LMFDB - Embedded newform 680.2.co.a.99.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(99,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 8, 8, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.99"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.co (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$832$
Relative dimension:	$104$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			99.6
Character	$\chi$	$=$	680.99
Dual form			680.2.co.a.419.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40033 + 0.197690i) q^{2} +(2.34414 + 0.466278i) q^{3} +(1.92184 - 0.553661i) q^{4} +(0.931769 - 2.03268i) q^{5} +(-3.37474 - 0.189530i) q^{6} +(-3.26252 - 2.17994i) q^{7} +(-2.58175 + 1.15523i) q^{8} +(2.50594 + 1.03799i) q^{9} +(-0.902942 + 3.03063i) q^{10} +(-4.47201 + 0.889539i) q^{11} +(4.76322 - 0.401747i) q^{12} +(-2.59200 - 2.59200i) q^{13} +(4.99955 + 2.40767i) q^{14} +(3.13200 - 4.33043i) q^{15} +(3.38692 - 2.12809i) q^{16} +(-1.63989 - 3.78296i) q^{17} +(-3.71434 - 0.958134i) q^{18} +(5.14362 - 2.13056i) q^{19} +(0.665291 - 4.42237i) q^{20} +(-6.63134 - 6.63134i) q^{21} +(6.08643 - 2.12972i) q^{22} +(0.179613 + 0.902978i) q^{23} +(-6.59065 + 1.50422i) q^{24} +(-3.26361 - 3.78799i) q^{25} +(4.14207 + 3.11724i) q^{26} +(-0.571520 - 0.381877i) q^{27} +(-7.47698 - 2.38317i) q^{28} +(6.41183 - 4.28425i) q^{29} +(-3.52974 + 6.68319i) q^{30} +(-1.04009 + 5.22889i) q^{31} +(-4.32210 + 3.64959i) q^{32} -10.8978 q^{33} +(3.04423 + 4.97319i) q^{34} +(-7.47105 + 4.60046i) q^{35} +(5.39070 + 0.607415i) q^{36} +(0.0703496 - 0.353672i) q^{37} +(-6.78157 + 4.00032i) q^{38} +(-4.86742 - 7.28461i) q^{39} +(-0.0573685 + 6.32430i) q^{40} +(3.97256 + 2.65438i) q^{41} +(10.5970 + 7.97510i) q^{42} +(3.92775 - 9.48244i) q^{43} +(-8.10198 + 4.18553i) q^{44} +(4.44487 - 4.12661i) q^{45} +(-0.430027 - 1.22896i) q^{46} +(6.80788 + 6.80788i) q^{47} +(8.93170 - 3.40930i) q^{48} +(3.21308 + 7.75705i) q^{49} +(5.31897 + 4.65924i) q^{50} +(-2.08022 - 9.63243i) q^{51} +(-6.41650 - 3.54632i) q^{52} +(-3.46766 + 1.43635i) q^{53} +(0.875808 + 0.421770i) q^{54} +(-2.35873 + 9.91903i) q^{55} +(10.9413 + 1.85910i) q^{56} +(13.0508 - 2.59597i) q^{57} +(-8.13172 + 7.26691i) q^{58} +(-4.65744 + 11.2441i) q^{59} +(3.62159 - 10.0565i) q^{60} +(5.85771 + 3.91400i) q^{61} +(0.422771 - 7.52778i) q^{62} +(-5.91290 - 8.84928i) q^{63} +(5.33087 - 5.96505i) q^{64} +(-7.68387 + 2.85357i) q^{65} +(15.2605 - 2.15438i) q^{66} -1.46951 q^{67} +(-5.24608 - 6.36229i) q^{68} +2.20046i q^{69} +(9.55246 - 7.91911i) q^{70} +(-5.00381 - 0.995320i) q^{71} +(-7.66884 + 0.215107i) q^{72} +(-1.29762 - 1.94202i) q^{73} +(-0.0285954 + 0.509164i) q^{74} +(-5.88411 - 10.4013i) q^{75} +(8.70560 - 6.94241i) q^{76} +(16.5292 + 6.84660i) q^{77} +(8.25608 + 9.23861i) q^{78} +(-3.17636 - 15.9686i) q^{79} +(-1.16991 - 8.86743i) q^{80} +(-6.91555 - 6.91555i) q^{81} +(-6.08763 - 2.93167i) q^{82} +(0.503868 - 0.208709i) q^{83} +(-16.4159 - 9.07284i) q^{84} +(-9.21756 - 0.191466i) q^{85} +(-3.62556 + 14.0550i) q^{86} +(17.0279 - 7.05318i) q^{87} +(10.5180 - 7.46279i) q^{88} +(4.27302 - 4.27302i) q^{89} +(-5.40849 + 6.65732i) q^{90} +(2.80603 + 14.1069i) q^{91} +(0.845131 + 1.63593i) q^{92} +(-4.87624 + 11.7723i) q^{93} +(-10.8791 - 8.18742i) q^{94} +(0.461918 - 12.4406i) q^{95} +(-11.8333 + 6.53984i) q^{96} +(7.41774 - 4.95638i) q^{97} +(-6.03285 - 10.2272i) q^{98} +(-12.1299 - 2.41279i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 832 q - 16 q^{4} - 16 q^{6} - 32 q^{9} - 8 q^{10} - 32 q^{11} - 16 q^{14} - 32 q^{19} - 8 q^{20} - 32 q^{24} - 16 q^{25} - 48 q^{26} + 56 q^{30} + 48 q^{34} - 32 q^{35} + 48 q^{36} - 72 q^{40} - 32 q^{41}+ \cdots - 128 q^{99}+O(q^{100}) $ 832 * q - 16 * q^4 - 16 * q^6 - 32 * q^9 - 8 * q^10 - 32 * q^11 - 16 * q^14 - 32 * q^19 - 8 * q^20 - 32 * q^24 - 16 * q^25 - 48 * q^26 + 56 * q^30 + 48 * q^34 - 32 * q^35 + 48 * q^36 - 72 * q^40 - 32 * q^41 - 48 * q^44 - 32 * q^46 - 32 * q^49 - 32 * q^51 + 32 * q^54 - 16 * q^56 - 32 * q^59 - 112 * q^60 - 16 * q^64 - 96 * q^65 - 48 * q^66 - 80 * q^70 - 16 * q^74 - 16 * q^75 - 16 * q^76 - 104 * q^80 - 32 * q^81 - 192 * q^86 - 32 * q^89 + 72 * q^90 - 32 * q^91 - 16 * q^94 + 288 * q^96 - 128 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$-1$	$e\left(\frac{9}{16}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.40033	+	0.197690i	−0.990181	+	0.139788i
$2$	−1.40033	+	0.197690i	−0.990181	+	0.139788i
$3$	2.34414	+	0.466278i	1.35339	+	0.269206i	0.817912	−	0.575343i	$-0.195132\pi$
$3$	2.34414	+	0.466278i	1.35339	+	0.269206i	0.535478	+	0.844549i	$0.320132\pi$
$4$	1.92184	−	0.553661i	0.960919	−	0.276830i
$5$	0.931769	−	2.03268i	0.416700	−	0.909044i
$5$	0.931769	−	2.03268i	0.416700	−	0.909044i
$6$	−3.37474	−	0.189530i	−1.37773	−	0.0773755i
$7$	−3.26252	−	2.17994i	−1.23312	−	0.823941i	−0.243813	−	0.969822i	$-0.578398\pi$
$7$	−3.26252	−	2.17994i	−1.23312	−	0.823941i	−0.989302	+	0.145881i	$0.953398\pi$
$8$	−2.58175	+	1.15523i	−0.912786	+	0.408437i
$9$	2.50594	+	1.03799i	0.835313	+	0.345998i
$10$	−0.902942	+	3.03063i	−0.285535	+	0.958368i
$11$	−4.47201	+	0.889539i	−1.34836	+	0.268206i	−0.815873	−	0.578231i	$-0.803743\pi$
$11$	−4.47201	+	0.889539i	−1.34836	+	0.268206i	−0.532489	+	0.846437i	$0.678743\pi$
$12$	4.76322	−	0.401747i	1.37502	−	0.115975i
$13$	−2.59200	−	2.59200i	−0.718892	−	0.718892i	0.249486	−	0.968378i	$-0.419738\pi$
$13$	−2.59200	−	2.59200i	−0.718892	−	0.718892i	−0.968378	+	0.249486i	$0.919738\pi$
$14$	4.99955	+	2.40767i	1.33618	+	0.643477i
$15$	3.13200	−	4.33043i	0.808678	−	1.11811i
$16$	3.38692	−	2.12809i	0.846730	−	0.532023i
$17$	−1.63989	−	3.78296i	−0.397732	−	0.917502i
$17$	−1.63989	−	3.78296i	−0.397732	−	0.917502i
$18$	−3.71434	−	0.958134i	−0.875478	−	0.225834i
$19$	5.14362	−	2.13056i	1.18003	−	0.488784i	0.295533	−	0.955333i	$-0.404503\pi$
$19$	5.14362	−	2.13056i	1.18003	−	0.488784i	0.884495	+	0.466549i	$0.154503\pi$
$20$	0.665291	−	4.42237i	0.148764	−	0.988873i
$21$	−6.63134	−	6.63134i	−1.44708	−	1.44708i
$22$	6.08643	−	2.12972i	1.29763	−	0.454057i
$23$	0.179613	+	0.902978i	0.0374520	+	0.188284i	0.994983	−	0.100048i	$-0.0318995\pi$
$23$	0.179613	+	0.902978i	0.0374520	+	0.188284i	−0.957531	+	0.288331i	$0.906900\pi$
$24$	−6.59065	+	1.50422i	−1.34531	+	0.307047i
$25$	−3.26361	−	3.78799i	−0.652722	−	0.757597i
$26$	4.14207	+	3.11724i	0.812326	+	0.611341i
$27$	−0.571520	−	0.381877i	−0.109989	−	0.0734923i
$28$	−7.47698	−	2.38317i	−1.41302	−	0.450377i
$29$	6.41183	−	4.28425i	1.19065	−	0.795565i	0.207474	−	0.978240i	$-0.433476\pi$
$29$	6.41183	−	4.28425i	1.19065	−	0.795565i	0.983173	+	0.182675i	$0.0584757\pi$
$30$	−3.52974	+	6.68319i	−0.644439	+	1.22018i
$31$	−1.04009	+	5.22889i	−0.186806	+	0.939137i	0.767669	+	0.640846i	$0.221416\pi$
$31$	−1.04009	+	5.22889i	−0.186806	+	0.939137i	−0.954475	+	0.298290i	$0.903584\pi$
$32$	−4.32210	+	3.64959i	−0.764046	+	0.645162i
$33$	−10.8978			−1.89706
$34$	3.04423	+	4.97319i	0.522082	+	0.852895i
$35$	−7.47105	+	4.60046i	−1.26284	+	0.777620i
$36$	5.39070	+	0.607415i	0.898451	+	0.101236i
$37$	0.0703496	−	0.353672i	0.0115654	−	0.0581432i	−0.974572	−	0.224076i	$-0.928064\pi$
$37$	0.0703496	−	0.353672i	0.0115654	−	0.0581432i	0.986137	+	0.165933i	$0.0530635\pi$
$38$	−6.78157	+	4.00032i	−1.10012	+	0.648938i
$39$	−4.86742	−	7.28461i	−0.779411	−	1.16647i
$40$	−0.0573685	+	6.32430i	−0.00907076	+	0.999959i
$41$	3.97256	+	2.65438i	0.620409	+	0.414544i	0.825662	−	0.564165i	$-0.190802\pi$
$41$	3.97256	+	2.65438i	0.620409	+	0.414544i	−0.205253	+	0.978709i	$0.565802\pi$
$42$	10.5970	+	7.97510i	1.63515	+	1.23058i
$43$	3.92775	−	9.48244i	0.598977	−	1.44606i	−0.275649	−	0.961258i	$-0.588893\pi$
$43$	3.92775	−	9.48244i	0.598977	−	1.44606i	0.874625	−	0.484799i	$-0.161107\pi$
$44$	−8.10198	+	4.18553i	−1.22142	+	0.630992i
$45$	4.44487	−	4.12661i	0.662602	−	0.615159i
$46$	−0.430027	−	1.22896i	−0.0634040	−	0.181200i
$47$	6.80788	+	6.80788i	0.993032	+	0.993032i	0.999976	−	0.00694410i	$-0.00221039\pi$
$47$	6.80788	+	6.80788i	0.993032	+	0.993032i	−0.00694410	+	0.999976i	$0.502210\pi$
$48$	8.93170	−	3.40930i	1.28918	−	0.492090i
$49$	3.21308	+	7.75705i	0.459011	+	1.10815i
$50$	5.31897	+	4.65924i	0.752216	+	0.658916i
$51$	−2.08022	−	9.63243i	−0.291289	−	1.34881i
$52$	−6.41650	−	3.54632i	−0.889808	−	0.491786i
$53$	−3.46766	+	1.43635i	−0.476320	+	0.197298i	−0.607910	−	0.794006i	$-0.707992\pi$
$53$	−3.46766	+	1.43635i	−0.476320	+	0.197298i	0.131590	+	0.991304i	$0.457992\pi$
$54$	0.875808	+	0.421770i	0.119182	+	0.0573956i
$55$	−2.35873	+	9.91903i	−0.318052	+	1.33748i
$56$	10.9413	+	1.85910i	1.46210	+	0.248432i
$57$	13.0508	−	2.59597i	1.72862	−	0.343844i
$58$	−8.13172	+	7.26691i	−1.06775	+	0.954192i
$59$	−4.65744	+	11.2441i	−0.606347	+	1.46385i	0.260597	+	0.965448i	$0.416080\pi$
$59$	−4.65744	+	11.2441i	−0.606347	+	1.46385i	−0.866945	+	0.498404i	$0.833920\pi$
$60$	3.62159	−	10.0565i	0.467546	−	1.29828i
$61$	5.85771	+	3.91400i	0.750003	+	0.501136i	0.870858	−	0.491534i	$-0.163564\pi$
$61$	5.85771	+	3.91400i	0.750003	+	0.501136i	−0.120855	+	0.992670i	$0.538564\pi$
$62$	0.422771	−	7.52778i	0.0536919	−	0.956029i
$63$	−5.91290	−	8.84928i	−0.744955	−	1.11490i
$64$	5.33087	−	5.96505i	0.666358	−	0.745632i
$65$	−7.68387	+	2.85357i	−0.953067	+	0.353942i
$66$	15.2605	−	2.15438i	1.87844	−	0.265186i
$67$	−1.46951			−0.179530			−0.0897649	−	0.995963i	$-0.528612\pi$
$67$	−1.46951			−0.179530			−0.0897649	+	0.995963i	$0.528612\pi$
$68$	−5.24608	−	6.36229i	−0.636180	−	0.771540i
$69$			2.20046i			0.264904i
$70$	9.55246	−	7.91911i	1.14174	−	0.946514i
$71$	−5.00381	−	0.995320i	−0.593843	−	0.118123i	−0.110986	−	0.993822i	$-0.535401\pi$
$71$	−5.00381	−	0.995320i	−0.593843	−	0.118123i	−0.482857	+	0.875699i	$0.660401\pi$
$72$	−7.66884	+	0.215107i	−0.903781	+	0.0253505i
$73$	−1.29762	−	1.94202i	−0.151875	−	0.227297i	0.747729	−	0.664004i	$-0.231144\pi$
$73$	−1.29762	−	1.94202i	−0.151875	−	0.227297i	−0.899603	+	0.436708i	$0.856144\pi$
$74$	−0.0285954	+	0.509164i	−0.00332414	+	0.0591891i
$75$	−5.88411	−	10.4013i	−0.679438	−	1.20104i
$76$	8.70560	−	6.94241i	0.998601	−	0.796349i
$77$	16.5292	+	6.84660i	1.88367	+	0.780243i
$78$	8.25608	+	9.23861i	0.934817	+	1.04607i
$79$	−3.17636	−	15.9686i	−0.357368	−	1.79661i	−0.572368	−	0.819997i	$-0.693975\pi$
$79$	−3.17636	−	15.9686i	−0.357368	−	1.79661i	0.215000	−	0.976614i	$-0.431025\pi$
$80$	−1.16991	−	8.86743i	−0.130800	−	0.991409i
$81$	−6.91555	−	6.91555i	−0.768394	−	0.768394i
$82$	−6.08763	−	2.93167i	−0.672266	−	0.323748i
$83$	0.503868	−	0.208709i	0.0553067	−	0.0229088i	−0.354859	−	0.934920i	$-0.615471\pi$
$83$	0.503868	−	0.208709i	0.0553067	−	0.0229088i	0.410165	+	0.912011i	$0.365471\pi$
$84$	−16.4159	−	9.07284i	−1.79112	−	0.989928i
$85$	−9.21756	−	0.191466i	−0.999784	−	0.0207674i
$86$	−3.62556	+	14.0550i	−0.390955	+	1.51559i
$87$	17.0279	−	7.05318i	1.82558	−	0.756181i
$88$	10.5180	−	7.46279i	1.12122	−	0.795536i
$89$	4.27302	−	4.27302i	0.452939	−	0.452939i	−0.443390	−	0.896329i	$-0.646224\pi$
$89$	4.27302	−	4.27302i	0.452939	−	0.452939i	0.896329	+	0.443390i	$0.146224\pi$
$90$	−5.40849	+	6.65732i	−0.570105	+	0.701743i
$91$	2.80603	+	14.1069i	0.294152	+	1.47880i
$92$	0.845131	+	1.63593i	0.0881110	+	0.170558i
$93$	−4.87624	+	11.7723i	−0.505643	+	1.22073i
$94$	−10.8791	−	8.18742i	−1.12210	−	0.844468i
$95$	0.461918	−	12.4406i	0.0473918	−	1.27637i
$96$	−11.8333	+	6.53984i	−1.20773	+	0.667470i
$97$	7.41774	−	4.95638i	0.753157	−	0.503244i	−0.118744	−	0.992925i	$-0.537887\pi$
$97$	7.41774	−	4.95638i	0.753157	−	0.503244i	0.871902	+	0.489681i	$0.162887\pi$
$98$	−6.03285	−	10.2272i	−0.609410	−	1.03311i
$99$	−12.1299	−	2.41279i	−1.21910	−	0.242495i
$100$	−8.36939	−	5.47296i	−0.836939	−	0.547296i
$101$	−3.04355			−0.302845			−0.151422	−	0.988469i	$-0.548385\pi$
$101$	−3.04355			−0.302845			−0.151422	+	0.988469i	$0.548385\pi$
$102$	4.81722	+	13.0773i	0.476976	+	1.29485i
$103$	15.8306			1.55983			0.779916	−	0.625884i	$-0.215262\pi$
$103$	15.8306			1.55983			0.779916	+	0.625884i	$0.215262\pi$
$104$	9.68627	+	3.69753i	0.949817	+	0.362573i
$105$	−19.6583	+	7.30054i	−1.91845	+	0.712459i
$106$	4.57191	−	2.69688i	0.444063	−	0.261945i
$107$	8.78974	+	13.1548i	0.849736	+	1.27172i	0.960614	+	0.277886i	$0.0896339\pi$
$107$	8.78974	+	13.1548i	0.849736	+	1.27172i	−0.110878	+	0.993834i	$0.535366\pi$
$108$	−1.30980	−	0.417478i	−0.126035	−	0.0401718i
$109$	4.77820	−	7.15108i	0.457669	−	0.684950i	−0.528828	−	0.848729i	$-0.677368\pi$
$109$	4.77820	−	7.15108i	0.457669	−	0.684950i	0.986497	+	0.163779i	$0.0523685\pi$
$110$	1.34211	−	14.3562i	0.127965	−	1.36881i
$111$	0.329819	−	0.796253i	0.0313050	−	0.0755770i
$112$	−15.6890	−	0.440355i	−1.48247	−	0.0416097i
$113$	−1.10382	−	5.54930i	−0.103839	−	0.522034i	−0.997335	−	0.0729621i	$-0.976755\pi$
$113$	−1.10382	−	5.54930i	−0.103839	−	0.522034i	0.893496	−	0.449072i	$-0.148245\pi$
$114$	−17.7622	+	6.21522i	−1.66358	+	0.582108i
$115$	2.00283	+	0.476270i	0.186765	+	0.0444124i
$116$	9.95048	−	11.7836i	0.923879	−	1.09408i
$117$	−3.80492	−	9.18588i	−0.351765	−	0.849235i
$118$	4.29911	−	16.6661i	0.395765	−	1.53424i
$119$	−2.89647	+	15.9168i	−0.265519	+	1.45909i
$120$	−3.08336	+	14.7983i	−0.281471	+	1.35089i
$121$	9.04494	−	3.74654i	0.822267	−	0.340594i
$122$	−8.97648	−	4.32287i	−0.812692	−	0.391375i
$123$	8.07455	+	8.07455i	0.728058	+	0.728058i
$124$	0.896147	+	10.6249i	0.0804764	+	0.954148i
$125$	−10.7407	+	3.10436i	−0.960679	+	0.277663i
$126$	10.0294	+	11.2230i	0.893491	+	0.999822i
$127$	−0.0439562	+	0.106120i	−0.00390048	+	0.00941660i	−0.925818	−	0.377970i	$-0.876622\pi$
$127$	−0.0439562	+	0.106120i	−0.00390048	+	0.00941660i	0.921917	+	0.387387i	$0.126622\pi$
$128$	−6.28573	+	9.40689i	−0.555585	+	0.831459i
$129$	13.6287	−	20.3967i	1.19994	−	1.79583i
$130$	10.1958	−	5.51496i	0.894233	−	0.483694i
$131$	0.765534	+	1.14570i	0.0668851	+	0.100101i	0.863404	−	0.504513i	$-0.168328\pi$
$131$	0.765534	+	1.14570i	0.0668851	+	0.100101i	−0.796519	+	0.604613i	$0.793328\pi$
$132$	−20.9438	+	6.03368i	−1.82292	+	0.525165i
$133$	−21.4257	−	4.26183i	−1.85784	−	0.369547i
$134$	2.05780	−	0.290508i	0.177767	−	0.0250961i
$135$	−1.30876	+	0.805898i	−0.112640	+	0.0693606i
$136$	8.60399	+	7.87219i	0.737786	+	0.675035i
$137$		−	0.511771i		−	0.0437235i	−0.999761	−	0.0218618i	$-0.993041\pi$
$137$		−	0.511771i		−	0.0437235i	0.999761	−	0.0218618i	$-0.00695937\pi$
$138$	−0.435008	−	3.08136i	−0.0370303	−	0.262303i
$139$	−2.89015	+	14.5298i	−0.245139	+	1.23240i	0.640475	+	0.767979i	$0.278737\pi$
$139$	−2.89015	+	14.5298i	−0.245139	+	1.23240i	−0.885615	+	0.464420i	$0.846263\pi$
$140$	−11.8111	+	12.9778i	−0.998216	+	1.09682i
$141$	12.7843	+	19.1330i	1.07663	+	1.61129i
$142$	7.20374	+	0.404572i	0.604525	+	0.0339510i
$143$	13.8972	+	9.28578i	1.16214	+	0.776516i
$144$	10.6964	−	1.81727i	0.891363	−	0.151439i
$145$	−2.73418	−	17.0252i	−0.227061	−	1.41386i
$146$	2.20101	+	2.46294i	0.182157	+	0.203835i
$147$	3.91495	+	19.6818i	0.322900	+	1.62333i
$148$	−0.0606135	−	0.718649i	−0.00498240	−	0.0590726i
$149$	2.75273	−	2.75273i	0.225512	−	0.225512i	−0.585303	−	0.810815i	$-0.699024\pi$
$149$	2.75273	−	2.75273i	0.225512	−	0.225512i	0.810815	+	0.585303i	$0.199024\pi$
$150$	10.2959	+	13.4020i	0.840658	+	1.09427i
$151$	4.95287	−	2.05155i	0.403059	−	0.166953i	−0.171938	−	0.985108i	$-0.555003\pi$
$151$	4.95287	−	2.05155i	0.403059	−	0.166953i	0.574998	+	0.818155i	$0.305003\pi$
$152$	−10.8183	+	11.4427i	−0.877476	+	0.928122i
$153$	−0.182777	−	11.1821i	−0.0147766	−	0.904016i
$154$	−24.4998	−	6.31984i	−1.97425	−	0.509268i
$155$	9.65956	+	6.98630i	0.775875	+	0.561153i
$156$	−13.3876	−	11.3049i	−1.07187	−	0.905120i
$157$	4.51349	−	4.51349i	0.360216	−	0.360216i	−0.503676	−	0.863892i	$-0.668020\pi$
$157$	4.51349	−	4.51349i	0.360216	−	0.360216i	0.863892	+	0.503676i	$0.168020\pi$
$158$	7.60478	+	21.7334i	0.605004	+	1.72902i
$159$	−8.79842	+	1.75011i	−0.697760	+	0.138793i
$160$	3.39126	+	12.1860i	0.268103	+	0.963390i
$161$	1.38245	−	3.33753i	0.108952	−	0.263034i
$162$	11.0512	+	8.31691i	0.868262	+	0.653438i
$163$	6.61701	+	4.42135i	0.518284	+	0.346307i	0.787040	−	0.616902i	$-0.211612\pi$
$163$	6.61701	+	4.42135i	0.518284	+	0.346307i	−0.268756	+	0.963208i	$0.586612\pi$
$164$	9.10424	+	2.90183i	0.710922	+	0.226595i
$165$	−10.1542	+	22.1518i	−0.790506	+	1.72451i
$166$	−0.664321	+	0.391871i	−0.0515613	+	0.0304151i
$167$	−21.6482	−	4.30609i	−1.67519	−	0.333216i	−0.736095	−	0.676879i	$-0.763332\pi$
$167$	−21.6482	−	4.30609i	−1.67519	−	0.333216i	−0.939093	+	0.343663i	$0.888332\pi$
$168$	24.7812	+	9.45970i	1.91191	+	0.729832i
$169$			0.436957i			0.0336121i
$170$	12.9455	−	1.55410i	0.992871	−	0.119194i
$171$	15.1011			1.15481
$172$	2.29845	−	20.3983i	0.175255	−	1.55536i
$173$	0.446248	−	2.24344i	0.0339276	−	0.170566i	−0.960107	−	0.279634i	$-0.909787\pi$
$173$	0.446248	−	2.24344i	0.0339276	−	0.170566i	0.994034	+	0.109068i	$0.0347868\pi$
$174$	−22.4503	+	13.2430i	−1.70195	+	1.00395i
$175$	2.38999	+	19.4729i	0.180666	+	1.47201i
$176$	−13.2533	+	12.5297i	−0.999007	+	0.944458i
$177$	−16.1606	+	24.1860i	−1.21470	+	1.81793i
$178$	−5.13890	+	6.82837i	−0.385177	+	0.511808i
$179$	18.5999	+	7.70433i	1.39022	+	0.575848i	0.947194	−	0.320660i	$-0.103905\pi$
$179$	18.5999	+	7.70433i	1.39022	+	0.575848i	0.443026	+	0.896509i	$0.353905\pi$
$180$	6.25758	−	10.3916i	0.466412	−	0.774546i
$181$	−1.89114	−	9.50740i	−0.140567	−	0.706679i	−0.985210	−	0.171349i	$-0.945187\pi$
$181$	−1.89114	−	9.50740i	−0.140567	−	0.706679i	0.844643	−	0.535330i	$-0.179813\pi$
$182$	−6.71815	−	19.1995i	−0.497982	−	1.42316i
$183$	11.9063	+	11.9063i	0.880138	+	0.880138i
$184$	−1.50687	−	2.12377i	−0.111088	−	0.156566i
$185$	−0.653353	−	0.472539i	−0.0480355	−	0.0347418i
$186$	4.50108	−	17.4490i	0.330035	−	1.27943i
$187$	10.6987	+	15.4587i	0.782366	+	1.13045i
$188$	16.8529	+	9.31439i	1.22912	+	0.679321i
$189$	1.03212	+	2.49176i	0.0750758	+	0.181249i
$190$	1.81253	+	17.5122i	0.131495	+	1.27047i
$191$	9.48621	+	9.48621i	0.686398	+	0.686398i	0.961434	−	0.275036i	$-0.0886898\pi$
$191$	9.48621	+	9.48621i	0.686398	+	0.686398i	−0.275036	+	0.961434i	$0.588690\pi$
$192$	15.2777	−	11.4973i	1.10257	−	0.829743i
$193$	−16.2854	+	3.23937i	−1.17225	+	0.233175i	−0.742546	−	0.669795i	$-0.766382\pi$
$193$	−16.2854	+	3.23937i	−1.17225	+	0.233175i	−0.429703	+	0.902970i	$0.641382\pi$
$194$	−9.40745	+	8.40696i	−0.675415	+	0.603585i
$195$	−19.3426	+	3.10635i	−1.38515	+	0.222451i
$196$	10.4698	+	13.1288i	0.747842	+	0.937774i
$197$	−3.50032	+	5.23860i	−0.249388	+	0.373235i	−0.934950	−	0.354779i	$-0.884556\pi$
$197$	−3.50032	+	5.23860i	−0.249388	+	0.373235i	0.685563	+	0.728014i	$0.259556\pi$
$198$	17.4629	+	0.980739i	1.24103	+	0.0696981i
$199$	16.4254	−	10.9751i	1.16436	−	0.778003i	0.185526	−	0.982639i	$-0.440601\pi$
$199$	16.4254	−	10.9751i	1.16436	−	0.778003i	0.978838	+	0.204636i	$0.0656012\pi$
$200$	12.8018	+	6.00940i	0.905227	+	0.424929i
$201$	−3.44475	−	0.685203i	−0.242974	−	0.0483305i
$202$	4.26197	−	0.601679i	0.299871	−	0.0423340i
$203$	−30.2581			−2.12371
$204$	−9.33094	−	17.3602i	−0.653297	−	1.21546i
$205$	9.09702	−	5.60169i	0.635364	−	0.391239i
$206$	−22.1680	+	3.12954i	−1.54452	+	0.218045i
$207$	−0.487185	+	2.44924i	−0.0338617	+	0.170234i
$208$	−14.2949	−	3.26288i	−0.991175	−	0.226240i
$209$	−21.1071	+	14.1033i	−1.46001	+	0.975548i
$210$	26.0848	−	14.1094i	1.80002	−	0.973640i
$211$	−11.4223	−	7.63211i	−0.786341	−	0.525416i	0.0963625	−	0.995346i	$-0.469279\pi$
$211$	−11.4223	−	7.63211i	−0.786341	−	0.525416i	−0.882704	+	0.469930i	$0.844279\pi$
$212$	−5.86903	+	4.68034i	−0.403086	+	0.321447i
$213$	−11.2655	−	4.66634i	−0.771902	−	0.319732i
$214$	−14.9091	−	16.6834i	−1.01916	−	1.14045i
$215$	−15.6150	−	16.8193i	−1.06494	−	1.14707i
$216$	1.91668	+	0.325672i	0.130413	+	0.0221592i
$217$	14.7920	−	14.7920i	1.00415	−	1.00415i
$218$	−5.27735	+	10.9585i	−0.357427	+	0.742201i
$219$	−2.13628	−	5.15743i	−0.144356	−	0.348507i
$220$	0.958680	+	20.3687i	0.0646342	+	1.37326i
$221$	−5.55484	+	14.0560i	−0.373659	+	0.945511i
$222$	−0.304444	+	1.18022i	−0.0204329	+	0.0792110i
$223$	3.79526	−	1.57205i	0.254149	−	0.105272i	−0.251972	−	0.967735i	$-0.581079\pi$
$223$	3.79526	−	1.57205i	0.254149	−	0.105272i	0.506121	+	0.862463i	$0.331079\pi$
$224$	22.0568	−	2.48491i	1.47373	−	0.166030i
$225$	−4.24650	−	12.8801i	−0.283100	−	0.858672i
$226$	2.64275	+	7.55262i	0.175793	+	0.502393i
$227$	−11.2406	+	2.23589i	−0.746064	+	0.148401i	−0.553461	−	0.832875i	$-0.686693\pi$
$227$	−11.2406	+	2.23589i	−0.746064	+	0.148401i	−0.192603	+	0.981277i	$0.561693\pi$
$228$	23.6442	−	12.2147i	1.56588	−	0.808941i
$229$	−12.7667	−	5.28813i	−0.843646	−	0.349450i	−0.0813557	−	0.996685i	$-0.525925\pi$
$229$	−12.7667	−	5.28813i	−0.843646	−	0.349450i	−0.762290	+	0.647236i	$0.775925\pi$
$230$	−2.89877	−	0.270995i	−0.191139	−	0.0178689i
$231$	35.5542	+	23.7566i	2.33930	+	1.56307i
$232$	−11.6044	+	18.4680i	−0.761869	+	1.21249i
$233$	6.35815	−	4.24838i	0.416536	−	0.278321i	−0.329591	−	0.944124i	$-0.606911\pi$
$233$	6.35815	−	4.24838i	0.416536	−	0.278321i	0.746127	+	0.665803i	$0.231911\pi$
$234$	7.14409	+	12.1111i	0.467024	+	0.791725i
$235$	20.1817	−	7.49490i	1.31651	−	0.488913i
$236$	−2.72545	+	24.1879i	−0.177412	+	1.57450i
$237$		−	38.9138i		−	2.52772i
$238$	0.909411	−	22.8614i	0.0589484	−	1.48188i
$239$		−	9.80482i		−	0.634221i	−0.948389	−	0.317111i	$-0.897287\pi$
$239$		−	9.80482i		−	0.634221i	0.948389	−	0.317111i	$-0.102713\pi$
$240$	1.39225	−	21.3320i	0.0898694	−	1.37697i
$241$	4.89692	−	24.6185i	0.315438	−	1.58581i	−0.419549	−	0.907733i	$-0.637812\pi$
$241$	4.89692	−	24.6185i	0.315438	−	1.58581i	0.734987	−	0.678081i	$-0.237188\pi$
$242$	−11.9252	+	7.03447i	−0.766583	+	0.452193i
$243$	−11.8408	−	17.7210i	−0.759589	−	1.13680i
$244$	13.4246	+	4.27888i	0.859422	+	0.273927i
$245$	18.7615	+	0.696614i	1.19863	+	0.0445050i
$246$	−12.9033	−	9.71077i	−0.822683	−	0.619136i
$247$	−18.8547	−	7.80987i	−1.19970	−	0.496930i
$248$	−3.35534	−	14.7012i	−0.213064	−	0.933530i
$249$	1.27845	−	0.254300i	0.0810188	−	0.0161156i
$250$	14.4268	−	6.47045i	0.912432	−	0.409227i
$251$	−6.86396	−	6.86396i	−0.433249	−	0.433249i	0.456483	−	0.889732i	$-0.349109\pi$
$251$	−6.86396	−	6.86396i	−0.433249	−	0.433249i	−0.889732	+	0.456483i	$0.849109\pi$
$252$	−16.2631	−	13.7331i	−1.02448	−	0.865106i
$253$	−1.60647	−	3.87835i	−0.100998	−	0.243830i
$254$	0.0405743	−	0.157292i	0.00254586	−	0.00986938i
$255$	−21.5180	−	4.74677i	−1.34751	−	0.297254i
$256$	6.94244	−	14.4154i	0.433903	−	0.900960i
$257$	3.92692	+	9.48042i	0.244954	+	0.591372i	0.997762	−	0.0668687i	$-0.0213009\pi$
$257$	3.92692	+	9.48042i	0.244954	+	0.591372i	−0.752807	+	0.658241i	$0.771301\pi$
$258$	−15.0524	+	31.2564i	−0.937120	+	1.94594i
$259$	−1.00050	+	1.00050i	−0.0621681	+	0.0621681i
$260$	−13.1872	+	9.73837i	−0.817838	+	0.603948i
$261$	20.5147	−	4.08063i	1.26983	−	0.252584i
$262$	−1.29849	−	1.45302i	−0.0802212	−	0.0897680i
$263$	−0.0375011	+	0.0905357i	−0.00231242	+	0.00558267i	−0.925032	−	0.379890i	$-0.875962\pi$
$263$	−0.0375011	+	0.0905357i	−0.00231242	+	0.00558267i	0.922719	+	0.385473i	$0.125962\pi$
$264$	28.1354	−	12.5895i	1.73161	−	0.774831i
$265$	−0.311410	+	8.38701i	−0.0191297	+	0.515210i
$266$	30.8455	+	1.73232i	1.89126	+	0.106216i
$267$	12.0090	−	8.02415i	0.734938	−	0.491070i
$268$	−2.82417	+	0.813613i	−0.172514	+	0.0496993i
$269$	−2.87657	+	14.4615i	−0.175388	+	0.881733i	0.788421	+	0.615136i	$0.210899\pi$
$269$	−2.87657	+	14.4615i	−0.175388	+	0.881733i	−0.963808	+	0.266596i	$0.914101\pi$
$270$	1.67338	−	1.38725i	0.101838	−	0.0844253i
$271$	−0.683525			−0.0415212			−0.0207606	−	0.999784i	$-0.506609\pi$
$271$	−0.683525			−0.0415212			−0.0207606	+	0.999784i	$0.506609\pi$
$272$	−13.6047	−	9.32273i	−0.824903	−	0.565274i
$273$			34.3769i			2.08058i
$274$	0.101172	+	0.716647i	0.00611201	+	0.0432942i
$275$	17.9645	+	14.0368i	1.08330	+	0.846452i
$276$	1.21831	+	4.22892i	0.0733334	+	0.254551i
$277$	−0.550047	+	0.367530i	−0.0330491	+	0.0220827i	−0.571985	−	0.820264i	$-0.693826\pi$
$277$	−0.550047	+	0.367530i	−0.0330491	+	0.0220827i	0.538936	+	0.842347i	$0.318826\pi$
$278$	1.17477	−	20.9178i	0.0704582	−	1.25457i
$279$	−8.03396	+	12.0237i	−0.480981	+	0.719839i
$280$	13.9738	−	20.5081i	0.835093	−	1.22559i
$281$	−3.22542	−	1.33601i	−0.192413	−	0.0796999i	0.284397	−	0.958707i	$-0.408207\pi$
$281$	−3.22542	−	1.33601i	−0.192413	−	0.0796999i	−0.476809	+	0.879007i	$0.658207\pi$
$282$	−21.6846	−	24.2652i	−1.29130	−	1.44497i
$283$	6.44222	+	32.3872i	0.382950	+	1.92522i	0.379417	+	0.925226i	$0.376125\pi$
$283$	6.44222	+	32.3872i	0.382950	+	1.92522i	0.00353307	+	0.999994i	$0.498875\pi$
$284$	−10.1676	+	0.857572i	−0.603335	+	0.0508875i
$285$	6.88356	−	28.9470i	0.407747	−	1.71467i
$286$	−21.2963	−	10.2558i	−1.25928	−	0.606439i
$287$	−7.17414	−	17.3199i	−0.423476	−	1.02236i
$288$	−14.6192	+	4.65933i	−0.861442	+	0.274554i
$289$	−11.6215	+	12.4073i	−0.683619	+	0.729839i
$290$	7.19445	+	23.3003i	0.422472	+	1.36824i
$291$	19.6993	−	8.15971i	1.15479	−	0.478331i
$292$	−3.56903	−	3.01381i	−0.208862	−	0.176370i
$293$	−16.9794	+	16.9794i	−0.991948	+	0.991948i	−0.999968	−	0.00802018i	$-0.997447\pi$
$293$	−16.9794	+	16.9794i	−0.991948	+	0.991948i	0.00802018	+	0.999968i	$0.497447\pi$
$294$	−9.37311	−	26.7870i	−0.546651	−	1.56225i
$295$	18.5160	+	19.9440i	1.07804	+	1.16118i
$296$	0.226948	+	0.994362i	0.0131911	+	0.0577961i
$297$	2.89554	+	1.19937i	0.168016	+	0.0695946i
$298$	−3.31054	+	4.39891i	−0.191774	+	0.254822i
$299$	1.87496	−	2.80608i	0.108432	−	0.162280i
$300$	−17.0671	−	16.7319i	−0.985370	−	0.966014i
$301$	−33.4855	+	22.3743i	−1.93007	+	1.28963i
$302$	−6.53008	+	3.85197i	−0.375764	+	0.221656i
$303$	−7.13451	−	1.41914i	−0.409867	−	0.0815276i
$304$	12.8870	−	18.1621i	0.739121	−	1.04167i
$305$	13.4140	−	8.25994i	0.768081	−	0.472963i
$306$	2.46652	+	15.6224i	0.141002	+	0.893074i
$307$			13.7086i			0.782389i	0.920308	+	0.391194i	$0.127938\pi$
$307$			13.7086i			0.782389i	−0.920308	+	0.391194i	$0.872062\pi$
$308$	35.5571	+	4.00651i	2.02605	+	0.228292i
$309$	37.1091	+	7.38145i	2.11106	+	0.419916i
$310$	−14.9077	−	7.87352i	−0.846699	−	0.447186i
$311$	−7.45495	−	11.1571i	−0.422731	−	0.632662i	0.557579	−	0.830124i	$-0.311730\pi$
$311$	−7.45495	−	11.1571i	−0.422731	−	0.632662i	−0.980311	+	0.197462i	$0.936730\pi$
$312$	20.9819	+	13.1840i	1.18787	+	0.746399i
$313$	15.2275	−	22.7895i	0.860707	−	1.28814i	−0.0954940	−	0.995430i	$-0.530443\pi$
$313$	15.2275	−	22.7895i	0.860707	−	1.28814i	0.956201	−	0.292710i	$-0.0945569\pi$
$314$	−5.42810	+	7.21264i	−0.306325	+	0.407033i
$315$	−23.4973	+	3.77357i	−1.32392	+	0.212617i
$316$	−14.9456	−	28.9305i	−0.840758	−	1.62747i
$317$	14.8132	−	2.94654i	0.831995	−	0.165494i	0.239325	−	0.970940i	$-0.423074\pi$
$317$	14.8132	−	2.94654i	0.831995	−	0.165494i	0.592670	+	0.805445i	$0.298074\pi$
$318$	11.9747	−	4.19009i	0.671508	−	0.234969i
$319$	−24.8628	+	24.8628i	−1.39205	+	1.39205i
$320$	−7.15793	−	16.3940i	−0.400141	−	0.916454i
$321$	14.4706	+	34.9351i	0.807670	+	1.94989i
$322$	−1.27609	+	4.94693i	−0.0711136	+	0.275682i
$323$	−16.4948	−	15.9642i	−0.917794	−	0.888273i
$324$	−17.1194	−	9.46169i	−0.951080	−	0.525650i
$325$	−1.35918	+	18.2778i	−0.0753938	+	1.01387i
$326$	−10.1400	−	4.88322i	−0.561605	−	0.270457i
$327$	14.5352	−	14.5352i	0.803797	−	0.803797i
$328$	−13.3226	−	2.26371i	−0.735617	−	0.124992i
$329$	−7.37003	−	37.0516i	−0.406323	−	2.04272i
$330$	9.84008	−	33.0272i	0.541679	−	1.81808i
$331$	3.81761	−	9.21654i	0.209835	−	0.506587i	−0.783562	−	0.621314i	$-0.786599\pi$
$331$	3.81761	−	9.21654i	0.209835	−	0.506587i	0.993397	+	0.114727i	$0.0365993\pi$
$332$	0.852799	−	0.680077i	0.0468034	−	0.0373241i
$333$	0.543401	−	0.813257i	0.0297782	−	0.0445662i
$334$	31.1658	+	1.75032i	1.70532	+	0.0957732i
$335$	−1.36925	+	2.98706i	−0.0748101	+	0.163200i
$336$	−36.5719	−	8.34770i	−1.99516	−	0.455404i
$337$	0.977162	−	4.91252i	0.0532294	−	0.267602i	−0.945001	−	0.327067i	$-0.893940\pi$
$337$	0.977162	−	4.91252i	0.0532294	−	0.267602i	0.998230	+	0.0594653i	$0.0189396\pi$
$338$	−0.0863820	−	0.611884i	−0.00469856	−	0.0332821i
$339$		−	13.5230i		−	0.734469i
$340$	−17.8207	+	4.73543i	−0.966461	+	0.256815i
$341$		−	24.3089i		−	1.31640i
$342$	−21.1465	+	2.98533i	−1.14347	+	0.161428i
$343$	1.06876	−	5.37303i	0.0577077	−	0.290116i
$344$	0.813960	+	29.0188i	0.0438858	+	1.56459i
$345$	4.47283	+	2.05032i	0.240809	+	0.110385i
$346$	−0.181389	+	3.22977i	−0.00975152	+	0.173634i
$347$	9.84813	−	14.7388i	0.528675	−	0.791219i	−0.466986	−	0.884264i	$-0.654660\pi$
$347$	9.84813	−	14.7388i	0.528675	−	0.791219i	0.995662	+	0.0930459i	$0.0296603\pi$
$348$	28.8198	−	22.9828i	1.54490	−	1.23200i
$349$	1.50710	−	3.63846i	0.0806732	−	0.194762i	−0.878396	−	0.477933i	$-0.841386\pi$
$349$	1.50710	−	3.63846i	0.0806732	−	0.194762i	0.959070	+	0.283171i	$0.0913862\pi$
$350$	−7.19635	−	26.7959i	−0.384661	−	1.43230i
$351$	0.491554	+	2.47121i	0.0262372	+	0.131903i
$352$	16.0820	−	20.1657i	0.857174	−	1.07483i
$353$	18.3644	−	18.3644i	0.977441	−	0.977441i	−0.0223106	−	0.999751i	$-0.507102\pi$
$353$	18.3644	−	18.3644i	0.977441	−	0.977441i	0.999751	+	0.0223106i	$0.00710226\pi$
$354$	17.8488	−	37.0631i	0.948651	−	1.96988i
$355$	−6.68557	+	9.24376i	−0.354833	+	0.490608i
$356$	5.84625	−	10.5779i	0.309851	−	0.560625i
$357$	−14.2114	+	35.9607i	−0.752147	+	1.90324i
$358$	−27.5690	−	7.11158i	−1.45707	−	0.375858i
$359$	−1.95366	−	4.71656i	−0.103110	−	0.248930i	0.863902	−	0.503660i	$-0.168014\pi$
$359$	−1.95366	−	4.71656i	−0.103110	−	0.248930i	−0.967012	+	0.254730i	$0.918014\pi$
$360$	−6.70834	+	15.7888i	−0.353561	+	0.832140i
$361$	8.48255	−	8.48255i	0.446450	−	0.446450i
$362$	4.52773	+	12.9396i	0.237972	+	0.680091i
$363$	22.9495	−	4.56495i	1.20454	−	0.239598i
$364$	13.2032	+	25.5575i	0.692034	+	1.33958i
$365$	−5.15660	+	0.828131i	−0.269909	+	0.0433463i
$366$	−19.0265	−	14.3190i	−0.994529	−	0.748464i
$367$	−13.4769	+	20.1695i	−0.703486	+	1.05284i	0.291859	+	0.956461i	$0.405726\pi$
$367$	−13.4769	+	20.1695i	−0.703486	+	1.05284i	−0.995345	+	0.0963796i	$0.969274\pi$
$368$	2.52996	+	2.67608i	0.131883	+	0.139500i
$369$	7.19976	+	10.7752i	0.374805	+	0.560935i
$370$	1.00832	+	0.532548i	0.0524203	+	0.0276859i
$371$	14.4445	+	2.87318i	0.749919	+	0.149168i
$372$	−2.85349	+	25.3242i	−0.147946	+	1.31300i
$373$			19.7455i			1.02239i	0.859466	+	0.511193i	$0.170796\pi$
$373$			19.7455i			1.02239i	−0.859466	+	0.511193i	$0.829204\pi$
$374$	−18.0377	−	19.5322i	−0.932707	−	1.00999i
$375$	−26.6252	+	2.26890i	−1.37492	+	0.117165i
$376$	−25.4410	−	9.71155i	−1.31202	−	0.500835i
$377$	−27.7243	−	5.51470i	−1.42787	−	0.284022i
$378$	−1.93790	−	3.28524i	−0.0996751	−	0.168975i
$379$	−8.27557	+	5.52956i	−0.425087	+	0.284034i	−0.749656	−	0.661828i	$-0.769781\pi$
$379$	−8.27557	+	5.52956i	−0.425087	+	0.284034i	0.324568	+	0.945862i	$0.394781\pi$
$380$	−6.00012	−	24.1645i	−0.307799	−	1.23961i
$381$	−0.152521	+	0.228264i	−0.00781388	+	0.0116943i
$382$	−15.1591	−	11.4085i	−0.775609	−	0.583709i
$383$	−5.66150	−	2.34507i	−0.289289	−	0.119827i	0.233320	−	0.972400i	$-0.425041\pi$
$383$	−5.66150	−	2.34507i	−0.289289	−	0.119827i	−0.522609	+	0.852573i	$0.675041\pi$
$384$	−19.1209	+	19.1202i	−0.975758	+	0.975722i
$385$	29.3183	−	27.2191i	1.49420	−	1.38721i
$386$	22.1645	−	7.75564i	1.12814	−	0.394751i
$387$	19.6854	−	19.6854i	1.00067	−	1.00067i
$388$	11.5115	−	13.6323i	0.584410	−	0.692073i
$389$	1.89148	−	0.783477i	0.0959019	−	0.0397239i	−0.334217	−	0.942496i	$-0.608472\pi$
$389$	1.89148	−	0.783477i	0.0959019	−	0.0397239i	0.430119	+	0.902772i	$0.358472\pi$
$390$	26.4719	−	8.17376i	1.34046	−	0.413894i
$391$	3.12138	−	2.16025i	0.157855	−	0.109249i
$392$	−17.2566	−	16.3149i	−0.871588	−	0.824027i
$393$	1.26030	+	3.04264i	0.0635739	+	0.153481i
$394$	3.86598	−	8.02774i	0.194765	−	0.404432i
$395$	−35.4188	−	8.42255i	−1.78211	−	0.423784i
$396$	−24.6476	+	2.07887i	−1.23859	+	0.104467i
$397$	4.56700	+	22.9599i	0.229211	+	1.15232i	0.908317	+	0.418282i	$0.137368\pi$
$397$	4.56700	+	22.9599i	0.229211	+	1.15232i	−0.679106	+	0.734040i	$0.737632\pi$
$398$	−20.8312	+	18.6158i	−1.04418	+	0.933128i
$399$	−48.2375	−	19.9806i	−2.41490	−	1.00028i
$400$	−19.1148	−	5.88433i	−0.955739	−	0.294217i
$401$	3.78856	−	5.66999i	0.189192	−	0.283146i	−0.724732	−	0.689030i	$-0.758037\pi$
$401$	3.78856	−	5.66999i	0.189192	−	0.283146i	0.913924	+	0.405885i	$0.133037\pi$
$402$	4.95924	+	0.278518i	0.247344	+	0.0138912i
$403$	16.2492	−	10.8574i	0.809431	−	0.540845i
$404$	−5.84921	+	1.68510i	−0.291009	+	0.0838366i
$405$	−20.5008	+	7.61343i	−1.01869	+	0.378314i
$406$	42.3713	−	5.98172i	2.10285	−	0.296868i
$407$			1.64420i			0.0815001i
$408$	16.4983	+	22.4654i	0.816788	+	1.11220i
$409$	10.2902			0.508817			0.254408	−	0.967097i	$-0.418119\pi$
$409$	10.2902			0.508817			0.254408	+	0.967097i	$0.418119\pi$
$410$	−11.6314	+	9.64259i	−0.574435	+	0.476214i
$411$	0.238628	−	1.19966i	0.0117706	−	0.0591750i
$412$	30.4238	−	8.76476i	1.49887	−	0.431809i
$413$	39.7064	−	26.5310i	1.95382	−	1.30550i
$414$	0.198028	−	3.52606i	0.00973256	−	0.173296i
$415$	0.0452494	−	1.21867i	0.00222121	−	0.0598224i
$416$	20.6626	+	1.74314i	1.01307	+	0.0854647i
$417$	−13.5498	+	32.7122i	−0.663538	+	1.60192i
$418$	26.7688	−	23.9220i	1.30931	−	1.17006i
$419$	16.2560	−	3.23351i	0.794155	−	0.157967i	0.218691	−	0.975794i	$-0.429821\pi$
$419$	16.2560	−	3.23351i	0.794155	−	0.157967i	0.575464	+	0.817827i	$0.304821\pi$
$420$	−33.7380	+	24.9145i	−1.64625	+	1.21570i
$421$	−2.94115	+	2.94115i	−0.143343	+	0.143343i	−0.775137	−	0.631794i	$-0.782319\pi$
$421$	−2.94115	+	2.94115i	−0.143343	+	0.143343i	0.631794	+	0.775137i	$0.282319\pi$
$422$	17.5037	+	8.42940i	0.852067	+	0.410337i
$423$	9.99360	+	24.1267i	0.485905	+	1.17308i
$424$	7.29331	−	7.71426i	0.354194	−	0.374638i
$425$	−8.97783	+	18.5580i	−0.435489	+	0.900194i
$426$	16.6979	+	4.30733i	0.809018	+	0.208691i
$427$	−10.5786	−	25.5390i	−0.511934	−	1.23592i
$428$	24.1757	+	20.4148i	1.16858	+	0.986787i
$429$	28.2471	+	28.2471i	1.36378	+	1.36378i
$430$	25.1912	+	20.4656i	1.21483	+	0.986941i
$431$	−17.0186	+	3.38521i	−0.819757	+	0.163060i	−0.587116	−	0.809503i	$-0.699737\pi$
$431$	−17.0186	+	3.38521i	−0.819757	+	0.163060i	−0.232641	+	0.972563i	$0.574737\pi$
$432$	−2.74836	−	0.0771404i	−0.132231	−	0.00371142i
$433$	3.29235	+	1.36374i	0.158220	+	0.0655371i	0.460388	−	0.887718i	$-0.347710\pi$
$433$	3.29235	+	1.36374i	0.158220	+	0.0655371i	−0.302168	+	0.953255i	$0.597710\pi$
$434$	−17.7894	+	23.6379i	−0.853920	+	1.13466i
$435$	1.52917	−	41.1843i	0.0733182	−	1.97463i
$436$	5.22365	−	16.3887i	0.250167	−	0.784878i
$437$	2.84771	+	4.26190i	0.136224	+	0.203874i
$438$	4.01106	+	6.79977i	0.191656	+	0.324905i
$439$	−1.21847	+	6.12565i	−0.0581543	+	0.292361i	−0.998908	−	0.0467306i	$-0.985120\pi$
$439$	−1.21847	+	6.12565i	−0.0581543	+	0.292361i	0.940753	+	0.339092i	$0.110120\pi$
$440$	−5.36915	−	28.3334i	−0.255964	−	1.35074i
$441$			22.7739i			1.08447i
$442$	4.99986	−	20.7812i	0.237819	−	0.988461i
$443$		−	6.80280i		−	0.323211i	−0.986855	−	0.161605i	$-0.948333\pi$
$443$		−	6.80280i		−	0.323211i	0.986855	−	0.161605i	$-0.0516672\pi$
$444$	0.193004	−	1.71288i	0.00915956	−	0.0812896i
$445$	−4.70423	−	12.6672i	−0.223002	−	0.600482i
$446$	−5.00383	+	2.95166i	−0.236938	+	0.139765i
$447$	7.73632	−	5.16925i	0.365915	−	0.244497i
$448$	−30.3955	+	7.84010i	−1.43605	+	0.370410i
$449$	−1.86224	−	1.24431i	−0.0878846	−	0.0587226i	0.510852	−	0.859669i	$-0.329330\pi$
$449$	−1.86224	−	1.24431i	−0.0878846	−	0.0587226i	−0.598736	+	0.800946i	$0.704330\pi$
$450$	8.49276	+	17.1968i	0.400352	+	0.810667i
$451$	−20.1265	−	8.33667i	−0.947720	−	0.392558i
$452$	−5.19380	−	10.0537i	−0.244296	−	0.472886i
$453$	12.5668	−	2.49970i	0.590441	−	0.117446i
$454$	15.2985	−	5.35313i	0.717994	−	0.251235i
$455$	31.2894	+	7.44058i	1.46687	+	0.348820i
$456$	−30.6950	+	21.7789i	−1.43742	+	1.01989i
$457$	2.99300	−	1.23974i	0.140007	−	0.0579926i	−0.311580	−	0.950220i	$-0.600858\pi$
$457$	2.99300	−	1.23974i	0.140007	−	0.0579926i	0.451587	+	0.892227i	$0.350858\pi$
$458$	18.9229	+	4.88128i	0.884211	+	0.228087i
$459$	−0.507396	+	2.78827i	−0.0236832	+	0.130145i
$460$	4.11280	−	0.193574i	0.191760	−	0.00902545i
$461$	−11.3434	−	27.3855i	−0.528317	−	1.27547i	−0.932625	−	0.360847i	$-0.882488\pi$
$461$	−11.3434	−	27.3855i	−0.528317	−	1.27547i	0.404308	−	0.914623i	$-0.367512\pi$
$462$	−54.4840	−	26.2383i	−2.53483	−	1.22072i
$463$	11.1954	−	11.1954i	0.520295	−	0.520295i	−0.397365	−	0.917661i	$-0.630075\pi$
$463$	11.1954	−	11.1954i	0.520295	−	0.520295i	0.917661	+	0.397365i	$0.130075\pi$
$464$	12.5991	−	28.1554i	0.584898	−	1.30708i
$465$	19.3858	+	20.8809i	0.898995	+	0.968329i
$466$	−8.06363	+	7.20607i	−0.373541	+	0.333815i
$467$	24.6597	+	10.2144i	1.14111	+	0.472664i	0.871544	−	0.490317i	$-0.163119\pi$
$467$	24.6597	+	10.2144i	1.14111	+	0.472664i	0.269569	+	0.962981i	$0.413119\pi$
$468$	−12.3983	−	15.5471i	−0.573112	−	0.718667i
$469$	4.79432	+	3.20346i	0.221381	+	0.147922i
$470$	−26.7793	+	14.4850i	−1.23524	+	0.668144i
$471$	12.6848	−	8.47572i	0.584485	−	0.390540i
$472$	−0.965175	−	34.4098i	−0.0444258	−	1.58384i
$473$	−9.12997	+	45.8995i	−0.419796	+	2.11046i
$474$	7.69285	+	54.4920i	0.353344	+	2.50290i
$475$	−24.8573	−	12.5307i	−1.14053	−	0.574946i
$476$	3.24599	+	32.1932i	0.148780	+	1.47557i
$477$	−10.1807			−0.466141
$478$	1.93831	+	13.7300i	0.0886564	+	0.627994i
$479$	21.0206	+	4.18127i	0.960458	+	0.191047i	0.650333	−	0.759649i	$-0.274629\pi$
$479$	21.0206	+	4.18127i	0.960458	+	0.191047i	0.310124	+	0.950696i	$0.399629\pi$
$480$	2.26751	+	30.1470i	0.103497	+	1.37602i
$481$	−1.09906	+	0.734371i	−0.0501130	+	0.0334844i
$482$	−1.99047	+	35.4420i	−0.0906635	+	1.61434i
$483$	4.79687	−	7.17902i	0.218265	−	0.326657i
$484$	15.3086	−	12.2081i	0.695845	−	0.554912i
$485$	−3.16312	−	19.6961i	−0.143630	−	0.894355i
$486$	20.0843	+	22.4745i	0.911042	+	1.01946i
$487$	8.01628	−	1.59454i	0.363252	−	0.0722554i	−0.0100898	−	0.999949i	$-0.503212\pi$
$487$	8.01628	−	1.59454i	0.363252	−	0.0722554i	0.373342	+	0.927694i	$0.378212\pi$
$488$	−19.6447	−	3.33793i	−0.889276	−	0.151101i
$489$	13.4496	+	13.4496i	0.608213	+	0.608213i
$490$	−26.4099	+	2.73346i	−1.19308	+	0.123485i
$491$	10.7442	+	25.9389i	0.484881	+	1.17061i	0.957265	+	0.289213i	$0.0933936\pi$
$491$	10.7442	+	25.9389i	0.484881	+	1.17061i	−0.472384	+	0.881393i	$0.656606\pi$
$492$	19.9885	+	11.0474i	0.901153	+	0.498056i
$493$	−26.7218	−	17.2300i	−1.20349	−	0.776000i
$494$	27.9467	+	7.20900i	1.25738	+	0.324348i
$495$	−16.2067	+	22.4081i	−0.728439	+	1.00717i
$496$	7.60486	+	19.9232i	0.341468	+	0.894580i
$497$	14.1553	+	14.1553i	0.634951	+	0.634951i
$498$	−1.73998	+	0.608841i	−0.0779705	+	0.0272828i
$499$	1.17888	+	5.92664i	0.0527740	+	0.265313i	0.998160	−	0.0606413i	$-0.0193146\pi$
$499$	1.17888	+	5.92664i	0.0527740	+	0.265313i	−0.945386	+	0.325954i	$0.894315\pi$
$500$	−18.9231	+	11.9128i	−0.846269	+	0.532756i
$501$	−48.7386	−	20.1882i	−2.17748	−	0.901941i
$502$	10.9687	+	8.25486i	0.489558	+	0.368432i
$503$	−5.93663	+	8.88480i	−0.264701	+	0.396154i	−0.939882	−	0.341499i	$-0.889066\pi$
$503$	−5.93663	+	8.88480i	−0.264701	+	0.396154i	0.675181	+	0.737652i	$0.264066\pi$
$504$	25.4886	+	16.0158i	1.13535	+	0.713402i
$505$	−2.83589	+	6.18658i	−0.126195	+	0.275299i
$506$	3.01629	+	5.11339i	0.134091	+	0.227318i
$507$	−0.203744	+	1.02429i	−0.00904858	+	0.0454903i
$508$	−0.0257224	+	0.228282i	−0.00114125	+	0.0101284i
$509$	23.6042			1.04624			0.523119	−	0.852260i	$-0.324768\pi$
$509$	23.6042			1.04624			0.523119	+	0.852260i	$0.324768\pi$
$510$	31.0706	+	2.39316i	1.37583	+	0.105971i
$511$			9.16462i			0.405419i
$512$	−6.87193	+	21.5587i	−0.303699	+	0.952768i
$513$	−3.75329	−	0.746576i	−0.165712	−	0.0329622i
$514$	−7.37315	−	12.4994i	−0.325216	−	0.551324i
$515$	14.7504	−	32.1785i	0.649982	−	1.41796i
$516$	14.8992	−	46.7449i	0.655901	−	2.05783i
$517$	−36.5008	−	24.3891i	−1.60530	−	1.07263i
$518$	1.20324	−	1.59882i	0.0528674	−	0.0702481i
$519$	2.09214	−	5.05087i	0.0918347	−	0.221709i
$520$	16.5413	−	16.2439i	0.725384	−	0.712342i
$521$	−43.0892	+	8.57097i	−1.88777	+	0.375501i	−0.996895	−	0.0787455i	$-0.974909\pi$
$521$	−43.0892	+	8.57097i	−1.88777	+	0.375501i	−0.890876	+	0.454246i	$0.849909\pi$
$522$	−27.9206	+	9.76976i	−1.22205	+	0.427611i
$523$	−19.8325	+	19.8325i	−0.867213	+	0.867213i	−0.992163	−	0.124950i	$-0.960123\pi$
$523$	−19.8325	+	19.8325i	−0.867213	+	0.867213i	0.124950	+	0.992163i	$0.460123\pi$
$524$	2.10556	+	1.77801i	0.0919820	+	0.0776727i
$525$	−3.47731	+	46.7615i	−0.151762	+	2.04084i
$526$	0.0346159	−	0.134193i	0.00150932	−	0.00585111i
$527$	21.4863	−	4.64018i	0.935958	−	0.202130i
$528$	−36.9100	+	23.1915i	−1.60630	+	1.00928i
$529$	20.4661	−	8.47735i	0.889831	−	0.368580i
$530$	−1.22195	−	11.8061i	−0.0530781	−	0.512825i
$531$	−23.3425	+	23.3425i	−1.01298	+	1.01298i
$532$	−43.5362	+	3.67201i	−1.88753	+	0.159202i
$533$	−3.41673	−	17.1770i	−0.147995	−	0.744020i
$534$	−15.2302	+	13.6105i	−0.659076	+	0.588983i
$535$	34.9295	−	5.60955i	1.51014	−	0.242522i
$536$	3.79392	−	1.69763i	0.163872	−	0.0733266i
$537$	40.0084	+	26.7327i	1.72649	+	1.15360i
$538$	1.16925	−	20.8195i	0.0504101	−	0.897592i
$539$	−21.2691	−	31.8315i	−0.916125	−	1.37108i
$540$	−2.06903	+	2.27341i	−0.0890369	+	0.0978322i
$541$	−2.49301	+	12.5332i	−0.107183	+	0.538844i	0.889463	+	0.457007i	$0.151079\pi$
$541$	−2.49301	+	12.5332i	−0.107183	+	0.538844i	−0.996646	+	0.0818367i	$0.973921\pi$
$542$	0.957159	−	0.135126i	0.0411135	−	0.00580415i
$543$		−	23.1685i		−	0.994254i
$544$	20.8940	+	10.3654i	0.895822	+	0.444412i
$545$	−10.0837	−	16.3757i	−0.431939	−	0.701459i
$546$	−6.79596	−	48.1389i	−0.290840	−	2.06016i
$547$	21.1858	+	4.21411i	0.905839	+	0.180183i	0.625962	−	0.779853i	$-0.284706\pi$
$547$	21.1858	+	4.21411i	0.905839	+	0.180183i	0.279877	+	0.960036i	$0.409706\pi$
$548$	−0.283348	−	0.983540i	−0.0121040	−	0.0420148i
$549$	10.6164	+	15.8885i	0.453096	+	0.678105i
$550$	−27.9311	−	16.1048i	−1.19099	−	0.686709i
$551$	23.8522	−	35.6974i	1.01614	−	1.52076i
$552$	−2.54204	−	5.68103i	−0.108197	−	0.241801i
$553$	−24.4478	+	59.0222i	−1.03963	+	2.50988i
$554$	0.697590	−	0.623401i	0.0296378	−	0.0264858i
$555$	−1.31122	−	1.41234i	−0.0556580	−	0.0599506i
$556$	2.49017	+	29.5240i	0.105607	+	1.25210i
$557$	18.7288	+	18.7288i	0.793566	+	0.793566i	0.982072	−	0.188506i	$-0.0603646\pi$
$557$	18.7288	+	18.7288i	0.793566	+	0.793566i	−0.188506	+	0.982072i	$0.560365\pi$
$558$	8.87323	−	18.4253i	0.375634	−	0.780006i
$559$	−34.7593	+	14.3978i	−1.47016	+	0.608960i
$560$	−15.5136	+	31.4805i	−0.655571	+	1.33029i
$561$	17.8712	+	41.2259i	0.754522	+	1.74056i
$562$	4.78077	+	1.23322i	0.201664	+	0.0520204i
$563$	−15.5236	−	37.4773i	−0.654242	−	1.57948i	−0.806562	−	0.591149i	$-0.798675\pi$
$563$	−15.5236	−	37.4773i	−0.654242	−	1.57948i	0.152320	−	0.988331i	$-0.451325\pi$
$564$	35.1625	+	29.6924i	1.48061	+	1.25027i
$565$	−12.3085	−	2.92694i	−0.517821	−	0.123137i
$566$	−15.4238	−	44.0792i	−0.648312	−	1.85279i
$567$	7.48659	+	37.6376i	0.314407	+	1.58063i
$568$	14.0684	−	3.21091i	0.590298	−	0.134727i
$569$	−3.89578	+	9.40524i	−0.163320	+	0.394288i	−0.984260	−	0.176725i	$-0.943450\pi$
$569$	−3.89578	+	9.40524i	−0.163320	+	0.394288i	0.820941	+	0.571014i	$0.193450\pi$
$570$	−3.91672	+	41.8961i	−0.164053	+	1.75484i
$571$	−12.8978	+	19.3030i	−0.539758	+	0.807805i	−0.996656	−	0.0817144i	$-0.973960\pi$
$571$	−12.8978	+	19.3030i	−0.539758	+	0.807805i	0.456898	+	0.889519i	$0.348960\pi$
$572$	31.8493	+	10.1515i	1.33168	+	0.424454i
$573$	17.8138	+	26.6602i	0.744182	+	1.11375i
$574$	13.4701	+	22.8353i	0.562232	+	0.953127i
$575$	2.83428	−	3.62734i	0.118198	−	0.151271i
$576$	19.5505	−	9.41465i	0.814605	−	0.392277i
$577$	6.29670			0.262135			0.131068	−	0.991373i	$-0.458159\pi$
$577$	6.29670			0.262135			0.131068	+	0.991373i	$0.458159\pi$
$578$	13.8212	−	19.6717i	0.574884	−	0.818235i
$579$	−39.6857			−1.64928
$580$	−14.6808	−	31.2058i	−0.609588	−	1.29575i
$581$	−2.09885	−	0.417488i	−0.0870751	−	0.0173203i
$582$	−25.9724	+	15.3206i	−1.07659	+	0.635060i
$583$	14.2297	−	9.50800i	0.589335	−	0.393781i
$584$	5.59362	+	3.51476i	0.231466	+	0.145442i
$585$	−22.2173	−	0.824929i	−0.918573	−	0.0341066i
$586$	20.4201	−	27.1334i	0.843546	−	1.12087i
$587$	14.0882	−	34.0120i	0.581484	−	1.40383i	−0.309984	−	0.950742i	$-0.600324\pi$
$587$	14.0882	−	34.0120i	0.581484	−	1.40383i	0.891468	−	0.453084i	$-0.149676\pi$
$588$	18.4210	+	35.6577i	0.759667	+	1.47050i
$589$	5.79062	+	29.1114i	0.238598	+	1.19952i
$590$	−29.8711	−	24.2677i	−1.22978	−	0.999085i
$591$	−10.6479	+	10.6479i	−0.437996	+	0.437996i
$592$	−0.514377	−	1.34757i	−0.0211408	−	0.0553847i
$593$	38.7460	−	16.0491i	1.59111	−	0.659058i	0.600985	−	0.799260i	$-0.294775\pi$
$593$	38.7460	−	16.0491i	1.59111	−	0.659058i	0.990123	+	0.140202i	$0.0447752\pi$
$594$	−4.29181	−	1.10709i	−0.176095	−	0.0454247i
$595$	29.6550	+	20.7184i	1.21574	+	0.849372i
$596$	3.76622	−	6.81438i	0.154270	−	0.279128i
$597$	43.6208	−	18.0683i	1.78528	−	0.739488i
$598$	−2.07083	+	4.30009i	−0.0846825	+	0.175844i
$599$	−1.88813	−	1.88813i	−0.0771469	−	0.0771469i	0.667480	−	0.744627i	$-0.267373\pi$
$599$	−1.88813	−	1.88813i	−0.0771469	−	0.0771469i	−0.744627	+	0.667480i	$0.767373\pi$
$600$	27.2073	+	20.0561i	1.11073	+	0.818787i
$601$	8.47834	+	42.6235i	0.345839	+	1.73865i	0.627028	+	0.778997i	$0.284271\pi$
$601$	8.47834	+	42.6235i	0.345839	+	1.73865i	−0.281189	+	0.959652i	$0.590729\pi$
$602$	42.4676	−	37.9511i	1.73085	−	1.54677i
$603$	−3.68251	−	1.52535i	−0.149964	−	0.0621169i
$604$	8.38276	−	6.68496i	0.341090	−	0.272007i
$605$	0.812272	−	21.8764i	0.0330236	−	0.889403i
$606$	10.2712	+	0.576845i	0.417239	+	0.0234327i
$607$	−19.8321	−	29.6808i	−0.804959	−	1.20471i	−0.975640	−	0.219380i	$-0.929597\pi$
$607$	−19.8321	−	29.6808i	−0.804959	−	1.20471i	0.170681	−	0.985326i	$-0.445403\pi$
$608$	−14.4556	+	27.9806i	−0.586251	+	1.13476i
$609$	−70.9293	−	14.1087i	−2.87420	−	0.571714i
$610$	−17.1510	+	14.2184i	−0.694426	+	0.575687i
$611$		−	35.2921i		−	1.42777i
$612$	−6.54233	−	21.3889i	−0.264458	−	0.864595i
$613$	9.33065			0.376862			0.188431	−	0.982086i	$-0.439660\pi$
$613$	9.33065			0.376862			0.188431	+	0.982086i	$0.439660\pi$
$614$	−2.71004	−	19.1965i	−0.109368	−	0.774707i
$615$	23.9366	−	8.88940i	0.965219	−	0.358455i
$616$	−50.5836	+	1.41884i	−2.03807	+	0.0571668i
$617$	13.5087	+	20.2172i	0.543840	+	0.813914i	0.996991	−	0.0775202i	$-0.0247002\pi$
$617$	13.5087	+	20.2172i	0.543840	+	0.813914i	−0.453151	+	0.891434i	$0.649700\pi$
$618$	−53.4241	−	3.00037i	−2.14903	−	0.120693i
$619$	−8.28021	−	5.53266i	−0.332810	−	0.222376i	0.377925	−	0.925836i	$-0.376638\pi$
$619$	−8.28021	−	5.53266i	−0.332810	−	0.222376i	−0.710735	+	0.703460i	$0.751638\pi$
$620$	22.4322	+	8.07841i	0.900897	+	0.324437i
$621$	0.242174	−	0.584660i	0.00971811	−	0.0234616i
$622$	12.6450	+	14.1499i	0.507019	+	0.567358i
$623$	−23.2558	+	4.62586i	−0.931722	+	0.185331i
$624$	−31.9879	−	14.3141i	−1.28054	−	0.573021i
$625$	−3.69768	+	24.7250i	−0.147907	+	0.989001i
$626$	−16.8182	+	34.9231i	−0.672190	+	1.39581i
$627$	−56.0542	+	23.2184i	−2.23859	+	0.927253i
$628$	6.17526	−	11.1731i	0.246420	−	0.445857i
$629$	−1.45329	+	0.313853i	−0.0579465	+	0.0125141i
$630$	32.1579	−	9.92940i	1.28120	−	0.395597i
$631$	−0.898540	−	2.16927i	−0.0357703	−	0.0863572i	0.904985	−	0.425444i	$-0.139882\pi$
$631$	−0.898540	−	2.16927i	−0.0357703	−	0.0863572i	−0.940755	+	0.339087i	$0.889882\pi$
$632$	26.6481	+	37.5576i	1.06000	+	1.49396i
$633$	−23.2167	−	23.2167i	−0.922781	−	0.922781i
$634$	−20.1609	+	7.05455i	−0.800692	+	0.280172i
$635$	0.174751	+	0.188228i	0.00693477	+	0.00746961i
$636$	−15.9402	+	8.23478i	−0.632069	+	0.326530i
$637$	11.7780	−	28.4346i	0.466661	−	1.12662i
$638$	29.9009	−	39.7312i	1.18379	−	1.57297i
$639$	−11.5061	−	7.68814i	−0.455175	−	0.304138i
$640$	13.2644	+	21.5420i	0.524321	+	0.851521i
$641$	−10.0703	−	15.0713i	−0.397753	−	0.595279i	0.577495	−	0.816394i	$-0.304030\pi$
$641$	−10.0703	−	15.0713i	−0.397753	−	0.595279i	−0.975248	+	0.221115i	$0.929030\pi$
$642$	−27.1699	−	46.0599i	−1.07231	−	1.81784i
$643$	−7.50116	+	37.7109i	−0.295817	+	1.48717i	0.491638	+	0.870800i	$0.336398\pi$
$643$	−7.50116	+	37.7109i	−0.295817	+	1.48717i	−0.787455	+	0.616373i	$0.788602\pi$
$644$	0.808984	−	7.17959i	0.0318784	−	0.282916i
$645$	−28.7614	−	46.7078i	−1.13248	−	1.83912i
$646$	26.2541	+	19.0943i	1.03295	+	0.751255i
$647$	34.4957			1.35616			0.678082	−	0.734986i	$-0.262811\pi$
$647$	34.4957			1.35616			0.678082	+	0.734986i	$0.262811\pi$
$648$	25.8433	+	9.86514i	1.01522	+	0.387539i
$649$	10.8261	−	54.4266i	0.424962	−	2.13643i
$650$	−1.71003	−	25.8636i	−0.0670728	−	1.01445i
$651$	41.5717	−	27.7773i	1.62932	−	1.08868i
$652$	15.1648	+	4.83353i	0.593898	+	0.189296i
$653$	−28.3642	−	18.9524i	−1.10998	−	0.741663i	−0.141295	−	0.989968i	$-0.545127\pi$
$653$	−28.3642	−	18.9524i	−1.10998	−	0.741663i	−0.968682	+	0.248305i	$0.920127\pi$
$654$	−17.4806	+	23.2275i	−0.683544	+	0.908266i
$655$	3.04215	−	0.488559i	0.118867	−	0.0190896i
$656$	19.1035	+	0.536192i	0.745866	+	0.0209348i
$657$	−1.23594	−	6.21351i	−0.0482188	−	0.242412i
$658$	17.6452	+	50.4275i	0.687881	+	1.96587i
$659$	−15.8705	−	15.8705i	−0.618225	−	0.618225i	0.326851	−	0.945076i	$-0.394013\pi$
$659$	−15.8705	−	15.8705i	−0.618225	−	0.618225i	−0.945076	+	0.326851i	$0.894013\pi$
$660$	−7.25021	+	48.1941i	−0.282214	+	1.87595i
$661$	42.0281	−	17.4086i	1.63471	−	0.677117i	0.638958	−	0.769242i	$-0.279366\pi$
$661$	42.0281	−	17.4086i	1.63471	−	0.677117i	0.995747	+	0.0921247i	$0.0293658\pi$
$662$	−3.52390	+	13.6609i	−0.136960	+	0.530945i
$663$	−19.5753	+	30.3592i	−0.760243	+	1.17905i
$664$	−1.05975	+	1.12092i	−0.0411264	+	0.0435002i
$665$	−28.6267	+	39.5805i	−1.11010	+	1.53487i
$666$	−0.600167	+	1.24625i	−0.0232560	+	0.0482913i
$667$	5.02023	+	5.02023i	0.194384	+	0.194384i
$668$	−43.9884	+	3.71015i	−1.70196	+	0.143550i
$669$	9.62963	−	1.91545i	0.372303	−	0.0740556i
$670$	1.32689	−	4.45355i	0.0512621	−	0.172056i
$671$	−29.6774	−	12.2928i	−1.14568	−	0.474558i
$672$	52.8629	+	4.45963i	2.03923	+	0.172034i
$673$	−9.09081	−	6.07429i	−0.350425	−	0.234147i	0.367882	−	0.929872i	$-0.380083\pi$
$673$	−9.09081	−	6.07429i	−0.350425	−	0.234147i	−0.718308	+	0.695726i	$0.755083\pi$
$674$	−0.397191	+	7.07232i	−0.0152992	+	0.272416i
$675$	0.418672	+	3.41121i	0.0161147	+	0.131297i
$676$	0.241926	+	0.839761i	0.00930485	+	0.0322985i
$677$	37.5884	+	7.47680i	1.44464	+	0.287357i	0.854293	−	0.519792i	$-0.173991\pi$
$677$	37.5884	+	7.47680i	1.44464	+	0.287357i	0.590348	+	0.807149i	$0.298991\pi$
$678$	2.67336	+	18.9367i	0.102670	+	0.727258i
$679$	−35.0051			−1.34337
$680$	24.0186	−	10.1541i	0.921072	−	0.389393i
$681$	−27.3921			−1.04967
$682$	4.80561	+	34.0404i	0.184016	+	1.30347i
$683$	−42.5055	−	8.45487i	−1.62643	−	0.323517i	−0.704152	−	0.710049i	$-0.748673\pi$
$683$	−42.5055	−	8.45487i	−1.62643	−	0.323517i	−0.922276	+	0.386533i	$0.873673\pi$
$684$	29.0219	−	8.36090i	1.10968	−	0.319687i
$685$	−1.04027	−	0.476852i	−0.0397466	−	0.0182196i
$686$	−0.434424	+	7.73528i	−0.0165864	+	0.295334i
$687$	−27.4611	−	18.3489i	−1.04771	−	0.700056i
$688$	−6.87652	−	40.4749i	−0.262165	−	1.54309i
$689$	12.7112	+	5.26516i	0.484259	+	0.200587i
$690$	−6.66876	−	1.98688i	−0.253875	−	0.0756394i
$691$	3.87548	−	0.770880i	0.147430	−	0.0293257i	−0.120823	−	0.992674i	$-0.538553\pi$
$691$	3.87548	−	0.770880i	0.147430	−	0.0293257i	0.268254	+	0.963348i	$0.413553\pi$
$692$	−0.384490	−	4.55860i	−0.0146161	−	0.173292i
$693$	34.3143	+	34.3143i	1.30349	+	1.30349i
$694$	−10.8769	+	22.5860i	−0.412882	+	0.857352i
$695$	26.8415	+	19.4132i	1.01816	+	0.736383i
$696$	−35.8137	+	37.8808i	−1.35751	+	1.43587i
$697$	3.52684	−	19.3809i	0.133589	−	0.734104i
$698$	−1.39115	+	5.39298i	−0.0526557	+	0.204127i
$699$	16.8853	−	6.99413i	0.638662	−	0.264542i
$700$	15.3745	+	36.1004i	0.581103	+	1.36447i
$701$	28.3534	+	28.3534i	1.07089	+	1.07089i	0.997287	+	0.0736061i	$0.0234508\pi$
$701$	28.3534	+	28.3534i	1.07089	+	1.07089i	0.0736061	+	0.997287i	$0.476549\pi$
$702$	−1.17687	−	3.36333i	−0.0444181	−	0.126941i
$703$	−0.391666	−	1.96904i	−0.0147720	−	0.0742636i
$704$	−18.5336	+	31.4178i	−0.698510	+	1.18410i
$705$	50.8033	−	8.15883i	1.91336	−	0.307279i
$706$	−22.0858	+	29.3467i	−0.831209	+	1.10448i
$707$	9.92964	+	6.63477i	0.373442	+	0.249526i
$708$	−17.6671	+	55.4290i	−0.663972	+	2.08315i
$709$	5.51967	−	3.68813i	0.207296	−	0.138511i	−0.447589	−	0.894239i	$-0.647717\pi$
$709$	5.51967	−	3.68813i	0.207296	−	0.138511i	0.654885	+	0.755729i	$0.272717\pi$
$710$	7.53460	−	14.2660i	0.282768	−	0.535392i
$711$	8.61558	−	43.3135i	0.323110	−	1.62438i
$712$	−6.09553	+	15.9682i	−0.228440	+	0.598434i
$713$	−4.90839			−0.183821
$714$	12.7916	−	53.1662i	0.478712	−	1.98970i
$715$	31.8240	−	19.5963i	1.19015	−	0.732861i
$716$	40.0115	+	4.50843i	1.49530	+	0.168488i
$717$	4.57178	−	22.9839i	0.170736	−	0.858349i
$718$	3.66818	+	6.21851i	0.136895	+	0.232073i
$719$	−14.1109	−	21.1184i	−0.526247	−	0.787584i	0.469181	−	0.883102i	$-0.344549\pi$
$719$	−14.1109	−	21.1184i	−0.526247	−	0.787584i	−0.995428	+	0.0955181i	$0.969549\pi$
$720$	6.27261	−	23.4356i	0.233766	−	0.873393i
$721$	−51.6475	−	34.5097i	−1.92345	−	1.28521i
$722$	−10.2014	+	13.5553i	−0.379658	+	0.504475i
$723$	22.9581	−	55.4258i	0.853821	−	2.06131i
$724$	−8.89834	−	17.2246i	−0.330704	−	0.640148i
$725$	−37.1544	−	10.3058i	−1.37988	−	0.382748i
$726$	−31.2344	+	10.9293i	−1.15922	+	0.405625i
$727$	20.6777	+	20.6777i	0.766894	+	0.766894i	0.977559	−	0.210664i	$-0.0675626\pi$
$727$	20.6777	+	20.6777i	0.766894	+	0.766894i	−0.210664	+	0.977559i	$0.567563\pi$
$728$	−23.5412	−	33.1788i	−0.872496	−	1.22969i
$729$	−8.26559	−	19.9549i	−0.306133	−	0.739070i
$730$	7.05722	−	2.17906i	0.261199	−	0.0806507i
$731$	−42.3127	+	0.691624i	−1.56499	+	0.0255807i
$732$	29.4740	+	16.2899i	1.08939	+	0.602092i
$733$	14.0320	−	5.81223i	0.518282	−	0.214679i	−0.108180	−	0.994131i	$-0.534502\pi$
$733$	14.0320	−	5.81223i	0.518282	−	0.214679i	0.626462	+	0.779452i	$0.284502\pi$
$734$	14.8847	−	30.9082i	0.549404	−	1.14084i
$735$	43.6547	+	10.3810i	1.61023	+	0.382910i
$736$	−4.07180	−	3.24724i	−0.150089	−	0.119695i
$737$	6.57169	−	1.30719i	0.242071	−	0.0481510i
$738$	−12.2122	−	13.6655i	−0.449536	−	0.503034i
$739$	−14.1071	+	34.0577i	−0.518940	+	1.25283i	0.419616	+	0.907702i	$0.362165\pi$
$739$	−14.1071	+	34.0577i	−0.518940	+	1.25283i	−0.938555	+	0.345129i	$0.887835\pi$
$740$	−1.51726	−	0.546407i	−0.0557758	−	0.0200863i
$741$	−40.5565	−	27.0990i	−1.48988	−	0.995506i
$742$	−20.7950	−	1.16788i	−0.763408	−	0.0428741i
$743$	−3.25494	−	4.87137i	−0.119412	−	0.178713i	0.766948	−	0.641709i	$-0.221774\pi$
$743$	−3.25494	−	4.87137i	−0.119412	−	0.178713i	−0.886360	+	0.462996i	$0.846774\pi$
$744$	−1.01052	−	36.0263i	−0.0370474	−	1.32079i
$745$	−3.03052	−	8.16034i	−0.111030	−	0.298972i
$746$	−3.90349	−	27.6502i	−0.142917	−	1.01235i
$747$	1.47930			0.0541248
$748$	29.1200	+	23.7856i	1.06473	+	0.869689i
$749$		−	62.0788i		−	2.26831i
$750$	36.8355	−	8.44074i	1.34504	−	0.308212i
$751$	−26.5470	−	5.28053i	−0.968714	−	0.192689i	−0.314716	−	0.949186i	$-0.601909\pi$
$751$	−26.5470	−	5.28053i	−0.968714	−	0.192689i	−0.653998	+	0.756497i	$0.726909\pi$
$752$	37.5456	+	8.56994i	1.36915	+	0.312514i
$753$	−12.8896	−	19.2906i	−0.469722	−	0.702989i
$754$	39.9133	+	2.24159i	1.45356	+	0.0816338i
$755$	0.444788	−	11.9792i	0.0161875	−	0.435968i
$756$	3.36316	+	4.21732i	0.122317	+	0.153382i
$757$	−12.9400	−	5.35991i	−0.470311	−	0.194809i	0.134924	−	0.990856i	$-0.456921\pi$
$757$	−12.9400	−	5.35991i	−0.470311	−	0.194809i	−0.605235	+	0.796047i	$0.706921\pi$
$758$	10.4954	−	9.37919i	0.381209	−	0.340668i
$759$	−1.95739	−	9.84047i	−0.0710488	−	0.357186i
$760$	13.1792	+	32.6520i	0.478060	+	1.18441i
$761$	−2.01273	−	2.01273i	−0.0729613	−	0.0729613i	0.669684	−	0.742646i	$-0.266429\pi$
$761$	−2.01273	−	2.01273i	−0.0729613	−	0.0729613i	−0.742646	+	0.669684i	$0.766429\pi$
$762$	0.168454	−	0.349796i	0.00610244	−	0.0126718i
$763$	−31.1779	+	12.9143i	−1.12872	+	0.467530i
$764$	23.4831	+	12.9788i	0.849589	+	0.469557i
$765$	−22.8999	−	10.0476i	−0.827947	−	0.363271i
$766$	8.39155	+	2.16465i	0.303199	+	0.0782119i
$767$	41.2167	−	17.0725i	1.48825	−	0.616453i
$768$	22.9956	−	30.5545i	0.829783	−	1.10254i
$769$	−33.0517	+	33.0517i	−1.19188	+	1.19188i	−0.215336	+	0.976540i	$0.569085\pi$
$769$	−33.0517	+	33.0517i	−1.19188	+	1.19188i	−0.976540	+	0.215336i	$0.930915\pi$
$770$	−35.6744	+	43.9116i	−1.28561	+	1.58246i
$771$	4.78473	+	24.0545i	0.172318	+	0.866300i
$772$	−29.5044	+	15.2421i	−1.06189	+	0.548576i
$773$	1.45401	−	3.51030i	0.0522972	−	0.126257i	−0.895572	−	0.444917i	$-0.853233\pi$
$773$	1.45401	−	3.51030i	0.0522972	−	0.126257i	0.947869	+	0.318661i	$0.103233\pi$
$774$	−23.6744	+	31.4577i	−0.850960	+	1.13072i
$775$	23.2014	−	13.1252i	0.833420	−	0.471472i
$776$	−13.4250	+	21.3654i	−0.481929	+	0.766972i
$777$	−2.81183	+	1.87880i	−0.100874	+	0.0674017i
$778$	−2.49381	+	1.47105i	−0.0894074	+	0.0527398i
$779$	26.0886	+	5.18935i	0.934723	+	0.185928i
$780$	−35.4535	+	16.6792i	−1.26944	+	0.597210i
$781$	23.2625			0.832397
$782$	−3.94389	+	3.64213i	−0.141033	+	0.130242i
$783$	−5.30055			−0.189426
$784$	27.3902	+	19.4348i	0.978220	+	0.694099i
$785$	−4.96897	−	13.3800i	−0.177350	−	0.477554i
$786$	−2.36634	−	4.01155i	−0.0844044	−	0.143087i
$787$	−21.8309	−	32.6723i	−0.778188	−	1.16464i	−0.982596	−	0.185755i	$-0.940527\pi$
$787$	−21.8309	−	32.6723i	−0.778188	−	1.16464i	0.204408	−	0.978886i	$-0.434473\pi$
$788$	−3.82664	+	12.0057i	−0.136318	+	0.427687i
$789$	−0.130123	+	0.194742i	−0.00463249	+	0.00693302i
$790$	51.2630	+	4.79239i	1.82386	+	0.170506i
$791$	−8.49591	+	20.5109i	−0.302080	+	0.729285i
$792$	34.1038	−	7.78368i	1.21183	−	0.276581i
$793$	−5.03811	−	25.3283i	−0.178909	−	0.899435i
$794$	−10.9342	−	31.2485i	−0.388041	−	1.10897i
$795$	−4.64067	+	19.5151i	−0.164588	+	0.692130i
$796$	25.4904	−	30.1864i	0.903484	−	1.06993i
$797$	−3.98586	−	9.62271i	−0.141186	−	0.340854i	0.837431	−	0.546543i	$-0.184056\pi$
$797$	−3.98586	−	9.62271i	−0.141186	−	0.340854i	−0.978617	+	0.205689i	$0.934056\pi$
$798$	71.4983	+	18.4434i	2.53101	+	0.652889i
$799$	14.5898	−	36.9181i	0.516148	−	1.30607i
$800$	27.9302	+	4.46120i	0.987483	+	0.157727i
$801$	15.1433	−	6.27256i	0.535062	−	0.221630i
$802$	−4.18433	+	8.68880i	−0.147754	+	0.306812i
$803$	7.53047	+	7.53047i	0.265744	+	0.265744i
$804$	−6.99962	+	0.590374i	−0.246857	+	0.0208209i
$805$	−5.49601	−	5.91989i	−0.193709	−	0.208649i
$806$	−20.6079	+	18.4162i	−0.725881	+	0.648683i
$807$	−13.4862	+	32.5585i	−0.474735	+	1.14611i
$808$	7.85769	−	3.51602i	0.276433	−	0.123693i
$809$	19.0699	−	28.5401i	0.670461	−	1.00342i	−0.327816	−	0.944741i	$-0.606313\pi$
$809$	19.0699	−	28.5401i	0.670461	−	1.00342i	0.998277	−	0.0586741i	$-0.0186873\pi$
$810$	27.2028	−	14.7141i	0.955809	−	0.517001i
$811$	−24.6409	−	36.8776i	−0.865257	−	1.29495i	−0.954278	−	0.298919i	$-0.903374\pi$
$811$	−24.6409	−	36.8776i	−0.865257	−	1.29495i	0.0890210	−	0.996030i	$-0.471626\pi$
$812$	−58.1512	+	16.7528i	−2.04071	+	0.587906i
$813$	−1.60228	−	0.318713i	−0.0561943	−	0.0111777i
$814$	−0.325042	−	2.30242i	−0.0113927	−	0.0806999i
$815$	15.1527	−	9.33062i	0.530777	−	0.326837i
$816$	−27.5442	−	28.1973i	−0.964241	−	0.987105i
$817$		−	57.1424i		−	1.99916i
$818$	−14.4096	+	2.03426i	−0.503821	+	0.0711264i
$819$	−7.61111	+	38.2636i	−0.265954	+	1.33704i
$820$	14.3816	−	15.8022i	0.502226	−	0.551837i
$821$	−15.3596	−	22.9873i	−0.536055	−	0.802263i	0.460282	−	0.887773i	$-0.347748\pi$
$821$	−15.3596	−	22.9873i	−0.536055	−	0.802263i	−0.996337	+	0.0855095i	$0.972748\pi$
$822$	−0.0969961	+	1.72710i	−0.00338313	+	0.0602394i
$823$	−34.6801	−	23.1725i	−1.20887	−	0.807743i	−0.222931	−	0.974834i	$-0.571563\pi$
$823$	−34.6801	−	23.1725i	−1.20887	−	0.807743i	−0.985941	+	0.167091i	$0.946563\pi$
$824$	−40.8706	+	18.2880i	−1.42379	+	0.637093i
$825$	35.5662	+	41.2807i	1.23826	+	1.43721i
$826$	−50.3571	+	45.0016i	−1.75215	+	1.56581i
$827$	1.07430	+	5.40087i	0.0373570	+	0.187807i	0.994958	−	0.100291i	$-0.0319773\pi$
$827$	1.07430	+	5.40087i	0.0373570	+	0.187807i	−0.957601	+	0.288097i	$0.906977\pi$
$828$	0.419761	+	4.97679i	0.0145877	+	0.172955i
$829$	13.8990	−	13.8990i	0.482733	−	0.482733i	−0.423270	−	0.906003i	$-0.639118\pi$
$829$	13.8990	−	13.8990i	0.482733	−	0.482733i	0.906003	+	0.423270i	$0.139118\pi$
$830$	0.177555	+	1.71549i	0.00616304	+	0.0595455i
$831$	−1.46076	+	0.605066i	−0.0506732	+	0.0209895i
$832$	−29.2791	+	1.64382i	−1.01507	+	0.0569891i
$833$	24.0755	−	24.8756i	0.834167	−	0.861890i
$834$	12.5074	−	48.4865i	0.433094	−	1.67895i
$835$	−28.9241	+	39.9917i	−1.00096	+	1.38397i
$836$	−32.7560	+	38.7905i	−1.13289	+	1.34160i
$837$	2.59123	−	2.59123i	0.0895659	−	0.0895659i
$838$	−22.1244	+	7.74161i	−0.764276	+	0.267430i
$839$	24.2909	−	4.83176i	0.838616	−	0.166811i	0.242945	−	0.970040i	$-0.421886\pi$
$839$	24.2909	−	4.83176i	0.838616	−	0.166811i	0.595670	+	0.803229i	$0.296886\pi$
$840$	42.3190	−	41.5581i	1.46014	−	1.43389i
$841$	11.6590	−	28.1473i	0.402034	−	0.970596i
$842$	3.53714	−	4.70000i	0.121898	−	0.161973i
$843$	−6.93789	−	4.63575i	−0.238954	−	0.159664i
$844$	−26.1773	−	8.34362i	−0.901061	−	0.287199i
$845$	0.888196	+	0.407143i	0.0305549	+	0.0140062i
$846$	−18.7639	−	31.8096i	−0.645117	−	1.09364i
$847$	−37.6765	−	7.49433i	−1.29458	−	0.257508i
$848$	−8.68799	+	12.2443i	−0.298347	+	0.420471i
$849$			78.9240i			2.70867i
$850$	8.90318	−	27.7621i	0.305377	−	0.952232i
$851$	0.331993			0.0113806
$852$	−24.2341	−	2.73066i	−0.830247	−	0.0935508i
$853$	−7.81852	+	39.3064i	−0.267701	+	1.34582i	0.579682	+	0.814842i	$0.303177\pi$
$853$	−7.81852	+	39.3064i	−0.267701	+	1.34582i	−0.847383	+	0.530981i	$0.821823\pi$
$854$	19.8623	+	33.6717i	0.679674	+	1.15222i
$855$	14.0708	−	30.6958i	0.481210	−	1.04977i
$856$	−37.8898	−	23.8081i	−1.29505	−	0.813745i
$857$	−12.2410	+	18.3199i	−0.418144	+	0.625797i	−0.979420	−	0.201832i	$-0.935311\pi$
$857$	−12.2410	+	18.3199i	−0.418144	+	0.625797i	0.561276	+	0.827629i	$0.310311\pi$
$858$	−45.1394	−	33.9711i	−1.54103	−	1.15975i
$859$	35.1470	+	14.5584i	1.19920	+	0.496725i	0.890740	−	0.454513i	$-0.150187\pi$
$859$	35.1470	+	14.5584i	1.19920	+	0.496725i	0.308460	+	0.951237i	$0.400187\pi$
$860$	−39.3218	−	23.6786i	−1.34086	−	0.807433i
$861$	−8.74129	−	43.9454i	−0.297902	−	1.49766i
$862$	23.1624	−	8.10480i	0.788914	−	0.276051i
$863$	−16.5319	−	16.5319i	−0.562753	−	0.562753i	0.367336	−	0.930088i	$-0.380270\pi$
$863$	−16.5319	−	16.5319i	−0.562753	−	0.562753i	−0.930088	+	0.367336i	$0.880270\pi$
$864$	3.86386	−	0.435301i	0.131451	−	0.0148092i
$865$	−4.14441	−	2.99745i	−0.140914	−	0.101916i
$866$	−4.87997	−	1.25882i	−0.165828	−	0.0427763i
$867$	−33.0277	+	23.6655i	−1.12168	+	0.803722i
$868$	20.2381	−	36.6176i	0.686925	−	1.24288i
$869$	28.4094	+	68.5864i	0.963724	+	2.32663i
$870$	6.00036	+	57.9738i	0.203431	+	1.96550i
$871$	3.80899	+	3.80899i	0.129063	+	0.129063i
$872$	−4.07494	+	23.9823i	−0.137995	+	0.812142i
$873$	23.7331	−	4.72081i	0.803244	−	0.159775i
$874$	−4.83026	−	5.40509i	−0.163386	−	0.182830i
$875$	41.8091	+	13.2861i	1.41341	+	0.449153i
$876$	−6.96104	−	8.72896i	−0.235192	−	0.294924i
$877$	−23.7519	+	35.5473i	−0.802045	+	1.20035i	0.174420	+	0.984671i	$0.444195\pi$
$877$	−23.7519	+	35.5473i	−0.802045	+	1.20035i	−0.976465	+	0.215674i	$0.930805\pi$
$878$	0.495276	−	8.81880i	0.0167148	−	0.297620i
$879$	−47.7192	+	31.8850i	−1.60953	+	1.07545i
$880$	13.1198	+	38.6146i	0.442268	+	1.30170i
$881$	−9.33174	−	1.85620i	−0.314394	−	0.0625369i	0.0353710	−	0.999374i	$-0.488739\pi$
$881$	−9.33174	−	1.85620i	−0.314394	−	0.0625369i	−0.349765	+	0.936837i	$0.613739\pi$
$882$	−4.50216	−	31.8909i	−0.151595	−	1.07382i
$883$	15.9439			0.536556			0.268278	−	0.963341i	$-0.413545\pi$
$883$	15.9439			0.536556			0.268278	+	0.963341i	$0.413545\pi$
$884$	−2.89322	+	30.0889i	−0.0973094	+	1.01200i
$885$	34.1046	+	55.3851i	1.14641	+	1.86175i
$886$	1.34484	+	9.52615i	0.0451809	+	0.320037i
$887$	−7.28154	+	36.6068i	−0.244490	+	1.22914i	0.642115	+	0.766609i	$0.278057\pi$
$887$	−7.28154	+	36.6068i	−0.244490	+	1.22914i	−0.886605	+	0.462527i	$0.846943\pi$
$888$	0.0683493	+	2.43674i	0.00229365	+	0.0817718i
$889$	0.374743	−	0.250395i	0.0125685	−	0.00839798i
$890$	9.09164	+	16.8082i	0.304753	+	0.563413i
$891$	37.0781	+	24.7748i	1.24216	+	0.829986i
$892$	6.42349	−	5.12250i	0.215074	−	0.171514i
$893$	49.5218	+	20.5126i	1.65718	+	0.686428i
$894$	−9.81148	+	8.76803i	−0.328145	+	0.293247i
$895$	32.9913	−	30.6290i	1.10278	−	1.02382i
$896$	41.0138	−	16.9876i	1.37017	−	0.567516i
$897$	5.70359	−	5.70359i	0.190437	−	0.190437i
$898$	2.85374	+	1.37430i	0.0952304	+	0.0458609i
$899$	15.7330	+	37.9828i	0.524725	+	1.26680i
$900$	−15.2923	−	22.4023i	−0.509743	−	0.746743i
$901$	11.1202	+	10.7626i	0.370469	+	0.358553i
$902$	29.8318	+	7.69527i	0.993290	+	0.256224i
$903$	−88.9275	+	36.8350i	−2.95932	+	1.22579i
$904$	9.26053	+	13.0517i	0.308001	+	0.434094i
$905$	−21.0876	−	5.01461i	−0.700977	−	0.166691i
$906$	−17.1035	+	5.98473i	−0.568226	+	0.198829i
$907$	−17.2832	+	3.43783i	−0.573878	+	0.114151i	−0.473493	−	0.880797i	$-0.657007\pi$
$907$	−17.2832	+	3.43783i	−0.573878	+	0.114151i	−0.100384	+	0.994949i	$0.532007\pi$
$908$	−20.3647	+	10.5205i	−0.675825	+	0.349135i
$909$	−7.62695	−	3.15919i	−0.252970	−	0.104784i
$910$	−45.2863	−	4.23366i	−1.50123	−	0.140344i
$911$	10.4738	+	6.99838i	0.347013	+	0.231867i	0.716846	−	0.697231i	$-0.245585\pi$
$911$	10.4738	+	6.99838i	0.347013	+	0.231867i	−0.369833	+	0.929098i	$0.620585\pi$
$912$	38.6776	−	36.5657i	1.28074	−	1.21081i
$913$	−2.06765	+	1.38156i	−0.0684292	+	0.0457230i
$914$	−3.94610	+	2.32773i	−0.130525	+	0.0769944i
$915$	35.2956	−	13.1078i	1.16684	−	0.433331i
$916$	−27.4633	−	3.09452i	−0.907413	−	0.102246i
$917$		−	5.40670i		−	0.178545i
$918$	0.159308	−	4.00480i	0.00525796	−	0.132178i
$919$		−	18.4561i		−	0.608810i	−0.952543	−	0.304405i	$-0.901542\pi$
$919$		−	18.4561i		−	0.608810i	0.952543	−	0.304405i	$-0.0984575\pi$
$920$	−5.72100	+	1.08413i	−0.188616	+	0.0357426i
$921$	−6.39200	+	32.1348i	−0.210624	+	1.05888i
$922$	21.2984	+	36.1062i	0.701424	+	1.18909i
$923$	10.3900	+	15.5498i	0.341992	+	0.511827i
$924$	81.4826	+	25.9713i	2.68058	+	0.854393i
$925$	−1.56930	+	0.887763i	−0.0515982	+	0.0291895i
$926$	−13.4640	+	17.8905i	−0.442456	+	0.587918i
$927$	39.6704	+	16.4320i	1.30295	+	0.539699i
$928$	−12.0768	+	41.9175i	−0.396441	+	1.37601i
$929$	−4.11323	+	0.818172i	−0.134951	+	0.0268433i	−0.262103	−	0.965040i	$-0.584416\pi$
$929$	−4.11323	+	0.818172i	−0.134951	+	0.0268433i	0.127153	+	0.991883i	$0.459416\pi$
$930$	−31.2744	−	25.4078i	−1.02553	−	0.833153i
$931$	33.0537	+	33.0537i	1.08329	+	1.08329i
$932$	9.86717	−	11.6850i	0.323210	−	0.382753i
$933$	−12.2731	−	29.6299i	−0.401804	−	0.970040i
$934$	−36.5509	−	9.42850i	−1.19598	−	0.308510i
$935$	41.3913	−	7.34313i	1.35364	−	0.240146i
$936$	20.4352	+	19.3201i	0.667945	+	0.631497i
$937$	3.53005	+	8.52230i	0.115322	+	0.278412i	0.970993	−	0.239109i	$-0.0768552\pi$
$937$	3.53005	+	8.52230i	0.115322	+	0.278412i	−0.855671	+	0.517520i	$0.826855\pi$
$938$	−7.34691	−	3.53811i	−0.239885	−	0.115523i
$939$	46.3216	−	46.3216i	1.51165	−	1.51165i
$940$	34.6362	−	25.5778i	1.12971	−	0.834255i
$941$	−27.4188	+	5.45393i	−0.893826	+	0.177793i	−0.620573	−	0.784149i	$-0.713100\pi$
$941$	−27.4188	+	5.45393i	−0.893826	+	0.177793i	−0.273254	+	0.961942i	$0.588100\pi$
$942$	−16.0873	+	14.3764i	−0.524154	+	0.468410i
$943$	−1.68332	+	4.06389i	−0.0548164	+	0.132339i
$944$	8.15402	+	47.9942i	0.265391	+	1.56208i
$945$	6.02666	+	0.223770i	0.196047	+	0.00727924i
$946$	3.71110	−	66.0792i	0.120658	−	2.14842i
$947$	−22.1033	+	14.7690i	−0.718262	+	0.479927i	−0.860205	−	0.509948i	$-0.829665\pi$
$947$	−22.1033	+	14.7690i	−0.718262	+	0.479927i	0.141944	+	0.989875i	$0.454665\pi$
$948$	−21.5450	−	74.7859i	−0.699750	−	2.42893i
$949$	−1.67030	+	8.39716i	−0.0542202	+	0.272583i
$950$	37.2856	+	12.6330i	1.20970	+	0.409869i
$951$	36.0982			1.17057
$952$	−10.9097	−	44.4394i	−0.353586	−	1.44029i
$953$			29.2476i			0.947423i	0.880680	+	0.473712i	$0.157086\pi$
$953$			29.2476i			0.947423i	−0.880680	+	0.473712i	$0.842914\pi$
$954$	14.2563	−	2.01261i	0.461564	−	0.0651608i
$955$	28.1214	−	10.4435i	0.909988	−	0.337944i
$956$	−5.42855	−	18.8433i	−0.175572	−	0.609435i
$957$	−69.8749	+	46.6889i	−2.25873	+	1.50924i
$958$	−30.2624	−	1.69958i	−0.977733	−	0.0549109i
$959$	−1.11563	+	1.66966i	−0.0360256	+	0.0539162i
$960$	−9.13502	−	41.7675i	−0.294831	−	1.34804i
$961$	2.38074	+	0.986135i	0.0767981	+	0.0318108i
$962$	1.39387	−	1.24563i	0.0449403	−	0.0401609i
$963$	8.37198	+	42.0888i	0.269783	+	1.35629i
$964$	−4.21920	−	50.0239i	−0.135891	−	1.61116i
$965$	−8.58963	+	36.1214i	−0.276510	+	1.16279i
$966$	−5.29797	+	11.0013i	−0.170459	+	0.353960i
$967$	−9.36775	−	22.6157i	−0.301246	−	0.727273i	−0.999930	−	0.0118423i	$-0.996230\pi$
$967$	−9.36775	−	22.6157i	−0.301246	−	0.727273i	0.698683	−	0.715431i	$-0.253770\pi$
$968$	−19.0236	+	20.1217i	−0.611443	+	0.646734i
$969$	−31.2223	−	45.1135i	−1.00301	−	1.44926i
$970$	8.32313	+	26.9557i	0.267240	+	0.865496i
$971$	−20.8027	+	8.61677i	−0.667591	+	0.276525i	−0.690629	−	0.723209i	$-0.742666\pi$
$971$	−20.8027	+	8.61677i	−0.667591	+	0.276525i	0.0230378	+	0.999735i	$0.492666\pi$
$972$	−32.5676	−	27.5011i	−1.04461	−	0.882100i
$973$	41.1033	−	41.1033i	1.31771	−	1.31771i
$974$	−10.9102	+	3.81761i	−0.349585	+	0.122324i
$975$	−11.7086	+	42.2119i	−0.374977	+	1.35186i
$976$	28.1690	+	0.790640i	0.901666	+	0.0253078i
$977$	8.74595	+	3.62269i	0.279808	+	0.115900i	0.518174	−	0.855275i	$-0.326612\pi$
$977$	8.74595	+	3.62269i	0.279808	+	0.115900i	−0.238366	+	0.971175i	$0.576612\pi$
$978$	−21.4927	−	16.1750i	−0.687262	−	0.517221i
$979$	−15.3080	+	22.9100i	−0.489246	+	0.732208i
$980$	36.4422	−	9.04872i	1.16410	−	0.289051i
$981$	19.3967	−	12.9604i	0.619288	−	0.413795i
$982$	−20.1733	−	34.1989i	−0.643757	−	1.09133i
$983$	1.89298	+	0.376537i	0.0603766	+	0.0120097i	0.225186	−	0.974316i	$-0.427701\pi$
$983$	1.89298	+	0.376537i	0.0603766	+	0.0120097i	−0.164810	+	0.986325i	$0.552701\pi$
$984$	−30.1745	−	11.5185i	−0.961927	−	0.367196i
$985$	7.38693	+	11.9962i	0.235367	+	0.382231i
$986$	40.8255	+	18.8450i	1.30015	+	0.600147i
$987$		−	90.2907i		−	2.87399i
$988$	−40.5597	−	4.57019i	−1.29038	−	0.145397i
$989$	9.26790	+	1.84350i	0.294702	+	0.0586199i
$990$	18.2649	−	34.5827i	0.580496	−	1.09911i
$991$	1.36456	+	2.04221i	0.0433468	+	0.0648730i	0.852510	−	0.522711i	$-0.175079\pi$
$991$	1.36456	+	2.04221i	0.0433468	+	0.0648730i	−0.809163	+	0.587584i	$0.800079\pi$
$992$	−14.5879	−	26.3957i	−0.463167	−	0.838064i
$993$	13.2465	−	19.8248i	0.420365	−	0.629120i
$994$	−22.6204	−	17.0237i	−0.717475	−	0.539958i
$995$	−7.00422	−	43.6138i	−0.222049	−	1.38265i
$996$	2.31619	−	1.19655i	0.0733912	−	0.0379143i
$997$	−24.6522	+	4.90362i	−0.780742	+	0.155299i	−0.569342	−	0.822101i	$-0.692802\pi$
$997$	−24.6522	+	4.90362i	−0.780742	+	0.155299i	−0.211399	+	0.977400i	$0.567802\pi$
$998$	−2.82246	−	8.06618i	−0.0893433	−	0.255331i
$999$	−0.175265	+	0.175265i	−0.00554515	+	0.00554515i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.co.a.99.6	✓	832
5.4	even	2	inner	680.2.co.a.99.99	yes	832
8.3	odd	2	inner	680.2.co.a.99.83	yes	832
17.11	odd	16	inner	680.2.co.a.419.22	yes	832
40.19	odd	2	inner	680.2.co.a.99.22	yes	832
85.79	odd	16	inner	680.2.co.a.419.83	yes	832
136.11	even	16	inner	680.2.co.a.419.99	yes	832
680.419	even	16	inner	680.2.co.a.419.6	yes	832

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.co.a.99.6	✓	832	1.1	even	1	trivial
680.2.co.a.99.22	yes	832	40.19	odd	2	inner
680.2.co.a.99.83	yes	832	8.3	odd	2	inner
680.2.co.a.99.99	yes	832	5.4	even	2	inner
680.2.co.a.419.6	yes	832	680.419	even	16	inner
680.2.co.a.419.22	yes	832	17.11	odd	16	inner
680.2.co.a.419.83	yes	832	85.79	odd	16	inner
680.2.co.a.419.99	yes	832	136.11	even	16	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.co (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40033 + 0.197690i) q^{2} +(2.34414 + 0.466278i) q^{3} +(1.92184 - 0.553661i) q^{4} +(0.931769 - 2.03268i) q^{5} +(-3.37474 - 0.189530i) q^{6} +(-3.26252 - 2.17994i) q^{7} +(-2.58175 + 1.15523i) q^{8} +(2.50594 + 1.03799i) q^{9} +(-0.902942 + 3.03063i) q^{10} +(-4.47201 + 0.889539i) q^{11} +(4.76322 - 0.401747i) q^{12} +(-2.59200 - 2.59200i) q^{13} +(4.99955 + 2.40767i) q^{14} +(3.13200 - 4.33043i) q^{15} +(3.38692 - 2.12809i) q^{16} +(-1.63989 - 3.78296i) q^{17} +(-3.71434 - 0.958134i) q^{18} +(5.14362 - 2.13056i) q^{19} +(0.665291 - 4.42237i) q^{20} +(-6.63134 - 6.63134i) q^{21} +(6.08643 - 2.12972i) q^{22} +(0.179613 + 0.902978i) q^{23} +(-6.59065 + 1.50422i) q^{24} +(-3.26361 - 3.78799i) q^{25} +(4.14207 + 3.11724i) q^{26} +(-0.571520 - 0.381877i) q^{27} +(-7.47698 - 2.38317i) q^{28} +(6.41183 - 4.28425i) q^{29} +(-3.52974 + 6.68319i) q^{30} +(-1.04009 + 5.22889i) q^{31} +(-4.32210 + 3.64959i) q^{32} -10.8978 q^{33} +(3.04423 + 4.97319i) q^{34} +(-7.47105 + 4.60046i) q^{35} +(5.39070 + 0.607415i) q^{36} +(0.0703496 - 0.353672i) q^{37} +(-6.78157 + 4.00032i) q^{38} +(-4.86742 - 7.28461i) q^{39} +(-0.0573685 + 6.32430i) q^{40} +(3.97256 + 2.65438i) q^{41} +(10.5970 + 7.97510i) q^{42} +(3.92775 - 9.48244i) q^{43} +(-8.10198 + 4.18553i) q^{44} +(4.44487 - 4.12661i) q^{45} +(-0.430027 - 1.22896i) q^{46} +(6.80788 + 6.80788i) q^{47} +(8.93170 - 3.40930i) q^{48} +(3.21308 + 7.75705i) q^{49} +(5.31897 + 4.65924i) q^{50} +(-2.08022 - 9.63243i) q^{51} +(-6.41650 - 3.54632i) q^{52} +(-3.46766 + 1.43635i) q^{53} +(0.875808 + 0.421770i) q^{54} +(-2.35873 + 9.91903i) q^{55} +(10.9413 + 1.85910i) q^{56} +(13.0508 - 2.59597i) q^{57} +(-8.13172 + 7.26691i) q^{58} +(-4.65744 + 11.2441i) q^{59} +(3.62159 - 10.0565i) q^{60} +(5.85771 + 3.91400i) q^{61} +(0.422771 - 7.52778i) q^{62} +(-5.91290 - 8.84928i) q^{63} +(5.33087 - 5.96505i) q^{64} +(-7.68387 + 2.85357i) q^{65} +(15.2605 - 2.15438i) q^{66} -1.46951 q^{67} +(-5.24608 - 6.36229i) q^{68} +2.20046i q^{69} +(9.55246 - 7.91911i) q^{70} +(-5.00381 - 0.995320i) q^{71} +(-7.66884 + 0.215107i) q^{72} +(-1.29762 - 1.94202i) q^{73} +(-0.0285954 + 0.509164i) q^{74} +(-5.88411 - 10.4013i) q^{75} +(8.70560 - 6.94241i) q^{76} +(16.5292 + 6.84660i) q^{77} +(8.25608 + 9.23861i) q^{78} +(-3.17636 - 15.9686i) q^{79} +(-1.16991 - 8.86743i) q^{80} +(-6.91555 - 6.91555i) q^{81} +(-6.08763 - 2.93167i) q^{82} +(0.503868 - 0.208709i) q^{83} +(-16.4159 - 9.07284i) q^{84} +(-9.21756 - 0.191466i) q^{85} +(-3.62556 + 14.0550i) q^{86} +(17.0279 - 7.05318i) q^{87} +(10.5180 - 7.46279i) q^{88} +(4.27302 - 4.27302i) q^{89} +(-5.40849 + 6.65732i) q^{90} +(2.80603 + 14.1069i) q^{91} +(0.845131 + 1.63593i) q^{92} +(-4.87624 + 11.7723i) q^{93} +(-10.8791 - 8.18742i) q^{94} +(0.461918 - 12.4406i) q^{95} +(-11.8333 + 6.53984i) q^{96} +(7.41774 - 4.95638i) q^{97} +(-6.03285 - 10.2272i) q^{98} +(-12.1299 - 2.41279i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 832 q - 16 q^{4} - 16 q^{6} - 32 q^{9} - 8 q^{10} - 32 q^{11} - 16 q^{14} - 32 q^{19} - 8 q^{20} - 32 q^{24} - 16 q^{25} - 48 q^{26} + 56 q^{30} + 48 q^{34} - 32 q^{35} + 48 q^{36} - 72 q^{40} - 32 q^{41}+ \cdots - 128 q^{99}+O(q^{100}) \) 832 * q - 16 * q^4 - 16 * q^6 - 32 * q^9 - 8 * q^10 - 32 * q^11 - 16 * q^14 - 32 * q^19 - 8 * q^20 - 32 * q^24 - 16 * q^25 - 48 * q^26 + 56 * q^30 + 48 * q^34 - 32 * q^35 + 48 * q^36 - 72 * q^40 - 32 * q^41 - 48 * q^44 - 32 * q^46 - 32 * q^49 - 32 * q^51 + 32 * q^54 - 16 * q^56 - 32 * q^59 - 112 * q^60 - 16 * q^64 - 96 * q^65 - 48 * q^66 - 80 * q^70 - 16 * q^74 - 16 * q^75 - 16 * q^76 - 104 * q^80 - 32 * q^81 - 192 * q^86 - 32 * q^89 + 72 * q^90 - 32 * q^91 - 16 * q^94 + 288 * q^96 - 128 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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