LMFDB - Embedded newform 35.3.l.a.23.4

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			23.4
Character	$\chi$	$=$	35.23
Dual form			35.3.l.a.32.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.330037 + 1.23172i) q^{2} +(1.07605 - 4.01589i) q^{3} +(2.05590 - 1.18698i) q^{4} +(-3.17921 + 3.85910i) q^{5} +5.30157 q^{6} +(-5.79445 + 3.92739i) q^{7} +(5.74725 + 5.74725i) q^{8} +(-7.17525 - 4.14263i) q^{9} +O(q^{10})$	\(q+(0.330037 + 1.23172i) q^{2} +(1.07605 - 4.01589i) q^{3} +(2.05590 - 1.18698i) q^{4} +(-3.17921 + 3.85910i) q^{5} +5.30157 q^{6} +(-5.79445 + 3.92739i) q^{7} +(5.74725 + 5.74725i) q^{8} +(-7.17525 - 4.14263i) q^{9} +(-5.80257 - 2.64224i) q^{10} +(2.98240 + 5.16566i) q^{11} +(-2.55450 - 9.53353i) q^{12} +(-15.4106 - 15.4106i) q^{13} +(-6.74980 - 5.84093i) q^{14} +(12.0767 + 16.9200i) q^{15} +(-0.434268 + 0.752174i) q^{16} +(0.846962 + 0.226943i) q^{17} +(2.73444 - 10.2051i) q^{18} +(18.0198 + 10.4038i) q^{19} +(-1.95549 + 11.7076i) q^{20} +(9.53681 + 27.4959i) q^{21} +(-5.37832 + 5.37832i) q^{22} +(-11.6614 + 3.12465i) q^{23} +(29.2647 - 16.8960i) q^{24} +(-4.78525 - 24.5378i) q^{25} +(13.8954 - 24.0675i) q^{26} +(2.10122 - 2.10122i) q^{27} +(-7.25111 + 14.9522i) q^{28} -7.52964i q^{29} +(-16.8548 + 20.4593i) q^{30} +(-9.90283 - 17.1522i) q^{31} +(30.3338 + 8.12792i) q^{32} +(23.9539 - 6.41844i) q^{33} +1.11811i q^{34} +(3.26561 - 34.8473i) q^{35} -19.6688 q^{36} +(-3.59463 - 13.4154i) q^{37} +(-6.86725 + 25.6289i) q^{38} +(-78.4697 + 45.3045i) q^{39} +(-40.4509 + 3.90748i) q^{40} +12.0569 q^{41} +(-30.7197 + 20.8213i) q^{42} +(12.3503 + 12.3503i) q^{43} +(12.2630 + 7.08007i) q^{44} +(38.7984 - 14.5197i) q^{45} +(-7.69736 - 13.3322i) q^{46} +(11.7711 + 43.9302i) q^{47} +(2.55335 + 2.55335i) q^{48} +(18.1513 - 45.5141i) q^{49} +(28.6442 - 13.9924i) q^{50} +(1.82275 - 3.15710i) q^{51} +(-49.9746 - 13.3907i) q^{52} +(2.62121 - 9.78248i) q^{53} +(3.28158 + 1.89462i) q^{54} +(-29.4164 - 4.91337i) q^{55} +(-55.8739 - 10.7305i) q^{56} +(61.1707 - 61.1707i) q^{57} +(9.27437 - 2.48506i) q^{58} +(-18.2765 + 10.5519i) q^{59} +(44.9121 + 20.4510i) q^{60} +(-15.1204 + 26.1893i) q^{61} +(17.8583 - 17.8583i) q^{62} +(57.8463 - 4.17570i) q^{63} +43.5193i q^{64} +(108.464 - 10.4774i) q^{65} +(15.8114 + 27.3861i) q^{66} +(69.6836 + 18.6717i) q^{67} +(2.01065 - 0.538751i) q^{68} +50.1930i q^{69} +(43.9998 - 7.47861i) q^{70} -128.667 q^{71} +(-17.4292 - 65.0467i) q^{72} +(-19.4392 + 72.5481i) q^{73} +(15.3375 - 8.85513i) q^{74} +(-103.690 - 7.18694i) q^{75} +49.3961 q^{76} +(-37.5689 - 18.2191i) q^{77} +(-81.7002 - 81.7002i) q^{78} +(14.8579 + 8.57820i) q^{79} +(-1.52208 - 4.06720i) q^{80} +(-43.4609 - 75.2765i) q^{81} +(3.97924 + 14.8507i) q^{82} +(4.42198 + 4.42198i) q^{83} +(52.2438 + 45.2091i) q^{84} +(-3.56846 + 2.54701i) q^{85} +(-11.1360 + 19.2881i) q^{86} +(-30.2382 - 8.10230i) q^{87} +(-12.5478 + 46.8289i) q^{88} +(-94.1599 - 54.3633i) q^{89} +(30.6890 + 42.9966i) q^{90} +(149.819 + 28.7725i) q^{91} +(-20.2657 + 20.2657i) q^{92} +(-79.5373 + 21.3120i) q^{93} +(-50.2247 + 28.9972i) q^{94} +(-97.4379 + 36.4645i) q^{95} +(65.2816 - 113.071i) q^{96} +(-55.4317 + 55.4317i) q^{97} +(62.0510 + 7.33588i) q^{98} -49.4198i 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 $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.330037	+	1.23172i	0.165019	+	0.615858i	0.998038	+	0.0626137i	$0.0199436\pi$
$2$	0.330037	+	1.23172i	0.165019	+	0.615858i	−0.833019	+	0.553244i	$0.813390\pi$
$3$	1.07605	−	4.01589i	0.358685	−	1.33863i	−0.517099	−	0.855926i	$-0.672988\pi$
$3$	1.07605	−	4.01589i	0.358685	−	1.33863i	0.875784	−	0.482704i	$-0.160345\pi$
$4$	2.05590	−	1.18698i	0.513976	−	0.296744i
$5$	−3.17921	+	3.85910i	−0.635842	+	0.771819i
$5$	−3.17921	+	3.85910i	−0.635842	+	0.771819i
$6$	5.30157			0.883595
$7$	−5.79445	+	3.92739i	−0.827778	+	0.561055i
$7$	−5.79445	+	3.92739i	−0.827778	+	0.561055i
$8$	5.74725	+	5.74725i	0.718407	+	0.718407i
$9$	−7.17525	−	4.14263i	−0.797250	−	0.460292i
$10$	−5.80257	−	2.64224i	−0.580257	−	0.264224i
$11$	2.98240	+	5.16566i	0.271127	+	0.469605i	0.969151	−	0.246469i	$-0.0792704\pi$
$11$	2.98240	+	5.16566i	0.271127	+	0.469605i	−0.698024	+	0.716075i	$0.745937\pi$
$12$	−2.55450	−	9.53353i	−0.212875	−	0.794461i
$13$	−15.4106	−	15.4106i	−1.18543	−	1.18543i	−0.978318	−	0.207110i	$-0.933594\pi$
$13$	−15.4106	−	15.4106i	−1.18543	−	1.18543i	−0.207110	−	0.978318i	$-0.566406\pi$
$14$	−6.74980	−	5.84093i	−0.482129	−	0.417209i
$15$	12.0767	+	16.9200i	0.805113	+	1.12800i
$16$	−0.434268	+	0.752174i	−0.0271418	+	0.0470109i
$17$	0.846962	+	0.226943i	0.0498213	+	0.0133496i	0.283644	−	0.958930i	$-0.408457\pi$
$17$	0.846962	+	0.226943i	0.0498213	+	0.0133496i	−0.233822	+	0.972279i	$0.575123\pi$
$18$	2.73444	−	10.2051i	0.151914	−	0.566949i
$19$	18.0198	+	10.4038i	0.948412	+	0.547566i	0.892587	−	0.450874i	$-0.148888\pi$
$19$	18.0198	+	10.4038i	0.948412	+	0.547566i	0.0558250	+	0.998441i	$0.482221\pi$
$20$	−1.95549	+	11.7076i	−0.0977747	+	0.585379i
$21$	9.53681	+	27.4959i	0.454134	+	1.30933i
$22$	−5.37832	+	5.37832i	−0.244469	+	0.244469i
$23$	−11.6614	+	3.12465i	−0.507015	+	0.135854i	−0.503254	−	0.864139i	$-0.667864\pi$
$23$	−11.6614	+	3.12465i	−0.507015	+	0.135854i	−0.00376143	+	0.999993i	$0.501197\pi$
$24$	29.2647	−	16.8960i	1.21936	−	0.703999i
$25$	−4.78525	−	24.5378i	−0.191410	−	0.981510i
$26$	13.8954	−	24.0675i	0.534437	−	0.925672i
$27$	2.10122	−	2.10122i	0.0778228	−	0.0778228i
$28$	−7.25111	+	14.9522i	−0.258968	+	0.534007i
$29$		−	7.52964i		−	0.259643i	−0.991537	−	0.129821i	$-0.958560\pi$
$29$		−	7.52964i		−	0.259643i	0.991537	−	0.129821i	$-0.0414404\pi$
$30$	−16.8548	+	20.4593i	−0.561827	+	0.681976i
$31$	−9.90283	−	17.1522i	−0.319446	−	0.553297i	0.660926	−	0.750451i	$-0.270164\pi$
$31$	−9.90283	−	17.1522i	−0.319446	−	0.553297i	−0.980373	+	0.197154i	$0.936830\pi$
$32$	30.3338	+	8.12792i	0.947931	+	0.253997i
$33$	23.9539	−	6.41844i	0.725877	−	0.194498i
$34$			1.11811i			0.0328857i
$35$	3.26561	−	34.8473i	0.0933032	−	0.995638i
$36$	−19.6688			−0.546356
$37$	−3.59463	−	13.4154i	−0.0971523	−	0.362577i	0.900185	−	0.435508i	$-0.143431\pi$
$37$	−3.59463	−	13.4154i	−0.0971523	−	0.362577i	−0.997337	+	0.0729310i	$0.976765\pi$
$38$	−6.86725	+	25.6289i	−0.180717	+	0.674446i
$39$	−78.4697	+	45.3045i	−2.01204	+	1.16165i
$40$	−40.4509	+	3.90748i	−1.01127	+	0.0976869i
$41$	12.0569			0.294072			0.147036	−	0.989131i	$-0.453027\pi$
$41$	12.0569			0.294072			0.147036	+	0.989131i	$0.453027\pi$
$42$	−30.7197	+	20.8213i	−0.731421	+	0.495746i
$43$	12.3503	+	12.3503i	0.287215	+	0.287215i	0.835978	−	0.548763i	$-0.184901\pi$
$43$	12.3503	+	12.3503i	0.287215	+	0.287215i	−0.548763	+	0.835978i	$0.684901\pi$
$44$	12.2630	+	7.08007i	0.278705	+	0.160911i
$45$	38.7984	−	14.5197i	0.862187	−	0.322659i
$46$	−7.69736	−	13.3322i	−0.167334	−	0.289831i
$47$	11.7711	+	43.9302i	0.250448	+	0.934686i	0.970566	+	0.240834i	$0.0774210\pi$
$47$	11.7711	+	43.9302i	0.250448	+	0.934686i	−0.720118	+	0.693852i	$0.755912\pi$
$48$	2.55335	+	2.55335i	0.0531949	+	0.0531949i
$49$	18.1513	−	45.5141i	0.370434	−	0.928859i
$50$	28.6442	−	13.9924i	0.572884	−	0.279849i
$51$	1.82275	−	3.15710i	0.0357403	−	0.0619039i
$52$	−49.9746	−	13.3907i	−0.961050	−	0.257513i
$53$	2.62121	−	9.78248i	0.0494567	−	0.184575i	−0.936779	−	0.349923i	$-0.886208\pi$
$53$	2.62121	−	9.78248i	0.0494567	−	0.184575i	0.986235	+	0.165348i	$0.0528746\pi$
$54$	3.28158	+	1.89462i	0.0607700	+	0.0350856i
$55$	−29.4164	−	4.91337i	−0.534844	−	0.0893340i
$56$	−55.8739	−	10.7305i	−0.997747	−	0.191616i
$57$	61.1707	−	61.1707i	1.07317	−	1.07317i
$58$	9.27437	−	2.48506i	0.159903	−	0.0428459i
$59$	−18.2765	+	10.5519i	−0.309771	+	0.178847i	−0.646824	−	0.762639i	$-0.723903\pi$
$59$	−18.2765	+	10.5519i	−0.309771	+	0.178847i	0.337053	+	0.941486i	$0.390570\pi$
$60$	44.9121	+	20.4510i	0.748535	+	0.340851i
$61$	−15.1204	+	26.1893i	−0.247876	+	0.429333i	−0.962936	−	0.269729i	$-0.913066\pi$
$61$	−15.1204	+	26.1893i	−0.247876	+	0.429333i	0.715061	+	0.699062i	$0.246399\pi$
$62$	17.8583	−	17.8583i	0.288038	−	0.288038i
$63$	57.8463	−	4.17570i	0.918195	−	0.0662810i
$64$			43.5193i			0.679988i
$65$	108.464	−	10.4774i	1.66868	−	0.161191i
$66$	15.8114	+	27.3861i	0.239566	+	0.414941i
$67$	69.6836	+	18.6717i	1.04005	+	0.278682i	0.738136	−	0.674652i	$-0.235706\pi$
$67$	69.6836	+	18.6717i	1.04005	+	0.278682i	0.301918	+	0.953334i	$0.402373\pi$
$68$	2.01065	−	0.538751i	0.0295683	−	0.00792281i
$69$			50.1930i			0.727435i
$70$	43.9998	−	7.47861i	0.628568	−	0.106837i
$71$	−128.667			−1.81222			−0.906108	−	0.423047i	$-0.860960\pi$
$71$	−128.667			−1.81222			−0.906108	+	0.423047i	$0.860960\pi$
$72$	−17.4292	−	65.0467i	−0.242072	−	0.903427i
$73$	−19.4392	+	72.5481i	−0.266290	+	0.993810i	0.695165	+	0.718850i	$0.255331\pi$
$73$	−19.4392	+	72.5481i	−0.266290	+	0.993810i	−0.961456	+	0.274960i	$0.911335\pi$
$74$	15.3375	−	8.85513i	0.207264	−	0.119664i
$75$	−103.690	−	7.18694i	−1.38253	−	0.0958259i
$76$	49.3961			0.649948
$77$	−37.5689	−	18.2191i	−0.487907	−	0.236612i
$78$	−81.7002	−	81.7002i	−1.04744	−	1.04744i
$79$	14.8579	+	8.57820i	0.188074	+	0.108585i	0.591081	−	0.806612i	$-0.298701\pi$
$79$	14.8579	+	8.57820i	0.188074	+	0.108585i	−0.403006	+	0.915197i	$0.632035\pi$
$80$	−1.52208	−	4.06720i	−0.0190260	−	0.0508400i
$81$	−43.4609	−	75.2765i	−0.536554	−	0.929339i
$82$	3.97924	+	14.8507i	0.0485273	+	0.181106i
$83$	4.42198	+	4.42198i	0.0532769	+	0.0532769i	0.733243	−	0.679966i	$-0.238006\pi$
$83$	4.42198	+	4.42198i	0.0532769	+	0.0532769i	−0.679966	+	0.733243i	$0.738006\pi$
$84$	52.2438	+	45.2091i	0.621950	+	0.538203i
$85$	−3.56846	+	2.54701i	−0.0419819	+	0.0299648i
$86$	−11.1360	+	19.2881i	−0.129488	+	0.224280i
$87$	−30.2382	−	8.10230i	−0.347565	−	0.0931299i
$88$	−12.5478	+	46.8289i	−0.142588	+	0.532147i
$89$	−94.1599	−	54.3633i	−1.05798	−	0.610823i	−0.133105	−	0.991102i	$-0.542495\pi$
$89$	−94.1599	−	54.3633i	−1.05798	−	0.610823i	−0.924872	+	0.380279i	$0.875828\pi$
$90$	30.6890	+	42.9966i	0.340989	+	0.477740i
$91$	149.819	+	28.7725i	1.64636	+	0.316181i
$92$	−20.2657	+	20.2657i	−0.220280	+	0.220280i
$93$	−79.5373	+	21.3120i	−0.855240	+	0.229161i
$94$	−50.2247	+	28.9972i	−0.534305	+	0.308481i
$95$	−97.4379	+	36.4645i	−1.02566	+	0.383837i
$96$	65.2816	−	113.071i	0.680017	−	1.17782i
$97$	−55.4317	+	55.4317i	−0.571461	+	0.571461i	−0.932537	−	0.361076i	$-0.882410\pi$
$97$	−55.4317	+	55.4317i	−0.571461	+	0.571461i	0.361076	+	0.932537i	$0.382410\pi$
$98$	62.0510	+	7.33588i	0.633173	+	0.0748559i
$99$		−	49.4198i		−	0.499190i
$100$	−38.9637	−	44.7673i	−0.389637	−	0.447673i
$101$	80.0618	+	138.671i	0.792691	+	1.37298i	0.924295	+	0.381678i	$0.124654\pi$
$101$	80.0618	+	138.671i	0.792691	+	1.37298i	−0.131605	+	0.991302i	$0.542013\pi$
$102$	4.49023	+	1.20315i	0.0440218	+	0.0117956i
$103$	119.986	−	32.1500i	1.16491	−	0.312136i	0.375984	−	0.926626i	$-0.377305\pi$
$103$	119.986	−	32.1500i	1.16491	−	0.312136i	0.788925	+	0.614490i	$0.210638\pi$
$104$		−	177.137i		−	1.70324i
$105$	−136.429	−	50.6119i	−1.29932	−	0.482019i
$106$	12.9143			0.121833
$107$	34.9296	+	130.359i	0.326445	+	1.21831i	0.912852	+	0.408292i	$0.133875\pi$
$107$	34.9296	+	130.359i	0.326445	+	1.21831i	−0.586407	+	0.810017i	$0.699458\pi$
$108$	1.82580	−	6.81399i	0.0169056	−	0.0630925i
$109$	113.564	−	65.5664i	1.04187	−	0.601527i	0.121511	−	0.992590i	$-0.461226\pi$
$109$	113.564	−	65.5664i	1.04187	−	0.601527i	0.920364	+	0.391064i	$0.127893\pi$
$110$	−3.65664	−	37.8543i	−0.0332422	−	0.344130i
$111$	−57.7426			−0.520204
$112$	−0.437735	−	6.06397i	−0.00390835	−	0.0541426i
$113$	−54.8723	−	54.8723i	−0.485596	−	0.485596i	0.421317	−	0.906913i	$-0.361568\pi$
$113$	−54.8723	−	54.8723i	−0.485596	−	0.485596i	−0.906913	+	0.421317i	$0.861568\pi$
$114$	95.5334	+	55.1562i	0.838013	+	0.483827i
$115$	25.0156	−	54.9362i	0.217527	−	0.477706i
$116$	−8.93750	−	15.4802i	−0.0770474	−	0.133450i
$117$	46.7343	+	174.415i	0.399439	+	1.49072i
$118$	−19.0289	−	19.0289i	−0.161262	−	0.161262i
$119$	−5.79897	+	2.01134i	−0.0487308	+	0.0169020i
$120$	−27.8354	+	166.651i	−0.231962	+	1.38876i
$121$	42.7106	−	73.9770i	0.352980	−	0.611380i
$122$	−37.2481	−	9.98059i	−0.305312	−	0.0818081i
$123$	12.9739	−	48.4193i	0.105479	−	0.393653i
$124$	−40.7185	−	23.5088i	−0.328375	−	0.189587i
$125$	109.907	+	59.5440i	0.879255	+	0.476352i
$126$	24.2347	+	69.8720i	0.192339	+	0.554540i
$127$	119.378	−	119.378i	0.939985	−	0.939985i	−0.0583136	−	0.998298i	$-0.518572\pi$
$127$	119.378	−	119.378i	0.939985	−	0.939985i	0.998298	+	0.0583136i	$0.0185723\pi$
$128$	67.7318	−	18.1487i	0.529155	−	0.141787i
$129$	62.8868	−	36.3077i	0.487495	−	0.281455i
$130$	48.7024	+	130.139i	0.374634	+	1.00107i
$131$	−25.8642	+	44.7981i	−0.197437	+	0.341970i	−0.947697	−	0.319173i	$-0.896595\pi$
$131$	−25.8642	+	44.7981i	−0.197437	+	0.341970i	0.750260	+	0.661143i	$0.229928\pi$
$132$	41.6285	−	41.6285i	0.315367	−	0.315367i
$133$	−145.275	+	10.4868i	−1.09229	+	0.0788482i
$134$			91.9927i			0.686513i
$135$	1.42859	+	14.7890i	0.0105821	+	0.109548i
$136$	3.56341	+	6.17200i	0.0262015	+	0.0453824i
$137$	−188.944	−	50.6274i	−1.37915	−	0.369543i	−0.508339	−	0.861157i	$-0.669740\pi$
$137$	−188.944	−	50.6274i	−1.37915	−	0.369543i	−0.870813	+	0.491614i	$0.836407\pi$
$138$	−61.8235	+	16.5656i	−0.447996	+	0.120040i
$139$			127.517i			0.917386i	0.888595	+	0.458693i	$0.151682\pi$
$139$			127.517i			0.917386i	−0.888595	+	0.458693i	$0.848318\pi$
$140$	−34.6492	−	75.5189i	−0.247494	−	0.539421i
$141$	189.085			1.34103
$142$	−42.4650	−	158.481i	−0.299049	−	1.11607i
$143$	33.6453	−	125.566i	0.235282	−	0.878085i
$144$	6.23196	−	3.59802i	0.0432775	−	0.0249863i
$145$	29.0576	+	23.9383i	0.200397	+	0.165092i
$146$	−95.7743			−0.655988
$147$	−163.248	−	121.869i	−1.11053	−	0.829042i
$148$	−23.3139	−	23.3139i	−0.157527	−	0.157527i
$149$	−192.034	−	110.871i	−1.28882	−	0.744100i	−0.310375	−	0.950614i	$-0.600455\pi$
$149$	−192.034	−	110.871i	−1.28882	−	0.744100i	−0.978444	+	0.206514i	$0.933788\pi$
$150$	−25.3693	−	130.089i	−0.169129	−	0.867258i
$151$	33.2375	+	57.5691i	0.220116	+	0.381252i	0.954843	−	0.297111i	$-0.0960231\pi$
$151$	33.2375	+	57.5691i	0.220116	+	0.381252i	−0.734727	+	0.678363i	$0.762690\pi$
$152$	43.7715	+	163.358i	0.287971	+	1.07472i
$153$	−5.13702	−	5.13702i	−0.0335753	−	0.0335753i
$154$	10.0417	−	52.2872i	0.0652056	−	0.339527i
$155$	97.6752	+	16.3145i	0.630162	+	0.105255i
$156$	−107.551	+	186.283i	−0.689428	+	1.19412i
$157$	−93.2888	−	24.9966i	−0.594196	−	0.159214i	−0.0508258	−	0.998708i	$-0.516185\pi$
$157$	−93.2888	−	24.9966i	−0.594196	−	0.159214i	−0.543370	+	0.839493i	$0.682852\pi$
$158$	−5.66225	+	21.1318i	−0.0358370	+	0.133746i
$159$	−36.4648	−	21.0530i	−0.229338	−	0.132409i
$160$	−127.804	+	91.2207i	−0.798774	+	0.570129i
$161$	55.2994	−	63.9043i	0.343475	−	0.396921i
$162$	78.3755	−	78.3755i	0.483799	−	0.483799i
$163$	−41.7669	+	11.1914i	−0.256238	+	0.0686589i	−0.384651	−	0.923062i	$-0.625678\pi$
$163$	−41.7669	+	11.1914i	−0.256238	+	0.0686589i	0.128413	+	0.991721i	$0.459012\pi$
$164$	24.7879	−	14.3113i	0.151146	−	0.0872641i
$165$	−51.3852	+	112.846i	−0.311426	+	0.683916i
$166$	−3.98720	+	6.90604i	−0.0240193	+	0.0416026i
$167$	133.439	−	133.439i	0.799038	−	0.799038i	−0.183906	−	0.982944i	$-0.558874\pi$
$167$	133.439	−	133.439i	0.799038	−	0.799038i	0.982944	+	0.183906i	$0.0588743\pi$
$168$	−103.216	+	212.837i	−0.614380	+	1.26688i
$169$			305.971i			1.81048i
$170$	−4.31491	−	3.55472i	−0.0253818	−	0.0209101i
$171$	−86.1978	−	149.299i	−0.504081	−	0.873094i
$172$	40.0504	+	10.7315i	0.232851	+	0.0623923i
$173$	216.197	−	57.9299i	1.24970	−	0.334855i	0.427477	−	0.904026i	$-0.359402\pi$
$173$	216.197	−	57.9299i	1.24970	−	0.334855i	0.822219	+	0.569171i	$0.192736\pi$
$174$		−	39.9189i		−	0.229419i
$175$	124.097	+	123.389i	0.709126	+	0.705082i
$176$	−5.18064			−0.0294354
$177$	22.7089	+	84.7509i	0.128299	+	0.478819i
$178$	35.8838	−	133.920i	0.201594	−	0.752360i
$179$	78.9406	−	45.5764i	0.441009	−	0.254617i	−0.263016	−	0.964791i	$-0.584717\pi$
$179$	78.9406	−	45.5764i	0.441009	−	0.254617i	0.704026	+	0.710175i	$0.251384\pi$
$180$	62.5313	−	75.9039i	0.347396	−	0.421688i
$181$	−146.339			−0.808505			−0.404253	−	0.914647i	$-0.632468\pi$
$181$	−146.339			−0.808505			−0.404253	+	0.914647i	$0.632468\pi$
$182$	14.0063	+	194.030i	0.0769576	+	1.06610i
$183$	88.9030	+	88.9030i	0.485809	+	0.485809i
$184$	−84.9789	−	49.0626i	−0.461842	−	0.266645i
$185$	63.1993	+	28.7782i	0.341618	+	0.155558i
$186$	−52.5005	−	90.9336i	−0.282261	−	0.488890i
$187$	1.35367	+	5.05195i	0.00723885	+	0.0270158i
$188$	76.3443	+	76.3443i	0.406087	+	0.406087i
$189$	−3.92310	+	20.4277i	−0.0207572	+	0.108083i
$190$	−77.0721	−	107.981i	−0.405643	−	0.568322i
$191$	−42.2285	+	73.1419i	−0.221092	+	0.382942i	−0.955140	−	0.296156i	$-0.904295\pi$
$191$	−42.2285	+	73.1419i	−0.221092	+	0.382942i	0.734048	+	0.679097i	$0.237629\pi$
$192$	174.769	+	46.8291i	0.910253	+	0.243901i
$193$	27.9071	−	104.151i	0.144596	−	0.539641i	−0.855177	−	0.518337i	$-0.826551\pi$
$193$	27.9071	−	104.151i	0.144596	−	0.539641i	0.999773	−	0.0213045i	$-0.00678193\pi$
$194$	−86.5706	−	49.9816i	−0.446240	−	0.257637i
$195$	74.6372	−	446.855i	0.382755	−	2.29156i
$196$	−16.7069	−	115.118i	−0.0852390	−	0.587335i
$197$	−49.0877	+	49.0877i	−0.249176	+	0.249176i	−0.820633	−	0.571456i	$-0.806379\pi$
$197$	−49.0877	+	49.0877i	−0.249176	+	0.249176i	0.571456	+	0.820633i	$0.306379\pi$
$198$	60.8712	−	16.3104i	0.307430	−	0.0823757i
$199$	180.471	−	104.195i	0.906891	−	0.523594i	0.0274617	−	0.999623i	$-0.491258\pi$
$199$	180.471	−	104.195i	0.906891	−	0.523594i	0.879430	+	0.476029i	$0.157924\pi$
$200$	113.523	−	168.527i	0.567613	−	0.842634i
$201$	149.967	−	259.750i	0.746103	−	1.29229i
$202$	−144.380	+	144.380i	−0.714752	+	0.714752i
$203$	29.5718	+	43.6301i	0.145674	+	0.214927i
$204$		−	8.65426i		−	0.0424228i
$205$	−38.3316	+	46.5289i	−0.186983	+	0.226970i
$206$	79.1994	+	137.177i	0.384463	+	0.665910i
$207$	96.6174	+	25.8885i	0.466751	+	0.125065i
$208$	18.2837	−	4.89911i	0.0879026	−	0.0235534i
$209$			124.112i			0.593839i
$210$	17.3129	−	184.746i	0.0824422	−	0.879741i
$211$	−297.303			−1.40902			−0.704509	−	0.709695i	$-0.748833\pi$
$211$	−297.303			−1.40902			−0.704509	+	0.709695i	$0.748833\pi$
$212$	−6.22262	−	23.2231i	−0.0293520	−	0.109543i
$213$	−138.453	+	516.714i	−0.650014	+	2.42589i
$214$	−149.037	+	86.0466i	−0.696435	+	0.402087i
$215$	−86.9249	+	8.39677i	−0.404302	+	0.0390547i
$216$	24.1524			0.111817
$217$	124.745	+	60.4953i	0.574861	+	0.278780i
$218$	118.240	+	118.240i	0.542383	+	0.542383i
$219$	270.428	+	156.131i	1.23483	+	0.712929i
$220$	−66.3094	+	24.8152i	−0.301406	+	0.112796i
$221$	−9.55484	−	16.5495i	−0.0432346	−	0.0748845i
$222$	−19.0572	−	71.1225i	−0.0858433	−	0.320372i
$223$	−40.6433	−	40.6433i	−0.182257	−	0.182257i	0.610082	−	0.792339i	$-0.291137\pi$
$223$	−40.6433	−	40.6433i	−0.182257	−	0.182257i	−0.792339	+	0.610082i	$0.791137\pi$
$224$	−207.689	+	72.0357i	−0.927183	+	0.321588i
$225$	−67.3155	+	195.888i	−0.299180	+	0.870613i
$226$	49.4772	−	85.6970i	0.218926	−	0.379190i
$227$	−58.4709	−	15.6672i	−0.257581	−	0.0690186i	0.127718	−	0.991811i	$-0.459235\pi$
$227$	−58.4709	−	15.6672i	−0.257581	−	0.0690186i	−0.385299	+	0.922792i	$0.625902\pi$
$228$	53.1528	−	198.369i	0.233126	−	0.870040i
$229$	12.9816	+	7.49491i	0.0566881	+	0.0327289i	0.528076	−	0.849197i	$-0.322914\pi$
$229$	12.9816	+	7.49491i	0.0566881	+	0.0327289i	−0.471388	+	0.881926i	$0.656247\pi$
$230$	75.9218	+	12.6811i	0.330095	+	0.0551351i
$231$	−113.592	+	131.268i	−0.491741	+	0.568258i
$232$	43.2747	−	43.2747i	0.186529	−	0.186529i
$233$	−222.828	+	59.7065i	−0.956341	+	0.256251i	−0.703051	−	0.711139i	$-0.748179\pi$
$233$	−222.828	+	59.7065i	−0.956341	+	0.256251i	−0.253290	+	0.967390i	$0.581513\pi$
$234$	−199.405	+	115.127i	−0.852160	+	0.491995i
$235$	−206.954	−	94.2378i	−0.880654	−	0.401012i
$236$	−25.0498	+	43.3876i	−0.106143	+	0.183846i
$237$	50.4370	−	50.4370i	0.212814	−	0.212814i
$238$	−4.39127	−	6.47886i	−0.0184507	−	0.0272221i
$239$		−	382.834i		−	1.60182i	−0.598786	−	0.800909i	$-0.704350\pi$
$239$		−	382.834i		−	1.60182i	0.598786	−	0.800909i	$-0.295650\pi$
$240$	−17.9713	+	1.73599i	−0.0748803	+	0.00723329i
$241$	−140.302	−	243.009i	−0.582164	−	1.00834i	−0.995222	−	0.0976334i	$-0.968873\pi$
$241$	−140.302	−	243.009i	−0.582164	−	1.00834i	0.413058	−	0.910705i	$-0.364461\pi$
$242$	105.215	+	28.1922i	0.434771	+	0.116497i
$243$	−323.236	+	86.6107i	−1.33019	+	0.356423i
$244$			71.7903i			0.294222i
$245$	117.936	+	214.746i	0.481373	+	0.876516i
$246$	63.9207			0.259840
$247$	−117.368	−	438.023i	−0.475174	−	1.77337i
$248$	41.6640	−	155.492i	0.168000	−	0.626984i
$249$	22.5165	−	12.9999i	0.0904276	−	0.0522084i
$250$	−37.0679	+	155.026i	−0.148271	+	0.620103i
$251$	−20.4968			−0.0816607			−0.0408303	−	0.999166i	$-0.513000\pi$
$251$	−20.4968			−0.0816607			−0.0408303	+	0.999166i	$0.513000\pi$
$252$	113.970	−	77.2470i	0.452262	−	0.306536i
$253$	−50.9196	−	50.9196i	−0.201263	−	0.201263i
$254$	186.439	+	107.641i	0.734012	+	0.423782i
$255$	6.38864	+	17.0713i	0.0250535	+	0.0669461i
$256$	131.747	+	228.192i	0.514635	+	0.891374i
$257$	−96.3170	−	359.460i	−0.374774	−	1.39868i	−0.853674	−	0.520807i	$-0.825631\pi$
$257$	−96.3170	−	359.460i	−0.374774	−	1.39868i	0.478900	−	0.877869i	$-0.341036\pi$
$258$	65.4758	+	65.4758i	0.253782	+	0.253782i
$259$	73.5162	+	63.6171i	0.283846	+	0.245626i
$260$	210.556	−	150.285i	0.809829	−	0.578019i
$261$	−31.1925	+	54.0270i	−0.119512	+	0.207000i
$262$	−63.7147	−	17.0723i	−0.243186	−	0.0651614i
$263$	−87.6239	+	327.017i	−0.333171	+	1.24341i	0.572668	+	0.819788i	$0.305909\pi$
$263$	−87.6239	+	327.017i	−0.333171	+	1.24341i	−0.905839	+	0.423623i	$0.860758\pi$
$264$	174.558	+	100.781i	0.661204	+	0.381746i
$265$	29.4182	+	41.2160i	0.111012	+	0.155532i
$266$	−60.8628	−	175.476i	−0.228807	−	0.659684i
$267$	−319.638	+	319.638i	−1.19715	+	1.19715i
$268$	165.426	−	44.3256i	0.617260	−	0.165394i
$269$	75.2656	−	43.4546i	0.279798	−	0.161541i	−0.353534	−	0.935422i	$-0.615020\pi$
$269$	75.2656	−	43.4546i	0.279798	−	0.161541i	0.633332	+	0.773880i	$0.281687\pi$
$270$	−17.7443	+	6.64053i	−0.0657198	+	0.0245946i
$271$	−99.4914	+	172.324i	−0.367127	+	0.635882i	−0.989115	−	0.147144i	$-0.952992\pi$
$271$	−99.4914	+	172.324i	−0.367127	+	0.635882i	0.621988	+	0.783027i	$0.286325\pi$
$272$	−0.538509	+	0.538509i	−0.00197981	+	0.00197981i
$273$	276.760	−	570.695i	1.01377	−	2.09046i
$274$		−	249.434i		−	0.910343i
$275$	112.482	−	97.9002i	0.409026	−	0.356001i
$276$	59.5779	+	103.192i	0.215862	+	0.373884i
$277$	360.205	+	96.5166i	1.30038	+	0.348435i	0.841593	−	0.540112i	$-0.181618\pi$
$277$	360.205	+	96.5166i	1.30038	+	0.348435i	0.458785	+	0.888547i	$0.348285\pi$
$278$	−157.064	+	42.0852i	−0.564979	+	0.151386i
$279$			164.095i			0.588154i
$280$	219.045	−	181.508i	0.782303	−	0.648243i
$281$	119.086			0.423794			0.211897	−	0.977292i	$-0.432036\pi$
$281$	119.086			0.423794			0.211897	+	0.977292i	$0.432036\pi$
$282$	62.4052	+	232.899i	0.221295	+	0.825884i
$283$	−2.52412	+	9.42015i	−0.00891916	+	0.0332868i	−0.970242	−	0.242137i	$-0.922152\pi$
$283$	−2.52412	+	9.42015i	−0.00891916	+	0.0332868i	0.961323	+	0.275424i	$0.0888182\pi$
$284$	−264.527	+	152.725i	−0.931435	+	0.537764i
$285$	41.5891	+	430.538i	0.145927	+	1.51066i
$286$	165.766			0.579601
$287$	−69.8633	+	47.3523i	−0.243426	+	0.164990i
$288$	−183.981	−	183.981i	−0.638825	−	0.638825i
$289$	−249.616	−	144.116i	−0.863721	−	0.498670i
$290$	−19.8951	+	43.6912i	−0.0686037	+	0.150659i
$291$	162.960	+	282.255i	0.560000	+	0.969949i
$292$	46.1478	+	172.226i	0.158040	+	0.589814i
$293$	−26.5947	−	26.5947i	−0.0907669	−	0.0907669i	0.660265	−	0.751032i	$-0.270444\pi$
$293$	−26.5947	−	26.5947i	−0.0907669	−	0.0907669i	−0.751032	+	0.660265i	$0.770444\pi$
$294$	96.2303	−	241.296i	0.327314	−	0.820735i
$295$	17.3839	−	104.078i	0.0589284	−	0.352806i
$296$	56.4422	−	97.7608i	0.190683	−	0.330273i
$297$	17.1208	+	4.58751i	0.0576458	+	0.0154462i
$298$	73.1830	−	273.123i	0.245581	−	0.916519i
$299$	227.861	+	131.555i	0.762076	+	0.439985i
$300$	−221.708	+	108.302i	−0.739025	+	0.361007i
$301$	−120.067	−	23.0587i	−0.398894	−	0.0766071i
$302$	−59.9391	+	59.9391i	−0.198474	+	0.198474i
$303$	643.038	−	172.302i	2.12224	−	0.568652i
$304$	−15.6509	+	9.03604i	−0.0514832	+	0.0297238i
$305$	−52.9961	−	141.612i	−0.173758	−	0.464303i
$306$	4.63194	−	8.02275i	0.0151370	−	0.0262181i
$307$	−66.6628	+	66.6628i	−0.217143	+	0.217143i	−0.807293	−	0.590151i	$-0.799068\pi$
$307$	−66.6628	+	66.6628i	−0.217143	+	0.217143i	0.590151	+	0.807293i	$0.299068\pi$
$308$	−98.8637	+	7.13658i	−0.320986	+	0.0231707i
$309$		−	516.444i		−	1.67134i
$310$	12.1416	+	125.692i	0.0391665	+	0.405459i
$311$	108.760	+	188.377i	0.349710	+	0.605715i	0.986198	−	0.165571i	$-0.0529469\pi$
$311$	108.760	+	188.377i	0.349710	+	0.605715i	−0.636488	+	0.771287i	$0.719614\pi$
$312$	−711.362	−	190.609i	−2.28001	−	0.610926i
$313$	−176.359	+	47.2552i	−0.563447	+	0.150975i	−0.529290	−	0.848441i	$-0.677541\pi$
$313$	−176.359	+	47.2552i	−0.563447	+	0.150975i	−0.0341576	+	0.999416i	$0.510875\pi$
$314$		−	123.155i		−	0.392213i
$315$	−167.791	+	236.510i	−0.532670	+	0.750825i
$316$	40.7285			0.128888
$317$	128.330	+	478.934i	0.404826	+	1.51083i	0.804376	+	0.594120i	$0.202500\pi$
$317$	128.330	+	478.934i	0.404826	+	1.51083i	−0.399550	+	0.916711i	$0.630834\pi$
$318$	13.8965	−	51.8625i	0.0436997	−	0.163090i
$319$	38.8955	−	22.4564i	0.121930	−	0.0703961i
$320$	−167.945	−	138.357i	−0.524828	−	0.432365i
$321$	561.093			1.74795
$322$	96.9627	+	47.0224i	0.301126	+	0.146032i
$323$	12.9011	+	12.9011i	0.0399413	+	0.0399413i
$324$	−178.703	−	103.174i	−0.551552	−	0.318439i
$325$	−304.397	+	451.884i	−0.936607	+	1.39041i
$326$	−27.5692	−	47.7513i	−0.0845682	−	0.146476i
$327$	−141.106	−	526.615i	−0.431517	−	1.61044i
$328$	69.2943	+	69.2943i	0.211263	+	0.211263i
$329$	−240.738	−	208.322i	−0.731726	−	0.633197i
$330$	−155.953	−	26.0486i	−0.472586	−	0.0789351i
$331$	232.008	−	401.849i	0.700930	−	1.21405i	−0.267210	−	0.963638i	$-0.586102\pi$
$331$	232.008	−	401.849i	0.700930	−	1.21405i	0.968140	−	0.250408i	$-0.0805648\pi$
$332$	14.3400	+	3.84238i	0.0431926	+	0.0115734i
$333$	−29.7825	+	111.150i	−0.0894369	+	0.333783i
$334$	208.399	+	120.319i	0.623949	+	0.360237i
$335$	−293.595	+	209.555i	−0.876402	+	0.625536i
$336$	−24.8233	−	4.76727i	−0.0738788	−	0.0141883i
$337$	−85.3188	+	85.3188i	−0.253171	+	0.253171i	−0.822270	−	0.569098i	$-0.807292\pi$
$337$	−85.3188	+	85.3188i	−0.253171	+	0.253171i	0.569098	+	0.822270i	$0.307292\pi$
$338$	−376.869	+	100.982i	−1.11500	+	0.298762i
$339$	−279.407	+	161.316i	−0.824209	+	0.475857i
$340$	−4.31318	+	9.47208i	−0.0126858	+	0.0278591i
$341$	59.0683	−	102.309i	0.173221	−	0.300027i
$342$	155.445	−	155.445i	0.454519	−	0.454519i
$343$	73.5747	+	335.016i	0.214503	+	0.976723i
$344$			141.960i			0.412675i
$345$	−193.700	−	159.574i	−0.561448	−	0.462534i
$346$	142.706	+	247.175i	0.412446	+	0.714378i
$347$	10.2392	+	2.74359i	0.0295078	+	0.00790660i	0.273543	−	0.961860i	$-0.411804\pi$
$347$	10.2392	+	2.74359i	0.0295078	+	0.00790660i	−0.244035	+	0.969766i	$0.578471\pi$
$348$	−71.7840	+	19.2345i	−0.206276	+	0.0552715i
$349$		−	32.0826i		−	0.0919272i	−0.998943	−	0.0459636i	$-0.985364\pi$
$349$		−	32.0826i		−	0.0919272i	0.998943	−	0.0459636i	$-0.0146358\pi$
$350$	−111.024	+	193.575i	−0.317211	+	0.553072i
$351$	−64.7618			−0.184507
$352$	48.4813	+	180.935i	0.137731	+	0.514019i
$353$	129.836	−	484.555i	0.367807	−	1.37268i	−0.495768	−	0.868455i	$-0.665113\pi$
$353$	129.836	−	484.555i	0.367807	−	1.37268i	0.863575	−	0.504221i	$-0.168220\pi$
$354$	−96.8942	+	55.9419i	−0.273712	+	0.158028i
$355$	409.060	−	496.539i	1.15228	−	1.39870i
$356$	−258.112			−0.725033
$357$	1.83730	+	25.4523i	0.00514651	+	0.0712950i
$358$	82.1905	+	82.1905i	0.229582	+	0.229582i
$359$	361.528	+	208.728i	1.00704	+	0.581415i	0.910324	−	0.413897i	$-0.135833\pi$
$359$	361.528	+	208.728i	1.00704	+	0.581415i	0.0967169	+	0.995312i	$0.469166\pi$
$360$	306.433	+	139.536i	0.851202	+	0.387600i
$361$	35.9763	+	62.3128i	0.0996574	+	0.172612i
$362$	−48.2975	−	180.249i	−0.133418	−	0.497924i
$363$	−251.124	−	251.124i	−0.691803	−	0.691803i
$364$	342.166	−	118.678i	0.940015	−	0.326039i
$365$	−218.169	−	305.663i	−0.597723	−	0.837434i
$366$	−80.1619	+	138.844i	−0.219022	+	0.379356i
$367$	321.300	+	86.0920i	0.875476	+	0.234583i	0.668454	−	0.743753i	$-0.266956\pi$
$367$	321.300	+	86.0920i	0.875476	+	0.234583i	0.207022	+	0.978336i	$0.433623\pi$
$368$	2.71387	−	10.1283i	0.00737465	−	0.0275226i
$369$	−86.5115	−	49.9475i	−0.234449	−	0.135359i
$370$	−14.5885	+	87.3414i	−0.0394283	+	0.236058i
$371$	23.2311	+	66.9786i	0.0626176	+	0.180535i
$372$	−138.224	+	138.224i	−0.371571	+	0.371571i
$373$	−406.480	+	108.916i	−1.08976	+	0.292000i	−0.758587	−	0.651571i	$-0.774110\pi$
$373$	−406.480	+	108.916i	−1.08976	+	0.292000i	−0.331170	+	0.943571i	$0.607443\pi$
$374$	−5.77580	+	3.33466i	−0.0154433	+	0.00891620i
$375$	357.388	−	377.301i	0.953034	−	1.00614i
$376$	−184.827	+	320.130i	−0.491561	+	0.851408i
$377$	−116.036	+	116.036i	−0.307788	+	0.307788i
$378$	−26.4558	+	1.90974i	−0.0699890	+	0.00505223i
$379$			513.773i			1.35560i	0.735246	+	0.677801i	$0.237067\pi$
$379$			513.773i			1.35560i	−0.735246	+	0.677801i	$0.762933\pi$
$380$	−157.040	+	190.624i	−0.413264	+	0.501642i
$381$	−350.952	−	607.866i	−0.921133	−	1.59545i
$382$	−104.027	−	27.8739i	−0.272322	−	0.0729684i
$383$	140.238	−	37.5765i	0.366155	−	0.0981111i	−0.0710499	−	0.997473i	$-0.522635\pi$
$383$	140.238	−	37.5765i	0.366155	−	0.0981111i	0.437205	+	0.899362i	$0.355968\pi$
$384$		−	291.533i		−	0.759199i
$385$	189.749	−	87.0594i	0.492854	−	0.226128i
$386$	137.494			0.356203
$387$	−37.4536	−	139.779i	−0.0967793	−	0.361185i
$388$	−48.1661	+	179.758i	−0.124139	+	0.463295i
$389$	356.579	−	205.871i	0.916655	−	0.529231i	0.0340888	−	0.999419i	$-0.489147\pi$
$389$	356.579	−	205.871i	0.916655	−	0.529231i	0.882566	+	0.470188i	$0.155814\pi$
$390$	575.031	−	55.5468i	1.47444	−	0.142428i
$391$	−10.5858			−0.0270737
$392$	365.901	−	157.261i	0.933421	−	0.401176i
$393$	152.073	+	152.073i	0.386954	+	0.386954i
$394$	−76.6629	−	44.2613i	−0.194576	−	0.112338i
$395$	−80.3404	+	30.0661i	−0.203393	+	0.0761166i
$396$	−58.6602	−	101.602i	−0.148132	−	0.256572i
$397$	−37.6216	−	140.406i	−0.0947646	−	0.353666i	0.902219	−	0.431278i	$-0.141937\pi$
$397$	−37.6216	−	140.406i	−0.0947646	−	0.353666i	−0.996984	+	0.0776117i	$0.975271\pi$
$398$	187.901	+	187.901i	0.472113	+	0.472113i
$399$	−114.209	+	594.691i	−0.286239	+	1.49045i
$400$	20.5348	+	7.05663i	0.0513369	+	0.0176416i
$401$	26.5072	−	45.9119i	0.0661028	−	0.114493i	−0.831080	−	0.556153i	$-0.812277\pi$
$401$	26.5072	−	45.9119i	0.0661028	−	0.114493i	0.897183	+	0.441660i	$0.145610\pi$
$402$	369.432	+	98.9891i	0.918986	+	0.246242i
$403$	−111.717	+	416.933i	−0.277213	+	1.03457i
$404$	329.198	+	190.063i	0.814848	+	0.470453i
$405$	428.671	+	71.6000i	1.05845	+	0.176790i
$406$	−43.9801	+	50.8236i	−0.108325	+	0.125181i
$407$	58.5786	−	58.5786i	0.143928	−	0.143928i
$408$	28.6205	−	7.66884i	0.0701483	−	0.0187962i
$409$	251.839	−	145.399i	0.615742	−	0.355499i	−0.159467	−	0.987203i	$-0.550978\pi$
$409$	251.839	−	145.399i	0.615742	−	0.355499i	0.775209	+	0.631704i	$0.217644\pi$
$410$	−69.9612	−	31.8573i	−0.170637	−	0.0777007i
$411$	−406.628	+	704.300i	−0.989362	+	1.71363i
$412$	208.517	−	208.517i	0.506110	−	0.506110i
$413$	64.4607	−	132.922i	0.156079	−	0.321844i
$414$			127.549i			0.308090i
$415$	−31.1233	+	3.00644i	−0.0749958	+	0.00724444i
$416$	−342.205	−	592.716i	−0.822608	−	1.42480i
$417$	512.093	+	137.215i	1.22804	+	0.329053i
$418$	−152.871	+	40.9617i	−0.365721	+	0.0979945i
$419$		−	290.268i		−	0.692764i	−0.938094	−	0.346382i	$-0.887410\pi$
$419$		−	290.268i		−	0.692764i	0.938094	−	0.346382i	$-0.112590\pi$
$420$	−340.560	+	57.8847i	−0.810857	+	0.137821i
$421$	256.502			0.609268			0.304634	−	0.952470i	$-0.401466\pi$
$421$	256.502			0.609268			0.304634	+	0.952470i	$0.401466\pi$
$422$	−98.1210	−	366.193i	−0.232514	−	0.867755i
$423$	97.5264	−	363.973i	0.230559	−	0.860457i
$424$	71.2871	−	41.1576i	0.168130	−	0.0970699i
$425$	1.51574	−	21.8685i	0.00356646	−	0.0514553i
$426$	−682.139			−1.60126
$427$	−15.2411	−	211.136i	−0.0356935	−	0.494464i
$428$	226.545	+	226.545i	0.529310	+	0.529310i
$429$	−468.055	−	270.232i	−1.09104	−	0.629911i
$430$	−39.0309	−	104.296i	−0.0907695	−	0.242548i
$431$	−145.835	−	252.594i	−0.338364	−	0.586064i	0.645761	−	0.763540i	$-0.276540\pi$
$431$	−145.835	−	252.594i	−0.338364	−	0.586064i	−0.984125	+	0.177475i	$0.943207\pi$
$432$	0.667990	+	2.49297i	0.00154627	+	0.00577077i
$433$	−122.368	−	122.368i	−0.282605	−	0.282605i	0.551542	−	0.834147i	$-0.314040\pi$
$433$	−122.368	−	122.368i	−0.282605	−	0.282605i	−0.834147	+	0.551542i	$0.814040\pi$
$434$	−33.3426	+	173.616i	−0.0768263	+	0.400036i
$435$	127.401	−	90.9332i	0.292876	−	0.209042i
$436$	155.652	−	269.596i	0.356999	−	0.618340i
$437$	−242.644	−	65.0162i	−0.555249	−	0.148779i
$438$	−103.058	+	384.619i	−0.235293	+	0.878125i
$439$	−752.706	−	434.575i	−1.71459	−	0.989921i	−0.928108	−	0.372312i	$-0.878565\pi$
$439$	−752.706	−	434.575i	−1.71459	−	0.989921i	−0.786485	−	0.617609i	$-0.788101\pi$
$440$	−140.825	−	197.302i	−0.320058	−	0.448414i
$441$	−318.788	+	251.381i	−0.722875	+	0.570024i
$442$	17.2308	−	17.2308i	0.0389837	−	0.0389837i
$443$	−128.725	+	34.4919i	−0.290576	+	0.0778597i	−0.401163	−	0.916007i	$-0.631394\pi$
$443$	−128.725	+	34.4919i	−0.290576	+	0.0778597i	0.110586	+	0.993867i	$0.464727\pi$
$444$	−118.713	+	68.5391i	−0.267372	+	0.154367i
$445$	509.147	−	190.540i	1.14415	−	0.428180i
$446$	36.6472	−	63.4748i	0.0821686	−	0.142320i
$447$	−651.884	+	651.884i	−1.45835	+	1.45835i
$448$	−170.917	−	252.170i	−0.381511	−	0.562880i
$449$			758.129i			1.68848i	0.535963	+	0.844242i	$0.319949\pi$
$449$			758.129i			1.68848i	−0.535963	+	0.844242i	$0.680051\pi$
$450$	−263.495	−	18.2633i	−0.585544	−	0.0405851i
$451$	35.9586	+	62.2821i	0.0797307	+	0.138098i
$452$	−177.944	−	47.6801i	−0.393682	−	0.105487i
$453$	266.956	−	71.5307i	0.589308	−	0.157905i
$454$		−	77.1902i		−	0.170023i
$455$	−587.342	+	486.692i	−1.29086	+	1.06965i
$456$	703.127			1.54194
$457$	189.049	+	705.542i	0.413675	+	1.54386i	0.787475	+	0.616347i	$0.211388\pi$
$457$	189.049	+	705.542i	0.413675	+	1.54386i	−0.373800	+	0.927509i	$0.621945\pi$
$458$	−4.94720	+	18.4632i	−0.0108017	+	0.0403126i
$459$	2.25650	−	1.30279i	0.00491613	−	0.00283833i
$460$	−13.7784	−	142.636i	−0.0299530	−	0.310079i
$461$	702.980			1.52490			0.762452	−	0.647045i	$-0.223996\pi$
$461$	702.980			1.52490			0.762452	+	0.647045i	$0.223996\pi$
$462$	−199.174	−	96.5900i	−0.431113	−	0.209069i
$463$	618.405	+	618.405i	1.33565	+	1.33565i	0.900227	+	0.435420i	$0.143400\pi$
$463$	618.405	+	618.405i	1.33565	+	1.33565i	0.435420	+	0.900227i	$0.356600\pi$
$464$	5.66360	+	3.26988i	0.0122060	+	0.00704716i
$465$	170.621	−	374.697i	0.366927	−	0.805801i
$466$	−147.083	−	254.755i	−0.315628	−	0.546684i
$467$	32.4072	+	120.945i	0.0693943	+	0.258983i	0.991904	−	0.126991i	$-0.0405320\pi$
$467$	32.4072	+	120.945i	0.0693943	+	0.258983i	−0.922510	+	0.385974i	$0.873865\pi$
$468$	303.108	+	303.108i	0.647666	+	0.647666i
$469$	−477.109	+	165.482i	−1.01729	+	0.352841i
$470$	47.7717	−	286.010i	0.101642	−	0.608532i
$471$	−200.768	+	347.740i	−0.426258	+	0.738301i
$472$	−165.684	−	44.3950i	−0.351026	−	0.0940572i
$473$	−26.9639	+	100.631i	−0.0570061	+	0.212750i
$474$	78.7701	+	45.4779i	0.166182	+	0.0959450i
$475$	169.056	−	491.951i	0.355906	−	1.03569i
$476$	−9.53471	+	11.0184i	−0.0200309	+	0.0231478i
$477$	−59.3330	+	59.3330i	−0.124388	+	0.124388i
$478$	471.543	−	126.350i	0.986492	−	0.264330i
$479$	−644.603	+	372.161i	−1.34573	+	0.776955i	−0.987641	−	0.156734i	$-0.949903\pi$
$479$	−644.603	+	372.161i	−1.34573	+	0.776955i	−0.358085	+	0.933689i	$0.616570\pi$
$480$	228.808	+	611.405i	0.476684	+	1.27376i
$481$	−151.343	+	262.134i	−0.314642	+	0.544976i
$482$	253.014	−	253.014i	0.524925	−	0.524925i
$483$	−197.127	−	290.841i	−0.408131	−	0.602155i
$484$		−	202.786i		−	0.418980i
$485$	−37.6872	−	390.145i	−0.0777056	−	0.804423i
$486$	−213.359	−	369.549i	−0.439011	−	0.760390i
$487$	−647.035	−	173.372i	−1.32861	−	0.356001i	−0.476416	−	0.879220i	$-0.658064\pi$
$487$	−647.035	−	173.372i	−1.32861	−	0.356001i	−0.852198	+	0.523219i	$0.824731\pi$
$488$	−237.417	+	63.6158i	−0.486511	+	0.130360i
$489$			179.774i			0.367635i
$490$	−225.583	+	216.138i	−0.460373	+	0.441099i
$491$	−61.5033			−0.125261			−0.0626307	−	0.998037i	$-0.519949\pi$
$491$	−61.5033			−0.125261			−0.0626307	+	0.998037i	$0.519949\pi$
$492$	−30.7995	−	114.945i	−0.0626006	−	0.233629i
$493$	1.70880	−	6.37731i	0.00346612	−	0.0129357i
$494$	500.784	−	289.128i	1.01373	−	0.585279i
$495$	190.716	+	157.116i	0.385285	+	0.317406i
$496$	17.2019			0.0346813
$497$	745.556	−	505.326i	1.50011	−	1.01675i
$498$	23.4434	+	23.4434i	0.0470752	+	0.0470752i
$499$	41.8687	+	24.1729i	0.0839052	+	0.0484427i	0.541366	−	0.840787i	$-0.317908\pi$
$499$	41.8687	+	24.1729i	0.0839052	+	0.0484427i	−0.457460	+	0.889230i	$0.651241\pi$
$500$	296.635	−	8.04021i	0.593270	−	0.0160804i
$501$	−392.289	−	679.465i	−0.783013	−	1.35622i
$502$	−6.76472	−	25.2463i	−0.0134755	−	0.0502914i
$503$	−571.523	−	571.523i	−1.13623	−	1.13623i	−0.989120	−	0.147108i	$-0.953003\pi$
$503$	−571.523	−	571.523i	−1.13623	−	1.13623i	−0.147108	−	0.989120i	$-0.546997\pi$
$504$	356.456	+	308.459i	0.707254	+	0.612021i
$505$	−789.678	−	131.898i	−1.56372	−	0.261185i
$506$	45.9131	−	79.5239i	0.0907374	−	0.157162i
$507$	1228.74	+	329.241i	2.42356	+	0.649391i
$508$	103.731	−	387.129i	0.204195	−	0.762064i
$509$	579.164	+	334.381i	1.13785	+	0.656936i	0.945897	−	0.324468i	$-0.105185\pi$
$509$	579.164	+	334.381i	1.13785	+	0.656936i	0.191950	+	0.981405i	$0.438519\pi$
$510$	−18.9185	+	13.5031i	−0.0370950	+	0.0264767i
$511$	−172.285	−	496.722i	−0.337152	−	0.972058i
$512$	−39.2534	+	39.2534i	−0.0766668	+	0.0766668i
$513$	59.7241	−	16.0030i	0.116421	−	0.0311950i
$514$	410.964	−	237.270i	0.799541	−	0.461615i
$515$	−257.389	+	565.248i	−0.499785	+	1.09757i
$516$	86.1929	−	149.290i	0.167040	−	0.289323i
$517$	−191.823	+	191.823i	−0.371030	+	0.371030i
$518$	−54.0951	+	111.547i	−0.104431	+	0.215342i
$519$		−	930.561i		−	1.79299i
$520$	683.588	+	563.155i	1.31459	+	1.08299i
$521$	478.134	+	828.153i	0.917724	+	1.58954i	0.802863	+	0.596163i	$0.203309\pi$
$521$	478.134	+	828.153i	0.917724	+	1.58954i	0.114861	+	0.993382i	$0.463358\pi$
$522$	−76.8406	−	20.5894i	−0.147204	−	0.0394432i
$523$	867.796	−	232.525i	1.65927	−	0.444599i	0.697080	−	0.716993i	$-0.254482\pi$
$523$	867.796	−	232.525i	1.65927	−	0.444599i	0.962186	+	0.272394i	$0.0878155\pi$
$524$			122.801i			0.234353i
$525$	629.053	−	365.587i	1.19820	−	0.696356i
$526$	−431.711			−0.820743
$527$	−4.49475	−	16.7746i	−0.00852893	−	0.0318304i
$528$	−5.57465	+	20.8049i	−0.0105580	+	0.0394031i
$529$	−331.904	+	191.625i	−0.627417	+	0.362239i
$530$	−41.0573	+	49.8376i	−0.0774667	+	0.0940332i
$531$	174.851			0.329287
$532$	−286.223	+	193.997i	−0.538013	+	0.364657i
$533$	−185.804	−	185.804i	−0.348601	−	0.348601i
$534$	−499.196	−	288.211i	−0.934823	−	0.539720i
$535$	−614.116	−	279.642i	−1.14788	−	0.522695i
$536$	293.179	+	507.800i	0.546975	+	0.947388i
$537$	−98.0853	−	366.059i	−0.182654	−	0.681675i
$538$	78.3641	+	78.3641i	0.145658	+	0.145658i
$539$	289.245	−	41.9776i	0.536632	−	0.0778805i
$540$	20.4912	+	28.7090i	0.0379467	+	0.0531649i
$541$	−454.145	+	786.602i	−0.839455	+	1.45398i	0.0508961	+	0.998704i	$0.483792\pi$
$541$	−454.145	+	786.602i	−0.839455	+	1.45398i	−0.890351	+	0.455275i	$0.849541\pi$
$542$	−245.090	−	65.6717i	−0.452196	−	0.121165i
$543$	−157.469	+	587.683i	−0.289999	+	1.08229i
$544$	23.8470	+	13.7681i	0.0438364	+	0.0253089i
$545$	−108.018	+	646.705i	−0.198198	+	1.18661i
$546$	794.276	+	152.539i	1.45472	+	0.279376i
$547$	153.413	−	153.413i	0.280462	−	0.280462i	−0.552831	−	0.833293i	$-0.686453\pi$
$547$	153.413	−	153.413i	0.280462	−	0.280462i	0.833293	+	0.552831i	$0.186453\pi$
$548$	−448.544	+	120.187i	−0.818511	+	0.219319i
$549$	216.985	−	125.277i	0.395237	−	0.228190i
$550$	157.709	+	106.235i	0.286743	+	0.193155i
$551$	78.3365	−	135.683i	0.142172	−	0.246248i
$552$	−288.472	+	288.472i	−0.522594	+	0.522594i
$553$	−119.783	+	8.64668i	−0.216606	+	0.0156359i
$554$			475.524i			0.858346i
$555$	183.576	−	222.834i	0.330767	−	0.401503i
$556$	151.359	+	262.162i	0.272229	+	0.471514i
$557$	−413.039	−	110.673i	−0.741542	−	0.198696i	−0.131779	−	0.991279i	$-0.542069\pi$
$557$	−413.039	−	110.673i	−0.741542	−	0.198696i	−0.609763	+	0.792584i	$0.708735\pi$
$558$	−202.118	+	54.1575i	−0.362219	+	0.0970564i
$559$		−	380.649i		−	0.680946i
$560$	24.7931	+	17.5894i	0.0442734	+	0.0314096i
$561$	21.7447			0.0387606
$562$	39.3028	+	146.680i	0.0699338	+	0.260997i
$563$	47.7474	−	178.196i	0.0848088	−	0.316511i	−0.910469	−	0.413577i	$-0.864279\pi$
$563$	47.7474	−	178.196i	0.0848088	−	0.316511i	0.995278	+	0.0970662i	$0.0309459\pi$
$564$	388.741	−	224.440i	0.689257	−	0.397943i
$565$	386.208	−	37.3069i	0.683554	−	0.0660300i
$566$	−12.4360			−0.0219717
$567$	547.472	+	265.498i	0.965559	+	0.468251i
$568$	−739.484	−	739.484i	−1.30191	−	1.30191i
$569$	211.620	+	122.179i	0.371916	+	0.214726i	0.674295	−	0.738462i	$-0.264448\pi$
$569$	211.620	+	122.179i	0.371916	+	0.214726i	−0.302379	+	0.953188i	$0.597781\pi$
$570$	−516.574	+	193.319i	−0.906270	+	0.339157i
$571$	−89.0175	−	154.183i	−0.155897	−	0.270022i	0.777488	−	0.628898i	$-0.216494\pi$
$571$	−89.0175	−	154.183i	−0.155897	−	0.270022i	−0.933385	+	0.358875i	$0.883160\pi$
$572$	−79.8724	−	298.088i	−0.139637	−	0.521133i
$573$	248.290	+	248.290i	0.433315	+	0.433315i
$574$	−81.3820	−	70.4237i	−0.141780	−	0.122689i
$575$	132.474	+	271.191i	0.230390	+	0.471637i
$576$	180.284	−	312.261i	0.312993	−	0.542120i
$577$	−489.160	−	131.070i	−0.847765	−	0.227158i	−0.191316	−	0.981528i	$-0.561276\pi$
$577$	−489.160	−	131.070i	−0.847765	−	0.227158i	−0.656449	+	0.754370i	$0.727942\pi$
$578$	95.1270	−	355.019i	0.164580	−	0.614219i
$579$	−388.228	−	224.144i	−0.670515	−	0.387122i
$580$	88.1538	+	14.7242i	0.151989	+	0.0253865i
$581$	−42.9898	−	8.25612i	−0.0739927	−	0.0142102i
$582$	−293.875	+	293.875i	−0.504940	+	0.504940i
$583$	58.3504	−	15.6349i	0.100086	−	0.0268181i
$584$	−528.674	+	305.230i	−0.905264	+	0.522655i
$585$	−821.662	−	374.149i	−1.40455	−	0.639571i
$586$	23.9799	−	41.5343i	0.0409213	−	0.0708777i
$587$	178.183	−	178.183i	0.303548	−	0.303548i	−0.538852	−	0.842400i	$-0.681142\pi$
$587$	178.183	−	178.183i	0.303548	−	0.303548i	0.842400	+	0.538852i	$0.181142\pi$
$588$	−480.277	−	56.7800i	−0.816798	−	0.0965646i
$589$		−	412.107i		−	0.699671i
$590$	133.931	−	12.9375i	0.227002	−	0.0219280i
$591$	144.310	+	249.952i	0.244179	+	0.422931i
$592$	11.6517	+	3.12207i	0.0196820	+	0.00527377i
$593$	−879.002	+	235.528i	−1.48230	+	0.397180i	−0.907128	−	0.420854i	$-0.861730\pi$
$593$	−879.002	+	235.528i	−1.48230	+	0.397180i	−0.575169	+	0.818034i	$0.695064\pi$
$594$			22.6020i			0.0380505i
$595$	10.6742	−	28.7732i	0.0179398	−	0.0483584i
$596$	−526.405			−0.883229
$597$	−224.239	−	836.873i	−0.375610	−	1.40180i
$598$	−86.8363	+	324.078i	−0.145211	+	0.541936i
$599$	3.19934	−	1.84714i	0.00534113	−	0.00308371i	−0.497327	−	0.867563i	$-0.665685\pi$
$599$	3.19934	−	1.84714i	0.00534113	−	0.00308371i	0.502668	+	0.864479i	$0.332352\pi$
$600$	−554.628	−	637.239i	−0.924380	−	1.06206i
$601$	77.7927			0.129439			0.0647194	−	0.997904i	$-0.479385\pi$
$601$	77.7927			0.129439			0.0647194	+	0.997904i	$0.479385\pi$
$602$	−11.2249	−	155.499i	−0.0186459	−	0.258304i
$603$	−422.647	−	422.647i	−0.700907	−	0.700907i
$604$	136.666	+	78.9043i	0.226269	+	0.130636i
$605$	149.698	+	400.013i	0.247435	+	0.661178i
$606$	424.453	+	735.174i	0.700418	+	1.21316i
$607$	177.801	+	663.561i	0.292917	+	1.09318i	0.942857	+	0.333197i	$0.108127\pi$
$607$	177.801	+	663.561i	0.292917	+	1.09318i	−0.649940	+	0.759985i	$0.725206\pi$
$608$	462.049	+	462.049i	0.759949	+	0.759949i
$609$	207.035	−	71.8087i	0.339958	−	0.117912i
$610$	156.936	−	112.013i	0.257271	−	0.183629i
$611$	495.591	−	858.388i	0.811114	−	1.40489i
$612$	−16.6587	−	4.46369i	−0.0272202	−	0.00729362i
$613$	68.3861	−	255.220i	0.111560	−	0.416346i	−0.887447	−	0.460910i	$-0.847523\pi$
$613$	68.3861	−	255.220i	0.111560	−	0.416346i	0.999007	+	0.0445637i	$0.0141898\pi$
$614$	−104.111	−	60.1084i	−0.169561	−	0.0978964i
$615$	145.608	+	204.003i	0.236761	+	0.331712i
$616$	−111.208	−	320.628i	−0.180532	−	0.520500i
$617$	285.496	−	285.496i	0.462717	−	0.462717i	−0.436828	−	0.899545i	$-0.643898\pi$
$617$	285.496	−	285.496i	0.462717	−	0.462717i	0.899545	+	0.436828i	$0.143898\pi$
$618$	636.112	−	170.446i	1.02931	−	0.275802i
$619$	296.838	−	171.380i	0.479545	−	0.276866i	−0.240682	−	0.970604i	$-0.577371\pi$
$619$	296.838	−	171.380i	0.479545	−	0.276866i	0.720227	+	0.693739i	$0.244038\pi$
$620$	220.176	−	82.3971i	0.355122	−	0.132899i
$621$	−17.9375	+	31.0686i	−0.0288848	+	0.0500299i
$622$	−196.133	+	196.133i	−0.315326	+	0.315326i
$623$	759.110	−	54.7972i	1.21848	−	0.0879570i
$624$		−	78.6972i		−	0.126117i
$625$	−579.203	+	234.838i	−0.926725	+	0.375741i
$626$	−116.410	−	201.628i	−0.185959	−	0.322090i
$627$	498.422	+	133.552i	0.794931	+	0.213001i
$628$	−221.463	+	59.3409i	−0.352648	+	0.0944918i
$629$		−	12.1781i		−	0.0193610i
$630$	−346.690	−	128.614i	−0.550302	−	0.204149i
$631$	651.848			1.03304			0.516520	−	0.856275i	$-0.327227\pi$
$631$	651.848			1.03304			0.516520	+	0.856275i	$0.327227\pi$
$632$	36.0909	+	134.693i	0.0571059	+	0.213122i
$633$	−319.914	+	1193.94i	−0.505394	+	1.88615i
$634$	−547.556	+	316.132i	−0.863653	+	0.498630i
$635$	81.1635	+	840.219i	0.127816	+	1.32318i
$636$	−99.9574			−0.157166
$637$	−981.119	+	421.676i	−1.54022	+	0.661972i
$638$	40.4968	+	40.4968i	0.0634746	+	0.0634746i
$639$	923.219	+	533.021i	1.44479	+	0.834149i
$640$	−145.296	+	319.082i	−0.227025	+	0.498566i
$641$	222.071	+	384.639i	0.346445	+	0.600061i	0.985615	−	0.169005i	$-0.0540553\pi$
$641$	222.071	+	384.639i	0.346445	+	0.600061i	−0.639170	+	0.769065i	$0.720722\pi$
$642$	185.182	+	691.107i	0.288445	+	1.07649i
$643$	−251.202	−	251.202i	−0.390672	−	0.390672i	0.484255	−	0.874927i	$-0.339091\pi$
$643$	−251.202	−	251.202i	−0.390672	−	0.390672i	−0.874927	+	0.484255i	$0.839091\pi$
$644$	37.8374	−	197.020i	0.0587537	−	0.305932i
$645$	−59.8155	+	358.116i	−0.0927371	+	0.555219i
$646$	−11.6326	+	20.1482i	−0.0180071	+	0.0311892i
$647$	−239.862	−	64.2707i	−0.370729	−	0.0993365i	0.0686441	−	0.997641i	$-0.478133\pi$
$647$	−239.862	−	64.2707i	−0.370729	−	0.0993365i	−0.439373	+	0.898305i	$0.644799\pi$
$648$	182.852	−	682.414i	0.282179	−	1.05311i
$649$	−109.016	−	62.9401i	−0.167975	−	0.0969802i
$650$	−657.055	−	225.792i	−1.01085	−	0.347373i
$651$	377.175	−	435.865i	0.579377	−	0.669531i
$652$	−72.5847	+	72.5847i	−0.111326	+	0.111326i
$653$	729.993	−	195.601i	1.11791	−	0.299542i	0.347870	−	0.937543i	$-0.386905\pi$
$653$	729.993	−	195.601i	1.11791	−	0.299542i	0.770036	+	0.638000i	$0.220238\pi$
$654$	602.069	−	347.605i	0.920595	−	0.531506i
$655$	−90.6525	−	242.235i	−0.138401	−	0.369825i
$656$	−5.23595	+	9.06892i	−0.00798162	+	0.0138246i
$657$	440.021	−	440.021i	0.669743	−	0.669743i
$658$	177.141	−	365.274i	0.269211	−	0.555128i
$659$		−	587.795i		−	0.891950i	−0.895045	−	0.445975i	$-0.852857\pi$
$659$		−	587.795i		−	0.891950i	0.895045	−	0.445975i	$-0.147143\pi$
$660$	28.3026	+	292.994i	0.0428827	+	0.443930i
$661$	−87.0160	−	150.716i	−0.131643	−	0.228012i	0.792667	−	0.609655i	$-0.208692\pi$
$661$	−87.0160	−	150.716i	−0.131643	−	0.228012i	−0.924310	+	0.381642i	$0.875359\pi$
$662$	571.535	+	153.142i	0.863346	+	0.231333i
$663$	−76.7423	+	20.5630i	−0.115750	+	0.0310152i
$664$			50.8285i			0.0765489i
$665$	421.389	−	593.968i	0.633667	−	0.893185i
$666$	−146.734			−0.220322
$667$	23.5275	+	87.8058i	0.0352736	+	0.131643i
$668$	115.949	−	432.728i	0.173576	−	0.647796i
$669$	−206.954	+	119.485i	−0.309348	+	0.178602i
$670$	−355.009	−	292.464i	−0.529864	−	0.436514i
$671$	−180.380			−0.268823
$672$	65.8027	+	911.571i	0.0979207	+	1.35650i
$673$	280.346	+	280.346i	0.416562	+	0.416562i	0.884017	−	0.467455i	$-0.154829\pi$
$673$	280.346	+	280.346i	0.416562	+	0.416562i	−0.467455	+	0.884017i	$0.654829\pi$
$674$	−133.247	−	76.9301i	−0.197696	−	0.114140i
$675$	−61.6139	−	41.5043i	−0.0912799	−	0.0614878i
$676$	363.180	+	629.046i	0.537249	+	0.930542i
$677$	89.6728	+	334.663i	0.132456	+	0.494333i	0.999995	−	0.00303575i	$-0.000966312\pi$
$677$	89.6728	+	334.663i	0.132456	+	0.494333i	−0.867539	+	0.497369i	$0.834300\pi$
$678$	−290.910	−	290.910i	−0.429070	−	0.429070i
$679$	103.495	−	538.898i	0.152422	−	0.793664i
$680$	−35.1472	−	5.87056i	−0.0516870	−	0.00863318i
$681$	−125.836	+	217.954i	−0.184781	+	0.320050i
$682$	145.511	+	38.9895i	0.213359	+	0.0571693i
$683$	105.000	−	391.865i	0.153733	−	0.573741i	−0.845477	−	0.534012i	$-0.820684\pi$
$683$	105.000	−	391.865i	0.153733	−	0.573741i	0.999210	−	0.0397293i	$-0.0126496\pi$
$684$	−354.429	−	204.630i	−0.518171	−	0.299166i
$685$	796.068	−	568.198i	1.16214	−	0.829486i
$686$	−388.362	+	201.191i	−0.566125	+	0.293281i
$687$	44.0676	−	44.0676i	0.0641450	−	0.0641450i
$688$	−14.6529	+	3.92623i	−0.0212978	+	0.00570673i
$689$	−191.148	+	110.359i	−0.277428	+	0.160173i
$690$	132.622	−	291.248i	0.192206	−	0.422099i
$691$	207.562	−	359.508i	0.300380	−	0.520273i	−0.675842	−	0.737046i	$-0.736220\pi$
$691$	207.562	−	359.508i	0.300380	−	0.520273i	0.976222	+	0.216773i	$0.0695533\pi$
$692$	375.720	−	375.720i	0.542948	−	0.542948i
$693$	194.091	+	286.361i	0.280073	+	0.413219i
$694$			13.5173i			0.0194774i
$695$	−492.099	−	405.402i	−0.708056	−	0.583313i
$696$	−127.221	−	220.353i	−0.182788	−	0.316599i
$697$	10.2118	+	2.73623i	0.0146510	+	0.00392573i
$698$	39.5166	−	10.5884i	0.0566140	−	0.0151697i
$699$			959.098i			1.37210i
$700$	401.592	+	106.376i	0.573703	+	0.151966i
$701$	−13.0606			−0.0186314			−0.00931568	−	0.999957i	$-0.502965\pi$
$701$	−13.0606			−0.0186314			−0.00931568	+	0.999957i	$0.502965\pi$
$702$	−21.3738	−	79.7681i	−0.0304470	−	0.113630i
$703$	74.7954	−	279.140i	0.106395	−	0.397070i
$704$	−224.806	+	129.792i	−0.319326	+	0.184363i
$705$	−601.142	+	729.698i	−0.852683	+	1.03503i
$706$	639.684			0.906068
$707$	−1008.53	−	489.089i	−1.42649	−	0.691780i
$708$	147.285	+	147.285i	0.208029	+	0.208029i
$709$	201.983	+	116.615i	0.284885	+	0.164478i	0.635633	−	0.771992i	$-0.280739\pi$
$709$	201.983	+	116.615i	0.284885	+	0.164478i	−0.350748	+	0.936470i	$0.614073\pi$
$710$	746.600	+	339.969i	1.05155	+	0.478830i
$711$	−71.0726	−	123.101i	−0.0999615	−	0.173138i
$712$	−228.722	−	853.601i	−0.321238	−	1.19888i
$713$	169.075	+	169.075i	0.237132	+	0.237132i
$714$	−30.7436	+	10.6632i	−0.0430583	+	0.0149345i
$715$	377.606	+	529.042i	0.528120	+	0.739918i
$716$	108.196	−	187.401i	0.151112	−	0.261734i
$717$	−1537.42	−	411.951i	−2.14424	−	0.574548i
$718$	−137.776	+	514.187i	−0.191889	+	0.716138i
$719$	−154.548	−	89.2281i	−0.214948	−	0.124100i	0.388661	−	0.921381i	$-0.372938\pi$
$719$	−154.548	−	89.2281i	−0.214948	−	0.124100i	−0.603609	+	0.797281i	$0.706271\pi$
$720$	−5.92759	+	35.4886i	−0.00823277	+	0.0492897i
$721$	−568.985	+	657.522i	−0.789161	+	0.911958i
$722$	−64.8781	+	64.8781i	−0.0898589	+	0.0898589i
$723$	−1126.87	+	301.944i	−1.55860	+	0.417627i
$724$	−300.860	+	173.701i	−0.415552	+	0.239919i
$725$	−184.760	+	36.0312i	−0.254842	+	0.0496982i
$726$	226.433	−	392.194i	0.311892	−	0.540212i
$727$	536.560	−	536.560i	0.738047	−	0.738047i	−0.234153	−	0.972200i	$-0.575232\pi$
$727$	536.560	−	536.560i	0.738047	−	0.738047i	0.972200	+	0.234153i	$0.0752316\pi$
$728$	695.685	+	1026.41i	0.955611	+	1.40990i
$729$			608.980i			0.835363i
$730$	304.487	−	369.602i	0.417105	−	0.506304i
$731$	7.65740	+	13.2630i	0.0104752	+	0.0181436i
$732$	288.302	+	77.2502i	0.393855	+	0.105533i
$733$	254.908	−	68.3024i	0.347760	−	0.0931820i	−0.0807110	−	0.996738i	$-0.525719\pi$
$733$	254.908	−	68.3024i	0.347760	−	0.0931820i	0.428471	+	0.903556i	$0.359052\pi$
$734$			424.163i			0.577879i
$735$	989.304	−	242.541i	1.34599	−	0.329988i
$736$	−379.130			−0.515122
$737$	111.373	+	415.648i	0.151116	+	0.563973i
$738$	32.9690	−	123.042i	0.0446735	−	0.166724i
$739$	−262.146	+	151.350i	−0.354730	+	0.204804i	−0.666767	−	0.745267i	$-0.732322\pi$
$739$	−262.146	+	151.350i	−0.354730	+	0.204804i	0.312037	+	0.950070i	$0.398989\pi$
$740$	164.091	−	15.8508i	0.221744	−	0.0214200i
$741$	−1885.35			−2.54433
$742$	−74.8314	+	50.7195i	−0.100851	+	0.0683552i
$743$	−767.699	−	767.699i	−1.03324	−	1.03324i	−0.999428	−	0.0338136i	$-0.989235\pi$
$743$	−767.699	−	767.699i	−1.03324	−	1.03324i	−0.0338136	−	0.999428i	$-0.510765\pi$
$744$	−579.607	−	334.636i	−0.779041	−	0.449780i
$745$	1038.38	−	388.596i	1.39380	−	0.521605i
$746$	−268.307	−	464.721i	−0.359660	−	0.622950i
$747$	−13.4102	−	50.0474i	−0.0179520	−	0.0669979i
$748$	8.77955	+	8.77955i	0.0117374	+	0.0117374i
$749$	−714.368	−	618.177i	−0.953762	−	0.825336i
$750$	582.679	+	315.676i	0.776905	+	0.420902i
$751$	−519.734	+	900.206i	−0.692056	+	1.19868i	0.279107	+	0.960260i	$0.409962\pi$
$751$	−519.734	+	900.206i	−0.692056	+	1.19868i	−0.971163	+	0.238416i	$0.923372\pi$
$752$	−38.1550	−	10.2236i	−0.0507380	−	0.0135952i
$753$	−22.0557	+	82.3130i	−0.0292904	+	0.109313i
$754$	−181.219	−	104.627i	−0.240344	−	0.138763i
$755$	−327.834	−	54.7574i	−0.434217	−	0.0725263i
$756$	16.1816	+	46.6539i	0.0214043	+	0.0617116i
$757$	612.294	−	612.294i	0.808843	−	0.808843i	−0.175616	−	0.984459i	$-0.556192\pi$
$757$	612.294	−	612.294i	0.808843	−	0.808843i	0.984459	+	0.175616i	$0.0561916\pi$
$758$	−632.822	+	169.564i	−0.834857	+	0.223699i
$759$	−259.280	+	149.695i	−0.341607	+	0.197227i
$760$	−769.572	−	350.430i	−1.01259	−	0.461092i
$761$	340.196	−	589.237i	0.447038	−	0.774293i	−0.551154	−	0.834404i	$-0.685812\pi$
$761$	340.196	−	589.237i	0.447038	−	0.774293i	0.998192	+	0.0601112i	$0.0191455\pi$
$762$	632.891	−	632.891i	0.830566	−	0.830566i
$763$	−400.538	+	825.932i	−0.524952	+	1.08248i
$764$			200.497i			0.262430i
$765$	36.1559	−	3.49259i	0.0472626	−	0.00456547i
$766$	92.5672	+	160.331i	0.120845	+	0.209310i
$767$	444.263	+	119.040i	0.579221	+	0.155202i
$768$	1058.16	−	283.533i	1.37781	−	0.369183i
$769$			1288.89i			1.67606i	0.545627	+	0.838028i	$0.316292\pi$
$769$			1288.89i			1.67606i	−0.545627	+	0.838028i	$0.683708\pi$
$770$	169.857	+	204.984i	0.220593	+	0.266212i
$771$	−1547.19			−2.00674
$772$	−66.2502	−	247.249i	−0.0858163	−	0.320271i
$773$	81.4217	−	303.870i	0.105332	−	0.393105i	−0.893051	−	0.449956i	$-0.851440\pi$
$773$	81.4217	−	303.870i	0.105332	−	0.393105i	0.998383	+	0.0568517i	$0.0181062\pi$
$774$	159.807	−	92.2644i	0.206468	−	0.119205i
$775$	−373.489	+	325.071i	−0.481921	+	0.419446i
$776$	−637.160			−0.821083
$777$	334.587	−	226.778i	0.430614	−	0.291863i
$778$	371.259	+	371.259i	0.477196	+	0.477196i
$779$	217.264	+	125.437i	0.278901	+	0.161024i
$780$	−376.959	−	1007.28i	−0.483281	−	1.29139i
$781$	−383.737	−	664.651i	−0.491340	−	0.851026i
$782$	−3.49372	−	13.0387i	−0.00446767	−	0.0166736i
$783$	−15.8214	−	15.8214i	−0.0202061	−	0.0202061i
$784$	26.3520	+	33.4182i	0.0336122	+	0.0426253i
$785$	393.049	−	280.541i	0.500699	−	0.357377i
$786$	−137.121	+	237.500i	−0.174454	+	0.302163i
$787$	1339.58	+	358.940i	1.70214	+	0.456086i	0.973476	−	0.228789i	$-0.0734766\pi$
$787$	1339.58	+	358.940i	1.70214	+	0.456086i	0.728660	+	0.684875i	$0.240143\pi$
$788$	−42.6537	+	159.186i	−0.0541290	+	0.202012i
$789$	1218.98	+	703.776i	1.54496	+	0.891985i
$790$	−63.5482	−	89.0336i	−0.0804407	−	0.112701i
$791$	533.460	+	102.450i	0.674412	+	0.129520i
$792$	284.028	−	284.028i	0.358622	−	0.358622i
$793$	636.606	−	170.578i	0.802782	−	0.215105i
$794$	160.523	−	92.6781i	0.202170	−	0.116723i
$795$	197.175	−	73.7893i	0.248018	−	0.0928168i
$796$	247.354	−	428.431i	0.310747	−	0.538229i
$797$	−905.526	+	905.526i	−1.13617	+	1.13617i	−0.147038	+	0.989131i	$0.546974\pi$
$797$	−905.526	+	905.526i	−1.13617	+	1.13617i	−0.989131	+	0.147038i	$0.953026\pi$
$798$	−770.183	+	55.5965i	−0.965142	+	0.0696699i
$799$			39.8786i			0.0499106i
$800$	54.2862	−	783.217i	0.0678577	−	0.979022i
$801$	450.414	+	780.140i	0.562314	+	0.973957i
$802$	65.2987	+	17.4967i	0.0814198	+	0.0218164i
$803$	−432.734	+	115.951i	−0.538897	+	0.144397i
$804$		−	712.028i		−	0.885606i
$805$	70.8042	+	416.571i	0.0879556	+	0.517479i
$806$	−550.414			−0.682895
$807$	−93.5190	−	349.018i	−0.115885	−	0.432488i
$808$	−336.842	+	1257.11i	−0.416884	+	1.55583i
$809$	313.879	−	181.218i	0.387983	−	0.224002i	−0.293303	−	0.956020i	$-0.594754\pi$
$809$	313.879	−	181.218i	0.387983	−	0.224002i	0.681286	+	0.732017i	$0.261421\pi$
$810$	53.2864	+	551.631i	0.0657857	+	0.681026i
$811$	668.488			0.824276			0.412138	−	0.911121i	$-0.364782\pi$
$811$	668.488			0.824276			0.412138	+	0.911121i	$0.364782\pi$
$812$	112.585	+	54.5983i	0.138651	+	0.0672392i
$813$	584.976	+	584.976i	0.719528	+	0.719528i
$814$	91.4852	+	52.8190i	0.112390	+	0.0648882i
$815$	89.5969	−	196.762i	0.109935	−	0.241426i
$816$	1.58313	+	2.74206i	0.00194011	+	0.00336036i
$817$	94.0606	+	351.039i	0.115129	+	0.429668i
$818$	262.206	+	262.206i	0.320546	+	0.320546i
$819$	−955.794	−	827.094i	−1.16703	−	1.00988i
$820$	−23.5773	+	141.158i	−0.0287528	+	0.172143i
$821$	360.015	−	623.564i	0.438508	−	0.759518i	−0.559067	−	0.829123i	$-0.688840\pi$
$821$	360.015	−	623.564i	0.438508	−	0.759518i	0.997575	+	0.0696047i	$0.0221738\pi$
$822$	−1001.70	−	268.405i	−1.21861	−	0.326526i
$823$	189.403	−	706.861i	0.230137	−	0.858884i	−0.750144	−	0.661275i	$-0.770016\pi$
$823$	189.403	−	706.861i	0.230137	−	0.858884i	0.980281	−	0.197609i	$-0.0633176\pi$
$824$	874.362	+	504.813i	1.06112	+	0.612637i
$825$	−272.120	−	557.062i	−0.329842	−	0.675227i
$826$	184.996	+	35.5282i	0.223966	+	0.0430123i
$827$	−709.579	+	709.579i	−0.858016	+	0.858016i	−0.991104	−	0.133088i	$-0.957511\pi$
$827$	−709.579	+	709.579i	−0.858016	+	0.858016i	0.133088	+	0.991104i	$0.457511\pi$
$828$	229.365	−	61.4582i	0.277011	−	0.0742249i
$829$	1403.34	−	810.220i	1.69281	−	0.977346i	0.740582	−	0.671966i	$-0.234550\pi$
$829$	1403.34	−	810.220i	1.69281	−	0.977346i	0.952231	−	0.305379i	$-0.0987832\pi$
$830$	−13.9749	−	37.3428i	−0.0168372	−	0.0449913i
$831$	775.200	−	1342.69i	0.932852	−	1.61575i
$832$	670.656	−	670.656i	0.806077	−	0.806077i
$833$	25.7025	−	34.4294i	0.0308554	−	0.0413318i
$834$			676.039i			0.810598i
$835$	90.7235	+	939.187i	0.108651	+	1.12477i
$836$	147.319	+	255.163i	0.176218	+	0.305219i
$837$	−56.8484	−	15.2325i	−0.0679193	−	0.0181989i
$838$	357.527	−	95.7992i	0.426644	−	0.114319i
$839$		−	451.819i		−	0.538521i	−0.963067	−	0.269260i	$-0.913221\pi$
$839$		−	451.819i		−	0.538521i	0.963067	−	0.269260i	$-0.0867793\pi$
$840$	−493.212	−	1074.97i	−0.587158	−	1.27973i
$841$	784.305			0.932586
$842$	84.6551	+	315.937i	0.100540	+	0.375222i
$843$	128.143	−	478.236i	0.152008	−	0.567303i
$844$	−611.226	+	352.892i	−0.724202	+	0.418118i
$845$	−1180.77	−	972.745i	−1.39736	−	1.15118i
$846$	480.499			0.567966
$847$	43.0516	+	596.397i	0.0508283	+	0.704129i
$848$	6.21982	+	6.21982i	0.00733470	+	0.00733470i
$849$	35.1142	+	20.2732i	0.0413595	+	0.0238789i
$850$	27.4360	−	5.35045i	0.0322777	−	0.00629465i
$851$	83.8366	+	145.209i	0.0985154	+	0.170634i
$852$	328.681	+	1226.65i	0.385776	+	1.43973i
$853$	−466.163	−	466.163i	−0.546499	−	0.546499i	0.378928	−	0.925426i	$-0.376293\pi$
$853$	−466.163	−	466.163i	−0.546499	−	0.546499i	−0.925426	+	0.378928i	$0.876293\pi$
$854$	255.030	−	88.4555i	0.298630	−	0.103578i
$855$	850.200	+	142.007i	0.994386	+	0.166090i
$856$	−548.457	+	949.955i	−0.640721	+	1.10976i
$857$	−150.738	−	40.3902i	−0.175891	−	0.0471298i	0.169799	−	0.985479i	$-0.445688\pi$
$857$	−150.738	−	40.3902i	−0.175891	−	0.0471298i	−0.345689	+	0.938349i	$0.612355\pi$
$858$	178.373	−	665.697i	0.207894	−	0.775871i
$859$	14.0348	+	8.10300i	0.0163386	+	0.00943307i	0.508147	−	0.861270i	$-0.330331\pi$
$859$	14.0348	+	8.10300i	0.0163386	+	0.00943307i	−0.491808	+	0.870703i	$0.663664\pi$
$860$	−168.743	+	120.441i	−0.196212	+	0.140047i
$861$	114.985	+	331.517i	0.133548	+	0.385037i
$862$	262.993	−	262.993i	0.305096	−	0.305096i
$863$	−1578.10	+	422.849i	−1.82862	+	0.489976i	−0.997783	−	0.0665465i	$-0.978802\pi$
$863$	−1578.10	+	422.849i	−1.82862	+	0.489976i	−0.830832	+	0.556523i	$0.812135\pi$
$864$	80.8163	−	46.6593i	0.0935374	−	0.0540038i
$865$	−463.780	+	1018.50i	−0.536162	+	1.17745i
$866$	110.337	−	191.109i	0.127409	−	0.220680i
$867$	−847.352	+	847.352i	−0.977338	+	0.977338i
$868$	328.270	−	23.6965i	0.378191	−	0.0273001i
$869$			102.334i			0.117761i
$870$	154.051	+	126.911i	0.177070	+	0.145874i
$871$	−786.122	−	1361.60i	−0.902552	−	1.56327i
$872$	1029.51	+	275.856i	1.18063	+	0.316349i
$873$	627.369	−	168.103i	0.718636	−	0.192558i
$874$		−	320.326i		−	0.366506i
$875$	−870.702	+	86.6222i	−0.995088	+	0.0989968i
$876$	741.297			0.846230
$877$	−177.417	−	662.129i	−0.202300	−	0.754993i	−0.990256	−	0.139261i	$-0.955527\pi$
$877$	−177.417	−	662.129i	−0.202300	−	0.754993i	0.787956	−	0.615732i	$-0.211139\pi$
$878$	286.852	−	1070.55i	0.326711	−	1.21930i
$879$	−135.419	+	78.1840i	−0.154060	+	0.0889466i
$880$	16.4703	−	19.9926i	0.0187163	−	0.0227188i
$881$	−974.437			−1.10606			−0.553029	−	0.833162i	$-0.686528\pi$
$881$	−974.437			−1.10606			−0.553029	+	0.833162i	$0.686528\pi$
$882$	−414.841	−	309.691i	−0.470342	−	0.351124i
$883$	191.886	+	191.886i	0.217311	+	0.217311i	0.807365	−	0.590053i	$-0.200893\pi$
$883$	191.886	+	191.886i	0.217311	+	0.217311i	−0.590053	+	0.807365i	$0.700893\pi$
$884$	−39.2876	−	22.6827i	−0.0444430	−	0.0256592i
$885$	−399.258	−	181.805i	−0.451139	−	0.205429i
$886$	−84.9683	−	147.169i	−0.0959010	−	0.166105i
$887$	254.165	+	948.556i	0.286544	+	1.06940i	0.947703	+	0.319152i	$0.103398\pi$
$887$	254.165	+	948.556i	0.286544	+	1.06940i	−0.661159	+	0.750246i	$0.729935\pi$
$888$	−331.862	−	331.862i	−0.373718	−	0.373718i
$889$	−222.886	+	1160.57i	−0.250716	+	1.30548i
$890$	402.729	+	564.239i	0.452504	+	0.633977i
$891$	259.235	−	449.008i	0.290949	−	0.503938i
$892$	−131.801	−	35.3161i	−0.147759	−	0.0395920i
$893$	−244.927	+	914.079i	−0.274274	+	1.02360i
$894$	−1018.08	−	587.790i	−1.13879	−	0.657483i
$895$	−75.0852	+	449.536i	−0.0838940	+	0.502275i
$896$	−321.192	+	371.171i	−0.358473	+	0.414253i
$897$	773.502	−	773.502i	0.862321	−	0.862321i
$898$	−933.799	+	250.211i	−1.03987	+	0.278631i
$899$	−129.150	+	74.5647i	−0.143659	+	0.0829418i
$900$	94.1201	+	482.629i	0.104578	+	0.536254i
$901$	4.44012	−	7.69052i	0.00492799	−	0.00853554i
$902$	−64.8461	+	64.8461i	−0.0718915	+	0.0718915i
$903$	−221.800	+	457.364i	−0.245626	+	0.506494i
$904$		−	630.730i		−	0.697711i
$905$	465.244	−	564.738i	0.514082	−	0.624020i
$906$	176.211	+	305.206i	0.194493	+	0.336872i
$907$	−864.080	−	231.530i	−0.952680	−	0.255270i	−0.251181	−	0.967940i	$-0.580819\pi$
$907$	−864.080	−	231.530i	−0.952680	−	0.255270i	−0.701499	+	0.712670i	$0.747485\pi$
$908$	−138.807	+	37.1932i	−0.152871	+	0.0409617i
$909$		−	1326.67i		−	1.45948i
$910$	−793.310	−	562.811i	−0.871770	−	0.618474i
$911$	670.054			0.735515			0.367757	−	0.929922i	$-0.380126\pi$
$911$	670.054			0.735515			0.367757	+	0.929922i	$0.380126\pi$
$912$	19.4465	+	72.5755i	0.0213230	+	0.0795784i
$913$	−9.65436	+	36.0305i	−0.0105743	+	0.0394639i
$914$	−806.634	+	465.710i	−0.882532	+	0.509530i
$915$	−625.727	+	60.4439i	−0.683854	+	0.0660589i
$916$	35.5851			0.0388484
$917$	−26.0707	−	361.159i	−0.0284304	−	0.393849i
$918$	2.34940	+	2.34940i	0.00255926	+	0.00255926i
$919$	224.983	+	129.894i	0.244813	+	0.141343i	0.617387	−	0.786660i	$-0.288191\pi$
$919$	224.983	+	129.894i	0.244813	+	0.141343i	−0.372574	+	0.928003i	$0.621525\pi$
$920$	459.503	−	171.962i	0.499460	−	0.186915i
$921$	195.978	+	339.443i	0.212788	+	0.368559i
$922$	232.010	+	865.872i	0.251637	+	0.939123i
$923$	1982.83	+	1982.83i	2.14825	+	2.14825i
$924$	−77.7229	+	404.705i	−0.0841157	+	0.437992i
$925$	−311.982	+	152.400i	−0.337277	+	0.164757i
$926$	−557.602	+	965.795i	−0.602162	+	1.04298i
$927$	−994.112	−	266.372i	−1.07240	−	0.287348i
$928$	61.2003	−	228.402i	0.0659486	−	0.246123i
$929$	−1154.31	−	666.442i	−1.24253	−	0.717376i	−0.272922	−	0.962036i	$-0.587990\pi$
$929$	−1154.31	−	666.442i	−1.24253	−	0.717376i	−0.969609	+	0.244660i	$0.921324\pi$
$930$	517.832	+	86.4924i	0.556808	+	0.0930026i
$931$	800.600	−	631.315i	0.859936	−	0.678104i
$932$	−387.242	+	387.242i	−0.415495	+	0.415495i
$933$	873.534	−	234.063i	0.936264	−	0.250871i
$934$	−138.274	+	79.8328i	−0.148045	+	0.0854741i
$935$	−23.7995	−	10.8373i	−0.0254541	−	0.0115907i
$936$	−733.812	+	1271.00i	−0.783988	+	1.35791i
$937$	343.232	−	343.232i	0.366310	−	0.366310i	−0.499820	−	0.866129i	$-0.666600\pi$
$937$	343.232	−	343.232i	0.366310	−	0.366310i	0.866129	+	0.499820i	$0.166600\pi$
$938$	−361.291	−	533.047i	−0.385171	−	0.568280i
$939$			759.087i			0.808400i
$940$	−537.335	+	51.9054i	−0.571633	+	0.0552186i
$941$	556.358	+	963.640i	0.591241	+	1.02406i	0.994066	+	0.108783i	$0.0346952\pi$
$941$	556.358	+	963.640i	0.591241	+	1.02406i	−0.402824	+	0.915277i	$0.631971\pi$
$942$	−494.577	−	132.521i	−0.525029	−	0.140681i
$943$	−140.600	+	37.6737i	−0.149099	+	0.0399509i
$944$		−	18.3295i		−	0.0194168i
$945$	−66.3600	−	80.0835i	−0.0702222	−	0.0847444i
$946$	−132.847			−0.140431
$947$	−438.497	−	1636.49i	−0.463038	−	1.72808i	−0.663314	−	0.748341i	$-0.730851\pi$
$947$	−438.497	−	1636.49i	−0.463038	−	1.72808i	0.200277	−	0.979739i	$-0.435816\pi$
$948$	43.8261	−	163.561i	0.0462300	−	0.172533i
$949$	1417.58	−	818.438i	1.49376	−	0.862421i
$950$	661.738	+	45.8662i	0.696566	+	0.0482802i
$951$	2061.43			2.16765
$952$	−44.8878	−	21.7685i	−0.0471511	−	0.0228660i
$953$	−892.480	−	892.480i	−0.936495	−	0.936495i	0.0616058	−	0.998101i	$-0.480378\pi$
$953$	−892.480	−	892.480i	−0.936495	−	0.936495i	−0.998101	+	0.0616058i	$0.980378\pi$
$954$	−92.6634	−	53.4993i	−0.0971315	−	0.0560789i
$955$	−148.008	−	395.497i	−0.154983	−	0.414133i
$956$	−454.416	−	787.071i	−0.475330	−	0.823296i
$957$	−48.3285	−	180.364i	−0.0505000	−	0.188469i
$958$	−671.140	−	671.140i	−0.700563	−	0.700563i
$959$	1293.66	−	448.698i	1.34897	−	0.467881i
$960$	−736.344	+	525.569i	−0.767025	+	0.547468i
$961$	284.368	−	492.540i	0.295908	−	0.512528i
$962$	−372.823	−	99.8975i	−0.387550	−	0.103844i
$963$	289.401	−	1080.06i	0.300520	−	1.12156i
$964$	−576.893	−	333.069i	−0.598437	−	0.345508i
$965$	313.205	+	438.813i	0.324565	+	0.454729i
$966$	293.174	−	338.793i	0.303492	−	0.350717i
$967$	456.890	−	456.890i	0.472482	−	0.472482i	−0.430235	−	0.902717i	$-0.641569\pi$
$967$	456.890	−	456.890i	0.472482	−	0.472482i	0.902717	+	0.430235i	$0.141569\pi$
$968$	670.634	−	179.696i	0.692803	−	0.185636i
$969$	65.6914	−	37.9270i	0.0677930	−	0.0391403i
$970$	468.110	−	175.182i	0.482587	−	0.180600i
$971$	−659.395	+	1142.11i	−0.679089	+	1.17622i	0.296167	+	0.955136i	$0.404291\pi$
$971$	−659.395	+	1142.11i	−0.679089	+	1.17622i	−0.975256	+	0.221080i	$0.929042\pi$
$972$	−561.736	+	561.736i	−0.577918	+	0.577918i
$973$	−500.807	−	738.889i	−0.514704	−	0.759393i
$974$		−	854.182i		−	0.876984i
$975$	1487.17	+	1708.68i	1.52530	+	1.75249i
$976$	−13.1326	−	22.7464i	−0.0134556	−	0.0233057i
$977$	664.423	+	178.032i	0.680065	+	0.182223i	0.582284	−	0.812985i	$-0.302159\pi$
$977$	664.423	+	178.032i	0.680065	+	0.182223i	0.0977804	+	0.995208i	$0.468826\pi$
$978$	−221.430	+	59.3320i	−0.226411	+	0.0606666i
$979$		−	648.531i		−	0.662442i
$980$	497.365	+	301.510i	0.507515	+	0.307663i
$981$	−1086.47			−1.10751
$982$	−20.2984	−	75.7546i	−0.0206704	−	0.0771432i
$983$	−103.362	+	385.752i	−0.105149	+	0.392423i	−0.998362	−	0.0572115i	$-0.981779\pi$
$983$	−103.362	+	385.752i	−0.105149	+	0.392423i	0.893213	+	0.449634i	$0.148446\pi$
$984$	352.843	−	203.714i	0.358580	−	0.207026i
$985$	−33.3741	−	345.495i	−0.0338823	−	0.350756i
$986$	8.41900			0.00853854
$987$	−1095.64	+	742.611i	−1.11008	+	0.752392i
$988$	−761.221	−	761.221i	−0.770466	−	0.770466i
$989$	−182.611	−	105.431i	−0.184642	−	0.106603i
$990$	−130.579	+	286.762i	−0.131898	+	0.289658i
$991$	352.050	+	609.769i	0.355248	+	0.615307i	0.987160	−	0.159733i	$-0.0510632\pi$
$991$	352.050	+	609.769i	0.355248	+	0.615307i	−0.631913	+	0.775040i	$0.717730\pi$
$992$	−160.979	−	600.781i	−0.162277	−	0.605626i
$993$	−1364.13	−	1364.13i	−1.37375	−	1.37375i
$994$	868.479	+	751.536i	0.873721	+	0.756073i
$995$	−171.657	+	1027.71i	−0.172520	+	1.03288i
$996$	30.8611	−	53.4531i	0.0309851	−	0.0536677i
$997$	710.472	+	190.370i	0.712610	+	0.190943i	0.596872	−	0.802336i	$-0.296410\pi$
$997$	710.472	+	190.370i	0.712610	+	0.190943i	0.115738	+	0.993280i	$0.463077\pi$
$998$	−15.9559	+	59.5483i	−0.0159879	+	0.0596676i
$999$	−35.7417	−	20.6355i	−0.0357774	−	0.0206561i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.3.l.a.23.4	yes	24
3.2	odd	2		315.3.ca.a.163.3		24
5.2	odd	4	inner	35.3.l.a.2.3	✓	24
5.3	odd	4		175.3.p.c.107.4		24
5.4	even	2		175.3.p.c.93.3		24
7.2	even	3		245.3.g.c.148.4		12
7.3	odd	6		245.3.m.b.18.3		24
7.4	even	3	inner	35.3.l.a.18.3	yes	24
7.5	odd	6		245.3.g.b.148.4		12
7.6	odd	2		245.3.m.b.128.4		24
15.2	even	4		315.3.ca.a.37.4		24
21.11	odd	6		315.3.ca.a.298.4		24
35.2	odd	12		245.3.g.c.197.4		12
35.4	even	6		175.3.p.c.18.4		24
35.12	even	12		245.3.g.b.197.4		12
35.17	even	12		245.3.m.b.67.4		24
35.18	odd	12		175.3.p.c.32.3		24
35.27	even	4		245.3.m.b.177.3		24
35.32	odd	12	inner	35.3.l.a.32.4	yes	24
105.32	even	12		315.3.ca.a.172.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.3.l.a.2.3	✓	24	5.2	odd	4	inner
35.3.l.a.18.3	yes	24	7.4	even	3	inner
35.3.l.a.23.4	yes	24	1.1	even	1	trivial
35.3.l.a.32.4	yes	24	35.32	odd	12	inner
175.3.p.c.18.4		24	35.4	even	6
175.3.p.c.32.3		24	35.18	odd	12
175.3.p.c.93.3		24	5.4	even	2
175.3.p.c.107.4		24	5.3	odd	4
245.3.g.b.148.4		12	7.5	odd	6
245.3.g.b.197.4		12	35.12	even	12
245.3.g.c.148.4		12	7.2	even	3
245.3.g.c.197.4		12	35.2	odd	12
245.3.m.b.18.3		24	7.3	odd	6
245.3.m.b.67.4		24	35.17	even	12
245.3.m.b.128.4		24	7.6	odd	2
245.3.m.b.177.3		24	35.27	even	4
315.3.ca.a.37.4		24	15.2	even	4
315.3.ca.a.163.3		24	3.2	odd	2
315.3.ca.a.172.3		24	105.32	even	12
315.3.ca.a.298.4		24	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.330037 + 1.23172i) q^{2} +(1.07605 - 4.01589i) q^{3} +(2.05590 - 1.18698i) q^{4} +(-3.17921 + 3.85910i) q^{5} +5.30157 q^{6} +(-5.79445 + 3.92739i) q^{7} +(5.74725 + 5.74725i) q^{8} +(-7.17525 - 4.14263i) q^{9} +O(q^{10})\)	\(q+(0.330037 + 1.23172i) q^{2} +(1.07605 - 4.01589i) q^{3} +(2.05590 - 1.18698i) q^{4} +(-3.17921 + 3.85910i) q^{5} +5.30157 q^{6} +(-5.79445 + 3.92739i) q^{7} +(5.74725 + 5.74725i) q^{8} +(-7.17525 - 4.14263i) q^{9} +(-5.80257 - 2.64224i) q^{10} +(2.98240 + 5.16566i) q^{11} +(-2.55450 - 9.53353i) q^{12} +(-15.4106 - 15.4106i) q^{13} +(-6.74980 - 5.84093i) q^{14} +(12.0767 + 16.9200i) q^{15} +(-0.434268 + 0.752174i) q^{16} +(0.846962 + 0.226943i) q^{17} +(2.73444 - 10.2051i) q^{18} +(18.0198 + 10.4038i) q^{19} +(-1.95549 + 11.7076i) q^{20} +(9.53681 + 27.4959i) q^{21} +(-5.37832 + 5.37832i) q^{22} +(-11.6614 + 3.12465i) q^{23} +(29.2647 - 16.8960i) q^{24} +(-4.78525 - 24.5378i) q^{25} +(13.8954 - 24.0675i) q^{26} +(2.10122 - 2.10122i) q^{27} +(-7.25111 + 14.9522i) q^{28} -7.52964i q^{29} +(-16.8548 + 20.4593i) q^{30} +(-9.90283 - 17.1522i) q^{31} +(30.3338 + 8.12792i) q^{32} +(23.9539 - 6.41844i) q^{33} +1.11811i q^{34} +(3.26561 - 34.8473i) q^{35} -19.6688 q^{36} +(-3.59463 - 13.4154i) q^{37} +(-6.86725 + 25.6289i) q^{38} +(-78.4697 + 45.3045i) q^{39} +(-40.4509 + 3.90748i) q^{40} +12.0569 q^{41} +(-30.7197 + 20.8213i) q^{42} +(12.3503 + 12.3503i) q^{43} +(12.2630 + 7.08007i) q^{44} +(38.7984 - 14.5197i) q^{45} +(-7.69736 - 13.3322i) q^{46} +(11.7711 + 43.9302i) q^{47} +(2.55335 + 2.55335i) q^{48} +(18.1513 - 45.5141i) q^{49} +(28.6442 - 13.9924i) q^{50} +(1.82275 - 3.15710i) q^{51} +(-49.9746 - 13.3907i) q^{52} +(2.62121 - 9.78248i) q^{53} +(3.28158 + 1.89462i) q^{54} +(-29.4164 - 4.91337i) q^{55} +(-55.8739 - 10.7305i) q^{56} +(61.1707 - 61.1707i) q^{57} +(9.27437 - 2.48506i) q^{58} +(-18.2765 + 10.5519i) q^{59} +(44.9121 + 20.4510i) q^{60} +(-15.1204 + 26.1893i) q^{61} +(17.8583 - 17.8583i) q^{62} +(57.8463 - 4.17570i) q^{63} +43.5193i q^{64} +(108.464 - 10.4774i) q^{65} +(15.8114 + 27.3861i) q^{66} +(69.6836 + 18.6717i) q^{67} +(2.01065 - 0.538751i) q^{68} +50.1930i q^{69} +(43.9998 - 7.47861i) q^{70} -128.667 q^{71} +(-17.4292 - 65.0467i) q^{72} +(-19.4392 + 72.5481i) q^{73} +(15.3375 - 8.85513i) q^{74} +(-103.690 - 7.18694i) q^{75} +49.3961 q^{76} +(-37.5689 - 18.2191i) q^{77} +(-81.7002 - 81.7002i) q^{78} +(14.8579 + 8.57820i) q^{79} +(-1.52208 - 4.06720i) q^{80} +(-43.4609 - 75.2765i) q^{81} +(3.97924 + 14.8507i) q^{82} +(4.42198 + 4.42198i) q^{83} +(52.2438 + 45.2091i) q^{84} +(-3.56846 + 2.54701i) q^{85} +(-11.1360 + 19.2881i) q^{86} +(-30.2382 - 8.10230i) q^{87} +(-12.5478 + 46.8289i) q^{88} +(-94.1599 - 54.3633i) q^{89} +(30.6890 + 42.9966i) q^{90} +(149.819 + 28.7725i) q^{91} +(-20.2657 + 20.2657i) q^{92} +(-79.5373 + 21.3120i) q^{93} +(-50.2247 + 28.9972i) q^{94} +(-97.4379 + 36.4645i) q^{95} +(65.2816 - 113.071i) q^{96} +(-55.4317 + 55.4317i) q^{97} +(62.0510 + 7.33588i) q^{98} -49.4198i 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more