LMFDB - Embedded newform 96.3.m.a.43.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [96,3,Mod(19,96)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(96, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 7, 0]))

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

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

chi := DirichletCharacter("96.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 96 = 2^{5} \cdot 3 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	96.m (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.61581053786$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			43.1
Character	$\chi$	$=$	96.43
Dual form			96.3.m.a.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.99199 - 0.178809i) q^{2} +(0.662827 + 1.60021i) q^{3} +(3.93605 + 0.712374i) q^{4} +(-1.28772 + 3.10884i) q^{5} +(-1.03421 - 3.30612i) q^{6} +(0.299204 - 0.299204i) q^{7} +(-7.71320 - 2.12285i) q^{8} +(-2.12132 + 2.12132i) q^{9} +O(q^{10})$	\(q+(-1.99199 - 0.178809i) q^{2} +(0.662827 + 1.60021i) q^{3} +(3.93605 + 0.712374i) q^{4} +(-1.28772 + 3.10884i) q^{5} +(-1.03421 - 3.30612i) q^{6} +(0.299204 - 0.299204i) q^{7} +(-7.71320 - 2.12285i) q^{8} +(-2.12132 + 2.12132i) q^{9} +(3.12102 - 5.96252i) q^{10} +(-4.96585 + 11.9886i) q^{11} +(1.46898 + 6.77068i) q^{12} +(4.82065 + 11.6381i) q^{13} +(-0.649513 + 0.542512i) q^{14} -5.82832 q^{15} +(14.9850 + 5.60788i) q^{16} +14.2262i q^{17} +(4.60496 - 3.84634i) q^{18} +(-7.21158 + 2.98713i) q^{19} +(-7.28320 + 11.3192i) q^{20} +(0.677110 + 0.280468i) q^{21} +(12.0356 - 22.9933i) q^{22} +(-13.1712 - 13.1712i) q^{23} +(-1.71553 - 13.7498i) q^{24} +(9.67103 + 9.67103i) q^{25} +(-7.52169 - 24.0449i) q^{26} +(-4.80062 - 1.98848i) q^{27} +(1.39083 - 0.964540i) q^{28} +(39.0765 - 16.1860i) q^{29} +(11.6100 + 1.04216i) q^{30} -42.8706i q^{31} +(-28.8473 - 13.8503i) q^{32} -22.4758 q^{33} +(2.54378 - 28.3385i) q^{34} +(0.544886 + 1.31547i) q^{35} +(-9.86080 + 6.83846i) q^{36} +(3.17745 - 7.67105i) q^{37} +(14.8995 - 4.66084i) q^{38} +(-15.4281 + 15.4281i) q^{39} +(16.5321 - 21.2455i) q^{40} +(46.2561 - 46.2561i) q^{41} +(-1.29865 - 0.679763i) q^{42} +(-9.80640 + 23.6747i) q^{43} +(-28.0862 + 43.6503i) q^{44} +(-3.86317 - 9.32651i) q^{45} +(23.8818 + 28.5921i) q^{46} -27.4402 q^{47} +(0.958727 + 27.6962i) q^{48} +48.8210i q^{49} +(-17.5353 - 20.9939i) q^{50} +(-22.7649 + 9.42952i) q^{51} +(10.6837 + 49.2422i) q^{52} +(24.9355 + 10.3286i) q^{53} +(9.20723 + 4.81943i) q^{54} +(-30.8760 - 30.8760i) q^{55} +(-2.94299 + 1.67266i) q^{56} +(-9.56006 - 9.56006i) q^{57} +(-80.7342 + 25.2551i) q^{58} +(90.6328 + 37.5413i) q^{59} +(-22.9406 - 4.15194i) q^{60} +(63.0111 - 26.1000i) q^{61} +(-7.66567 + 85.3979i) q^{62} +1.26942i q^{63} +(54.9871 + 32.7479i) q^{64} -42.3885 q^{65} +(44.7715 + 4.01888i) q^{66} +(-24.6996 - 59.6302i) q^{67} +(-10.1344 + 55.9951i) q^{68} +(12.3464 - 29.8070i) q^{69} +(-0.850189 - 2.71784i) q^{70} +(52.2102 - 52.2102i) q^{71} +(20.8654 - 11.8589i) q^{72} +(-64.8423 + 64.8423i) q^{73} +(-7.70112 + 14.7125i) q^{74} +(-9.06542 + 21.8859i) q^{75} +(-30.5131 + 6.62018i) q^{76} +(2.10124 + 5.07285i) q^{77} +(33.4912 - 27.9739i) q^{78} -84.3643 q^{79} +(-36.7306 + 39.3647i) q^{80} -9.00000i q^{81} +(-100.413 + 83.8707i) q^{82} +(56.8626 - 23.5533i) q^{83} +(2.46534 + 1.58629i) q^{84} +(-44.2270 - 18.3194i) q^{85} +(23.7675 - 45.4064i) q^{86} +(51.8019 + 51.8019i) q^{87} +(63.7526 - 81.9289i) q^{88} +(-47.1748 - 47.1748i) q^{89} +(6.02773 + 19.2691i) q^{90} +(4.92452 + 2.03980i) q^{91} +(-42.4599 - 61.2256i) q^{92} +(68.6018 - 28.4158i) q^{93} +(54.6607 + 4.90658i) q^{94} -26.2662i q^{95} +(3.04257 - 55.3421i) q^{96} -128.441 q^{97} +(8.72965 - 97.2509i) q^{98} +(-14.8975 - 35.9658i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q+O(q^{10}) $ 64 * q	$ 64 q + 40 q^{10} + 48 q^{12} + 32 q^{14} - 8 q^{16} - 24 q^{18} - 160 q^{20} - 184 q^{22} + 128 q^{23} - 72 q^{24} - 200 q^{26} - 120 q^{28} + 40 q^{32} + 120 q^{34} - 192 q^{35} + 280 q^{38} + 584 q^{40} - 192 q^{43} + 104 q^{44} + 32 q^{46} - 312 q^{50} - 192 q^{51} - 424 q^{52} + 320 q^{53} - 72 q^{54} - 256 q^{55} - 392 q^{56} - 352 q^{58} - 256 q^{59} - 144 q^{60} + 64 q^{61} - 48 q^{62} + 408 q^{64} + 144 q^{66} + 64 q^{67} + 856 q^{68} - 192 q^{69} + 984 q^{70} + 512 q^{71} + 1056 q^{74} + 384 q^{75} + 296 q^{76} - 448 q^{77} + 360 q^{78} + 512 q^{79} + 328 q^{80} - 760 q^{82} - 448 q^{86} - 1072 q^{88} + 192 q^{91} - 784 q^{92} - 480 q^{94} + 600 q^{96} + 272 q^{98}+O(q^{100}) $ 64 * q + 40 * q^10 + 48 * q^12 + 32 * q^14 - 8 * q^16 - 24 * q^18 - 160 * q^20 - 184 * q^22 + 128 * q^23 - 72 * q^24 - 200 * q^26 - 120 * q^28 + 40 * q^32 + 120 * q^34 - 192 * q^35 + 280 * q^38 + 584 * q^40 - 192 * q^43 + 104 * q^44 + 32 * q^46 - 312 * q^50 - 192 * q^51 - 424 * q^52 + 320 * q^53 - 72 * q^54 - 256 * q^55 - 392 * q^56 - 352 * q^58 - 256 * q^59 - 144 * q^60 + 64 * q^61 - 48 * q^62 + 408 * q^64 + 144 * q^66 + 64 * q^67 + 856 * q^68 - 192 * q^69 + 984 * q^70 + 512 * q^71 + 1056 * q^74 + 384 * q^75 + 296 * q^76 - 448 * q^77 + 360 * q^78 + 512 * q^79 + 328 * q^80 - 760 * q^82 - 448 * q^86 - 1072 * q^88 + 192 * q^91 - 784 * q^92 - 480 * q^94 + 600 * q^96 + 272 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/96\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$65$
$\chi(n)$	$-1$	$e\left(\frac{5}{8}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.99199	−	0.178809i	−0.995995	−	0.0894047i
$2$	−1.99199	−	0.178809i	−0.995995	−	0.0894047i
$3$	0.662827	+	1.60021i	0.220942	+	0.533402i
$3$	0.662827	+	1.60021i	0.220942	+	0.533402i
$4$	3.93605	+	0.712374i	0.984014	+	0.178093i
$5$	−1.28772	+	3.10884i	−0.257545	+	0.621768i	−0.998775	−	0.0494831i	$-0.984243\pi$
$5$	−1.28772	+	3.10884i	−0.257545	+	0.621768i	0.741230	+	0.671251i	$0.234243\pi$
$6$	−1.03421	−	3.30612i	−0.172369	−	0.551019i
$7$	0.299204	−	0.299204i	0.0427435	−	0.0427435i	−0.685412	−	0.728155i	$-0.740378\pi$
$7$	0.299204	−	0.299204i	0.0427435	−	0.0427435i	0.728155	+	0.685412i	$0.240378\pi$
$8$	−7.71320	−	2.12285i	−0.964151	−	0.265356i
$9$	−2.12132	+	2.12132i	−0.235702	+	0.235702i
$10$	3.12102	−	5.96252i	0.312102	−	0.596252i
$11$	−4.96585	+	11.9886i	−0.451441	+	1.08987i	0.520334	+	0.853963i	$0.325807\pi$
$11$	−4.96585	+	11.9886i	−0.451441	+	1.08987i	−0.971775	+	0.235911i	$0.924193\pi$
$12$	1.46898	+	6.77068i	0.122415	+	0.564223i
$13$	4.82065	+	11.6381i	0.370819	+	0.895236i	0.993612	+	0.112850i	$0.0359979\pi$
$13$	4.82065	+	11.6381i	0.370819	+	0.895236i	−0.622793	+	0.782387i	$0.714002\pi$
$14$	−0.649513	+	0.542512i	−0.0463938	+	0.0387509i
$15$	−5.82832			−0.388555
$16$	14.9850	+	5.60788i	0.936565	+	0.350493i
$17$			14.2262i			0.836836i	0.908255	+	0.418418i	$0.137415\pi$
$17$			14.2262i			0.836836i	−0.908255	+	0.418418i	$0.862585\pi$
$18$	4.60496	−	3.84634i	0.255831	−	0.213685i
$19$	−7.21158	+	2.98713i	−0.379557	+	0.157217i	−0.564301	−	0.825569i	$-0.690854\pi$
$19$	−7.21158	+	2.98713i	−0.379557	+	0.157217i	0.184744	+	0.982787i	$0.440854\pi$
$20$	−7.28320	+	11.3192i	−0.364160	+	0.565961i
$21$	0.677110	+	0.280468i	0.0322433	+	0.0133556i
$22$	12.0356	−	22.9933i	0.547073	−	1.04515i
$23$	−13.1712	−	13.1712i	−0.572663	−	0.572663i	0.360209	−	0.932872i	$-0.382705\pi$
$23$	−13.1712	−	13.1712i	−0.572663	−	0.572663i	−0.932872	+	0.360209i	$0.882705\pi$
$24$	−1.71553	−	13.7498i	−0.0714804	−	0.572908i
$25$	9.67103	+	9.67103i	0.386841	+	0.386841i
$26$	−7.52169	−	24.0449i	−0.289296	−	0.924804i
$27$	−4.80062	−	1.98848i	−0.177801	−	0.0736475i
$28$	1.39083	−	0.964540i	0.0496725	−	0.0344478i
$29$	39.0765	−	16.1860i	1.34746	−	0.558138i	0.411879	−	0.911238i	$-0.364872\pi$
$29$	39.0765	−	16.1860i	1.34746	−	0.558138i	0.935586	+	0.353100i	$0.114872\pi$
$30$	11.6100	+	1.04216i	0.386999	+	0.0347386i
$31$		−	42.8706i		−	1.38292i	−0.722413	−	0.691461i	$-0.756967\pi$
$31$		−	42.8706i		−	1.38292i	0.722413	−	0.691461i	$-0.243033\pi$
$32$	−28.8473	−	13.8503i	−0.901479	−	0.432822i
$33$	−22.4758			−0.681083
$34$	2.54378	−	28.3385i	0.0748171	−	0.833485i
$35$	0.544886	+	1.31547i	0.0155682	+	0.0375849i
$36$	−9.86080	+	6.83846i	−0.273911	+	0.189957i
$37$	3.17745	−	7.67105i	0.0858771	−	0.207326i	−0.875107	−	0.483930i	$-0.839209\pi$
$37$	3.17745	−	7.67105i	0.0858771	−	0.207326i	0.960984	+	0.276604i	$0.0892090\pi$
$38$	14.8995	−	4.66084i	0.392093	−	0.122654i
$39$	−15.4281	+	15.4281i	−0.395591	+	0.395591i
$40$	16.5321	−	21.2455i	0.413301	−	0.531137i
$41$	46.2561	−	46.2561i	1.12820	−	1.12820i	0.137728	−	0.990470i	$-0.456020\pi$
$41$	46.2561	−	46.2561i	1.12820	−	1.12820i	0.990470	−	0.137728i	$-0.0439800\pi$
$42$	−1.29865	−	0.679763i	−0.0309201	−	0.0161848i
$43$	−9.80640	+	23.6747i	−0.228056	+	0.550575i	−0.995941	−	0.0900126i	$-0.971309\pi$
$43$	−9.80640	+	23.6747i	−0.228056	+	0.550575i	0.767885	+	0.640588i	$0.221309\pi$
$44$	−28.0862	+	43.6503i	−0.638323	+	0.992052i
$45$	−3.86317	−	9.32651i	−0.0858482	−	0.207256i
$46$	23.8818	+	28.5921i	0.519171	+	0.621568i
$47$	−27.4402			−0.583835			−0.291918	−	0.956443i	$-0.594293\pi$
$47$	−27.4402			−0.583835			−0.291918	+	0.956443i	$0.594293\pi$
$48$	0.958727	+	27.6962i	0.0199735	+	0.577005i
$49$			48.8210i			0.996346i
$50$	−17.5353	−	20.9939i	−0.350707	−	0.419877i
$51$	−22.7649	+	9.42952i	−0.446370	+	0.184893i
$52$	10.6837	+	49.2422i	0.205455	+	0.946965i
$53$	24.9355	+	10.3286i	0.470482	+	0.194880i	0.605311	−	0.795989i	$-0.293049\pi$
$53$	24.9355	+	10.3286i	0.470482	+	0.194880i	−0.134830	+	0.990869i	$0.543049\pi$
$54$	9.20723	+	4.81943i	0.170504	+	0.0892488i
$55$	−30.8760	−	30.8760i	−0.561382	−	0.561382i
$56$	−2.94299	+	1.67266i	−0.0525534	+	0.0298689i
$57$	−9.56006	−	9.56006i	−0.167720	−	0.167720i
$58$	−80.7342	+	25.2551i	−1.39197	+	0.435433i
$59$	90.6328	+	37.5413i	1.53615	+	0.636294i	0.980746	−	0.195287i	$-0.0625638\pi$
$59$	90.6328	+	37.5413i	1.53615	+	0.636294i	0.555404	+	0.831581i	$0.312564\pi$
$60$	−22.9406	−	4.15194i	−0.382343	−	0.0691990i
$61$	63.0111	−	26.1000i	1.03297	−	0.427870i	0.199185	−	0.979962i	$-0.436170\pi$
$61$	63.0111	−	26.1000i	1.03297	−	0.427870i	0.833783	+	0.552092i	$0.186170\pi$
$62$	−7.66567	+	85.3979i	−0.123640	+	1.37738i
$63$			1.26942i			0.0201495i
$64$	54.9871	+	32.7479i	0.859173	+	0.511686i
$65$	−42.3885			−0.652131
$66$	44.7715	+	4.01888i	0.678356	+	0.0608921i
$67$	−24.6996	−	59.6302i	−0.368651	−	0.890003i	−0.993972	−	0.109635i	$-0.965032\pi$
$67$	−24.6996	−	59.6302i	−0.368651	−	0.890003i	0.625321	−	0.780368i	$-0.284968\pi$
$68$	−10.1344	+	55.9951i	−0.149035	+	0.823458i
$69$	12.3464	−	29.8070i	0.178934	−	0.431985i
$70$	−0.850189	−	2.71784i	−0.0121456	−	0.0388262i
$71$	52.2102	−	52.2102i	0.735355	−	0.735355i	−0.236320	−	0.971675i	$-0.575941\pi$
$71$	52.2102	−	52.2102i	0.735355	−	0.735355i	0.971675	+	0.236320i	$0.0759413\pi$
$72$	20.8654	−	11.8589i	0.289797	−	0.164708i
$73$	−64.8423	+	64.8423i	−0.888251	+	0.888251i	−0.994355	−	0.106104i	$-0.966162\pi$
$73$	−64.8423	+	64.8423i	−0.888251	+	0.888251i	0.106104	+	0.994355i	$0.466162\pi$
$74$	−7.70112	+	14.7125i	−0.104069	+	0.198818i
$75$	−9.06542	+	21.8859i	−0.120872	+	0.291811i
$76$	−30.5131	+	6.62018i	−0.401488	+	0.0871076i
$77$	2.10124	+	5.07285i	0.0272889	+	0.0658812i
$78$	33.4912	−	27.9739i	0.429375	−	0.358639i
$79$	−84.3643			−1.06790			−0.533952	−	0.845515i	$-0.679294\pi$
$79$	−84.3643			−1.06790			−0.533952	+	0.845515i	$0.679294\pi$
$80$	−36.7306	+	39.3647i	−0.459132	+	0.492059i
$81$		−	9.00000i		−	0.111111i
$82$	−100.413	+	83.8707i	−1.22455	+	1.02281i
$83$	56.8626	−	23.5533i	0.685092	−	0.283774i	−0.0128618	−	0.999917i	$-0.504094\pi$
$83$	56.8626	−	23.5533i	0.685092	−	0.283774i	0.697954	+	0.716143i	$0.254094\pi$
$84$	2.46534	+	1.58629i	0.0293493	+	0.0188844i
$85$	−44.2270	−	18.3194i	−0.520317	−	0.215523i
$86$	23.7675	−	45.4064i	0.276366	−	0.527981i
$87$	51.8019	+	51.8019i	0.595424	+	0.595424i
$88$	63.7526	−	81.9289i	0.724461	−	0.931010i
$89$	−47.1748	−	47.1748i	−0.530054	−	0.530054i	0.390534	−	0.920588i	$-0.372290\pi$
$89$	−47.1748	−	47.1748i	−0.530054	−	0.530054i	−0.920588	+	0.390534i	$0.872290\pi$
$90$	6.02773	+	19.2691i	0.0669747	+	0.214101i
$91$	4.92452	+	2.03980i	0.0541156	+	0.0224154i
$92$	−42.4599	−	61.2256i	−0.461520	−	0.665495i
$93$	68.6018	−	28.4158i	0.737654	−	0.305546i
$94$	54.6607	+	4.90658i	0.581497	+	0.0521976i
$95$		−	26.2662i		−	0.276486i
$96$	3.04257	−	55.3421i	0.0316935	−	0.576480i
$97$	−128.441			−1.32413			−0.662066	−	0.749446i	$-0.730320\pi$
$97$	−128.441			−1.32413			−0.662066	+	0.749446i	$0.730320\pi$
$98$	8.72965	−	97.2509i	0.0890781	−	0.992356i
$99$	−14.8975	−	35.9658i	−0.150480	−	0.363291i
$100$	31.1763	+	44.9551i	0.311763	+	0.449551i
$101$	15.5588	−	37.5621i	0.154047	−	0.371902i	−0.827949	−	0.560803i	$-0.810492\pi$
$101$	15.5588	−	37.5621i	0.154047	−	0.371902i	0.981996	+	0.188901i	$0.0604924\pi$
$102$	47.0335	−	14.7129i	0.461113	−	0.144244i
$103$	133.190	−	133.190i	1.29311	−	1.29311i	0.360252	−	0.932855i	$-0.382691\pi$
$103$	133.190	−	133.190i	1.29311	−	1.29311i	0.932855	−	0.360252i	$-0.117309\pi$
$104$	−12.4768	−	100.000i	−0.119969	−	0.961542i
$105$	−1.74386	+	1.74386i	−0.0166082	+	0.0166082i
$106$	−47.8245	−	25.0332i	−0.451174	−	0.236163i
$107$	−68.3844	+	165.095i	−0.639106	+	1.54294i	0.188765	+	0.982022i	$0.439551\pi$
$107$	−68.3844	+	165.095i	−0.639106	+	1.54294i	−0.827872	+	0.560917i	$0.810449\pi$
$108$	−17.4790	−	11.2466i	−0.161842	−	0.104135i
$109$	63.9826	+	154.468i	0.586996	+	1.41713i	0.886361	+	0.462995i	$0.153225\pi$
$109$	63.9826	+	154.468i	0.586996	+	1.41713i	−0.299365	+	0.954139i	$0.596775\pi$
$110$	55.9838	+	67.0257i	0.508944	+	0.609324i
$111$	14.3814			0.129562
$112$	6.16150	−	2.80569i	0.0550134	−	0.0250508i
$113$			29.5094i			0.261145i	0.991439	+	0.130572i	$0.0416815\pi$
$113$			29.5094i			0.261145i	−0.991439	+	0.130572i	$0.958318\pi$
$114$	17.3341	+	20.7530i	0.152054	+	0.182044i
$115$	57.9082	−	23.9863i	0.503549	−	0.208577i
$116$	165.338	−	35.8720i	1.42532	−	0.309241i
$117$	−34.9142	−	14.4619i	−0.298412	−	0.123606i
$118$	−173.827	−	90.9880i	−1.47311	−	0.771085i
$119$	4.25655	+	4.25655i	0.0357693	+	0.0357693i
$120$	44.9550	+	12.3726i	0.374625	+	0.103105i
$121$	−33.5073	−	33.5073i	−0.276920	−	0.276920i
$122$	−130.184	+	40.7241i	−1.06709	+	0.333804i
$123$	104.679	+	43.3595i	0.851050	+	0.352516i
$124$	30.5399	−	168.741i	0.246289	−	1.36081i
$125$	−120.240	+	49.8051i	−0.961922	+	0.398441i
$126$	0.226984	−	2.52867i	0.00180146	−	0.0200688i
$127$			154.012i			1.21269i	0.795202	+	0.606345i	$0.207365\pi$
$127$			154.012i			1.21269i	−0.795202	+	0.606345i	$0.792635\pi$
$128$	−103.678	−	75.0657i	−0.809985	−	0.586451i
$129$	−44.3844			−0.344065
$130$	84.4376	+	7.57947i	0.649520	+	0.0583036i
$131$	45.2112	+	109.150i	0.345124	+	0.833202i	0.997181	+	0.0750327i	$0.0239061\pi$
$131$	45.2112	+	109.150i	0.345124	+	0.833202i	−0.652057	+	0.758170i	$0.726094\pi$
$132$	−88.4658	−	16.0111i	−0.670195	−	0.121296i
$133$	−1.26397	+	3.05150i	−0.00950355	+	0.0229436i
$134$	38.5390	+	123.199i	0.287604	+	0.919398i
$135$	12.3637	−	12.3637i	0.0915832	−	0.0915832i
$136$	30.2000	−	109.730i	0.222059	−	0.806836i
$137$	122.088	−	122.088i	0.891152	−	0.891152i	−0.103480	−	0.994632i	$-0.532998\pi$
$137$	122.088	−	122.088i	0.891152	−	0.891152i	0.994632	+	0.103480i	$0.0329976\pi$
$138$	−29.9238	+	57.1675i	−0.216839	+	0.414257i
$139$	4.37735	−	10.5679i	0.0314917	−	0.0760277i	−0.907351	−	0.420373i	$-0.861899\pi$
$139$	4.37735	−	10.5679i	0.0314917	−	0.0760277i	0.938843	+	0.344345i	$0.111899\pi$
$140$	1.20759	+	5.56593i	0.00862567	+	0.0397566i
$141$	−18.1881	−	43.9101i	−0.128994	−	0.311419i
$142$	−113.338	+	94.6666i	−0.798155	+	0.666666i
$143$	−163.463			−1.14310
$144$	−43.6842	+	19.8920i	−0.303363	+	0.138139i
$145$			142.326i			0.981555i
$146$	140.760	−	117.571i	0.964108	−	0.805280i
$147$	−78.1236	+	32.3599i	−0.531453	+	0.220135i
$148$	17.9713	−	27.9301i	0.121428	−	0.188717i
$149$	−197.635	−	81.8629i	−1.32641	−	0.549415i	−0.396778	−	0.917915i	$-0.629872\pi$
$149$	−197.635	−	81.8629i	−1.32641	−	0.549415i	−0.929628	+	0.368499i	$0.879872\pi$
$150$	21.9716	−	41.9754i	0.146478	−	0.279836i
$151$	96.2016	+	96.2016i	0.637097	+	0.637097i	0.949838	−	0.312742i	$-0.101247\pi$
$151$	96.2016	+	96.2016i	0.637097	+	0.637097i	−0.312742	+	0.949838i	$0.601247\pi$
$152$	61.9656	−	7.73130i	0.407668	−	0.0508638i
$153$	−30.1783	−	30.1783i	−0.197244	−	0.197244i
$154$	−3.27858	−	10.4808i	−0.0212895	−	0.0680571i
$155$	133.278	+	55.2055i	0.859857	+	0.356164i
$156$	−71.7162	+	49.7351i	−0.459719	+	0.318815i
$157$	71.2949	−	29.5313i	0.454107	−	0.188097i	−0.143893	−	0.989593i	$-0.545962\pi$
$157$	71.2949	−	29.5313i	0.454107	−	0.188097i	0.598000	+	0.801496i	$0.295962\pi$
$158$	168.053	+	15.0851i	1.06363	+	0.0954756i
$159$			46.7481i			0.294013i
$160$	80.2058	−	71.8463i	0.501286	−	0.449039i
$161$	−7.88179			−0.0489552
$162$	−1.60929	+	17.9279i	−0.00993386	+	0.110666i
$163$	−53.9712	−	130.298i	−0.331112	−	0.799374i	−0.998505	−	0.0546684i	$-0.982590\pi$
$163$	−53.9712	−	130.298i	−0.331112	−	0.799374i	0.667393	−	0.744706i	$-0.267410\pi$
$164$	215.018	−	149.115i	1.31109	−	0.909238i
$165$	28.9425	−	69.8735i	0.175409	−	0.423476i
$166$	−117.481	+	36.7503i	−0.707719	+	0.221387i
$167$	−67.9852	+	67.9852i	−0.407097	+	0.407097i	−0.880725	−	0.473628i	$-0.842944\pi$
$167$	−67.9852	+	67.9852i	−0.407097	+	0.407097i	0.473628	+	0.880725i	$0.342944\pi$
$168$	−4.62730	−	3.60071i	−0.0275434	−	0.0214328i
$169$	7.29493	−	7.29493i	0.0431653	−	0.0431653i
$170$	84.8240	+	44.4003i	0.498965	+	0.261178i
$171$	8.96140	−	21.6347i	0.0524058	−	0.126519i
$172$	−55.4638	+	86.1992i	−0.322464	+	0.501158i
$173$	6.07918	+	14.6764i	0.0351398	+	0.0848349i	0.940475	−	0.339862i	$-0.110381\pi$
$173$	6.07918	+	14.6764i	0.0351398	+	0.0848349i	−0.905335	+	0.424697i	$0.860381\pi$
$174$	−93.9263	−	112.452i	−0.539806	−	0.646274i
$175$	5.78723			0.0330699
$176$	−141.644	+	151.802i	−0.804797	+	0.862512i
$177$			169.915i			0.959970i
$178$	85.5365	+	102.407i	0.480542	+	0.575321i
$179$	−80.2273	+	33.2312i	−0.448197	+	0.185649i	−0.595354	−	0.803464i	$-0.702988\pi$
$179$	−80.2273	+	33.2312i	−0.448197	+	0.185649i	0.147156	+	0.989113i	$0.452988\pi$
$180$	−8.56168	−	39.4617i	−0.0475649	−	0.219232i
$181$	−196.299	−	81.3097i	−1.08452	−	0.449225i	−0.232430	−	0.972613i	$-0.574668\pi$
$181$	−196.299	−	81.3097i	−1.08452	−	0.449225i	−0.852094	+	0.523388i	$0.824668\pi$
$182$	−9.44487	−	4.94382i	−0.0518949	−	0.0271639i
$183$	83.5309	+	83.5309i	0.456453	+	0.456453i
$184$	73.6320	+	129.553i	0.400174	+	0.704092i
$185$	19.7564	+	19.7564i	0.106791	+	0.106791i
$186$	−141.735	+	44.3374i	−0.762017	+	0.238373i
$187$	−170.553	−	70.6452i	−0.912046	−	0.377782i
$188$	−108.006	−	19.5477i	−0.574502	−	0.103977i
$189$	−2.03133	+	0.841404i	−0.0107478	+	0.00445187i
$190$	−4.69665	+	52.3221i	−0.0247192	+	0.275379i
$191$		−	111.802i		−	0.585349i	−0.956212	−	0.292674i	$-0.905455\pi$
$191$		−	111.802i		−	0.585349i	0.956212	−	0.292674i	$-0.0945452\pi$
$192$	−15.9565	+	109.697i	−0.0831066	+	0.571338i
$193$	322.455			1.67075			0.835375	−	0.549681i	$-0.185251\pi$
$193$	322.455			1.67075			0.835375	+	0.549681i	$0.185251\pi$
$194$	255.853	+	22.9664i	1.31883	+	0.118384i
$195$	−28.0963	−	67.8304i	−0.144083	−	0.347848i
$196$	−34.7788	+	192.162i	−0.177443	+	0.980418i
$197$	−123.572	+	298.329i	−0.627270	+	1.51436i	0.215733	+	0.976452i	$0.430786\pi$
$197$	−123.572	+	298.329i	−0.627270	+	1.51436i	−0.843002	+	0.537910i	$0.819214\pi$
$198$	23.2447	+	74.3074i	0.117398	+	0.375290i
$199$	145.723	−	145.723i	0.732277	−	0.732277i	−0.238793	−	0.971070i	$-0.576752\pi$
$199$	145.723	−	145.723i	0.732277	−	0.732277i	0.971070	+	0.238793i	$0.0767518\pi$
$200$	−54.0645	−	95.1247i	−0.270323	−	0.475624i
$201$	79.0490	−	79.0490i	0.393279	−	0.393279i
$202$	−37.7094	+	72.0414i	−0.186680	+	0.356641i
$203$	6.84893	−	16.5348i	0.0337386	−	0.0814521i
$204$	−96.3211	+	20.8980i	−0.472162	+	0.102441i
$205$	84.2377	+	203.368i	0.410916	+	0.992038i
$206$	−289.129	+	241.498i	−1.40354	+	1.17232i
$207$	55.8808			0.269956
$208$	6.97269	+	201.431i	0.0335225	+	0.968417i
$209$		−	101.290i		−	0.484643i
$210$	3.78557	−	3.16193i	0.0180265	−	0.0150568i
$211$	267.560	−	110.827i	1.26806	−	0.525246i	0.355683	−	0.934607i	$-0.384248\pi$
$211$	267.560	−	110.827i	1.26806	−	0.525246i	0.912373	+	0.409361i	$0.134248\pi$
$212$	90.7897	+	58.4175i	0.428253	+	0.275554i
$213$	118.154	+	48.9408i	0.554711	+	0.229769i
$214$	165.742	−	316.639i	0.774493	−	1.47962i
$215$	−60.9730	−	60.9730i	−0.283595	−	0.283595i
$216$	32.8069	+	25.5285i	0.151884	+	0.118188i
$217$	−12.8271	−	12.8271i	−0.0591110	−	0.0591110i
$218$	−99.8324	−	319.139i	−0.457947	−	1.46394i
$219$	−146.740	−	60.7818i	−0.670047	−	0.277543i
$220$	−99.5344	−	143.525i	−0.452429	−	0.652386i
$221$	−165.566	+	68.5795i	−0.749166	+	0.310315i
$222$	−28.6476	−	2.57153i	−0.129043	−	0.0115834i
$223$			193.054i			0.865713i	0.901463	+	0.432856i	$0.142494\pi$
$223$			193.054i			0.865713i	−0.901463	+	0.432856i	$0.857506\pi$
$224$	−12.7753	+	4.48717i	−0.0570327	+	0.0200320i
$225$	−41.0307			−0.182359
$226$	5.27656	−	58.7824i	0.0233476	−	0.260099i
$227$	−94.3483	−	227.777i	−0.415631	−	1.00342i	−0.983598	−	0.180372i	$-0.942270\pi$
$227$	−94.3483	−	227.777i	−0.415631	−	1.00342i	0.567967	−	0.823051i	$-0.307730\pi$
$228$	−30.8186	−	44.4392i	−0.135169	−	0.194909i
$229$	136.702	−	330.028i	0.596952	−	1.44117i	−0.279721	−	0.960081i	$-0.590242\pi$
$229$	136.702	−	330.028i	0.596952	−	1.44117i	0.876673	−	0.481087i	$-0.159758\pi$
$230$	−119.641	+	37.4260i	−0.520180	+	0.162722i
$231$	−6.72485	+	6.72485i	−0.0291119	+	0.0291119i
$232$	−335.765	+	41.8927i	−1.44726	+	0.180572i
$233$	266.816	−	266.816i	1.14513	−	1.14513i	0.157635	−	0.987497i	$-0.449613\pi$
$233$	266.816	−	266.816i	1.14513	−	1.14513i	0.987497	−	0.157635i	$-0.0503870\pi$
$234$	66.9629	+	35.0511i	0.286166	+	0.149791i
$235$	35.3354	−	85.3073i	0.150364	−	0.363010i
$236$	329.992	+	212.329i	1.39827	+	0.899700i
$237$	−55.9190	−	135.000i	−0.235945	−	0.569622i
$238$	−7.71789	−	9.24011i	−0.0324281	−	0.0388240i
$239$	−233.139			−0.975477			−0.487739	−	0.872990i	$-0.662178\pi$
$239$	−233.139			−0.975477			−0.487739	+	0.872990i	$0.662178\pi$
$240$	−87.3376	−	32.6845i	−0.363907	−	0.136186i
$241$		−	166.617i		−	0.691359i	−0.938353	−	0.345679i	$-0.887648\pi$
$241$		−	166.617i		−	0.691359i	0.938353	−	0.345679i	$-0.112352\pi$
$242$	60.7548	+	72.7377i	0.251053	+	0.300569i
$243$	14.4019	−	5.96544i	0.0592669	−	0.0245492i
$244$	266.608	−	57.8438i	1.09266	−	0.237065i
$245$	−151.776	−	62.8679i	−0.619496	−	0.256603i
$246$	−200.767	−	105.089i	−0.816125	−	0.427193i
$247$	−69.5289	−	69.5289i	−0.281494	−	0.281494i
$248$	−91.0077	+	330.670i	−0.366966	+	1.33335i
$249$	75.3802	+	75.3802i	0.302732	+	0.302732i
$250$	248.423	−	77.7113i	0.993692	−	0.310845i
$251$	−49.4220	−	20.4713i	−0.196900	−	0.0815588i	0.282054	−	0.959398i	$-0.408984\pi$
$251$	−49.4220	−	20.4713i	−0.196900	−	0.0815588i	−0.478955	+	0.877840i	$0.658984\pi$
$252$	−0.904299	+	4.99649i	−0.00358849	+	0.0198274i
$253$	223.311	−	92.4986i	0.882653	−	0.365607i
$254$	27.5387	−	306.790i	0.108420	−	1.20783i
$255$		−	82.9149i		−	0.325156i
$256$	193.103	+	168.069i	0.754310	+	0.656519i
$257$	180.127			0.700883			0.350442	−	0.936585i	$-0.386031\pi$
$257$	180.127			0.700883			0.350442	+	0.936585i	$0.386031\pi$
$258$	88.4133	+	7.93635i	0.342687	+	0.0307611i
$259$	−1.34450	−	3.24592i	−0.00519114	−	0.0125325i
$260$	−166.844	−	30.1965i	−0.641706	−	0.116140i
$261$	−48.5580	+	117.229i	−0.186046	+	0.449155i
$262$	−70.5433	−	225.509i	−0.269249	−	0.860721i
$263$	28.6670	−	28.6670i	0.109000	−	0.109000i	−0.650503	−	0.759503i	$-0.725442\pi$
$263$	28.6670	−	28.6670i	0.109000	−	0.109000i	0.759503	+	0.650503i	$0.225442\pi$
$264$	173.360	+	47.7126i	0.656667	+	0.180729i
$265$	−64.2201	+	64.2201i	−0.242340	+	0.242340i
$266$	3.06346	−	5.85255i	0.0115168	−	0.0220021i
$267$	44.2207	−	106.758i	0.165621	−	0.399844i
$268$	−54.7401	−	252.303i	−0.204254	−	0.941429i
$269$	74.9194	+	180.871i	0.278511	+	0.672385i	0.999795	−	0.0202547i	$-0.00644772\pi$
$269$	74.9194	+	180.871i	0.278511	+	0.672385i	−0.721284	+	0.692639i	$0.756448\pi$
$270$	−26.8392	+	22.4177i	−0.0994044	+	0.0830285i
$271$	122.777			0.453051			0.226526	−	0.974005i	$-0.427263\pi$
$271$	122.777			0.453051			0.226526	+	0.974005i	$0.427263\pi$
$272$	−79.7789	+	213.180i	−0.293305	+	0.783752i
$273$			9.23229i			0.0338179i
$274$	−265.028	+	221.367i	−0.967257	+	0.807910i
$275$	−163.967	+	67.9174i	−0.596244	+	0.246972i
$276$	69.8300	−	108.527i	0.253007	−	0.393212i
$277$	−111.134	−	46.0331i	−0.401205	−	0.166185i	0.172951	−	0.984930i	$-0.444670\pi$
$277$	−111.134	−	46.0331i	−0.401205	−	0.166185i	−0.574156	+	0.818746i	$0.694670\pi$
$278$	−10.6093	+	20.2684i	−0.0381629	+	0.0729078i
$279$	90.9423	+	90.9423i	0.325958	+	0.325958i
$280$	−1.41027	−	11.3032i	−0.00503669	−	0.0403686i
$281$	−21.4422	−	21.4422i	−0.0763068	−	0.0763068i	0.667923	−	0.744230i	$-0.267183\pi$
$281$	−21.4422	−	21.4422i	−0.0763068	−	0.0763068i	−0.744230	+	0.667923i	$0.767183\pi$
$282$	28.3791	+	90.7206i	0.100635	+	0.321704i
$283$	−362.267	−	150.056i	−1.28010	−	0.530233i	−0.364077	−	0.931369i	$-0.618616\pi$
$283$	−362.267	−	150.056i	−1.28010	−	0.530233i	−0.916019	+	0.401136i	$0.868616\pi$
$284$	242.696	−	168.309i	0.854562	−	0.592638i
$285$	42.0314	−	17.4100i	0.147478	−	0.0610876i
$286$	325.617	+	29.2287i	1.13852	+	0.102198i
$287$		−	27.6801i		−	0.0964463i
$288$	90.5754	−	31.8135i	0.314498	−	0.110463i
$289$	86.6150			0.299706
$290$	25.4492	−	283.511i	0.0877557	−	0.977625i
$291$	−85.1341	−	205.532i	−0.292557	−	0.706295i
$292$	−301.415	+	209.031i	−1.03224	+	0.715859i
$293$	−75.0184	+	181.110i	−0.256035	+	0.618124i	−0.998669	−	0.0515736i	$-0.983576\pi$
$293$	−75.0184	+	181.110i	−0.256035	+	0.618124i	0.742634	+	0.669698i	$0.233576\pi$
$294$	161.408	−	50.4913i	0.549006	−	0.171739i
$295$	−233.420	+	233.420i	−0.791254	+	0.791254i
$296$	−40.7928	+	52.4232i	−0.137814	+	0.177105i
$297$	47.6783	−	47.6783i	0.160533	−	0.160533i
$298$	379.048	+	198.409i	1.27197	+	0.665802i
$299$	89.7940	−	216.782i	0.300314	−	0.725023i
$300$	−51.2729	+	79.6860i	−0.170910	+	0.265620i
$301$	4.14947	+	10.0177i	0.0137856	+	0.0332814i
$302$	−174.431	−	208.834i	−0.577586	−	0.691505i
$303$	70.4199			0.232409
$304$	−124.817	+	4.32065i	−0.410583	+	0.0142127i
$305$			229.501i			0.752462i
$306$	54.7188	+	65.5112i	0.178820	+	0.214089i
$307$	−287.553	+	119.108i	−0.936655	+	0.387975i	−0.798199	−	0.602393i	$-0.794214\pi$
$307$	−287.553	+	119.108i	−0.936655	+	0.387975i	−0.138456	+	0.990369i	$0.544214\pi$
$308$	4.65684	+	21.4639i	0.0151196	+	0.0696879i
$309$	301.414	+	124.850i	0.975448	+	0.404044i
$310$	−255.617	−	133.800i	−0.824570	−	0.431613i
$311$	114.138	+	114.138i	0.367005	+	0.367005i	0.866384	−	0.499379i	$-0.166438\pi$
$311$	114.138	+	114.138i	0.367005	+	0.367005i	−0.499379	+	0.866384i	$0.666438\pi$
$312$	151.751	−	86.2484i	0.486382	−	0.276437i
$313$	147.798	+	147.798i	0.472199	+	0.472199i	0.902626	−	0.430426i	$-0.141637\pi$
$313$	147.798	+	147.798i	0.472199	+	0.472199i	−0.430426	+	0.902626i	$0.641637\pi$
$314$	−147.299	+	46.0779i	−0.469106	+	0.146745i
$315$	−3.94641	−	1.63466i	−0.0125283	−	0.00518939i
$316$	−332.063	−	60.0989i	−1.05083	−	0.190187i
$317$	37.8967	−	15.6973i	0.119548	−	0.0495184i	−0.322108	−	0.946703i	$-0.604391\pi$
$317$	37.8967	−	15.6973i	0.119548	−	0.0495184i	0.441656	+	0.897185i	$0.354391\pi$
$318$	8.35900	−	93.1217i	0.0262862	−	0.292836i
$319$			548.850i			1.72053i
$320$	−172.616	+	128.776i	−0.539425	+	0.402424i
$321$	−309.512			−0.964213
$322$	15.7004	+	1.40934i	0.0487592	+	0.00437683i
$323$	−42.4956	−	102.593i	−0.131565	−	0.317627i
$324$	6.41136	−	35.4245i	0.0197882	−	0.109335i
$325$	−65.9315	+	159.173i	−0.202866	+	0.489762i
$326$	84.2116	+	269.203i	0.258318	+	0.825776i
$327$	−204.771	+	204.771i	−0.626210	+	0.626210i
$328$	−454.978	+	258.588i	−1.38713	+	0.788379i
$329$	−8.21024	+	8.21024i	−0.0249552	+	0.0249552i
$330$	−70.1473	+	134.012i	−0.212568	+	0.406097i
$331$	−191.878	+	463.233i	−0.579691	+	1.39950i	0.313401	+	0.949621i	$0.398532\pi$
$331$	−191.878	+	463.233i	−0.579691	+	1.39950i	−0.893091	+	0.449876i	$0.851468\pi$
$332$	240.593	−	52.1995i	0.724678	−	0.157227i
$333$	9.53236	+	23.0132i	0.0286257	+	0.0691086i
$334$	147.582	−	123.270i	0.441863	−	0.369071i
$335$	217.187			0.648319
$336$	8.57369	+	7.99998i	0.0255169	+	0.0238095i
$337$		−	326.416i		−	0.968594i	−0.874904	−	0.484297i	$-0.839075\pi$
$337$		−	326.416i		−	0.968594i	0.874904	−	0.484297i	$-0.160925\pi$
$338$	−15.8358	+	13.2270i	−0.0468516	+	0.0391332i
$339$	−47.2211	+	19.5596i	−0.139295	+	0.0576980i
$340$	−161.030	−	103.612i	−0.473616	−	0.304742i
$341$	513.959	+	212.889i	1.50721	+	0.624308i
$342$	−21.7195	+	41.4938i	−0.0635073	+	0.121327i
$343$	29.2685	+	29.2685i	0.0853308	+	0.0853308i
$344$	125.897	−	161.791i	0.365978	−	0.470322i
$345$	76.7662	+	76.7662i	0.222511	+	0.222511i
$346$	−9.48539	−	30.3224i	−0.0274144	−	0.0876369i
$347$	637.279	+	263.969i	1.83654	+	0.760719i	0.960379	+	0.278697i	$0.0899024\pi$
$347$	637.279	+	263.969i	1.83654	+	0.760719i	0.876159	+	0.482022i	$0.160098\pi$
$348$	166.993	+	240.797i	0.479864	+	0.691947i
$349$	−475.160	+	196.818i	−1.36149	+	0.563948i	−0.939468	−	0.342638i	$-0.888680\pi$
$349$	−475.160	+	196.818i	−1.36149	+	0.563948i	−0.422022	+	0.906585i	$0.638680\pi$
$350$	−11.5281	−	1.03481i	−0.0329375	−	0.00295660i
$351$		−	65.4557i		−	0.186484i
$352$	309.298	−	277.061i	0.878686	−	0.787105i
$353$	94.9702			0.269037			0.134519	−	0.990911i	$-0.457051\pi$
$353$	94.9702			0.269037			0.134519	+	0.990911i	$0.457051\pi$
$354$	30.3823	−	338.468i	0.0858258	−	0.956125i
$355$	95.0808	+	229.545i	0.267833	+	0.646607i
$356$	−152.077	−	219.289i	−0.427182	−	0.615980i
$357$	−3.99000	+	9.63271i	−0.0111765	+	0.0269824i
$358$	165.754	−	51.8509i	0.463000	−	0.144835i
$359$	−250.696	+	250.696i	−0.698318	+	0.698318i	−0.964048	−	0.265730i	$-0.914387\pi$
$359$	−250.696	+	250.696i	−0.698318	+	0.698318i	0.265730	+	0.964048i	$0.414387\pi$
$360$	9.99866	+	80.1382i	0.0277741	+	0.222606i
$361$	−212.182	+	212.182i	−0.587761	+	0.587761i
$362$	376.487	+	197.068i	1.04002	+	0.544388i
$363$	31.4091	−	75.8282i	0.0865263	−	0.208893i
$364$	17.9301	+	11.5369i	0.0492585	+	0.0316947i
$365$	−118.085	−	285.083i	−0.323521	−	0.781050i
$366$	−151.457	−	181.329i	−0.413816	−	0.495434i
$367$	−64.0086			−0.174410			−0.0872052	−	0.996190i	$-0.527794\pi$
$367$	−64.0086			−0.174410			−0.0872052	+	0.996190i	$0.527794\pi$
$368$	−123.509	−	271.234i	−0.335622	−	0.737050i
$369$			196.248i			0.531838i
$370$	−35.8219	−	42.8871i	−0.0968159	−	0.115911i
$371$	10.5512	−	4.37045i	0.0284399	−	0.0117802i
$372$	290.263	−	62.9760i	0.780277	−	0.169290i
$373$	−139.819	−	57.9148i	−0.374849	−	0.155268i	0.187301	−	0.982302i	$-0.440026\pi$
$373$	−139.819	−	57.9148i	−0.374849	−	0.155268i	−0.562151	+	0.827035i	$0.690026\pi$
$374$	327.107	+	171.221i	0.874618	+	0.457810i
$375$	−159.397	−	159.397i	−0.425058	−	0.425058i
$376$	211.652	+	58.2514i	0.562905	+	0.154924i
$377$	376.748	+	376.748i	0.999331	+	0.999331i
$378$	4.19684	−	1.31285i	0.0111028	−	0.00347314i
$379$	−215.831	−	89.4001i	−0.569475	−	0.235884i	0.0793180	−	0.996849i	$-0.474726\pi$
$379$	−215.831	−	89.4001i	−0.569475	−	0.235884i	−0.648793	+	0.760965i	$0.724726\pi$
$380$	18.7114	−	103.385i	0.0492404	−	0.272066i
$381$	−246.450	+	102.083i	−0.646851	+	0.267934i
$382$	−19.9912	+	222.708i	−0.0523330	+	0.583005i
$383$		−	670.955i		−	1.75184i	−0.482456	−	0.875920i	$-0.660255\pi$
$383$		−	670.955i		−	1.75184i	0.482456	−	0.875920i	$-0.339745\pi$
$384$	51.3999	−	215.662i	0.133854	−	0.561619i
$385$	−18.4765			−0.0479909
$386$	−642.327	−	57.6579i	−1.66406	−	0.149373i
$387$	−29.4192	−	71.0242i	−0.0760186	−	0.183525i
$388$	−505.550	−	91.4978i	−1.30296	−	0.235819i
$389$	−48.6958	+	117.562i	−0.125182	+	0.302216i	−0.974029	−	0.226422i	$-0.927297\pi$
$389$	−48.6958	+	117.562i	−0.125182	+	0.302216i	0.848847	+	0.528638i	$0.177297\pi$
$390$	43.8388	+	140.141i	0.112407	+	0.359337i
$391$	187.377	−	187.377i	0.479225	−	0.479225i
$392$	103.639	−	376.566i	0.264386	−	0.960628i
$393$	−144.695	+	144.695i	−0.368179	+	0.368179i
$394$	299.499	−	572.174i	0.760149	−	1.45222i
$395$	108.638	−	262.275i	0.275033	−	0.663987i
$396$	−33.0164	−	152.176i	−0.0833748	−	0.384283i
$397$	−236.960	−	572.072i	−0.596876	−	1.44099i	−0.876748	−	0.480949i	$-0.840292\pi$
$397$	−236.960	−	572.072i	−0.596876	−	1.44099i	0.279872	−	0.960037i	$-0.409708\pi$
$398$	−316.336	+	264.223i	−0.794814	+	0.663876i
$399$	−5.72082			−0.0143379
$400$	90.6868	+	199.155i	0.226717	+	0.497887i
$401$		−	442.573i		−	1.10367i	−0.833953	−	0.551836i	$-0.813927\pi$
$401$		−	442.573i		−	1.10367i	0.833953	−	0.551836i	$-0.186073\pi$
$402$	−171.600	+	143.330i	−0.426865	+	0.356543i
$403$	498.931	−	206.664i	1.23804	−	0.512814i
$404$	87.9984	−	136.763i	0.217818	−	0.338522i
$405$	27.9795	+	11.5895i	0.0690853	+	0.0286161i
$406$	−16.5996	+	31.7125i	−0.0408857	+	0.0781096i
$407$	76.1865	+	76.1865i	0.187191	+	0.187191i
$408$	195.608	−	24.4055i	0.479430	−	0.0598174i
$409$	−362.585	−	362.585i	−0.886515	−	0.886515i	0.107671	−	0.994187i	$-0.465661\pi$
$409$	−362.585	−	362.585i	−0.886515	−	0.886515i	−0.994187	+	0.107671i	$0.965661\pi$
$410$	−131.437	−	420.169i	−0.320577	−	1.02480i
$411$	276.289	+	114.443i	0.672236	+	0.278449i
$412$	619.124	−	429.362i	1.50273	−	1.04214i
$413$	38.3503	−	15.8852i	0.0928578	−	0.0384630i
$414$	−111.314	−	9.99202i	−0.268875	−	0.0241353i
$415$			207.107i			0.499052i
$416$	22.1282	−	402.495i	0.0531928	−	0.967536i
$417$	19.8122			0.0475112
$418$	−18.1117	+	201.770i	−0.0433294	+	0.482702i
$419$	117.453	+	283.556i	0.280317	+	0.676745i	0.999843	−	0.0177204i	$-0.00564087\pi$
$419$	117.453	+	283.556i	0.280317	+	0.676745i	−0.719526	+	0.694466i	$0.755641\pi$
$420$	−8.10620	+	5.62165i	−0.0193005	+	0.0133849i
$421$	119.461	−	288.405i	0.283756	−	0.685048i	−0.716161	−	0.697935i	$-0.754102\pi$
$421$	119.461	−	288.405i	0.283756	−	0.685048i	0.999917	+	0.0128872i	$0.00410223\pi$
$422$	−552.794	+	172.924i	−1.30994	+	0.409772i
$423$	58.2096	−	58.2096i	0.137611	−	0.137611i
$424$	−170.407	−	132.601i	−0.401903	−	0.312738i
$425$	−137.582	+	137.582i	−0.323723	+	0.323723i
$426$	−226.610	−	118.617i	−0.531947	−	0.278443i
$427$	11.0439	−	26.6624i	0.0258640	−	0.0624413i
$428$	−386.774	+	601.106i	−0.903677	+	1.40445i
$429$	−108.348	−	261.574i	−0.252559	−	0.609731i
$430$	110.555	+	132.360i	0.257105	+	0.307814i
$431$	404.132			0.937661			0.468831	−	0.883288i	$-0.344675\pi$
$431$	404.132			0.937661			0.468831	+	0.883288i	$0.344675\pi$
$432$	−60.7863	−	56.7188i	−0.140709	−	0.131294i
$433$		−	575.186i		−	1.32837i	−0.747567	−	0.664187i	$-0.768778\pi$
$433$		−	575.186i		−	1.32837i	0.747567	−	0.664187i	$-0.231222\pi$
$434$	23.2578	+	27.8450i	0.0535894	+	0.0641590i
$435$	−227.750	+	94.3372i	−0.523564	+	0.216867i
$436$	141.800	+	653.572i	0.325230	+	1.49902i
$437$	134.330	+	55.6412i	0.307390	+	0.127325i
$438$	281.437	+	147.315i	0.642550	+	0.336337i
$439$	−279.855	−	279.855i	−0.637483	−	0.637483i	0.312451	−	0.949934i	$-0.398850\pi$
$439$	−279.855	−	279.855i	−0.637483	−	0.637483i	−0.949934	+	0.312451i	$0.898850\pi$
$440$	172.608	+	303.698i	0.392291	+	0.690223i
$441$	−103.565	−	103.565i	−0.234841	−	0.234841i
$442$	342.068	−	107.005i	0.773909	−	0.242093i
$443$	−117.497	−	48.6690i	−0.265231	−	0.109862i	0.246105	−	0.969243i	$-0.420849\pi$
$443$	−117.497	−	48.6690i	−0.265231	−	0.109862i	−0.511336	+	0.859381i	$0.670849\pi$
$444$	56.6058	+	10.2449i	0.127491	+	0.0230741i
$445$	207.407	−	85.9108i	0.466083	−	0.193058i
$446$	34.5199	−	384.562i	0.0773988	−	0.862246i
$447$		−	370.517i		−	0.828897i
$448$	26.2507	−	6.65406i	0.0585953	−	0.0148528i
$449$	−178.652			−0.397889			−0.198945	−	0.980011i	$-0.563751\pi$
$449$	−178.652			−0.397889			−0.198945	+	0.980011i	$0.563751\pi$
$450$	81.7328	+	7.33668i	0.181628	+	0.0163037i
$451$	324.846	+	784.248i	0.720279	+	1.73891i
$452$	−21.0217	+	116.151i	−0.0465082	+	0.256970i
$453$	−90.1774	+	217.707i	−0.199067	+	0.480590i
$454$	147.212	+	470.600i	0.324256	+	1.03656i
$455$	−12.6828	+	12.6828i	−0.0278744	+	0.0278744i
$456$	53.4441	+	94.0332i	0.117202	+	0.206213i
$457$	−497.621	+	497.621i	−1.08889	+	1.08889i	−0.0932416	+	0.995644i	$0.529723\pi$
$457$	−497.621	+	497.621i	−1.08889	+	1.08889i	−0.995644	+	0.0932416i	$0.970277\pi$
$458$	−331.321	+	632.968i	−0.723408	+	1.38203i
$459$	28.2886	−	68.2946i	0.0616308	−	0.148790i
$460$	245.017	−	53.1593i	0.532645	−	0.115564i
$461$	−136.971	−	330.678i	−0.297118	−	0.717305i	−0.999982	−	0.00598148i	$-0.998096\pi$
$461$	−136.971	−	330.678i	−0.297118	−	0.717305i	0.702865	−	0.711324i	$-0.251904\pi$
$462$	14.5983	−	12.1934i	0.0315980	−	0.0263926i
$463$	503.664			1.08783			0.543914	−	0.839141i	$-0.316942\pi$
$463$	503.664			1.08783			0.543914	+	0.839141i	$0.316942\pi$
$464$	676.332	−	23.4118i	1.45761	−	0.0504564i
$465$			249.864i			0.537341i
$466$	−579.204	+	483.786i	−1.24293	+	1.03817i
$467$	83.8581	−	34.7352i	0.179568	−	0.0743794i	−0.291088	−	0.956696i	$-0.594017\pi$
$467$	83.8581	−	34.7352i	0.179568	−	0.0743794i	0.470656	+	0.882317i	$0.344017\pi$
$468$	−127.122	−	81.7950i	−0.271628	−	0.174776i
$469$	−25.2319	−	10.4514i	−0.0537993	−	0.0222844i
$470$	−85.6416	+	163.613i	−0.182216	+	0.348113i
$471$	94.5123	+	94.5123i	0.200663	+	0.200663i
$472$	−619.375	−	481.964i	−1.31224	−	1.02111i
$473$	−235.130	−	235.130i	−0.497104	−	0.497104i
$474$	87.2507	+	278.918i	0.184073	+	0.588435i
$475$	−98.6320	−	40.8547i	−0.207646	−	0.0860099i
$476$	13.7217	+	19.7862i	0.0288272	+	0.0415677i
$477$	−74.8066	+	30.9859i	−0.156827	+	0.0649599i
$478$	464.411	+	41.6875i	0.971571	+	0.0872123i
$479$		−	120.133i		−	0.250800i	−0.992106	−	0.125400i	$-0.959979\pi$
$479$		−	120.133i		−	0.250800i	0.992106	−	0.125400i	$-0.0400214\pi$
$480$	168.131	+	80.7241i	0.350274	+	0.168175i
$481$	104.594			0.217450
$482$	−29.7928	+	331.900i	−0.0618108	+	0.688590i
$483$	−5.22426	−	12.6125i	−0.0108163	−	0.0261128i
$484$	−108.017	−	155.756i	−0.223175	−	0.321811i
$485$	165.396	−	399.302i	0.341023	−	0.823302i
$486$	−29.7550	+	9.30792i	−0.0612244	+	0.0191521i
$487$	196.583	−	196.583i	0.403661	−	0.403661i	−0.475860	−	0.879521i	$-0.657863\pi$
$487$	196.583	−	196.583i	0.403661	−	0.403661i	0.879521	+	0.475860i	$0.157863\pi$
$488$	−541.424	+	67.5522i	−1.10947	+	0.138427i
$489$	172.730	−	172.730i	0.353231	−	0.353231i
$490$	291.096	+	152.371i	0.594073	+	0.310962i
$491$	25.1938	−	60.8233i	0.0513113	−	0.123876i	−0.896145	−	0.443761i	$-0.853644\pi$
$491$	25.1938	−	60.8233i	0.0513113	−	0.123876i	0.947457	+	0.319884i	$0.103644\pi$
$492$	381.135	+	245.236i	0.774664	+	0.498447i
$493$	230.266	+	555.910i	0.467070	+	1.12761i
$494$	126.069	+	150.933i	0.255200	+	0.305533i
$495$	130.996			0.264638
$496$	240.413	−	642.418i	0.484704	−	1.29520i
$497$		−	31.2431i		−	0.0628633i
$498$	−136.678	−	163.635i	−0.274454	−	0.328585i
$499$	288.656	−	119.565i	0.578468	−	0.239609i	−0.0742124	−	0.997242i	$-0.523644\pi$
$499$	288.656	−	119.565i	0.578468	−	0.239609i	0.652681	+	0.757633i	$0.273644\pi$
$500$	−508.752	+	110.380i	−1.01750	+	0.220759i
$501$	−153.853	−	63.7279i	−0.307092	−	0.127201i
$502$	94.7877	+	49.6157i	0.188820	+	0.0988360i
$503$	−484.334	−	484.334i	−0.962890	−	0.962890i	0.0364453	−	0.999336i	$-0.488397\pi$
$503$	−484.334	−	484.334i	−0.962890	−	0.962890i	−0.999336	+	0.0364453i	$0.988397\pi$
$504$	2.69478	−	9.79127i	0.00534678	−	0.0194271i
$505$	96.7393	+	96.7393i	0.191563	+	0.191563i
$506$	−461.374	+	144.326i	−0.911806	+	0.285229i
$507$	16.5087	+	6.83811i	0.0325615	+	0.0134874i
$508$	−109.714	+	606.198i	−0.215972	+	1.19330i
$509$	−411.196	+	170.323i	−0.807850	+	0.334622i	−0.748096	−	0.663591i	$-0.769032\pi$
$509$	−411.196	+	170.323i	−0.807850	+	0.334622i	−0.0597540	+	0.998213i	$0.519032\pi$
$510$	−14.8260	+	165.166i	−0.0290705	+	0.323854i
$511$			38.8022i			0.0759339i
$512$	−354.608	−	369.320i	−0.692593	−	0.721328i
$513$	40.5599			0.0790641
$514$	−358.811	−	32.2084i	−0.698077	−	0.0626623i
$515$	242.554	+	585.578i	0.470979	+	1.13704i
$516$	−174.699	−	31.6183i	−0.338565	−	0.0612757i
$517$	136.264	−	328.971i	0.263567	−	0.636307i
$518$	2.09784	+	6.70626i	0.00404988	+	0.0129464i
$519$	−19.4559	+	19.4559i	−0.0374873	+	0.0374873i
$520$	326.951	+	89.9843i	0.628753	+	0.173047i
$521$	−524.951	+	524.951i	−1.00758	+	1.00758i	−0.00761264	+	0.999971i	$0.502423\pi$
$521$	−524.951	+	524.951i	−1.00758	+	1.00758i	−0.999971	+	0.00761264i	$0.997577\pi$
$522$	117.689	−	224.837i	0.225458	−	0.430723i
$523$	140.079	−	338.180i	0.267837	−	0.646615i	−0.731544	−	0.681794i	$-0.761200\pi$
$523$	140.079	−	338.180i	0.267837	−	0.646615i	0.999381	+	0.0351789i	$0.0112001\pi$
$524$	100.199	+	461.826i	0.191219	+	0.881347i
$525$	3.83593	+	9.26076i	0.00730654	+	0.0176395i
$526$	−62.2304	+	51.9785i	−0.118309	+	0.0988185i
$527$	609.886			1.15728
$528$	−336.800	−	126.041i	−0.637879	−	0.238715i
$529$		−	182.037i		−	0.344115i
$530$	139.409	−	116.443i	0.263036	−	0.219703i
$531$	−271.898	+	112.624i	−0.512050	+	0.212098i
$532$	−7.14887	+	11.1104i	−0.0134377	+	0.0208843i
$533$	761.317	+	315.348i	1.42836	+	0.591647i
$534$	−107.177	+	204.754i	−0.200705	+	0.383435i
$535$	−425.192	−	425.192i	−0.794751	−	0.794751i
$536$	63.9276	+	512.373i	0.119268	+	0.955920i
$537$	−106.354	−	106.354i	−0.198052	−	0.198052i
$538$	−116.897	−	373.691i	−0.217281	−	0.694592i
$539$	−585.296	−	242.437i	−1.08589	−	0.449791i
$540$	57.4719	−	39.8567i	0.106429	−	0.0738087i
$541$	715.798	−	296.493i	1.32310	−	0.548047i	0.394422	−	0.918929i	$-0.370945\pi$
$541$	715.798	−	296.493i	1.32310	−	0.548047i	0.928680	+	0.370882i	$0.120945\pi$
$542$	−244.570	−	21.9537i	−0.451237	−	0.0405049i
$543$		−	368.013i		−	0.677741i
$544$	197.038	−	410.388i	0.362201	−	0.754390i
$545$	−562.606			−1.03231
$546$	1.65082	−	18.3906i	0.00302348	−	0.0336825i
$547$	361.167	+	871.935i	0.660269	+	1.59403i	0.797381	+	0.603476i	$0.206218\pi$
$547$	361.167	+	871.935i	0.660269	+	1.59403i	−0.137112	+	0.990556i	$0.543782\pi$
$548$	567.516	−	393.572i	1.03561	−	0.718197i
$549$	−78.3001	+	189.033i	−0.142623	+	0.344323i
$550$	338.765	−	105.972i	0.615937	−	0.192676i
$551$	−233.453	+	233.453i	−0.423690	+	0.423690i
$552$	−158.506	+	203.698i	−0.287149	+	0.369017i
$553$	−25.2422	+	25.2422i	−0.0456459	+	0.0456459i
$554$	213.146	+	111.569i	0.384741	+	0.201389i
$555$	−18.5192	+	44.7093i	−0.0333680	+	0.0805574i
$556$	24.7577	−	38.4774i	0.0445283	−	0.0692039i
$557$	−129.332	−	312.235i	−0.232194	−	0.560565i	0.764241	−	0.644930i	$-0.223114\pi$
$557$	−129.332	−	312.235i	−0.232194	−	0.560565i	−0.996435	+	0.0843656i	$0.973114\pi$
$558$	−164.895	−	197.418i	−0.295511	−	0.353795i
$559$	−322.801			−0.577462
$560$	0.788134	+	22.7680i	0.00140738	+	0.0406572i
$561$		−	319.745i		−	0.569955i
$562$	38.8786	+	46.5468i	0.0691791	+	0.0828234i
$563$	−164.657	+	68.2032i	−0.292464	+	0.121142i	−0.524091	−	0.851662i	$-0.675595\pi$
$563$	−164.657	+	68.2032i	−0.292464	+	0.121142i	0.231628	+	0.972805i	$0.425595\pi$
$564$	−40.3091	−	185.789i	−0.0714701	−	0.329413i
$565$	−91.7399	−	37.9999i	−0.162371	−	0.0672565i
$566$	694.801	+	363.687i	1.22756	+	0.642556i
$567$	−2.69284	−	2.69284i	−0.00474928	−	0.00474928i
$568$	−513.543	+	291.874i	−0.904124	+	0.513863i
$569$	30.4839	+	30.4839i	0.0535746	+	0.0535746i	0.733387	−	0.679812i	$-0.237939\pi$
$569$	30.4839	+	30.4839i	0.0535746	+	0.0535746i	−0.679812	+	0.733387i	$0.737939\pi$
$570$	−86.8391	+	27.1649i	−0.152349	+	0.0476577i
$571$	275.863	+	114.266i	0.483123	+	0.200116i	0.610933	−	0.791683i	$-0.290795\pi$
$571$	275.863	+	114.266i	0.483123	+	0.200116i	−0.127810	+	0.991799i	$0.540795\pi$
$572$	−643.399	−	116.447i	−1.12482	−	0.203578i
$573$	178.906	−	74.1051i	0.312226	−	0.129328i
$574$	−4.94946	+	55.1385i	−0.00862275	+	0.0960600i
$575$		−	254.759i		−	0.443059i
$576$	−186.114	+	47.1764i	−0.323114	+	0.0819035i
$577$	562.753			0.975308			0.487654	−	0.873037i	$-0.337853\pi$
$577$	562.753			0.975308			0.487654	+	0.873037i	$0.337853\pi$
$578$	−172.536	−	15.4876i	−0.298506	−	0.0267951i
$579$	213.732	+	515.994i	0.369139	+	0.891181i
$580$	−101.389	+	560.201i	−0.174809	+	0.965864i
$581$	9.96631	−	24.0608i	0.0171537	−	0.0414127i
$582$	132.835	+	424.640i	0.228239	+	0.729622i
$583$	−247.652	+	247.652i	−0.424789	+	0.424789i
$584$	637.792	−	362.492i	1.09211	−	0.620705i
$585$	89.9197	−	89.9197i	0.153709	−	0.153709i
$586$	181.820	−	347.356i	0.310273	−	0.592758i
$587$	−118.470	+	286.012i	−0.201823	+	0.487244i	−0.992091	−	0.125517i	$-0.959941\pi$
$587$	−118.470	+	286.012i	−0.201823	+	0.487244i	0.790269	+	0.612761i	$0.209941\pi$
$588$	−330.551	+	71.7169i	−0.562162	+	0.121968i
$589$	128.060	+	309.165i	0.217420	+	0.524897i
$590$	506.708	−	423.233i	0.858827	−	0.717343i
$591$	−559.296			−0.946355
$592$	90.6327	−	97.1323i	0.153096	−	0.164075i
$593$			764.721i			1.28958i	0.764360	+	0.644790i	$0.223055\pi$
$593$			764.721i			1.28958i	−0.764360	+	0.644790i	$0.776945\pi$
$594$	−103.500	+	86.4494i	−0.174242	+	0.145538i
$595$	−18.7142	+	7.75166i	−0.0314524	+	0.0130280i
$596$	−719.583	−	463.006i	−1.20735	−	0.776856i
$597$	329.776	+	136.598i	0.552389	+	0.228807i
$598$	−217.631	+	415.771i	−0.363932	+	0.695270i
$599$	445.545	+	445.545i	0.743814	+	0.743814i	0.973310	−	0.229495i	$-0.0737076\pi$
$599$	445.545	+	445.545i	0.743814	+	0.743814i	−0.229495	+	0.973310i	$0.573708\pi$
$600$	116.384	−	149.566i	0.193973	−	0.249276i
$601$	−395.260	−	395.260i	−0.657671	−	0.657671i	0.297158	−	0.954828i	$-0.403961\pi$
$601$	−395.260	−	395.260i	−0.657671	−	0.657671i	−0.954828	+	0.297158i	$0.903961\pi$
$602$	−6.47444	−	20.6971i	−0.0107549	−	0.0343806i
$603$	178.891	+	74.0989i	0.296668	+	0.122884i
$604$	310.123	+	447.186i	0.513449	+	0.740374i
$605$	147.317	−	61.0207i	0.243499	−	0.100861i
$606$	−140.276	−	12.5918i	−0.231478	−	0.0207785i
$607$		−	530.402i		−	0.873808i	−0.899508	−	0.436904i	$-0.856075\pi$
$607$		−	530.402i		−	0.873808i	0.899508	−	0.436904i	$-0.143925\pi$
$608$	249.407	+	13.7118i	0.410210	+	0.0225523i
$609$	30.9987			0.0509010
$610$	41.0369	−	457.164i	0.0672736	−	0.749448i
$611$	−132.280	−	319.352i	−0.216497	−	0.522670i
$612$	−97.2854	−	140.282i	−0.158963	−	0.229219i
$613$	90.9390	−	219.546i	0.148351	−	0.358150i	−0.832183	−	0.554501i	$-0.812909\pi$
$613$	90.9390	−	219.546i	0.148351	−	0.358150i	0.980534	+	0.196351i	$0.0629091\pi$
$614$	594.101	−	185.846i	0.967591	−	0.302680i
$615$	−269.595	+	269.595i	−0.438367	+	0.438367i
$616$	−5.43844	−	43.5886i	−0.00882864	−	0.0707606i
$617$	199.027	−	199.027i	0.322572	−	0.322572i	−0.527181	−	0.849753i	$-0.676751\pi$
$617$	199.027	−	199.027i	0.322572	−	0.322572i	0.849753	+	0.527181i	$0.176751\pi$
$618$	−578.089	−	302.595i	−0.935419	−	0.489636i
$619$	−43.5847	+	105.223i	−0.0704115	+	0.169988i	−0.955167	−	0.296066i	$-0.904325\pi$
$619$	−43.5847	+	105.223i	−0.0704115	+	0.169988i	0.884756	+	0.466055i	$0.154325\pi$
$620$	485.262	+	312.235i	0.782680	+	0.503605i
$621$	37.0393	+	89.4209i	0.0596447	+	0.143995i
$622$	−206.954	−	247.772i	−0.332723	−	0.398347i
$623$	−28.2299			−0.0453128
$624$	−317.709	+	144.671i	−0.509149	+	0.231845i
$625$		−	96.0200i		−	0.153632i
$626$	−267.985	−	320.841i	−0.428092	−	0.512525i
$627$	162.086	−	67.1380i	0.258510	−	0.107078i
$628$	301.658	−	65.4482i	0.480347	−	0.104217i
$629$	109.130	+	45.2031i	0.173498	+	0.0718651i
$630$	7.56892	+	3.96188i	0.0120142	+	0.00628870i
$631$	56.0461	+	56.0461i	0.0888211	+	0.0888211i	0.750121	−	0.661300i	$-0.229995\pi$
$631$	56.0461	+	56.0461i	0.0888211	+	0.0888211i	−0.661300	+	0.750121i	$0.729995\pi$
$632$	650.719	+	179.092i	1.02962	+	0.283374i
$633$	354.692	+	354.692i	0.560335	+	0.560335i
$634$	−78.2967	+	24.4926i	−0.123496	+	0.0386319i
$635$	−478.797	−	198.324i	−0.754011	−	0.312321i
$636$	−33.3021	+	184.003i	−0.0523618	+	0.289313i
$637$	−568.182	+	235.349i	−0.891965	+	0.369464i
$638$	98.1396	−	1093.30i	0.153824	−	1.71364i
$639$			221.509i			0.346650i
$640$	366.876	−	225.654i	0.573243	−	0.352585i
$641$	−599.557			−0.935346			−0.467673	−	0.883902i	$-0.654907\pi$
$641$	−599.557			−0.935346			−0.467673	+	0.883902i	$0.654907\pi$
$642$	616.546	+	55.3437i	0.960352	+	0.0862052i
$643$	−260.711	−	629.412i	−0.405460	−	0.978868i	−0.986317	−	0.164862i	$-0.947282\pi$
$643$	−260.711	−	629.412i	−0.405460	−	0.978868i	0.580856	−	0.814006i	$-0.302718\pi$
$644$	−31.0231	−	5.61478i	−0.0481726	−	0.00871860i
$645$	57.1548	−	137.984i	0.0886121	−	0.213929i
$646$	66.3061	+	211.964i	0.102641	+	0.328117i
$647$	−101.612	+	101.612i	−0.157051	+	0.157051i	−0.781259	−	0.624207i	$-0.785422\pi$
$647$	−101.612	+	101.612i	−0.157051	+	0.157051i	0.624207	+	0.781259i	$0.285422\pi$
$648$	−19.1056	+	69.4188i	−0.0294840	+	0.107128i
$649$	−900.137	+	900.137i	−1.38696	+	1.38696i
$650$	159.797	−	305.281i	0.245841	−	0.469664i
$651$	12.0238	−	29.0281i	0.0184698	−	0.0445900i
$652$	−119.613	−	551.308i	−0.183455	−	0.845564i
$653$	−195.126	−	471.077i	−0.298815	−	0.721404i	−0.999965	−	0.00838966i	$-0.997329\pi$
$653$	−195.126	−	471.077i	−0.298815	−	0.721404i	0.701150	−	0.713014i	$-0.252671\pi$
$654$	444.516	−	371.286i	0.679688	−	0.567716i
$655$	−397.548			−0.606943
$656$	952.549	−	433.751i	1.45206	−	0.661206i
$657$		−	275.103i		−	0.418725i
$658$	17.8228	−	14.8867i	0.0270863	−	0.0226241i
$659$	−350.759	+	145.289i	−0.532259	+	0.220469i	−0.632592	−	0.774485i	$-0.718009\pi$
$659$	−350.759	+	145.289i	−0.532259	+	0.220469i	0.100333	+	0.994954i	$0.468009\pi$
$660$	163.695	−	254.408i	0.248023	−	0.385466i
$661$	878.519	+	363.895i	1.32908	+	0.550521i	0.930392	−	0.366567i	$-0.119467\pi$
$661$	878.519	+	363.895i	1.32908	+	0.550521i	0.398684	+	0.917088i	$0.369467\pi$
$662$	465.049	−	888.447i	0.702491	−	1.34207i
$663$	−219.483	−	219.483i	−0.331045	−	0.331045i
$664$	−488.593	+	60.9606i	−0.735833	+	0.0918082i
$665$	−7.85897	−	7.85897i	−0.0118180	−	0.0118180i
$666$	−14.8734	−	47.5465i	−0.0223324	−	0.0713911i
$667$	−727.876	−	301.496i	−1.09127	−	0.452018i
$668$	−316.024	+	219.163i	−0.473091	+	0.328088i
$669$	−308.926	+	127.961i	−0.461773	+	0.191273i
$670$	−432.634	−	38.8351i	−0.645722	−	0.0579628i
$671$			885.024i			1.31896i
$672$	−15.6482	−	17.4689i	−0.0232861	−	0.0259954i
$673$	728.501			1.08247			0.541234	−	0.840872i	$-0.317957\pi$
$673$	728.501			1.08247			0.541234	+	0.840872i	$0.317957\pi$
$674$	−58.3663	+	650.218i	−0.0865969	+	0.964715i
$675$	−27.1963	−	65.6576i	−0.0402908	−	0.0972705i
$676$	33.9099	−	23.5165i	0.0501626	−	0.0347877i
$677$	193.837	−	467.963i	0.286317	−	0.691231i	−0.713640	−	0.700513i	$-0.752955\pi$
$677$	193.837	−	467.963i	0.286317	−	0.691231i	0.999957	+	0.00928194i	$0.00295457\pi$
$678$	97.5614	−	30.5190i	0.143896	−	0.0450133i
$679$	−38.4301	+	38.4301i	−0.0565980	+	0.0565980i
$680$	302.242	+	235.188i	0.444474	+	0.345865i
$681$	301.954	−	301.954i	0.443397	−	0.443397i
$682$	−985.735	−	515.973i	−1.44536	−	0.756559i
$683$	260.936	−	629.955i	0.382044	−	0.922336i	−0.609526	−	0.792766i	$-0.708640\pi$
$683$	260.936	−	629.955i	0.382044	−	0.922336i	0.991570	−	0.129570i	$-0.0413597\pi$
$684$	50.6846	−	78.7716i	0.0741002	−	0.115163i
$685$	222.336	+	536.767i	0.324578	+	0.783601i
$686$	−53.0690	−	63.5360i	−0.0773601	−	0.0926181i
$687$	618.722			0.900614
$688$	−279.714	+	299.774i	−0.406562	+	0.435718i
$689$			339.992i			0.493457i
$690$	−139.191	−	166.644i	−0.201726	−	0.241513i
$691$	−24.3590	+	10.0898i	−0.0352517	+	0.0146018i	−0.400240	−	0.916411i	$-0.631073\pi$
$691$	−24.3590	+	10.0898i	−0.0352517	+	0.0146018i	0.364988	+	0.931012i	$0.381073\pi$
$692$	13.4729	+	62.0979i	0.0194695	+	0.0897369i
$693$	−15.2186	−	6.30373i	−0.0219604	−	0.00909629i
$694$	−1222.25	−	639.776i	−1.76117	−	0.921868i
$695$	27.2169	+	27.2169i	0.0391611	+	0.0391611i
$696$	−289.591	−	509.526i	−0.416079	−	0.732078i
$697$	658.049	+	658.049i	0.944117	+	0.944117i
$698$	981.707	−	307.096i	1.40646	−	0.439966i
$699$	603.813	+	250.108i	0.863824	+	0.357808i
$700$	22.7789	+	4.12267i	0.0325412	+	0.00588953i
$701$	766.778	−	317.610i	1.09383	−	0.453081i	0.238492	−	0.971144i	$-0.423347\pi$
$701$	766.778	−	317.610i	1.09383	−	0.453081i	0.855342	+	0.518064i	$0.173347\pi$
$702$	−11.7041	+	130.387i	−0.0166725	+	0.185737i
$703$			64.8118i			0.0921932i
$704$	−665.659	+	496.598i	−0.945538	+	0.705394i
$705$	159.931			0.226852
$706$	−189.180	−	16.9816i	−0.267960	−	0.0240532i
$707$	−6.58351	−	15.8940i	−0.00931190	−	0.0224809i
$708$	−121.043	+	668.793i	−0.170964	+	0.944623i
$709$	−417.396	+	1007.68i	−0.588711	+	1.42127i	0.296024	+	0.955181i	$0.404339\pi$
$709$	−417.396	+	1007.68i	−0.588711	+	1.42127i	−0.884735	+	0.466094i	$0.845661\pi$
$710$	−148.355	−	474.254i	−0.208951	−	0.667963i
$711$	178.964	−	178.964i	0.251707	−	0.251707i
$712$	263.724	+	464.014i	0.370399	+	0.651705i
$713$	−564.659	+	564.659i	−0.791948	+	0.791948i
$714$	9.67046	−	18.4748i	0.0135441	−	0.0258751i
$715$	210.495	−	508.180i	0.294399	−	0.710741i
$716$	−339.452	+	73.6482i	−0.474095	+	0.102861i
$717$	−154.531	−	373.071i	−0.215524	−	0.520322i
$718$	544.211	−	454.558i	0.757954	−	0.633088i
$719$	−1091.07			−1.51748			−0.758741	−	0.651392i	$-0.774185\pi$
$719$	−1091.07			−1.51748			−0.758741	+	0.651392i	$0.774185\pi$
$720$	−5.58777	−	161.422i	−0.00776079	−	0.224198i
$721$		−	79.7021i		−	0.110544i
$722$	460.604	−	384.724i	0.637956	−	0.532859i
$723$	266.622	−	110.439i	0.368772	−	0.152750i
$724$	−714.721	−	459.878i	−0.987183	−	0.635190i
$725$	534.445	+	221.374i	0.737166	+	0.305344i
$726$	−76.1254	+	145.433i	−0.104856	+	0.200321i
$727$	−514.752	−	514.752i	−0.708050	−	0.708050i	0.258075	−	0.966125i	$-0.416912\pi$
$727$	−514.752	−	514.752i	−0.708050	−	0.708050i	−0.966125	+	0.258075i	$0.916912\pi$
$728$	−33.6537	−	26.1874i	−0.0462276	−	0.0359717i
$729$	19.0919	+	19.0919i	0.0261891	+	0.0261891i
$730$	184.249	+	588.998i	0.252396	+	0.806846i
$731$	−336.802	−	139.508i	−0.460741	−	0.190845i
$732$	269.277	+	388.287i	0.367865	+	0.530447i
$733$	−376.597	+	155.991i	−0.513774	+	0.212812i	−0.624480	−	0.781041i	$-0.714689\pi$
$733$	−376.597	+	155.991i	−0.513774	+	0.212812i	0.110705	+	0.993853i	$0.464689\pi$
$734$	127.505	+	11.4453i	0.173712	+	0.0155931i
$735$		−	284.544i		−	0.387135i
$736$	197.529	+	562.381i	0.268382	+	0.764105i
$737$	837.538			1.13641
$738$	35.0910	−	390.924i	0.0475488	−	0.529708i
$739$	−79.9969	−	193.130i	−0.108250	−	0.261339i	0.860467	−	0.509506i	$-0.170172\pi$
$739$	−79.9969	−	193.130i	−0.108250	−	0.261339i	−0.968717	+	0.248167i	$0.920172\pi$
$740$	63.6883	+	91.8361i	0.0860652	+	0.124103i
$741$	65.1750	−	157.346i	0.0879554	−	0.212343i
$742$	−21.7994	+	6.81924i	−0.0293792	+	0.00919035i
$743$	212.905	−	212.905i	0.286547	−	0.286547i	−0.549166	−	0.835713i	$-0.685054\pi$
$743$	212.905	−	212.905i	0.286547	−	0.286547i	0.835713	+	0.549166i	$0.185054\pi$
$744$	−589.462	+	73.5458i	−0.792288	+	0.0988519i
$745$	508.997	−	508.997i	0.683217	−	0.683217i
$746$	268.162	+	140.367i	0.359467	+	0.188159i
$747$	−70.6598	+	170.588i	−0.0945914	+	0.228364i
$748$	−620.978	−	399.560i	−0.830185	−	0.534172i
$749$	28.9361	+	69.8579i	0.0386330	+	0.0932683i
$750$	289.016	+	346.019i	0.385354	+	0.461359i
$751$	418.329			0.557029			0.278514	−	0.960432i	$-0.410158\pi$
$751$	418.329			0.557029			0.278514	+	0.960432i	$0.410158\pi$
$752$	−411.193	−	153.882i	−0.546800	−	0.204630i
$753$		−	92.6543i		−	0.123047i
$754$	−683.112	−	817.845i	−0.905985	−	1.08467i
$755$	−422.956	+	175.194i	−0.560207	+	0.232045i
$756$	−8.59482	+	1.86475i	−0.0113688	+	0.00246660i
$757$	−1241.05	−	514.062i	−1.63944	−	0.679078i	−0.643197	−	0.765701i	$-0.722392\pi$
$757$	−1241.05	−	514.062i	−1.63944	−	0.679078i	−0.996241	+	0.0866229i	$0.972392\pi$
$758$	413.948	+	216.677i	0.546105	+	0.285853i
$759$	296.034	+	296.034i	0.390031	+	0.390031i
$760$	−55.7591	+	202.597i	−0.0733673	+	0.266575i
$761$	−436.079	−	436.079i	−0.573034	−	0.573034i	0.359941	−	0.932975i	$-0.382797\pi$
$761$	−436.079	−	436.079i	−0.573034	−	0.573034i	−0.932975	+	0.359941i	$0.882797\pi$
$762$	509.180	−	159.281i	0.668215	−	0.209030i
$763$	65.3613	+	27.0735i	0.0856635	+	0.0354830i
$764$	79.6445	−	440.057i	0.104247	−	0.575991i
$765$	132.681	−	54.9582i	0.173439	−	0.0718408i
$766$	−119.973	+	1336.54i	−0.156623	+	1.74483i
$767$			1235.77i			1.61117i
$768$	−140.951	+	420.406i	−0.183529	+	0.547403i
$769$	−13.4129			−0.0174420			−0.00872100	−	0.999962i	$-0.502776\pi$
$769$	−13.4129			−0.0174420			−0.00872100	+	0.999962i	$0.502776\pi$
$770$	36.8050	+	3.30377i	0.0477987	+	0.00429061i
$771$	119.393	+	288.240i	0.154855	+	0.373853i
$772$	1269.20	+	229.708i	1.64404	+	0.297549i
$773$	−131.361	+	317.133i	−0.169936	+	0.410262i	−0.985787	−	0.168000i	$-0.946269\pi$
$773$	−131.361	+	317.133i	−0.169936	+	0.410262i	0.815851	+	0.578262i	$0.196269\pi$
$774$	45.9029	+	146.740i	0.0593061	+	0.189587i
$775$	414.603	−	414.603i	0.534971	−	0.534971i
$776$	990.690	+	272.660i	1.27666	+	0.351366i
$777$	4.30297	−	4.30297i	0.00553793	−	0.00553793i
$778$	118.023	−	225.475i	0.151700	−	0.289814i
$779$	−195.406	+	471.753i	−0.250843	+	0.605587i
$780$	−62.2679	−	286.999i	−0.0798306	−	0.367948i
$781$	366.660	+	885.196i	0.469475	+	1.13341i
$782$	−406.758	+	339.748i	−0.520150	+	0.434461i
$783$	−219.777			−0.280686
$784$	−273.782	+	731.584i	−0.349212	+	0.933143i
$785$			259.672i			0.330793i
$786$	314.103	−	262.357i	0.399622	−	0.333788i
$787$	333.352	−	138.079i	0.423574	−	0.175450i	−0.160706	−	0.987002i	$-0.551377\pi$
$787$	333.352	−	138.079i	0.423574	−	0.175450i	0.584280	+	0.811552i	$0.301377\pi$
$788$	−698.908	+	1086.21i	−0.886940	+	1.37844i
$789$	64.8744	+	26.8719i	0.0822236	+	0.0340581i
$790$	−263.303	+	503.024i	−0.333295	+	0.636739i
$791$	8.82934	+	8.82934i	0.0111622	+	0.0111622i
$792$	38.5578	+	309.037i	0.0486841	+	0.390198i
$793$	607.508	+	607.508i	0.766089	+	0.766089i
$794$	369.730	+	1181.93i	0.465655	+	1.48858i
$795$	−145.332	−	60.1986i	−0.182808	−	0.0757215i
$796$	677.384	−	469.765i	0.850985	−	0.590157i
$797$	−112.247	+	46.4941i	−0.140837	+	0.0583364i	−0.451989	−	0.892024i	$-0.649285\pi$
$797$	−112.247	+	46.4941i	−0.140837	+	0.0583364i	0.311152	+	0.950360i	$0.399285\pi$
$798$	11.3958	+	1.02294i	0.0142805	+	0.00128188i
$799$		−	390.371i		−	0.488574i
$800$	−145.037	−	412.930i	−0.181296	−	0.516163i
$801$	200.146			0.249870
$802$	−79.1362	+	881.601i	−0.0986735	+	1.09925i
$803$	−455.372	−	1099.37i	−0.567089	−	1.36907i
$804$	367.454	−	254.829i	0.457032	−	0.316951i
$805$	10.1496	−	24.5032i	0.0126081	−	0.0304388i
$806$	−1030.82	+	322.459i	−1.27893	+	0.400074i
$807$	−239.773	+	239.773i	−0.297117	+	0.297117i
$808$	−199.746	+	256.696i	−0.247211	+	0.317693i
$809$	580.413	−	580.413i	0.717445	−	0.717445i	−0.250636	−	0.968081i	$-0.580640\pi$
$809$	580.413	−	580.413i	0.717445	−	0.717445i	0.968081	+	0.250636i	$0.0806397\pi$
$810$	−53.6627	−	28.0892i	−0.0662502	−	0.0346780i
$811$	−339.019	+	818.463i	−0.418025	+	1.00920i	0.564894	+	0.825164i	$0.308917\pi$
$811$	−339.019	+	818.463i	−0.418025	+	1.00920i	−0.982919	+	0.184039i	$0.941083\pi$
$812$	38.7367	−	60.2028i	0.0477053	−	0.0741414i
$813$	81.3798	+	196.468i	0.100098	+	0.241658i
$814$	−138.140	−	165.386i	−0.169705	−	0.203177i
$815$	474.575			0.582301
$816$	−394.012	+	13.6391i	−0.482858	+	0.0167145i
$817$		−	200.025i		−	0.244829i
$818$	657.432	+	787.099i	0.803706	+	0.962224i
$819$	−14.7736	+	6.11941i	−0.0180385	+	0.00747181i
$820$	186.690	+	860.476i	0.227671	+	1.04936i
$821$	−1146.82	−	475.027i	−1.39685	−	0.578596i	−0.447921	−	0.894073i	$-0.647835\pi$
$821$	−1146.82	−	475.027i	−1.39685	−	0.578596i	−0.948933	+	0.315477i	$0.897835\pi$
$822$	−529.901	−	277.372i	−0.644649	−	0.337435i
$823$	−249.699	−	249.699i	−0.303400	−	0.303400i	0.538942	−	0.842343i	$-0.318824\pi$
$823$	−249.699	−	249.699i	−0.303400	−	0.303400i	−0.842343	+	0.538942i	$0.818824\pi$
$824$	−1310.06	+	744.580i	−1.58988	+	0.903617i
$825$	−217.364	−	217.364i	−0.263471	−	0.263471i
$826$	−79.2338	+	24.7858i	−0.0959248	+	0.0300070i
$827$	240.890	+	99.7800i	0.291282	+	0.120653i	0.523540	−	0.852001i	$-0.324611\pi$
$827$	240.890	+	99.7800i	0.291282	+	0.120653i	−0.232258	+	0.972654i	$0.574611\pi$
$828$	219.950	+	39.8080i	0.265640	+	0.0480773i
$829$	−598.623	+	247.958i	−0.722102	+	0.299104i	−0.713302	−	0.700857i	$-0.752801\pi$
$829$	−598.623	+	247.958i	−0.722102	+	0.299104i	−0.00880001	+	0.999961i	$0.502801\pi$
$830$	37.0326	−	412.555i	0.0446176	−	0.497054i
$831$		−	208.349i		−	0.250721i
$832$	−116.049	+	797.809i	−0.139482	+	0.958906i
$833$	−694.537			−0.833778
$834$	−39.4657	−	3.54261i	−0.0473210	−	0.00424773i
$835$	−123.809	−	298.901i	−0.148274	−	0.357965i
$836$	72.1566	−	398.685i	0.0863118	−	0.476896i
$837$	−85.2474	+	205.805i	−0.101849	+	0.245885i
$838$	−183.262	−	585.843i	−0.218690	−	0.699097i
$839$	−297.257	+	297.257i	−0.354300	+	0.354300i	−0.861707	−	0.507407i	$-0.830604\pi$
$839$	−297.257	+	297.257i	−0.354300	+	0.354300i	0.507407	+	0.861707i	$0.330604\pi$
$840$	17.1527	−	9.74880i	0.0204199	−	0.0116057i
$841$	670.308	−	670.308i	0.797037	−	0.797037i
$842$	−289.536	+	553.140i	−0.343867	+	0.656936i
$843$	20.0995	−	48.5245i	0.0238428	−	0.0575616i
$844$	1132.08	−	245.618i	1.34133	−	0.291017i
$845$	13.2849	+	32.0726i	0.0157218	+	0.0379557i
$846$	−126.361	+	105.544i	−0.149363	+	0.124757i
$847$	−20.0511			−0.0236731
$848$	315.738	+	294.611i	0.372333	+	0.347418i
$849$		−	679.163i		−	0.799957i
$850$	298.663	−	249.461i	0.351368	−	0.293484i
$851$	−142.888	+	59.1863i	−0.167906	+	0.0695491i
$852$	430.195	+	276.803i	0.504923	+	0.324886i
$853$	367.244	+	152.118i	0.430533	+	0.178333i	0.587417	−	0.809285i	$-0.300145\pi$
$853$	367.244	+	152.118i	0.430533	+	0.178333i	−0.156884	+	0.987617i	$0.550145\pi$
$854$	−26.7669	+	51.1366i	−0.0313430	+	0.0598789i
$855$	55.7191	+	55.7191i	0.0651685	+	0.0651685i
$856$	877.933	−	1128.24i	1.02562	−	1.31804i
$857$	−284.228	−	284.228i	−0.331654	−	0.331654i	0.521560	−	0.853214i	$-0.325350\pi$
$857$	−284.228	−	284.228i	−0.331654	−	0.331654i	−0.853214	+	0.521560i	$0.825350\pi$
$858$	169.056	+	540.428i	0.197035	+	0.629869i
$859$	187.472	+	77.6533i	0.218244	+	0.0903996i	0.489127	−	0.872213i	$-0.337316\pi$
$859$	187.472	+	77.6533i	0.218244	+	0.0903996i	−0.270883	+	0.962612i	$0.587316\pi$
$860$	−196.557	−	283.429i	−0.228555	−	0.329568i
$861$	44.2938	−	18.3471i	0.0514446	−	0.0213091i
$862$	−805.027	−	72.2626i	−0.933906	−	0.0838314i
$863$		−	155.379i		−	0.180045i	−0.995940	−	0.0900223i	$-0.971306\pi$
$863$		−	155.379i		−	0.180045i	0.995940	−	0.0900223i	$-0.0286938\pi$
$864$	110.944	+	123.852i	0.128407	+	0.143348i
$865$	−53.4550			−0.0617977
$866$	−102.849	+	1145.76i	−0.118763	+	1.32305i
$867$	57.4107	+	138.602i	0.0662177	+	0.159864i
$868$	−41.3504	−	59.6257i	−0.0476387	−	0.0686933i
$869$	418.940	−	1011.41i	0.482095	−	1.16388i
$870$	470.545	−	147.195i	0.540856	−	0.169190i
$871$	574.912	−	574.912i	0.660060	−	0.660060i
$872$	−165.600	−	1327.27i	−0.189908	−	1.52209i
$873$	272.464	−	272.464i	0.312101	−	0.312101i
$874$	−257.634	−	134.856i	−0.294776	−	0.154298i
$875$	−21.0745	+	50.8783i	−0.0240851	+	0.0581467i
$876$	−534.279	−	343.775i	−0.609907	−	0.392437i
$877$	−559.170	−	1349.96i	−0.637594	−	1.53929i	−0.829876	−	0.557948i	$-0.811589\pi$
$877$	−559.170	−	1349.96i	−0.637594	−	1.53929i	0.192282	−	0.981340i	$-0.438411\pi$
$878$	507.428	+	607.509i	0.577936	+	0.691924i
$879$	−339.538			−0.386278
$880$	−289.530	−	635.828i	−0.329011	−	0.722532i
$881$		−	1124.37i		−	1.27624i	−0.769935	−	0.638122i	$-0.779712\pi$
$881$		−	1124.37i		−	1.27624i	0.769935	−	0.638122i	$-0.220288\pi$
$882$	187.782	+	224.819i	0.212905	+	0.254896i
$883$	−326.685	+	135.317i	−0.369971	+	0.153247i	−0.559920	−	0.828547i	$-0.689168\pi$
$883$	−326.685	+	135.317i	−0.369971	+	0.153247i	0.189948	+	0.981794i	$0.439168\pi$
$884$	−700.530	+	151.988i	−0.792454	+	0.171932i
$885$	−528.237	−	218.803i	−0.596878	−	0.247235i
$886$	225.351	+	117.958i	0.254347	+	0.133135i
$887$	1183.52	+	1183.52i	1.33429	+	1.33429i	0.901486	+	0.432809i	$0.142477\pi$
$887$	1183.52	+	1183.52i	1.33429	+	1.33429i	0.432809	+	0.901486i	$0.357523\pi$
$888$	−110.926	−	30.5294i	−0.124917	−	0.0343800i
$889$	46.0809	+	46.0809i	0.0518346	+	0.0518346i
$890$	−428.515	+	134.047i	−0.481477	+	0.150615i
$891$	107.898	+	44.6926i	0.121097	+	0.0501601i
$892$	−137.527	+	759.871i	−0.154178	+	0.851873i
$893$	197.887	−	81.9676i	0.221598	−	0.0917891i
$894$	−66.2519	+	738.066i	−0.0741073	+	0.825577i
$895$		−	292.206i		−	0.326488i
$896$	−53.4809	+	8.56095i	−0.0596885	+	0.00955464i
$897$	406.413			0.453081
$898$	355.874	+	31.9447i	0.396296	+	0.0355732i
$899$	−693.904	−	1675.23i	−0.771862	−	1.86344i
$900$	−161.499	−	29.2292i	−0.179443	−	0.0324769i
$901$	−146.937	+	354.738i	−0.163082	+	0.393716i
$902$	−506.859	−	1620.30i	−0.561928	−	1.79634i
$903$	−13.2800	+	13.2800i	−0.0147065	+	0.0147065i
$904$	62.6439	−	227.612i	0.0692963	−	0.251783i
$905$	505.557	−	505.557i	0.558627	−	0.558627i
$906$	218.561	−	417.547i	0.241237	−	0.460868i
$907$	489.527	−	1181.82i	0.539721	−	1.30300i	−0.385197	−	0.922834i	$-0.625867\pi$
$907$	489.527	−	1181.82i	0.539721	−	1.30300i	0.924918	−	0.380167i	$-0.124133\pi$
$908$	−209.098	−	963.754i	−0.230284	−	1.06140i
$909$	46.6763	+	112.686i	0.0513490	+	0.123967i
$910$	27.5319	−	22.9963i	0.0302549	−	0.0252707i
$911$	1491.52			1.63724			0.818618	−	0.574338i	$-0.194741\pi$
$911$	1491.52			1.63724			0.818618	+	0.574338i	$0.194741\pi$
$912$	−89.6462	−	196.870i	−0.0982963	−	0.215866i
$913$			798.666i			0.874771i
$914$	1080.23	−	902.276i	1.18188	−	0.987173i
$915$	−367.249	+	152.119i	−0.401365	+	0.166251i
$916$	773.169	−	1201.62i	0.844071	−	1.31182i
$917$	46.1854	+	19.1306i	0.0503658	+	0.0208622i
$918$	−68.5623	+	130.984i	−0.0746866	+	0.142684i
$919$	959.292	+	959.292i	1.04384	+	1.04384i	0.998994	+	0.0448498i	$0.0142809\pi$
$919$	959.292	+	959.292i	1.04384	+	1.04384i	0.0448498	+	0.998994i	$0.485719\pi$
$920$	−497.577	+	62.0815i	−0.540844	+	0.0674799i
$921$	−381.196	−	381.196i	−0.413894	−	0.413894i
$922$	213.717	+	683.199i	0.231797	+	0.740996i
$923$	859.314	+	355.939i	0.931001	+	0.385633i
$924$	−31.2600	+	21.6788i	−0.0338311	+	0.0234619i
$925$	104.916	−	43.4577i	0.113423	−	0.0469813i
$926$	−1003.29	−	90.0599i	−1.08347	−	0.0972569i
$927$			565.078i			0.609577i
$928$	−1351.43	−	74.2986i	−1.45629	−	0.0800631i
$929$	−503.989			−0.542507			−0.271253	−	0.962508i	$-0.587438\pi$
$929$	−503.989			−0.542507			−0.271253	+	0.962508i	$0.587438\pi$
$930$	44.6780	−	497.726i	0.0480408	−	0.535189i
$931$	−145.835	−	352.076i	−0.156643	−	0.378170i
$932$	1240.27	−	860.129i	1.33077	−	0.922886i
$933$	−106.991	+	258.299i	−0.114674	+	0.276848i
$934$	−173.256	+	54.1975i	−0.185498	+	0.0580273i
$935$	439.249	−	439.249i	0.469785	−	0.469785i
$936$	238.600	+	185.665i	0.254915	+	0.198361i
$937$	910.460	−	910.460i	0.971675	−	0.971675i	−0.0279344	−	0.999610i	$-0.508893\pi$
$937$	910.460	−	910.460i	0.971675	−	0.971675i	0.999610	+	0.0279344i	$0.00889294\pi$
$938$	48.3928	+	25.3307i	0.0515915	+	0.0270051i
$939$	−138.543	+	334.473i	−0.147543	+	0.356201i
$940$	199.853	−	310.602i	0.212609	−	0.330428i
$941$	−153.916	−	371.585i	−0.163566	−	0.394883i	0.820752	−	0.571284i	$-0.193554\pi$
$941$	−153.916	−	371.585i	−0.163566	−	0.394883i	−0.984318	+	0.176401i	$0.943554\pi$
$942$	−171.368	−	205.167i	−0.181919	−	0.217800i
$943$	−1218.50			−1.29215
$944$	1147.61	+	1070.82i	1.21569	+	1.13434i
$945$		−	7.39857i		−	0.00782917i
$946$	426.334	+	510.421i	0.450670	+	0.539557i
$947$	776.879	−	321.794i	0.820358	−	0.339803i	0.0672795	−	0.997734i	$-0.478568\pi$
$947$	776.879	−	321.794i	0.820358	−	0.339803i	0.753078	+	0.657931i	$0.228568\pi$
$948$	−123.929	−	571.204i	−0.130727	−	0.602536i
$949$	−1067.22	−	442.058i	−1.12457	−	0.465814i
$950$	189.169	+	99.0185i	0.199125	+	0.104230i
$951$	50.2379	+	50.2379i	0.0528264	+	0.0528264i
$952$	−23.7956	−	41.8676i	−0.0249954	−	0.0439786i
$953$	1293.17	+	1293.17i	1.35695	+	1.35695i	0.877658	+	0.479288i	$0.159105\pi$
$953$	1293.17	+	1293.17i	1.35695	+	1.35695i	0.479288	+	0.877658i	$0.340895\pi$
$954$	154.555	−	48.3475i	0.162007	−	0.0506787i
$955$	347.573	+	143.969i	0.363951	+	0.150753i
$956$	−917.648	−	166.082i	−0.959883	−	0.173726i
$957$	−878.273	+	363.793i	−0.917736	+	0.380139i
$958$	−21.4809	+	239.304i	−0.0224227	+	0.249795i
$959$		−	73.0585i		−	0.0761819i
$960$	−320.482	−	190.865i	−0.333836	−	0.198818i
$961$	−876.889			−0.912476
$962$	−208.350	−	18.7023i	−0.216580	−	0.0194411i
$963$	−205.153	−	495.284i	−0.213035	−	0.514313i
$964$	118.694	−	655.815i	0.123126	−	0.680306i
$965$	−415.232	+	1002.46i	−0.430292	+	1.03882i
$966$	8.15145	+	26.0581i	0.00843836	+	0.0269753i
$967$	−35.9430	+	35.9430i	−0.0371696	+	0.0371696i	−0.725447	−	0.688278i	$-0.758367\pi$
$967$	−35.9430	+	35.9430i	−0.0371696	+	0.0371696i	0.688278	+	0.725447i	$0.258367\pi$
$968$	187.318	+	329.580i	0.193510	+	0.340475i
$969$	136.003	−	136.003i	0.140354	−	0.140354i
$970$	−400.867	+	765.831i	−0.413264	+	0.789516i
$971$	−201.889	+	487.402i	−0.207918	+	0.501959i	−0.993095	−	0.117313i	$-0.962572\pi$
$971$	−201.889	+	487.402i	−0.207918	+	0.501959i	0.785177	+	0.619272i	$0.212572\pi$
$972$	60.9361	−	13.2208i	0.0626915	−	0.0136017i
$973$	−1.85223	−	4.47167i	−0.00190363	−	0.00459576i
$974$	−426.742	+	356.440i	−0.438133	+	0.365955i
$975$	−298.410			−0.306062
$976$	1090.59	−	37.7516i	1.11741	−	0.0386800i
$977$			1036.76i			1.06117i	0.847631	+	0.530585i	$0.178028\pi$
$977$			1036.76i			1.06117i	−0.847631	+	0.530585i	$0.821972\pi$
$978$	−374.962	+	313.191i	−0.383397	+	0.320236i
$979$	799.824	−	331.298i	0.816981	−	0.338404i
$980$	−552.615	−	355.573i	−0.563893	−	0.362829i
$981$	−463.403	−	191.948i	−0.472378	−	0.195665i
$982$	−61.0617	+	116.655i	−0.0621809	+	0.118793i
$983$	457.721	+	457.721i	0.465637	+	0.465637i	0.900498	−	0.434861i	$-0.143202\pi$
$983$	457.721	+	457.721i	0.465637	+	0.465637i	−0.434861	+	0.900498i	$0.643202\pi$
$984$	−715.366	−	556.659i	−0.726998	−	0.565710i
$985$	−768.331	−	768.331i	−0.780032	−	0.780032i
$986$	−359.285	−	1148.54i	−0.364386	−	1.16485i
$987$	−18.5801	−	7.69611i	−0.0188248	−	0.00779748i
$988$	−224.139	−	323.200i	−0.226861	−	0.327126i
$989$	440.988	−	182.663i	0.445893	−	0.184695i
$990$	−260.943	−	23.4233i	−0.263578	−	0.0236599i
$991$		−	426.790i		−	0.430666i	−0.976541	−	0.215333i	$-0.930916\pi$
$991$		−	426.790i		−	0.430666i	0.976541	−	0.215333i	$-0.0690837\pi$
$992$	−593.772	+	1236.70i	−0.598560	+	1.24668i
$993$	−868.451			−0.874573
$994$	−5.58656	+	62.2359i	−0.00562028	+	0.0626116i
$995$	265.379	+	640.681i	0.266712	+	0.643900i
$996$	243.002	+	350.399i	0.243978	+	0.351807i
$997$	−518.461	+	1251.67i	−0.520021	+	1.25544i	0.417869	+	0.908507i	$0.362777\pi$
$997$	−518.461	+	1251.67i	−0.520021	+	1.25544i	−0.937890	+	0.346934i	$0.887223\pi$
$998$	−596.379	+	186.558i	−0.597574	+	0.186932i
$999$	−30.5075	+	30.5075i	−0.0305380	+	0.0305380i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	96.3.m.a.43.1	✓	64
3.2	odd	2		288.3.u.b.235.16		64
4.3	odd	2		384.3.m.a.79.3		64
32.3	odd	8	inner	96.3.m.a.67.1	yes	64
32.29	even	8		384.3.m.a.175.3		64
96.35	even	8		288.3.u.b.163.16		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.3.m.a.43.1	✓	64	1.1	even	1	trivial
96.3.m.a.67.1	yes	64	32.3	odd	8	inner
288.3.u.b.163.16		64	96.35	even	8
288.3.u.b.235.16		64	3.2	odd	2
384.3.m.a.79.3		64	4.3	odd	2
384.3.m.a.175.3		64	32.29	even	8

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:	\( N \)	\(=\)	\( 96 = 2^{5} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	96.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.99199 - 0.178809i) q^{2} +(0.662827 + 1.60021i) q^{3} +(3.93605 + 0.712374i) q^{4} +(-1.28772 + 3.10884i) q^{5} +(-1.03421 - 3.30612i) q^{6} +(0.299204 - 0.299204i) q^{7} +(-7.71320 - 2.12285i) q^{8} +(-2.12132 + 2.12132i) q^{9} +O(q^{10})\)	\(q+(-1.99199 - 0.178809i) q^{2} +(0.662827 + 1.60021i) q^{3} +(3.93605 + 0.712374i) q^{4} +(-1.28772 + 3.10884i) q^{5} +(-1.03421 - 3.30612i) q^{6} +(0.299204 - 0.299204i) q^{7} +(-7.71320 - 2.12285i) q^{8} +(-2.12132 + 2.12132i) q^{9} +(3.12102 - 5.96252i) q^{10} +(-4.96585 + 11.9886i) q^{11} +(1.46898 + 6.77068i) q^{12} +(4.82065 + 11.6381i) q^{13} +(-0.649513 + 0.542512i) q^{14} -5.82832 q^{15} +(14.9850 + 5.60788i) q^{16} +14.2262i q^{17} +(4.60496 - 3.84634i) q^{18} +(-7.21158 + 2.98713i) q^{19} +(-7.28320 + 11.3192i) q^{20} +(0.677110 + 0.280468i) q^{21} +(12.0356 - 22.9933i) q^{22} +(-13.1712 - 13.1712i) q^{23} +(-1.71553 - 13.7498i) q^{24} +(9.67103 + 9.67103i) q^{25} +(-7.52169 - 24.0449i) q^{26} +(-4.80062 - 1.98848i) q^{27} +(1.39083 - 0.964540i) q^{28} +(39.0765 - 16.1860i) q^{29} +(11.6100 + 1.04216i) q^{30} -42.8706i q^{31} +(-28.8473 - 13.8503i) q^{32} -22.4758 q^{33} +(2.54378 - 28.3385i) q^{34} +(0.544886 + 1.31547i) q^{35} +(-9.86080 + 6.83846i) q^{36} +(3.17745 - 7.67105i) q^{37} +(14.8995 - 4.66084i) q^{38} +(-15.4281 + 15.4281i) q^{39} +(16.5321 - 21.2455i) q^{40} +(46.2561 - 46.2561i) q^{41} +(-1.29865 - 0.679763i) q^{42} +(-9.80640 + 23.6747i) q^{43} +(-28.0862 + 43.6503i) q^{44} +(-3.86317 - 9.32651i) q^{45} +(23.8818 + 28.5921i) q^{46} -27.4402 q^{47} +(0.958727 + 27.6962i) q^{48} +48.8210i q^{49} +(-17.5353 - 20.9939i) q^{50} +(-22.7649 + 9.42952i) q^{51} +(10.6837 + 49.2422i) q^{52} +(24.9355 + 10.3286i) q^{53} +(9.20723 + 4.81943i) q^{54} +(-30.8760 - 30.8760i) q^{55} +(-2.94299 + 1.67266i) q^{56} +(-9.56006 - 9.56006i) q^{57} +(-80.7342 + 25.2551i) q^{58} +(90.6328 + 37.5413i) q^{59} +(-22.9406 - 4.15194i) q^{60} +(63.0111 - 26.1000i) q^{61} +(-7.66567 + 85.3979i) q^{62} +1.26942i q^{63} +(54.9871 + 32.7479i) q^{64} -42.3885 q^{65} +(44.7715 + 4.01888i) q^{66} +(-24.6996 - 59.6302i) q^{67} +(-10.1344 + 55.9951i) q^{68} +(12.3464 - 29.8070i) q^{69} +(-0.850189 - 2.71784i) q^{70} +(52.2102 - 52.2102i) q^{71} +(20.8654 - 11.8589i) q^{72} +(-64.8423 + 64.8423i) q^{73} +(-7.70112 + 14.7125i) q^{74} +(-9.06542 + 21.8859i) q^{75} +(-30.5131 + 6.62018i) q^{76} +(2.10124 + 5.07285i) q^{77} +(33.4912 - 27.9739i) q^{78} -84.3643 q^{79} +(-36.7306 + 39.3647i) q^{80} -9.00000i q^{81} +(-100.413 + 83.8707i) q^{82} +(56.8626 - 23.5533i) q^{83} +(2.46534 + 1.58629i) q^{84} +(-44.2270 - 18.3194i) q^{85} +(23.7675 - 45.4064i) q^{86} +(51.8019 + 51.8019i) q^{87} +(63.7526 - 81.9289i) q^{88} +(-47.1748 - 47.1748i) q^{89} +(6.02773 + 19.2691i) q^{90} +(4.92452 + 2.03980i) q^{91} +(-42.4599 - 61.2256i) q^{92} +(68.6018 - 28.4158i) q^{93} +(54.6607 + 4.90658i) q^{94} -26.2662i q^{95} +(3.04257 - 55.3421i) q^{96} -128.441 q^{97} +(8.72965 - 97.2509i) q^{98} +(-14.8975 - 35.9658i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 64 * q	\( 64 q + 40 q^{10} + 48 q^{12} + 32 q^{14} - 8 q^{16} - 24 q^{18} - 160 q^{20} - 184 q^{22} + 128 q^{23} - 72 q^{24} - 200 q^{26} - 120 q^{28} + 40 q^{32} + 120 q^{34} - 192 q^{35} + 280 q^{38} + 584 q^{40} - 192 q^{43} + 104 q^{44} + 32 q^{46} - 312 q^{50} - 192 q^{51} - 424 q^{52} + 320 q^{53} - 72 q^{54} - 256 q^{55} - 392 q^{56} - 352 q^{58} - 256 q^{59} - 144 q^{60} + 64 q^{61} - 48 q^{62} + 408 q^{64} + 144 q^{66} + 64 q^{67} + 856 q^{68} - 192 q^{69} + 984 q^{70} + 512 q^{71} + 1056 q^{74} + 384 q^{75} + 296 q^{76} - 448 q^{77} + 360 q^{78} + 512 q^{79} + 328 q^{80} - 760 q^{82} - 448 q^{86} - 1072 q^{88} + 192 q^{91} - 784 q^{92} - 480 q^{94} + 600 q^{96} + 272 q^{98}+O(q^{100}) \) 64 * q + 40 * q^10 + 48 * q^12 + 32 * q^14 - 8 * q^16 - 24 * q^18 - 160 * q^20 - 184 * q^22 + 128 * q^23 - 72 * q^24 - 200 * q^26 - 120 * q^28 + 40 * q^32 + 120 * q^34 - 192 * q^35 + 280 * q^38 + 584 * q^40 - 192 * q^43 + 104 * q^44 + 32 * q^46 - 312 * q^50 - 192 * q^51 - 424 * q^52 + 320 * q^53 - 72 * q^54 - 256 * q^55 - 392 * q^56 - 352 * q^58 - 256 * q^59 - 144 * q^60 + 64 * q^61 - 48 * q^62 + 408 * q^64 + 144 * q^66 + 64 * q^67 + 856 * q^68 - 192 * q^69 + 984 * q^70 + 512 * q^71 + 1056 * q^74 + 384 * q^75 + 296 * q^76 - 448 * q^77 + 360 * q^78 + 512 * q^79 + 328 * q^80 - 760 * q^82 - 448 * q^86 - 1072 * q^88 + 192 * q^91 - 784 * q^92 - 480 * q^94 + 600 * q^96 + 272 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more