LMFDB - Embedded newform 770.2.i.j.331.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(221,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("770.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.i (of order $3$, degree $2$, 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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			331.3
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	770.331
Dual form			770.2.i.j.221.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.766044 + 1.32683i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.53209 q^{6} +(1.28699 + 2.31164i) q^{7} -1.00000 q^{8} +(0.326352 - 0.565258i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.766044 + 1.32683i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.53209 q^{6} +(1.28699 + 2.31164i) q^{7} -1.00000 q^{8} +(0.326352 - 0.565258i) q^{9} +(0.500000 + 0.866025i) q^{10} +(0.500000 + 0.866025i) q^{11} +(0.766044 - 1.32683i) q^{12} +4.36959 q^{13} +(2.64543 + 0.0412527i) q^{14} -1.53209 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.17365 - 3.76487i) q^{17} +(-0.326352 - 0.565258i) q^{18} +(-3.35117 + 5.80439i) q^{19} +1.00000 q^{20} +(-2.08125 + 3.47843i) q^{21} +1.00000 q^{22} +(-3.57398 + 6.19031i) q^{23} +(-0.766044 - 1.32683i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(2.18479 - 3.78417i) q^{26} +5.59627 q^{27} +(1.35844 - 2.27038i) q^{28} +7.39693 q^{29} +(-0.766044 + 1.32683i) q^{30} +(3.16637 + 5.48432i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.766044 + 1.32683i) q^{33} -4.34730 q^{34} +(-2.64543 - 0.0412527i) q^{35} -0.652704 q^{36} +(-0.946967 + 1.64019i) q^{37} +(3.35117 + 5.80439i) q^{38} +(3.34730 + 5.79769i) q^{39} +(0.500000 - 0.866025i) q^{40} +8.69459 q^{41} +(1.97178 + 3.54163i) q^{42} -9.27631 q^{43} +(0.500000 - 0.866025i) q^{44} +(0.326352 + 0.565258i) q^{45} +(3.57398 + 6.19031i) q^{46} +(6.24897 - 10.8235i) q^{47} -1.53209 q^{48} +(-3.68732 + 5.95010i) q^{49} -1.00000 q^{50} +(3.33022 - 5.76811i) q^{51} +(-2.18479 - 3.78417i) q^{52} +(-1.11334 - 1.92836i) q^{53} +(2.79813 - 4.84651i) q^{54} -1.00000 q^{55} +(-1.28699 - 2.31164i) q^{56} -10.2686 q^{57} +(3.69846 - 6.40593i) q^{58} +(-2.69459 - 4.66717i) q^{59} +(0.766044 + 1.32683i) q^{60} +(3.40033 - 5.88954i) q^{61} +6.33275 q^{62} +(1.72668 + 0.0269258i) q^{63} +1.00000 q^{64} +(-2.18479 + 3.78417i) q^{65} +(0.766044 + 1.32683i) q^{66} +(-4.72668 - 8.18685i) q^{67} +(-2.17365 + 3.76487i) q^{68} -10.9513 q^{69} +(-1.35844 + 2.27038i) q^{70} -1.18479 q^{71} +(-0.326352 + 0.565258i) q^{72} +(2.56418 + 4.44129i) q^{73} +(0.946967 + 1.64019i) q^{74} +(0.766044 - 1.32683i) q^{75} +6.70233 q^{76} +(-1.35844 + 2.27038i) q^{77} +6.69459 q^{78} +(-3.53209 + 6.11776i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(3.30793 + 5.72951i) q^{81} +(4.34730 - 7.52974i) q^{82} -15.5175 q^{83} +(4.05303 + 0.0632028i) q^{84} +4.34730 q^{85} +(-4.63816 + 8.03352i) q^{86} +(5.66637 + 9.81445i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(7.21941 - 12.5044i) q^{89} +0.652704 q^{90} +(5.62361 + 10.1009i) q^{91} +7.14796 q^{92} +(-4.85117 + 8.40247i) q^{93} +(-6.24897 - 10.8235i) q^{94} +(-3.35117 - 5.80439i) q^{95} +(-0.766044 + 1.32683i) q^{96} +2.93582 q^{97} +(3.30928 + 6.16836i) q^{98} +0.652704 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{4} - 3 q^{5} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 6 * q + 3 * q^2 - 3 * q^4 - 3 * q^5 - 6 * q^8 + 3 * q^9	$ 6 q + 3 q^{2} - 3 q^{4} - 3 q^{5} - 6 q^{8} + 3 q^{9} + 3 q^{10} + 3 q^{11} + 12 q^{13} - 3 q^{16} - 12 q^{17} - 3 q^{18} + 6 q^{19} + 6 q^{20} - 15 q^{21} + 6 q^{22} - 6 q^{23} - 3 q^{25} + 6 q^{26} + 6 q^{27} - 12 q^{29} + 3 q^{32} - 24 q^{34} - 6 q^{36} - 18 q^{37} - 6 q^{38} + 18 q^{39} + 3 q^{40} + 48 q^{41} - 3 q^{42} + 12 q^{43} + 3 q^{44} + 3 q^{45} + 6 q^{46} + 12 q^{47} - 6 q^{50} - 3 q^{51} - 6 q^{52} + 3 q^{54} - 6 q^{55} - 42 q^{57} - 6 q^{58} - 12 q^{59} + 6 q^{61} - 3 q^{63} + 6 q^{64} - 6 q^{65} - 15 q^{67} - 12 q^{68} + 12 q^{69} - 3 q^{72} - 3 q^{73} + 18 q^{74} - 12 q^{76} + 36 q^{78} - 12 q^{79} - 3 q^{80} + 9 q^{81} + 24 q^{82} - 48 q^{83} + 12 q^{84} + 24 q^{85} + 6 q^{86} + 15 q^{87} - 3 q^{88} + 12 q^{89} + 6 q^{90} - 36 q^{91} + 12 q^{92} - 3 q^{93} - 12 q^{94} + 6 q^{95} + 36 q^{97} + 6 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 - 3 * q^4 - 3 * q^5 - 6 * q^8 + 3 * q^9 + 3 * q^10 + 3 * q^11 + 12 * q^13 - 3 * q^16 - 12 * q^17 - 3 * q^18 + 6 * q^19 + 6 * q^20 - 15 * q^21 + 6 * q^22 - 6 * q^23 - 3 * q^25 + 6 * q^26 + 6 * q^27 - 12 * q^29 + 3 * q^32 - 24 * q^34 - 6 * q^36 - 18 * q^37 - 6 * q^38 + 18 * q^39 + 3 * q^40 + 48 * q^41 - 3 * q^42 + 12 * q^43 + 3 * q^44 + 3 * q^45 + 6 * q^46 + 12 * q^47 - 6 * q^50 - 3 * q^51 - 6 * q^52 + 3 * q^54 - 6 * q^55 - 42 * q^57 - 6 * q^58 - 12 * q^59 + 6 * q^61 - 3 * q^63 + 6 * q^64 - 6 * q^65 - 15 * q^67 - 12 * q^68 + 12 * q^69 - 3 * q^72 - 3 * q^73 + 18 * q^74 - 12 * q^76 + 36 * q^78 - 12 * q^79 - 3 * q^80 + 9 * q^81 + 24 * q^82 - 48 * q^83 + 12 * q^84 + 24 * q^85 + 6 * q^86 + 15 * q^87 - 3 * q^88 + 12 * q^89 + 6 * q^90 - 36 * q^91 + 12 * q^92 - 3 * q^93 - 12 * q^94 + 6 * q^95 + 36 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	0.766044	+	1.32683i	0.442276	+	0.766044i	0.997858	−	0.0654173i	$-0.0208378\pi$
$3$	0.766044	+	1.32683i	0.442276	+	0.766044i	−0.555582	+	0.831462i	$0.687505\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	1.53209			0.625473
$7$	1.28699	+	2.31164i	0.486436	+	0.873716i
$7$	1.28699	+	2.31164i	0.486436	+	0.873716i
$8$	−1.00000			−0.353553
$9$	0.326352	−	0.565258i	0.108784	−	0.188419i
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	0.766044	−	1.32683i	0.221138	−	0.383022i
$13$	4.36959			1.21190			0.605952	−	0.795501i	$-0.292792\pi$
$13$	4.36959			1.21190			0.605952	+	0.795501i	$0.292792\pi$
$14$	2.64543	+	0.0412527i	0.707021	+	0.0110252i
$15$	−1.53209			−0.395584
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.17365	−	3.76487i	−0.527187	−	0.913115i	−0.999498	−	0.0316828i	$-0.989913\pi$
$17$	−2.17365	−	3.76487i	−0.527187	−	0.913115i	0.472311	−	0.881432i	$-0.343420\pi$
$18$	−0.326352	−	0.565258i	−0.0769219	−	0.133233i
$19$	−3.35117	+	5.80439i	−0.768810	+	1.33162i	0.169398	+	0.985548i	$0.445818\pi$
$19$	−3.35117	+	5.80439i	−0.768810	+	1.33162i	−0.938208	+	0.346071i	$0.887516\pi$
$20$	1.00000			0.223607
$21$	−2.08125	+	3.47843i	−0.454166	+	0.759055i
$22$	1.00000			0.213201
$23$	−3.57398	+	6.19031i	−0.745226	+	1.29077i	0.204863	+	0.978791i	$0.434325\pi$
$23$	−3.57398	+	6.19031i	−0.745226	+	1.29077i	−0.950089	+	0.311979i	$0.899008\pi$
$24$	−0.766044	−	1.32683i	−0.156368	−	0.270838i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	2.18479	−	3.78417i	0.428473	−	0.742137i
$27$	5.59627			1.07700
$28$	1.35844	−	2.27038i	0.256721	−	0.429062i
$29$	7.39693			1.37357			0.686787	−	0.726858i	$-0.259020\pi$
$29$	7.39693			1.37357			0.686787	+	0.726858i	$0.259020\pi$
$30$	−0.766044	+	1.32683i	−0.139860	+	0.242245i
$31$	3.16637	+	5.48432i	0.568698	+	0.985013i	0.996695	+	0.0812332i	$0.0258859\pi$
$31$	3.16637	+	5.48432i	0.568698	+	0.985013i	−0.427998	+	0.903780i	$0.640781\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−0.766044	+	1.32683i	−0.133351	+	0.230971i
$34$	−4.34730			−0.745555
$35$	−2.64543	−	0.0412527i	−0.447159	−	0.00697298i
$36$	−0.652704			−0.108784
$37$	−0.946967	+	1.64019i	−0.155680	+	0.269646i	−0.933307	−	0.359081i	$-0.883090\pi$
$37$	−0.946967	+	1.64019i	−0.155680	+	0.269646i	0.777626	+	0.628727i	$0.216424\pi$
$38$	3.35117	+	5.80439i	0.543631	+	0.941597i
$39$	3.34730	+	5.79769i	0.535996	+	0.928373i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	8.69459			1.35787			0.678934	−	0.734200i	$-0.262442\pi$
$41$	8.69459			1.35787			0.678934	+	0.734200i	$0.262442\pi$
$42$	1.97178	+	3.54163i	0.304252	+	0.546486i
$43$	−9.27631			−1.41462			−0.707312	−	0.706901i	$-0.750092\pi$
$43$	−9.27631			−1.41462			−0.707312	+	0.706901i	$0.750092\pi$
$44$	0.500000	−	0.866025i	0.0753778	−	0.130558i
$45$	0.326352	+	0.565258i	0.0486497	+	0.0842637i
$46$	3.57398	+	6.19031i	0.526954	+	0.912712i
$47$	6.24897	−	10.8235i	0.911506	−	1.57877i	0.0995682	−	0.995031i	$-0.468254\pi$
$47$	6.24897	−	10.8235i	0.911506	−	1.57877i	0.811938	−	0.583744i	$-0.198413\pi$
$48$	−1.53209			−0.221138
$49$	−3.68732	+	5.95010i	−0.526760	+	0.850014i
$50$	−1.00000			−0.141421
$51$	3.33022	−	5.76811i	0.466324	−	0.807698i
$52$	−2.18479	−	3.78417i	−0.302976	−	0.524770i
$53$	−1.11334	−	1.92836i	−0.152929	−	0.264881i	0.779374	−	0.626559i	$-0.215537\pi$
$53$	−1.11334	−	1.92836i	−0.152929	−	0.264881i	−0.932303	+	0.361678i	$0.882204\pi$
$54$	2.79813	−	4.84651i	0.380778	−	0.659526i
$55$	−1.00000			−0.134840
$56$	−1.28699	−	2.31164i	−0.171981	−	0.308905i
$57$	−10.2686			−1.36011
$58$	3.69846	−	6.40593i	0.485632	−	0.841139i
$59$	−2.69459	−	4.66717i	−0.350806	−	0.607614i	0.635585	−	0.772031i	$-0.280759\pi$
$59$	−2.69459	−	4.66717i	−0.350806	−	0.607614i	−0.986391	+	0.164417i	$0.947426\pi$
$60$	0.766044	+	1.32683i	0.0988959	+	0.171293i
$61$	3.40033	−	5.88954i	0.435368	−	0.754079i	−0.561958	−	0.827166i	$-0.689952\pi$
$61$	3.40033	−	5.88954i	0.435368	−	0.754079i	0.997326	+	0.0730870i	$0.0232851\pi$
$62$	6.33275			0.804260
$63$	1.72668	+	0.0269258i	0.217541	+	0.00339233i
$64$	1.00000			0.125000
$65$	−2.18479	+	3.78417i	−0.270990	+	0.469369i
$66$	0.766044	+	1.32683i	0.0942936	+	0.163321i
$67$	−4.72668	−	8.18685i	−0.577456	−	1.00018i	−0.995770	−	0.0918807i	$-0.970712\pi$
$67$	−4.72668	−	8.18685i	−0.577456	−	1.00018i	0.418314	−	0.908303i	$-0.362621\pi$
$68$	−2.17365	+	3.76487i	−0.263594	+	0.456557i
$69$	−10.9513			−1.31838
$70$	−1.35844	+	2.27038i	−0.162365	+	0.271363i
$71$	−1.18479			−0.140609			−0.0703045	−	0.997526i	$-0.522397\pi$
$71$	−1.18479			−0.140609			−0.0703045	+	0.997526i	$0.522397\pi$
$72$	−0.326352	+	0.565258i	−0.0384609	+	0.0666163i
$73$	2.56418	+	4.44129i	0.300114	+	0.519813i	0.976162	−	0.217045i	$-0.0696418\pi$
$73$	2.56418	+	4.44129i	0.300114	+	0.519813i	−0.676047	+	0.736858i	$0.736309\pi$
$74$	0.946967	+	1.64019i	0.110083	+	0.190669i
$75$	0.766044	−	1.32683i	0.0884552	−	0.153209i
$76$	6.70233			0.768810
$77$	−1.35844	+	2.27038i	−0.154809	+	0.258734i
$78$	6.69459			0.758013
$79$	−3.53209	+	6.11776i	−0.397391	+	0.688301i	−0.993403	−	0.114674i	$-0.963418\pi$
$79$	−3.53209	+	6.11776i	−0.397391	+	0.688301i	0.596012	+	0.802975i	$0.296751\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	3.30793	+	5.72951i	0.367548	+	0.636612i
$82$	4.34730	−	7.52974i	0.480079	−	0.831520i
$83$	−15.5175			−1.70327			−0.851636	−	0.524134i	$-0.824389\pi$
$83$	−15.5175			−1.70327			−0.851636	+	0.524134i	$0.824389\pi$
$84$	4.05303	+	0.0632028i	0.442222	+	0.00689599i
$85$	4.34730			0.471530
$86$	−4.63816	+	8.03352i	−0.500145	+	0.866277i
$87$	5.66637	+	9.81445i	0.607499	+	1.05222i
$88$	−0.500000	−	0.866025i	−0.0533002	−	0.0923186i
$89$	7.21941	−	12.5044i	0.765256	−	1.32546i	−0.174856	−	0.984594i	$-0.555946\pi$
$89$	7.21941	−	12.5044i	0.765256	−	1.32546i	0.940111	−	0.340868i	$-0.110721\pi$
$90$	0.652704			0.0688010
$91$	5.62361	+	10.1009i	0.589514	+	1.05886i
$92$	7.14796			0.745226
$93$	−4.85117	+	8.40247i	−0.503043	+	0.871295i
$94$	−6.24897	−	10.8235i	−0.644532	−	1.11636i
$95$	−3.35117	−	5.80439i	−0.343822	−	0.595518i
$96$	−0.766044	+	1.32683i	−0.0781841	+	0.135419i
$97$	2.93582			0.298088			0.149044	−	0.988831i	$-0.452380\pi$
$97$	2.93582			0.298088			0.149044	+	0.988831i	$0.452380\pi$
$98$	3.30928	+	6.16836i	0.334288	+	0.623099i
$99$	0.652704			0.0655992
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−6.72668	−	11.6510i	−0.669330	−	1.15931i	−0.978092	−	0.208174i	$-0.933248\pi$
$101$	−6.72668	−	11.6510i	−0.669330	−	1.15931i	0.308762	−	0.951139i	$-0.400085\pi$
$102$	−3.33022	−	5.76811i	−0.329741	−	0.571128i
$103$	3.65270	−	6.32667i	0.359912	−	0.623385i	−0.628034	−	0.778186i	$-0.716140\pi$
$103$	3.65270	−	6.32667i	0.359912	−	0.623385i	0.987946	+	0.154801i	$0.0494735\pi$
$104$	−4.36959			−0.428473
$105$	−1.97178	−	3.54163i	−0.192426	−	0.345628i
$106$	−2.22668			−0.216274
$107$	−1.95811	+	3.39155i	−0.189298	+	0.327873i	−0.945016	−	0.327023i	$-0.893954\pi$
$107$	−1.95811	+	3.39155i	−0.189298	+	0.327873i	0.755719	+	0.654897i	$0.227288\pi$
$108$	−2.79813	−	4.84651i	−0.269251	−	0.466356i
$109$	−9.48545	−	16.4293i	−0.908542	−	1.57364i	−0.816091	−	0.577923i	$-0.803863\pi$
$109$	−9.48545	−	16.4293i	−0.908542	−	1.57364i	−0.0924501	−	0.995717i	$-0.529470\pi$
$110$	−0.500000	+	0.866025i	−0.0476731	+	0.0825723i
$111$	−2.90167			−0.275415
$112$	−2.64543	−	0.0412527i	−0.249970	−	0.00389801i
$113$	4.56624			0.429555			0.214778	−	0.976663i	$-0.431097\pi$
$113$	4.56624			0.429555			0.214778	+	0.976663i	$0.431097\pi$
$114$	−5.13429	+	8.89284i	−0.480870	+	0.832891i
$115$	−3.57398	−	6.19031i	−0.333275	−	0.577250i
$116$	−3.69846	−	6.40593i	−0.343394	−	0.594775i
$117$	1.42602	−	2.46994i	0.131836	−	0.228346i
$118$	−5.38919			−0.496115
$119$	5.90554	−	9.87003i	0.541360	−	0.904784i
$120$	1.53209			0.139860
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−3.40033	−	5.88954i	−0.307851	−	0.533214i
$123$	6.66044	+	11.5362i	0.600552	+	1.04019i
$124$	3.16637	−	5.48432i	0.284349	−	0.492507i
$125$	1.00000			0.0894427
$126$	0.886659	−	1.48189i	0.0789899	−	0.132017i
$127$	−1.00000			−0.0887357			−0.0443678	−	0.999015i	$-0.514127\pi$
$127$	−1.00000			−0.0887357			−0.0443678	+	0.999015i	$0.514127\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−7.10607	−	12.3081i	−0.625654	−	1.08367i
$130$	2.18479	+	3.78417i	0.191619	+	0.331894i
$131$	−0.109470	+	0.189608i	−0.00956447	+	0.0165662i	−0.870768	−	0.491694i	$-0.836378\pi$
$131$	−0.109470	+	0.189608i	−0.00956447	+	0.0165662i	0.861204	+	0.508260i	$0.169711\pi$
$132$	1.53209			0.133351
$133$	−17.7306	−	0.276489i	−1.53743	−	0.0239747i
$134$	−9.45336			−0.816646
$135$	−2.79813	+	4.84651i	−0.240825	+	0.417121i
$136$	2.17365	+	3.76487i	0.186389	+	0.322835i
$137$	7.70233	+	13.3408i	0.658055	+	1.13978i	0.981119	+	0.193407i	$0.0619538\pi$
$137$	7.70233	+	13.3408i	0.658055	+	1.13978i	−0.323064	+	0.946377i	$0.604713\pi$
$138$	−5.47565	+	9.48411i	−0.466118	+	0.807341i
$139$	4.71419			0.399853			0.199926	−	0.979811i	$-0.435930\pi$
$139$	4.71419			0.399853			0.199926	+	0.979811i	$0.435930\pi$
$140$	1.28699	+	2.31164i	0.108770	+	0.195369i
$141$	19.1480			1.61255
$142$	−0.592396	+	1.02606i	−0.0497128	+	0.0861051i
$143$	2.18479	+	3.78417i	0.182702	+	0.316448i
$144$	0.326352	+	0.565258i	0.0271960	+	0.0471048i
$145$	−3.69846	+	6.40593i	−0.307141	+	0.531983i
$146$	5.12836			0.424426
$147$	−10.7194	−	0.334397i	−0.884122	−	0.0275806i
$148$	1.89393			0.155680
$149$	2.87211	−	4.97464i	0.235293	−	0.407539i	−0.724065	−	0.689732i	$-0.757729\pi$
$149$	2.87211	−	4.97464i	0.235293	−	0.407539i	0.959358	+	0.282193i	$0.0910619\pi$
$150$	−0.766044	−	1.32683i	−0.0625473	−	0.108335i
$151$	−10.8229	−	18.7459i	−0.880759	−	1.52552i	−0.850499	−	0.525977i	$-0.823700\pi$
$151$	−10.8229	−	18.7459i	−0.880759	−	1.52552i	−0.0302605	−	0.999542i	$-0.509634\pi$
$152$	3.35117	−	5.80439i	0.271816	−	0.470798i
$153$	−2.83750			−0.229398
$154$	1.28699	+	2.31164i	0.103709	+	0.186277i
$155$	−6.33275			−0.508659
$156$	3.34730	−	5.79769i	0.267998	−	0.464186i
$157$	−0.875515	−	1.51644i	−0.0698737	−	0.121025i	0.828972	−	0.559290i	$-0.188926\pi$
$157$	−0.875515	−	1.51644i	−0.0698737	−	0.121025i	−0.898846	+	0.438266i	$0.855593\pi$
$158$	3.53209	+	6.11776i	0.280998	+	0.486703i
$159$	1.70574	−	2.95442i	0.135274	−	0.234301i
$160$	−1.00000			−0.0790569
$161$	−18.9094	−	0.294872i	−1.49027	−	0.0232392i
$162$	6.61587			0.519792
$163$	−2.66772	+	4.62062i	−0.208952	+	0.361915i	−0.951385	−	0.308005i	$-0.900339\pi$
$163$	−2.66772	+	4.62062i	−0.208952	+	0.361915i	0.742433	+	0.669921i	$0.233672\pi$
$164$	−4.34730	−	7.52974i	−0.339467	−	0.587974i
$165$	−0.766044	−	1.32683i	−0.0596365	−	0.103293i
$166$	−7.75877	+	13.4386i	−0.602197	+	1.04304i
$167$	3.44831			0.266838			0.133419	−	0.991060i	$-0.457404\pi$
$167$	3.44831			0.266838			0.133419	+	0.991060i	$0.457404\pi$
$168$	2.08125	−	3.47843i	0.160572	−	0.268367i
$169$	6.09327			0.468713
$170$	2.17365	−	3.76487i	0.166711	−	0.288752i
$171$	2.18732	+	3.78855i	0.167268	+	0.289717i
$172$	4.63816	+	8.03352i	0.353656	+	0.612550i
$173$	3.63041	−	6.28806i	0.276015	−	0.478073i	−0.694375	−	0.719613i	$-0.744319\pi$
$173$	3.63041	−	6.28806i	0.276015	−	0.478073i	0.970391	+	0.241540i	$0.0776526\pi$
$174$	11.3327			0.859133
$175$	1.35844	−	2.27038i	0.102688	−	0.171625i
$176$	−1.00000			−0.0753778
$177$	4.12836	−	7.15052i	0.310306	−	0.537466i
$178$	−7.21941	−	12.5044i	−0.541117	−	0.937243i
$179$	4.45336	+	7.71345i	0.332860	+	0.576530i	0.983071	−	0.183223i	$-0.0586530\pi$
$179$	4.45336	+	7.71345i	0.332860	+	0.576530i	−0.650211	+	0.759753i	$0.725320\pi$
$180$	0.326352	−	0.565258i	0.0243248	−	0.0421318i
$181$	−3.71419			−0.276074			−0.138037	−	0.990427i	$-0.544079\pi$
$181$	−3.71419			−0.276074			−0.138037	+	0.990427i	$0.544079\pi$
$182$	11.5594	+	0.180257i	0.856842	+	0.0133615i
$183$	10.4192			0.770211
$184$	3.57398	−	6.19031i	0.263477	−	0.456356i
$185$	−0.946967	−	1.64019i	−0.0696224	−	0.120589i
$186$	4.85117	+	8.40247i	0.355705	+	0.616099i
$187$	2.17365	−	3.76487i	0.158953	−	0.275314i
$188$	−12.4979			−0.911506
$189$	7.20233	+	12.9365i	0.523893	+	0.940994i
$190$	−6.70233			−0.486238
$191$	4.19459	−	7.26525i	0.303510	−	0.525695i	−0.673418	−	0.739262i	$-0.735175\pi$
$191$	4.19459	−	7.26525i	0.303510	−	0.525695i	0.976928	+	0.213567i	$0.0685081\pi$
$192$	0.766044	+	1.32683i	0.0552845	+	0.0957556i
$193$	−4.28359	−	7.41939i	−0.308339	−	0.534059i	0.669660	−	0.742668i	$-0.266440\pi$
$193$	−4.28359	−	7.41939i	−0.308339	−	0.534059i	−0.977999	+	0.208609i	$0.933107\pi$
$194$	1.46791	−	2.54250i	0.105390	−	0.182541i
$195$	−6.69459			−0.479410
$196$	6.99660	+	0.218262i	0.499757	+	0.0155902i
$197$	−16.6263			−1.18457			−0.592287	−	0.805727i	$-0.701775\pi$
$197$	−16.6263			−1.18457			−0.592287	+	0.805727i	$0.701775\pi$
$198$	0.326352	−	0.565258i	0.0231928	−	0.0401711i
$199$	12.3059	+	21.3144i	0.872340	+	1.51094i	0.859569	+	0.511019i	$0.170732\pi$
$199$	12.3059	+	21.3144i	0.872340	+	1.51094i	0.0127710	+	0.999918i	$0.495935\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	7.24170	−	12.5430i	0.510790	−	0.884714i
$202$	−13.4534			−0.946575
$203$	9.51976	+	17.0990i	0.668156	+	1.20011i
$204$	−6.66044			−0.466324
$205$	−4.34730	+	7.52974i	−0.303628	+	0.525900i
$206$	−3.65270	−	6.32667i	−0.254496	−	0.440800i
$207$	2.33275	+	4.04044i	0.162137	+	0.280830i
$208$	−2.18479	+	3.78417i	−0.151488	+	0.262385i
$209$	−6.70233			−0.463610
$210$	−4.05303	−	0.0632028i	−0.279686	−	0.00436141i
$211$	28.8307			1.98479			0.992393	−	0.123108i	$-0.0392862\pi$
$211$	28.8307			1.98479			0.992393	+	0.123108i	$0.0392862\pi$
$212$	−1.11334	+	1.92836i	−0.0764646	+	0.132441i
$213$	−0.907604	−	1.57202i	−0.0621880	−	0.107713i
$214$	1.95811	+	3.39155i	0.133854	+	0.231841i
$215$	4.63816	−	8.03352i	0.316320	−	0.547882i
$216$	−5.59627			−0.380778
$217$	−8.60266	+	14.3778i	−0.583987	+	0.976026i
$218$	−18.9709			−1.28487
$219$	−3.92855	+	6.80445i	−0.265467	+	0.459802i
$220$	0.500000	+	0.866025i	0.0337100	+	0.0583874i
$221$	−9.49794	−	16.4509i	−0.638901	−	1.10661i
$222$	−1.45084	+	2.51292i	−0.0973738	+	0.168656i
$223$	−4.61081			−0.308763			−0.154381	−	0.988011i	$-0.549338\pi$
$223$	−4.61081			−0.308763			−0.154381	+	0.988011i	$0.549338\pi$
$224$	−1.35844	+	2.27038i	−0.0907646	+	0.151696i
$225$	−0.652704			−0.0435136
$226$	2.28312	−	3.95448i	0.151871	−	0.263048i
$227$	−5.88713	−	10.1968i	−0.390742	−	0.676785i	0.601805	−	0.798643i	$-0.294448\pi$
$227$	−5.88713	−	10.1968i	−0.390742	−	0.676785i	−0.992548	+	0.121857i	$0.961115\pi$
$228$	5.13429	+	8.89284i	0.340026	+	0.588943i
$229$	−11.5963	+	20.0853i	−0.766303	+	1.32728i	0.173252	+	0.984878i	$0.444572\pi$
$229$	−11.5963	+	20.0853i	−0.766303	+	1.32728i	−0.939555	+	0.342398i	$0.888761\pi$
$230$	−7.14796			−0.471322
$231$	−4.05303	−	0.0632028i	−0.266670	−	0.00415844i
$232$	−7.39693			−0.485632
$233$	−2.76604	+	4.79093i	−0.181210	+	0.313864i	−0.942293	−	0.334790i	$-0.891335\pi$
$233$	−2.76604	+	4.79093i	−0.181210	+	0.313864i	0.761083	+	0.648654i	$0.224668\pi$
$234$	−1.42602	−	2.46994i	−0.0932220	−	0.161465i
$235$	6.24897	+	10.8235i	0.407638	+	0.706050i
$236$	−2.69459	+	4.66717i	−0.175403	+	0.303807i
$237$	−10.8229			−0.703026
$238$	−5.59492	−	10.0494i	−0.362665	−	0.651404i
$239$	−23.4492			−1.51681			−0.758403	−	0.651786i	$-0.774020\pi$
$239$	−23.4492			−1.51681			−0.758403	+	0.651786i	$0.774020\pi$
$240$	0.766044	−	1.32683i	0.0494480	−	0.0856464i
$241$	−13.8229	−	23.9420i	−0.890414	−	1.54224i	−0.839379	−	0.543546i	$-0.817081\pi$
$241$	−13.8229	−	23.9420i	−0.890414	−	1.54224i	−0.0510350	−	0.998697i	$-0.516252\pi$
$242$	0.500000	+	0.866025i	0.0321412	+	0.0556702i
$243$	3.32635	−	5.76141i	0.213386	−	0.369595i
$244$	−6.80066			−0.435368
$245$	−3.30928	−	6.16836i	−0.211422	−	0.394082i
$246$	13.3209			0.849309
$247$	−14.6432	+	25.3628i	−0.931725	+	1.61380i
$248$	−3.16637	−	5.48432i	−0.201065	−	0.348255i
$249$	−11.8871	−	20.5891i	−0.753316	−	1.30478i
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	24.4243			1.54165			0.770823	−	0.637049i	$-0.219845\pi$
$251$	24.4243			1.54165			0.770823	+	0.637049i	$0.219845\pi$
$252$	−0.840022	−	1.50881i	−0.0529164	−	0.0950463i
$253$	−7.14796			−0.449388
$254$	−0.500000	+	0.866025i	−0.0313728	+	0.0543393i
$255$	3.33022	+	5.76811i	0.208547	+	0.361213i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.26857	−	10.8575i	0.391023	−	0.677271i	−0.601562	−	0.798826i	$-0.705455\pi$
$257$	6.26857	−	10.8575i	0.391023	−	0.677271i	0.992585	+	0.121555i	$0.0387881\pi$
$258$	−14.2121			−0.884809
$259$	−5.01027	−	0.0781298i	−0.311323	−	0.00485475i
$260$	4.36959			0.270990
$261$	2.41400	−	4.18117i	0.149423	−	0.258808i
$262$	0.109470	+	0.189608i	0.00676310	+	0.0117140i
$263$	−10.7738	−	18.6607i	−0.664340	−	1.15067i	−0.979464	−	0.201620i	$-0.935379\pi$
$263$	−10.7738	−	18.6607i	−0.664340	−	1.15067i	0.315124	−	0.949051i	$-0.397954\pi$
$264$	0.766044	−	1.32683i	0.0471468	−	0.0816606i
$265$	2.22668			0.136784
$266$	−9.10472	+	15.2169i	−0.558246	+	0.933006i
$267$	22.1215			1.35382
$268$	−4.72668	+	8.18685i	−0.288728	+	0.500092i
$269$	6.84255	+	11.8516i	0.417198	+	0.722607i	0.995656	−	0.0931042i	$-0.0296790\pi$
$269$	6.84255	+	11.8516i	0.417198	+	0.722607i	−0.578459	+	0.815712i	$0.696346\pi$
$270$	2.79813	+	4.84651i	0.170289	+	0.294949i
$271$	9.23442	−	15.9945i	0.560951	−	0.971596i	−0.436463	−	0.899722i	$-0.643769\pi$
$271$	9.23442	−	15.9945i	0.560951	−	0.971596i	0.997414	−	0.0718736i	$-0.0228978\pi$
$272$	4.34730			0.263594
$273$	−9.09421	+	15.1993i	−0.550406	+	0.919903i
$274$	15.4047			0.930630
$275$	0.500000	−	0.866025i	0.0301511	−	0.0522233i
$276$	5.47565	+	9.48411i	0.329596	+	0.570876i
$277$	8.85978	+	15.3456i	0.532333	+	0.922028i	0.999287	+	0.0377462i	$0.0120179\pi$
$277$	8.85978	+	15.3456i	0.532333	+	0.922028i	−0.466954	+	0.884281i	$0.654649\pi$
$278$	2.35710	−	4.08261i	0.141369	−	0.244859i
$279$	4.13341			0.247461
$280$	2.64543	+	0.0412527i	0.158095	+	0.00246532i
$281$	18.9222			1.12880			0.564402	−	0.825500i	$-0.309107\pi$
$281$	18.9222			1.12880			0.564402	+	0.825500i	$0.309107\pi$
$282$	9.57398	−	16.5826i	0.570122	−	0.987480i
$283$	1.89393	+	3.28039i	0.112583	+	0.194999i	0.916811	−	0.399322i	$-0.130754\pi$
$283$	1.89393	+	3.28039i	0.112583	+	0.194999i	−0.804228	+	0.594321i	$0.797421\pi$
$284$	0.592396	+	1.02606i	0.0351523	+	0.0608855i
$285$	5.13429	−	8.89284i	0.304129	−	0.526767i
$286$	4.36959			0.258379
$287$	11.1898	+	20.0987i	0.660516	+	1.18639i
$288$	0.652704			0.0384609
$289$	−0.949493	+	1.64457i	−0.0558525	+	0.0967394i
$290$	3.69846	+	6.40593i	0.217181	+	0.376169i
$291$	2.24897	+	3.89533i	0.131837	+	0.228348i
$292$	2.56418	−	4.44129i	0.150057	−	0.259907i
$293$	−20.7939			−1.21479			−0.607395	−	0.794400i	$-0.707785\pi$
$293$	−20.7939			−1.21479			−0.607395	+	0.794400i	$0.707785\pi$
$294$	−5.64930	+	9.11608i	−0.329474	+	0.531661i
$295$	5.38919			0.313771
$296$	0.946967	−	1.64019i	0.0550413	−	0.0953344i
$297$	2.79813	+	4.84651i	0.162364	+	0.281223i
$298$	−2.87211	−	4.97464i	−0.166377	−	0.288173i
$299$	−15.6168	+	27.0491i	−0.903143	+	1.56429i
$300$	−1.53209			−0.0884552
$301$	−11.9385	−	21.4435i	−0.688124	−	1.23598i
$302$	−21.6459			−1.24558
$303$	10.3059	−	17.8503i	0.592057	−	1.02547i
$304$	−3.35117	−	5.80439i	−0.192203	−	0.332905i
$305$	3.40033	+	5.88954i	0.194702	+	0.337234i
$306$	−1.41875	+	2.45734i	−0.0811044	+	0.140477i
$307$	−22.1385			−1.26351			−0.631754	−	0.775169i	$-0.717665\pi$
$307$	−22.1385			−1.26351			−0.631754	+	0.775169i	$0.717665\pi$
$308$	2.64543	+	0.0412527i	0.150737	+	0.00235059i
$309$	11.1925			0.636721
$310$	−3.16637	+	5.48432i	−0.179838	+	0.311489i
$311$	−12.5510	−	21.7389i	−0.711700	−	1.23270i	−0.964218	−	0.265109i	$-0.914592\pi$
$311$	−12.5510	−	21.7389i	−0.711700	−	1.23270i	0.252518	−	0.967592i	$-0.418741\pi$
$312$	−3.34730	−	5.79769i	−0.189503	−	0.328229i
$313$	−16.0993	+	27.8847i	−0.909984	+	1.57614i	−0.0959002	+	0.995391i	$0.530573\pi$
$313$	−16.0993	+	27.8847i	−0.909984	+	1.57614i	−0.814084	+	0.580748i	$0.802760\pi$
$314$	−1.75103			−0.0988163
$315$	−0.886659	+	1.48189i	−0.0499576	+	0.0834949i
$316$	7.06418			0.397391
$317$	7.82682	−	13.5564i	0.439598	−	0.761406i	−0.558060	−	0.829800i	$-0.688454\pi$
$317$	7.82682	−	13.5564i	0.439598	−	0.761406i	0.997658	+	0.0683944i	$0.0217876\pi$
$318$	−1.70574	−	2.95442i	−0.0956530	−	0.165676i
$319$	3.69846	+	6.40593i	0.207074	+	0.358663i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	−6.00000			−0.334887
$322$	−9.71007	+	16.2286i	−0.541121	+	0.904384i
$323$	29.1370			1.62123
$324$	3.30793	−	5.72951i	0.183774	−	0.318306i
$325$	−2.18479	−	3.78417i	−0.121190	−	0.209908i
$326$	2.66772	+	4.62062i	0.147751	+	0.255913i
$327$	14.5326	−	25.1711i	0.803652	−	1.39197i
$328$	−8.69459			−0.480079
$329$	33.0624	+	0.515574i	1.82279	+	0.0284245i
$330$	−1.53209			−0.0843387
$331$	−4.16250	+	7.20967i	−0.228792	+	0.396279i	−0.957450	−	0.288598i	$-0.906811\pi$
$331$	−4.16250	+	7.20967i	−0.228792	+	0.396279i	0.728658	+	0.684877i	$0.240144\pi$
$332$	7.75877	+	13.4386i	0.425818	+	0.737538i
$333$	0.618089	+	1.07056i	0.0338710	+	0.0586664i
$334$	1.72416	−	2.98632i	0.0943416	−	0.163404i
$335$	9.45336			0.516492
$336$	−1.97178	−	3.54163i	−0.107570	−	0.193212i
$337$	0.135163			0.00736278			0.00368139	−	0.999993i	$-0.498828\pi$
$337$	0.135163			0.00736278			0.00368139	+	0.999993i	$0.498828\pi$
$338$	3.04664	−	5.27693i	0.165715	−	0.287027i
$339$	3.49794	+	6.05861i	0.189982	+	0.329059i
$340$	−2.17365	−	3.76487i	−0.117883	−	0.204179i
$341$	−3.16637	+	5.48432i	−0.171469	+	0.296993i
$342$	4.37464			0.236553
$343$	−18.5000	−	0.866025i	−0.998906	−	0.0467610i
$344$	9.27631			0.500145
$345$	5.47565	−	9.48411i	0.294799	−	0.510607i
$346$	−3.63041	−	6.28806i	−0.195172	−	0.338048i
$347$	9.68004	+	16.7663i	0.519652	+	0.900064i	0.999739	+	0.0228429i	$0.00727174\pi$
$347$	9.68004	+	16.7663i	0.519652	+	0.900064i	−0.480087	+	0.877221i	$0.659395\pi$
$348$	5.66637	−	9.81445i	0.303750	−	0.526110i
$349$	27.2276			1.45746			0.728730	−	0.684801i	$-0.240111\pi$
$349$	27.2276			1.45746			0.728730	+	0.684801i	$0.240111\pi$
$350$	−1.28699	−	2.31164i	−0.0687925	−	0.123562i
$351$	24.4534			1.30522
$352$	−0.500000	+	0.866025i	−0.0266501	+	0.0461593i
$353$	−2.47565	−	4.28795i	−0.131766	−	0.228225i	0.792592	−	0.609753i	$-0.208731\pi$
$353$	−2.47565	−	4.28795i	−0.131766	−	0.228225i	−0.924357	+	0.381528i	$0.875398\pi$
$354$	−4.12836	−	7.15052i	−0.219420	−	0.380046i
$355$	0.592396	−	1.02606i	0.0314411	−	0.0544576i
$356$	−14.4388			−0.765256
$357$	17.6197	+	0.274761i	0.932535	+	0.0145419i
$358$	8.90673			0.470735
$359$	5.90673	−	10.2308i	0.311745	−	0.539958i	−0.666995	−	0.745062i	$-0.732420\pi$
$359$	5.90673	−	10.2308i	0.311745	−	0.539958i	0.978740	+	0.205104i	$0.0657532\pi$
$360$	−0.326352	−	0.565258i	−0.0172003	−	0.0297917i
$361$	−12.9606	−	22.4485i	−0.682139	−	1.18150i
$362$	−1.85710	+	3.21659i	−0.0976068	+	0.169060i
$363$	−1.53209			−0.0804138
$364$	5.93582	−	9.92063i	0.311122	−	0.519982i
$365$	−5.12836			−0.268430
$366$	5.20961	−	9.02330i	0.272311	−	0.471656i
$367$	8.04963	+	13.9424i	0.420187	+	0.727786i	0.995957	−	0.0898259i	$-0.0286311\pi$
$367$	8.04963	+	13.9424i	0.420187	+	0.727786i	−0.575770	+	0.817612i	$0.695298\pi$
$368$	−3.57398	−	6.19031i	−0.186306	−	0.322692i
$369$	2.83750	−	4.91469i	0.147714	−	0.255848i
$370$	−1.89393			−0.0984609
$371$	3.02481	−	5.05542i	0.157041	−	0.262464i
$372$	9.70233			0.503043
$373$	−15.6186	+	27.0521i	−0.808698	+	1.40071i	0.105068	+	0.994465i	$0.466494\pi$
$373$	−15.6186	+	27.0521i	−0.808698	+	1.40071i	−0.913766	+	0.406241i	$0.866839\pi$
$374$	−2.17365	−	3.76487i	−0.112397	−	0.194677i
$375$	0.766044	+	1.32683i	0.0395584	+	0.0685171i
$376$	−6.24897	+	10.8235i	−0.322266	+	0.558181i
$377$	32.3215			1.66464
$378$	14.8045	+	0.230861i	0.761463	+	0.0118742i
$379$	17.4783			0.897802			0.448901	−	0.893581i	$-0.351816\pi$
$379$	17.4783			0.897802			0.448901	+	0.893581i	$0.351816\pi$
$380$	−3.35117	+	5.80439i	−0.171911	+	0.297759i
$381$	−0.766044	−	1.32683i	−0.0392456	−	0.0679755i
$382$	−4.19459	−	7.26525i	−0.214614	−	0.371722i
$383$	8.41921	−	14.5825i	0.430202	−	0.745131i	−0.566689	−	0.823932i	$-0.691776\pi$
$383$	8.41921	−	14.5825i	0.430202	−	0.745131i	0.996890	+	0.0788007i	$0.0251091\pi$
$384$	1.53209			0.0781841
$385$	−1.28699	−	2.31164i	−0.0655910	−	0.117812i
$386$	−8.56717			−0.436058
$387$	−3.02734	+	5.24351i	−0.153888	+	0.266543i
$388$	−1.46791	−	2.54250i	−0.0745219	−	0.129076i
$389$	9.46110	+	16.3871i	0.479697	+	0.830860i	0.999729	−	0.0232873i	$-0.00741325\pi$
$389$	9.46110	+	16.3871i	0.479697	+	0.830860i	−0.520032	+	0.854147i	$0.674080\pi$
$390$	−3.34730	+	5.79769i	−0.169497	+	0.293577i
$391$	31.0743			1.57149
$392$	3.68732	−	5.95010i	0.186238	−	0.300525i
$393$	−0.335437			−0.0169205
$394$	−8.31315	+	14.3988i	−0.418810	+	0.725401i
$395$	−3.53209	−	6.11776i	−0.177719	−	0.307818i
$396$	−0.326352	−	0.565258i	−0.0163998	−	0.0284053i
$397$	−7.30840	+	12.6585i	−0.366798	+	0.635313i	−0.989063	−	0.147494i	$-0.952879\pi$
$397$	−7.30840	+	12.6585i	−0.366798	+	0.635313i	0.622265	+	0.782807i	$0.286213\pi$
$398$	24.6117			1.23368
$399$	−13.2155	−	23.7372i	−0.661604	−	1.18835i
$400$	1.00000			0.0500000
$401$	3.23396	−	5.60138i	0.161496	−	0.279719i	−0.773909	−	0.633296i	$-0.781701\pi$
$401$	3.23396	−	5.60138i	0.161496	−	0.279719i	0.935405	+	0.353577i	$0.115035\pi$
$402$	−7.24170	−	12.5430i	−0.361183	−	0.625587i
$403$	13.8357	+	23.9642i	0.689207	+	1.19374i
$404$	−6.72668	+	11.6510i	−0.334665	+	0.579657i
$405$	−6.61587			−0.328745
$406$	19.5680	+	0.305143i	0.971146	+	0.0151440i
$407$	−1.89393			−0.0938788
$408$	−3.33022	+	5.76811i	−0.164871	+	0.285564i
$409$	1.08378	+	1.87716i	0.0535894	+	0.0928195i	0.891576	−	0.452872i	$-0.149600\pi$
$409$	1.08378	+	1.87716i	0.0535894	+	0.0928195i	−0.837986	+	0.545691i	$0.816267\pi$
$410$	4.34730	+	7.52974i	0.214698	+	0.371867i
$411$	−11.8007	+	20.4393i	−0.582084	+	1.00820i
$412$	−7.30541			−0.359912
$413$	7.32089	−	12.2355i	0.360237	−	0.602070i
$414$	4.66550			0.229297
$415$	7.75877	−	13.4386i	0.380863	−	0.659674i
$416$	2.18479	+	3.78417i	0.107118	+	0.185534i
$417$	3.61128	+	6.25492i	0.176845	+	0.306305i
$418$	−3.35117	+	5.80439i	−0.163911	+	0.283902i
$419$	24.6709			1.20525			0.602626	−	0.798024i	$-0.294121\pi$
$419$	24.6709			1.20525			0.602626	+	0.798024i	$0.294121\pi$
$420$	−2.08125	+	3.47843i	−0.101555	+	0.169730i
$421$	9.83244			0.479204			0.239602	−	0.970871i	$-0.422983\pi$
$421$	9.83244			0.479204			0.239602	+	0.970871i	$0.422983\pi$
$422$	14.4153	−	24.9681i	0.701728	−	1.21543i
$423$	−4.07873	−	7.06456i	−0.198314	−	0.343491i
$424$	1.11334	+	1.92836i	0.0540686	+	0.0936496i
$425$	−2.17365	+	3.76487i	−0.105437	+	0.182623i
$426$	−1.81521			−0.0879471
$427$	17.9907	+	0.280545i	0.870629	+	0.0135765i
$428$	3.91622			0.189298
$429$	−3.34730	+	5.79769i	−0.161609	+	0.279915i
$430$	−4.63816	−	8.03352i	−0.223672	−	0.387411i
$431$	−3.51754	−	6.09256i	−0.169434	−	0.293468i	0.768787	−	0.639505i	$-0.220861\pi$
$431$	−3.51754	−	6.09256i	−0.169434	−	0.293468i	−0.938221	+	0.346037i	$0.887527\pi$
$432$	−2.79813	+	4.84651i	−0.134625	+	0.233178i
$433$	−15.9864			−0.768257			−0.384128	−	0.923280i	$-0.625498\pi$
$433$	−15.9864			−0.768257			−0.384128	+	0.923280i	$0.625498\pi$
$434$	8.15018	+	14.6390i	0.391221	+	0.702695i
$435$	−11.3327			−0.543364
$436$	−9.48545	+	16.4293i	−0.454271	+	0.786820i
$437$	−23.9540	−	41.4895i	−1.14587	−	1.98471i
$438$	3.92855	+	6.80445i	0.187713	+	0.325129i
$439$	−0.674992	+	1.16912i	−0.0322156	+	0.0557991i	−0.881684	−	0.471841i	$-0.843590\pi$
$439$	−0.674992	+	1.16912i	−0.0322156	+	0.0557991i	0.849468	+	0.527640i	$0.176923\pi$
$440$	1.00000			0.0476731
$441$	2.15998	+	4.02611i	0.102856	+	0.191720i
$442$	−18.9959			−0.903542
$443$	3.84255	−	6.65549i	0.182565	−	0.316212i	−0.760188	−	0.649703i	$-0.774893\pi$
$443$	3.84255	−	6.65549i	0.182565	−	0.316212i	0.942753	+	0.333491i	$0.108227\pi$
$444$	1.45084	+	2.51292i	0.0688537	+	0.119258i
$445$	7.21941	+	12.5044i	0.342233	+	0.592765i
$446$	−2.30541	+	3.99308i	−0.109164	+	0.189078i
$447$	8.80066			0.416257
$448$	1.28699	+	2.31164i	0.0608045	+	0.109215i
$449$	21.9959			1.03805			0.519025	−	0.854759i	$-0.326295\pi$
$449$	21.9959			1.03805			0.519025	+	0.854759i	$0.326295\pi$
$450$	−0.326352	+	0.565258i	−0.0153844	+	0.0266465i
$451$	4.34730	+	7.52974i	0.204706	+	0.354562i
$452$	−2.28312	−	3.95448i	−0.107389	−	0.186003i
$453$	16.5817	−	28.7204i	0.779077	−	1.34940i
$454$	−11.7743			−0.552593
$455$	−11.5594	−	0.180257i	−0.541914	−	0.00845058i
$456$	10.2686			0.480870
$457$	−8.00387	+	13.8631i	−0.374405	+	0.648489i	−0.990238	−	0.139388i	$-0.955486\pi$
$457$	−8.00387	+	13.8631i	−0.374405	+	0.648489i	0.615833	+	0.787877i	$0.288820\pi$
$458$	11.5963	+	20.0853i	0.541858	+	0.938526i
$459$	−12.1643	−	21.0692i	−0.567782	−	0.983427i
$460$	−3.57398	+	6.19031i	−0.166638	+	0.288625i
$461$	13.7128			0.638667			0.319334	−	0.947642i	$-0.396541\pi$
$461$	13.7128			0.638667			0.319334	+	0.947642i	$0.396541\pi$
$462$	−2.08125	+	3.47843i	−0.0968286	+	0.161831i
$463$	28.0838			1.30516			0.652582	−	0.757718i	$-0.273686\pi$
$463$	28.0838			1.30516			0.652582	+	0.757718i	$0.273686\pi$
$464$	−3.69846	+	6.40593i	−0.171697	+	0.297388i
$465$	−4.85117	−	8.40247i	−0.224967	−	0.389655i
$466$	2.76604	+	4.79093i	0.128135	+	0.221936i
$467$	−7.86824	+	13.6282i	−0.364099	+	0.630638i	−0.988631	−	0.150361i	$-0.951956\pi$
$467$	−7.86824	+	13.6282i	−0.364099	+	0.630638i	0.624532	+	0.780999i	$0.285290\pi$
$468$	−2.85204			−0.131836
$469$	12.8418	−	21.4628i	0.592981	−	0.991058i
$470$	12.4979			0.576487
$471$	1.34137	−	2.32332i	0.0618069	−	0.107053i
$472$	2.69459	+	4.66717i	0.124029	+	0.214824i
$473$	−4.63816	−	8.03352i	−0.213263	−	0.369382i
$474$	−5.41147	+	9.37295i	−0.248557	+	0.430514i
$475$	6.70233			0.307524
$476$	−11.5005	−	0.179338i	−0.527123	−	0.00821993i
$477$	−1.45336			−0.0665449
$478$	−11.7246	+	20.3076i	−0.536272	+	0.928850i
$479$	14.1702	+	24.5436i	0.647455	+	1.12142i	0.983729	+	0.179661i	$0.0575000\pi$
$479$	14.1702	+	24.5436i	0.647455	+	1.12142i	−0.336274	+	0.941764i	$0.609167\pi$
$480$	−0.766044	−	1.32683i	−0.0349650	−	0.0605611i
$481$	−4.13785	+	7.16697i	−0.188670	+	0.326786i
$482$	−27.6459			−1.25924
$483$	−14.0942	−	25.3154i	−0.641309	−	1.15189i
$484$	1.00000			0.0454545
$485$	−1.46791	+	2.54250i	−0.0666544	+	0.115449i
$486$	−3.32635	−	5.76141i	−0.150886	−	0.261343i
$487$	−2.40373	−	4.16339i	−0.108924	−	0.188661i	0.806411	−	0.591356i	$-0.201407\pi$
$487$	−2.40373	−	4.16339i	−0.108924	−	0.188661i	−0.915334	+	0.402694i	$0.868074\pi$
$488$	−3.40033	+	5.88954i	−0.153926	+	0.266607i
$489$	−8.17436			−0.369657
$490$	−6.99660	−	0.218262i	−0.316074	−	0.00986008i
$491$	−42.3022			−1.90907			−0.954536	−	0.298095i	$-0.903649\pi$
$491$	−42.3022			−1.90907			−0.954536	+	0.298095i	$0.903649\pi$
$492$	6.66044	−	11.5362i	0.300276	−	0.520093i
$493$	−16.0783	−	27.8485i	−0.724131	−	1.25423i
$494$	14.6432	+	25.3628i	0.658829	+	1.14113i
$495$	−0.326352	+	0.565258i	−0.0146684	+	0.0254065i
$496$	−6.33275			−0.284349
$497$	−1.52481	−	2.73881i	−0.0683973	−	0.122852i
$498$	−23.7743			−1.06535
$499$	−13.2121	+	22.8841i	−0.591456	+	1.02443i	0.402580	+	0.915385i	$0.368113\pi$
$499$	−13.2121	+	22.8841i	−0.591456	+	1.02443i	−0.994037	+	0.109048i	$0.965220\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	2.64156	+	4.57531i	0.118016	+	0.204410i
$502$	12.2121	−	21.1520i	0.545054	−	0.944062i
$503$	−7.96492			−0.355138			−0.177569	−	0.984108i	$-0.556823\pi$
$503$	−7.96492			−0.355138			−0.177569	+	0.984108i	$0.556823\pi$
$504$	−1.72668	−	0.0269258i	−0.0769125	−	0.00119937i
$505$	13.4534			0.598667
$506$	−3.57398	+	6.19031i	−0.158883	+	0.275193i
$507$	4.66772	+	8.08473i	0.207301	+	0.359055i
$508$	0.500000	+	0.866025i	0.0221839	+	0.0384237i
$509$	1.04189	−	1.80460i	0.0461809	−	0.0799877i	−0.842011	−	0.539460i	$-0.818628\pi$
$509$	1.04189	−	1.80460i	0.0461809	−	0.0799877i	0.888192	+	0.459473i	$0.151962\pi$
$510$	6.66044			0.294929
$511$	−6.96657	+	11.6433i	−0.308183	+	0.515071i
$512$	−1.00000			−0.0441942
$513$	−18.7540	+	32.4829i	−0.828010	+	1.43416i
$514$	−6.26857	−	10.8575i	−0.276495	−	0.478903i
$515$	3.65270	+	6.32667i	0.160957	+	0.278786i
$516$	−7.10607	+	12.3081i	−0.312827	+	0.541833i
$517$	12.4979			0.549659
$518$	−2.57280	+	4.29995i	−0.113042	+	0.188929i
$519$	11.1242			0.488300
$520$	2.18479	−	3.78417i	0.0958095	−	0.165947i
$521$	1.48040	+	2.56413i	0.0648575	+	0.112336i	0.896631	−	0.442779i	$-0.146007\pi$
$521$	1.48040	+	2.56413i	0.0648575	+	0.112336i	−0.831773	+	0.555115i	$0.812674\pi$
$522$	−2.41400	−	4.18117i	−0.105658	−	0.183005i
$523$	11.6604	−	20.1965i	0.509876	−	0.883131i	−0.490059	−	0.871689i	$-0.663025\pi$
$523$	11.6604	−	20.1965i	0.509876	−	0.883131i	0.999935	−	0.0114412i	$-0.00364192\pi$
$524$	0.218941			0.00956447
$525$	4.05303	+	0.0632028i	0.176889	+	0.00275839i
$526$	−21.5476			−0.939519
$527$	13.7652	−	23.8420i	0.599620	−	1.03857i
$528$	−0.766044	−	1.32683i	−0.0333378	−	0.0577428i
$529$	−14.0466	−	24.3295i	−0.610723	−	1.05780i
$530$	1.11334	−	1.92836i	0.0483604	−	0.0837627i
$531$	−3.51754			−0.152648
$532$	8.62583	+	15.4934i	0.373977	+	0.671722i
$533$	37.9918			1.64561
$534$	11.0608	−	19.1578i	0.478647	−	0.829040i
$535$	−1.95811	−	3.39155i	−0.0846565	−	0.146629i
$536$	4.72668	+	8.18685i	0.204162	+	0.353618i
$537$	−6.82295	+	11.8177i	−0.294432	+	0.509971i
$538$	13.6851			0.590006
$539$	−6.99660	−	0.218262i	−0.301365	−	0.00940121i
$540$	5.59627			0.240825
$541$	−14.3059	+	24.7785i	−0.615058	+	1.06531i	0.375317	+	0.926897i	$0.377534\pi$
$541$	−14.3059	+	24.7785i	−0.615058	+	1.06531i	−0.990374	+	0.138414i	$0.955799\pi$
$542$	−9.23442	−	15.9945i	−0.396652	−	0.687022i
$543$	−2.84524	−	4.92809i	−0.122101	−	0.211485i
$544$	2.17365	−	3.76487i	0.0931944	−	0.161417i
$545$	18.9709			0.812624
$546$	8.61587	+	15.4755i	0.368725	+	0.662289i
$547$	−5.26083			−0.224937			−0.112468	−	0.993655i	$-0.535876\pi$
$547$	−5.26083			−0.224937			−0.112468	+	0.993655i	$0.535876\pi$
$548$	7.70233	−	13.3408i	0.329027	−	0.569892i
$549$	−2.21941	−	3.84413i	−0.0947220	−	0.164063i
$550$	−0.500000	−	0.866025i	−0.0213201	−	0.0369274i
$551$	−24.7883	+	42.9347i	−1.05602	+	1.82908i
$552$	10.9513			0.466118
$553$	−18.6878	−	0.291416i	−0.794685	−	0.0123923i
$554$	17.7196			0.752832
$555$	1.45084	−	2.51292i	0.0615846	−	0.106668i
$556$	−2.35710	−	4.08261i	−0.0999632	−	0.173141i
$557$	−18.0692	−	31.2968i	−0.765618	−	1.32609i	−0.939919	−	0.341397i	$-0.889100\pi$
$557$	−18.0692	−	31.2968i	−0.765618	−	1.32609i	0.174301	−	0.984692i	$-0.444233\pi$
$558$	2.06670	−	3.57964i	0.0874906	−	0.151538i
$559$	−40.5336			−1.71439
$560$	1.35844	−	2.27038i	0.0574046	−	0.0959412i
$561$	6.66044			0.281204
$562$	9.46110	−	16.3871i	0.399093	−	0.691249i
$563$	15.3182	+	26.5319i	0.645585	+	1.11819i	0.984166	+	0.177249i	$0.0567198\pi$
$563$	15.3182	+	26.5319i	0.645585	+	1.11819i	−0.338581	+	0.940937i	$0.609947\pi$
$564$	−9.57398	−	16.5826i	−0.403137	−	0.698254i
$565$	−2.28312	+	3.95448i	−0.0960515	+	0.166366i
$566$	3.78787			0.159216
$567$	−8.98726	+	15.0206i	−0.377430	+	0.630804i
$568$	1.18479			0.0497128
$569$	−8.24628	+	14.2830i	−0.345702	+	0.598774i	−0.985481	−	0.169785i	$-0.945693\pi$
$569$	−8.24628	+	14.2830i	−0.345702	+	0.598774i	0.639779	+	0.768559i	$0.279026\pi$
$570$	−5.13429	−	8.89284i	−0.215052	−	0.372480i
$571$	15.1446	+	26.2311i	0.633780	+	1.09774i	0.986772	+	0.162113i	$0.0518308\pi$
$571$	15.1446	+	26.2311i	0.633780	+	1.09774i	−0.352992	+	0.935626i	$0.614836\pi$
$572$	2.18479	−	3.78417i	0.0913508	−	0.158224i
$573$	12.8530			0.536941
$574$	23.0009	+	0.358675i	0.960040	+	0.0149708i
$575$	7.14796			0.298090
$576$	0.326352	−	0.565258i	0.0135980	−	0.0235524i
$577$	10.3500	+	17.9267i	0.430876	+	0.746298i	0.996949	−	0.0780566i	$-0.0248715\pi$
$577$	10.3500	+	17.9267i	0.430876	+	0.746298i	−0.566073	+	0.824355i	$0.691538\pi$
$578$	0.949493	+	1.64457i	0.0394937	+	0.0684051i
$579$	6.56283	−	11.3672i	0.272742	−	0.472403i
$580$	7.39693			0.307141
$581$	−19.9709	−	35.8709i	−0.828533	−	1.48818i
$582$	4.49794			0.186446
$583$	1.11334	−	1.92836i	0.0461099	−	0.0798646i
$584$	−2.56418	−	4.44129i	−0.106106	−	0.183782i
$585$	1.42602	+	2.46994i	0.0589588	+	0.102120i
$586$	−10.3969	+	18.0080i	−0.429493	+	0.743904i
$587$	−1.63909			−0.0676525			−0.0338262	−	0.999428i	$-0.510769\pi$
$587$	−1.63909			−0.0676525			−0.0338262	+	0.999428i	$0.510769\pi$
$588$	5.07011	+	9.45048i	0.209088	+	0.389731i
$589$	−42.4442			−1.74888
$590$	2.69459	−	4.66717i	0.110935	−	0.192144i
$591$	−12.7365	−	22.0602i	−0.523909	−	0.907437i
$592$	−0.946967	−	1.64019i	−0.0389201	−	0.0674116i
$593$	−15.7101	+	27.2106i	−0.645135	+	1.11741i	0.339135	+	0.940738i	$0.389866\pi$
$593$	−15.7101	+	27.2106i	−0.645135	+	1.11741i	−0.984270	+	0.176670i	$0.943468\pi$
$594$	5.59627			0.229618
$595$	5.59492	+	10.0494i	0.229369	+	0.411984i
$596$	−5.74422			−0.235293
$597$	−18.8537	+	32.6556i	−0.771630	+	1.33650i
$598$	15.6168	+	27.0491i	0.638618	+	1.10612i
$599$	−18.8760	−	32.6942i	−0.771252	−	1.33585i	−0.936877	−	0.349658i	$-0.886298\pi$
$599$	−18.8760	−	32.6942i	−0.771252	−	1.33585i	0.165626	−	0.986189i	$-0.447036\pi$
$600$	−0.766044	+	1.32683i	−0.0312736	+	0.0541675i
$601$	7.28993			0.297362			0.148681	−	0.988885i	$-0.452497\pi$
$601$	7.28993			0.297362			0.148681	+	0.988885i	$0.452497\pi$
$602$	−24.5398	−	0.382673i	−1.00017	−	0.0155966i
$603$	−6.17024			−0.251272
$604$	−10.8229	+	18.7459i	−0.440380	+	0.762760i
$605$	−0.500000	−	0.866025i	−0.0203279	−	0.0352089i
$606$	−10.3059	−	17.8503i	−0.418648	−	0.725119i
$607$	6.74376	−	11.6805i	0.273721	−	0.474098i	−0.696091	−	0.717954i	$-0.745079\pi$
$607$	6.74376	−	11.6805i	0.273721	−	0.474098i	0.969812	+	0.243856i	$0.0784123\pi$
$608$	−6.70233			−0.271816
$609$	−15.3949	+	25.7297i	−0.623831	+	1.04262i
$610$	6.80066			0.275351
$611$	27.3054	−	47.2944i	1.10466	−	1.91332i
$612$	1.41875	+	2.45734i	0.0573495	+	0.0993322i
$613$	−5.12836	−	8.88257i	−0.207132	−	0.358764i	0.743678	−	0.668538i	$-0.233080\pi$
$613$	−5.12836	−	8.88257i	−0.207132	−	0.358764i	−0.950810	+	0.309775i	$0.899746\pi$
$614$	−11.0692	+	19.1725i	−0.446718	+	0.773738i
$615$	−13.3209			−0.537150
$616$	1.35844	−	2.27038i	0.0547331	−	0.0914763i
$617$	13.7980			0.555485			0.277743	−	0.960656i	$-0.410414\pi$
$617$	13.7980			0.555485			0.277743	+	0.960656i	$0.410414\pi$
$618$	5.59627	−	9.69302i	0.225115	−	0.389910i
$619$	19.0077	+	32.9224i	0.763986	+	1.32326i	0.940781	+	0.339014i	$0.110094\pi$
$619$	19.0077	+	32.9224i	0.763986	+	1.32326i	−0.176796	+	0.984248i	$0.556573\pi$
$620$	3.16637	+	5.48432i	0.127165	+	0.220256i
$621$	−20.0009	+	34.6426i	−0.802610	+	1.39016i
$622$	−25.1019			−1.00650
$623$	38.1969	+	0.595640i	1.53033	+	0.0238638i
$624$	−6.69459			−0.267998
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	16.0993	+	27.8847i	0.643456	+	1.11450i
$627$	−5.13429	−	8.89284i	−0.205044	−	0.355146i
$628$	−0.875515	+	1.51644i	−0.0349368	+	0.0605124i
$629$	8.23349			0.328291
$630$	0.840022	+	1.50881i	0.0334673	+	0.0601125i
$631$	−20.6195			−0.820849			−0.410424	−	0.911895i	$-0.634619\pi$
$631$	−20.6195			−0.820849			−0.410424	+	0.911895i	$0.634619\pi$
$632$	3.53209	−	6.11776i	0.140499	−	0.243351i
$633$	22.0856	+	38.2534i	0.877823	+	1.52043i
$634$	−7.82682	−	13.5564i	−0.310843	−	0.538395i
$635$	0.500000	−	0.866025i	0.0198419	−	0.0343672i
$636$	−3.41147			−0.135274
$637$	−16.1121	+	25.9995i	−0.638383	+	1.03014i
$638$	7.39693			0.292847
$639$	−0.386659	+	0.669713i	−0.0152960	+	0.0264935i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	6.42649	+	11.1310i	0.253831	+	0.439648i	0.964577	−	0.263800i	$-0.0849759\pi$
$641$	6.42649	+	11.1310i	0.253831	+	0.439648i	−0.710746	+	0.703448i	$0.751643\pi$
$642$	−3.00000	+	5.19615i	−0.118401	+	0.205076i
$643$	−16.0760			−0.633977			−0.316989	−	0.948429i	$-0.602672\pi$
$643$	−16.0760			−0.633977			−0.316989	+	0.948429i	$0.602672\pi$
$644$	9.19934	+	16.5235i	0.362505	+	0.651116i
$645$	14.2121			0.559602
$646$	14.5685	−	25.2334i	0.573191	−	0.992795i
$647$	14.6946	+	25.4518i	0.577704	+	1.00061i	0.995742	+	0.0921832i	$0.0293846\pi$
$647$	14.6946	+	25.4518i	0.577704	+	1.00061i	−0.418038	+	0.908430i	$0.637282\pi$
$648$	−3.30793	−	5.72951i	−0.129948	−	0.225076i
$649$	2.69459	−	4.66717i	0.105772	−	0.183203i
$650$	−4.36959			−0.171389
$651$	−25.6668	−	0.400247i	−1.00596	−	0.0156869i
$652$	5.33544			0.208952
$653$	−18.2456	+	31.6022i	−0.714004	+	1.23669i	0.249338	+	0.968416i	$0.419787\pi$
$653$	−18.2456	+	31.6022i	−0.714004	+	1.23669i	−0.963342	+	0.268275i	$0.913546\pi$
$654$	−14.5326	−	25.1711i	−0.568268	−	0.984269i
$655$	−0.109470	−	0.189608i	−0.00427736	−	0.00740861i
$656$	−4.34730	+	7.52974i	−0.169733	+	0.293987i
$657$	3.34730			0.130590
$658$	16.9777	−	28.3751i	0.661860	−	1.10618i
$659$	−23.9932			−0.934642			−0.467321	−	0.884088i	$-0.654781\pi$
$659$	−23.9932			−0.934642			−0.467321	+	0.884088i	$0.654781\pi$
$660$	−0.766044	+	1.32683i	−0.0298182	+	0.0516467i
$661$	−7.49794	−	12.9868i	−0.291636	−	0.505129i	0.682561	−	0.730829i	$-0.260866\pi$
$661$	−7.49794	−	12.9868i	−0.291636	−	0.505129i	−0.974197	+	0.225700i	$0.927533\pi$
$662$	4.16250	+	7.20967i	0.161780	+	0.280212i
$663$	14.5517	−	25.2043i	0.565141	−	0.978853i
$664$	15.5175			0.602197
$665$	9.10472	−	15.2169i	0.353066	−	0.590085i
$666$	1.23618			0.0479009
$667$	−26.4365	+	45.7893i	−1.02362	+	1.77297i
$668$	−1.72416	−	2.98632i	−0.0667096	−	0.115544i
$669$	−3.53209	−	6.11776i	−0.136558	−	0.236526i
$670$	4.72668	−	8.18685i	0.182608	−	0.316286i
$671$	6.80066			0.262537
$672$	−4.05303	−	0.0632028i	−0.156349	−	0.00243810i
$673$	−4.81614			−0.185649			−0.0928243	−	0.995683i	$-0.529589\pi$
$673$	−4.81614			−0.185649			−0.0928243	+	0.995683i	$0.529589\pi$
$674$	0.0675813	−	0.117054i	0.00260314	−	0.00450876i
$675$	−2.79813	−	4.84651i	−0.107700	−	0.186542i
$676$	−3.04664	−	5.27693i	−0.117178	−	0.202959i
$677$	−2.55169	+	4.41966i	−0.0980694	+	0.169861i	−0.910885	−	0.412659i	$-0.864600\pi$
$677$	−2.55169	+	4.41966i	−0.0980694	+	0.169861i	0.812816	+	0.582520i	$0.197933\pi$
$678$	6.99588			0.268675
$679$	3.77837	+	6.78655i	0.145001	+	0.260444i
$680$	−4.34730			−0.166711
$681$	9.01960	−	15.6224i	0.345632	−	0.598652i
$682$	3.16637	+	5.48432i	0.121247	+	0.210006i
$683$	−25.3243	−	43.8630i	−0.969007	−	1.67837i	−0.698440	−	0.715668i	$-0.746122\pi$
$683$	−25.3243	−	43.8630i	−0.969007	−	1.67837i	−0.270567	−	0.962701i	$-0.587211\pi$
$684$	2.18732	−	3.78855i	0.0836342	−	0.144859i
$685$	−15.4047			−0.588582
$686$	−10.0000	+	15.5885i	−0.381802	+	0.595170i
$687$	−35.5330			−1.35567
$688$	4.63816	−	8.03352i	0.176828	−	0.306275i
$689$	−4.86484	−	8.42615i	−0.185336	−	0.321011i
$690$	−5.47565	−	9.48411i	−0.208455	−	0.361054i
$691$	−12.8571	+	22.2691i	−0.489107	+	0.847158i	−0.999921	−	0.0125328i	$-0.996011\pi$
$691$	−12.8571	+	22.2691i	−0.489107	+	0.847158i	0.510814	+	0.859691i	$0.329344\pi$
$692$	−7.26083			−0.276015
$693$	0.840022	+	1.50881i	0.0319098	+	0.0573151i
$694$	19.3601			0.734899
$695$	−2.35710	+	4.08261i	−0.0894098	+	0.154862i
$696$	−5.66637	−	9.81445i	−0.214783	−	0.372016i
$697$	−18.8990	−	32.7340i	−0.715850	−	1.23989i
$698$	13.6138	−	23.5798i	0.515290	−	0.892509i
$699$	−8.47565			−0.320579
$700$	−2.64543	−	0.0412527i	−0.0999878	−	0.00155920i
$701$	−25.9249			−0.979170			−0.489585	−	0.871956i	$-0.662852\pi$
$701$	−25.9249			−0.979170			−0.489585	+	0.871956i	$0.662852\pi$
$702$	12.2267	−	21.1772i	0.461466	−	0.799283i
$703$	−6.34689	−	10.9931i	−0.239377	−	0.414614i
$704$	0.500000	+	0.866025i	0.0188445	+	0.0326396i
$705$	−9.57398	+	16.5826i	−0.360577	+	0.624537i
$706$	−4.95130			−0.186345
$707$	18.2756	−	30.5443i	0.687325	−	1.14874i
$708$	−8.25671			−0.310306
$709$	2.68004	−	4.64197i	0.100651	−	0.174333i	−0.811302	−	0.584627i	$-0.801241\pi$
$709$	2.68004	−	4.64197i	0.100651	−	0.174333i	0.911953	+	0.410294i	$0.134574\pi$
$710$	−0.592396	−	1.02606i	−0.0222322	−	0.0385074i
$711$	2.30541	+	3.99308i	0.0864595	+	0.149752i
$712$	−7.21941	+	12.5044i	−0.270559	+	0.468621i
$713$	−45.2662			−1.69523
$714$	9.04782	−	15.1218i	0.338606	−	0.565918i
$715$	−4.36959			−0.163413
$716$	4.45336	−	7.71345i	0.166430	−	0.288265i
$717$	−17.9632	−	31.1131i	−0.670847	−	1.16194i
$718$	−5.90673	−	10.2308i	−0.220437	−	0.381808i
$719$	13.0535	−	22.6093i	0.486813	−	0.843186i	−0.513072	−	0.858346i	$-0.671492\pi$
$719$	13.0535	−	22.6093i	0.486813	−	0.843186i	0.999885	+	0.0151602i	$0.00482583\pi$
$720$	−0.652704			−0.0243248
$721$	19.3259	+	0.301368i	0.719736	+	0.0112235i
$722$	−25.9213			−0.964690
$723$	21.1780	−	36.6813i	0.787618	−	1.36419i
$724$	1.85710	+	3.21659i	0.0690184	+	0.119543i
$725$	−3.69846	−	6.40593i	−0.137357	−	0.237910i
$726$	−0.766044	+	1.32683i	−0.0284306	+	0.0492432i
$727$	49.6614			1.84184			0.920919	−	0.389753i	$-0.127440\pi$
$727$	49.6614			1.84184			0.920919	+	0.389753i	$0.127440\pi$
$728$	−5.62361	−	10.1009i	−0.208425	−	0.374364i
$729$	30.0401			1.11260
$730$	−2.56418	+	4.44129i	−0.0949045	+	0.164379i
$731$	20.1634	+	34.9241i	0.745772	+	1.29171i
$732$	−5.20961	−	9.02330i	−0.192553	−	0.333511i
$733$	13.5621	−	23.4903i	0.500928	−	0.867633i	−0.499071	−	0.866561i	$-0.666325\pi$
$733$	13.5621	−	23.4903i	0.500928	−	0.867633i	0.999999	−	0.00107221i	$-0.000341294\pi$
$734$	16.0993			0.594235
$735$	5.64930	−	9.11608i	0.208378	−	0.336252i
$736$	−7.14796			−0.263477
$737$	4.72668	−	8.18685i	0.174110	−	0.301567i
$738$	−2.83750	−	4.91469i	−0.104450	−	0.180912i
$739$	2.81996	+	4.88431i	0.103734	+	0.179672i	0.913220	−	0.407467i	$-0.133588\pi$
$739$	2.81996	+	4.88431i	0.103734	+	0.179672i	−0.809486	+	0.587139i	$0.800254\pi$
$740$	−0.946967	+	1.64019i	−0.0348112	+	0.0602947i
$741$	−44.8694			−1.64832
$742$	−2.86571	−	5.14728i	−0.105204	−	0.188962i
$743$	−4.38413			−0.160838			−0.0804191	−	0.996761i	$-0.525626\pi$
$743$	−4.38413			−0.160838			−0.0804191	+	0.996761i	$0.525626\pi$
$744$	4.85117	−	8.40247i	0.177852	−	0.308049i
$745$	2.87211	+	4.97464i	0.105226	+	0.182257i
$746$	15.6186	+	27.0521i	0.571836	+	0.990449i
$747$	−5.06418	+	8.77141i	−0.185289	+	0.320929i
$748$	−4.34730			−0.158953
$749$	−10.3601	−	0.161555i	−0.378549	−	0.00590308i
$750$	1.53209			0.0559440
$751$	−10.0530	+	17.4124i	−0.366840	+	0.635386i	−0.989070	−	0.147449i	$-0.952894\pi$
$751$	−10.0530	+	17.4124i	−0.366840	+	0.635386i	0.622229	+	0.782835i	$0.286227\pi$
$752$	6.24897	+	10.8235i	0.227877	+	0.394694i
$753$	18.7101	+	32.4068i	0.681833	+	1.18097i
$754$	16.1607	−	27.9912i	0.588540	−	1.01938i
$755$	21.6459			0.787775
$756$	7.60220	−	12.7057i	0.276489	−	0.462101i
$757$	−26.9709			−0.980274			−0.490137	−	0.871645i	$-0.663053\pi$
$757$	−26.9709			−0.980274			−0.490137	+	0.871645i	$0.663053\pi$
$758$	8.73917	−	15.1367i	0.317421	−	0.549789i
$759$	−5.47565	−	9.48411i	−0.198754	−	0.344251i
$760$	3.35117	+	5.80439i	0.121560	+	0.210547i
$761$	7.34049	−	12.7141i	0.266093	−	0.460886i	−0.701757	−	0.712417i	$-0.747601\pi$
$761$	7.34049	−	12.7141i	0.266093	−	0.460886i	0.967849	+	0.251531i	$0.0809340\pi$
$762$	−1.53209			−0.0555017
$763$	25.7708	−	43.0712i	0.932967	−	1.55928i
$764$	−8.38919			−0.303510
$765$	1.41875	−	2.45734i	0.0512949	−	0.0888455i
$766$	−8.41921	−	14.5825i	−0.304199	−	0.526887i
$767$	−11.7743	−	20.3936i	−0.425144	−	0.736370i
$768$	0.766044	−	1.32683i	0.0276422	−	0.0478778i
$769$	−12.9412			−0.466672			−0.233336	−	0.972396i	$-0.574964\pi$
$769$	−12.9412			−0.466672			−0.233336	+	0.972396i	$0.574964\pi$
$770$	−2.64543	−	0.0412527i	−0.0953347	−	0.00148664i
$771$	19.2080			0.691760
$772$	−4.28359	+	7.41939i	−0.154170	+	0.267030i
$773$	−14.1104	−	24.4399i	−0.507516	−	0.879043i	−0.999962	−	0.00870053i	$-0.997230\pi$
$773$	−14.1104	−	24.4399i	−0.507516	−	0.879043i	0.492446	−	0.870343i	$-0.336103\pi$
$774$	3.02734	+	5.24351i	0.108816	+	0.188474i
$775$	3.16637	−	5.48432i	0.113740	−	0.197003i
$776$	−2.93582			−0.105390
$777$	−3.73442	−	6.70761i	−0.133972	−	0.240634i
$778$	18.9222			0.678394
$779$	−29.1370	+	50.4668i	−1.04394	+	1.80816i
$780$	3.34730	+	5.79769i	0.119852	+	0.207591i
$781$	−0.592396	−	1.02606i	−0.0211976	−	0.0367153i
$782$	15.5371	−	26.9111i	0.555607	−	0.962340i
$783$	41.3952			1.47934
$784$	−3.30928	−	6.16836i	−0.118188	−	0.220299i
$785$	1.75103			0.0624969
$786$	−0.167718	+	0.290497i	−0.00598232	+	0.0103617i
$787$	−7.53714	−	13.0547i	−0.268670	−	0.465350i	0.699849	−	0.714291i	$-0.253251\pi$
$787$	−7.53714	−	13.0547i	−0.268670	−	0.465350i	−0.968519	+	0.248941i	$0.919917\pi$
$788$	8.31315	+	14.3988i	0.296144	+	0.512936i
$789$	16.5064	−	28.5899i	0.587643	−	1.01783i
$790$	−7.06418			−0.251332
$791$	5.87670	+	10.5555i	0.208951	+	0.375310i
$792$	−0.652704			−0.0231928
$793$	14.8580	−	25.7349i	0.527624	−	0.913872i
$794$	7.30840	+	12.6585i	0.259365	+	0.449234i
$795$	1.70574	+	2.95442i	0.0604963	+	0.104783i
$796$	12.3059	−	21.3144i	0.436170	−	0.755469i
$797$	−4.58584			−0.162439			−0.0812193	−	0.996696i	$-0.525881\pi$
$797$	−4.58584			−0.162439			−0.0812193	+	0.996696i	$0.525881\pi$
$798$	−27.1648	−	0.423606i	−0.961623	−	0.0149955i
$799$	−54.3323			−1.92214
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	−4.71213	−	8.16165i	−0.166495	−	0.288378i
$802$	−3.23396	−	5.60138i	−0.114195	−	0.197791i
$803$	−2.56418	+	4.44129i	−0.0904879	+	0.156730i
$804$	−14.4834			−0.510790
$805$	9.71007	−	16.2286i	0.342235	−	0.571983i
$806$	27.6715			0.974686
$807$	−10.4834	+	18.1578i	−0.369033	+	0.639184i
$808$	6.72668	+	11.6510i	0.236644	+	0.409879i
$809$	8.15064	+	14.1173i	0.286561	+	0.496339i	0.972987	−	0.230861i	$-0.0741544\pi$
$809$	8.15064	+	14.1173i	0.286561	+	0.496339i	−0.686425	+	0.727200i	$0.740821\pi$
$810$	−3.30793	+	5.72951i	−0.116229	+	0.201314i
$811$	−14.5458			−0.510773			−0.255386	−	0.966839i	$-0.582203\pi$
$811$	−14.5458			−0.510773			−0.255386	+	0.966839i	$0.582203\pi$
$812$	10.0483	−	16.7939i	0.352626	−	0.589349i
$813$	28.2959			0.992381
$814$	−0.946967	+	1.64019i	−0.0331912	+	0.0574888i
$815$	−2.66772	−	4.62062i	−0.0934461	−	0.161853i
$816$	3.33022	+	5.76811i	0.116581	+	0.201924i
$817$	31.0865	−	53.8433i	1.08758	−	1.88374i
$818$	2.16756			0.0757868
$819$	7.54488	+	0.117654i	0.263640	+	0.00411118i
$820$	8.69459			0.303628
$821$	−24.8063	+	42.9658i	−0.865747	+	1.49952i	0.000556003		1.00000i	$0.499823\pi$
$821$	−24.8063	+	42.9658i	−0.865747	+	1.49952i	−0.866303	+	0.499518i	$0.833510\pi$
$822$	11.8007	+	20.4393i	0.411595	+	0.712904i
$823$	−14.8648	−	25.7467i	−0.518156	−	0.897472i	−0.999778	−	0.0210928i	$-0.993285\pi$
$823$	−14.8648	−	25.7467i	−0.518156	−	0.897472i	0.481622	−	0.876379i	$-0.340048\pi$
$824$	−3.65270	+	6.32667i	−0.127248	+	0.220400i
$825$	1.53209			0.0533405
$826$	−6.93582	−	12.4578i	−0.241328	−	0.433463i
$827$	−43.6067			−1.51635			−0.758177	−	0.652049i	$-0.773910\pi$
$827$	−43.6067			−1.51635			−0.758177	+	0.652049i	$0.773910\pi$
$828$	2.33275	−	4.04044i	0.0810686	−	0.140415i
$829$	−13.6432	−	23.6307i	−0.473848	−	0.820729i	0.525704	−	0.850668i	$-0.323802\pi$
$829$	−13.6432	−	23.6307i	−0.473848	−	0.820729i	−0.999552	+	0.0299387i	$0.990469\pi$
$830$	−7.75877	−	13.4386i	−0.269311	−	0.466460i
$831$	−13.5740	+	23.5108i	−0.470876	+	0.815581i
$832$	4.36959			0.151488
$833$	30.4163	+	0.948850i	1.05386	+	0.0328757i
$834$	7.22256			0.250097
$835$	−1.72416	+	2.98632i	−0.0596669	+	0.103346i
$836$	3.35117	+	5.80439i	0.115903	+	0.200749i
$837$	17.7199	+	30.6917i	0.612488	+	1.06086i
$838$	12.3354	−	21.3656i	0.426121	−	0.738063i
$839$	8.96080			0.309361			0.154681	−	0.987965i	$-0.450565\pi$
$839$	8.96080			0.309361			0.154681	+	0.987965i	$0.450565\pi$
$840$	1.97178	+	3.54163i	0.0680329	+	0.122198i
$841$	25.7145			0.886707
$842$	4.91622	−	8.51515i	0.169424	−	0.293451i
$843$	14.4953	+	25.1065i	0.499243	+	0.864714i
$844$	−14.4153	−	24.9681i	−0.496197	−	0.859438i
$845$	−3.04664	+	5.27693i	−0.104807	+	0.181532i
$846$	−8.15745			−0.280459
$847$	−2.64543	−	0.0412527i	−0.0908980	−	0.00141746i
$848$	2.22668			0.0764646
$849$	−2.90167	+	5.02585i	−0.0995852	+	0.172487i
$850$	2.17365	+	3.76487i	0.0745555	+	0.129134i
$851$	−6.76888	−	11.7240i	−0.232034	−	0.401895i
$852$	−0.907604	+	1.57202i	−0.0310940	+	0.0538564i
$853$	−11.9317			−0.408534			−0.204267	−	0.978915i	$-0.565481\pi$
$853$	−11.9317			−0.408534			−0.204267	+	0.978915i	$0.565481\pi$
$854$	9.23829	−	15.4401i	0.316128	−	0.528349i
$855$	−4.37464			−0.149609
$856$	1.95811	−	3.39155i	0.0669269	−	0.115921i
$857$	13.6343	+	23.6153i	0.465738	+	0.806682i	0.999235	−	0.0391200i	$-0.0124555\pi$
$857$	13.6343	+	23.6153i	0.465738	+	0.806682i	−0.533496	+	0.845802i	$0.679122\pi$
$858$	3.34730	+	5.79769i	0.114275	+	0.197930i
$859$	9.90167	−	17.1502i	0.337841	−	0.585157i	−0.646186	−	0.763180i	$-0.723637\pi$
$859$	9.90167	−	17.1502i	0.337841	−	0.585157i	0.984026	+	0.178023i	$0.0569701\pi$
$860$	−9.27631			−0.316320
$861$	−18.0956	+	30.2435i	−0.616698	+	1.03070i
$862$	−7.03508			−0.239616
$863$	2.31315	−	4.00649i	0.0787405	−	0.136383i	−0.823966	−	0.566639i	$-0.808243\pi$
$863$	2.31315	−	4.00649i	0.0787405	−	0.136383i	0.902707	+	0.430256i	$0.141577\pi$
$864$	2.79813	+	4.84651i	0.0951944	+	0.164882i
$865$	3.63041	+	6.28806i	0.123438	+	0.213801i
$866$	−7.99319	+	13.8446i	−0.271620	+	0.470459i
$867$	−2.90941			−0.0988089
$868$	16.7528	+	0.261243i	0.568628	+	0.00886716i
$869$	−7.06418			−0.239636
$870$	−5.66637	+	9.81445i	−0.192108	+	0.332741i
$871$	−20.6536	−	35.7731i	−0.699822	−	1.21213i
$872$	9.48545	+	16.4293i	0.321218	+	0.556366i
$873$	0.958111	−	1.65950i	0.0324271	−	0.0561655i
$874$	−47.9080			−1.62051
$875$	1.28699	+	2.31164i	0.0435082	+	0.0781475i
$876$	7.85710			0.265467
$877$	−13.4979	+	23.3791i	−0.455793	+	0.789457i	−0.998733	−	0.0503145i	$-0.983978\pi$
$877$	−13.4979	+	23.3791i	−0.455793	+	0.789457i	0.542940	+	0.839771i	$0.317311\pi$
$878$	0.674992	+	1.16912i	0.0227799	+	0.0394559i
$879$	−15.9290	−	27.5899i	−0.537272	−	0.930583i
$880$	0.500000	−	0.866025i	0.0168550	−	0.0291937i
$881$	13.8324			0.466027			0.233013	−	0.972474i	$-0.425141\pi$
$881$	13.8324			0.466027			0.233013	+	0.972474i	$0.425141\pi$
$882$	4.56670	+	0.142460i	0.153769	+	0.00479689i
$883$	−39.2739			−1.32167			−0.660837	−	0.750530i	$-0.729798\pi$
$883$	−39.2739			−1.32167			−0.660837	+	0.750530i	$0.729798\pi$
$884$	−9.49794	+	16.4509i	−0.319450	+	0.553304i
$885$	4.12836	+	7.15052i	0.138773	+	0.240362i
$886$	−3.84255	−	6.65549i	−0.129093	−	0.223596i
$887$	23.4884	−	40.6832i	0.788665	−	1.36601i	−0.138120	−	0.990415i	$-0.544106\pi$
$887$	23.4884	−	40.6832i	0.788665	−	1.36601i	0.926785	−	0.375592i	$-0.122561\pi$
$888$	2.90167			0.0973738
$889$	−1.28699	−	2.31164i	−0.0431642	−	0.0775298i
$890$	14.4388			0.483990
$891$	−3.30793	+	5.72951i	−0.110820	+	0.191946i
$892$	2.30541	+	3.99308i	0.0771907	+	0.133698i
$893$	41.8827	+	72.5429i	1.40155	+	2.42756i
$894$	4.40033	−	7.62159i	0.147169	−	0.254904i
$895$	−8.90673			−0.297719
$896$	2.64543	+	0.0412527i	0.0883776	+	0.00137816i
$897$	−47.8527			−1.59775
$898$	10.9979	−	19.0490i	0.367006	−	0.635673i
$899$	23.4214	+	40.5671i	0.781149	+	1.35299i
$900$	0.326352	+	0.565258i	0.0108784	+	0.0188419i
$901$	−4.84002	+	8.38316i	−0.161245	+	0.279284i
$902$	8.69459			0.289498
$903$	19.3063	−	32.2670i	0.642475	−	1.07378i
$904$	−4.56624			−0.151871
$905$	1.85710	−	3.21659i	0.0617320	−	0.106923i
$906$	−16.5817	−	28.7204i	−0.550891	−	0.954171i
$907$	−10.5728	−	18.3126i	−0.351064	−	0.608061i	0.635372	−	0.772206i	$-0.280847\pi$
$907$	−10.5728	−	18.3126i	−0.351064	−	0.608061i	−0.986436	+	0.164145i	$0.947513\pi$
$908$	−5.88713	+	10.1968i	−0.195371	+	0.338393i
$909$	−8.78106			−0.291249
$910$	−5.93582	+	9.92063i	−0.196771	+	0.328866i
$911$	−9.01279			−0.298607			−0.149304	−	0.988791i	$-0.547703\pi$
$911$	−9.01279			−0.298607			−0.149304	+	0.988791i	$0.547703\pi$
$912$	5.13429	−	8.89284i	0.170013	−	0.294471i
$913$	−7.75877	−	13.4386i	−0.256778	−	0.444752i
$914$	8.00387	+	13.8631i	0.264745	+	0.458551i
$915$	−5.20961	+	9.02330i	−0.172224	+	0.298301i
$916$	23.1925			0.766303
$917$	−0.579193	−	0.00903189i	−0.0191266	−	0.000298259i
$918$	−24.3286			−0.802964
$919$	20.3746	−	35.2899i	0.672097	−	1.16411i	−0.305211	−	0.952285i	$-0.598727\pi$
$919$	20.3746	−	35.2899i	0.672097	−	1.16411i	0.977308	−	0.211822i	$-0.0679397\pi$
$920$	3.57398	+	6.19031i	0.117831	+	0.204089i
$921$	−16.9590	−	29.3739i	−0.558820	−	0.967904i
$922$	6.85638	−	11.8756i	0.225803	−	0.391102i
$923$	−5.17705			−0.170405
$924$	1.97178	+	3.54163i	0.0648668	+	0.116511i
$925$	1.89393			0.0622721
$926$	14.0419	−	24.3213i	0.461445	−	0.799246i
$927$	−2.38413	−	4.12944i	−0.0783052	−	0.135629i
$928$	3.69846	+	6.40593i	0.121408	+	0.210285i
$929$	−0.449493	+	0.778544i	−0.0147474	+	0.0255432i	−0.873305	−	0.487174i	$-0.838028\pi$
$929$	−0.449493	+	0.778544i	−0.0147474	+	0.0255432i	0.858558	+	0.512717i	$0.171361\pi$
$930$	−9.70233			−0.318152
$931$	−22.1799	−	41.3424i	−0.726916	−	1.35494i
$932$	5.53209			0.181210
$933$	19.2292	−	33.3060i	0.629536	−	1.09039i
$934$	7.86824	+	13.6282i	0.257457	+	0.445928i
$935$	2.17365	+	3.76487i	0.0710859	+	0.123124i
$936$	−1.42602	+	2.46994i	−0.0466110	+	0.0807326i
$937$	4.86753			0.159015			0.0795076	−	0.996834i	$-0.474665\pi$
$937$	4.86753			0.159015			0.0795076	+	0.996834i	$0.474665\pi$
$938$	−12.1664	−	21.8527i	−0.397246	−	0.713517i
$939$	−49.3310			−1.60986
$940$	6.24897	−	10.8235i	0.203819	−	0.353025i
$941$	−2.98499	−	5.17015i	−0.0973077	−	0.168542i	0.813262	−	0.581898i	$-0.197690\pi$
$941$	−2.98499	−	5.17015i	−0.0973077	−	0.168542i	−0.910569	+	0.413356i	$0.864356\pi$
$942$	−1.34137	−	2.32332i	−0.0437041	−	0.0756977i
$943$	−31.0743	+	53.8222i	−1.01192	+	1.75269i
$944$	5.38919			0.175403
$945$	−14.8045	−	0.230861i	−0.481591	−	0.00750991i
$946$	−9.27631			−0.301599
$947$	−8.65317	+	14.9877i	−0.281190	+	0.487036i	−0.971678	−	0.236308i	$-0.924063\pi$
$947$	−8.65317	+	14.9877i	−0.281190	+	0.487036i	0.690488	+	0.723344i	$0.257396\pi$
$948$	5.41147	+	9.37295i	0.175757	+	0.304419i
$949$	11.2044	+	19.4066i	0.363710	+	0.629964i
$950$	3.35117	−	5.80439i	0.108726	−	0.188319i
$951$	23.9828			0.777694
$952$	−5.90554	+	9.87003i	−0.191400	+	0.319889i
$953$	−3.42065			−0.110806			−0.0554028	−	0.998464i	$-0.517644\pi$
$953$	−3.42065			−0.110806			−0.0554028	+	0.998464i	$0.517644\pi$
$954$	−0.726682	+	1.25865i	−0.0235272	+	0.0407503i
$955$	4.19459	+	7.26525i	0.135734	+	0.235098i
$956$	11.7246	+	20.3076i	0.379201	+	0.656796i
$957$	−5.66637	+	9.81445i	−0.183168	+	0.317256i
$958$	28.3405			0.915640
$959$	−20.9263	+	34.9745i	−0.675746	+	1.12939i
$960$	−1.53209			−0.0494480
$961$	−4.55185	+	7.88404i	−0.146834	+	0.254324i
$962$	4.13785	+	7.16697i	0.133410	+	0.231072i
$963$	1.27807	+	2.21368i	0.0411851	+	0.0713347i
$964$	−13.8229	+	23.9420i	−0.445207	+	0.771121i
$965$	8.56717			0.275787
$966$	−28.9709	−	0.451771i	−0.932124	−	0.0145355i
$967$	−16.5348			−0.531723			−0.265861	−	0.964011i	$-0.585656\pi$
$967$	−16.5348			−0.531723			−0.265861	+	0.964011i	$0.585656\pi$
$968$	0.500000	−	0.866025i	0.0160706	−	0.0278351i
$969$	22.3203	+	38.6598i	0.717030	+	1.24193i
$970$	1.46791	+	2.54250i	0.0471318	+	0.0816346i
$971$	−14.9263	+	25.8532i	−0.479009	+	0.829667i	−0.999710	−	0.0240715i	$-0.992337\pi$
$971$	−14.9263	+	25.8532i	−0.479009	+	0.829667i	0.520702	+	0.853739i	$0.325670\pi$
$972$	−6.65270			−0.213386
$973$	6.06711	+	10.8975i	0.194503	+	0.349358i
$974$	−4.80747			−0.154041
$975$	3.34730	−	5.79769i	0.107199	−	0.185675i
$976$	3.40033	+	5.88954i	0.108842	+	0.188520i
$977$	11.8307	+	20.4914i	0.378497	+	0.655577i	0.990844	−	0.135013i	$-0.0431076\pi$
$977$	11.8307	+	20.4914i	0.378497	+	0.655577i	−0.612347	+	0.790589i	$0.709774\pi$
$978$	−4.08718	+	7.07921i	−0.130694	+	0.226368i
$979$	14.4388			0.461467
$980$	−3.68732	+	5.95010i	−0.117787	+	0.190069i
$981$	−12.3824			−0.395339
$982$	−21.1511	+	36.6348i	−0.674959	+	1.16906i
$983$	5.28312	+	9.15063i	0.168505	+	0.291860i	0.937895	−	0.346920i	$-0.112773\pi$
$983$	5.28312	+	9.15063i	0.168505	+	0.291860i	−0.769389	+	0.638780i	$0.779439\pi$
$984$	−6.66044	−	11.5362i	−0.212327	−	0.367762i
$985$	8.31315	−	14.3988i	0.264879	−	0.458784i
$986$	−32.1566			−1.02408
$987$	24.6432	+	44.2631i	0.784402	+	1.40891i
$988$	29.2864			0.931725
$989$	33.1533	−	57.4233i	1.05421	−	1.82595i
$990$	0.326352	+	0.565258i	0.0103721	+	0.0179651i
$991$	−10.8696	−	18.8267i	−0.345284	−	0.598049i	0.640122	−	0.768274i	$-0.278884\pi$
$991$	−10.8696	−	18.8267i	−0.345284	−	0.598049i	−0.985405	+	0.170225i	$0.945551\pi$
$992$	−3.16637	+	5.48432i	−0.100532	+	0.174127i
$993$	−12.7547			−0.404757
$994$	−3.13429	−	0.0488759i	−0.0994135	−	0.00155025i
$995$	−24.6117			−0.780245
$996$	−11.8871	+	20.5891i	−0.376658	+	0.652391i
$997$	23.2918	+	40.3426i	0.737658	+	1.27766i	0.953547	+	0.301244i	$0.0974019\pi$
$997$	23.2918	+	40.3426i	0.737658	+	1.27766i	−0.215889	+	0.976418i	$0.569265\pi$
$998$	13.2121	+	22.8841i	0.418223	+	0.724383i
$999$	−5.29948	+	9.17896i	−0.167668	+	0.290410i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.i.j.331.3	yes	6
7.2	even	3		5390.2.a.bx.1.1		3
7.4	even	3	inner	770.2.i.j.221.3	✓	6
7.5	odd	6		5390.2.a.bv.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.i.j.221.3	✓	6	7.4	even	3	inner
770.2.i.j.331.3	yes	6	1.1	even	1	trivial
5390.2.a.bv.1.3		3	7.5	odd	6
5390.2.a.bx.1.1		3	7.2	even	3

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.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.766044 + 1.32683i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.53209 q^{6} +(1.28699 + 2.31164i) q^{7} -1.00000 q^{8} +(0.326352 - 0.565258i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.766044 + 1.32683i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.53209 q^{6} +(1.28699 + 2.31164i) q^{7} -1.00000 q^{8} +(0.326352 - 0.565258i) q^{9} +(0.500000 + 0.866025i) q^{10} +(0.500000 + 0.866025i) q^{11} +(0.766044 - 1.32683i) q^{12} +4.36959 q^{13} +(2.64543 + 0.0412527i) q^{14} -1.53209 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.17365 - 3.76487i) q^{17} +(-0.326352 - 0.565258i) q^{18} +(-3.35117 + 5.80439i) q^{19} +1.00000 q^{20} +(-2.08125 + 3.47843i) q^{21} +1.00000 q^{22} +(-3.57398 + 6.19031i) q^{23} +(-0.766044 - 1.32683i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(2.18479 - 3.78417i) q^{26} +5.59627 q^{27} +(1.35844 - 2.27038i) q^{28} +7.39693 q^{29} +(-0.766044 + 1.32683i) q^{30} +(3.16637 + 5.48432i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.766044 + 1.32683i) q^{33} -4.34730 q^{34} +(-2.64543 - 0.0412527i) q^{35} -0.652704 q^{36} +(-0.946967 + 1.64019i) q^{37} +(3.35117 + 5.80439i) q^{38} +(3.34730 + 5.79769i) q^{39} +(0.500000 - 0.866025i) q^{40} +8.69459 q^{41} +(1.97178 + 3.54163i) q^{42} -9.27631 q^{43} +(0.500000 - 0.866025i) q^{44} +(0.326352 + 0.565258i) q^{45} +(3.57398 + 6.19031i) q^{46} +(6.24897 - 10.8235i) q^{47} -1.53209 q^{48} +(-3.68732 + 5.95010i) q^{49} -1.00000 q^{50} +(3.33022 - 5.76811i) q^{51} +(-2.18479 - 3.78417i) q^{52} +(-1.11334 - 1.92836i) q^{53} +(2.79813 - 4.84651i) q^{54} -1.00000 q^{55} +(-1.28699 - 2.31164i) q^{56} -10.2686 q^{57} +(3.69846 - 6.40593i) q^{58} +(-2.69459 - 4.66717i) q^{59} +(0.766044 + 1.32683i) q^{60} +(3.40033 - 5.88954i) q^{61} +6.33275 q^{62} +(1.72668 + 0.0269258i) q^{63} +1.00000 q^{64} +(-2.18479 + 3.78417i) q^{65} +(0.766044 + 1.32683i) q^{66} +(-4.72668 - 8.18685i) q^{67} +(-2.17365 + 3.76487i) q^{68} -10.9513 q^{69} +(-1.35844 + 2.27038i) q^{70} -1.18479 q^{71} +(-0.326352 + 0.565258i) q^{72} +(2.56418 + 4.44129i) q^{73} +(0.946967 + 1.64019i) q^{74} +(0.766044 - 1.32683i) q^{75} +6.70233 q^{76} +(-1.35844 + 2.27038i) q^{77} +6.69459 q^{78} +(-3.53209 + 6.11776i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(3.30793 + 5.72951i) q^{81} +(4.34730 - 7.52974i) q^{82} -15.5175 q^{83} +(4.05303 + 0.0632028i) q^{84} +4.34730 q^{85} +(-4.63816 + 8.03352i) q^{86} +(5.66637 + 9.81445i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(7.21941 - 12.5044i) q^{89} +0.652704 q^{90} +(5.62361 + 10.1009i) q^{91} +7.14796 q^{92} +(-4.85117 + 8.40247i) q^{93} +(-6.24897 - 10.8235i) q^{94} +(-3.35117 - 5.80439i) q^{95} +(-0.766044 + 1.32683i) q^{96} +2.93582 q^{97} +(3.30928 + 6.16836i) q^{98} +0.652704 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{4} - 3 q^{5} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 6 * q + 3 * q^2 - 3 * q^4 - 3 * q^5 - 6 * q^8 + 3 * q^9	\( 6 q + 3 q^{2} - 3 q^{4} - 3 q^{5} - 6 q^{8} + 3 q^{9} + 3 q^{10} + 3 q^{11} + 12 q^{13} - 3 q^{16} - 12 q^{17} - 3 q^{18} + 6 q^{19} + 6 q^{20} - 15 q^{21} + 6 q^{22} - 6 q^{23} - 3 q^{25} + 6 q^{26} + 6 q^{27} - 12 q^{29} + 3 q^{32} - 24 q^{34} - 6 q^{36} - 18 q^{37} - 6 q^{38} + 18 q^{39} + 3 q^{40} + 48 q^{41} - 3 q^{42} + 12 q^{43} + 3 q^{44} + 3 q^{45} + 6 q^{46} + 12 q^{47} - 6 q^{50} - 3 q^{51} - 6 q^{52} + 3 q^{54} - 6 q^{55} - 42 q^{57} - 6 q^{58} - 12 q^{59} + 6 q^{61} - 3 q^{63} + 6 q^{64} - 6 q^{65} - 15 q^{67} - 12 q^{68} + 12 q^{69} - 3 q^{72} - 3 q^{73} + 18 q^{74} - 12 q^{76} + 36 q^{78} - 12 q^{79} - 3 q^{80} + 9 q^{81} + 24 q^{82} - 48 q^{83} + 12 q^{84} + 24 q^{85} + 6 q^{86} + 15 q^{87} - 3 q^{88} + 12 q^{89} + 6 q^{90} - 36 q^{91} + 12 q^{92} - 3 q^{93} - 12 q^{94} + 6 q^{95} + 36 q^{97} + 6 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^4 - 3 * q^5 - 6 * q^8 + 3 * q^9 + 3 * q^10 + 3 * q^11 + 12 * q^13 - 3 * q^16 - 12 * q^17 - 3 * q^18 + 6 * q^19 + 6 * q^20 - 15 * q^21 + 6 * q^22 - 6 * q^23 - 3 * q^25 + 6 * q^26 + 6 * q^27 - 12 * q^29 + 3 * q^32 - 24 * q^34 - 6 * q^36 - 18 * q^37 - 6 * q^38 + 18 * q^39 + 3 * q^40 + 48 * q^41 - 3 * q^42 + 12 * q^43 + 3 * q^44 + 3 * q^45 + 6 * q^46 + 12 * q^47 - 6 * q^50 - 3 * q^51 - 6 * q^52 + 3 * q^54 - 6 * q^55 - 42 * q^57 - 6 * q^58 - 12 * q^59 + 6 * q^61 - 3 * q^63 + 6 * q^64 - 6 * q^65 - 15 * q^67 - 12 * q^68 + 12 * q^69 - 3 * q^72 - 3 * q^73 + 18 * q^74 - 12 * q^76 + 36 * q^78 - 12 * q^79 - 3 * q^80 + 9 * q^81 + 24 * q^82 - 48 * q^83 + 12 * q^84 + 24 * q^85 + 6 * q^86 + 15 * q^87 - 3 * q^88 + 12 * q^89 + 6 * q^90 - 36 * q^91 + 12 * q^92 - 3 * q^93 - 12 * q^94 + 6 * q^95 + 36 * q^97 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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