{80} +(13.8312 + 23.9563i) q^{81} +(-210.412 + 56.3797i) q^{82} +(-63.1958 + 63.1958i) q^{83} +(-30.9412 + 92.0711i) q^{84} +(-75.6014 - 29.5307i) q^{85} +(-48.5606 + 84.1094i) q^{86} +(-4.31124 + 16.0898i) q^{87} +(22.7745 + 6.10240i) q^{88} +(52.1411 + 30.1037i) q^{89} +(45.7653 - 117.163i) q^{90} +(-4.87059 - 24.1018i) q^{91} +(197.321 + 197.321i) q^{92} +(-11.8468 - 44.2129i) q^{93} +(-218.460 + 126.128i) q^{94} +(8.70822 - 11.8391i) q^{95} +(37.4843 - 64.9247i) q^{96} +(51.7791 + 51.7791i) q^{97} +(110.354 + 142.015i) q^{98} +8.04610i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{2} - 2 q^{3} - 4 q^{5} - 6 q^{7} - 36 q^{8}+O(q^{10}) $ 24 * q - 2 * q^2 - 2 * q^3 - 4 * q^5 - 6 * q^7 - 36 * q^8	$ 24 q - 2 q^{2} - 2 q^{3} - 4 q^{5} - 6 q^{7} - 36 q^{8} + 14 q^{10} - 24 q^{11} - 46 q^{12} - 8 q^{13} + 52 q^{15} + 20 q^{16} - 48 q^{17} - 4 q^{18} - 72 q^{20} + 56 q^{21} + 104 q^{22} - 86 q^{23} - 16 q^{25} + 140 q^{26} + 76 q^{27} + 186 q^{28} + 64 q^{30} + 120 q^{31} + 130 q^{32} + 116 q^{33} - 240 q^{35} - 496 q^{36} + 44 q^{37} + 16 q^{38} - 158 q^{40} + 16 q^{41} - 370 q^{42} - 196 q^{43} - 104 q^{45} - 148 q^{46} - 208 q^{47} - 52 q^{48} + 580 q^{50} - 160 q^{51} - 288 q^{52} - 72 q^{53} + 208 q^{55} + 420 q^{56} + 656 q^{57} - 2 q^{58} + 262 q^{60} + 308 q^{61} + 176 q^{62} + 212 q^{63} + 132 q^{65} + 316 q^{66} + 198 q^{67} + 332 q^{68} - 200 q^{70} - 792 q^{71} + 308 q^{72} + 380 q^{73} - 450 q^{75} - 400 q^{76} - 472 q^{77} - 720 q^{78} - 324 q^{80} - 352 q^{81} - 818 q^{82} - 460 q^{83} + 144 q^{85} - 336 q^{86} - 214 q^{87} - 288 q^{88} + 120 q^{90} + 984 q^{91} + 1372 q^{92} - 68 q^{93} - 88 q^{95} + 816 q^{96} - 72 q^{97} + 482 q^{98}+O(q^{100}) $ 24 * q - 2 * q^2 - 2 * q^3 - 4 * q^5 - 6 * q^7 - 36 * q^8 + 14 * q^10 - 24 * q^11 - 46 * q^12 - 8 * q^13 + 52 * q^15 + 20 * q^16 - 48 * q^17 - 4 * q^18 - 72 * q^20 + 56 * q^21 + 104 * q^22 - 86 * q^23 - 16 * q^25 + 140 * q^26 + 76 * q^27 + 186 * q^28 + 64 * q^30 + 120 * q^31 + 130 * q^32 + 116 * q^33 - 240 * q^35 - 496 * q^36 + 44 * q^37 + 16 * q^38 - 158 * q^40 + 16 * q^41 - 370 * q^42 - 196 * q^43 - 104 * q^45 - 148 * q^46 - 208 * q^47 - 52 * q^48 + 580 * q^50 - 160 * q^51 - 288 * q^52 - 72 * q^53 + 208 * q^55 + 420 * q^56 + 656 * q^57 - 2 * q^58 + 262 * q^60 + 308 * q^61 + 176 * q^62 + 212 * q^63 + 132 * q^65 + 316 * q^66 + 198 * q^67 + 332 * q^68 - 200 * q^70 - 792 * q^71 + 308 * q^72 + 380 * q^73 - 450 * q^75 - 400 * q^76 - 472 * q^77 - 720 * q^78 - 324 * q^80 - 352 * q^81 - 818 * q^82 - 460 * q^83 + 144 * q^85 - 336 * q^86 - 214 * q^87 - 288 * q^88 + 120 * q^90 + 984 * q^91 + 1372 * q^92 - 68 * q^93 - 88 * q^95 + 816 * q^96 - 72 * q^97 + 482 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−3.54535	+	0.949975i	−1.77268	+	0.474987i	−0.989217	−	0.146455i	$-0.953214\pi$
$2$	−3.54535	+	0.949975i	−1.77268	+	0.474987i	−0.783460	+	0.621443i	$0.786547\pi$
$3$	−1.41502	−	0.379154i	−0.471674	−	0.126385i	0.0151492	−	0.999885i	$-0.495178\pi$
$3$	−1.41502	−	0.379154i	−0.471674	−	0.126385i	−0.486823	+	0.873501i	$0.661844\pi$
$4$	8.20298	−	4.73599i	2.05075	−	1.18400i
$5$	0.551807	−	4.96946i	0.110361	−	0.993892i
$5$	0.551807	−	4.96946i	0.110361	−	0.993892i
$6$	5.37694			0.896156
$7$	3.87123	−	5.83212i	0.553033	−	0.833160i
$7$	3.87123	−	5.83212i	0.553033	−	0.833160i
$8$	−14.2019	+	14.2019i	−1.77523	+	1.77523i
$9$	−5.93570	−	3.42698i	−0.659522	−	0.380775i
$10$	2.76451	+	18.1427i	0.276451	+	1.81427i
$11$	−0.586967	−	1.01666i	−0.0533607	−	0.0924234i	0.838111	−	0.545499i	$-0.183660\pi$
$11$	−0.586967	−	1.01666i	−0.0533607	−	0.0924234i	−0.891472	+	0.453076i	$0.850327\pi$
$12$	−13.4031	+	3.59134i	−1.11692	+	0.299278i
$13$	2.48387	−	2.48387i	0.191067	−	0.191067i	−0.605090	−	0.796157i	$-0.706863\pi$
$13$	2.48387	−	2.48387i	0.191067	−	0.191067i	0.796157	+	0.605090i	$0.206863\pi$
$14$	−8.18451	+	24.3545i	−0.584608	+	1.73961i
$15$	−2.66501	+	6.82267i	−0.177667	+	0.454845i
$16$	17.9153	−	31.0302i	1.11971	−	1.93939i
$17$	4.20137	−	15.6797i	0.247139	−	0.922337i	−0.725157	−	0.688584i	$-0.758233\pi$
$17$	4.20137	−	15.6797i	0.247139	−	0.922337i	0.972296	−	0.233753i	$-0.0751006\pi$
$18$	24.2997	+	6.51109i	1.34998	+	0.361727i
$19$	2.54557	+	1.46969i	0.133978	+	0.0773520i	0.565491	−	0.824755i	$-0.308687\pi$
$19$	2.54557	+	1.46969i	0.133978	+	0.0773520i	−0.431513	+	0.902107i	$0.642020\pi$
$20$	−19.0089	−	43.3777i	−0.950443	−	2.16889i
$21$	−7.68914	+	6.78478i	−0.366150	+	0.323085i
$22$	3.04681	+	3.04681i	0.138491	+	0.138491i
$23$	7.62508	+	28.4572i	0.331525	+	1.23727i	0.907587	+	0.419863i	$0.137922\pi$
$23$	7.62508	+	28.4572i	0.331525	+	1.23727i	−0.576062	+	0.817406i	$0.695411\pi$
$24$	25.4807	−	14.7113i	1.06169	−	0.612969i
$25$	−24.3910	−	5.48436i	−0.975641	−	0.219374i
$26$	−6.44658	+	11.1658i	−0.247946	+	0.429454i
$27$	16.4226	+	16.4226i	0.608244	+	0.608244i
$28$	4.13475	−	66.1749i	0.147670	−	2.36339i
$29$		−	11.3707i		−	0.392093i	−0.980595	−	0.196046i	$-0.937190\pi$
$29$		−	11.3707i		−	0.392093i	0.980595	−	0.196046i	$-0.0628103\pi$
$30$	2.96703	−	26.7205i	0.0989010	−	0.890682i
$31$	15.6227	+	27.0593i	0.503959	+	0.872882i	0.999990	+	0.00457701i	$0.00145691\pi$
$31$	15.6227	+	27.0593i	0.503959	+	0.872882i	−0.496031	+	0.868305i	$0.665210\pi$
$32$	−13.2451	+	49.4315i	−0.413911	+	1.54474i
$33$	0.445102	+	1.66114i	0.0134879	+	0.0503377i
$34$			59.5814i			1.75239i
$35$	−26.8463	−	22.4561i	−0.767037	−	0.641603i
$36$	−64.9206			−1.80335
$37$	−37.0160	+	9.91842i	−1.00043	+	0.268065i	−0.721627	−	0.692282i	$-0.756605\pi$
$37$	−37.0160	+	9.91842i	−1.00043	+	0.268065i	−0.278806	+	0.960347i	$0.589939\pi$
$38$	−10.4211	−	2.79233i	−0.274240	−	0.0734824i
$39$	−4.45650	+	2.57296i	−0.114269	+	0.0659733i
$40$	62.7389	+	78.4123i	1.56847	+	1.96031i
$41$	59.3486			1.44753			0.723763	−	0.690048i	$-0.242411\pi$
$41$	59.3486			1.44753			0.723763	+	0.690048i	$0.242411\pi$
$42$	20.8154	−	31.3589i	0.495604	−	0.746641i
$43$	18.7104	−	18.7104i	0.435126	−	0.435126i	−0.455242	−	0.890368i	$-0.650447\pi$
$43$	18.7104	−	18.7104i	0.435126	−	0.435126i	0.890368	+	0.455242i	$0.150447\pi$
$44$	−9.62976	−	5.55975i	−0.218858	−	0.126358i
$45$	−20.3056	+	27.6062i	−0.451235	+	0.613471i
$46$	−54.0672	−	93.6472i	−1.17537	−	2.03581i
$47$	66.3850	−	17.7878i	1.41245	−	0.378464i	0.529649	−	0.848217i	$-0.322324\pi$
$47$	66.3850	−	17.7878i	1.41245	−	0.378464i	0.882798	+	0.469752i	$0.155657\pi$
$48$	−37.1157	+	37.1157i	−0.773244	+	0.773244i
$49$	−19.0272	−	45.1549i	−0.388310	−	0.921529i
$50$	91.6848	−	3.72685i	1.83370	−	0.0745370i
$51$	−11.8901	+	20.5942i	−0.233138	+	0.403807i
$52$	8.61155	−	32.1387i	0.165607	−	0.618052i
$53$	−7.25898	−	1.94504i	−0.136962	−	0.0366988i	0.189687	−	0.981845i	$-0.439253\pi$
$53$	−7.25898	−	1.94504i	−0.136962	−	0.0366988i	−0.326649	+	0.945146i	$0.605919\pi$
$54$	−73.8250	−	42.6229i	−1.36713	−	0.789312i
$55$	−5.37613	+	2.35591i	−0.0977478	+	0.0428348i
$56$	27.8483	+	137.806i	0.497291	+	2.46082i
$57$	−3.04480	−	3.04480i	−0.0534176	−	0.0534176i
$58$	10.8019	+	40.3131i	0.186239	+	0.695054i
$59$	5.15171	−	2.97434i	0.0873172	−	0.0504126i	−0.455706	−	0.890131i	$-0.650613\pi$
$59$	5.15171	−	2.97434i	0.0873172	−	0.0504126i	0.543023	+	0.839718i	$0.317280\pi$
$60$	10.4511	+	68.5877i	0.174185	+	1.14313i
$61$	0.00821757	−	0.0142333i	0.000134714	−	0.000233332i	−0.865958	−	0.500117i	$-0.833290\pi$
$61$	0.00821757	−	0.0142333i	0.000134714	−	0.000233332i	0.866093	+	0.499883i	$0.166624\pi$
$62$	−81.0937	−	81.0937i	−1.30796	−	1.30796i
$63$	−42.9650	+	21.3511i	−0.681984	+	0.338906i
$64$		−	44.5126i		−	0.695509i
$65$	−10.9729	−	13.7141i	−0.168813	−	0.210986i
$66$	−3.15609	−	5.46650i	−0.0478195	−	0.0828258i
$67$	−10.8655	+	40.5504i	−0.162171	+	0.605230i	0.836213	+	0.548405i	$0.184765\pi$
$67$	−10.8655	+	40.5504i	−0.162171	+	0.605230i	−0.998384	+	0.0568258i	$0.981902\pi$
$68$	−39.7953	−	148.518i	−0.585225	−	2.18409i
$69$		−	43.1586i		−	0.625487i
$70$	116.512	+	54.1116i	1.66446	+	0.773022i
$71$	−15.7230			−0.221451			−0.110726	−	0.993851i	$-0.535317\pi$
$71$	−15.7230			−0.221451			−0.110726	+	0.993851i	$0.535317\pi$
$72$	132.968	−	35.6286i	1.84677	−	0.494841i
$73$	35.8263	+	9.59964i	0.490772	+	0.131502i	0.495714	−	0.868486i	$-0.334906\pi$
$73$	35.8263	+	9.59964i	0.490772	+	0.131502i	−0.00494220	+	0.999988i	$0.501573\pi$
$74$	121.813	−	70.3286i	1.64612	−	0.950386i
$75$	32.4344	+	17.0084i	0.432459	+	0.226779i
$76$	27.8417			0.366339
$77$	−8.20155	−	0.512451i	−0.106514	−	0.00665521i
$78$	13.3556	−	13.3556i	0.171226	−	0.171226i
$79$	60.3579	+	34.8477i	0.764024	+	0.441110i	0.830739	−	0.556663i	$-0.187918\pi$
$79$	60.3579	+	34.8477i	0.764024	+	0.441110i	−0.0667145	+	0.997772i	$0.521252\pi$
$80$	−144.317	−	106.152i	−1.80397	−	1.32690i
$81$	13.8312	+	23.9563i	0.170755	+	0.295757i
$82$	−210.412	+	56.3797i	−2.56600	+	0.687557i
$83$	−63.1958	+	63.1958i	−0.761395	+	0.761395i	−0.976574	−	0.215180i	$-0.930966\pi$
$83$	−63.1958	+	63.1958i	−0.761395	+	0.761395i	0.215180	+	0.976574i	$0.430966\pi$
$84$	−30.9412	+	92.0711i	−0.368348	+	1.09608i
$85$	−75.6014	−	29.5307i	−0.889428	−	0.347420i
$86$	−48.5606	+	84.1094i	−0.564658	+	0.978016i
$87$	−4.31124	+	16.0898i	−0.0495545	+	0.184940i
$88$	22.7745	+	6.10240i	0.258801	+	0.0693455i
$89$	52.1411	+	30.1037i	0.585855	+	0.338243i	0.763457	−	0.645859i	$-0.223501\pi$
$89$	52.1411	+	30.1037i	0.585855	+	0.338243i	−0.177602	+	0.984102i	$0.556834\pi$
$90$	45.7653	−	117.163i	0.508503	−	1.30182i
$91$	−4.87059	−	24.1018i	−0.0535230	−	0.264855i
$92$	197.321	+	197.321i	2.14480	+	2.14480i
$93$	−11.8468	−	44.2129i	−0.127385	−	0.475408i
$94$	−218.460	+	126.128i	−2.32405	+	1.34179i
$95$	8.70822	−	11.8391i	0.0916655	−	0.124623i
$96$	37.4843	−	64.9247i	0.390462	−	0.676299i
$97$	51.7791	+	51.7791i	0.533805	+	0.533805i	0.921702	−	0.387898i	$-0.126799\pi$
$97$	51.7791	+	51.7791i	0.533805	+	0.533805i	−0.387898	+	0.921702i	$0.626799\pi$
$98$	110.354	+	142.015i	1.12606	+	1.44913i
$99$			8.04610i			0.0812737i
$100$	−226.053	+	70.5276i	−2.26053	+	0.705276i
$101$	−94.1409	−	163.057i	−0.932088	−	1.61442i	−0.779746	−	0.626096i	$-0.784652\pi$
$101$	−94.1409	−	163.057i	−0.932088	−	1.61442i	−0.152342	−	0.988328i	$-0.548682\pi$
$102$	22.5905	−	84.3089i	0.221475	−	0.826558i
$103$	−30.6253	−	114.295i	−0.297333	−	1.10966i	−0.939347	−	0.342969i	$-0.888567\pi$
$103$	−30.6253	−	114.295i	−0.297333	−	1.10966i	0.642013	−	0.766693i	$-0.278099\pi$
$104$			70.5512i			0.678377i
$105$	29.4737	+	41.9547i	0.280702	+	0.399569i
$106$	27.5834			0.260221
$107$	−45.1072	+	12.0864i	−0.421563	+	0.112957i	−0.463363	−	0.886169i	$-0.653357\pi$
$107$	−45.1072	+	12.0864i	−0.421563	+	0.112957i	0.0418001	+	0.999126i	$0.486691\pi$
$108$	212.492	+	56.9369i	1.96751	+	0.527194i
$109$	29.1458	−	16.8273i	0.267393	−	0.154379i	−0.360309	−	0.932833i	$-0.617329\pi$
$109$	29.1458	−	16.8273i	0.267393	−	0.154379i	0.627702	+	0.778454i	$0.283996\pi$
$110$	16.8222	−	13.4597i	0.152929	−	0.122361i
$111$	56.1391			0.505757
$112$	−111.617	−	224.609i	−0.996585	−	2.00544i
$113$	40.5401	−	40.5401i	0.358762	−	0.358762i	−0.504595	−	0.863356i	$-0.668358\pi$
$113$	40.5401	−	40.5401i	0.358762	−	0.358762i	0.863356	+	0.504595i	$0.168358\pi$
$114$	13.6874	+	7.90242i	0.120065	+	0.0693195i
$115$	145.624	−	22.1896i	1.26630	−	0.192953i
$116$	−53.8515	−	93.2736i	−0.464237	−	0.804082i
$117$	−23.2557	+	6.23134i	−0.198766	+	0.0532593i
$118$	−15.4391	+	15.4391i	−0.130840	+	0.130840i
$119$	−75.1815	−	85.2027i	−0.631777	−	0.715989i
$120$	−59.0466	−	134.743i	−0.492055	−	1.12286i
$121$	59.8109	−	103.596i	0.494305	−	0.856162i
$122$	−0.0156130	+	0.0582684i	−0.000127975	+	0.000477610i
$123$	−83.9795	−	22.5022i	−0.682760	−	0.182945i
$124$	256.306	+	147.978i	2.06698	+	1.19337i
$125$	−40.7134	+	118.184i	−0.325707	+	0.945471i
$126$	132.043	−	116.513i	1.04796	−	0.924705i
$127$	−30.4117	−	30.4117i	−0.239462	−	0.239462i	0.577165	−	0.816627i	$-0.304159\pi$
$127$	−30.4117	−	30.4117i	−0.239462	−	0.239462i	−0.816627	+	0.577165i	$0.804159\pi$
$128$	−10.6947	−	39.9133i	−0.0835526	−	0.311823i
$129$	−33.5697	+	19.3815i	−0.260231	+	0.150244i
$130$	51.9308	+	38.1974i	0.399467	+	0.293826i
$131$	−28.3295	+	49.0682i	−0.216256	+	0.374567i	−0.953660	−	0.300885i	$-0.902718\pi$
$131$	−28.3295	+	49.0682i	−0.216256	+	0.374567i	0.737404	+	0.675452i	$0.236051\pi$
$132$	11.5183	+	11.5183i	0.0872600	+	0.0872600i
$133$	18.4259	−	9.15659i	0.138541	−	0.0688465i
$134$		−	154.088i		−	1.14991i
$135$	90.6735	−	72.5493i	0.671656	−	0.537402i
$136$	163.014	+	282.349i	1.19863	+	2.07609i
$137$	−55.8359	+	208.383i	−0.407562	+	1.52104i	0.391721	+	0.920084i	$0.371880\pi$
$137$	−55.8359	+	208.383i	−0.407562	+	1.52104i	−0.799282	+	0.600956i	$0.794787\pi$
$138$	40.9996	+	153.013i	0.297098	+	1.10879i
$139$		−	169.451i		−	1.21907i	−0.792760	−	0.609534i	$-0.791356\pi$
$139$		−	169.451i		−	1.21907i	0.792760	−	0.609534i	$-0.208644\pi$
$140$	−326.572	−	57.0632i	−2.33265	−	0.407594i
$141$	−100.681			−0.714046
$142$	55.7438	−	14.9365i	0.392562	−	0.105187i
$143$	−3.98320	−	1.06729i	−0.0278545	−	0.00746359i
$144$	−212.680	+	122.791i	−1.47694	+	0.852712i
$145$	−56.5062	−	6.27442i	−0.389698	−	0.0432719i
$146$	−136.136			−0.932441
$147$	9.80319	+	71.1094i	0.0666884	+	0.483737i
$148$	−256.668	+	256.668i	−1.73424	+	1.73424i
$149$	129.356	+	74.6835i	0.868159	+	0.501232i	0.866736	−	0.498767i	$-0.166214\pi$
$149$	129.356	+	74.6835i	0.868159	+	0.501232i	0.00142291	+	0.999999i	$0.499547\pi$
$150$	−131.149	−	29.4891i	−0.874327	−	0.196594i
$151$	76.3156	+	132.182i	0.505401	+	0.875381i	0.999980	+	0.00624813i	$0.00198885\pi$
$151$	76.3156	+	132.182i	0.505401	+	0.875381i	−0.494579	+	0.869133i	$0.664678\pi$
$152$	−57.0243	+	15.2796i	−0.375160	+	0.100524i
$153$	−78.6721	+	78.6721i	−0.514197	+	0.514197i
$154$	29.5642	−	5.97444i	0.191975	−	0.0387951i
$155$	143.091	−	62.7049i	0.923167	−	0.404548i
$156$	−24.3710	+	42.2119i	−0.156225	+	0.270589i
$157$	35.8114	−	133.650i	0.228098	−	0.851275i	−0.753041	−	0.657974i	$-0.771414\pi$
$157$	35.8114	−	133.650i	0.228098	−	0.851275i	0.981139	−	0.193301i	$-0.0619195\pi$
$158$	−247.095	−	66.2088i	−1.56389	−	0.419043i
$159$	9.53415	+	5.50454i	0.0599632	+	0.0346198i
$160$	238.339	+	93.0978i	1.48962	+	0.581861i
$161$	195.484	+	65.6939i	1.21419	+	0.408037i
$162$	−71.7943	−	71.7943i	−0.443175	−	0.443175i
$163$	−2.79634	−	10.4361i	−0.0171555	−	0.0640250i	0.956817	−	0.290689i	$-0.0938846\pi$
$163$	−2.79634	−	10.4361i	−0.0171555	−	0.0640250i	−0.973973	+	0.226664i	$0.927218\pi$
$164$	486.835	−	281.074i	2.96851	−	1.71387i
$165$	8.50059	−	1.29529i	0.0515187	−	0.00785021i
$166$	164.017	−	284.086i	0.988054	−	1.71136i
$167$	−80.7727	−	80.7727i	−0.483669	−	0.483669i	0.422632	−	0.906301i	$-0.361106\pi$
$167$	−80.7727	−	80.7727i	−0.483669	−	0.483669i	−0.906301	+	0.422632i	$0.861106\pi$
$168$	12.8436	−	205.557i	0.0764503	−	1.22355i
$169$			156.661i			0.926987i
$170$	296.087	+	32.8774i	1.74169	+	0.193396i
$171$	−10.0732	−	17.4473i	−0.0589075	−	0.102031i
$172$	64.8687	−	242.093i	0.377144	−	1.40752i
$173$	58.4966	+	218.312i	0.338131	+	1.26192i	0.900435	+	0.434991i	$0.143248\pi$
$173$	58.4966	+	218.312i	0.338131	+	1.26192i	−0.562304	+	0.826930i	$0.690085\pi$
$174$		−	61.1395i		−	0.351376i
$175$	−126.409	+	121.020i	−0.722335	+	0.691543i
$176$	−42.0628			−0.238993
$177$	−8.41752	+	2.25547i	−0.0475566	+	0.0127427i
$178$	−213.456	−	57.1954i	−1.19919	−	0.321323i
$179$	−189.777	+	109.568i	−1.06021	+	0.612112i	−0.925490	−	0.378772i	$-0.876346\pi$
$179$	−189.777	+	109.568i	−1.06021	+	0.612112i	−0.134719	+	0.990884i	$0.543013\pi$
$180$	−35.8236	+	322.620i	−0.199020	+	1.79233i
$181$	−291.658			−1.61137			−0.805686	−	0.592343i	$-0.798203\pi$
$181$	−291.658			−1.61137			−0.805686	+	0.592343i	$0.798203\pi$
$182$	40.1641	+	80.8226i	0.220682	+	0.444080i
$183$	−0.0170246	+	0.0170246i	−9.30308e−5	+	9.30308e-5i
$184$	−512.436	−	295.855i	−2.78498	−	1.60791i
$185$	28.8635	+	189.423i	0.156019	+	1.02391i
$186$	84.0024	+	145.496i	0.451626	+	0.782239i
$187$	−18.4070	+	4.93213i	−0.0984330	+	0.0263750i
$188$	460.312	−	460.312i	2.44847	−	2.44847i
$189$	159.354	−	32.2029i	0.843144	−	0.170386i
$190$	−19.6268	+	50.2465i	−0.103299	+	0.264455i
$191$	−55.1786	+	95.5721i	−0.288893	+	0.500377i	−0.973546	−	0.228492i	$-0.926621\pi$
$191$	−55.1786	+	95.5721i	−0.288893	+	0.500377i	0.684653	+	0.728869i	$0.259954\pi$
$192$	−16.8771	+	62.9863i	−0.0879017	+	0.328053i
$193$	346.119	+	92.7422i	1.79336	+	0.480530i	0.992910	−	0.118868i	$-0.0379267\pi$
$193$	346.119	+	92.7422i	1.79336	+	0.480530i	0.800451	+	0.599398i	$0.204593\pi$
$194$	−232.764	−	134.386i	−1.19981	−	0.692713i
$195$	10.3271	+	23.5662i	0.0529594	+	0.120852i
$196$	−369.933	−	280.292i	−1.88741	−	1.43006i
$197$	−90.6810	−	90.6810i	−0.460309	−	0.460309i	0.438447	−	0.898757i	$-0.355529\pi$
$197$	−90.6810	−	90.6810i	−0.460309	−	0.460309i	−0.898757	+	0.438447i	$0.855529\pi$
$198$	−7.64359	−	28.5263i	−0.0386040	−	0.144072i
$199$	−280.150	+	161.744i	−1.40779	+	0.812786i	−0.995175	−	0.0981204i	$-0.968717\pi$
$199$	−280.150	+	161.744i	−1.40779	+	0.812786i	−0.412613	+	0.910907i	$0.635384\pi$
$200$	424.286	−	268.510i	2.12143	−	1.34255i
$201$	30.7497	−	53.2601i	0.152984	−	0.264975i
$202$	488.663	+	488.663i	2.41912	+	2.41912i
$203$	−66.3152	−	44.0186i	−0.326676	−	0.216840i
$204$			225.245i			1.10414i
$205$	32.7490	−	294.930i	0.159751	−	1.43868i
$206$	217.155	+	376.124i	1.05415	+	1.82584i
$207$	52.2620	−	195.044i	0.252473	−	0.942243i
$208$	−32.5757	−	121.574i	−0.156614	−	0.584491i
$209$		−	3.45064i		−	0.0165102i
$210$	−144.351	−	120.745i	−0.687385	−	0.574977i
$211$	−32.3501			−0.153318			−0.0766590	−	0.997057i	$-0.524425\pi$
$211$	−32.3501			−0.153318			−0.0766590	+	0.997057i	$0.524425\pi$
$212$	−68.7570	+	18.4234i	−0.324325	+	0.0869027i
$213$	22.2484	+	5.96145i	0.104453	+	0.0279880i
$214$	148.439	−	85.7015i	0.693642	−	0.400474i
$215$	−82.6560	−	103.305i	−0.384447	−	0.480489i
$216$	−466.463			−2.15955
$217$	218.292	+	13.6394i	1.00596	+	0.0628543i
$218$	−87.3467	+	87.3467i	−0.400673	+	0.400673i
$219$	−47.0553	−	27.1674i	−0.214864	−	0.124052i
$220$	−32.9427	+	44.7868i	−0.149740	+	0.203576i
$221$	−28.5107	−	49.3820i	−0.129008	−	0.223448i
$222$	−199.033	+	53.3307i	−0.896545	+	0.240228i
$223$	182.276	−	182.276i	0.817382	−	0.817382i	−0.168346	−	0.985728i	$-0.553843\pi$
$223$	182.276	−	182.276i	0.817382	−	0.817382i	0.985728	+	0.168346i	$0.0538427\pi$
$224$	237.016	+	268.608i	1.05811	+	1.19914i
$225$	125.983	+	116.141i	0.559924	+	0.516182i
$226$	−105.217	+	182.241i	−0.465561	+	0.806376i
$227$	54.1550	−	202.109i	0.238568	−	0.890349i	−0.737939	−	0.674867i	$-0.764201\pi$
$227$	54.1550	−	202.109i	0.238568	−	0.890349i	0.976508	−	0.215482i	$-0.0691323\pi$
$228$	−39.3966	−	10.5563i	−0.172792	−	0.0462996i
$229$	91.0319	+	52.5573i	0.397519	+	0.229508i	0.685413	−	0.728154i	$-0.259622\pi$
$229$	91.0319	+	52.5573i	0.397519	+	0.229508i	−0.287894	+	0.957662i	$0.592955\pi$
$230$	−495.210	+	217.010i	−2.15309	+	0.943520i
$231$	11.4111	+	3.83478i	0.0493986	+	0.0166008i
$232$	161.485	+	161.485i	0.696057	+	0.696057i
$233$	−13.2386	−	49.4071i	−0.0568180	−	0.212048i	0.931680	−	0.363279i	$-0.118343\pi$
$233$	−13.2386	−	49.4071i	−0.0568180	−	0.212048i	−0.988498	+	0.151231i	$0.951676\pi$
$234$	76.5300	−	44.1846i	0.327051	−	0.188823i
$235$	−51.7641	−	339.713i	−0.220273	−	1.44559i
$236$	28.1729	−	48.7969i	0.119377	−	0.206767i
$237$	−72.1951	−	72.1951i	−0.304621	−	0.304621i
$238$	347.485	+	230.653i	1.46002	+	0.969131i
$239$			58.4297i			0.244476i	0.992501	+	0.122238i	$0.0390071\pi$
$239$			58.4297i			0.244476i	−0.992501	+	0.122238i	$0.960993\pi$
$240$	163.964	+	204.926i	0.683185	+	0.853857i
$241$	−103.305	−	178.930i	−0.428653	−	0.742449i	0.568101	−	0.822959i	$-0.307678\pi$
$241$	−103.305	−	178.930i	−0.428653	−	0.742449i	−0.996754	+	0.0805104i	$0.974345\pi$
$242$	−113.638	+	424.102i	−0.469578	+	1.75249i
$243$	−64.5881	−	241.046i	−0.265795	−	0.991959i
$244$		−	0.155673i		−	0.000638006i
$245$	−234.895	+	69.6379i	−0.958754	+	0.284236i
$246$	319.114			1.29721
$247$	9.97339	−	2.67236i	0.0403781	−	0.0108193i
$248$	−606.165	−	162.421i	−2.44421	−	0.654925i
$249$	113.384	−	65.4624i	0.455359	−	0.262901i
$250$	32.0719	−	457.680i	0.128287	−	1.83072i
$251$	357.500			1.42430			0.712151	−	0.702026i	$-0.247721\pi$
$251$	357.500			1.42430			0.712151	+	0.702026i	$0.247721\pi$
$252$	−251.322	+	378.624i	−0.997311	+	1.50248i
$253$	24.4555	−	24.4555i	0.0966622	−	0.0966622i
$254$	136.711	+	78.9299i	0.538231	+	0.310748i
$255$	95.7809	+	70.4511i	0.375611	+	0.276279i
$256$	164.858	+	285.543i	0.643978	+	1.11540i
$257$	14.1907	−	3.80238i	0.0552167	−	0.0147953i	−0.231105	−	0.972929i	$-0.574234\pi$
$257$	14.1907	−	3.80238i	0.0552167	−	0.0147953i	0.286322	+	0.958134i	$0.407567\pi$
$258$	100.605	−	100.605i	0.389941	−	0.389941i
$259$	−85.4522	+	254.278i	−0.329931	+	0.981769i
$260$	−154.960	−	60.5291i	−0.596000	−	0.232804i
$261$	−38.9671	+	67.4930i	−0.149299	+	0.258594i
$262$	53.8247	−	200.877i	0.205438	−	0.766704i
$263$	−255.305	−	68.4088i	−0.970741	−	0.260109i	−0.261601	−	0.965176i	$-0.584250\pi$
$263$	−255.305	−	68.4088i	−0.970741	−	0.260109i	−0.709141	+	0.705067i	$0.750917\pi$
$264$	−29.9126	−	17.2701i	−0.113305	−	0.0654169i
$265$	−13.6713	+	34.9999i	−0.0515900	+	0.132075i
$266$	−56.6278	+	49.9675i	−0.212886	+	0.187848i
$267$	−62.3668	−	62.3668i	−0.233583	−	0.233583i
$268$	102.917	+	384.093i	0.384020	+	1.43318i
$269$	−225.615	+	130.259i	−0.838717	+	0.484234i	−0.856828	−	0.515602i	$-0.827568\pi$
$269$	−225.615	+	130.259i	−0.838717	+	0.484234i	0.0181109	+	0.999836i	$0.494235\pi$
$270$	−252.550	+	343.351i	−0.935369	+	1.27167i
$271$	−177.157	+	306.844i	−0.653715	+	1.13227i	0.328500	+	0.944504i	$0.393457\pi$
$271$	−177.157	+	306.844i	−0.653715	+	1.13227i	−0.982214	+	0.187763i	$0.939876\pi$
$272$	−411.276	−	411.276i	−1.51204	−	1.51204i
$273$	−2.24632	+	35.9513i	−0.00822828	+	0.131690i
$274$		−	791.833i		−	2.88990i
$275$	8.74102	+	28.0165i	0.0317855	+	0.101878i
$276$	−204.399	−	354.029i	−0.740576	−	1.28271i
$277$	23.9573	−	89.4100i	0.0864886	−	0.322780i	−0.909103	−	0.416571i	$-0.863232\pi$
$277$	23.9573	−	89.4100i	0.0864886	−	0.322780i	0.995592	+	0.0937909i	$0.0298985\pi$
$278$	160.974	+	600.762i	0.579042	+	2.16102i
$279$		−	214.155i		−	0.767580i
$280$	700.187	−	62.3487i	2.50067	−	0.222674i
$281$	14.0935			0.0501547			0.0250774	−	0.999686i	$-0.492017\pi$
$281$	14.0935			0.0501547			0.0250774	+	0.999686i	$0.492017\pi$
$282$	356.948	−	95.6440i	1.26577	−	0.339163i
$283$	394.478	+	105.700i	1.39392	+	0.373499i	0.876156	−	0.482027i	$-0.160099\pi$
$283$	394.478	+	105.700i	1.39392	+	0.373499i	0.517760	+	0.855526i	$0.326766\pi$
$284$	−128.976	+	74.4642i	−0.454140	+	0.262198i
$285$	−16.8112	+	13.4509i	−0.0589866	+	0.0471961i
$286$	15.1357			0.0529222
$287$	229.752	−	346.128i	0.800530	−	1.20602i
$288$	248.020	−	248.020i	0.861181	−	0.861181i
$289$	22.0791	+	12.7474i	0.0763984	+	0.0441086i
$290$	206.295	−	31.4344i	0.711362	−	0.108394i
$291$	−53.6362	−	92.9007i	−0.184317	−	0.319246i
$292$	339.346	−	90.9276i	1.16215	−	0.311396i
$293$	−272.948	+	272.948i	−0.931564	+	0.931564i	−0.997804	−	0.0662402i	$-0.978900\pi$
$293$	−272.948	+	272.948i	−0.931564	+	0.931564i	0.0662402	+	0.997804i	$0.478900\pi$
$294$	−102.308	−	242.795i	−0.347986	−	0.825834i
$295$	−11.9381	−	27.2425i	−0.0404682	−	0.0923474i
$296$	384.837	−	666.557i	1.30013	−	2.25188i
$297$	7.05663	−	26.3357i	0.0237597	−	0.0886723i
$298$	−529.559	−	141.895i	−1.77704	−	0.476158i
$299$	89.6237	+	51.7442i	0.299745	+	0.173058i
$300$	346.611	−	14.0892i	1.15537	−	0.0469640i
$301$	−36.6890	−	181.553i	−0.121890	−	0.603168i
$302$	−396.136	−	396.136i	−1.31171	−	1.31171i
$303$	71.3878	+	266.423i	0.235603	+	0.879283i
$304$	91.2094	−	52.6598i	0.300031	−	0.173223i
$305$	−0.0661970	−	0.0486909i	−0.000217039	−	0.000159642i
$306$	204.184	−	353.657i	0.667268	−	1.15574i
$307$	149.471	+	149.471i	0.486877	+	0.486877i	0.907319	−	0.420442i	$-0.138125\pi$
$307$	149.471	+	149.471i	0.486877	+	0.486877i	−0.420442	+	0.907319i	$0.638125\pi$
$308$	−69.7041	+	34.6389i	−0.226312	+	0.112464i
$309$			173.342i			0.560977i
$310$	−447.740	+	358.244i	−1.44432	+	1.15563i
$311$	60.8111	+	105.328i	0.195534	+	0.338675i	0.947075	−	0.321011i	$-0.104023\pi$
$311$	60.8111	+	105.328i	0.195534	+	0.338675i	−0.751541	+	0.659686i	$0.770689\pi$
$312$	26.7498	−	99.8315i	0.0857364	−	0.319973i
$313$	−49.8952	−	186.211i	−0.159409	−	0.594924i	−0.998687	−	0.0512215i	$-0.983689\pi$
$313$	−49.8952	−	186.211i	−0.159409	−	0.594924i	0.839278	−	0.543703i	$-0.182978\pi$
$314$			507.857i			1.61738i
$315$	82.3949	+	225.294i	0.261571	+	0.715220i
$316$	660.153			2.08909
$317$	−531.897	+	142.521i	−1.67791	+	0.449594i	−0.967225	−	0.253919i	$-0.918280\pi$
$317$	−531.897	+	142.521i	−1.67791	+	0.449594i	−0.710682	+	0.703513i	$0.751614\pi$
$318$	−39.0311	−	10.4583i	−0.122739	−	0.0328879i
$319$	−11.5601	+	6.67423i	−0.0362386	+	0.0209223i
$320$	−221.203	−	24.5624i	−0.691261	−	0.0767573i
$321$	68.4103			0.213116
$322$	−755.468	−	47.2033i	−2.34617	−	0.146594i
$323$	33.7392	−	33.7392i	0.104456	−	0.104456i
$324$	226.914	+	131.009i	0.700351	+	0.404348i
$325$	−74.2066	+	46.9617i	−0.228328	+	0.144497i
$326$	19.8280	+	34.3431i	0.0608222	+	0.105347i
$327$	−47.6221	+	12.7603i	−0.145633	+	0.0390223i
$328$	−842.861	+	842.861i	−2.56970	+	2.56970i
$329$	153.251	−	456.026i	0.465809	−	1.38610i
$330$	−28.9071	+	12.6676i	−0.0875973	+	0.0383866i
$331$	−311.306	+	539.198i	−0.940501	+	1.62900i	−0.175983	+	0.984393i	$0.556310\pi$
$331$	−311.306	+	539.198i	−0.940501	+	1.62900i	−0.764518	+	0.644602i	$0.777023\pi$
$332$	−219.099	+	817.688i	−0.659937	+	2.46292i
$333$	253.706	+	67.9804i	0.761881	+	0.204145i
$334$	363.100	+	209.636i	1.08713	+	0.627652i
$335$	195.518	+	76.3714i	0.583636	+	0.227974i
$336$	72.7798	+	360.147i	0.216606	+	1.07187i
$337$	298.924	+	298.924i	0.887015	+	0.887015i	0.994235	−	0.107220i	$-0.0341949\pi$
$337$	298.924	+	298.924i	0.887015	+	0.887015i	−0.107220	+	0.994235i	$0.534195\pi$
$338$	−148.824	−	555.418i	−0.440307	−	1.64325i
$339$	−72.7360	+	41.9941i	−0.214560	+	0.123877i
$340$	−760.014	+	115.808i	−2.23533	+	0.340611i
$341$	18.3401	−	31.7659i	0.0537831	−	0.0931551i
$342$	52.2874	+	52.2874i	0.152887	+	0.152887i
$343$	−337.007	−	63.8364i	−0.982529	−	0.186112i
$344$			531.446i			1.54490i
$345$	−214.475	−	23.8152i	−0.621666	−	0.0690296i
$346$	−414.782	−	718.424i	−1.19879	−	2.07637i
$347$	5.84351	−	21.8083i	0.0168401	−	0.0628480i	−0.956994	−	0.290106i	$-0.906309\pi$
$347$	5.84351	−	21.8083i	0.0168401	−	0.0628480i	0.973835	+	0.227258i	$0.0729761\pi$
$348$	40.8360	+	152.402i	0.117345	+	0.437937i
$349$		−	267.249i		−	0.765758i	−0.923799	−	0.382879i	$-0.874933\pi$
$349$		−	267.249i		−	0.765758i	0.923799	−	0.382879i	$-0.125067\pi$
$350$	333.197	−	549.144i	0.951993	−	1.56898i
$351$	81.5832			0.232431
$352$	58.0294	−	15.5489i	0.164856	−	0.0441731i
$353$	306.996	+	82.2594i	0.869678	+	0.233030i	0.665949	−	0.745998i	$-0.268027\pi$
$353$	306.996	+	82.2594i	0.869678	+	0.233030i	0.203730	+	0.979027i	$0.434694\pi$
$354$	27.7004	−	15.9929i	0.0782498	−	0.0451776i
$355$	−8.67608	+	78.1350i	−0.0244397	+	0.220099i
$356$	570.283			1.60192
$357$	74.0785	+	149.069i	0.207503	+	0.417560i
$358$	568.741	−	568.741i	1.58866	−	1.58866i
$359$	327.578	+	189.127i	0.912473	+	0.526816i	0.881226	−	0.472695i	$-0.156719\pi$
$359$	327.578	+	189.127i	0.912473	+	0.526816i	0.0312469	+	0.999512i	$0.490052\pi$
$360$	−103.682	−	680.437i	−0.288006	−	1.89010i
$361$	−176.180	−	305.153i	−0.488033	−	0.845299i
$362$	1034.03	−	277.068i	2.85644	−	0.765381i
$363$	−123.912	+	123.912i	−0.341357	+	0.341357i
$364$	−154.100	−	174.640i	−0.423350	−	0.479780i
$365$	67.4742	−	172.740i	0.184861	−	0.473261i
$366$	0.0441854	−	0.0765313i	0.000120725	−	0.000209102i
$367$	−113.673	+	424.235i	−0.309737	+	1.15595i	0.619054	+	0.785348i	$0.287516\pi$
$367$	−113.673	+	424.235i	−0.309737	+	1.15595i	−0.928791	+	0.370605i	$0.879150\pi$
$368$	1019.64	+	273.211i	2.77075	+	0.742421i
$369$	−352.275	−	203.386i	−0.954676	−	0.551183i
$370$	−282.278	−	644.151i	−0.762913	−	1.74095i
$371$	−39.4449	+	34.8055i	−0.106320	+	0.0938155i
$372$	−306.571	−	306.571i	−0.824117	−	0.824117i
$373$	−135.336	−	505.079i	−0.362830	−	1.35410i	−0.870339	−	0.492454i	$-0.836100\pi$
$373$	−135.336	−	505.079i	−0.362830	−	1.35410i	0.507509	−	0.861647i	$-0.330567\pi$
$374$	60.5738	−	34.9723i	0.161962	−	0.0935089i
$375$	102.420	−	151.796i	0.273121	−	0.404789i
$376$	−690.172	+	1195.41i	−1.83556	+	3.17929i
$377$	−28.2433	−	28.2433i	−0.0749160	−	0.0749160i
$378$	−534.375	+	265.553i	−1.41369	+	0.702521i
$379$			438.406i			1.15674i	0.815773	+	0.578372i	$0.196312\pi$
$379$			438.406i			1.15674i	−0.815773	+	0.578372i	$0.803688\pi$
$380$	15.3633	−	138.358i	0.0404296	−	0.364101i
$381$	31.5025	+	54.5639i	0.0826837	+	0.143212i
$382$	104.836	−	391.255i	0.274441	−	1.02423i
$383$	−53.8012	−	200.789i	−0.140473	−	0.524253i	−0.999915	−	0.0130198i	$-0.995856\pi$
$383$	−53.8012	−	200.789i	−0.140473	−	0.524253i	0.859442	−	0.511233i	$-0.170811\pi$
$384$			60.5331i			0.157638i
$385$	−7.07228	+	40.4745i	−0.0183695	+	0.105129i
$386$	−1315.22			−3.40730
$387$	−175.179	+	46.9392i	−0.452660	+	0.121290i
$388$	669.968	+	179.517i	1.72672	+	0.462674i
$389$	217.843	−	125.772i	0.560007	−	0.323320i	−0.193141	−	0.981171i	$-0.561868\pi$
$389$	217.843	−	125.772i	0.560007	−	0.323320i	0.753148	+	0.657851i	$0.228534\pi$
$390$	−59.0004	−	73.7399i	−0.151283	−	0.189077i
$391$	478.237			1.22311
$392$	911.506	+	371.063i	2.32527	+	0.946590i
$393$	58.6913	−	58.6913i	0.149342	−	0.149342i
$394$	407.641	+	235.351i	1.03462	+	0.597339i
$395$	206.480	−	280.717i	0.522734	−	0.710676i
$396$	38.1063	+	66.0020i	0.0962280	+	0.166672i
$397$	−258.277	+	69.2050i	−0.650571	+	0.174320i	−0.568987	−	0.822347i	$-0.692664\pi$
$397$	−258.277	+	69.2050i	−0.650571	+	0.174320i	−0.0815838	+	0.996666i	$0.525998\pi$
$398$	839.576	−	839.576i	2.10949	−	2.10949i
$399$	−29.5448	+	5.97052i	−0.0740471	+	0.0149637i
$400$	−607.153	+	658.604i	−1.51788	+	1.64651i
$401$	331.345	−	573.906i	0.826296	−	1.43119i	−0.0746287	−	0.997211i	$-0.523777\pi$
$401$	331.345	−	573.906i	0.826296	−	1.43119i	0.900925	−	0.433975i	$-0.142890\pi$
$402$	−58.4229	+	218.037i	−0.145331	+	0.542381i
$403$	106.017	+	28.4071i	0.263069	+	0.0704890i
$404$	−1544.47	−	891.701i	−3.82295	−	2.20718i
$405$	126.682	−	55.5142i	0.312795	−	0.137072i
$406$	276.927	+	93.0636i	0.682087	+	0.229221i
$407$	31.8108	+	31.8108i	0.0781593	+	0.0781593i
$408$	−123.615	−	461.337i	−0.302978	−	1.13073i
$409$	−217.013	+	125.293i	−0.530595	+	0.306339i	−0.741259	−	0.671219i	$-0.765771\pi$
$409$	−217.013	+	125.293i	−0.530595	+	0.306339i	0.210664	+	0.977559i	$0.432438\pi$
$410$	164.070	+	1076.74i	0.400170	+	2.62620i
$411$	158.018	−	273.695i	0.384472	−	0.665925i
$412$	−792.520	−	792.520i	−1.92359	−	1.92359i
$413$	2.59675	−	41.5597i	0.00628752	−	0.100629i
$414$			741.149i			1.79021i
$415$	279.177	+	348.921i	0.672715	+	0.840772i
$416$	89.8823	+	155.681i	0.216063	+	0.374233i
$417$	−64.2478	+	239.776i	−0.154072	+	0.575003i
$418$	3.27802	+	12.2337i	0.00784215	+	0.0292673i
$419$		−	195.592i		−	0.466807i	−0.972380	−	0.233403i	$-0.925014\pi$
$419$		−	195.592i		−	0.466807i	0.972380	−	0.233403i	$-0.0749862\pi$
$420$	440.470	+	204.566i	1.04874	+	0.487063i
$421$	−134.668			−0.319877			−0.159939	−	0.987127i	$-0.551130\pi$
$421$	−134.668			−0.319877			−0.159939	+	0.987127i	$0.551130\pi$
$422$	114.692	−	30.7318i	0.271783	−	0.0728241i
$423$	−455.000	−	121.917i	−1.07565	−	0.288220i
$424$	130.714	−	75.4680i	0.308289	−	0.177991i
$425$	−188.469	+	359.403i	−0.443456	+	0.845653i
$426$	−84.5418			−0.198455
$427$	−0.0511979	−	0.103026i	−0.000119901	−	0.000241279i
$428$	−312.772	+	312.772i	−0.730777	+	0.730777i
$429$	5.23164	+	3.02049i	0.0121950	+	0.00704076i
$430$	391.182	+	287.732i	0.909726	+	0.669144i
$431$	−259.076	−	448.733i	−0.601105	−	1.04114i	−0.992654	−	0.120987i	$-0.961394\pi$
$431$	−259.076	−	448.733i	−0.601105	−	1.04114i	0.391549	−	0.920157i	$-0.371939\pi$
$432$	803.812	−	215.381i	1.86068	−	0.498566i
$433$	−370.568	+	370.568i	−0.855815	+	0.855815i	−0.990842	−	0.135027i	$-0.956888\pi$
$433$	−370.568	+	370.568i	−0.855815	+	0.855815i	0.135027	+	0.990842i	$0.456888\pi$
$434$	−786.881	+	159.016i	−1.81309	+	0.366396i
$435$	77.5785	+	30.3030i	0.178341	+	0.0696620i
$436$	159.388	−	276.069i	0.365570	−	0.633185i
$437$	−22.4130	+	83.6464i	−0.0512883	+	0.191410i
$438$	192.636	+	51.6166i	0.439808	+	0.117846i
$439$	129.219	+	74.6045i	0.294348	+	0.169942i	0.639901	−	0.768457i	$-0.278975\pi$
$439$	129.219	+	74.6045i	0.294348	+	0.169942i	−0.345553	+	0.938399i	$0.612309\pi$
$440$	42.8928	−	109.809i	0.0974835	−	0.249567i
$441$	−41.8053	+	333.232i	−0.0947967	+	0.755628i
$442$	147.992	+	147.992i	0.334824	+	0.334824i
$443$	157.215	+	586.733i	0.354886	+	1.32445i	0.880627	+	0.473809i	$0.157121\pi$
$443$	157.215	+	586.733i	0.354886	+	1.32445i	−0.525741	+	0.850645i	$0.676212\pi$
$444$	460.508	−	265.874i	1.03718	−	0.598816i
$445$	178.371	−	242.501i	0.400833	−	0.544947i
$446$	−473.076	+	819.391i	−1.06071	+	1.83720i
$447$	−154.724	−	154.724i	−0.346140	−	0.346140i
$448$	−259.603	−	172.318i	−0.579470	−	0.384639i
$449$		−	653.166i		−	1.45471i	−0.686259	−	0.727357i	$-0.740749\pi$
$449$		−	653.166i		−	1.45471i	0.686259	−	0.727357i	$-0.259251\pi$
$450$	−556.985	−	292.080i	−1.23775	−	0.649067i
$451$	−34.8357	−	60.3372i	−0.0772410	−	0.133785i
$452$	140.552	−	524.547i	0.310956	−	1.16050i
$453$	−57.8707	−	215.976i	−0.127750	−	0.476769i
$454$			767.995i			1.69162i
$455$	−122.461	+	10.9046i	−0.269144	+	0.0239662i
$456$	86.4839			0.189658
$457$	100.694	−	26.9808i	0.220336	−	0.0590390i	−0.146962	−	0.989142i	$-0.546949\pi$
$457$	100.694	−	26.9808i	0.220336	−	0.0590390i	0.367298	+	0.930103i	$0.380283\pi$
$458$	−372.668	−	99.8562i	−0.813687	−	0.218027i
$459$	326.499	−	188.504i	0.711327	−	0.410685i
$460$	1089.46	−	871.697i	2.36840	−	1.89499i
$461$	−51.4142			−0.111527			−0.0557637	−	0.998444i	$-0.517759\pi$
$461$	−51.4142			−0.111527			−0.0557637	+	0.998444i	$0.517759\pi$
$462$	−44.0992	−	2.75542i	−0.0954529	−	0.00596411i
$463$	−47.6581	+	47.6581i	−0.102933	+	0.102933i	−0.756698	−	0.653765i	$-0.773189\pi$
$463$	−47.6581	+	47.6581i	−0.102933	+	0.102933i	0.653765	+	0.756698i	$0.273189\pi$
$464$	−352.835	−	203.709i	−0.760420	−	0.439028i
$465$	−226.252	+	34.4753i	−0.486562	+	0.0741404i
$466$	93.8710	+	162.589i	0.201440	+	0.348904i
$467$	195.292	−	52.3282i	0.418183	−	0.112052i	−0.0435908	−	0.999049i	$-0.513880\pi$
$467$	195.292	−	52.3282i	0.418183	−	0.112052i	0.461774	+	0.886998i	$0.347213\pi$
$468$	−161.254	+	161.254i	−0.344560	+	0.344560i
$469$	194.432	+	220.349i	0.414568	+	0.469827i
$470$	506.241	+	1155.23i	1.07711	+	2.45793i
$471$	−101.348	+	175.540i	−0.215176	+	0.372696i
$472$	−30.9227	+	115.405i	−0.0655143	+	0.244503i
$473$	−30.0045	−	8.03967i	−0.0634344	−	0.0169972i
$474$	324.541	+	187.374i	0.684685	+	0.395303i
$475$	−54.0289	−	49.8080i	−0.113745	−	0.104859i
$476$	−1020.23	−	342.857i	−2.14334	−	0.720287i
$477$	36.4215	+	36.4215i	0.0763554	+	0.0763554i
$478$	−55.5068	−	207.154i	−0.116123	−	0.433377i
$479$	560.143	−	323.399i	1.16940	−	0.675154i	0.215862	−	0.976424i	$-0.430744\pi$
$479$	560.143	−	323.399i	1.16940	−	0.675154i	0.953539	+	0.301270i	$0.0974104\pi$
$480$	−301.957	−	222.103i	−0.629076	−	0.462714i
$481$	−67.3069	+	116.579i	−0.139931	+	0.242368i
$482$	536.233	+	536.233i	1.11252	+	1.11252i
$483$	−251.706	−	167.077i	−0.521130	−	0.345915i
$484$		−	1133.06i		−	2.34103i
$485$	285.886	−	228.742i	0.589455	−	0.471633i
$486$	457.975	+	793.236i	0.942336	+	1.63217i
$487$	−134.259	+	501.060i	−0.275685	+	1.02887i	0.679695	+	0.733494i	$0.262112\pi$
$487$	−134.259	+	501.060i	−0.275685	+	1.02887i	−0.955381	+	0.295377i	$0.904555\pi$
$488$	0.0854340	+	0.318844i	0.000175070	+	0.000653369i
$489$			15.8275i			0.0323671i
$490$	766.631	−	470.035i	1.56455	−	0.959256i
$491$	142.382			0.289984			0.144992	−	0.989433i	$-0.453684\pi$
$491$	142.382			0.289984			0.144992	+	0.989433i	$0.453684\pi$
$492$	−795.453	+	213.141i	−1.61677	+	0.433213i
$493$	−178.289	−	47.7725i	−0.361642	−	0.0969016i
$494$	−32.8205	+	18.9489i	−0.0664383	+	0.0383582i
$495$	39.9848	+	4.43989i	0.0807773	+	0.00896948i
$496$	1119.54			2.25714
$497$	−60.8675	+	91.6986i	−0.122470	+	0.184504i
$498$	−339.800	+	339.800i	−0.682329	+	0.682329i
$499$	−847.182	−	489.121i	−1.69776	−	0.980202i	−0.947880	−	0.318627i	$-0.896778\pi$
$499$	−847.182	−	489.121i	−1.69776	−	0.980202i	−0.749879	−	0.661575i	$-0.769888\pi$
$500$	225.746	+	1162.28i	0.451493	+	2.32456i
$501$	83.6698	+	144.920i	0.167006	+	0.289262i
$502$	−1267.46	+	339.616i	−2.52483	+	0.676526i
$503$	−233.167	+	233.167i	−0.463553	+	0.463553i	−0.899818	−	0.436265i	$-0.856301\pi$
$503$	−233.167	+	233.167i	−0.463553	+	0.463553i	0.436265	+	0.899818i	$0.356301\pi$
$504$	306.958	−	913.409i	0.609044	−	1.81232i
$505$	−862.252	+	377.853i	−1.70743	+	0.748224i
$506$	−63.4714	+	109.936i	−0.125438	+	0.217264i
$507$	59.3985	−	221.678i	0.117157	−	0.437235i
$508$	−393.496	−	105.437i	−0.774599	−	0.207553i
$509$	838.493	+	484.104i	1.64733	+	0.951089i	0.978126	+	0.208014i	$0.0666998\pi$
$509$	838.493	+	484.104i	1.64733	+	0.951089i	0.669208	+	0.743075i	$0.266634\pi$
$510$	−406.504	−	158.785i	−0.797066	−	0.311343i
$511$	194.678	−	171.781i	0.380975	−	0.336166i
$512$	−738.866	−	738.866i	−1.44310	−	1.44310i
$513$	17.6688	+	65.9410i	0.0344422	+	0.128540i
$514$	−46.6988	+	26.9616i	−0.0908538	+	0.0524544i
$515$	−584.885	+	89.1223i	−1.13570	+	0.173053i
$516$	−183.581	+	317.972i	−0.355778	+	0.616225i
$517$	−57.0500	−	57.0500i	−0.110348	−	0.110348i
$518$	61.4003	−	982.684i	0.118533	−	1.89707i
$519$		−	331.096i		−	0.637949i
$520$	350.601	+	38.9306i	0.674233	+	0.0748666i
$521$	13.0561	+	22.6139i	0.0250597	+	0.0434048i	0.878283	−	0.478141i	$-0.158689\pi$
$521$	13.0561	+	22.6139i	0.0250597	+	0.0434048i	−0.853224	+	0.521545i	$0.825356\pi$
$522$	74.0355	−	276.304i	0.141831	−	0.529319i
$523$	14.8325	+	55.3556i	0.0283604	+	0.105842i	0.978655	−	0.205509i	$-0.0658850\pi$
$523$	14.8325	+	55.3556i	0.0283604	+	0.105842i	−0.950295	+	0.311351i	$0.899218\pi$
$524$			536.674i			1.02419i
$525$	224.756	−	123.318i	0.428107	−	0.234891i
$526$	970.133			1.84436
$527$	489.920	−	131.274i	0.929639	−	0.249096i
$528$	59.5197	+	15.9483i	0.112727	+	0.0302050i
$529$	−293.542	+	169.477i	−0.554900	+	0.320372i
$530$	15.2207	−	137.075i	0.0287183	−	0.258631i
$531$	−40.7720			−0.0767835
$532$	107.782	−	162.376i	0.202597	−	0.305218i
$533$	147.414	−	147.414i	0.276574	−	0.276574i
$534$	280.359	+	161.865i	0.525017	+	0.303119i
$535$	35.1726	+	230.828i	0.0657432	+	0.431454i
$536$	−421.582	−	730.202i	−0.786534	−	1.36232i
$537$	310.082	−	83.0862i	0.577434	−	0.154723i
$538$	676.142	−	676.142i	1.25677	−	1.25677i
$539$	−34.7388	+	45.8486i	−0.0644504	+	0.0850623i
$540$	400.200	−	1024.55i	0.741111	−	1.89731i
$541$	290.337	−	502.879i	0.536667	−	0.929535i	−0.462413	−	0.886665i	$-0.653016\pi$
$541$	290.337	−	502.879i	0.536667	−	0.929535i	0.999081	−	0.0428707i	$-0.0136504\pi$
$542$	336.589	−	1256.17i	0.621012	−	2.31765i
$543$	412.703	+	110.583i	0.760042	+	0.203653i
$544$	719.425	+	415.360i	1.32247	+	0.763530i
$545$	−67.5399	−	154.124i	−0.123926	−	0.282797i
$546$	−26.1889	−	129.594i	−0.0479649	−	0.237352i
$547$	200.743	+	200.743i	0.366988	+	0.366988i	0.866378	−	0.499389i	$-0.166442\pi$
$547$	200.743	+	200.743i	0.366988	+	0.366988i	−0.499389	+	0.866378i	$0.666442\pi$
$548$	528.877	+	1973.80i	0.965104	+	3.60182i
$549$	−0.0975541	+	0.0563229i	−0.000177694	+	0.000102592i
$550$	−57.6049	−	91.0245i	−0.104736	−	0.165499i
$551$	16.7114	−	28.9449i	0.0303292	−	0.0525317i
$552$	612.933	+	612.933i	1.11039	+	1.11039i
$553$	436.895	−	217.111i	0.790045	−	0.392606i
$554$			339.749i			0.613265i
$555$	30.9779	−	278.981i	0.0558161	−	0.502668i
$556$	−802.517	−	1390.00i	−1.44338	−	2.50000i
$557$	−122.418	+	456.872i	−0.219782	+	0.820236i	0.764647	+	0.644450i	$0.222913\pi$
$557$	−122.418	+	456.872i	−0.219782	+	0.820236i	−0.984428	+	0.175786i	$0.943753\pi$
$558$	203.442	+	759.255i	0.364591	+	1.36067i
$559$		−	92.9484i		−	0.166276i
$560$	−1177.78	+	430.738i	−2.10317	+	0.769174i
$561$	27.9163			0.0497617
$562$	−49.9664	+	13.3884i	−0.0889081	+	0.0238229i
$563$	−366.481	−	98.1984i	−0.650944	−	0.174420i	−0.0817883	−	0.996650i	$-0.526063\pi$
$563$	−366.481	−	98.1984i	−0.650944	−	0.174420i	−0.569156	+	0.822230i	$0.692730\pi$
$564$	−825.881	+	476.822i	−1.46433	+	0.845430i
$565$	−179.092	−	223.832i	−0.316977	−	0.396164i
$566$	−1498.98			−2.64837
$567$	193.260	+	12.0753i	0.340846	+	0.0212968i
$568$	223.297	−	223.297i	0.393128	−	0.393128i
$569$	−416.460	−	240.443i	−0.731916	−	0.422572i	0.0872069	−	0.996190i	$-0.472206\pi$
$569$	−416.460	−	240.443i	−0.731916	−	0.422572i	−0.819123	+	0.573619i	$0.805539\pi$
$570$	46.8235	−	63.6583i	0.0821466	−	0.111681i
$571$	419.663	+	726.877i	0.734961	+	1.27299i	0.954740	+	0.297440i	$0.0961329\pi$
$571$	419.663	+	726.877i	0.734961	+	1.27299i	−0.219779	+	0.975550i	$0.570534\pi$
$572$	−37.7288	+	10.1094i	−0.0659594	+	0.0176738i
$573$	114.315	−	114.315i	0.199503	−	0.199503i
$574$	−485.739	+	1445.40i	−0.846236	+	2.51813i
$575$	−29.9140	−	735.919i	−0.0520244	−	1.27986i
$576$	−152.544	+	264.213i	−0.264833	+	0.458704i
$577$	186.976	−	697.804i	0.324049	−	1.20937i	−0.591216	−	0.806513i	$-0.701352\pi$
$577$	186.976	−	697.804i	0.324049	−	1.20937i	0.915265	−	0.402853i	$-0.131981\pi$
$578$	−90.3881	−	24.2194i	−0.156381	−	0.0419021i
$579$	−454.602	−	262.464i	−0.785150	−	0.453306i
$580$	−493.235	+	216.144i	−0.850405	+	0.372662i
$581$	123.920	+	613.210i	0.213287	+	1.05544i
$582$	278.413	+	278.413i	0.478372	+	0.478372i
$583$	2.28335	+	8.52157i	0.00391655	+	0.0146168i
$584$	−645.134	+	372.468i	−1.10468	+	0.637788i
$585$	18.1337	+	119.007i	0.0309978	+	0.203430i
$586$	708.404	−	1226.99i	1.20888	−	2.09384i
$587$	−421.963	−	421.963i	−0.718847	−	0.718847i	0.249522	−	0.968369i	$-0.419726\pi$
$587$	−421.963	−	421.963i	−0.718847	−	0.718847i	−0.968369	+	0.249522i	$0.919726\pi$
$588$	417.189	+	536.881i	0.709505	+	0.913063i
$589$			91.8421i			0.155929i
$590$	68.2045	+	85.2433i	0.115601	+	0.144480i
$591$	93.9335	+	162.698i	0.158940	+	0.275292i
$592$	−355.382	+	1326.31i	−0.600308	+	2.24038i
$593$	101.013	+	376.987i	0.170343	+	0.635728i	0.997298	+	0.0734605i	$0.0234043\pi$
$593$	101.013	+	376.987i	0.170343	+	0.635728i	−0.826955	+	0.562268i	$0.809929\pi$
$594$			100.073i			0.168473i
$595$	−464.897	+	326.596i	−0.781339	+	0.548901i
$596$	1414.80			2.37383
$597$	457.744	−	122.652i	0.766740	−	0.205447i
$598$	−366.903	−	98.3114i	−0.613551	−	0.164400i
$599$	−909.142	+	524.893i	−1.51777	+	0.876283i	−0.517984	+	0.855390i	$0.673317\pi$
$599$	−909.142	+	524.893i	−1.51777	+	0.876283i	−0.999782	+	0.0208923i	$0.993349\pi$
$600$	−702.181	+	219.078i	−1.17030	+	0.365129i
$601$	−205.229			−0.341479			−0.170739	−	0.985316i	$-0.554616\pi$
$601$	−205.229			−0.341479			−0.170739	+	0.985316i	$0.554616\pi$
$602$	302.547	+	608.818i	0.502569	+	1.01133i
$603$	203.460	−	203.460i	0.337412	−	0.337412i
$604$	1252.03	+	722.860i	2.07290	+	1.19679i
$605$	−481.810	−	354.393i	−0.796380	−	0.585773i
$606$	−506.190	−	876.746i	−0.835297	−	1.44678i
$607$	136.929	−	36.6899i	0.225583	−	0.0604447i	−0.144257	−	0.989540i	$-0.546079\pi$
$607$	136.929	−	36.6899i	0.225583	−	0.0604447i	0.369840	+	0.929096i	$0.379413\pi$
$608$	−106.365	+	106.365i	−0.174943	+	0.174943i
$609$	77.1476	+	87.4308i	0.126679	+	0.143565i
$610$	0.280947	+	0.109741i	0.000460569	+	0.000179903i
$611$	120.709	−	209.074i	0.197560	−	0.342184i
$612$	−272.755	+	1017.94i	−0.445679	+	1.66330i
$613$	230.303	+	61.7096i	0.375699	+	0.100668i	0.441727	−	0.897150i	$-0.354366\pi$
$613$	230.303	+	61.7096i	0.375699	+	0.100668i	−0.0660280	+	0.997818i	$0.521033\pi$
$614$	−671.922	−	387.934i	−1.09434	−	0.631815i
$615$	−158.164	+	404.916i	−0.257178	+	0.658400i
$616$	123.755	−	109.200i	0.200901	−	0.177272i
$617$	−96.9272	−	96.9272i	−0.157094	−	0.157094i	0.624183	−	0.781278i	$-0.285432\pi$
$617$	−96.9272	−	96.9272i	−0.157094	−	0.157094i	−0.781278	+	0.624183i	$0.785432\pi$
$618$	−164.670	−	614.558i	−0.266457	−	0.994431i
$619$	853.884	−	492.990i	1.37946	−	0.796430i	0.387363	−	0.921927i	$-0.373386\pi$
$619$	853.884	−	492.990i	1.37946	−	0.796430i	0.992094	+	0.125498i	$0.0400528\pi$
$620$	876.802	−	1192.04i	1.41420	−	1.92265i
$621$	−342.117	+	592.565i	−0.550914	+	0.954210i
$622$	−315.656	−	315.656i	−0.507485	−	0.507485i
$623$	377.418	−	187.555i	0.605807	−	0.301051i
$624$			184.381i			0.295483i
$625$	564.844	+	267.538i	0.903750	+	0.428061i
$626$	353.792	+	612.786i	0.565163	+	0.978891i
$627$	−1.30832	+	4.88272i	−0.00208664	+	0.00778744i
$628$	−339.206	−	1265.93i	−0.540136	−	2.01582i
$629$			622.072i			0.988986i
$630$	−506.143	−	720.475i	−0.803402	−	1.14361i
$631$	−930.705			−1.47497			−0.737484	−	0.675365i	$-0.763986\pi$
$631$	−930.705			−1.47497			−0.737484	+	0.675365i	$0.763986\pi$
$632$	−1352.10	+	362.294i	−2.13940	+	0.573249i
$633$	45.7760	+	12.2657i	0.0723160	+	0.0193770i
$634$	1750.37	−	1010.58i	2.76084	−	1.59397i
$635$	−167.911	+	134.348i	−0.264427	+	0.211572i
$636$	104.278			0.163959
$637$	−159.420	−	64.8979i	−0.250267	−	0.101881i
$638$	34.6443	−	34.6443i	0.0543014	−	0.0543014i
$639$	93.3273	+	53.8825i	0.146052	+	0.0843232i
$640$	−204.249	+	31.1226i	−0.319139	+	0.0486291i
$641$	177.889	+	308.112i	0.277518	+	0.480674i	0.970767	−	0.240023i	$-0.0771550\pi$
$641$	177.889	+	308.112i	0.277518	+	0.480674i	−0.693250	+	0.720698i	$0.743822\pi$
$642$	−242.539	+	64.9881i	−0.377786	+	0.101228i
$643$	366.310	−	366.310i	0.569689	−	0.569689i	−0.362352	−	0.932041i	$-0.618026\pi$
$643$	366.310	−	366.310i	0.569689	−	0.569689i	0.932041	+	0.362352i	$0.118026\pi$
$644$	1914.68	−	386.925i	2.97310	−	0.600815i
$645$	77.7915	+	177.518i	0.120607	+	0.275222i
$646$	−87.5660	+	151.669i	−0.135551	+	0.234781i
$647$	−211.714	+	790.128i	−0.327225	+	1.22122i	0.584832	+	0.811154i	$0.301160\pi$
$647$	−211.714	+	790.128i	−0.327225	+	1.22122i	−0.912057	+	0.410064i	$0.865506\pi$
$648$	−536.653	−	143.796i	−0.828168	−	0.221907i
$649$	−6.04777	−	3.49168i	−0.00931860	−	0.00538010i
$650$	218.476	−	236.990i	0.336117	−	0.364600i
$651$	−303.717	−	102.066i	−0.466539	−	0.156784i
$652$	−72.3635	−	72.3635i	−0.110987	−	0.110987i
$653$	8.24671	+	30.7771i	0.0126290	+	0.0471319i	0.971953	−	0.235176i	$-0.0755667\pi$
$653$	8.24671	+	30.7771i	0.0126290	+	0.0471319i	−0.959324	+	0.282308i	$0.908900\pi$
$654$	156.715	−	90.4796i	0.239626	−	0.138348i
$655$	228.210	+	167.859i	0.348412	+	0.256273i
$656$	1063.25	−	1841.60i	1.62080	−	2.80731i
$657$	−179.757	−	179.757i	−0.273602	−	0.273602i
$658$	−110.116	+	1762.36i	−0.167350	+	2.67836i
$659$			495.313i			0.751612i	0.926698	+	0.375806i	$0.122634\pi$
$659$			495.313i			0.751612i	−0.926698	+	0.375806i	$0.877366\pi$
$660$	63.5957	−	50.8839i	0.0963571	−	0.0770969i
$661$	428.787	+	742.682i	0.648695	+	1.12357i	0.983435	+	0.181262i	$0.0580182\pi$
$661$	428.787	+	742.682i	0.648695	+	1.12357i	−0.334740	+	0.942311i	$0.608648\pi$
$662$	591.465	−	2207.38i	0.893452	−	3.33441i
$663$	21.6199	+	80.6866i	0.0326092	+	0.121699i
$664$		−	1795.00i		−	2.70331i
$665$	−35.3357	−	96.6194i	−0.0531365	−	0.145292i
$666$	−964.058			−1.44753
$667$	323.578	−	86.7024i	0.485124	−	0.129989i
$668$	−1045.12	−	280.038i	−1.56455	−	0.419219i
$669$	−327.035	+	188.814i	−0.488842	+	0.282233i
$670$	−765.732	−	85.0266i	−1.14288	−	0.126905i
$671$	−0.0192938			−2.87538e−5
$672$	−233.538	−	469.951i	−0.347527	−	0.699333i
$673$	−692.154	+	692.154i	−1.02846	+	1.02846i	−0.0288771	+	0.999583i	$0.509193\pi$
$673$	−692.154	+	692.154i	−1.02846	+	1.02846i	−0.999583	+	0.0288771i	$0.990807\pi$
$674$	−1343.76	−	775.822i	−1.99371	−	1.15107i
$675$	−310.496	−	490.631i	−0.459995	−	0.726861i
$676$	741.944	+	1285.09i	1.09755	+	1.90101i
$677$	433.146	−	116.061i	0.639802	−	0.171435i	0.0756885	−	0.997132i	$-0.475885\pi$
$677$	433.146	−	116.061i	0.639802	−	0.171435i	0.564114	+	0.825697i	$0.309218\pi$
$678$	217.981	−	217.981i	0.321507	−	0.321507i
$679$	502.430	−	101.533i	0.739956	−	0.149533i
$680$	1493.07	−	654.290i	2.19570	−	0.962191i
$681$	−153.261	+	265.456i	−0.225053	+	0.389803i
$682$	−34.8452	+	130.044i	−0.0510926	+	0.190680i
$683$	502.785	+	134.721i	0.736142	+	0.197249i	0.607363	−	0.794425i	$-0.292228\pi$
$683$	502.785	+	134.721i	0.736142	+	0.197249i	0.128779	+	0.991673i	$0.458894\pi$
$684$	−165.260	−	95.4130i	−0.241608	−	0.139493i
$685$	1004.74	+	392.461i	1.46677	+	0.572936i
$686$	1255.45	−	93.8259i	1.83011	−	0.136772i
$687$	−108.885	−	108.885i	−0.158493	−	0.158493i
$688$	−245.385	−	915.789i	−0.356664	−	1.33109i
$689$	−22.8616	+	13.1991i	−0.0331808	+	0.0191570i
$690$	783.013	−	119.312i	1.13480	−	0.172916i
$691$	124.505	−	215.649i	0.180181	−	0.312083i	−0.761761	−	0.647858i	$-0.775665\pi$
$691$	124.505	−	215.649i	0.180181	−	0.312083i	0.941942	+	0.335775i	$0.108998\pi$
$692$	1513.77	+	1513.77i	2.18753	+	2.18753i
$693$	46.9258	+	31.1483i	0.0677140	+	0.0449470i
$694$			82.8692i			0.119408i
$695$	−842.077	−	93.5040i	−1.21162	−	0.134538i
$696$	−167.277	−	289.733i	−0.240341	−	0.416283i
$697$	249.345	−	930.569i	0.357741	−	1.33511i
$698$	253.880	+	947.494i	0.363725	+	1.35744i
$699$			74.9316i			0.107198i
$700$	−463.778	+	1591.40i	−0.662539	+	2.27342i
$701$	954.149			1.36113			0.680563	−	0.732690i	$-0.261735\pi$
$701$	954.149			1.36113			0.680563	+	0.732690i	$0.261735\pi$
$702$	−289.241	+	77.5020i	−0.412025	+	0.110402i
$703$	−108.804	−	29.1540i	−0.154771	−	0.0414708i
$704$	−45.2541	+	26.1274i	−0.0642813	+	0.0371128i
$705$	−55.5562	+	500.328i	−0.0788031	+	0.709685i
$706$	−1166.56			−1.65234
$707$	−1315.41	−	82.1896i	−1.86055	−	0.116251i
$708$	−58.3668	+	58.3668i	−0.0824390	+	0.0824390i
$709$	−19.0690	−	11.0095i	−0.0268957	−	0.0155282i	0.486492	−	0.873685i	$-0.338276\pi$
$709$	−19.0690	−	11.0095i	−0.0268957	−	0.0155282i	−0.513388	+	0.858157i	$0.671610\pi$
$710$	−43.4665	−	285.258i	−0.0612204	−	0.401772i
$711$	−238.844	−	413.691i	−0.335927	−	0.581843i
$712$	−1168.03	+	312.972i	−1.64049	+	0.439568i
$713$	−650.908	+	650.908i	−0.912915	+	0.912915i
$714$	−404.246	−	458.129i	−0.566171	−	0.641638i
$715$	−7.50183	+	19.2054i	−0.0104921	+	0.0268607i
$716$	−1037.83	+	1797.57i	−1.44948	+	2.51057i
$717$	22.1539	−	82.6793i	0.0308980	−	0.115313i
$718$	−1341.04	−	359.332i	−1.86775	−	0.500462i
$719$	−217.588	−	125.625i	−0.302626	−	0.174721i	0.340996	−	0.940065i	$-0.389236\pi$
$719$	−217.588	−	125.625i	−0.302626	−	0.174721i	−0.643622	+	0.765343i	$0.722569\pi$
$720$	492.845	+	1124.66i	0.684506	+	1.56203i
$721$	−785.141	−	263.853i	−1.08896	−	0.365954i
$722$	914.508	+	914.508i	1.26663	+	1.26663i
$723$	78.3372	+	292.359i	0.108350	+	0.404369i
$724$	−2392.47	+	1381.29i	−3.30451	+	1.90786i
$725$	−62.3610	+	277.343i	−0.0860151	+	0.382542i
$726$	321.600	−	557.027i	0.442975	−	0.767255i
$727$	−157.277	−	157.277i	−0.216338	−	0.216338i	0.590615	−	0.806953i	$-0.298885\pi$
$727$	−157.277	−	157.277i	−0.216338	−	0.216338i	−0.806953	+	0.590615i	$0.798885\pi$
$728$	411.463	+	273.120i	0.565196	+	0.375165i
$729$			116.613i			0.159963i
$730$	−75.1210	+	676.524i	−0.102905	+	0.926745i
$731$	−214.765	−	371.983i	−0.293796	−	0.508869i
$732$	−0.0590242	+	0.220281i	−8.06341e−5	+	0.000300931i
$733$	−86.3385	−	322.220i	−0.117788	−	0.439590i	0.881692	−	0.471825i	$-0.156404\pi$
$733$	−86.3385	−	322.220i	−0.117788	−	0.439590i	−0.999480	+	0.0322341i	$0.989738\pi$
$734$		−	1612.05i		−	2.19625i
$735$	358.785	−	9.47790i	0.488142	−	0.0128951i
$736$	−1507.68			−2.04848
$737$	47.6036	−	12.7553i	0.0645910	−	0.0173071i
$738$	1442.15	+	386.424i	1.95414	+	0.523609i
$739$	−342.328	+	197.643i	−0.463231	+	0.267446i	−0.713402	−	0.700755i	$-0.752847\pi$
$739$	−342.328	+	197.643i	−0.463231	+	0.267446i	0.250171	+	0.968202i	$0.419513\pi$
$740$	1133.87	+	1417.13i	1.53226	+	1.91504i
$741$	−15.1258			−0.0204127
$742$	106.782	−	160.870i	0.143911	−	0.216805i
$743$	500.455	−	500.455i	0.673560	−	0.673560i	−0.284975	−	0.958535i	$-0.591985\pi$
$743$	500.455	−	500.455i	0.673560	−	0.673560i	0.958535	+	0.284975i	$0.0919853\pi$
$744$	796.154	+	459.660i	1.07010	+	0.617822i
$745$	442.516	−	601.617i	0.593981	−	0.807539i
$746$	959.625	+	1662.12i	1.28636	+	2.22804i
$747$	591.682	−	158.541i	0.792077	−	0.212236i
$748$	−127.633	+	127.633i	−0.170633	+	0.170633i
$749$	−104.131	+	309.860i	−0.139027	+	0.413698i
$750$	−218.914	+	635.467i	−0.291885	+	0.847289i
$751$	399.343	−	691.683i	0.531749	−	0.921016i	−0.467564	−	0.883959i	$-0.654868\pi$
$751$	399.343	−	691.683i	0.531749	−	0.921016i	0.999313	−	0.0370570i	$-0.0117983\pi$
$752$	637.348	−	2378.61i	0.847537	−	3.16305i
$753$	−505.870	−	135.547i	−0.671806	−	0.180010i
$754$	126.963	+	73.3021i	0.168386	+	0.0972177i
$755$	698.987	−	306.308i	0.925810	−	0.405706i
$756$	1154.67	−	1018.86i	1.52734	−	1.34770i
$757$	−456.836	−	456.836i	−0.603482	−	0.603482i	0.337753	−	0.941235i	$-0.390333\pi$
$757$	−456.836	−	456.836i	−0.603482	−	0.603482i	−0.941235	+	0.337753i	$0.890333\pi$
$758$	−416.475	−	1554.31i	−0.549439	−	2.05053i
$759$	−43.8775	+	25.3327i	−0.0578096	+	0.0333764i
$760$	44.4650	+	291.811i	0.0585066	+	0.383962i
$761$	523.481	−	906.696i	0.687886	−	1.19145i	−0.284635	−	0.958636i	$-0.591872\pi$
$761$	523.481	−	906.696i	0.687886	−	1.19145i	0.972521	−	0.232817i	$-0.0747943\pi$
$762$	−163.522	−	163.522i	−0.214596	−	0.214596i
$763$	14.6911	−	235.124i	0.0192544	−	0.308158i
$764$			1045.30i			1.36820i
$765$	347.546	+	434.370i	0.454309	+	0.567804i
$766$	381.489	+	660.758i	0.498027	+	0.862608i
$767$	5.40830	−	20.1841i	0.00705124	−	0.0263156i
$768$	−125.013	−	466.556i	−0.162778	−	0.607495i
$769$		−	627.616i		−	0.816146i	−0.912949	−	0.408073i	$-0.866201\pi$
$769$		−	627.616i		−	0.816146i	0.912949	−	0.408073i	$-0.133799\pi$
$770$	−13.3760	−	150.215i	−0.0173715	−	0.195084i
$771$	−21.5218			−0.0279141
$772$	3278.43	−	878.453i	4.24667	−	1.13789i
$773$	177.506	+	47.5625i	0.229632	+	0.0615297i	0.371800	−	0.928313i	$-0.378741\pi$
$773$	177.506	+	47.5625i	0.229632	+	0.0615297i	−0.142168	+	0.989843i	$0.545407\pi$
$774$	576.482	−	332.832i	0.744809	−	0.430016i
$775$	−232.651	−	745.685i	−0.300195	−	0.962175i
$776$	−1470.72			−1.89526
$777$	217.327	−	327.410i	0.279700	−	0.421377i
$778$	−652.850	+	652.850i	−0.839139	+	0.839139i
$779$	151.076	+	87.2239i	0.193936	+	0.111969i
$780$	196.322	+	144.404i	0.251695	+	0.185133i
$781$	9.22891	+	15.9849i	0.0118168	+	0.0204673i
$782$	−1695.52	+	454.313i	−2.16818	+	0.580962i
$783$	186.736	−	186.736i	0.238488	−	0.238488i
$784$	−1742.04	−	218.547i	−2.22199	−	0.278758i
$785$	−644.408	−	251.713i	−0.820902	−	0.320653i
$786$	−152.326	+	263.837i	−0.193799	+	0.335670i
$787$	−280.881	+	1048.26i	−0.356901	+	1.33197i	0.521173	+	0.853451i	$0.325494\pi$
$787$	−280.881	+	1048.26i	−0.356901	+	1.33197i	−0.878075	+	0.478523i	$0.841172\pi$
$788$	−1173.32	−	314.390i	−1.48898	−	0.398972i
$789$	335.325	+	193.600i	0.424999	+	0.245374i
$790$	−465.370	+	1191.39i	−0.589076	+	1.50809i
$791$	−79.4945	−	393.374i	−0.100499	−	0.497313i
$792$	−114.270	−	114.270i	−0.144280	−	0.144280i
$793$	−0.0149422	−	0.0557649i	−1.88426e−5	−	7.03215e-5i
$794$	849.939	−	490.712i	1.07045	−	0.618026i
$795$	32.6156	−	44.3421i	0.0410259	−	0.0557762i
$796$	−1532.04	+	2653.57i	−1.92467	+	3.33363i
$797$	174.158	+	174.158i	0.218516	+	0.218516i	0.807873	−	0.589357i	$-0.200619\pi$
$797$	174.158	+	174.158i	0.218516	+	0.218516i	−0.589357	+	0.807873i	$0.700619\pi$
$798$	99.0749	−	49.2344i	0.124154	−	0.0616972i
$799$		−	1115.63i		−	1.39629i
$800$	594.163	−	1133.04i	0.742704	−	1.41631i
$801$	−206.329	−	357.373i	−0.257589	−	0.446158i
$802$	−629.538	+	2349.47i	−0.784960	+	2.92951i
$803$	−11.2693	−	42.0578i	−0.0140341	−	0.0523758i
$804$		−	582.522i		−	0.724529i
$805$	434.333	−	935.200i	0.539544	−	1.16174i
$806$	−402.853			−0.499817
$807$	368.638	−	98.7763i	0.456800	−	0.122399i
$808$	3652.69	+	978.735i	4.52066	+	1.21131i
$809$	−394.796	+	227.936i	−0.488005	+	0.281750i	−0.723746	−	0.690066i	$-0.757582\pi$
$809$	−394.796	+	227.936i	−0.488005	+	0.281750i	0.235741	+	0.971816i	$0.424248\pi$
$810$	−396.395	+	317.162i	−0.489377	+	0.391558i
$811$	−509.754			−0.628550			−0.314275	−	0.949332i	$-0.601761\pi$
$811$	−509.754			−0.628550			−0.314275	+	0.949332i	$0.601761\pi$
$812$	−752.454	−	47.0150i	−0.926667	−	0.0579002i
$813$	367.022	−	367.022i	0.451441	−	0.451441i
$814$	−143.000	−	82.5612i	−0.175676	−	0.101427i
$815$	−53.4047	+	8.13759i	−0.0655272	+	0.00998477i
$816$	426.027	+	737.901i	0.522092	+	0.904291i
$817$	75.1272	−	20.1303i	0.0919549	−	0.0246392i
$818$	650.365	−	650.365i	0.795067	−	0.795067i
$819$	−53.6862	+	159.753i	−0.0655509	+	0.195058i
$820$	−1128.15	−	2574.41i	−1.37579	−	3.13952i
$821$	−534.939	+	926.542i	−0.651571	+	1.12855i	0.331171	+	0.943571i	$0.392556\pi$
$821$	−534.939	+	926.542i	−0.651571	+	1.12855i	−0.982742	+	0.184983i	$0.940777\pi$
$822$	−300.226	+	1120.46i	−0.365239	+	1.36309i
$823$	−429.895	−	115.190i	−0.522351	−	0.139964i	−0.0119972	−	0.999928i	$-0.503819\pi$
$823$	−429.895	−	115.190i	−0.522351	−	0.139964i	−0.510354	+	0.859964i	$0.670486\pi$
$824$	2058.14	+	1188.27i	2.49775	+	1.44208i
$825$	−1.74618	−	42.9581i	−0.00211658	−	0.0520704i
$826$	30.2743	+	149.811i	0.0366517	+	0.181369i
$827$	645.053	+	645.053i	0.779992	+	0.779992i	0.979829	−	0.199837i	$-0.0640414\pi$
$827$	645.053	+	645.053i	0.779992	+	0.779992i	−0.199837	+	0.979829i	$0.564041\pi$
$828$	−495.025	−	1847.46i	−0.597856	−	2.23123i
$829$	30.6402	−	17.6901i	0.0369604	−	0.0213391i	−0.481406	−	0.876498i	$-0.659874\pi$
$829$	30.6402	−	17.6901i	0.0369604	−	0.0213391i	0.518366	+	0.855159i	$0.326540\pi$
$830$	−1321.25	−	971.836i	−1.59186	−	1.17089i
$831$	−67.8003	+	117.434i	−0.0815888	+	0.141316i
$832$	−110.563	−	110.563i	−0.132889	−	0.132889i
$833$	−787.957	+	108.628i	−0.945927	+	0.130406i
$834$		−	911.125i		−	1.09248i
$835$	−445.968	+	356.826i	−0.534093	+	0.427336i
$836$	−16.3422	−	28.3055i	−0.0195481	−	0.0338583i
$837$	−187.819	+	700.950i	−0.224396	+	0.837455i
$838$	185.807	+	693.443i	0.221727	+	0.827497i
$839$			1257.73i			1.49908i	0.661957	+	0.749541i	$0.269726\pi$
$839$			1257.73i			1.49908i	−0.661957	+	0.749541i	$0.730274\pi$
$840$	−1014.42	−	177.254i	−1.20764	−	0.211016i
$841$	711.707			0.846263
$842$	477.447	−	127.932i	0.567039	−	0.151938i
$843$	−19.9426	−	5.34360i	−0.0236567	−	0.00633878i
$844$	−265.367	+	153.210i	−0.314416	+	0.181528i
$845$	778.519	+	86.4465i	0.921324	+	0.102304i
$846$	1728.95			2.04368
$847$	−372.640	−	749.867i	−0.439952	−	0.885321i
$848$	−190.402	+	190.402i	−0.224530	+	0.224530i
$849$	−518.119	−	299.136i	−0.610269	−	0.352339i
$850$	326.766	−	1453.25i	0.384430	−	1.70971i
$851$	−564.500	−	977.743i	−0.663338	−	1.14893i
$852$	210.737	−	56.4668i	0.247344	−	0.0662756i
$853$	703.443	−	703.443i	0.824669	−	0.824669i	−0.162105	−	0.986774i	$-0.551828\pi$
$853$	703.443	−	703.443i	0.824669	−	0.824669i	0.986774	+	0.162105i	$0.0518282\pi$
$854$	0.279387	+	0.316627i	0.000327151	+	0.000370758i
$855$	−92.2619	+	40.4307i	−0.107909	+	0.0472874i
$856$	468.957	−	812.258i	0.547847	−	0.948899i
$857$	−14.5141	+	54.1673i	−0.0169359	+	0.0632057i	−0.973877	−	0.227078i	$-0.927083\pi$
$857$	−14.5141	+	54.1673i	−0.0169359	+	0.0632057i	0.956941	+	0.290283i	$0.0937495\pi$
$858$	−21.4174	−	5.73877i	−0.0249620	−	0.00668855i
$859$	1435.21	+	828.621i	1.67080	+	0.964635i	0.967193	+	0.254042i	$0.0817601\pi$
$859$	1435.21	+	828.621i	1.67080	+	0.964635i	0.703603	+	0.710593i	$0.251573\pi$
$860$	−1167.28	−	455.951i	−1.35730	−	0.530176i
$861$	−456.340	+	402.667i	−0.530011	+	0.467674i
$862$	1344.80	+	1344.80i	1.56009	+	1.56009i
$863$	67.3640	+	251.406i	0.0780580	+	0.291316i	0.993909	−	0.110201i	$-0.0351495\pi$
$863$	67.3640	+	251.406i	0.0780580	+	0.291316i	−0.915851	+	0.401518i	$0.868483\pi$
$864$	−1029.31	+	594.275i	−1.19134	+	0.687818i
$865$	1117.17	−	170.230i	1.29153	−	0.196798i
$866$	961.764	−	1665.82i	1.11058	−	1.92358i
$867$	−26.4092	−	26.4092i	−0.0304605	−	0.0304605i
$868$	1855.24	−	921.947i	2.13738	−	1.06215i
$869$		−	81.8178i		−	0.0941516i
$870$	−303.830	−	33.7372i	−0.349230	−	0.0387784i
$871$	73.7336	+	127.710i	0.0846540	+	0.146625i
$872$	−174.945	+	652.905i	−0.200626	+	0.748745i
$873$	−129.899	−	484.791i	−0.148796	−	0.555316i
$874$		−	317.848i		−	0.363670i
$875$	531.651	+	694.962i	0.607601	+	0.794242i
$876$	−514.658			−0.587509
$877$	−1455.89	+	390.105i	−1.66008	+	0.444817i	−0.962410	−	0.271601i	$-0.912447\pi$
$877$	−1455.89	+	390.105i	−1.66008	+	0.444817i	−0.697671	+	0.716418i	$0.745780\pi$
$878$	−528.999	−	141.745i	−0.602504	−	0.161440i
$879$	489.717	−	282.738i	0.557129	−	0.321659i
$880$	−23.2105	+	209.029i	−0.0263756	+	0.237533i
$881$	−87.7715			−0.0996272			−0.0498136	−	0.998759i	$-0.515863\pi$
$881$	−87.7715			−0.0996272			−0.0498136	+	0.998759i	$0.515863\pi$
$882$	−168.347	−	1221.14i	−0.190870	−	1.38451i
$883$	−472.621	+	472.621i	−0.535245	+	0.535245i	−0.922129	−	0.386884i	$-0.873551\pi$
$883$	−472.621	+	472.621i	−0.535245	+	0.535245i	0.386884	+	0.922129i	$0.373551\pi$
$884$	−467.746	−	270.053i	−0.529124	−	0.305490i
$885$	6.56360	+	43.0751i	0.00741650	+	0.0486724i
$886$	−1114.76	−	1930.83i	−1.25820	−	2.17926i
$887$	−1156.57	+	309.901i	−1.30391	+	0.349381i	−0.842927	−	0.538028i	$-0.819169\pi$
$887$	−1156.57	+	309.901i	−1.30391	+	0.349381i	−0.460982	+	0.887409i	$0.652503\pi$
$888$	−797.280	+	797.280i	−0.897838	+	0.897838i
$889$	−295.095	+	59.6339i	−0.331941	+	0.0670798i
$890$	−402.017	+	1029.20i	−0.451704	+	1.15641i
$891$	16.2369	−	28.1231i	0.0182232	−	0.0315636i
$892$	631.949	−	2358.47i	0.708463	−	2.64402i
$893$	195.131	+	52.2851i	0.218511	+	0.0585499i
$894$	695.537	+	401.569i	0.778006	+	0.449182i
$895$	439.773	+	1003.55i	0.491367	+	1.12129i
$896$	−274.181	−	92.1405i	−0.306005	−	0.102835i
$897$	−107.200	−	107.200i	−0.119510	−	0.119510i
$898$	620.492	+	2315.71i	0.690971	+	2.57874i
$899$	307.683	−	177.641i	0.342251	−	0.197599i
$900$	1583.48	+	356.048i	1.75942	+	0.395609i
$901$	−60.9953	+	105.647i	−0.0676974	+	0.117255i
$902$	180.824	+	180.824i	0.200470	+	0.200470i
$903$	−16.9210	+	270.813i	−0.0187386	+	0.299903i
$904$			1151.49i			1.27377i
$905$	−160.939	+	1449.38i	−0.177833	+	1.60153i
$906$	410.344	+	710.737i	0.452919	+	0.784478i
$907$	193.173	−	720.930i	0.212980	−	0.794851i	−0.773888	−	0.633322i	$-0.781691\pi$
$907$	193.173	−	720.930i	0.212980	−	0.794851i	0.986868	−	0.161529i	$-0.0516425\pi$
$908$	−512.955	−	1914.38i	−0.564929	−	2.10834i
$909$			1290.48i			1.41966i
$910$	423.808	−	154.995i	0.465723	−	0.170325i
$911$	−929.888			−1.02073			−0.510366	−	0.859957i	$-0.670490\pi$
$911$	−929.888			−1.02073			−0.510366	+	0.859957i	$0.670490\pi$
$912$	−149.029	+	39.9323i	−0.163409	+	0.0437854i
$913$	101.342	+	27.1546i	0.110999	+	0.0297422i
$914$	−331.364	+	191.313i	−0.362543	+	0.209314i
$915$	0.0752089	+	0.0939975i	8.21955e−5	+	0.000102730i
$916$	995.644			1.08695
$917$	176.501	+	355.176i	0.192477	+	0.387323i
$918$	−978.481	+	978.481i	−1.06588	+	1.06588i
$919$	−671.557	−	387.724i	−0.730748	−	0.421897i	0.0879480	−	0.996125i	$-0.471969\pi$
$919$	−671.557	−	387.724i	−0.730748	−	0.421897i	−0.818696	+	0.574228i	$0.805302\pi$
$920$	−1753.00	+	2383.27i	−1.90544	+	2.59052i
$921$	−154.832	−	268.177i	−0.168113	−	0.291181i
$922$	182.281	−	48.8421i	0.197702	−	0.0529741i
$923$	−39.0540	+	39.0540i	−0.0423120	+	0.0423120i
$924$	111.766	−	22.5861i	0.120959	−	0.0244439i
$925$	957.255	−	38.9110i	1.03487	−	0.0420660i
$926$	123.691	−	214.239i	0.133576	−	0.231360i
$927$	−209.905	+	783.375i	−0.226434	+	0.845064i
$928$	562.071	+	150.606i	0.605680	+	0.162291i
$929$	−1303.62	−	752.648i	−1.40326	−	0.810170i	−0.408531	−	0.912745i	$-0.633959\pi$
$929$	−1303.62	−	752.648i	−1.40326	−	0.810170i	−0.994725	+	0.102575i	$0.967292\pi$
$930$	769.391	−	337.160i	0.827302	−	0.362538i
$931$	17.9286	−	142.909i	0.0192573	−	0.153501i
$932$	−342.588	−	342.588i	−0.367583	−	0.367583i
$933$	−46.1135	−	172.098i	−0.0494250	−	0.184457i
$934$	−642.667	+	371.044i	−0.688081	+	0.397263i
$935$	14.3529	+	94.1943i	0.0153507	+	0.100743i
$936$	241.778	−	418.771i	0.258309	−	0.447405i
$937$	422.890	+	422.890i	0.451323	+	0.451323i	0.895793	−	0.444471i	$-0.146608\pi$
$937$	422.890	+	422.890i	0.451323	+	0.451323i	−0.444471	+	0.895793i	$0.646608\pi$
$938$	−898.657	−	596.508i	−0.958056	−	0.635936i
$939$			282.411i			0.300757i
$940$	−2033.50	−	2541.51i	−2.16330	−	2.70373i
$941$	402.993	+	698.004i	0.428260	+	0.741768i	0.996719	−	0.0809436i	$-0.0257934\pi$
$941$	402.993	+	698.004i	0.428260	+	0.741768i	−0.568459	+	0.822712i	$0.692460\pi$
$942$	192.556	−	718.628i	0.204412	−	0.762875i
$943$	452.538	+	1688.89i	0.479892	+	1.79098i
$944$		−	213.145i		−	0.225789i
$945$	−72.0981	−	809.673i	−0.0762943	−	0.856797i
$946$	114.014			0.120522
$947$	128.621	−	34.4640i	0.135820	−	0.0363928i	−0.190269	−	0.981732i	$-0.560936\pi$
$947$	128.621	−	34.4640i	0.135820	−	0.0363928i	0.326089	+	0.945339i	$0.394269\pi$
$948$	−934.131	−	250.300i	−0.985370	−	0.264029i
$949$	112.832	−	65.1437i	0.118896	−	0.0686446i
$950$	238.868	+	125.261i	0.251440	+	0.131854i
$951$	806.683			0.848247
$952$	2277.76	+	142.319i	2.39260	+	0.149495i
$953$	25.9574	−	25.9574i	0.0272376	−	0.0272376i	−0.693357	−	0.720594i	$-0.743869\pi$
$953$	25.9574	−	25.9574i	0.0272376	−	0.0272376i	0.720594	+	0.693357i	$0.243869\pi$
$954$	−163.727	−	94.5277i	−0.171621	−	0.0990856i
$955$	444.493	+	326.945i	0.465438	+	0.342351i
$956$	276.723	+	479.298i	0.289459	+	0.501358i
$957$	18.8883	−	5.06112i	0.0197370	−	0.00528852i
$958$	−1678.69	+	1678.69i	−1.75228	+	1.75228i
$959$	999.158	+	1132.34i	1.04187	+	1.18075i
$960$	303.695	+	118.626i	0.316349	+	0.123569i
$961$	−7.63849	+	13.2303i	−0.00794848	+	0.0137672i
$962$	127.880	−	477.254i	0.132931	−	0.496106i
$963$	309.163	+	82.8400i	0.321042	+	0.0860228i
$964$	−1694.82	−	978.507i	−1.75812	−	1.01505i
$965$	651.869	−	1668.85i	0.675512	−	1.72937i
$966$	1051.11	+	353.232i	1.08810	+	0.365665i
$967$	−478.254	−	478.254i	−0.494575	−	0.494575i	0.415169	−	0.909744i	$-0.363722\pi$
$967$	−478.254	−	478.254i	−0.494575	−	0.494575i	−0.909744	+	0.415169i	$0.863722\pi$
$968$	621.824	+	2320.68i	0.642380	+	2.39740i
$969$	−60.5340	+	34.9493i	−0.0624706	+	0.0360674i
$970$	−796.268	+	1082.55i	−0.820894	+	1.11604i
$971$	103.956	−	180.057i	0.107061	−	0.185435i	−0.807517	−	0.589844i	$-0.799189\pi$
$971$	103.956	−	180.057i	0.107061	−	0.185435i	0.914578	+	0.404409i	$0.132523\pi$
$972$	−1671.41	−	1671.41i	−1.71955	−	1.71955i
$973$	−988.255	−	655.982i	−1.01568	−	0.674185i
$974$		−	1903.98i		−	1.95480i
$975$	122.810	−	38.3161i	0.125959	−	0.0392985i
$976$	−0.294440	−	0.509986i	−0.000301681	−	0.000522526i
$977$	115.300	−	430.304i	0.118014	−	0.440434i	−0.881481	−	0.472220i	$-0.843453\pi$
$977$	115.300	−	430.304i	0.118014	−	0.440434i	0.999495	+	0.0317858i	$0.0101194\pi$
$978$	−15.0357	−	56.1142i	−0.0153740	−	0.0573764i
$979$		−	70.6795i		−	0.0721956i
$980$	−1597.03	+	1683.70i	−1.62963	+	1.71806i
$981$	−230.668			−0.235135
$982$	−504.794	+	135.259i	−0.514047	+	0.137739i
$983$	−131.962	−	35.3591i	−0.134244	−	0.0359706i	0.191071	−	0.981576i	$-0.438804\pi$
$983$	−131.962	−	35.3591i	−0.134244	−	0.0359706i	−0.325315	+	0.945606i	$0.605471\pi$
$984$	1512.24	−	873.093i	1.53683	−	0.887289i
$985$	−500.674	+	400.597i	−0.508298	+	0.406697i
$986$	677.481			0.687101
$987$	−389.757	+	587.181i	−0.394891	+	0.594915i
$988$	69.1552	−	69.1552i	0.0699952	−	0.0699952i
$989$	675.114	+	389.777i	0.682623	+	0.394112i
$990$	−145.978	+	22.2435i	−0.147452	+	0.0224682i
$991$	160.541	+	278.066i	0.161999	+	0.280591i	0.935586	−	0.353100i	$-0.114872\pi$
$991$	160.541	+	278.066i	0.161999	+	0.280591i	−0.773586	+	0.633691i	$0.781539\pi$
$992$	−1544.51	+	413.850i	−1.55697	+	0.417188i
$993$	644.943	−	644.943i	0.649490	−	0.649490i
$994$	128.685	−	382.927i	0.129462	−	0.385238i
$995$	649.194	+	1481.44i	0.652456	+	1.48889i
$996$	620.059	−	1073.97i	0.622550	−	1.07829i
$997$	9.33806	−	34.8501i	0.00936616	−	0.0349550i	−0.961085	−	0.276254i	$-0.910907\pi$
$997$	9.33806	−	34.8501i	0.00936616	−	0.0349550i	0.970451	+	0.241299i	$0.0775735\pi$
$998$	3468.21	+	929.305i	3.47516	+	0.931167i
$999$	−770.786	−	445.013i	−0.771557	−	0.445459i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.3.l.a.2.1	✓	24
3.2	odd	2		315.3.ca.a.37.6		24
5.2	odd	4		175.3.p.c.93.1		24
5.3	odd	4	inner	35.3.l.a.23.6	yes	24
5.4	even	2		175.3.p.c.107.6		24
7.2	even	3		245.3.g.c.197.6		12
7.3	odd	6		245.3.m.b.67.6		24
7.4	even	3	inner	35.3.l.a.32.6	yes	24
7.5	odd	6		245.3.g.b.197.6		12
7.6	odd	2		245.3.m.b.177.1		24
15.8	even	4		315.3.ca.a.163.1		24
21.11	odd	6		315.3.ca.a.172.1		24
35.3	even	12		245.3.m.b.18.1		24
35.4	even	6		175.3.p.c.32.1		24
35.13	even	4		245.3.m.b.128.6		24
35.18	odd	12	inner	35.3.l.a.18.1	yes	24
35.23	odd	12		245.3.g.c.148.6		12
35.32	odd	12		175.3.p.c.18.6		24
35.33	even	12		245.3.g.b.148.6		12
105.53	even	12		315.3.ca.a.298.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.3.l.a.2.1	✓	24	1.1	even	1	trivial
35.3.l.a.18.1	yes	24	35.18	odd	12	inner
35.3.l.a.23.6	yes	24	5.3	odd	4	inner
35.3.l.a.32.6	yes	24	7.4	even	3	inner
175.3.p.c.18.6		24	35.32	odd	12
175.3.p.c.32.1		24	35.4	even	6
175.3.p.c.93.1		24	5.2	odd	4
175.3.p.c.107.6		24	5.4	even	2
245.3.g.b.148.6		12	35.33	even	12
245.3.g.b.197.6		12	7.5	odd	6
245.3.g.c.148.6		12	35.23	odd	12
245.3.g.c.197.6		12	7.2	even	3
245.3.m.b.18.1		24	35.3	even	12
245.3.m.b.67.6		24	7.3	odd	6
245.3.m.b.128.6		24	35.13	even	4
245.3.m.b.177.1		24	7.6	odd	2
315.3.ca.a.37.6		24	3.2	odd	2
315.3.ca.a.163.1		24	15.8	even	4
315.3.ca.a.172.1		24	21.11	odd	6
315.3.ca.a.298.6		24	105.53	even	12

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:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	35.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.54535 + 0.949975i) q^{2} +(-1.41502 - 0.379154i) q^{3} +(8.20298 - 4.73599i) q^{4} +(0.551807 - 4.96946i) q^{5} +5.37694 q^{6} +(3.87123 - 5.83212i) q^{7} +(-14.2019 + 14.2019i) q^{8} +(-5.93570 - 3.42698i) q^{9} +O(q^{10})\)	\(q+(-3.54535 + 0.949975i) q^{2} +(-1.41502 - 0.379154i) q^{3} +(8.20298 - 4.73599i) q^{4} +(0.551807 - 4.96946i) q^{5} +5.37694 q^{6} +(3.87123 - 5.83212i) q^{7} +(-14.2019 + 14.2019i) q^{8} +(-5.93570 - 3.42698i) q^{9} +(2.76451 + 18.1427i) q^{10} +(-0.586967 - 1.01666i) q^{11} +(-13.4031 + 3.59134i) q^{12} +(2.48387 - 2.48387i) q^{13} +(-8.18451 + 24.3545i) q^{14} +(-2.66501 + 6.82267i) q^{15} +(17.9153 - 31.0302i) q^{16} +(4.20137 - 15.6797i) q^{17} +(24.2997 + 6.51109i) q^{18} +(2.54557 + 1.46969i) q^{19} +(-19.0089 - 43.3777i) q^{20} +(-7.68914 + 6.78478i) q^{21} +(3.04681 + 3.04681i) q^{22} +(7.62508 + 28.4572i) q^{23} +(25.4807 - 14.7113i) q^{24} +(-24.3910 - 5.48436i) q^{25} +(-6.44658 + 11.1658i) q^{26} +(16.4226 + 16.4226i) q^{27} +(4.13475 - 66.1749i) q^{28} -11.3707i q^{29} +(2.96703 - 26.7205i) q^{30} +(15.6227 + 27.0593i) q^{31} +(-13.2451 + 49.4315i) q^{32} +(0.445102 + 1.66114i) q^{33} +59.5814i q^{34} +(-26.8463 - 22.4561i) q^{35} -64.9206 q^{36} +(-37.0160 + 9.91842i) q^{37} +(-10.4211 - 2.79233i) q^{38} +(-4.45650 + 2.57296i) q^{39} +(62.7389 + 78.4123i) q^{40} +59.3486 q^{41} +(20.8154 - 31.3589i) q^{42} +(18.7104 - 18.7104i) q^{43} +(-9.62976 - 5.55975i) q^{44} +(-20.3056 + 27.6062i) q^{45} +(-54.0672 - 93.6472i) q^{46} +(66.3850 - 17.7878i) q^{47} +(-37.1157 + 37.1157i) q^{48} +(-19.0272 - 45.1549i) q^{49} +(91.6848 - 3.72685i) q^{50} +(-11.8901 + 20.5942i) q^{51} +(8.61155 - 32.1387i) q^{52} +(-7.25898 - 1.94504i) q^{53} +(-73.8250 - 42.6229i) q^{54} +(-5.37613 + 2.35591i) q^{55} +(27.8483 + 137.806i) q^{56} +(-3.04480 - 3.04480i) q^{57} +(10.8019 + 40.3131i) q^{58} +(5.15171 - 2.97434i) q^{59} +(10.4511 + 68.5877i) q^{60} +(0.00821757 - 0.0142333i) q^{61} +(-81.0937 - 81.0937i) q^{62} +(-42.9650 + 21.3511i) q^{63} -44.5126i q^{64} +(-10.9729 - 13.7141i) q^{65} +(-3.15609 - 5.46650i) q^{66} +(-10.8655 + 40.5504i) q^{67} +(-39.7953 - 148.518i) q^{68} -43.1586i q^{69} +(116.512 + 54.1116i) q^{70} -15.7230 q^{71} +(132.968 - 35.6286i) q^{72} +(35.8263 + 9.59964i) q^{73} +(121.813 - 70.3286i) q^{74} +(32.4344 + 17.0084i) q^{75} +27.8417 q^{76} +(-8.20155 - 0.512451i) q^{77} +(13.3556 - 13.3556i) q^{78} +(60.3579 + 34.8477i) q^{79} +(-144.317 - 106.152i) q^{80} +(13.8312 + 23.9563i) q^{81} +(-210.412 + 56.3797i) q^{82} +(-63.1958 + 63.1958i) q^{83} +(-30.9412 + 92.0711i) q^{84} +(-75.6014 - 29.5307i) q^{85} +(-48.5606 + 84.1094i) q^{86} +(-4.31124 + 16.0898i) q^{87} +(22.7745 + 6.10240i) q^{88} +(52.1411 + 30.1037i) q^{89} +(45.7653 - 117.163i) q^{90} +(-4.87059 - 24.1018i) q^{91} +(197.321 + 197.321i) q^{92} +(-11.8468 - 44.2129i) q^{93} +(-218.460 + 126.128i) q^{94} +(8.70822 - 11.8391i) q^{95} +(37.4843 - 64.9247i) q^{96} +(51.7791 + 51.7791i) q^{97} +(110.354 + 142.015i) q^{98} +8.04610i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} - 2 q^{3} - 4 q^{5} - 6 q^{7} - 36 q^{8}+O(q^{10}) \) 24 * q - 2 * q^2 - 2 * q^3 - 4 * q^5 - 6 * q^7 - 36 * q^8	\( 24 q - 2 q^{2} - 2 q^{3} - 4 q^{5} - 6 q^{7} - 36 q^{8} + 14 q^{10} - 24 q^{11} - 46 q^{12} - 8 q^{13} + 52 q^{15} + 20 q^{16} - 48 q^{17} - 4 q^{18} - 72 q^{20} + 56 q^{21} + 104 q^{22} - 86 q^{23} - 16 q^{25} + 140 q^{26} + 76 q^{27} + 186 q^{28} + 64 q^{30} + 120 q^{31} + 130 q^{32} + 116 q^{33} - 240 q^{35} - 496 q^{36} + 44 q^{37} + 16 q^{38} - 158 q^{40} + 16 q^{41} - 370 q^{42} - 196 q^{43} - 104 q^{45} - 148 q^{46} - 208 q^{47} - 52 q^{48} + 580 q^{50} - 160 q^{51} - 288 q^{52} - 72 q^{53} + 208 q^{55} + 420 q^{56} + 656 q^{57} - 2 q^{58} + 262 q^{60} + 308 q^{61} + 176 q^{62} + 212 q^{63} + 132 q^{65} + 316 q^{66} + 198 q^{67} + 332 q^{68} - 200 q^{70} - 792 q^{71} + 308 q^{72} + 380 q^{73} - 450 q^{75} - 400 q^{76} - 472 q^{77} - 720 q^{78} - 324 q^{80} - 352 q^{81} - 818 q^{82} - 460 q^{83} + 144 q^{85} - 336 q^{86} - 214 q^{87} - 288 q^{88} + 120 q^{90} + 984 q^{91} + 1372 q^{92} - 68 q^{93} - 88 q^{95} + 816 q^{96} - 72 q^{97} + 482 q^{98}+O(q^{100}) \) 24 * q - 2 * q^2 - 2 * q^3 - 4 * q^5 - 6 * q^7 - 36 * q^8 + 14 * q^10 - 24 * q^11 - 46 * q^12 - 8 * q^13 + 52 * q^15 + 20 * q^16 - 48 * q^17 - 4 * q^18 - 72 * q^20 + 56 * q^21 + 104 * q^22 - 86 * q^23 - 16 * q^25 + 140 * q^26 + 76 * q^27 + 186 * q^28 + 64 * q^30 + 120 * q^31 + 130 * q^32 + 116 * q^33 - 240 * q^35 - 496 * q^36 + 44 * q^37 + 16 * q^38 - 158 * q^40 + 16 * q^41 - 370 * q^42 - 196 * q^43 - 104 * q^45 - 148 * q^46 - 208 * q^47 - 52 * q^48 + 580 * q^50 - 160 * q^51 - 288 * q^52 - 72 * q^53 + 208 * q^55 + 420 * q^56 + 656 * q^57 - 2 * q^58 + 262 * q^60 + 308 * q^61 + 176 * q^62 + 212 * q^63 + 132 * q^65 + 316 * q^66 + 198 * q^67 + 332 * q^68 - 200 * q^70 - 792 * q^71 + 308 * q^72 + 380 * q^73 - 450 * q^75 - 400 * q^76 - 472 * q^77 - 720 * q^78 - 324 * q^80 - 352 * q^81 - 818 * q^82 - 460 * q^83 + 144 * q^85 - 336 * q^86 - 214 * q^87 - 288 * q^88 + 120 * q^90 + 984 * q^91 + 1372 * q^92 - 68 * q^93 - 88 * q^95 + 816 * q^96 - 72 * q^97 + 482 * q^98

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