LMFDB - Embedded newform 770.2.bd.a.527.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(263,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 8, 6]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("770.263");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.bd (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			527.12
Character	$\chi$	$=$	770.527
Dual form			770.2.bd.a.263.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(0.00659019 + 0.00176584i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.60119 + 1.56083i) q^{5} -0.00682267i q^{6} +(-1.96250 - 1.77443i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.59804 - 1.49998i) q^{9} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(0.00659019 + 0.00176584i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.60119 + 1.56083i) q^{5} -0.00682267i q^{6} +(-1.96250 - 1.77443i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.59804 - 1.49998i) q^{9} +(1.92207 + 1.14266i) q^{10} +(3.29278 - 0.397013i) q^{11} +(-0.00659019 + 0.00176584i) q^{12} +(2.97033 + 2.97033i) q^{13} +(-1.20604 + 2.35488i) q^{14} +(-0.0133083 + 0.00745875i) q^{15} +(0.500000 - 0.866025i) q^{16} +(1.42759 + 0.382521i) q^{17} +(-0.776445 + 2.89773i) q^{18} +(-1.40344 + 2.43083i) q^{19} +(0.606253 - 2.15231i) q^{20} +(-0.00979987 - 0.0151593i) q^{21} +(-1.23572 - 3.07782i) q^{22} +(0.541825 + 2.02212i) q^{23} +(0.00341134 + 0.00590861i) q^{24} +(0.127603 - 4.99837i) q^{25} +(2.10034 - 3.63789i) q^{26} +(-0.0289459 - 0.0289459i) q^{27} +(2.58679 + 0.555455i) q^{28} +10.6335 q^{29} +(0.0106490 + 0.0109244i) q^{30} +(4.05104 + 7.01662i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(0.0224011 + 0.00319812i) q^{33} -1.47795i q^{34} +(5.91192 - 0.221930i) q^{35} +2.99995 q^{36} +(5.44607 - 1.45927i) q^{37} +(2.71124 + 0.726474i) q^{38} +(0.0143299 + 0.0248202i) q^{39} +(-2.23589 - 0.0285352i) q^{40} +2.30516i q^{41} +(-0.0121064 + 0.0133895i) q^{42} +(5.58459 + 5.58459i) q^{43} +(-2.65312 + 1.99021i) q^{44} +(6.50116 - 1.65336i) q^{45} +(1.81298 - 1.04672i) q^{46} +(-10.0906 + 2.70377i) q^{47} +(0.00482436 - 0.00482436i) q^{48} +(0.702783 + 6.96463i) q^{49} +(-4.86108 + 1.17042i) q^{50} +(0.00873261 + 0.00504178i) q^{51} +(-4.05754 - 1.08722i) q^{52} +(-6.71753 - 1.79996i) q^{53} +(-0.0204679 + 0.0354514i) q^{54} +(-4.65268 + 5.77517i) q^{55} +(-0.132982 - 2.64241i) q^{56} +(-0.0135414 + 0.0135414i) q^{57} +(-2.75216 - 10.2712i) q^{58} +(7.82626 - 4.51850i) q^{59} +(0.00779596 - 0.0131136i) q^{60} +(7.92908 + 4.57785i) q^{61} +(5.72904 - 5.72904i) q^{62} +(2.43703 + 7.55374i) q^{63} +1.00000i q^{64} +(-9.39224 - 0.119867i) q^{65} +(-0.00270869 - 0.0224655i) q^{66} +(-0.482205 + 1.79961i) q^{67} +(-1.42759 + 0.382521i) q^{68} +0.0142829i q^{69} +(-1.74448 - 5.65303i) q^{70} -7.36990 q^{71} +(-0.776445 - 2.89773i) q^{72} +(3.08095 - 11.4983i) q^{73} +(-2.81909 - 4.88281i) q^{74} +(0.00966724 - 0.0327149i) q^{75} -2.80688i q^{76} +(-7.16653 - 5.06367i) q^{77} +(0.0202656 - 0.0202656i) q^{78} +(2.93208 - 5.07850i) q^{79} +(0.551127 + 2.16709i) q^{80} +(4.49979 + 7.79387i) q^{81} +(2.22661 - 0.596619i) q^{82} +(-5.05490 - 5.05490i) q^{83} +(0.0160666 + 0.00822840i) q^{84} +(-2.88289 + 1.61574i) q^{85} +(3.94890 - 6.83970i) q^{86} +(0.0700769 + 0.0187771i) q^{87} +(2.60908 + 2.04761i) q^{88} +(14.8653 + 8.58249i) q^{89} +(-3.27964 - 5.85171i) q^{90} +(-0.558613 - 11.0999i) q^{91} +(-1.48029 - 1.48029i) q^{92} +(0.0143070 + 0.0533943i) q^{93} +(5.22328 + 9.04699i) q^{94} +(-1.54695 - 6.08275i) q^{95} +(-0.00590861 - 0.00341134i) q^{96} +(-3.34628 - 3.34628i) q^{97} +(6.54542 - 2.48142i) q^{98} +(-9.15026 - 3.90764i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 8 q^{5}+O(q^{10}) $ 192 * q + 8 * q^5	$ 192 q + 8 q^{5} + 4 q^{11} + 16 q^{15} + 96 q^{16} + 24 q^{22} - 8 q^{23} + 24 q^{25} - 8 q^{26} - 16 q^{33} - 160 q^{36} - 40 q^{37} - 40 q^{42} + 32 q^{45} - 40 q^{47} + 40 q^{53} + 8 q^{55} + 16 q^{56} + 32 q^{58} - 48 q^{67} - 72 q^{70} + 32 q^{71} - 48 q^{75} - 72 q^{77} - 8 q^{80} + 64 q^{81} + 16 q^{82} - 12 q^{88} - 112 q^{91} - 16 q^{92} + 80 q^{93} - 64 q^{97}+O(q^{100}) $ 192 * q + 8 * q^5 + 4 * q^11 + 16 * q^15 + 96 * q^16 + 24 * q^22 - 8 * q^23 + 24 * q^25 - 8 * q^26 - 16 * q^33 - 160 * q^36 - 40 * q^37 - 40 * q^42 + 32 * q^45 - 40 * q^47 + 40 * q^53 + 8 * q^55 + 16 * q^56 + 32 * q^58 - 48 * q^67 - 72 * q^70 + 32 * q^71 - 48 * q^75 - 72 * q^77 - 8 * q^80 + 64 * q^81 + 16 * q^82 - 12 * q^88 - 112 * q^91 - 16 * q^92 + 80 * q^93 - 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$	0.00659019	+	0.00176584i	0.00380485	+	0.00101951i	0.260721	−	0.965414i	$-0.416040\pi$
$3$	0.00659019	+	0.00176584i	0.00380485	+	0.00101951i	−0.256916	+	0.966434i	$0.582706\pi$
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	−1.60119	+	1.56083i	−0.716073	+	0.698026i
$5$	−1.60119	+	1.56083i	−0.716073	+	0.698026i
$6$		−	0.00682267i		−	0.00278534i
$7$	−1.96250	−	1.77443i	−0.741754	−	0.670672i
$7$	−1.96250	−	1.77443i	−0.741754	−	0.670672i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−2.59804	−	1.49998i	−0.866012	−	0.499992i
$10$	1.92207	+	1.14266i	0.607811	+	0.361339i
$11$	3.29278	−	0.397013i	0.992810	−	0.119704i
$11$	3.29278	−	0.397013i	0.992810	−	0.119704i
$12$	−0.00659019	+	0.00176584i	−0.00190243	+	0.000509753i
$13$	2.97033	+	2.97033i	0.823821	+	0.823821i	0.986654	−	0.162833i	$-0.0520631\pi$
$13$	2.97033	+	2.97033i	0.823821	+	0.823821i	−0.162833	+	0.986654i	$0.552063\pi$
$14$	−1.20604	+	2.35488i	−0.322327	+	0.629369i
$15$	−0.0133083	+	0.00745875i	−0.00343619	+	0.00192584i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	1.42759	+	0.382521i	0.346241	+	0.0927750i	0.427749	−	0.903898i	$-0.359307\pi$
$17$	1.42759	+	0.382521i	0.346241	+	0.0927750i	−0.0815077	+	0.996673i	$0.525974\pi$
$18$	−0.776445	+	2.89773i	−0.183010	+	0.683002i
$19$	−1.40344	+	2.43083i	−0.321971	+	0.557671i	−0.980895	−	0.194539i	$-0.937679\pi$
$19$	−1.40344	+	2.43083i	−0.321971	+	0.557671i	0.658923	+	0.752210i	$0.271012\pi$
$20$	0.606253	−	2.15231i	0.135562	−	0.481272i
$21$	−0.00979987	−	0.0151593i	−0.00213851	−	0.00330803i
$22$	−1.23572	−	3.07782i	−0.263456	−	0.656194i
$23$	0.541825	+	2.02212i	0.112978	+	0.421641i	0.999128	−	0.0417590i	$-0.0132962\pi$
$23$	0.541825	+	2.02212i	0.112978	+	0.421641i	−0.886149	+	0.463400i	$0.846629\pi$
$24$	0.00341134	+	0.00590861i	0.000696336	+	0.00120609i
$25$	0.127603	−	4.99837i	0.0255206	−	0.999674i
$26$	2.10034	−	3.63789i	0.411910	−	0.713450i
$27$	−0.0289459	−	0.0289459i	−0.00557064	−	0.00557064i
$28$	2.58679	+	0.555455i	0.488857	+	0.104971i
$29$	10.6335			1.97459			0.987297	−	0.158885i	$-0.0507899\pi$
$29$	10.6335			1.97459			0.987297	+	0.158885i	$0.0507899\pi$
$30$	0.0106490	+	0.0109244i	0.00194424	+	0.00199451i
$31$	4.05104	+	7.01662i	0.727589	+	1.26022i	0.957899	+	0.287104i	$0.0926926\pi$
$31$	4.05104	+	7.01662i	0.727589	+	1.26022i	−0.230310	+	0.973117i	$0.573974\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$	0.0224011	+	0.00319812i	0.00389953	+	0.000556721i
$34$		−	1.47795i		−	0.253466i
$35$	5.91192	−	0.221930i	0.999296	−	0.0375130i
$36$	2.99995			0.499992
$37$	5.44607	−	1.45927i	0.895329	−	0.239903i	0.218320	−	0.975877i	$-0.429942\pi$
$37$	5.44607	−	1.45927i	0.895329	−	0.239903i	0.677009	+	0.735975i	$0.263276\pi$
$38$	2.71124	+	0.726474i	0.439821	+	0.117850i
$39$	0.0143299	+	0.0248202i	0.00229462	+	0.00397441i
$40$	−2.23589	−	0.0285352i	−0.353525	−	0.00451181i
$41$			2.30516i			0.360006i	0.983666	+	0.180003i	$0.0576107\pi$
$41$			2.30516i			0.360006i	−0.983666	+	0.180003i	$0.942389\pi$
$42$	−0.0121064	+	0.0133895i	−0.00186805	+	0.00206604i
$43$	5.58459	+	5.58459i	0.851642	+	0.851642i	0.990335	−	0.138694i	$-0.0442903\pi$
$43$	5.58459	+	5.58459i	0.851642	+	0.851642i	−0.138694	+	0.990335i	$0.544290\pi$
$44$	−2.65312	+	1.99021i	−0.399973	+	0.300036i
$45$	6.50116	−	1.65336i	0.969135	−	0.246468i
$46$	1.81298	−	1.04672i	0.267309	−	0.154331i
$47$	−10.0906	+	2.70377i	−1.47187	+	0.394385i	−0.903571	−	0.428439i	$-0.859064\pi$
$47$	−10.0906	+	2.70377i	−1.47187	+	0.394385i	−0.568296	+	0.822824i	$0.692397\pi$
$48$	0.00482436	−	0.00482436i	0.000696336	−	0.000696336i
$49$	0.702783	+	6.96463i	0.100398	+	0.994947i
$50$	−4.86108	+	1.17042i	−0.687461	+	0.165522i
$51$	0.00873261	+	0.00504178i	0.00122281	+	0.000705990i
$52$	−4.05754	−	1.08722i	−0.562680	−	0.150770i
$53$	−6.71753	−	1.79996i	−0.922723	−	0.247243i	−0.233974	−	0.972243i	$-0.575173\pi$
$53$	−6.71753	−	1.79996i	−0.922723	−	0.247243i	−0.688749	+	0.725000i	$0.741840\pi$
$54$	−0.0204679	+	0.0354514i	−0.00278532	+	0.00482432i
$55$	−4.65268	+	5.77517i	−0.627368	+	0.778723i
$56$	−0.132982	−	2.64241i	−0.0177704	−	0.353107i
$57$	−0.0135414	+	0.0135414i	−0.00179360	+	0.00179360i
$58$	−2.75216	−	10.2712i	−0.361376	−	1.34867i
$59$	7.82626	−	4.51850i	1.01889	−	0.588258i	0.105110	−	0.994461i	$-0.466481\pi$
$59$	7.82626	−	4.51850i	1.01889	−	0.588258i	0.913783	+	0.406203i	$0.133147\pi$
$60$	0.00779596	−	0.0131136i	0.00100645	−	0.00169296i
$61$	7.92908	+	4.57785i	1.01521	+	0.586134i	0.912714	−	0.408599i	$-0.133982\pi$
$61$	7.92908	+	4.57785i	1.01521	+	0.586134i	0.102500	+	0.994733i	$0.467316\pi$
$62$	5.72904	−	5.72904i	0.727589	−	0.727589i
$63$	2.43703	+	7.55374i	0.307037	+	0.951681i
$64$			1.00000i			0.125000i
$65$	−9.39224	−	0.119867i	−1.16496	−	0.0148677i
$66$	−0.00270869	−	0.0224655i	−0.000333416	−	0.00276532i
$67$	−0.482205	+	1.79961i	−0.0589107	+	0.219858i	−0.989105	−	0.147209i	$-0.952971\pi$
$67$	−0.482205	+	1.79961i	−0.0589107	+	0.219858i	0.930195	+	0.367066i	$0.119638\pi$
$68$	−1.42759	+	0.382521i	−0.173120	+	0.0463875i
$69$			0.0142829i			0.00171946i
$70$	−1.74448	−	5.65303i	−0.208506	−	0.675667i
$71$	−7.36990			−0.874646			−0.437323	−	0.899305i	$-0.644073\pi$
$71$	−7.36990			−0.874646			−0.437323	+	0.899305i	$0.644073\pi$
$72$	−0.776445	−	2.89773i	−0.0915049	−	0.341501i
$73$	3.08095	−	11.4983i	0.360598	−	1.34577i	−0.512694	−	0.858572i	$-0.671352\pi$
$73$	3.08095	−	11.4983i	0.360598	−	1.34577i	0.873292	−	0.487198i	$-0.161981\pi$
$74$	−2.81909	−	4.88281i	−0.327713	−	0.567616i
$75$	0.00966724	−	0.0327149i	0.00111628	−	0.00377759i
$76$		−	2.80688i		−	0.321971i
$77$	−7.16653	−	5.06367i	−0.816702	−	0.577059i
$78$	0.0202656	−	0.0202656i	0.00229462	−	0.00229462i
$79$	2.93208	−	5.07850i	0.329884	−	0.571376i	−0.652604	−	0.757699i	$-0.726324\pi$
$79$	2.93208	−	5.07850i	0.329884	−	0.571376i	0.982489	+	0.186323i	$0.0596569\pi$
$80$	0.551127	+	2.16709i	0.0616179	+	0.242288i
$81$	4.49979	+	7.79387i	0.499977	+	0.865985i
$82$	2.22661	−	0.596619i	0.245888	−	0.0658856i
$83$	−5.05490	−	5.05490i	−0.554848	−	0.554848i	0.372988	−	0.927836i	$-0.378333\pi$
$83$	−5.05490	−	5.05490i	−0.554848	−	0.554848i	−0.927836	+	0.372988i	$0.878333\pi$
$84$	0.0160666	+	0.00822840i	0.00175301	+	0.000897792i
$85$	−2.88289	+	1.61574i	−0.312693	+	0.175251i
$86$	3.94890	−	6.83970i	0.425821	−	0.737543i
$87$	0.0700769	+	0.0187771i	0.00751304	+	0.00201311i
$88$	2.60908	+	2.04761i	0.278128	+	0.218276i
$89$	14.8653	+	8.58249i	1.57572	+	0.909742i	0.995447	+	0.0953198i	$0.0303874\pi$
$89$	14.8653	+	8.58249i	1.57572	+	0.909742i	0.580273	+	0.814422i	$0.302946\pi$
$90$	−3.27964	−	5.85171i	−0.345705	−	0.616825i
$91$	−0.558613	−	11.0999i	−0.0585585	−	1.16359i
$92$	−1.48029	−	1.48029i	−0.154331	−	0.154331i
$93$	0.0143070	+	0.0533943i	0.00148356	+	0.00553674i
$94$	5.22328	+	9.04699i	0.538740	+	0.933126i
$95$	−1.54695	−	6.08275i	−0.158713	−	0.624077i
$96$	−0.00590861	−	0.00341134i	−0.000603045	−	0.000348168i
$97$	−3.34628	−	3.34628i	−0.339764	−	0.339764i	0.516515	−	0.856278i	$-0.327229\pi$
$97$	−3.34628	−	3.34628i	−0.339764	−	0.339764i	−0.856278	+	0.516515i	$0.827229\pi$
$98$	6.54542	−	2.48142i	0.661188	−	0.250661i
$99$	−9.15026	−	3.90764i	−0.919636	−	0.392732i
$100$	2.38868	+	4.39252i	0.238868	+	0.439252i
$101$	−4.44480	+	2.56621i	−0.442274	+	0.255347i	−0.704562	−	0.709643i	$-0.748856\pi$
$101$	−4.44480	+	2.56621i	−0.442274	+	0.255347i	0.262288	+	0.964990i	$0.415523\pi$
$102$	0.00260981	−	0.00973996i	0.000258410	−	0.000964400i
$103$	2.16231	+	8.06984i	0.213058	+	0.795145i	0.986841	+	0.161694i	$0.0516957\pi$
$103$	2.16231	+	8.06984i	0.213058	+	0.795145i	−0.773783	+	0.633451i	$0.781638\pi$
$104$			4.20068i			0.411910i
$105$	0.0393526	+	0.00897692i	0.00384042	+	0.000876058i
$106$			6.95449i			0.675480i
$107$	−2.10932	−	7.87209i	−0.203916	−	0.761024i	−0.989777	−	0.142621i	$-0.954447\pi$
$107$	−2.10932	−	7.87209i	−0.203916	−	0.761024i	0.785862	−	0.618402i	$-0.212220\pi$
$108$	0.0395409	+	0.0105949i	0.00380482	+	0.00101950i
$109$	−4.32671	−	7.49408i	−0.414423	−	0.717802i	0.580944	−	0.813943i	$-0.302683\pi$
$109$	−4.32671	−	7.49408i	−0.414423	−	0.717802i	−0.995368	+	0.0961409i	$0.969350\pi$
$110$	6.78258	+	2.99942i	0.646694	+	0.285984i
$111$	0.0384675			0.00365117
$112$	−2.51795	+	0.812356i	−0.237924	+	0.0767604i
$113$	−11.9840	+	11.9840i	−1.12736	+	1.12736i	−0.136757	+	0.990605i	$0.543668\pi$
$113$	−11.9840	+	11.9840i	−1.12736	+	1.12736i	−0.990605	+	0.136757i	$0.956332\pi$
$114$	0.0165847	+	0.00957521i	0.00155330	+	0.000896801i
$115$	−4.02375	−	2.39209i	−0.375217	−	0.223064i
$116$	−9.20889	+	5.31676i	−0.855024	+	0.493649i
$117$	−3.26160	−	12.1724i	−0.301535	−	1.12534i
$118$	−6.39012	−	6.39012i	−0.588258	−	0.588258i
$119$	−2.12288	−	3.28385i	−0.194604	−	0.301030i
$120$	−0.0146845	−	0.00413626i	−0.00134051	−	0.000377587i
$121$	10.6848	−	2.61455i	0.971342	−	0.237686i
$122$	2.36967	−	8.84374i	0.214540	−	0.800674i
$123$	−0.00407054	+	0.0151915i	−0.000367028	+	0.00136977i
$124$	−7.01662	−	4.05104i	−0.630111	−	0.363795i
$125$	7.59731	+	8.20250i	0.679524	+	0.733654i
$126$	6.66560	−	4.30904i	0.593819	−	0.383880i
$127$	1.41919	−	1.41919i	0.125933	−	0.125933i	−0.641331	−	0.767264i	$-0.721618\pi$
$127$	1.41919	−	1.41919i	0.125933	−	0.125933i	0.767264	+	0.641331i	$0.221618\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$	0.0269420	+	0.0466650i	0.00237211	+	0.00410862i
$130$	2.31511	+	9.10323i	0.203048	+	0.798406i
$131$	−2.95245	−	1.70460i	−0.257957	−	0.148931i	0.365445	−	0.930833i	$-0.380917\pi$
$131$	−2.95245	−	1.70460i	−0.257957	−	0.148931i	−0.623402	+	0.781901i	$0.714250\pi$
$132$	−0.0209990	+	0.00843090i	−0.00182773	+	0.000733816i
$133$	7.06759	−	2.28018i	0.612838	−	0.197717i
$134$	1.86310			0.160947
$135$	0.0915276	+	0.00116811i	0.00787744	+	0.000100535i
$136$	0.738974	+	1.27994i	0.0633665	+	0.109754i
$137$	−1.12980	+	4.21648i	−0.0965255	+	0.360238i	−0.997246	−	0.0741604i	$-0.976372\pi$
$137$	−1.12980	+	4.21648i	−0.0965255	+	0.360238i	0.900721	+	0.434398i	$0.143039\pi$
$138$	0.0137962	−	0.00369669i	0.00117441	−	0.000314683i
$139$	−9.64889			−0.818408			−0.409204	−	0.912443i	$-0.634194\pi$
$139$	−9.64889			−0.818408			−0.409204	+	0.912443i	$0.634194\pi$
$140$	−5.00890	+	3.14815i	−0.423330	+	0.266068i
$141$	−0.0712735			−0.00600231
$142$	1.90747	+	7.11877i	0.160071	+	0.597394i
$143$	10.9599	+	8.60137i	0.916512	+	0.719283i
$144$	−2.59804	+	1.49998i	−0.216503	+	0.124998i
$145$	−17.0263	+	16.5971i	−1.41395	+	1.37832i
$146$	−11.9039			−0.985172
$147$	−0.00766693	+	0.0471393i	−0.000632358	+	0.00388798i
$148$	−3.98680	+	3.98680i	−0.327713	+	0.327713i
$149$	−9.94665	+	17.2281i	−0.814861	+	1.41138i	0.0945661	+	0.995519i	$0.469854\pi$
$149$	−9.94665	+	17.2281i	−0.814861	+	1.41138i	−0.909427	+	0.415863i	$0.863480\pi$
$150$	−0.0341022		0.000870592i	−0.00278444		7.10835e-5i
$151$	18.0919	−	10.4453i	1.47230	−	0.850030i	0.472781	−	0.881180i	$-0.343250\pi$
$151$	18.0919	−	10.4453i	1.47230	−	0.850030i	0.999515	+	0.0311496i	$0.00991683\pi$
$152$	−2.71124	+	0.726474i	−0.219910	+	0.0589248i
$153$	−3.13515	−	3.13515i	−0.253462	−	0.253462i
$154$	−3.03630	+	8.23292i	−0.244672	+	0.663427i
$155$	−17.4382	−	4.91191i	−1.40067	−	0.394534i
$156$	−0.0248202	−	0.0143299i	−0.00198720	−	0.00114731i
$157$	−4.94775	+	18.4653i	−0.394874	+	1.47369i	0.427122	+	0.904194i	$0.359528\pi$
$157$	−4.94775	+	18.4653i	−0.394874	+	1.47369i	−0.821995	+	0.569494i	$0.807139\pi$
$158$	−5.66433	−	1.51775i	−0.450630	−	0.120746i
$159$	−0.0410914	−	0.0237241i	−0.00325876	−	0.00188144i
$160$	1.95060	−	1.09323i	0.154209	−	0.0864275i
$161$	2.52478	−	4.92983i	0.198981	−	0.388525i
$162$	6.36366	−	6.36366i	0.499977	−	0.499977i
$163$	−4.08693	−	15.2526i	−0.320113	−	1.19468i	−0.919134	−	0.393945i	$-0.871110\pi$
$163$	−4.08693	−	15.2526i	−0.320113	−	1.19468i	0.599021	−	0.800733i	$-0.295557\pi$
$164$	−1.15258	−	1.99633i	−0.0900014	−	0.155887i
$165$	−0.0408601	+	0.0298436i	−0.00318095	+	0.00232332i
$166$	−3.57436	+	6.19097i	−0.277424	+	0.480512i
$167$	−8.56049	+	8.56049i	−0.662431	+	0.662431i	−0.955952	−	0.293522i	$-0.905173\pi$
$167$	−8.56049	+	8.56049i	−0.662431	+	0.662431i	0.293522	+	0.955952i	$0.405173\pi$
$168$	0.00378969	−	0.0176488i	0.000292381	−	0.00136163i
$169$			4.64570i			0.357361i
$170$	2.30683	+	2.36647i	0.176926	+	0.181500i
$171$	7.29238	−	4.21025i	0.557662	−	0.321966i
$172$	−7.62869	−	2.04410i	−0.581682	−	0.155861i
$173$	17.8308	−	4.77775i	1.35565	−	0.363246i	0.493434	−	0.869783i	$-0.335741\pi$
$173$	17.8308	−	4.77775i	1.35565	−	0.363246i	0.862218	+	0.506538i	$0.169075\pi$
$174$		−	0.0725490i		−	0.00549992i
$175$	−9.11969	+	9.58286i	−0.689384	+	0.724396i
$176$	1.30257	−	3.05014i	0.0981846	−	0.229913i
$177$	0.0595555	−	0.0159579i	0.00447647	−	0.00119947i
$178$	4.44262	−	16.5801i	0.332989	−	1.24273i
$179$	−13.0168	+	7.51528i	−0.972924	+	0.561718i	−0.900127	−	0.435628i	$-0.856526\pi$
$179$	−13.0168	+	7.51528i	−0.972924	+	0.561718i	−0.0727979	+	0.997347i	$0.523193\pi$
$180$	−4.80349	+	4.68243i	−0.358031	+	0.349007i
$181$	20.8768			1.55176			0.775881	−	0.630879i	$-0.217306\pi$
$181$	20.8768			1.55176			0.775881	+	0.630879i	$0.217306\pi$
$182$	−10.5771	+	3.41244i	−0.784027	+	0.252947i
$183$	0.0441704	+	0.0441704i	0.00326517	+	0.00326517i
$184$	−1.04672	+	1.81298i	−0.0771656	+	0.133655i
$185$	−6.44250	+	10.8370i	−0.473662	+	0.796750i
$186$	0.0478721	−	0.0276389i	0.00351015	−	0.00202659i
$187$	4.85259	+	0.692786i	0.354857	+	0.0506615i
$188$	7.38684	−	7.38684i	0.538740	−	0.538740i
$189$	0.00544369	+	0.108169i	0.000395970	+	0.00786812i
$190$	−5.47510	+	3.06857i	−0.397206	+	0.222617i
$191$	−4.84645	+	8.39429i	−0.350676	+	0.607389i	−0.986368	−	0.164554i	$-0.947382\pi$
$191$	−4.84645	+	8.39429i	−0.350676	+	0.607389i	0.635692	+	0.771943i	$0.280715\pi$
$192$	−0.00176584	+	0.00659019i	−0.000127438	+	0.000475606i
$193$	1.84033	−	6.86821i	0.132470	−	0.494384i	−0.867526	−	0.497393i	$-0.834291\pi$
$193$	1.84033	−	6.86821i	0.132470	−	0.494384i	0.999995	+	0.00300819i	$0.000957537\pi$
$194$	−2.36618	+	4.09834i	−0.169882	+	0.294244i
$195$	−0.0616850	−	0.0173751i	−0.00441735	−	0.00124426i
$196$	−4.09094	−	5.68016i	−0.292210	−	0.405725i
$197$	5.60165	−	5.60165i	0.399101	−	0.399101i	−0.478815	−	0.877916i	$-0.658933\pi$
$197$	5.60165	−	5.60165i	0.399101	−	0.399101i	0.877916	+	0.478815i	$0.158933\pi$
$198$	−1.40622	+	9.84985i	−0.0999360	+	0.699998i
$199$	13.5690	−	7.83407i	0.961881	−	0.555342i	0.0651297	−	0.997877i	$-0.479254\pi$
$199$	13.5690	−	7.83407i	0.961881	−	0.555342i	0.896751	+	0.442534i	$0.145921\pi$
$200$	3.62461	−	3.44415i	0.256299	−	0.243538i
$201$	−0.00635564	+	0.0110083i	−0.000448292	+	0.000776465i
$202$	3.62916	+	3.62916i	0.255347	+	0.255347i
$203$	−20.8682	−	18.8684i	−1.46466	−	1.32431i
$204$	−0.0100836			−0.000705990
$205$	−3.59797	−	3.69099i	−0.251293	−	0.257790i
$206$	7.23522	−	4.17726i	0.504102	−	0.291043i
$207$	1.62545	−	6.06626i	0.112977	−	0.421634i
$208$	4.05754	−	1.08722i	0.281340	−	0.0753848i
$209$	−3.65614	+	8.56136i	−0.252901	+	0.592202i
$210$	−0.00151415	−	0.0403351i	−0.000104487	−	0.00278338i
$211$			22.7525i			1.56635i	0.621803	+	0.783174i	$0.286401\pi$
$211$			22.7525i			1.56635i	−0.621803	+	0.783174i	$0.713599\pi$
$212$	6.71753	−	1.79996i	0.461362	−	0.123621i
$213$	−0.0485691	−	0.0130140i	−0.00332790	−	0.000891707i
$214$	−7.05792	+	4.07489i	−0.482470	+	0.278554i
$215$	−17.6586	−	0.225365i	−1.20431	−	0.0153698i
$216$		−	0.0409357i		−	0.00278532i
$217$	4.50035	−	20.9584i	0.305503	−	1.42275i
$218$	−6.11889	+	6.11889i	−0.414423	+	0.414423i
$219$	0.0406081	−	0.0703353i	0.00274404	−	0.00475282i
$220$	1.14176	−	7.32778i	0.0769773	−	0.494039i
$221$	3.10419	+	5.37662i	0.208811	+	0.361670i
$222$	−0.00995612	−	0.0371568i	−0.000668211	−	0.00249380i
$223$	0.164394	−	0.164394i	0.0110086	−	0.0110086i	−0.701581	−	0.712590i	$-0.747522\pi$
$223$	0.164394	−	0.164394i	0.0110086	−	0.0110086i	0.712590	+	0.701581i	$0.247522\pi$
$224$	1.43637	+	2.22190i	0.0959714	+	0.148457i
$225$	−7.82896	+	12.7945i	−0.521931	+	0.852970i
$226$	14.6774	+	8.47398i	0.976324	+	0.563681i
$227$	−7.06816	−	1.89391i	−0.469130	−	0.125703i	0.0165067	−	0.999864i	$-0.494746\pi$
$227$	−7.06816	−	1.89391i	−0.469130	−	0.125703i	−0.485637	+	0.874161i	$0.661412\pi$
$228$	0.00495649	−	0.0184979i	0.000328252	−	0.00122505i
$229$	23.7722	+	13.7249i	1.57091	+	0.906966i	0.996058	+	0.0887092i	$0.0282742\pi$
$229$	23.7722	+	13.7249i	1.57091	+	0.906966i	0.574853	+	0.818257i	$0.305059\pi$
$230$	−1.26916	+	4.50576i	−0.0836859	+	0.297101i
$231$	−0.0382872	−	0.0460255i	−0.00251911	−	0.00302826i
$232$	7.51903	+	7.51903i	0.493649	+	0.493649i
$233$	3.66194	−	0.981214i	0.239902	−	0.0642815i	−0.136865	−	0.990590i	$-0.543703\pi$
$233$	3.66194	−	0.981214i	0.239902	−	0.0642815i	0.376767	+	0.926308i	$0.377036\pi$
$234$	−10.9135	+	6.30092i	−0.713439	+	0.411904i
$235$	11.9368	−	20.0790i	0.778672	−	1.30981i
$236$	−4.51850	+	7.82626i	−0.294129	+	0.509446i
$237$	0.0282908	−	0.0282908i	0.00183768	−	0.00183768i
$238$	−2.62252	+	2.90047i	−0.169993	+	0.188009i
$239$	−8.67669			−0.561248			−0.280624	−	0.959818i	$-0.590541\pi$
$239$	−8.67669			−0.561248			−0.280624	+	0.959818i	$0.590541\pi$
$240$	−0.000194686		0.0152547i	−1.25669e−5		0.000984688i
$241$	−5.44998	+	3.14654i	−0.351064	+	0.202687i	−0.665154	−	0.746706i	$-0.731634\pi$
$241$	−5.44998	+	3.14654i	−0.351064	+	0.202687i	0.314090	+	0.949393i	$0.398301\pi$
$242$	−5.29088	−	9.64399i	−0.340111	−	0.619939i
$243$	0.0476766	+	0.177932i	0.00305846	+	0.0114143i
$244$	−9.15571			−0.586134
$245$	−11.9959	−	10.0548i	−0.766391	−	0.642375i
$246$	0.0157274			0.00100274
$247$	−11.3890	+	3.05168i	−0.724667	+	0.194174i
$248$	−2.09698	+	7.82602i	−0.133158	+	0.496953i
$249$	−0.0243867	−	0.0422389i	−0.00154544	−	0.00267678i
$250$	5.95668	−	9.46140i	0.376733	−	0.598391i
$251$	8.90327			0.561969			0.280985	−	0.959712i	$-0.409339\pi$
$251$	8.90327			0.561969			0.280985	+	0.959712i	$0.409339\pi$
$252$	−5.88740	−	5.32321i	−0.370871	−	0.335331i
$253$	2.58691	+	6.44327i	0.162638	+	0.405085i
$254$	−1.73815	−	1.00352i	−0.109061	−	0.0629664i
$255$	−0.0218519	+	0.00555732i	−0.00136842	+	0.000348013i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−21.5226	+	5.76695i	−1.34254	+	0.359733i	−0.857376	−	0.514690i	$-0.827907\pi$
$257$	−21.5226	+	5.76695i	−1.34254	+	0.359733i	−0.485164	+	0.874423i	$0.661240\pi$
$258$	0.0381018	−	0.0381018i	0.00237211	−	0.00237211i
$259$	−13.2773	−	6.79987i	−0.825009	−	0.422523i
$260$	8.19385	−	4.59231i	0.508161	−	0.284803i
$261$	−27.6263	−	15.9500i	−1.71002	−	0.987282i
$262$	−0.882364	+	3.29303i	−0.0545126	+	0.203444i
$263$	5.88556	−	21.9652i	0.362919	−	1.35443i	−0.507301	−	0.861769i	$-0.669357\pi$
$263$	5.88556	−	21.9652i	0.362919	−	1.35443i	0.870220	−	0.492663i	$-0.163976\pi$
$264$	0.0135786	+	0.0181014i	0.000835703	+	0.00111406i
$265$	13.5654	−	7.60287i	0.833319	−	0.467040i
$266$	−4.03172	−	6.23661i	−0.247200	−	0.382391i
$267$	0.0828100	+	0.0828100i	0.00506789	+	0.00506789i
$268$	−0.482205	−	1.79961i	−0.0294553	−	0.109929i
$269$	−14.2081	+	8.20307i	−0.866286	+	0.500150i	−0.866112	−	0.499850i	$-0.833389\pi$
$269$	−14.2081	+	8.20307i	−0.866286	+	0.500150i	−0.000173516		1.00000i	$0.500055\pi$
$270$	−0.0225608	−	0.0887112i	−0.00137300	−	0.00539879i
$271$	12.0854	+	6.97749i	0.734133	+	0.423852i	0.819932	−	0.572460i	$-0.194011\pi$
$271$	12.0854	+	6.97749i	0.734133	+	0.423852i	−0.0857989	+	0.996312i	$0.527344\pi$
$272$	1.04507	−	1.04507i	0.0633665	−	0.0633665i
$273$	0.0159193	−	0.0741369i	0.000963477	−	0.00448697i
$274$	4.36522			0.263713
$275$	−1.56425	−	16.5092i	−0.0943278	−	0.995541i
$276$	−0.00714146	−	0.0123694i	−0.000429865	−	0.000744549i
$277$	22.7427	+	6.09390i	1.36648	+	0.366147i	0.866191	−	0.499713i	$-0.166561\pi$
$277$	22.7427	+	6.09390i	1.36648	+	0.366147i	0.500287	+	0.865860i	$0.333228\pi$
$278$	2.49732	+	9.32011i	0.149779	+	0.558983i
$279$		−	24.3059i		−	1.45516i
$280$	4.33728	+	4.02343i	0.259202	+	0.240446i
$281$			1.94356i			0.115943i	0.998318	+	0.0579715i	$0.0184632\pi$
$281$			1.94356i			0.115943i	−0.998318	+	0.0579715i	$0.981537\pi$
$282$	0.0184469	+	0.0688449i	0.00109850	+	0.00409965i
$283$	−6.02558	+	22.4878i	−0.358184	+	1.33676i	0.518247	+	0.855231i	$0.326585\pi$
$283$	−6.02558	+	22.4878i	−0.358184	+	1.33676i	−0.876430	+	0.481528i	$0.840082\pi$
$284$	6.38252	−	3.68495i	0.378733	−	0.218661i
$285$	0.000546461	−	0.0428182i	3.23695e−5	−	0.00253633i
$286$	5.47166	−	12.8126i	0.323546	−	0.757627i
$287$	4.09035	−	4.52387i	0.241446	−	0.267036i
$288$	2.12129	+	2.12129i	0.124998	+	0.124998i
$289$	−12.8307	−	7.40784i	−0.754750	−	0.435755i
$290$	20.4383	+	12.1504i	1.20018	+	0.713498i
$291$	−0.0161437	−	0.0279616i	−0.000946358	−	0.00163914i
$292$	3.08095	+	11.4983i	0.180299	+	0.672885i
$293$	8.65402	+	8.65402i	0.505573	+	0.505573i	0.913164	−	0.407591i	$-0.133631\pi$
$293$	8.65402	+	8.65402i	0.505573	+	0.505573i	−0.407591	+	0.913164i	$0.633631\pi$
$294$	0.0475174	−	0.00479485i	0.00277127	−	0.000279642i
$295$	−5.47870	+	19.4504i	−0.318982	+	1.13245i
$296$	4.88281	+	2.81909i	0.283808	+	0.163857i
$297$	−0.106804	−	0.0838205i	−0.00619742	−	0.00486376i
$298$	19.2155	+	5.14877i	1.11312	+	0.298260i
$299$	−4.39695	+	7.61575i	−0.254282	+	0.440430i
$300$	0.00798538	+	0.0331656i	0.000461036	+	0.00191481i
$301$	−1.05026	−	20.8692i	−0.0605361	−	1.20288i
$302$	−14.7720	−	14.7720i	−0.850030	−	0.850030i
$303$	−0.0338236	+	0.00906300i	−0.00194311	+	0.000520656i
$304$	1.40344	+	2.43083i	0.0804928	+	0.139418i
$305$	−19.8412	+	5.04596i	−1.13610	+	0.288931i
$306$	−2.21689	+	3.83976i	−0.126731	+	0.219505i
$307$	3.59001	−	3.59001i	0.204893	−	0.204893i	−0.597200	−	0.802092i	$-0.703720\pi$
$307$	3.59001	−	3.59001i	0.204893	−	0.204893i	0.802092	+	0.597200i	$0.203720\pi$
$308$	8.73824	+	0.802002i	0.497907	+	0.0456983i
$309$			0.0570001i			0.00324262i
$310$	−0.231195	+	18.1153i	−0.0131310	+	1.02888i
$311$	−3.38054	−	5.85527i	−0.191693	−	0.332022i	0.754119	−	0.656738i	$-0.228064\pi$
$311$	−3.38054	−	5.85527i	−0.191693	−	0.332022i	−0.945811	+	0.324717i	$0.894731\pi$
$312$	−0.00741771	+	0.0276833i	−0.000419945	+	0.00156726i
$313$	−7.25761	−	27.0858i	−0.410224	−	1.53098i	−0.794212	−	0.607640i	$-0.792116\pi$
$313$	−7.25761	−	27.0858i	−0.410224	−	1.53098i	0.383988	−	0.923338i	$-0.374550\pi$
$314$	19.1166			1.07881
$315$	−15.6923	−	8.29115i	−0.884159	−	0.467154i
$316$			5.86415i			0.329884i
$317$	4.26952	−	1.14402i	0.239800	−	0.0642543i	−0.136917	−	0.990583i	$-0.543719\pi$
$317$	4.26952	−	1.14402i	0.239800	−	0.0642543i	0.376718	+	0.926328i	$0.377053\pi$
$318$	−0.0122805	+	0.0458315i	−0.000688656	+	0.00257010i
$319$	35.0138	−	4.22164i	1.96040	−	0.236367i
$320$	−1.56083	−	1.60119i	−0.0872532	−	0.0895091i
$321$		−	0.0556033i		−	0.00310347i
$322$	−5.41531	−	1.16282i	−0.301783	−	0.0648013i
$323$	−2.93338	+	2.93338i	−0.163217	+	0.163217i
$324$	−7.79387	−	4.49979i	−0.432993	−	0.249988i
$325$	15.2258	−	14.4678i	0.844577	−	0.802528i
$326$	−13.6751	+	7.89535i	−0.757396	+	0.437283i
$327$	−0.0152805	−	0.0570277i	−0.000845015	−	0.00315364i
$328$	−1.62999	+	1.62999i	−0.0900014	+	0.0900014i
$329$	24.6004	+	12.5990i	1.35627	+	0.694603i
$330$	0.0394021	+	0.0317437i	0.00216901	+	0.00174743i
$331$	−4.90249	+	8.49136i	−0.269465	+	0.466728i	−0.968724	−	0.248141i	$-0.920180\pi$
$331$	−4.90249	+	8.49136i	−0.269465	+	0.466728i	0.699259	+	0.714869i	$0.253514\pi$
$332$	6.90513	+	1.85022i	0.378968	+	0.101544i
$333$	−16.3380	−	4.37774i	−0.895315	−	0.239899i
$334$	10.4844	+	6.05318i	0.573682	+	0.331215i
$335$	−2.03679	−	3.63416i	−0.111282	−	0.198555i
$336$	−0.0180283		0.000907289i	−0.000983523		4.94967e-5i
$337$	−0.178490	+	0.178490i	−0.00972298	+	0.00972298i	−0.711952	−	0.702229i	$-0.752188\pi$
$337$	−0.178490	+	0.178490i	−0.00972298	+	0.00972298i	0.702229	+	0.711952i	$0.252188\pi$
$338$	4.48740	−	1.20239i	0.244082	−	0.0654017i
$339$	−0.100139	+	0.0578152i	−0.00543879	+	0.00314009i
$340$	1.68878	−	2.84071i	0.0915872	−	0.154059i
$341$	16.1249	+	21.4958i	0.873211	+	1.16406i
$342$	−5.95420	−	5.95420i	−0.321966	−	0.321966i
$343$	10.9791	−	14.9151i	0.592813	−	0.805340i
$344$			7.89780i			0.425821i
$345$	−0.0222932	−	0.0228696i	−0.00120023	−	0.00123126i
$346$	−9.22991	−	15.9867i	−0.496203	−	0.859449i
$347$	−0.130836	−	0.0350573i	−0.00702362	−	0.00188197i	0.255306	−	0.966860i	$-0.417824\pi$
$347$	−0.130836	−	0.0350573i	−0.00702362	−	0.00188197i	−0.262329	+	0.964978i	$0.584491\pi$
$348$	−0.0700769	+	0.0187771i	−0.00375652	+	0.00100656i
$349$	16.1087			0.862278			0.431139	−	0.902285i	$-0.358112\pi$
$349$	16.1087			0.862278			0.431139	+	0.902285i	$0.358112\pi$
$350$	11.6167	+	6.32872i	0.620938	+	0.338284i
$351$		−	0.171958i		−	0.00917842i
$352$	−3.28333	−	0.468748i	−0.175002	−	0.0249844i
$353$	13.5832	+	3.63960i	0.722960	+	0.193717i	0.601492	−	0.798879i	$-0.294573\pi$
$353$	13.5832	+	3.63960i	0.722960	+	0.193717i	0.121468	+	0.992595i	$0.461240\pi$
$354$	−0.0308282	−	0.0533960i	−0.00163850	−	0.00283797i
$355$	11.8006	−	11.5032i	0.626310	−	0.610525i
$356$	−17.1650			−0.909742
$357$	−0.00819143	−	0.0253899i	−0.000433536	−	0.00134378i
$358$	10.6282	+	10.6282i	0.561718	+	0.561718i
$359$	5.61826	−	9.73111i	0.296520	−	0.513588i	−0.678817	−	0.734307i	$-0.737507\pi$
$359$	5.61826	−	9.73111i	0.296520	−	0.513588i	0.975337	+	0.220719i	$0.0708404\pi$
$360$	5.76611	+	3.42791i	0.303901	+	0.180667i
$361$	5.56071	+	9.63144i	0.292669	+	0.506918i
$362$	−5.40332	−	20.1655i	−0.283992	−	1.05987i
$363$	0.0750315	+	0.00163716i	0.00393813	+	8.59287e-5i
$364$	6.03372	+	9.33349i	0.316253	+	0.489208i
$365$	13.0137	+	23.2197i	0.681167	+	1.21538i
$366$	0.0312332	−	0.0540975i	0.00163259	−	0.00282772i
$367$	1.97745	−	7.37996i	0.103222	−	0.385231i	−0.894915	−	0.446236i	$-0.852764\pi$
$367$	1.97745	−	7.37996i	0.103222	−	0.385231i	0.998137	+	0.0610055i	$0.0194307\pi$
$368$	2.02212	+	0.541825i	0.105410	+	0.0282446i
$369$	3.45769	−	5.98889i	0.180000	−	0.311769i
$370$	12.1352	+	3.41817i	0.630877	+	0.177702i
$371$	9.98922	+	15.4522i	0.518614	+	0.802238i
$372$	−0.0390874	−	0.0390874i	−0.00202659	−	0.00202659i
$373$	−17.0724	+	4.57455i	−0.883978	+	0.236861i	−0.672123	−	0.740440i	$-0.734617\pi$
$373$	−17.0724	+	4.57455i	−0.883978	+	0.236861i	−0.211855	+	0.977301i	$0.567951\pi$
$374$	−0.586764	−	4.86655i	−0.0303409	−	0.251643i
$375$	0.0355834	+	0.0674716i	0.00183752	+	0.00348422i
$376$	−9.04699	−	5.22328i	−0.466563	−	0.269370i
$377$	31.5850	+	31.5850i	1.62671	+	1.62671i
$378$	0.103074	−	0.0332544i	0.00530156	−	0.00171042i
$379$		−	13.0024i		−	0.667886i	−0.942593	−	0.333943i	$-0.891621\pi$
$379$		−	13.0024i		−	0.667886i	0.942593	−	0.333943i	$-0.108379\pi$
$380$	4.38107	+	4.49434i	0.224744	+	0.230555i
$381$	0.0118588	−	0.00684668i	0.000607545	−	0.000350766i
$382$	9.36261	+	2.50870i	0.479033	+	0.128356i
$383$	−3.54099	−	13.2151i	−0.180936	−	0.675262i	−0.995464	−	0.0951382i	$-0.969671\pi$
$383$	−3.54099	−	13.2151i	−0.180936	−	0.675262i	0.814528	−	0.580124i	$-0.196996\pi$
$384$	0.00682267			0.000348168
$385$	19.3785	−	3.07787i	0.987620	−	0.156863i
$386$	−7.11049			−0.361914
$387$	−6.13221	−	22.8857i	−0.311718	−	1.16335i
$388$	4.57111	+	1.22482i	0.232063	+	0.0621810i
$389$	18.1394	−	10.4728i	0.919706	−	0.530993i	0.0361649	−	0.999346i	$-0.488486\pi$
$389$	18.1394	−	10.4728i	0.919706	−	0.530993i	0.883541	+	0.468353i	$0.155153\pi$
$390$	−0.000817814		0.0640801i	−4.14116e−5		0.00324482i
$391$			3.09401i			0.156471i
$392$	−4.42780	+	5.42168i	−0.223637	+	0.273836i
$393$	−0.0164472	−	0.0164472i	−0.000829650	−	0.000829650i
$394$	−6.86059	−	3.96096i	−0.345632	−	0.199551i
$395$	3.23189	+	12.7081i	0.162614	+	0.639415i
$396$	9.87818	−	1.19102i	0.496397	−	0.0598510i
$397$	2.55183	−	0.683761i	0.128073	−	0.0343170i	−0.194213	−	0.980959i	$-0.562215\pi$
$397$	2.55183	−	0.683761i	0.128073	−	0.0343170i	0.322286	+	0.946642i	$0.395549\pi$
$398$	−11.0790	−	11.0790i	−0.555342	−	0.555342i
$399$	0.0506032	−	0.00254665i	0.00253333	−	0.000127492i
$400$	−4.26492	−	2.60969i	−0.213246	−	0.130485i
$401$	7.16663	−	12.4130i	0.357884	−	0.619874i	−0.629723	−	0.776820i	$-0.716831\pi$
$401$	7.16663	−	12.4130i	0.357884	−	0.619874i	0.987607	+	0.156946i	$0.0501648\pi$
$402$	0.0122782	+	0.00328992i	0.000612379	+	0.000164086i
$403$	−8.80872	+	32.8746i	−0.438793	+	1.63760i
$404$	2.56621	−	4.44480i	0.127673	−	0.221137i
$405$	−19.3699	−	5.45602i	−0.962499	−	0.271112i
$406$	−12.8244	+	25.0407i	−0.636466	+	1.24275i
$407$	17.3534	−	6.96721i	0.860174	−	0.345352i
$408$	0.00260981	+	0.00973996i	0.000129205	+	0.000482200i
$409$	−7.47005	−	12.9385i	−0.369370	−	0.639768i	0.620097	−	0.784525i	$-0.287093\pi$
$409$	−7.47005	−	12.9385i	−0.369370	−	0.639768i	−0.989467	+	0.144757i	$0.953760\pi$
$410$	−2.63400	+	4.43067i	−0.130084	+	0.218815i
$411$	−0.0148912	+	0.0257924i	−0.000734530	+	0.00127224i
$412$	−5.90753	−	5.90753i	−0.291043	−	0.291043i
$413$	−23.3768	−	5.01964i	−1.15030	−	0.247000i
$414$	−6.28025			−0.308658
$415$	15.9837	+	0.203990i	0.784609	+	0.0100135i
$416$	−2.10034	−	3.63789i	−0.102978	−	0.178362i
$417$	−0.0635880	−	0.0170384i	−0.00311392	−	0.000834372i
$418$	9.21592	+	1.31572i	0.450765	+	0.0643540i
$419$		−	34.8851i		−	1.70425i	−0.523338	−	0.852125i	$-0.675313\pi$
$419$		−	34.8851i		−	1.70425i	0.523338	−	0.852125i	$-0.324687\pi$
$420$	−0.0385688	+	0.0119020i	−0.00188196	+	0.000580760i
$421$	−6.15419			−0.299937			−0.149968	−	0.988691i	$-0.547917\pi$
$421$	−6.15419			−0.299937			−0.149968	+	0.988691i	$0.547917\pi$
$422$	21.9772	−	5.88879i	1.06984	−	0.286662i
$423$	30.2714	+	8.11118i	1.47184	+	0.394379i
$424$	−3.47725	−	6.02277i	−0.168870	−	0.292491i
$425$	2.09415	−	7.08680i	0.101581	−	0.343760i
$426$			0.0502824i			0.00243619i
$427$	−7.43769	−	23.0536i	−0.359935	−	1.11564i
$428$	5.76277	+	5.76277i	0.278554	+	0.278554i
$429$	0.0570392	+	0.0760381i	0.00275388	+	0.00367115i
$430$	4.35269	+	17.1152i	0.209905	+	0.825369i
$431$	−27.4360	+	15.8402i	−1.32155	+	0.762994i	−0.983975	−	0.178306i	$-0.942938\pi$
$431$	−27.4360	+	15.8402i	−1.32155	+	0.762994i	−0.337570	+	0.941300i	$0.609605\pi$
$432$	−0.0395409	+	0.0105949i	−0.00190241	+	0.000509749i
$433$	−4.20694	+	4.20694i	−0.202173	+	0.202173i	−0.800930	−	0.598758i	$-0.795661\pi$
$433$	−4.20694	+	4.20694i	−0.202173	+	0.202173i	0.598758	+	0.800930i	$0.295661\pi$
$434$	−21.4090	+	1.07743i	−1.02767	+	0.0517182i
$435$	−0.141514	+	0.0793128i	−0.00678508	+	0.00380276i
$436$	7.49408	+	4.32671i	0.358901	+	0.207212i
$437$	−5.67584	−	1.52084i	−0.271512	−	0.0727515i
$438$	−0.0784488	−	0.0210203i	−0.00374843	−	0.00100439i
$439$	4.47112	−	7.74422i	0.213395	−	0.369611i	−0.739380	−	0.673289i	$-0.764881\pi$
$439$	4.47112	−	7.74422i	0.213395	−	0.369611i	0.952775	+	0.303677i	$0.0982145\pi$
$440$	−7.37360	+	0.793715i	−0.351523	+	0.0378389i
$441$	8.62093	−	19.1485i	0.410521	−	0.911834i
$442$	4.38999	−	4.38999i	0.208811	−	0.208811i
$443$	−8.25789	−	30.8189i	−0.392344	−	1.46425i	−0.826257	−	0.563294i	$-0.809534\pi$
$443$	−8.25789	−	30.8189i	−0.392344	−	1.46425i	0.433912	−	0.900955i	$-0.357133\pi$
$444$	−0.0333138	+	0.0192338i	−0.00158100	+	0.000912793i
$445$	−37.1980	+	9.46008i	−1.76335	+	0.448451i
$446$	−0.201340	−	0.116244i	−0.00953373	−	0.00550430i
$447$	−0.0959724	+	0.0959724i	−0.00453934	+	0.00453934i
$448$	1.77443	−	1.96250i	0.0838340	−	0.0927192i
$449$		−	11.3718i		−	0.536669i	−0.963326	−	0.268335i	$-0.913527\pi$
$449$		−	11.3718i		−	0.536669i	0.963326	−	0.268335i	$-0.0864733\pi$
$450$	14.3849	+	4.25072i	0.678109	+	0.200381i
$451$	0.915178	+	7.59038i	0.0430941	+	0.357417i
$452$	4.38645	−	16.3705i	0.206321	−	0.770002i
$453$	0.137674	−	0.0368896i	0.00646848	−	0.00173322i
$454$			7.31749i			0.343427i
$455$	18.2195	+	16.9011i	0.854145	+	0.792337i
$456$	−0.0191504			−0.000896801
$457$	0.638437	+	2.38268i	0.0298648	+	0.111457i	0.979249	−	0.202659i	$-0.0649584\pi$
$457$	0.638437	+	2.38268i	0.0298648	+	0.111457i	−0.949384	+	0.314116i	$0.898292\pi$
$458$	7.10452	−	26.5144i	0.331973	−	1.23894i
$459$	−0.0302504	−	0.0523953i	−0.00141197	−	0.00244560i
$460$	4.68071	+	0.0597370i	0.218239	+	0.00278525i
$461$		−	28.8909i		−	1.34558i	−0.739832	−	0.672792i	$-0.765095\pi$
$461$		−	28.8909i		−	1.34558i	0.739832	−	0.672792i	$-0.234905\pi$
$462$	−0.0345478	+	0.0488949i	−0.00160731	+	0.00227480i
$463$	12.4379	−	12.4379i	0.578039	−	0.578039i	−0.356324	−	0.934363i	$-0.615970\pi$
$463$	12.4379	−	12.4379i	0.578039	−	0.578039i	0.934363	+	0.356324i	$0.115970\pi$
$464$	5.31676	−	9.20889i	0.246824	−	0.427512i
$465$	−0.106248	−	0.0631636i	−0.00492712	−	0.00292914i
$466$	−1.89556	−	3.28321i	−0.0878102	−	0.152092i
$467$	−19.7990	+	5.30512i	−0.916188	+	0.245492i	−0.685955	−	0.727644i	$-0.740615\pi$
$467$	−19.7990	+	5.30512i	−0.916188	+	0.245492i	−0.230233	+	0.973136i	$0.573949\pi$
$468$	8.91085	+	8.91085i	0.411904	+	0.411904i
$469$	4.13961	−	2.67609i	0.191150	−	0.123570i
$470$	−22.4843	−	6.33326i	−1.03712	−	0.292131i
$471$	−0.0652133	+	0.112953i	−0.00300487	+	0.00520459i
$472$	8.72906	+	2.33895i	0.401788	+	0.107659i
$473$	20.6060	+	16.1717i	0.947463	+	0.743573i
$474$	−0.0346490	−	0.0200046i	−0.00159148	−	0.000918841i
$475$	11.9711	+	7.32510i	0.549272	+	0.336098i
$476$	3.48039	+	1.78246i	0.159524	+	0.0816990i
$477$	14.7525	+	14.7525i	0.675470	+	0.675470i
$478$	2.24569	+	8.38104i	0.102716	+	0.383340i
$479$	−4.23373	−	7.33304i	−0.193444	−	0.335055i	0.752945	−	0.658083i	$-0.228632\pi$
$479$	−4.23373	−	7.33304i	−0.193444	−	0.335055i	−0.946389	+	0.323028i	$0.895299\pi$
$480$	0.0147853	−	0.00376016i	0.000674854	−	0.000171627i
$481$	20.5111	+	11.8421i	0.935227	+	0.539954i
$482$	4.44989	+	4.44989i	0.202687	+	0.202687i
$483$	0.0253441	−	0.0280302i	0.00115319	−	0.00127542i
$484$	−7.94600	+	7.60665i	−0.361182	+	0.345757i
$485$	10.5810	+	0.135039i	0.480459	+	0.00613179i
$486$	0.159529	−	0.0921041i	0.00723639	−	0.00417793i
$487$	−6.09808	+	22.7584i	−0.276331	+	1.03128i	0.678614	+	0.734495i	$0.262581\pi$
$487$	−6.09808	+	22.7584i	−0.276331	+	1.03128i	−0.954944	+	0.296785i	$0.904086\pi$
$488$	2.36967	+	8.84374i	0.107270	+	0.400337i
$489$		−	0.107735i		−	0.00487193i
$490$	−6.60738	+	14.1895i	−0.298491	+	0.641017i
$491$		−	14.8951i		−	0.672208i	−0.941825	−	0.336104i	$-0.890891\pi$
$491$		−	14.8951i		−	0.672208i	0.941825	−	0.336104i	$-0.109109\pi$
$492$	−0.00407054	−	0.0151915i	−0.000183514	−	0.000684884i
$493$	15.1803	+	4.06754i	0.683685	+	0.183193i
$494$	5.89540	+	10.2111i	0.265247	+	0.459421i
$495$	20.7505	−	8.02517i	0.932663	−	0.360705i
$496$	8.10209			0.363795
$497$	14.4634	+	13.0774i	0.648772	+	0.586601i
$498$	−0.0344879	+	0.0344879i	−0.00154544	+	0.00154544i
$499$	−22.0026	−	12.7032i	−0.984972	−	0.568674i	−0.0812047	−	0.996697i	$-0.525877\pi$
$499$	−22.0026	−	12.7032i	−0.984972	−	0.568674i	−0.903768	+	0.428023i	$0.859210\pi$
$500$	−10.6807	−	3.30492i	−0.477656	−	0.147800i
$501$	−0.0715317	+	0.0412989i	−0.00319580	+	0.00184510i
$502$	−2.30434	−	8.59990i	−0.102848	−	0.383832i
$503$	−4.20904	−	4.20904i	−0.187672	−	0.187672i	0.607017	−	0.794689i	$-0.292366\pi$
$503$	−4.20904	−	4.20904i	−0.187672	−	0.187672i	−0.794689	+	0.607017i	$0.792366\pi$
$504$	−3.61806	+	7.06454i	−0.161161	+	0.314680i
$505$	3.11154	−	11.0466i	0.138462	−	0.491566i
$506$	5.55418	−	4.16641i	0.246913	−	0.185219i
$507$	−0.00820354	+	0.0306160i	−0.000364332	+	0.00135971i
$508$	−0.519460	+	1.93865i	−0.0230473	+	0.0860137i
$509$	3.72279	+	2.14935i	0.165010	+	0.0952684i	0.580231	−	0.814452i	$-0.302962\pi$
$509$	3.72279	+	2.14935i	0.165010	+	0.0952684i	−0.415221	+	0.909721i	$0.636296\pi$
$510$	0.0110236	+	0.0196690i	0.000488135	+	0.000870958i
$511$	−26.4492	+	17.0984i	−1.17005	+	0.756387i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	0.110986	−	0.0297387i	0.00490017	−	0.00131300i
$514$	11.1409	+	19.2966i	0.491404	+	0.851137i
$515$	−16.0579	−	9.54633i	−0.707597	−	0.420661i
$516$	−0.0466650	−	0.0269420i	−0.00205431	−	0.00118606i
$517$	−32.1527	+	12.9090i	−1.41407	+	0.567738i
$518$	−3.13176	+	14.5848i	−0.137602	+	0.640819i
$519$	0.125945			0.00552838
$520$	−6.55656	−	6.72607i	−0.287524	−	0.294958i
$521$	−2.28078	−	3.95042i	−0.0999226	−	0.173071i	0.811730	−	0.584033i	$-0.198526\pi$
$521$	−2.28078	−	3.95042i	−0.0999226	−	0.173071i	−0.911652	+	0.410962i	$0.865193\pi$
$522$	−8.25634	+	30.8131i	−0.361370	+	1.34865i
$523$	10.3473	−	2.77256i	0.452457	−	0.121235i	−0.0253919	−	0.999678i	$-0.508083\pi$
$523$	10.3473	−	2.77256i	0.452457	−	0.121235i	0.477849	+	0.878442i	$0.341417\pi$
$524$	3.40919			0.148931
$525$	−0.0770223	+	0.0470490i	−0.00336153	+	0.00205339i
$526$	−22.7400			−0.991513
$527$	3.09922	+	11.5664i	0.135004	+	0.503842i
$528$	0.0139702	−	0.0178009i	0.000607975	−	0.000774683i
$529$	16.1232	−	9.30873i	0.701009	−	0.404728i
$530$	−10.8548	−	11.1354i	−0.471502	−	0.483693i
$531$	−27.1105			−1.17650
$532$	−4.98062	+	5.50849i	−0.215937	+	0.238823i
$533$	−6.84708	+	6.84708i	−0.296580	+	0.296580i
$534$	0.0585555	−	0.101421i	0.00253394	−	0.00438892i
$535$	15.6644	+	9.31239i	0.677232	+	0.402610i
$536$	−1.61349	+	0.931548i	−0.0696921	+	0.0402367i
$537$	−0.0990543	+	0.0265415i	−0.00427451	+	0.00114535i
$538$	11.6009	+	11.6009i	0.500150	+	0.500150i
$539$	5.07915	+	22.6540i	0.218775	+	0.975775i
$540$	−0.0798493	+	0.0447522i	−0.00343616	+	0.00192583i
$541$	−12.8665	−	7.42850i	−0.553176	−	0.319376i	0.197226	−	0.980358i	$-0.436807\pi$
$541$	−12.8665	−	7.42850i	−0.553176	−	0.319376i	−0.750402	+	0.660982i	$0.770140\pi$
$542$	3.61181	−	13.4795i	0.155141	−	0.578993i
$543$	0.137582	+	0.0368651i	0.00590422	+	0.00158203i
$544$	−1.27994	−	0.738974i	−0.0548770	−	0.0316832i
$545$	18.6249	+	5.24616i	0.797802	+	0.224721i
$546$	−0.0757310	+	0.00381123i	−0.00324099	+	0.000163106i
$547$	−25.9425	+	25.9425i	−1.10922	+	1.10922i	−0.115968	+	0.993253i	$0.536997\pi$
$547$	−25.9425	+	25.9425i	−1.10922	+	1.10922i	−0.993253	+	0.115968i	$0.963003\pi$
$548$	−1.12980	−	4.21648i	−0.0482627	−	0.180119i
$549$	−13.7334	−	23.7869i	−0.586125	−	1.01520i
$550$	−15.5418	+	5.78384i	−0.662704	+	0.246624i
$551$	−14.9235	+	25.8483i	−0.635763	+	1.10117i
$552$	−0.0100995	+	0.0100995i	−0.000429865	+	0.000429865i
$553$	−14.7656	+	4.76378i	−0.627899	+	0.202576i
$554$		−	23.5450i		−	1.00033i
$555$	−0.0615937	+	0.0600413i	−0.00261451	+	0.00254861i
$556$	8.35618	−	4.82444i	0.354381	−	0.204602i
$557$	34.8347	+	9.33393i	1.47599	+	0.395491i	0.904982	−	0.425451i	$-0.139884\pi$
$557$	34.8347	+	9.33393i	1.47599	+	0.395491i	0.571012	+	0.820942i	$0.306551\pi$
$558$	−23.4777	+	6.29083i	−0.993890	+	0.266312i
$559$			33.1761i			1.40320i
$560$	2.76376	−	5.23083i	0.116790	−	0.221043i
$561$	0.0307562	+	0.0131345i	0.00129853	+	0.000554538i
$562$	1.87733	−	0.503030i	0.0791905	−	0.0212190i
$563$	1.39245	−	5.19670i	0.0586848	−	0.219015i	−0.930356	−	0.366658i	$-0.880502\pi$
$563$	1.39245	−	5.19670i	0.0586848	−	0.219015i	0.989041	+	0.147643i	$0.0471687\pi$
$564$	0.0617246	−	0.0356367i	0.00259908	−	0.00150058i
$565$	0.483613	−	37.8937i	0.0203458	−	1.59420i
$566$	23.2811			0.978576
$567$	4.99886	−	23.2800i	0.209932	−	0.977668i
$568$	−5.21130	−	5.21130i	−0.218661	−	0.218661i
$569$	0.113200	−	0.196068i	0.00474559	−	0.00821961i	−0.863643	−	0.504104i	$-0.831823\pi$
$569$	0.113200	−	0.196068i	0.00474559	−	0.00821961i	0.868388	+	0.495885i	$0.165156\pi$
$570$	−0.0415006	+	0.0105543i	−0.00173827	+	0.000442071i
$571$	18.4953	−	10.6783i	0.774004	−	0.446871i	−0.0602970	−	0.998180i	$-0.519205\pi$
$571$	18.4953	−	10.6783i	0.774004	−	0.446871i	0.834301	+	0.551309i	$0.185871\pi$
$572$	−13.7922	−	1.96906i	−0.576682	−	0.0823306i
$573$	−0.0467620	+	0.0467620i	−0.00195351	+	0.00195351i
$574$	−5.42838	−	2.78011i	−0.226576	−	0.116040i
$575$	10.1764	−	2.45021i	0.424387	−	0.102181i
$576$	1.49998	−	2.59804i	0.0624990	−	0.108251i
$577$	2.33773	−	8.72454i	0.0973212	−	0.363208i	−0.900040	−	0.435807i	$-0.856463\pi$
$577$	2.33773	−	8.72454i	0.0973212	−	0.363208i	0.997361	+	0.0725998i	$0.0231296\pi$
$578$	−3.83458	+	14.3108i	−0.159497	+	0.595252i
$579$	0.0242563	−	0.0420131i	0.00100806	−	0.00174600i
$580$	6.44660	−	22.8867i	0.267680	−	0.950317i
$581$	0.950646	+	18.8898i	0.0394395	+	0.783681i
$582$	−0.0228306	+	0.0228306i	−0.000946358	+	0.000946358i
$583$	−22.8339	−	3.25991i	−0.945684	−	0.135012i
$584$	10.3091	−	5.95194i	0.426592	−	0.246293i
$585$	24.2216	+	14.3996i	1.00144	+	0.595348i
$586$	6.11932	−	10.5990i	0.252787	−	0.437839i
$587$	15.4011	+	15.4011i	0.635672	+	0.635672i	0.949485	−	0.313813i	$-0.101607\pi$
$587$	15.4011	+	15.4011i	0.635672	+	0.635672i	−0.313813	+	0.949485i	$0.601607\pi$
$588$	−0.0169299	−	0.0446573i	−0.000698176	−	0.00184163i
$589$	−22.7416			−0.937051
$590$	20.2057	+	0.257872i	0.831855	+	0.0106164i
$591$	0.0468076	−	0.0270244i	0.00192541	−	0.00111163i
$592$	1.45927	−	5.44607i	0.0599756	−	0.223832i
$593$	−10.6820	+	2.86224i	−0.438658	+	0.117538i	−0.471387	−	0.881926i	$-0.656247\pi$
$593$	−10.6820	+	2.86224i	−0.438658	+	0.117538i	0.0327297	+	0.999464i	$0.489580\pi$
$594$	−0.0533214	+	0.124859i	−0.00218780	+	0.00512304i
$595$	8.52467	+	1.94461i	0.349477	+	0.0797211i
$596$		−	19.8933i		−	0.814861i
$597$	0.103256	−	0.0276674i	0.00422599	−	0.00113235i
$598$	8.49426	+	2.27603i	0.347356	+	0.0930738i
$599$	−8.14111	+	4.70027i	−0.332637	+	0.192048i	−0.657011	−	0.753881i	$-0.728180\pi$
$599$	−8.14111	+	4.70027i	−0.332637	+	0.192048i	0.324374	+	0.945929i	$0.394846\pi$
$600$	0.0299687	−	0.0162972i	0.00122347	−	0.000665329i
$601$			3.59744i			0.146743i	0.997305	+	0.0733713i	$0.0233758\pi$
$601$			3.59744i			0.146743i	−0.997305	+	0.0733713i	$0.976624\pi$
$602$	−19.8863	+	6.41582i	−0.810504	+	0.261489i
$603$	3.95216	−	3.95216i	0.160944	−	0.160944i
$604$	−10.4453	+	18.0919i	−0.425015	+	0.736148i
$605$	−13.0274	+	20.8635i	−0.529640	+	0.848222i
$606$	0.0175084	+	0.0303254i	0.000711229	+	0.00123188i
$607$	0.124485	+	0.464586i	0.00505270	+	0.0188569i	0.968406	−	0.249378i	$-0.0802262\pi$
$607$	0.124485	+	0.464586i	0.00505270	+	0.0188569i	−0.963353	+	0.268235i	$0.913560\pi$
$608$	1.98476	−	1.98476i	0.0804928	−	0.0804928i
$609$	−0.104207	−	0.161197i	−0.00422268	−	0.00653202i
$610$	10.0093	+	17.8591i	0.405265	+	0.723095i
$611$	−38.0035	−	21.9413i	−1.53746	−	0.887651i
$612$	4.28270	+	1.14755i	0.173118	+	0.0463868i
$613$	−0.969883	+	3.61965i	−0.0391732	+	0.146196i	−0.982743	−	0.184979i	$-0.940778\pi$
$613$	−0.969883	+	3.61965i	−0.0391732	+	0.146196i	0.943569	+	0.331175i	$0.107445\pi$
$614$	−4.39685	−	2.53852i	−0.177442	−	0.102446i
$615$	−0.0171936	−	0.0306778i	−0.000693314	−	0.00123705i
$616$	−1.48695	−	8.64806i	−0.0599108	−	0.348440i
$617$	9.50095	+	9.50095i	0.382494	+	0.382494i	0.872000	−	0.489506i	$-0.162823\pi$
$617$	9.50095	+	9.50095i	0.382494	+	0.382494i	−0.489506	+	0.872000i	$0.662823\pi$
$618$	0.0550579	−	0.0147527i	0.00221475	−	0.000593441i
$619$	−32.8356	+	18.9576i	−1.31977	+	0.761971i	−0.983692	−	0.179862i	$-0.942435\pi$
$619$	−32.8356	+	18.9576i	−1.31977	+	0.761971i	−0.336081	+	0.941833i	$0.609101\pi$
$620$	17.5579	−	4.46528i	0.705143	−	0.179330i
$621$	0.0428484	−	0.0742156i	0.00171945	−	0.00297817i
$622$	−4.78081	+	4.78081i	−0.191693	+	0.191693i
$623$	−13.9441	−	43.2206i	−0.558657	−	1.73160i
$624$	0.0286598			0.00114731
$625$	−24.9674	−	1.27561i	−0.998697	−	0.0510245i
$626$	−24.2844	+	14.0206i	−0.970601	+	0.560377i
$627$	−0.0392127	+	0.0499649i	−0.00156600	+	0.00199541i
$628$	−4.94775	−	18.4653i	−0.197437	−	0.736844i
$629$	8.33295			0.332256
$630$	−3.94718	+	17.3035i	−0.157260	+	0.689387i
$631$	−21.0063			−0.836247			−0.418124	−	0.908390i	$-0.637312\pi$
$631$	−21.0063			−0.836247			−0.418124	+	0.908390i	$0.637312\pi$
$632$	5.66433	−	1.51775i	0.225315	−	0.0603730i
$633$	−0.0401772	+	0.149944i	−0.00159690	+	0.00595972i
$634$	−2.21007	−	3.82795i	−0.0877730	−	0.152027i
$635$	−0.0572712	+	4.48751i	−0.00227274	+	0.178081i
$636$	0.0474482			0.00188144
$637$	−18.5997	+	22.7747i	−0.736949	+	0.902368i
$638$	−13.1400	−	32.7281i	−0.520219	−	1.29572i
$639$	19.1473	+	11.0547i	0.757454	+	0.437316i
$640$	−1.14266	+	1.92207i	−0.0451674	+	0.0759763i
$641$	−2.79176	−	4.83547i	−0.110268	−	0.190990i	0.805610	−	0.592446i	$-0.201838\pi$
$641$	−2.79176	−	4.83547i	−0.110268	−	0.190990i	−0.915878	+	0.401456i	$0.868504\pi$
$642$	−0.0537087	+	0.0143912i	−0.00211971	+	0.000567975i
$643$	−14.5678	+	14.5678i	−0.574499	+	0.574499i	−0.933382	−	0.358884i	$-0.883157\pi$
$643$	−14.5678	+	14.5678i	−0.574499	+	0.574499i	0.358884	+	0.933382i	$0.383157\pi$
$644$	0.278390	+	5.53175i	0.0109701	+	0.217981i
$645$	−0.115976	−	0.0326674i	−0.00456653	−	0.00128628i
$646$	3.59264	+	2.07421i	0.141350	+	0.0816087i
$647$	2.00932	−	7.49889i	0.0789946	−	0.294812i	−0.915115	−	0.403193i	$-0.867900\pi$
$647$	2.00932	−	7.49889i	0.0789946	−	0.294812i	0.994109	+	0.108382i	$0.0345668\pi$
$648$	−2.32926	+	8.69293i	−0.0915021	+	0.341490i
$649$	23.9762	−	17.9855i	0.941150	−	0.705994i
$650$	−17.9155	−	10.9625i	−0.702705	−	0.429984i
$651$	0.0666672	−	0.130173i	0.00261290	−	0.00510188i
$652$	11.1657	+	11.1657i	0.437283	+	0.437283i
$653$	12.2714	+	45.7974i	0.480216	+	1.79219i	0.600699	+	0.799475i	$0.294889\pi$
$653$	12.2714	+	45.7974i	0.480216	+	1.79219i	−0.120483	+	0.992715i	$0.538444\pi$
$654$	−0.0511296	+	0.0295197i	−0.00199933	+	0.00115431i
$655$	7.38801	−	1.87890i	0.288674	−	0.0734146i
$656$	1.99633	+	1.15258i	0.0779435	+	0.0450007i
$657$	−25.2515	+	25.2515i	−0.985156	+	0.985156i
$658$	5.80260	−	27.0230i	0.226209	−	1.05347i
$659$	−26.1138			−1.01725			−0.508624	−	0.860989i	$-0.669846\pi$
$659$	−26.1138			−1.01725			−0.508624	+	0.860989i	$0.669846\pi$
$660$	0.0204641	−	0.0462753i	0.000796563	−	0.00180127i
$661$	1.38186	+	2.39345i	0.0537481	+	0.0930944i	0.891648	−	0.452730i	$-0.149550\pi$
$661$	1.38186	+	2.39345i	0.0537481	+	0.0930944i	−0.837900	+	0.545824i	$0.816217\pi$
$662$	9.47089	+	2.53772i	0.368096	+	0.0986311i
$663$	0.0109630	+	0.0409144i	0.000425767	+	0.00158899i
$664$		−	7.14871i		−	0.277424i
$665$	−7.75755	+	14.6823i	−0.300825	+	0.569356i
$666$			16.9143i			0.655416i
$667$	5.76150	+	21.5022i	0.223086	+	0.832569i
$668$	3.13336	−	11.6939i	0.121233	−	0.452449i
$669$	0.00137368		0.000793093i	5.31094e−5		3.06627e-5i
$670$	−2.98316	+	2.90798i	−0.115250	+	0.112345i
$671$	27.9261	+	11.9259i	1.07808	+	0.460395i
$672$	0.00554243	+	0.0171792i	0.000213804	+	0.000662700i
$673$	31.9406	+	31.9406i	1.23122	+	1.23122i	0.963495	+	0.267725i	$0.0862720\pi$
$673$	31.9406	+	31.9406i	1.23122	+	1.23122i	0.267725	+	0.963495i	$0.413728\pi$
$674$	0.218605	+	0.126212i	0.00842035	+	0.00486149i
$675$	−0.148376	+	0.140989i	−0.00571100	+	0.00542666i
$676$	−2.32285	−	4.02329i	−0.0893403	−	0.154742i
$677$	−0.438007	−	1.63466i	−0.0168340	−	0.0628253i	0.956998	−	0.290095i	$-0.0936868\pi$
$677$	−0.438007	−	1.63466i	−0.0168340	−	0.0628253i	−0.973832	+	0.227270i	$0.927020\pi$
$678$	0.0817630	+	0.0817630i	0.00314009	+	0.00314009i
$679$	0.629316	+	12.5048i	0.0241509	+	0.479891i
$680$	−3.18101	−	0.896010i	−0.121986	−	0.0343604i
$681$	−0.0432362	−	0.0249624i	−0.00165681	−	0.000956562i
$682$	16.5900	−	21.1390i	0.635262	−	0.809453i
$683$	−30.4531	−	8.15987i	−1.16525	−	0.312229i	−0.376191	−	0.926542i	$-0.622766\pi$
$683$	−30.4531	−	8.15987i	−1.16525	−	0.312229i	−0.789062	+	0.614313i	$0.789433\pi$
$684$	−4.21025	+	7.29238i	−0.160983	+	0.278831i
$685$	−4.77219	−	8.51480i	−0.182336	−	0.325334i
$686$	−17.2485	−	6.74464i	−0.658550	−	0.257512i
$687$	0.132427	+	0.132427i	0.00505242	+	0.00505242i
$688$	7.62869	−	2.04410i	0.290841	−	0.0779306i
$689$	−14.6068	−	25.2997i	−0.556475	−	0.963842i
$690$	−0.0163205	+	0.0274527i	−0.000621309	+	0.00104511i
$691$	−7.54970	+	13.0765i	−0.287204	+	0.497452i	−0.973141	−	0.230209i	$-0.926059\pi$
$691$	−7.54970	+	13.0765i	−0.287204	+	0.497452i	0.685937	+	0.727661i	$0.259392\pi$
$692$	−13.0531	+	13.0531i	−0.496203	+	0.496203i
$693$	11.0235	+	23.9052i	0.418749	+	0.908085i
$694$			0.135451i			0.00514165i
$695$	15.4497	−	15.0603i	0.586040	−	0.571270i
$696$	0.0362745	+	0.0628293i	0.00137498	+	0.00238154i
$697$	−0.881772	+	3.29082i	−0.0333995	+	0.124649i
$698$	−4.16924	−	15.5598i	−0.157808	−	0.588947i
$699$	0.0258656			0.000978326
$700$	3.10645	−	12.8588i	0.117413	−	0.486019i
$701$		−	35.5069i		−	1.34108i	−0.741874	−	0.670539i	$-0.766063\pi$
$701$		−	35.5069i		−	1.34108i	0.741874	−	0.670539i	$-0.233937\pi$
$702$	−0.166098	+	0.0445059i	−0.00626898	+	0.00167977i
$703$	−4.09600	+	15.2865i	−0.154483	+	0.576540i
$704$	0.397013	+	3.29278i	0.0149630	+	0.124101i
$705$	0.114122	−	0.111246i	0.00429809	−	0.00418977i
$706$		−	14.0624i		−	0.529244i
$707$	13.2765	+	2.85082i	0.499313	+	0.107216i
$708$	−0.0435977	+	0.0435977i	−0.00163850	+	0.00163850i
$709$	28.3368	+	16.3603i	1.06421	+	0.614422i	0.926594	−	0.376063i	$-0.122723\pi$
$709$	28.3368	+	16.3603i	1.06421	+	0.614422i	0.137616	+	0.990486i	$0.456056\pi$
$710$	−14.1654	−	8.42125i	−0.531619	−	0.316044i
$711$	−15.2353	+	8.79609i	−0.571367	+	0.329879i
$712$	4.44262	+	16.5801i	0.166494	+	0.621365i
$713$	−11.9935	+	11.9935i	−0.449159	+	0.449159i
$714$	−0.0224047	+	0.0144837i	−0.000838473	+	0.000542039i
$715$	−30.9741	+	3.33414i	−1.15837	+	0.124690i
$716$	7.51528	−	13.0168i	0.280859	−	0.486462i
$717$	−0.0571810	−	0.0153216i	−0.00213547	−	0.000572196i
$718$	−10.8536	−	2.90822i	−0.405054	−	0.108534i
$719$	11.9428	+	6.89517i	0.445390	+	0.257146i	0.705881	−	0.708330i	$-0.250551\pi$
$719$	11.9428	+	6.89517i	0.445390	+	0.257146i	−0.260491	+	0.965476i	$0.583884\pi$
$720$	1.81873	−	6.45684i	0.0677801	−	0.240632i
$721$	10.0759	−	19.6739i	0.375245	−	0.732694i
$722$	7.86403	−	7.86403i	0.292669	−	0.292669i
$723$	−0.0414727	+	0.0111126i	−0.00154239	+	0.000413281i
$724$	−18.0799	+	10.4384i	−0.671933	+	0.387941i
$725$	1.35687	−	53.1503i	0.0503927	−	1.97395i
$726$	−0.0178382	−	0.0728986i	−0.000662038	−	0.00270552i
$727$	14.1938	+	14.1938i	0.526419	+	0.526419i	0.919503	−	0.393084i	$-0.128592\pi$
$727$	14.1938	+	14.1938i	0.526419	+	0.526419i	−0.393084	+	0.919503i	$0.628592\pi$
$728$	7.45382	−	8.24381i	0.276257	−	0.305536i
$729$		−	26.9975i		−	0.999907i
$730$	19.0603	−	18.5800i	0.705455	−	0.687675i
$731$	5.83627	+	10.1087i	0.215862	+	0.373884i
$732$	−0.0603379	−	0.0161675i	−0.00223015	−	0.000597568i
$733$	−9.66510	+	2.58976i	−0.356989	+	0.0956548i	−0.432856	−	0.901463i	$-0.642494\pi$
$733$	−9.66510	+	2.58976i	−0.356989	+	0.0956548i	0.0758673	+	0.997118i	$0.475827\pi$
$734$	−7.64030			−0.282009
$735$	−0.0613003	−	0.0874456i	−0.00226110	−	0.00322548i
$736$		−	2.09345i		−	0.0771656i
$737$	−0.873323	+	6.11716i	−0.0321693	+	0.225329i
$738$	−6.67974	−	1.78983i	−0.245885	−	0.0658846i
$739$	−22.1837	−	38.4232i	−0.816039	−	1.41342i	−0.908579	−	0.417712i	$-0.862832\pi$
$739$	−22.1837	−	38.4232i	−0.816039	−	1.41342i	0.0925402	−	0.995709i	$-0.470501\pi$
$740$	0.160887	−	12.6063i	0.00591431	−	0.463418i
$741$	−0.0804447			−0.00295521
$742$	12.3403	−	13.6482i	0.453026	−	0.501040i
$743$	−23.6676	−	23.6676i	−0.868280	−	0.868280i	0.124002	−	0.992282i	$-0.460427\pi$
$743$	−23.6676	−	23.6676i	−0.868280	−	0.868280i	−0.992282	+	0.124002i	$0.960427\pi$
$744$	−0.0276389	+	0.0478721i	−0.00101329	+	0.00175507i
$745$	−10.9637	−	43.1105i	−0.401680	−	1.57945i
$746$	8.83735	+	15.3067i	0.323558	+	0.560419i
$747$	5.55058	+	20.7151i	0.203085	+	0.757924i
$748$	−4.54886	+	1.82633i	−0.166323	+	0.0667771i
$749$	−9.82895	+	19.1918i	−0.359142	+	0.701253i
$750$	0.0559629	−	0.0518339i	0.00204348	−	0.00189271i
$751$	−8.41103	+	14.5683i	−0.306923	+	0.531606i	−0.977688	−	0.210064i	$-0.932633\pi$
$751$	−8.41103	+	14.5683i	−0.306923	+	0.531606i	0.670765	+	0.741670i	$0.265966\pi$
$752$	−2.70377	+	10.0906i	−0.0985964	+	0.367967i
$753$	0.0586743	+	0.0157217i	0.00213821	+	0.000572931i
$754$	22.3340	−	38.6836i	0.813356	−	1.40877i
$755$	−12.6650	+	44.9633i	−0.460928	+	1.63638i
$756$	−0.0587988	−	0.0909551i	−0.00213849	−	0.00330800i
$757$	9.61359	+	9.61359i	0.349412	+	0.349412i	0.859890	−	0.510479i	$-0.170532\pi$
$757$	9.61359	+	9.61359i	0.349412	+	0.349412i	−0.510479	+	0.859890i	$0.670532\pi$
$758$	−12.5593	+	3.36526i	−0.456175	+	0.122232i
$759$	0.00567050	+	0.0470305i	0.000205826	+	0.00170710i
$760$	3.20730	−	5.39501i	0.116341	−	0.195698i
$761$	−27.3375	−	15.7833i	−0.990982	−	0.572144i	−0.0854145	−	0.996346i	$-0.527221\pi$
$761$	−27.3375	−	15.7833i	−0.990982	−	0.572144i	−0.905568	+	0.424202i	$0.860555\pi$
$762$	−0.00968267	−	0.00968267i	−0.000350766	−	0.000350766i
$763$	−4.80658	+	22.3845i	−0.174010	+	0.810375i
$764$		−	9.69289i		−	0.350676i
$765$	9.91341	+	0.126519i	0.358420	+	0.00457429i
$766$	−11.8484	+	6.84066i	−0.428099	+	0.247163i
$767$	36.6680	+	9.82516i	1.32400	+	0.354766i
$768$	−0.00176584	−	0.00659019i	−6.37192e−5	−	0.000237803i
$769$	−6.83654			−0.246532			−0.123266	−	0.992374i	$-0.539337\pi$
$769$	−6.83654			−0.246532			−0.123266	+	0.992374i	$0.539337\pi$
$770$	−7.98852	−	17.9216i	−0.287886	−	0.645849i
$771$	−0.152021			−0.00547492
$772$	1.84033	+	6.86821i	0.0662349	+	0.247192i
$773$	−27.7911	−	7.44661i	−0.999578	−	0.267836i	−0.278309	−	0.960492i	$-0.589774\pi$
$773$	−27.7911	−	7.44661i	−0.999578	−	0.267836i	−0.721269	+	0.692655i	$0.756441\pi$
$774$	−20.5188	+	11.8465i	−0.737532	+	0.425814i
$775$	35.5886	−	19.3533i	1.27838	−	0.695191i
$776$		−	4.73236i		−	0.169882i
$777$	−0.0754923	−	0.0682580i	−0.00270827	−	0.00244874i
$778$	−14.8108	−	14.8108i	−0.530993	−	0.530993i
$779$	−5.60345	−	3.23515i	−0.200765	−	0.115911i
$780$	0.0621083	−	0.0157952i	0.00222383	−	0.000565559i
$781$	−24.2674	+	2.92594i	−0.868357	+	0.104699i
$782$	2.98858	−	0.800789i	0.106872	−	0.0286361i
$783$	−0.307797	−	0.307797i	−0.0109998	−	0.0109998i
$784$	6.38294	+	2.87369i	0.227962	+	0.102632i
$785$	−20.8989	−	37.2890i	−0.745914	−	1.33090i
$786$	−0.0116299	+	0.0201436i	−0.000414825	+	0.000718498i
$787$	7.39824	+	1.98235i	0.263719	+	0.0706632i	0.388255	−	0.921552i	$-0.373078\pi$
$787$	7.39824	+	1.98235i	0.263719	+	0.0706632i	−0.124537	+	0.992215i	$0.539744\pi$
$788$	−2.05035	+	7.65200i	−0.0730406	+	0.272591i
$789$	0.0775739	−	0.134362i	0.00276170	−	0.00478341i
$790$	11.4386	−	6.41087i	0.406968	−	0.228089i
$791$	44.7834	−	2.25377i	1.59231	−	0.0801347i
$792$	−3.70710	−	9.23333i	−0.131726	−	0.328092i
$793$	9.95423	+	37.1497i	0.353485	+	1.31922i
$794$	−1.32092	−	2.28791i	−0.0468779	−	0.0811949i
$795$	0.102824	−	0.0261500i	0.00364680	−	0.000927445i
$796$	−7.83407	+	13.5690i	−0.277671	+	0.480941i
$797$	−37.6370	−	37.6370i	−1.33317	−	1.33317i	−0.902519	−	0.430650i	$-0.858284\pi$
$797$	−37.6370	−	37.6370i	−1.33317	−	1.33317i	−0.430650	−	0.902519i	$-0.641716\pi$
$798$	−0.0155569	−	0.0482198i	−0.000550710	−	0.00170696i
$799$	−15.4395			−0.546209
$800$	−1.41693	+	4.79503i	−0.0500960	+	0.169530i
$801$	−25.7471	−	44.5952i	−0.909728	−	1.57569i
$802$	−13.8449	−	3.70972i	−0.488879	−	0.130995i
$803$	5.57992	−	39.0844i	0.196911	−	1.37926i
$804$		−	0.0127113i		−	0.000448292i
$805$	3.65199	+	11.8343i	0.128716	+	0.417106i
$806$	34.0343			1.19881
$807$	−0.108120	+	0.0289706i	−0.00380599	+	0.00101981i
$808$	−4.95753	−	1.32837i	−0.174405	−	0.0467317i
$809$	13.5321	+	23.4383i	0.475765	+	0.824048i	0.999615	−	0.0277622i	$-0.00883811\pi$
$809$	13.5321	+	23.4383i	0.475765	+	0.824048i	−0.523850	+	0.851811i	$0.675505\pi$
$810$	−0.256805	+	20.1220i	−0.00902319	+	0.707016i
$811$		−	4.82247i		−	0.169340i	−0.996409	−	0.0846700i	$-0.973016\pi$
$811$		−	4.82247i		−	0.169340i	0.996409	−	0.0846700i	$-0.0269836\pi$
$812$	27.5066	+	5.90644i	0.965294	+	0.207275i
$813$	0.0673238	+	0.0673238i	0.00236115	+	0.00236115i
$814$	−11.2212	−	14.9588i	−0.393302	−	0.524306i
$815$	30.3508	+	18.0433i	1.06314	+	0.632030i
$816$	0.00873261	−	0.00504178i	0.000305703	−	0.000176497i
$817$	−21.4128	+	5.73755i	−0.749140	+	0.200731i
$818$	−10.5642	+	10.5642i	−0.369370	+	0.369370i
$819$	−15.1983	+	29.6759i	−0.531072	+	1.03696i
$820$	4.96143	+	1.39751i	0.173261	+	0.0488032i
$821$	−13.9076	−	8.02954i	−0.485378	−	0.280233i	0.237277	−	0.971442i	$-0.423745\pi$
$821$	−13.9076	−	8.02954i	−0.485378	−	0.280233i	−0.722655	+	0.691209i	$0.757078\pi$
$822$	0.0287676	+	0.00770827i	0.00100339	+	0.000268857i
$823$	34.3796	+	9.21199i	1.19840	+	0.321110i	0.802200	−	0.597055i	$-0.203663\pi$
$823$	34.3796	+	9.21199i	1.19840	+	0.321110i	0.396198	+	0.918165i	$0.370329\pi$
$824$	−4.17726	+	7.23522i	−0.145522	+	0.252051i
$825$	0.0188438	−	0.111561i	0.000656058	−	0.00388405i
$826$	1.20175	+	23.8794i	0.0418143	+	0.830871i
$827$	2.51890	−	2.51890i	0.0875906	−	0.0875906i	−0.661954	−	0.749545i	$-0.730273\pi$
$827$	2.51890	−	2.51890i	0.0875906	−	0.0875906i	0.749545	+	0.661954i	$0.230273\pi$
$828$	1.62545	+	6.06626i	0.0564883	+	0.210817i
$829$	−2.42105	+	1.39780i	−0.0840867	+	0.0485475i	−0.541454	−	0.840731i	$-0.682126\pi$
$829$	−2.42105	+	1.39780i	−0.0840867	+	0.0485475i	0.457367	+	0.889278i	$0.348793\pi$
$830$	−3.93985	−	15.4919i	−0.136754	−	0.537731i
$831$	0.139118	+	0.0803199i	0.00482596	+	0.00278627i
$832$	−2.97033	+	2.97033i	−0.102978	+	0.102978i
$833$	−1.66083	+	10.2115i	−0.0575445	+	0.353806i
$834$			0.0658312i			0.00227955i
$835$	0.345457	−	27.0684i	0.0119550	−	0.936742i
$836$	−1.11437	−	9.24243i	−0.0385412	−	0.319656i
$837$	0.0858412	−	0.320364i	0.00296710	−	0.0110734i
$838$	−33.6965	+	9.02894i	−1.16402	+	0.311900i
$839$		−	16.7523i		−	0.578355i	−0.957276	−	0.289177i	$-0.906618\pi$
$839$		−	16.7523i		−	0.578355i	0.957276	−	0.289177i	$-0.0933818\pi$
$840$	0.0214788	+	0.0341741i	0.000741090	+	0.00117912i
$841$	84.0716			2.89902
$842$	1.59282	+	5.94449i	0.0548922	+	0.204861i
$843$	−0.00343201	+	0.0128084i	−0.000118205	+	0.000441146i
$844$	−11.3763	−	19.7043i	−0.391587	−	0.678249i
$845$	−7.25116	−	7.43863i	−0.249447	−	0.255897i
$846$		−	31.3392i		−	1.07746i
$847$	−25.6081	−	13.8283i	−0.879906	−	0.475147i
$848$	−4.91757	+	4.91757i	−0.168870	+	0.168870i
$849$	−0.0794195	+	0.137559i	−0.00272567	+	0.00472100i
$850$	−7.38733	−	0.188590i	−0.253383	−	0.00646859i
$851$	5.90163	+	10.2219i	0.202305	+	0.350403i
$852$	0.0485691	−	0.0130140i	0.00166395	−	0.000445854i
$853$	−28.7768	−	28.7768i	−0.985298	−	0.985298i	0.0145959	−	0.999893i	$-0.495354\pi$
$853$	−28.7768	−	28.7768i	−0.985298	−	0.985298i	−0.999893	+	0.0145959i	$0.995354\pi$
$854$	−20.3431	+	13.1510i	−0.696126	+	0.450017i
$855$	−5.10496	+	18.1236i	−0.174586	+	0.619814i
$856$	4.07489	−	7.05792i	0.139277	−	0.241235i
$857$	−22.2485	−	5.96148i	−0.759996	−	0.203640i	−0.142048	−	0.989860i	$-0.545369\pi$
$857$	−22.2485	−	5.96148i	−0.759996	−	0.203640i	−0.617947	+	0.786219i	$0.712036\pi$
$858$	0.0586843	−	0.0747757i	0.00200345	−	0.00255280i
$859$	13.3988	+	7.73578i	0.457160	+	0.263941i	0.710849	−	0.703344i	$-0.248311\pi$
$859$	13.3988	+	7.73578i	0.457160	+	0.263941i	−0.253689	+	0.967286i	$0.581644\pi$
$860$	15.4055	−	8.63412i	0.525322	−	0.294421i
$861$	0.0349446	−	0.0225903i	0.00119091	−	0.000769875i
$862$	22.4014	+	22.4014i	0.762994	+	0.762994i
$863$	4.66845	+	17.4229i	0.158916	+	0.593082i	0.998738	+	0.0502207i	$0.0159925\pi$
$863$	4.66845	+	17.4229i	0.158916	+	0.593082i	−0.839822	+	0.542861i	$0.817341\pi$
$864$	0.0204679	+	0.0354514i	0.000696331	+	0.00120608i
$865$	−21.0932	+	35.4810i	−0.717191	+	1.20639i
$866$	5.15243	+	2.97476i	0.175087	+	0.101086i
$867$	−0.0714761	−	0.0714761i	−0.00242745	−	0.00242745i
$868$	6.58178	+	20.4007i	0.223400	+	0.692444i
$869$	7.63844	−	17.8865i	0.259116	−	0.606756i
$870$	0.113237	+	0.116165i	0.00383909	+	0.00393835i
$871$	−6.77774	+	3.91313i	−0.229655	+	0.132591i
$872$	2.23967	−	8.35856i	0.0758447	−	0.283056i
$873$	3.67442	+	13.7131i	0.124360	+	0.464118i
$874$			5.87606i			0.198761i
$875$	−0.354911	−	29.5783i	−0.0119982	−	0.999928i
$876$			0.0812162i			0.00274404i
$877$	0.123132	+	0.459536i	0.00415788	+	0.0155174i	0.967974	−	0.251052i	$-0.0807765\pi$
$877$	0.123132	+	0.459536i	0.00415788	+	0.0155174i	−0.963816	+	0.266569i	$0.914110\pi$
$878$	−8.63755	−	2.31442i	−0.291503	−	0.0781080i
$879$	0.0417501	+	0.0723133i	0.00140820	+	0.00243907i
$880$	2.67510	+	6.91692i	0.0901776	+	0.233169i
$881$	−18.3306			−0.617574			−0.308787	−	0.951131i	$-0.599923\pi$
$881$	−18.3306			−0.617574			−0.308787	+	0.951131i	$0.599923\pi$
$882$	−20.7273	−	3.37118i	−0.697925	−	0.113513i
$883$	−37.5107	+	37.5107i	−1.26234	+	1.26234i	−0.312380	+	0.949957i	$0.601126\pi$
$883$	−37.5107	+	37.5107i	−1.26234	+	1.26234i	−0.949957	+	0.312380i	$0.898874\pi$
$884$	−5.37662	−	3.10419i	−0.180835	−	0.104405i
$885$	−0.0704520	+	0.118508i	−0.00236822	+	0.00398359i
$886$	−27.6315	+	15.9530i	−0.928297	+	0.535952i
$887$	13.1862	+	49.2116i	0.442750	+	1.65236i	0.721810	+	0.692091i	$0.243310\pi$
$887$	13.1862	+	49.2116i	0.442750	+	1.65236i	−0.279060	+	0.960274i	$0.590023\pi$
$888$	0.0272006	+	0.0272006i	0.000912793	+	0.000912793i
$889$	−5.30341	+	0.266899i	−0.177871	+	0.00895151i
$890$	18.7653	+	33.4820i	0.629014	+	1.12232i
$891$	17.9111	+	23.8770i	0.600043	+	0.799909i
$892$	−0.0601722	+	0.224566i	−0.00201471	+	0.00751902i
$893$	7.58916	−	28.3231i	0.253962	−	0.947797i
$894$	0.117542	+	0.0678627i	0.00393118	+	0.00226967i
$895$	9.11231	−	32.3505i	0.304591	−	1.08136i
$896$	−2.35488	−	1.20604i	−0.0786711	−	0.0402909i
$897$	−0.0424250	+	0.0424250i	−0.00141653	+	0.00141653i
$898$	−10.9843	+	2.94324i	−0.366552	+	0.0982173i
$899$	43.0768	+	74.6113i	1.43669	+	2.48843i
$900$	0.382802	−	14.9949i	0.0127601	−	0.499829i
$901$	−8.90134	−	5.13919i	−0.296547	−	0.171211i
$902$	7.09488	−	2.84853i	0.236234	−	0.0948457i
$903$	0.0299302	−	0.139387i	0.000996014	−	0.00463850i
$904$	−16.9480			−0.563681
$905$	−33.4277	+	32.5852i	−1.11118	+	1.08317i
$906$	−0.0712652	−	0.123435i	−0.00236763	−	0.00410085i
$907$	11.5373	−	43.0579i	0.383091	−	1.42971i	−0.458064	−	0.888919i	$-0.651457\pi$
$907$	11.5373	−	43.0579i	0.383091	−	1.42971i	0.841155	−	0.540795i	$-0.181876\pi$
$908$	7.06816	−	1.89391i	0.234565	−	0.0628515i
$909$	15.3970			0.510686
$910$	11.6097	−	21.9731i	0.384857	−	0.728400i
$911$	50.5541			1.67493			0.837465	−	0.546491i	$-0.184037\pi$
$911$	50.5541			1.67493			0.837465	+	0.546491i	$0.184037\pi$
$912$	0.00495649	+	0.0184979i	0.000164126	+	0.000612526i
$913$	−18.6515	−	14.6378i	−0.617275	−	0.484441i
$914$	2.13625	−	1.23337i	0.0706609	−	0.0407961i
$915$	−0.139668	−	0.00178249i	−0.00461727	−	5.89273e-5i
$916$	−27.4498			−0.906966
$917$	2.76948	+	8.58418i	0.0914562	+	0.283475i
$918$	−0.0427806	+	0.0427806i	−0.00141197	+	0.00141197i
$919$	20.6723	−	35.8055i	0.681916	−	1.18111i	−0.292479	−	0.956272i	$-0.594480\pi$
$919$	20.6723	−	35.8055i	0.681916	−	1.18111i	0.974395	−	0.224842i	$-0.0721865\pi$
$920$	−1.15376	−	4.53668i	−0.0380382	−	0.149570i
$921$	0.0299982	−	0.0173195i	0.000988475	−	0.000570696i
$922$	−27.9065	+	7.47752i	−0.919051	+	0.246259i
$923$	−21.8910	−	21.8910i	−0.720552	−	0.720552i
$924$	0.0561705	+	0.0207157i	0.00184787	+	0.000681495i
$925$	−6.59904	−	27.4077i	−0.216975	−	0.901159i
$926$	−15.2333	−	8.79493i	−0.500596	−	0.289019i
$927$	6.48682	−	24.2091i	0.213055	−	0.795133i
$928$	−10.2712	−	2.75216i	−0.337168	−	0.0903440i
$929$	−4.03294	−	2.32842i	−0.132317	−	0.0763930i	0.432381	−	0.901691i	$-0.357674\pi$
$929$	−4.03294	−	2.32842i	−0.132317	−	0.0763930i	−0.564697	+	0.825298i	$0.691007\pi$
$930$	−0.0335124	+	0.118975i	−0.00109891	+	0.00390136i
$931$	−17.9161	−	8.06610i	−0.587178	−	0.264356i
$932$	−2.68073	+	2.68073i	−0.0878102	+	0.0878102i
$933$	−0.0119390	−	0.0445568i	−0.000390864	−	0.00145873i
$934$	10.2487	+	17.7513i	0.335348	+	0.580840i
$935$	−8.85124	+	6.46481i	−0.289466	+	0.211422i
$936$	6.30092	−	10.9135i	0.205952	−	0.356719i
$937$	2.82226	−	2.82226i	0.0921993	−	0.0921993i	−0.659503	−	0.751702i	$-0.729233\pi$
$937$	2.82226	−	2.82226i	0.0921993	−	0.0921993i	0.751702	+	0.659503i	$0.229233\pi$
$938$	−3.65632	−	3.30594i	−0.119383	−	0.107943i
$939$		−	0.191316i		−	0.00624337i
$940$	−0.298095	+	23.3573i	−0.00972277	+	0.761832i
$941$	−17.9698	+	10.3749i	−0.585798	+	0.338211i	−0.763434	−	0.645886i	$-0.776488\pi$
$941$	−17.9698	+	10.3749i	−0.585798	+	0.338211i	0.177636	+	0.984096i	$0.443155\pi$
$942$	0.125982	+	0.0337569i	0.00410473	+	0.00109986i
$943$	−4.66131	+	1.24899i	−0.151793	+	0.0406728i
$944$		−	9.03699i		−	0.294129i
$945$	−0.177550	−	0.164702i	−0.00577569	−	0.00535775i
$946$	10.2874	−	24.0894i	0.334472	−	0.783213i
$947$	41.0928	−	11.0108i	1.33534	−	0.357802i	0.480635	−	0.876921i	$-0.340406\pi$
$947$	41.0928	−	11.0108i	1.33534	−	0.357802i	0.854702	+	0.519119i	$0.173740\pi$
$948$	−0.0103551	+	0.0386459i	−0.000336319	+	0.00125516i
$949$	43.3050	−	25.0022i	1.40574	−	0.811605i
$950$	3.97715	−	13.4591i	0.129036	−	0.436670i
$951$	0.0301571			0.000977912
$952$	0.820934	−	3.82314i	0.0266066	−	0.123909i
$953$	2.48049	+	2.48049i	0.0803509	+	0.0803509i	0.746140	−	0.665789i	$-0.231905\pi$
$953$	2.48049	+	2.48049i	0.0803509	+	0.0803509i	−0.665789	+	0.746140i	$0.731905\pi$
$954$	10.4316	−	18.0680i	0.337735	−	0.584974i
$955$	−5.34201	−	21.0053i	−0.172864	−	0.679716i
$956$	7.51423	−	4.33834i	0.243028	−	0.140312i
$957$	0.238202	+	0.0340072i	0.00769999	+	0.00109930i
$958$	−5.98740	+	5.98740i	−0.193444	+	0.193444i
$959$	9.69909	−	6.27007i	0.313200	−	0.202471i
$960$	−0.00745875	−	0.0133083i	−0.000240730	−	0.000429524i
$961$	−17.3219	+	30.0025i	−0.558772	+	0.967821i
$962$	6.12993	−	22.8772i	0.197637	−	0.737590i
$963$	−6.32786	+	23.6159i	−0.203912	+	0.761012i
$964$	3.14654	−	5.44998i	0.101343	−	0.175532i
$965$	7.77341	+	13.8697i	0.250235	+	0.446483i
$966$	−0.0336346	−	0.0172257i	−0.00108218	−	0.000554229i
$967$	9.12129	−	9.12129i	0.293321	−	0.293321i	−0.545070	−	0.838391i	$-0.683497\pi$
$967$	9.12129	−	9.12129i	0.293321	−	0.293321i	0.838391	+	0.545070i	$0.183497\pi$
$968$	9.40403	+	5.70650i	0.302257	+	0.183414i
$969$	−0.0245114	+	0.0141517i	−0.000787419	+	0.000454617i
$970$	−2.60813	−	10.2554i	−0.0837420	−	0.329282i
$971$	−16.3389	+	28.2999i	−0.524342	+	0.908186i	0.475257	+	0.879847i	$0.342355\pi$
$971$	−16.3389	+	28.2999i	−0.524342	+	0.908186i	−0.999598	+	0.0283391i	$0.990978\pi$
$972$	−0.130255	−	0.130255i	−0.00417793	−	0.00417793i
$973$	18.9359	+	17.1213i	0.607057	+	0.548883i
$974$	23.5612			0.754949
$975$	0.125889	−	0.0684592i	0.00403167	−	0.00219245i
$976$	7.92908	−	4.57785i	0.253804	−	0.146534i
$977$	−1.76749	+	6.59637i	−0.0565470	+	0.211036i	−0.988419	−	0.151752i	$-0.951509\pi$
$977$	−1.76749	+	6.59637i	−0.0565470	+	0.211036i	0.931872	+	0.362788i	$0.118175\pi$
$978$	−0.104064	+	0.0278838i	−0.00332759	+	0.000891625i
$979$	52.3555	+	22.3585i	1.67329	+	0.714581i
$980$	15.4161	+	2.70972i	0.492451	+	0.0865588i
$981$			25.9598i			0.828834i
$982$	−14.3876	+	3.85514i	−0.459126	+	0.123023i
$983$	−34.4744	−	9.23739i	−1.09956	−	0.294627i	−0.336976	−	0.941513i	$-0.609404\pi$
$983$	−34.4744	−	9.23739i	−1.09956	−	0.294627i	−0.762587	+	0.646886i	$0.776071\pi$
$984$	−0.0136203	+	0.00786368i	−0.000434199	+	0.000250685i
$985$	−0.226054	+	17.7125i	−0.00720267	+	0.564368i
$986$		−	15.7158i		−	0.500492i
$987$	0.139874	+	0.126470i	0.00445224	+	0.00402558i
$988$	8.33735	−	8.33735i	0.265247	−	0.265247i
$989$	−8.26682	+	14.3186i	−0.262870	+	0.455304i
$990$	−13.1223	−	17.9663i	−0.417055	−	0.571007i
$991$	10.4188	+	18.0459i	0.330965	+	0.573248i	0.982701	−	0.185198i	$-0.0592926\pi$
$991$	10.4188	+	18.0459i	0.330965	+	0.573248i	−0.651737	+	0.758445i	$0.725959\pi$
$992$	−2.09698	−	7.82602i	−0.0665790	−	0.248476i
$993$	−0.0473027	+	0.0473027i	−0.00150111	+	0.00150111i
$994$	8.88838	−	17.3552i	0.281922	−	0.550475i
$995$	−9.49885	+	33.7228i	−0.301134	+	1.06908i
$996$	0.0422389	+	0.0243867i	0.00133839	+	0.000772721i
$997$	11.4654	+	3.07216i	0.363114	+	0.0972962i	0.435763	−	0.900061i	$-0.356479\pi$
$997$	11.4654	+	3.07216i	0.363114	+	0.0972962i	−0.0726488	+	0.997358i	$0.523145\pi$
$998$	−6.57567	+	24.5407i	−0.208149	+	0.776823i
$999$	−0.199881	−	0.115402i	−0.00632397	−	0.00365115i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.bd.a.527.12	yes	192
5.3	odd	4	inner	770.2.bd.a.373.13	yes	192
7.4	even	3	inner	770.2.bd.a.417.37	yes	192
11.10	odd	2	inner	770.2.bd.a.527.36	yes	192
35.18	odd	12	inner	770.2.bd.a.263.36	yes	192
55.43	even	4	inner	770.2.bd.a.373.37	yes	192
77.32	odd	6	inner	770.2.bd.a.417.13	yes	192
385.263	even	12	inner	770.2.bd.a.263.12	✓	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bd.a.263.12	✓	192	385.263	even	12	inner
770.2.bd.a.263.36	yes	192	35.18	odd	12	inner
770.2.bd.a.373.13	yes	192	5.3	odd	4	inner
770.2.bd.a.373.37	yes	192	55.43	even	4	inner
770.2.bd.a.417.13	yes	192	77.32	odd	6	inner
770.2.bd.a.417.37	yes	192	7.4	even	3	inner
770.2.bd.a.527.12	yes	192	1.1	even	1	trivial
770.2.bd.a.527.36	yes	192	11.10	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(0.00659019 + 0.00176584i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.60119 + 1.56083i) q^{5} -0.00682267i q^{6} +(-1.96250 - 1.77443i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.59804 - 1.49998i) q^{9} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{2} +(0.00659019 + 0.00176584i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.60119 + 1.56083i) q^{5} -0.00682267i q^{6} +(-1.96250 - 1.77443i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.59804 - 1.49998i) q^{9} +(1.92207 + 1.14266i) q^{10} +(3.29278 - 0.397013i) q^{11} +(-0.00659019 + 0.00176584i) q^{12} +(2.97033 + 2.97033i) q^{13} +(-1.20604 + 2.35488i) q^{14} +(-0.0133083 + 0.00745875i) q^{15} +(0.500000 - 0.866025i) q^{16} +(1.42759 + 0.382521i) q^{17} +(-0.776445 + 2.89773i) q^{18} +(-1.40344 + 2.43083i) q^{19} +(0.606253 - 2.15231i) q^{20} +(-0.00979987 - 0.0151593i) q^{21} +(-1.23572 - 3.07782i) q^{22} +(0.541825 + 2.02212i) q^{23} +(0.00341134 + 0.00590861i) q^{24} +(0.127603 - 4.99837i) q^{25} +(2.10034 - 3.63789i) q^{26} +(-0.0289459 - 0.0289459i) q^{27} +(2.58679 + 0.555455i) q^{28} +10.6335 q^{29} +(0.0106490 + 0.0109244i) q^{30} +(4.05104 + 7.01662i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(0.0224011 + 0.00319812i) q^{33} -1.47795i q^{34} +(5.91192 - 0.221930i) q^{35} +2.99995 q^{36} +(5.44607 - 1.45927i) q^{37} +(2.71124 + 0.726474i) q^{38} +(0.0143299 + 0.0248202i) q^{39} +(-2.23589 - 0.0285352i) q^{40} +2.30516i q^{41} +(-0.0121064 + 0.0133895i) q^{42} +(5.58459 + 5.58459i) q^{43} +(-2.65312 + 1.99021i) q^{44} +(6.50116 - 1.65336i) q^{45} +(1.81298 - 1.04672i) q^{46} +(-10.0906 + 2.70377i) q^{47} +(0.00482436 - 0.00482436i) q^{48} +(0.702783 + 6.96463i) q^{49} +(-4.86108 + 1.17042i) q^{50} +(0.00873261 + 0.00504178i) q^{51} +(-4.05754 - 1.08722i) q^{52} +(-6.71753 - 1.79996i) q^{53} +(-0.0204679 + 0.0354514i) q^{54} +(-4.65268 + 5.77517i) q^{55} +(-0.132982 - 2.64241i) q^{56} +(-0.0135414 + 0.0135414i) q^{57} +(-2.75216 - 10.2712i) q^{58} +(7.82626 - 4.51850i) q^{59} +(0.00779596 - 0.0131136i) q^{60} +(7.92908 + 4.57785i) q^{61} +(5.72904 - 5.72904i) q^{62} +(2.43703 + 7.55374i) q^{63} +1.00000i q^{64} +(-9.39224 - 0.119867i) q^{65} +(-0.00270869 - 0.0224655i) q^{66} +(-0.482205 + 1.79961i) q^{67} +(-1.42759 + 0.382521i) q^{68} +0.0142829i q^{69} +(-1.74448 - 5.65303i) q^{70} -7.36990 q^{71} +(-0.776445 - 2.89773i) q^{72} +(3.08095 - 11.4983i) q^{73} +(-2.81909 - 4.88281i) q^{74} +(0.00966724 - 0.0327149i) q^{75} -2.80688i q^{76} +(-7.16653 - 5.06367i) q^{77} +(0.0202656 - 0.0202656i) q^{78} +(2.93208 - 5.07850i) q^{79} +(0.551127 + 2.16709i) q^{80} +(4.49979 + 7.79387i) q^{81} +(2.22661 - 0.596619i) q^{82} +(-5.05490 - 5.05490i) q^{83} +(0.0160666 + 0.00822840i) q^{84} +(-2.88289 + 1.61574i) q^{85} +(3.94890 - 6.83970i) q^{86} +(0.0700769 + 0.0187771i) q^{87} +(2.60908 + 2.04761i) q^{88} +(14.8653 + 8.58249i) q^{89} +(-3.27964 - 5.85171i) q^{90} +(-0.558613 - 11.0999i) q^{91} +(-1.48029 - 1.48029i) q^{92} +(0.0143070 + 0.0533943i) q^{93} +(5.22328 + 9.04699i) q^{94} +(-1.54695 - 6.08275i) q^{95} +(-0.00590861 - 0.00341134i) q^{96} +(-3.34628 - 3.34628i) q^{97} +(6.54542 - 2.48142i) q^{98} +(-9.15026 - 3.90764i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 8 q^{5}+O(q^{10}) \) 192 * q + 8 * q^5	\( 192 q + 8 q^{5} + 4 q^{11} + 16 q^{15} + 96 q^{16} + 24 q^{22} - 8 q^{23} + 24 q^{25} - 8 q^{26} - 16 q^{33} - 160 q^{36} - 40 q^{37} - 40 q^{42} + 32 q^{45} - 40 q^{47} + 40 q^{53} + 8 q^{55} + 16 q^{56} + 32 q^{58} - 48 q^{67} - 72 q^{70} + 32 q^{71} - 48 q^{75} - 72 q^{77} - 8 q^{80} + 64 q^{81} + 16 q^{82} - 12 q^{88} - 112 q^{91} - 16 q^{92} + 80 q^{93} - 64 q^{97}+O(q^{100}) \) 192 * q + 8 * q^5 + 4 * q^11 + 16 * q^15 + 96 * q^16 + 24 * q^22 - 8 * q^23 + 24 * q^25 - 8 * q^26 - 16 * q^33 - 160 * q^36 - 40 * q^37 - 40 * q^42 + 32 * q^45 - 40 * q^47 + 40 * q^53 + 8 * q^55 + 16 * q^56 + 32 * q^58 - 48 * q^67 - 72 * q^70 + 32 * q^71 - 48 * q^75 - 72 * q^77 - 8 * q^80 + 64 * q^81 + 16 * q^82 - 12 * q^88 - 112 * q^91 - 16 * q^92 + 80 * q^93 - 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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