LMFDB - Embedded newform 315.2.t.c.131.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(101,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("315.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.t (of order $6$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.1
Character	$\chi$	$=$	315.131
Dual form			315.2.t.c.101.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.51890i q^{2} +(-0.170788 + 1.72361i) q^{3} -4.34486 q^{4} +(-0.500000 - 0.866025i) q^{5} +(4.34160 + 0.430199i) q^{6} +(1.80687 - 1.93267i) q^{7} +5.90648i q^{8} +(-2.94166 - 0.588745i) q^{9} +O(q^{10})$	\(q-2.51890i q^{2} +(-0.170788 + 1.72361i) q^{3} -4.34486 q^{4} +(-0.500000 - 0.866025i) q^{5} +(4.34160 + 0.430199i) q^{6} +(1.80687 - 1.93267i) q^{7} +5.90648i q^{8} +(-2.94166 - 0.588745i) q^{9} +(-2.18143 + 1.25945i) q^{10} +(-5.56722 - 3.21424i) q^{11} +(0.742053 - 7.48885i) q^{12} +(-1.77286 - 1.02356i) q^{13} +(-4.86822 - 4.55132i) q^{14} +(1.57808 - 0.713898i) q^{15} +6.18812 q^{16} +(-1.68778 - 2.92333i) q^{17} +(-1.48299 + 7.40976i) q^{18} +(3.51581 + 2.02985i) q^{19} +(2.17243 + 3.76276i) q^{20} +(3.02259 + 3.44441i) q^{21} +(-8.09635 + 14.0233i) q^{22} +(-2.48399 + 1.43413i) q^{23} +(-10.1805 - 1.00876i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-2.57825 + 4.46565i) q^{26} +(1.51717 - 4.96973i) q^{27} +(-7.85059 + 8.39721i) q^{28} +(5.49358 - 3.17172i) q^{29} +(-1.79824 - 3.97504i) q^{30} -0.965448i q^{31} -3.77429i q^{32} +(6.49091 - 9.04677i) q^{33} +(-7.36357 + 4.25136i) q^{34} +(-2.57718 - 0.598455i) q^{35} +(12.7811 + 2.55802i) q^{36} +(-1.31513 + 2.27787i) q^{37} +(5.11299 - 8.85597i) q^{38} +(2.06700 - 2.88090i) q^{39} +(5.11516 - 2.95324i) q^{40} +(3.50381 - 6.06877i) q^{41} +(8.67614 - 7.61359i) q^{42} +(0.788442 + 1.36562i) q^{43} +(24.1888 + 13.9654i) q^{44} +(0.960963 + 2.84193i) q^{45} +(3.61244 + 6.25694i) q^{46} -6.05049 q^{47} +(-1.05686 + 10.6659i) q^{48} +(-0.470463 - 6.98417i) q^{49} +(2.18143 + 1.25945i) q^{50} +(5.32693 - 2.40981i) q^{51} +(7.70283 + 4.44723i) q^{52} +(-3.22776 + 1.86355i) q^{53} +(-12.5183 - 3.82160i) q^{54} +6.42848i q^{55} +(11.4153 + 10.6722i) q^{56} +(-4.09913 + 5.71320i) q^{57} +(-7.98926 - 13.8378i) q^{58} +14.3051 q^{59} +(-6.85656 + 3.10179i) q^{60} -7.33263i q^{61} -2.43187 q^{62} +(-6.45305 + 4.62149i) q^{63} +2.86917 q^{64} +2.04712i q^{65} +(-22.7879 - 16.3500i) q^{66} +15.3837 q^{67} +(7.33319 + 12.7015i) q^{68} +(-2.04765 - 4.52637i) q^{69} +(-1.50745 + 6.49166i) q^{70} -5.13122i q^{71} +(3.47741 - 17.3749i) q^{72} +(-9.61674 + 5.55223i) q^{73} +(5.73772 + 3.31267i) q^{74} +(-1.40730 - 1.00971i) q^{75} +(-15.2757 - 8.81943i) q^{76} +(-16.2713 + 4.95193i) q^{77} +(-7.25671 - 5.20657i) q^{78} -3.85016 q^{79} +(-3.09406 - 5.35907i) q^{80} +(8.30676 + 3.46378i) q^{81} +(-15.2866 - 8.82574i) q^{82} +(0.549429 + 0.951639i) q^{83} +(-13.1327 - 14.9655i) q^{84} +(-1.68778 + 2.92333i) q^{85} +(3.43987 - 1.98601i) q^{86} +(4.52857 + 10.0105i) q^{87} +(18.9848 - 32.8827i) q^{88} +(-0.423334 + 0.733236i) q^{89} +(7.15853 - 2.42057i) q^{90} +(-5.18153 + 1.57692i) q^{91} +(10.7926 - 6.23112i) q^{92} +(1.66406 + 0.164887i) q^{93} +15.2406i q^{94} -4.05970i q^{95} +(6.50540 + 0.644605i) q^{96} +(-2.96628 + 1.71258i) q^{97} +(-17.5924 + 1.18505i) q^{98} +(14.4845 + 12.7329i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - q^{3} - 32 q^{4} - 16 q^{5} - 2 q^{6} + q^{7} + q^{9}+O(q^{10}) $ 32 * q - q^3 - 32 * q^4 - 16 * q^5 - 2 * q^6 + q^7 + q^9	$ 32 q - q^{3} - 32 q^{4} - 16 q^{5} - 2 q^{6} + q^{7} + q^{9} + 3 q^{11} + 12 q^{12} + 6 q^{13} - 15 q^{14} - q^{15} + 32 q^{16} - 3 q^{17} - 13 q^{18} + 16 q^{20} - q^{21} - 21 q^{22} - 9 q^{23} - 4 q^{24} - 16 q^{25} + 12 q^{26} + 23 q^{27} - 31 q^{28} + 18 q^{29} - 2 q^{30} + 19 q^{33} - 30 q^{34} + q^{35} + 18 q^{36} - q^{37} - 30 q^{38} + 21 q^{39} + 6 q^{41} + 19 q^{42} - 19 q^{43} + 21 q^{44} - 8 q^{45} + 6 q^{46} - 30 q^{47} - 35 q^{48} + 5 q^{49} + 36 q^{51} + 21 q^{52} - 24 q^{53} - 59 q^{54} + 30 q^{56} + 27 q^{57} + 30 q^{59} + 3 q^{60} - 32 q^{63} + 76 q^{64} + 26 q^{66} - 50 q^{67} - 3 q^{68} - 50 q^{69} + 9 q^{70} - 14 q^{72} + 12 q^{73} + 60 q^{74} + 2 q^{75} + 54 q^{76} - 27 q^{77} - 42 q^{78} + 4 q^{79} - 16 q^{80} - 23 q^{81} - 24 q^{82} - 42 q^{83} - 72 q^{84} - 3 q^{85} + 51 q^{86} + 34 q^{87} + 42 q^{88} + 30 q^{89} + 41 q^{90} - 57 q^{91} + 6 q^{92} - 33 q^{93} + 15 q^{96} - 42 q^{97} + 6 q^{98} - q^{99}+O(q^{100}) $ 32 * q - q^3 - 32 * q^4 - 16 * q^5 - 2 * q^6 + q^7 + q^9 + 3 * q^11 + 12 * q^12 + 6 * q^13 - 15 * q^14 - q^15 + 32 * q^16 - 3 * q^17 - 13 * q^18 + 16 * q^20 - q^21 - 21 * q^22 - 9 * q^23 - 4 * q^24 - 16 * q^25 + 12 * q^26 + 23 * q^27 - 31 * q^28 + 18 * q^29 - 2 * q^30 + 19 * q^33 - 30 * q^34 + q^35 + 18 * q^36 - q^37 - 30 * q^38 + 21 * q^39 + 6 * q^41 + 19 * q^42 - 19 * q^43 + 21 * q^44 - 8 * q^45 + 6 * q^46 - 30 * q^47 - 35 * q^48 + 5 * q^49 + 36 * q^51 + 21 * q^52 - 24 * q^53 - 59 * q^54 + 30 * q^56 + 27 * q^57 + 30 * q^59 + 3 * q^60 - 32 * q^63 + 76 * q^64 + 26 * q^66 - 50 * q^67 - 3 * q^68 - 50 * q^69 + 9 * q^70 - 14 * q^72 + 12 * q^73 + 60 * q^74 + 2 * q^75 + 54 * q^76 - 27 * q^77 - 42 * q^78 + 4 * q^79 - 16 * q^80 - 23 * q^81 - 24 * q^82 - 42 * q^83 - 72 * q^84 - 3 * q^85 + 51 * q^86 + 34 * q^87 + 42 * q^88 + 30 * q^89 + 41 * q^90 - 57 * q^91 + 6 * q^92 - 33 * q^93 + 15 * q^96 - 42 * q^97 + 6 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$		−	2.51890i		−	1.78113i	−0.454854	−	0.890566i	$-0.650308\pi$
$2$		−	2.51890i		−	1.78113i	0.454854	−	0.890566i	$-0.349692\pi$
$3$	−0.170788	+	1.72361i	−0.0986048	+	0.995127i
$3$	−0.170788	+	1.72361i	−0.0986048	+	0.995127i
$4$	−4.34486			−2.17243
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	4.34160	+	0.430199i	1.77245	+	0.175628i
$7$	1.80687	−	1.93267i	0.682932	−	0.730482i
$7$	1.80687	−	1.93267i	0.682932	−	0.730482i
$8$			5.90648i			2.08826i
$9$	−2.94166	−	0.588745i	−0.980554	−	0.196248i
$10$	−2.18143	+	1.25945i	−0.689830	+	0.398273i
$11$	−5.56722	−	3.21424i	−1.67858	−	0.969129i	−0.962567	−	0.271044i	$-0.912631\pi$
$11$	−5.56722	−	3.21424i	−1.67858	−	0.969129i	−0.716014	−	0.698086i	$-0.754035\pi$
$12$	0.742053	−	7.48885i	0.214212	−	2.16185i
$13$	−1.77286	−	1.02356i	−0.491702	−	0.283884i	0.233578	−	0.972338i	$-0.424957\pi$
$13$	−1.77286	−	1.02356i	−0.491702	−	0.283884i	−0.725280	+	0.688454i	$0.758290\pi$
$14$	−4.86822	−	4.55132i	−1.30109	−	1.21639i
$15$	1.57808	−	0.713898i	0.407460	−	0.184328i
$16$	6.18812			1.54703
$17$	−1.68778	−	2.92333i	−0.409347	−	0.709011i	0.585469	−	0.810695i	$-0.300910\pi$
$17$	−1.68778	−	2.92333i	−0.409347	−	0.709011i	−0.994817	+	0.101684i	$0.967577\pi$
$18$	−1.48299	+	7.40976i	−0.349545	+	1.74650i
$19$	3.51581	+	2.02985i	0.806581	+	0.465680i	0.845767	−	0.533552i	$-0.179143\pi$
$19$	3.51581	+	2.02985i	0.806581	+	0.465680i	−0.0391861	+	0.999232i	$0.512477\pi$
$20$	2.17243	+	3.76276i	0.485771	+	0.841379i
$21$	3.02259	+	3.44441i	0.659582	+	0.751632i
$22$	−8.09635	+	14.0233i	−1.72615	+	2.98978i
$23$	−2.48399	+	1.43413i	−0.517949	+	0.299038i	−0.736095	−	0.676878i	$-0.763332\pi$
$23$	−2.48399	+	1.43413i	−0.517949	+	0.299038i	0.218146	+	0.975916i	$0.429999\pi$
$24$	−10.1805	−	1.00876i	−2.07808	−	0.205912i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−2.57825	+	4.46565i	−0.505636	+	0.875787i
$27$	1.51717	−	4.96973i	0.291979	−	0.956425i
$28$	−7.85059	+	8.39721i	−1.48362	+	1.58692i
$29$	5.49358	−	3.17172i	1.02013	−	0.588974i	0.105990	−	0.994367i	$-0.466199\pi$
$29$	5.49358	−	3.17172i	1.02013	−	0.588974i	0.914142	+	0.405393i	$0.132865\pi$
$30$	−1.79824	−	3.97504i	−0.328312	−	0.725739i
$31$		−	0.965448i		−	0.173400i	−0.996234	−	0.0866998i	$-0.972368\pi$
$31$		−	0.965448i		−	0.173400i	0.996234	−	0.0866998i	$-0.0276321\pi$
$32$		−	3.77429i		−	0.667207i
$33$	6.49091	−	9.04677i	1.12992	−	1.57484i
$34$	−7.36357	+	4.25136i	−1.26284	+	0.729102i
$35$	−2.57718	−	0.598455i	−0.435623	−	0.101157i
$36$	12.7811	+	2.55802i	2.13019	+	0.426337i
$37$	−1.31513	+	2.27787i	−0.216206	+	0.374479i	−0.953645	−	0.300934i	$-0.902701\pi$
$37$	−1.31513	+	2.27787i	−0.216206	+	0.374479i	0.737439	+	0.675413i	$0.236035\pi$
$38$	5.11299	−	8.85597i	0.829437	−	1.43663i
$39$	2.06700	−	2.88090i	0.330985	−	0.461314i
$40$	5.11516	−	2.95324i	0.808778	−	0.466948i
$41$	3.50381	−	6.06877i	0.547203	−	0.947783i	−0.451262	−	0.892391i	$-0.649026\pi$
$41$	3.50381	−	6.06877i	0.547203	−	0.947783i	0.998465	−	0.0553914i	$-0.0176406\pi$
$42$	8.67614	−	7.61359i	1.33876	−	1.17480i
$43$	0.788442	+	1.36562i	0.120236	+	0.208255i	0.919861	−	0.392245i	$-0.128301\pi$
$43$	0.788442	+	1.36562i	0.120236	+	0.208255i	−0.799625	+	0.600500i	$0.794968\pi$
$44$	24.1888	+	13.9654i	3.64660	+	2.10537i
$45$	0.960963	+	2.84193i	0.143252	+	0.423650i
$46$	3.61244	+	6.25694i	0.532626	+	0.922535i
$47$	−6.05049			−0.882554			−0.441277	−	0.897371i	$-0.645474\pi$
$47$	−6.05049			−0.882554			−0.441277	+	0.897371i	$0.645474\pi$
$48$	−1.05686	+	10.6659i	−0.152544	+	1.53949i
$49$	−0.470463	−	6.98417i	−0.0672090	−	0.997739i
$50$	2.18143	+	1.25945i	0.308501	+	0.178113i
$51$	5.32693	−	2.40981i	0.745919	−	0.337441i
$52$	7.70283	+	4.44723i	1.06819	+	0.616720i
$53$	−3.22776	+	1.86355i	−0.443366	+	0.255978i	−0.705025	−	0.709183i	$-0.749064\pi$
$53$	−3.22776	+	1.86355i	−0.443366	+	0.255978i	0.261658	+	0.965161i	$0.415731\pi$
$54$	−12.5183	−	3.82160i	−1.70352	−	0.520054i
$55$			6.42848i			0.866816i
$56$	11.4153	+	10.6722i	1.52543	+	1.42614i
$57$	−4.09913	+	5.71320i	−0.542943	+	0.756732i
$58$	−7.98926	−	13.8378i	−1.04904	−	1.81699i
$59$	14.3051			1.86237			0.931184	−	0.364550i	$-0.118777\pi$
$59$	14.3051			1.86237			0.931184	+	0.364550i	$0.118777\pi$
$60$	−6.85656	+	3.10179i	−0.885178	+	0.400439i
$61$		−	7.33263i		−	0.938847i	−0.882973	−	0.469423i	$-0.844462\pi$
$61$		−	7.33263i		−	0.938847i	0.882973	−	0.469423i	$-0.155538\pi$
$62$	−2.43187			−0.308848
$63$	−6.45305	+	4.62149i	−0.813007	+	0.582253i
$64$	2.86917			0.358646
$65$			2.04712i			0.253914i
$66$	−22.7879	−	16.3500i	−2.80500	−	2.01254i
$67$	15.3837			1.87942			0.939712	−	0.341967i	$-0.111093\pi$
$67$	15.3837			1.87942			0.939712	+	0.341967i	$0.111093\pi$
$68$	7.33319	+	12.7015i	0.889279	+	1.54028i
$69$	−2.04765	−	4.52637i	−0.246508	−	0.544911i
$70$	−1.50745	+	6.49166i	−0.180175	+	0.775902i
$71$		−	5.13122i		−	0.608963i	−0.952518	−	0.304482i	$-0.901517\pi$
$71$		−	5.13122i		−	0.608963i	0.952518	−	0.304482i	$-0.0984832\pi$
$72$	3.47741	−	17.3749i	0.409817	−	2.04765i
$73$	−9.61674	+	5.55223i	−1.12555	+	0.649839i	−0.942813	−	0.333322i	$-0.891830\pi$
$73$	−9.61674	+	5.55223i	−1.12555	+	0.649839i	−0.182741	+	0.983161i	$0.558497\pi$
$74$	5.73772	+	3.31267i	0.666997	+	0.385091i
$75$	−1.40730	−	1.00971i	−0.162501	−	0.116592i
$76$	−15.2757	−	8.81943i	−1.75224	−	1.01166i
$77$	−16.2713	+	4.95193i	−1.85429	+	0.564325i
$78$	−7.25671	−	5.20657i	−0.821661	−	0.589528i
$79$	−3.85016			−0.433176			−0.216588	−	0.976263i	$-0.569493\pi$
$79$	−3.85016			−0.433176			−0.216588	+	0.976263i	$0.569493\pi$
$80$	−3.09406	−	5.35907i	−0.345926	−	0.599162i
$81$	8.30676	+	3.46378i	0.922973	+	0.384865i
$82$	−15.2866	−	8.82574i	−1.68813	−	0.974640i
$83$	0.549429	+	0.951639i	0.0603076	+	0.104456i	0.894603	−	0.446862i	$-0.147458\pi$
$83$	0.549429	+	0.951639i	0.0603076	+	0.104456i	−0.834295	+	0.551318i	$0.814125\pi$
$84$	−13.1327	−	14.9655i	−1.43290	−	1.63287i
$85$	−1.68778	+	2.92333i	−0.183066	+	0.317079i
$86$	3.43987	−	1.98601i	0.370930	−	0.214157i
$87$	4.52857	+	10.0105i	0.485514	+	1.07324i
$88$	18.9848	−	32.8827i	2.02379	−	3.50531i
$89$	−0.423334	+	0.733236i	−0.0448733	+	0.0777229i	−0.887590	−	0.460635i	$-0.847622\pi$
$89$	−0.423334	+	0.733236i	−0.0448733	+	0.0777229i	0.842716	+	0.538358i	$0.180955\pi$
$90$	7.15853	−	2.42057i	0.754576	−	0.255151i
$91$	−5.18153	+	1.57692i	−0.543172	+	0.165306i
$92$	10.7926	−	6.23112i	1.12521	−	0.649639i
$93$	1.66406	+	0.164887i	0.172555	+	0.0170980i
$94$			15.2406i			1.57195i
$95$		−	4.05970i		−	0.416517i
$96$	6.50540	+	0.644605i	0.663955	+	0.0657898i
$97$	−2.96628	+	1.71258i	−0.301180	+	0.173886i	−0.642973	−	0.765889i	$-0.722299\pi$
$97$	−2.96628	+	1.71258i	−0.301180	+	0.173886i	0.341793	+	0.939775i	$0.388966\pi$
$98$	−17.5924	+	1.18505i	−1.77710	+	0.119708i
$99$	14.4845	+	12.7329i	1.45575	+	1.27970i
$100$	2.17243	−	3.76276i	0.217243	−	0.376276i
$101$	3.43027	−	5.94140i	0.341325	−	0.591192i	−0.643354	−	0.765569i	$-0.722458\pi$
$101$	3.43027	−	5.94140i	0.341325	−	0.591192i	0.984679	+	0.174377i	$0.0557911\pi$
$102$	−6.07007	−	13.4180i	−0.601027	−	1.32858i
$103$	12.5963	−	7.27245i	1.24115	−	0.716576i	0.271819	−	0.962348i	$-0.412375\pi$
$103$	12.5963	−	7.27245i	1.24115	−	0.716576i	0.969328	+	0.245772i	$0.0790415\pi$
$104$	6.04564	−	10.4714i	0.592824	−	1.02680i
$105$	1.47166	−	4.33984i	0.143619	−	0.423525i
$106$	4.69409	+	8.13040i	0.455930	+	0.789694i
$107$	5.34864	+	3.08804i	0.517072	+	0.298532i	0.735736	−	0.677268i	$-0.236836\pi$
$107$	5.34864	+	3.08804i	0.517072	+	0.298532i	−0.218664	+	0.975800i	$0.570170\pi$
$108$	−6.59190	+	21.5928i	−0.634305	+	2.07777i
$109$	−2.05801	−	3.56458i	−0.197122	−	0.341425i	0.750472	−	0.660902i	$-0.229826\pi$
$109$	−2.05801	−	3.56458i	−0.197122	−	0.341425i	−0.947594	+	0.319477i	$0.896493\pi$
$110$	16.1927			1.54391
$111$	−3.70154	−	2.65580i	−0.351335	−	0.252077i
$112$	11.1811	−	11.9596i	1.05651	−	1.13008i
$113$	−2.65000	−	1.52998i	−0.249291	−	0.143928i	0.370149	−	0.928973i	$-0.379307\pi$
$113$	−2.65000	−	1.52998i	−0.249291	−	0.143928i	−0.619439	+	0.785044i	$0.712640\pi$
$114$	14.3910	+	10.3253i	1.34784	+	0.967053i
$115$	2.48399	+	1.43413i	0.231634	+	0.133734i
$116$	−23.8689	+	13.7807i	−2.21617	+	1.27951i
$117$	4.61253	+	4.05473i	0.426429	+	0.374860i
$118$		−	36.0332i		−	3.31712i
$119$	−8.69944	−	2.02013i	−0.797476	−	0.185185i
$120$	4.21662	+	9.32093i	0.384923	+	0.850880i
$121$	15.1627	+	26.2625i	1.37842	+	2.38750i
$122$	−18.4702			−1.67221
$123$	9.86178	+	7.07567i	0.889207	+	0.637992i
$124$			4.19474i			0.376699i
$125$	1.00000			0.0894427
$126$	11.6411	+	16.2546i	1.03707	+	1.44807i
$127$	−2.38450			−0.211590			−0.105795	−	0.994388i	$-0.533739\pi$
$127$	−2.38450			−0.211590			−0.105795	+	0.994388i	$0.533739\pi$
$128$		−	14.7757i		−	1.30600i
$129$	−2.48846	+	1.12573i	−0.219096	+	0.0991153i
$130$	5.15649			0.452254
$131$	3.70602	+	6.41901i	0.323796	+	0.560832i	0.981268	−	0.192648i	$-0.0617074\pi$
$131$	3.70602	+	6.41901i	0.323796	+	0.560832i	−0.657472	+	0.753479i	$0.728374\pi$
$132$	−28.2021	+	39.3070i	−2.45468	+	3.42123i
$133$	10.2756	−	3.12724i	0.891010	−	0.271166i
$134$		−	38.7501i		−	3.34750i
$135$	−5.06250	+	1.17096i	−0.435710	+	0.100780i
$136$	17.2666	−	9.96886i	1.48060	−	0.854822i
$137$	−19.0198	−	10.9811i	−1.62497	−	0.938179i	−0.985562	−	0.169315i	$-0.945845\pi$
$137$	−19.0198	−	10.9811i	−1.62497	−	0.938179i	−0.639412	−	0.768864i	$-0.720822\pi$
$138$	−11.4015	+	5.15783i	−0.970559	+	0.439064i
$139$	−7.75114	−	4.47512i	−0.657443	−	0.379575i	0.133859	−	0.991000i	$-0.457263\pi$
$139$	−7.75114	−	4.47512i	−0.657443	−	0.379575i	−0.791302	+	0.611425i	$0.790596\pi$
$140$	11.1975	+	2.60021i	0.946361	+	0.219758i
$141$	1.03335	−	10.4287i	0.0870241	−	0.878253i
$142$	−12.9250			−1.08464
$143$	6.57993	+	11.3968i	0.550242	+	0.953046i
$144$	−18.2033	−	3.64323i	−1.51695	−	0.303602i
$145$	−5.49358	−	3.17172i	−0.456217	−	0.263397i
$146$	13.9855	+	24.2236i	1.15745	+	2.00476i
$147$	12.1183	+	0.381922i	0.999504	+	0.0315004i
$148$	5.71405	−	9.89702i	0.469692	−	0.813530i
$149$	−20.0506	+	11.5762i	−1.64261	+	0.948360i	−0.662707	+	0.748879i	$0.730592\pi$
$149$	−20.0506	+	11.5762i	−1.64261	+	0.948360i	−0.979902	+	0.199482i	$0.936074\pi$
$150$	−2.54337	+	3.54484i	−0.207665	+	0.289435i
$151$	−3.97241	+	6.88041i	−0.323270	+	0.559920i	−0.981161	−	0.193194i	$-0.938115\pi$
$151$	−3.97241	+	6.88041i	−0.323270	+	0.559920i	0.657891	+	0.753113i	$0.271449\pi$
$152$	−11.9893	+	20.7660i	−0.972459	+	1.68435i
$153$	3.24379	+	9.59311i	0.262245	+	0.775557i
$154$	12.4734	+	40.9858i	1.00514	+	3.30273i
$155$	−0.836103	+	0.482724i	−0.0671574	+	0.0387733i
$156$	−8.98084	+	12.5171i	−0.719043	+	1.00217i
$157$		−	12.2046i		−	0.974033i	−0.873393	−	0.487016i	$-0.838085\pi$
$157$		−	12.2046i		−	0.974033i	0.873393	−	0.487016i	$-0.161915\pi$
$158$			9.69816i			0.771544i
$159$	−2.66076	−	5.88166i	−0.211012	−	0.466446i
$160$	−3.26863	+	1.88715i	−0.258408	+	0.149192i
$161$	−1.71653	+	7.39204i	−0.135282	+	0.582575i
$162$	8.72492	−	20.9239i	0.685495	−	1.64394i
$163$	−2.39850	+	4.15432i	−0.187865	+	0.325391i	−0.944538	−	0.328402i	$-0.893490\pi$
$163$	−2.39850	+	4.15432i	−0.187865	+	0.325391i	0.756673	+	0.653793i	$0.226823\pi$
$164$	−15.2236	+	26.3680i	−1.18876	+	2.05899i
$165$	−11.0802	−	1.09791i	−0.862591	−	0.0854722i
$166$	2.39708	−	1.38396i	0.186050	−	0.107416i
$167$	0.142113	−	0.246147i	0.0109970	−	0.0190474i	−0.860475	−	0.509493i	$-0.829833\pi$
$167$	0.142113	−	0.246147i	0.0109970	−	0.0190474i	0.871472	+	0.490446i	$0.163166\pi$
$168$	−20.3444	+	17.8528i	−1.56960	+	1.37738i
$169$	−4.40465	−	7.62908i	−0.338819	−	0.586852i
$170$	7.36357	+	4.25136i	0.564760	+	0.326064i
$171$	−9.14725	−	8.04105i	−0.699507	−	0.614915i
$172$	−3.42567	−	5.93344i	−0.261205	−	0.452421i
$173$	12.5219			0.952021			0.476011	−	0.879439i	$-0.342082\pi$
$173$	12.5219			0.952021			0.476011	+	0.879439i	$0.342082\pi$
$174$	25.2154	−	11.4070i	1.91158	−	0.864764i
$175$	0.770312	+	2.53113i	0.0582301	+	0.191335i
$176$	−34.4506	−	19.8901i	−2.59681	−	1.49927i
$177$	−2.44315	+	24.6564i	−0.183638	+	1.85329i
$178$	1.84695	+	1.06634i	0.138435	+	0.0799253i
$179$	12.1696	−	7.02610i	0.909595	−	0.525155i	0.0292944	−	0.999571i	$-0.490674\pi$
$179$	12.1696	−	7.02610i	0.909595	−	0.525155i	0.880301	+	0.474416i	$0.157341\pi$
$180$	−4.17525	−	12.3478i	−0.311205	−	0.920350i
$181$		−	4.43857i		−	0.329916i	−0.986301	−	0.164958i	$-0.947251\pi$
$181$		−	4.43857i		−	0.329916i	0.986301	−	0.164958i	$-0.0527489\pi$
$182$	3.97211	+	13.0518i	0.294432	+	0.967461i
$183$	12.6386	+	1.25233i	0.934272	+	0.0925748i
$184$	−8.47069	−	14.6717i	−0.624468	−	1.08161i
$185$	2.63025			0.193380
$186$	0.415335	−	4.19159i	0.0304538	−	0.307342i
$187$			21.6997i			1.58684i
$188$	26.2886			1.91729
$189$	−6.86354	−	11.9118i	−0.499249	−	0.866458i
$190$	−10.2260			−0.741871
$191$		−	2.81804i		−	0.203906i	−0.994789	−	0.101953i	$-0.967491\pi$
$191$		−	2.81804i		−	0.203906i	0.994789	−	0.101953i	$-0.0325092\pi$
$192$	−0.490021	+	4.94532i	−0.0353642	+	0.356898i
$193$	−8.91937			−0.642030			−0.321015	−	0.947074i	$-0.604024\pi$
$193$	−8.91937			−0.642030			−0.321015	+	0.947074i	$0.604024\pi$
$194$	4.31382	+	7.47175i	0.309714	+	0.536441i
$195$	−3.52844	−	0.349625i	−0.252677	−	0.0250371i
$196$	2.04410	+	30.3453i	0.146007	+	2.16752i
$197$			21.8294i			1.55528i	0.628708	+	0.777641i	$0.283584\pi$
$197$			21.8294i			1.55528i	−0.628708	+	0.777641i	$0.716416\pi$
$198$	32.0729	−	36.4851i	2.27932	−	2.59288i
$199$	6.40750	−	3.69937i	0.454216	−	0.262241i	−0.255393	−	0.966837i	$-0.582205\pi$
$199$	6.40750	−	3.69937i	0.454216	−	0.262241i	0.709609	+	0.704596i	$0.248872\pi$
$200$	−5.11516	−	2.95324i	−0.361697	−	0.208826i
$201$	−2.62737	+	26.5156i	−0.185320	+	1.87026i
$202$	−14.9658	−	8.64051i	−1.05299	−	0.607944i
$203$	3.79627	−	16.3482i	0.266446	−	1.14742i
$204$	−23.1448	+	10.4703i	−1.62046	+	0.733067i
$205$	−7.00761			−0.489433
$206$	−18.3186	−	31.7287i	−1.27632	−	2.21065i
$207$	8.15141	−	2.75630i	0.566562	−	0.191576i
$208$	−10.9707	−	6.33391i	−0.760678	−	0.439177i
$209$	−13.0489	−	22.6013i	−0.902608	−	1.56336i
$210$	−10.9316	−	3.70696i	−0.754354	−	0.255804i
$211$	−0.359873	+	0.623319i	−0.0247747	+	0.0429111i	−0.878147	−	0.478391i	$-0.841220\pi$
$211$	−0.359873	+	0.623319i	−0.0247747	+	0.0429111i	0.853372	+	0.521302i	$0.174554\pi$
$212$	14.0242	−	8.09685i	0.963183	−	0.556094i
$213$	8.84421	+	0.876353i	0.605996	+	0.0600467i
$214$	7.77846	−	13.4727i	0.531725	−	0.920974i
$215$	0.788442	−	1.36562i	0.0537713	−	0.0931346i
$216$	29.3536	+	8.96113i	1.99726	+	0.609728i
$217$	−1.86590	−	1.74444i	−0.126665	−	0.118420i
$218$	−8.97882	+	5.18392i	−0.608122	+	0.351100i
$219$	−7.92745	−	17.5238i	−0.535687	−	1.18415i
$220$		−	27.9309i		−	1.88310i
$221$			6.91019i			0.464830i
$222$	−6.68970	+	9.32383i	−0.448983	+	0.625774i
$223$	16.8677	−	9.73854i	1.12954	−	0.652141i	0.185722	−	0.982602i	$-0.440538\pi$
$223$	16.8677	−	9.73854i	1.12954	−	0.652141i	0.943820	+	0.330461i	$0.107204\pi$
$224$	−7.29448	−	6.81964i	−0.487383	−	0.455656i
$225$	1.98070	−	2.25318i	0.132047	−	0.150212i
$226$	−3.85386	+	6.67508i	−0.256355	+	0.444020i
$227$	−1.90803	+	3.30480i	−0.126640	+	0.219348i	−0.922373	−	0.386301i	$-0.873753\pi$
$227$	−1.90803	+	3.30480i	−0.126640	+	0.219348i	0.795733	+	0.605648i	$0.207086\pi$
$228$	17.8102	−	24.8231i	1.17951	−	1.64395i
$229$	14.4169	−	8.32362i	0.952697	−	0.550040i	0.0587796	−	0.998271i	$-0.481279\pi$
$229$	14.4169	−	8.32362i	0.952697	−	0.550040i	0.893918	+	0.448231i	$0.147946\pi$
$230$	3.61244	−	6.25694i	0.238197	−	0.412570i
$231$	−5.75625	−	28.8911i	−0.378733	−	1.90090i
$232$	18.7337	+	32.4478i	1.22993	+	2.13030i
$233$	−9.82501	−	5.67247i	−0.643658	−	0.371616i	0.142364	−	0.989814i	$-0.454530\pi$
$233$	−9.82501	−	5.67247i	−0.643658	−	0.371616i	−0.786022	+	0.618198i	$0.787863\pi$
$234$	10.2135	−	11.6185i	0.667675	−	0.759526i
$235$	3.02524	+	5.23988i	0.197345	+	0.341812i
$236$	−62.1538			−4.04587
$237$	0.657562	−	6.63617i	0.0427133	−	0.431065i
$238$	−5.08850	+	21.9130i	−0.329838	+	1.42041i
$239$	−11.3941	−	6.57837i	−0.737022	−	0.425520i	0.0839637	−	0.996469i	$-0.473242\pi$
$239$	−11.3941	−	6.57837i	−0.737022	−	0.425520i	−0.820985	+	0.570949i	$0.806575\pi$
$240$	9.76537	−	4.41768i	0.630352	−	0.285160i
$241$	−14.3490	−	8.28439i	−0.924299	−	0.533644i	−0.0392949	−	0.999228i	$-0.512511\pi$
$241$	−14.3490	−	8.28439i	−0.924299	−	0.533644i	−0.885004	+	0.465583i	$0.845845\pi$
$242$	66.1526	−	38.1932i	4.25245	−	2.45515i
$243$	−7.38891	+	13.7260i	−0.473999	+	0.880526i
$244$			31.8593i			2.03958i
$245$	−5.81324	+	3.89952i	−0.371394	+	0.249131i
$246$	17.8229	−	24.8409i	1.13635	−	1.58380i
$247$	−4.15535	−	7.19728i	−0.264399	−	0.457952i
$248$	5.70240			0.362103
$249$	−1.73409	+	0.784472i	−0.109893	+	0.0497139i
$250$		−	2.51890i		−	0.159309i
$251$	21.1282			1.33360			0.666799	−	0.745238i	$-0.267664\pi$
$251$	21.1282			1.33360			0.666799	+	0.745238i	$0.267664\pi$
$252$	28.0376	−	20.0798i	1.76620	−	1.26491i
$253$	18.4386			1.15923
$254$			6.00632i			0.376870i
$255$	−4.75042	−	3.40835i	−0.297483	−	0.213439i
$256$	−31.4803			−1.96752
$257$	0.892116	+	1.54519i	0.0556487	+	0.0963863i	0.892508	−	0.451032i	$-0.148944\pi$
$257$	0.892116	+	1.54519i	0.0556487	+	0.0963863i	−0.836859	+	0.547418i	$0.815611\pi$
$258$	2.83561	+	6.26817i	0.176538	+	0.390239i
$259$	2.02612	+	6.65751i	0.125897	+	0.413678i
$260$		−	8.89446i		−	0.551611i
$261$	−18.0276	+	6.09581i	−1.11588	+	0.377321i
$262$	16.1689	−	9.33509i	0.998915	−	0.576724i
$263$	−19.7785	−	11.4191i	−1.21960	−	0.704134i	−0.254764	−	0.967003i	$-0.581998\pi$
$263$	−19.7785	−	11.4191i	−1.21960	−	0.704134i	−0.964831	+	0.262869i	$0.915331\pi$
$264$	53.4346	+	38.3384i	3.28867	+	2.35957i
$265$	3.22776	+	1.86355i	0.198279	+	0.114477i
$266$	−7.87720	−	25.8833i	−0.482982	−	1.58701i
$267$	−1.19151	−	0.854891i	−0.0729194	−	0.0523185i
$268$	−66.8403			−4.08292
$269$	−9.02105	−	15.6249i	−0.550023	−	0.952668i	−0.998272	−	0.0587593i	$-0.981286\pi$
$269$	−9.02105	−	15.6249i	−0.550023	−	0.952668i	0.448249	−	0.893909i	$-0.352048\pi$
$270$	2.94952	+	12.7519i	0.179502	+	0.776058i
$271$	4.07556	+	2.35303i	0.247573	+	0.142936i	0.618652	−	0.785665i	$-0.287679\pi$
$271$	4.07556	+	2.35303i	0.247573	+	0.142936i	−0.371080	+	0.928601i	$0.621012\pi$
$272$	−10.4442	−	18.0899i	−0.633272	−	1.09686i
$273$	−1.83305	−	9.20025i	−0.110941	−	0.556825i
$274$	−27.6603	+	47.9091i	−1.67102	+	2.89429i
$275$	5.56722	−	3.21424i	0.335716	−	0.193826i
$276$	8.89677	+	19.6665i	0.535522	+	1.18378i
$277$	−5.28900	+	9.16082i	−0.317785	+	0.550421i	−0.980026	−	0.198871i	$-0.936273\pi$
$277$	−5.28900	+	9.16082i	−0.317785	+	0.550421i	0.662240	+	0.749292i	$0.269606\pi$
$278$	−11.2724	+	19.5244i	−0.676073	+	1.17099i
$279$	−0.568403	+	2.84002i	−0.0340294	+	0.170028i
$280$	3.53477	−	15.2221i	0.211243	−	0.909692i
$281$	−5.88057	+	3.39515i	−0.350805	+	0.202537i	−0.665040	−	0.746808i	$-0.731585\pi$
$281$	−5.88057	+	3.39515i	−0.350805	+	0.202537i	0.314235	+	0.949345i	$0.398252\pi$
$282$	−26.2688	−	2.60292i	−1.56429	−	0.155001i
$283$			0.302966i			0.0180095i	0.999959	+	0.00900474i	$0.00286634\pi$
$283$			0.302966i			0.0180095i	−0.999959	+	0.00900474i	$0.997134\pi$
$284$			22.2944i			1.32293i
$285$	6.99734	+	0.693350i	0.414487	+	0.0410705i
$286$	28.7074	−	16.5742i	1.69750	−	0.980053i
$287$	−5.39805	−	17.7372i	−0.318637	−	1.04699i
$288$	−2.22210	+	11.1027i	−0.130938	+	0.654232i
$289$	2.80278	−	4.85456i	0.164869	−	0.285562i
$290$	−7.98926	+	13.8378i	−0.469145	+	0.812583i
$291$	−2.44521	−	5.40519i	−0.143341	−	0.316858i
$292$	41.7834	−	24.1237i	2.44519	−	1.41173i
$293$	−10.1619	+	17.6009i	−0.593662	+	1.02825i	0.400072	+	0.916484i	$0.368985\pi$
$293$	−10.1619	+	17.6009i	−0.593662	+	1.02825i	−0.993734	+	0.111769i	$0.964348\pi$
$294$	0.962023	−	30.5249i	0.0561063	−	1.78025i
$295$	−7.15256	−	12.3886i	−0.416438	−	0.721292i
$296$	−13.4542	−	7.76777i	−0.782008	−	0.451493i
$297$	−24.4203	+	22.7910i	−1.41701	+	1.32247i
$298$	29.1593	+	50.5055i	1.68916	+	2.92570i
$299$	5.87169			0.339569
$300$	6.11451	+	4.38706i	0.353021	+	0.253287i
$301$	4.06391	+	0.943695i	0.234240	+	0.0543937i
$302$	17.3311	+	10.0061i	0.997291	+	0.575786i
$303$	9.65481	+	6.92717i	0.554654	+	0.397956i
$304$	21.7562	+	12.5610i	1.24780	+	0.720420i
$305$	−6.35024	+	3.66631i	−0.363614	+	0.209933i
$306$	24.1641	−	8.17079i	1.38137	−	0.467093i
$307$		−	18.6913i		−	1.06677i	−0.845873	−	0.533385i	$-0.820920\pi$
$307$		−	18.6913i		−	1.06677i	0.845873	−	0.533385i	$-0.179080\pi$
$308$	70.6966	−	21.5155i	4.02831	−	1.22596i
$309$	10.3836	+	22.9531i	0.590701	+	1.30576i
$310$	1.21593	+	2.10606i	0.0690604	+	0.119616i
$311$	10.1961			0.578171			0.289085	−	0.957303i	$-0.406649\pi$
$311$	10.1961			0.578171			0.289085	+	0.957303i	$0.406649\pi$
$312$	17.0160	+	12.2087i	0.963341	+	0.691182i
$313$			4.33899i			0.245254i	0.992453	+	0.122627i	$0.0391319\pi$
$313$			4.33899i			0.245254i	−0.992453	+	0.122627i	$0.960868\pi$
$314$	−30.7422			−1.73488
$315$	7.22885	+	3.27776i	0.407300	+	0.184681i
$316$	16.7284			0.941046
$317$			12.6597i			0.711041i	0.934668	+	0.355521i	$0.115696\pi$
$317$			12.6597i			0.711041i	−0.934668	+	0.355521i	$0.884304\pi$
$318$	−14.8153	+	6.70220i	−0.830802	+	0.375841i
$319$	−40.7787			−2.28317
$320$	−1.43458	−	2.48477i	−0.0801956	−	0.138903i
$321$	−6.23606	+	8.69156i	−0.348063	+	0.485116i
$322$	18.6198	+	4.32377i	1.03764	+	0.240954i
$323$		−	13.7038i		−	0.762499i
$324$	−36.0917	−	15.0497i	−2.00510	−	0.836092i
$325$	1.77286	−	1.02356i	0.0983405	−	0.0567769i
$326$	10.4643	+	6.04158i	0.579565	+	0.334612i
$327$	6.49543	−	2.93842i	0.359198	−	0.162495i
$328$	35.8451	+	20.6952i	1.97921	+	1.14270i
$329$	−10.9324	+	11.6936i	−0.602724	+	0.644690i
$330$	−2.76553	+	27.9099i	−0.152237	+	1.53639i
$331$	−2.53095			−0.139114			−0.0695569	−	0.997578i	$-0.522159\pi$
$331$	−2.53095			−0.139114			−0.0695569	+	0.997578i	$0.522159\pi$
$332$	−2.38719	−	4.13474i	−0.131014	−	0.226923i
$333$	5.20974	−	5.92644i	0.285492	−	0.324767i
$334$	−0.620019	−	0.357968i	−0.0339259	−	0.0195871i
$335$	−7.69187	−	13.3227i	−0.420252	−	0.727898i
$336$	18.7041	+	21.3144i	1.02039	+	1.16280i
$337$	7.68180	−	13.3053i	0.418454	−	0.724784i	−0.577330	−	0.816511i	$-0.695905\pi$
$337$	7.68180	−	13.3053i	0.418454	−	0.724784i	0.995784	+	0.0917270i	$0.0292387\pi$
$338$	−19.2169	+	11.0949i	−1.04526	+	0.603482i
$339$	3.08967	−	4.30626i	0.167808	−	0.233884i
$340$	7.33319	−	12.7015i	0.397698	−	0.688833i
$341$	−3.10318	+	5.37487i	−0.168047	+	0.291065i
$342$	−20.2546	+	23.0410i	−1.09524	+	1.24592i
$343$	−14.3482	−	11.7102i	−0.774730	−	0.632292i
$344$	−8.06602	+	4.65692i	−0.434891	+	0.251084i
$345$	−2.89613	+	4.03650i	−0.155922	+	0.217318i
$346$		−	31.5414i		−	1.69568i
$347$			21.1197i			1.13376i	0.823799	+	0.566882i	$0.191851\pi$
$347$			21.1197i			1.13376i	−0.823799	+	0.566882i	$0.808149\pi$
$348$	−19.6760	−	43.4942i	−1.05475	−	2.33153i
$349$	28.9047	−	16.6881i	1.54723	−	0.893295i	0.548880	−	0.835901i	$-0.315054\pi$
$349$	28.9047	−	16.6881i	1.54723	−	0.893295i	0.998352	−	0.0573935i	$-0.0182790\pi$
$350$	6.37567	−	1.94034i	0.340794	−	0.103716i
$351$	−7.77654	+	7.25771i	−0.415081	+	0.387388i
$352$	−12.1315	+	21.0123i	−0.646610	+	1.11996i
$353$	−7.76354	+	13.4468i	−0.413212	+	0.715703i	−0.995239	−	0.0974659i	$-0.968926\pi$
$353$	−7.76354	+	13.4468i	−0.413212	+	0.715703i	0.582027	+	0.813169i	$0.302260\pi$
$354$	62.1072	+	6.15405i	3.30096	+	0.327084i
$355$	−4.44376	+	2.56561i	−0.235850	+	0.136168i
$356$	1.83933	−	3.18581i	0.0974842	−	0.168848i
$357$	4.96767	−	14.6494i	0.262917	−	0.775330i
$358$	−17.6980	−	30.6539i	−0.935371	−	1.62011i
$359$	6.70055	+	3.86856i	0.353642	+	0.204175i	0.666288	−	0.745695i	$-0.267882\pi$
$359$	6.70055	+	3.86856i	0.353642	+	0.204175i	−0.312646	+	0.949870i	$0.601215\pi$
$360$	−16.7858	+	5.67591i	−0.884689	+	0.299147i
$361$	−1.25941	−	2.18136i	−0.0662847	−	0.114808i
$362$	−11.1803			−0.587624
$363$	−47.8559	+	21.6492i	−2.51178	+	1.13629i
$364$	22.5130	−	6.85151i	1.18000	−	0.359117i
$365$	9.61674	+	5.55223i	0.503363	+	0.290617i
$366$	3.15449	−	31.8354i	0.164888	−	1.66406i
$367$	−8.02352	−	4.63238i	−0.418825	−	0.241808i	0.275750	−	0.961229i	$-0.411074\pi$
$367$	−8.02352	−	4.63238i	−0.418825	−	0.241808i	−0.694574	+	0.719421i	$0.744407\pi$
$368$	−15.3712	+	8.87459i	−0.801281	+	0.462620i
$369$	−13.8800	+	15.7894i	−0.722563	+	0.821965i
$370$		−	6.62535i		−	0.344436i
$371$	−2.23050	+	9.60538i	−0.115802	+	0.498686i
$372$	−7.23010	−	0.716413i	−0.374863	−	0.0371443i
$373$	−2.44141	−	4.22864i	−0.126411	−	0.218951i	0.795872	−	0.605464i	$-0.207013\pi$
$373$	−2.44141	−	4.22864i	−0.126411	−	0.218951i	−0.922284	+	0.386514i	$0.873679\pi$
$374$	54.6595			2.82638
$375$	−0.170788	+	1.72361i	−0.00881948	+	0.0890068i
$376$		−	35.7371i		−	1.84300i
$377$	−12.9858			−0.668802
$378$	−30.0047	+	17.2886i	−1.54328	+	0.889229i
$379$	−1.55787			−0.0800226			−0.0400113	−	0.999199i	$-0.512739\pi$
$379$	−1.55787			−0.0800226			−0.0400113	+	0.999199i	$0.512739\pi$
$380$			17.6389i			0.904854i
$381$	0.407245	−	4.10995i	0.0208638	−	0.210559i
$382$	−7.09837			−0.363184
$383$	14.0803	+	24.3877i	0.719468	+	1.24615i	0.961211	+	0.275814i	$0.0889475\pi$
$383$	14.0803	+	24.3877i	0.719468	+	1.24615i	−0.241743	+	0.970340i	$0.577719\pi$
$384$	25.4676	+	2.52352i	1.29964	+	0.128778i
$385$	12.4242	+	11.6154i	0.633194	+	0.591976i
$386$			22.4670i			1.14354i
$387$	−1.51533	−	4.48139i	−0.0770284	−	0.227802i
$388$	12.8881	−	7.44093i	0.654292	−	0.377756i
$389$	18.1454	+	10.4763i	0.920010	+	0.531168i	0.883638	−	0.468171i	$-0.155087\pi$
$389$	18.1454	+	10.4763i	0.920010	+	0.531168i	0.0363714	+	0.999338i	$0.488420\pi$
$390$	−0.880670	+	8.88778i	−0.0445944	+	0.450050i
$391$	8.38488	+	4.84102i	0.424042	+	0.244821i
$392$	41.2519	−	2.77878i	2.08353	−	0.140350i
$393$	−11.6968	+	5.29144i	−0.590026	+	0.266918i
$394$	54.9862			2.77016
$395$	1.92508	+	3.33433i	0.0968612	+	0.167768i
$396$	−62.9333	−	55.3226i	−3.16252	−	2.78007i
$397$	−19.5296	−	11.2754i	−0.980160	−	0.565896i	−0.0778416	−	0.996966i	$-0.524803\pi$
$397$	−19.5296	−	11.2754i	−0.980160	−	0.565896i	−0.902318	+	0.431070i	$0.858136\pi$
$398$	−9.31835	−	16.1399i	−0.467087	−	0.809018i
$399$	3.63518	+	18.2453i	0.181986	+	0.913407i
$400$	−3.09406	+	5.35907i	−0.154703	+	0.267953i
$401$	32.6687	−	18.8613i	1.63140	−	0.941888i	0.647736	−	0.761864i	$-0.275716\pi$
$401$	32.6687	−	18.8613i	1.63140	−	0.941888i	0.983662	−	0.180024i	$-0.0576176\pi$
$402$	66.7901	+	6.61808i	3.33119	+	0.330080i
$403$	−0.988194	+	1.71160i	−0.0492254	+	0.0852610i
$404$	−14.9041	+	25.8146i	−0.741505	+	1.28432i
$405$	−1.15366	−	8.92575i	−0.0573256	−	0.443524i
$406$	−41.1795	−	9.56243i	−2.04370	−	0.474575i
$407$	14.6432	−	8.45426i	0.725837	−	0.419062i
$408$	14.2335	+	31.4634i	0.704663	+	1.55767i
$409$		−	12.8572i		−	0.635749i	−0.948133	−	0.317875i	$-0.897031\pi$
$409$		−	12.8572i		−	0.635749i	0.948133	−	0.317875i	$-0.102969\pi$
$410$			17.6515i			0.871745i
$411$	22.1755	−	30.9073i	1.09384	−	1.52455i
$412$	−54.7290	+	31.5978i	−2.69631	+	1.55671i
$413$	25.8474	−	27.6471i	1.27187	−	1.36043i
$414$	−6.94285	−	20.5326i	−0.341222	−	1.00912i
$415$	0.549429	−	0.951639i	0.0269704	−	0.0467141i
$416$	−3.86321	+	6.69128i	−0.189410	+	0.328067i
$417$	9.03717	−	12.5956i	0.442552	−	0.616811i
$418$	−56.9304	+	32.8688i	−2.78456	+	1.60766i
$419$	−5.82993	+	10.0977i	−0.284811	+	0.493307i	−0.972563	−	0.232638i	$-0.925264\pi$
$419$	−5.82993	+	10.0977i	−0.284811	+	0.493307i	0.687752	+	0.725945i	$0.258597\pi$
$420$	−6.39415	+	18.8560i	−0.312002	+	0.920080i
$421$	9.66339	+	16.7375i	0.470965	+	0.815735i	0.999448	−	0.0332084i	$-0.0105725\pi$
$421$	9.66339	+	16.7375i	0.470965	+	0.815735i	−0.528484	+	0.848944i	$0.677239\pi$
$422$	1.57008	+	0.906486i	0.0764303	+	0.0441270i
$423$	17.7985	+	3.56220i	0.865392	+	0.173200i
$424$	−11.0070	−	19.0647i	−0.534547	−	0.925863i
$425$	3.37557			0.163739
$426$	2.20745	−	22.2777i	0.106951	−	1.07936i
$427$	−14.1716	−	13.2491i	−0.685811	−	0.641168i
$428$	−23.2391	−	13.4171i	−1.12330	−	0.648540i
$429$	−20.7674	+	9.39480i	−1.00266	+	0.453585i
$430$	−3.43987	−	1.98601i	−0.165885	−	0.0957738i
$431$	26.7643	−	15.4524i	1.28919	−	0.744314i	0.310679	−	0.950515i	$-0.399443\pi$
$431$	26.7643	−	15.4524i	1.28919	−	0.744314i	0.978510	+	0.206201i	$0.0661101\pi$
$432$	9.38842	−	30.7533i	0.451701	−	1.47962i
$433$			5.46755i			0.262754i	0.991333	+	0.131377i	$0.0419398\pi$
$433$			5.46755i			0.262754i	−0.991333	+	0.131377i	$0.958060\pi$
$434$	−4.39406	+	4.70001i	−0.210922	+	0.225608i
$435$	6.40505	−	8.92710i	0.307099	−	0.428022i
$436$	8.94177	+	15.4876i	0.428233	+	0.741722i
$437$	−11.6443			−0.557023
$438$	−44.1406	+	19.9685i	−2.10912	+	0.954130i
$439$		−	16.7135i		−	0.797692i	−0.917018	−	0.398846i	$-0.869411\pi$
$439$		−	16.7135i		−	0.797692i	0.917018	−	0.398846i	$-0.130589\pi$
$440$	−37.9697			−1.81013
$441$	−2.72796	+	20.8221i	−0.129903	+	0.991527i
$442$	17.4061			0.827923
$443$			32.2182i			1.53073i	0.643595	+	0.765367i	$0.277442\pi$
$443$			32.2182i			1.53073i	−0.643595	+	0.765367i	$0.722558\pi$
$444$	16.0827	+	11.5391i	0.763252	+	0.547621i
$445$	0.846668			0.0401359
$446$	−24.5304	−	42.4880i	−1.16155	−	2.01186i
$447$	−16.5285	−	36.5365i	−0.781770	−	1.72812i
$448$	5.18420	−	5.54516i	0.244931	−	0.261984i
$449$		−	5.63055i		−	0.265722i	−0.991135	−	0.132861i	$-0.957584\pi$
$449$		−	5.63055i		−	0.265722i	0.991135	−	0.132861i	$-0.0424164\pi$
$450$	−5.67554	−	4.98919i	−0.267548	−	0.235193i
$451$	−39.0130	+	22.5241i	−1.83705	+	1.06062i
$452$	11.5139	+	6.64754i	0.541567	+	0.312674i
$453$	−11.1807	−	8.02197i	−0.525315	−	0.376905i
$454$	8.32448	+	4.80614i	0.390687	+	0.225563i
$455$	3.95642	+	3.69887i	0.185480	+	0.173406i
$456$	−33.7449	−	24.2114i	−1.58025	−	1.13380i
$457$	26.4953			1.23940			0.619699	−	0.784840i	$-0.287255\pi$
$457$	26.4953			1.23940			0.619699	+	0.784840i	$0.287255\pi$
$458$	−20.9664	−	36.3148i	−0.979694	−	1.69688i
$459$	−17.0888	+	3.95264i	−0.797636	+	0.184493i
$460$	−10.7926	−	6.23112i	−0.503208	−	0.290527i
$461$	−5.97371	−	10.3468i	−0.278223	−	0.481897i	0.692720	−	0.721207i	$-0.256412\pi$
$461$	−5.97371	−	10.3468i	−0.278223	−	0.481897i	−0.970943	+	0.239310i	$0.923079\pi$
$462$	−72.7739	+	14.4994i	−3.38575	+	0.674574i
$463$	10.9579	−	18.9796i	0.509255	−	0.882055i	−0.490688	−	0.871336i	$-0.663254\pi$
$463$	10.9579	−	18.9796i	0.509255	−	0.882055i	0.999943	−	0.0107198i	$-0.00341229\pi$
$464$	33.9949	−	19.6270i	1.57818	−	0.911160i
$465$	−0.689231	−	1.52356i	−0.0319623	−	0.0706533i
$466$	−14.2884	+	24.7482i	−0.661898	+	1.14644i
$467$	−0.189973	+	0.329044i	−0.00879092	+	0.0152263i	−0.870387	−	0.492368i	$-0.836132\pi$
$467$	−0.189973	+	0.329044i	−0.00879092	+	0.0152263i	0.861596	+	0.507594i	$0.169465\pi$
$468$	−20.0408	−	17.6173i	−0.926388	−	0.814358i
$469$	27.7964	−	29.7318i	1.28352	−	1.37289i
$470$	13.1987	−	7.62029i	0.608812	−	0.351498i
$471$	21.0360	+	2.08440i	0.969286	+	0.0960443i
$472$			84.4929i			3.88910i
$473$		−	10.1370i		−	0.466098i
$474$	−16.7158	−	1.65633i	−0.767784	−	0.0760779i
$475$	−3.51581	+	2.02985i	−0.161316	+	0.0931360i
$476$	37.7979	+	8.77717i	1.73246	+	0.402301i
$477$	10.5921	−	3.58160i	0.484980	−	0.163990i
$478$	−16.5703	+	28.7006i	−0.757907	+	1.31273i
$479$	−10.5083	+	18.2009i	−0.480137	+	0.831622i	−0.999740	−	0.0227857i	$-0.992746\pi$
$479$	−10.5083	+	18.2009i	−0.480137	+	0.831622i	0.519603	+	0.854408i	$0.326080\pi$
$480$	−2.69446	−	5.95615i	−0.122985	−	0.271860i
$481$	4.66307	−	2.69222i	0.212618	−	0.122755i
$482$	−20.8676	+	36.1437i	−0.950491	+	1.64630i
$483$	−12.4478	−	4.22111i	−0.566396	−	0.192067i
$484$	−65.8797	−	114.107i	−2.99453	−	5.18668i
$485$	2.96628	+	1.71258i	0.134692	+	0.0777642i
$486$	34.5745	+	18.6119i	1.56833	+	0.844254i
$487$	5.21390	+	9.03074i	0.236264	+	0.409222i	0.959639	−	0.281234i	$-0.0907436\pi$
$487$	5.21390	+	9.03074i	0.236264	+	0.409222i	−0.723375	+	0.690455i	$0.757410\pi$
$488$	43.3100			1.96055
$489$	−6.75079	−	4.84358i	−0.305281	−	0.219034i
$490$	9.82250	+	14.6430i	0.443735	+	0.661502i
$491$	−2.34770	−	1.35544i	−0.105950	−	0.0611703i	0.446089	−	0.894989i	$-0.352817\pi$
$491$	−2.34770	−	1.35544i	−0.105950	−	0.0611703i	−0.552039	+	0.833818i	$0.686150\pi$
$492$	−42.8481	−	30.7428i	−1.93174	−	1.38599i
$493$	−18.5440	−	10.7064i	−0.835178	−	0.482190i
$494$	−18.1292	+	10.4669i	−0.815672	+	0.470929i
$495$	3.78474	−	18.9104i	0.170111	−	0.849960i
$496$		−	5.97430i		−	0.268254i
$497$	−9.91697	−	9.27142i	−0.444837	−	0.415880i
$498$	1.97601	+	4.36800i	0.0885470	+	0.195735i
$499$	0.278114	+	0.481707i	0.0124501	+	0.0215642i	0.872183	−	0.489179i	$-0.162704\pi$
$499$	0.278114	+	0.481707i	0.0124501	+	0.0215642i	−0.859733	+	0.510743i	$0.829370\pi$
$500$	−4.34486			−0.194308
$501$	0.399989	+	0.286986i	0.0178702	+	0.0128216i
$502$		−	53.2198i		−	2.37531i
$503$	40.9302			1.82499			0.912494	−	0.409090i	$-0.134154\pi$
$503$	40.9302			1.82499			0.912494	+	0.409090i	$0.134154\pi$
$504$	−27.2968	−	38.1148i	−1.21589	−	1.69777i
$505$	−6.86054			−0.305290
$506$		−	46.4450i		−	2.06473i
$507$	13.9018	−	6.28894i	0.617401	−	0.279302i
$508$	10.3603			0.459665
$509$	−0.976241	−	1.69090i	−0.0432711	−	0.0749478i	0.843579	−	0.537006i	$-0.180445\pi$
$509$	−0.976241	−	1.69090i	−0.0432711	−	0.0749478i	−0.886850	+	0.462058i	$0.847111\pi$
$510$	−8.58530	+	11.9658i	−0.380163	+	0.529856i
$511$	−6.64552	+	28.6182i	−0.293981	+	1.26599i
$512$			49.7442i			2.19841i
$513$	15.4219	−	14.3930i	0.680893	−	0.635465i
$514$	3.89218	−	2.24715i	0.171677	−	0.0991176i
$515$	−12.5963	−	7.27245i	−0.555058	−	0.320463i
$516$	10.8120	−	4.89116i	0.475972	−	0.215321i
$517$	33.6844	+	19.4477i	1.48144	+	0.855309i
$518$	16.7696	−	5.10359i	0.736815	−	0.224239i
$519$	−2.13859	+	21.5829i	−0.0938739	+	0.947382i
$520$	−12.0913			−0.530238
$521$	13.4712	+	23.3329i	0.590185	+	1.02223i	0.994207	+	0.107482i	$0.0342787\pi$
$521$	13.4712	+	23.3329i	0.590185	+	1.02223i	−0.404022	+	0.914749i	$0.632388\pi$
$522$	15.3548	+	45.4098i	0.672059	+	1.98753i
$523$	15.4251	+	8.90566i	0.674491	+	0.389417i	0.797776	−	0.602954i	$-0.206010\pi$
$523$	15.4251	+	8.90566i	0.674491	+	0.389417i	−0.123285	+	0.992371i	$0.539343\pi$
$524$	−16.1021	−	27.8897i	−0.703425	−	1.21837i
$525$	−4.49424	+	0.895429i	−0.196145	+	0.0390797i
$526$	−28.7637	+	49.8201i	−1.25416	+	2.17226i
$527$	−2.82232	+	1.62947i	−0.122942	+	0.0709807i
$528$	40.1665	−	55.9825i	1.74802	−	2.43632i
$529$	−7.38652	+	12.7938i	−0.321153	+	0.556253i
$530$	4.69409	−	8.13040i	0.203898	−	0.353162i
$531$	−42.0808	−	8.42207i	−1.82615	−	0.365487i
$532$	−44.6462	+	13.5874i	−1.93566	+	0.589089i
$533$	−12.4235	+	7.17271i	−0.538122	+	0.310685i
$534$	−2.15339	+	3.00130i	−0.0931861	+	0.129879i
$535$		−	6.17607i		−	0.267015i
$536$			90.8638i			3.92472i
$537$	10.0318	+	22.1755i	0.432905	+	0.956945i
$538$	−39.3576	+	22.7231i	−1.69683	+	0.979664i
$539$	−19.8296	+	40.3946i	−0.854122	+	1.73992i
$540$	21.9959	−	5.08765i	0.946551	−	0.218937i
$541$	6.42996	−	11.1370i	0.276446	−	0.478818i	−0.694053	−	0.719924i	$-0.744177\pi$
$541$	6.42996	−	11.1370i	0.276446	−	0.478818i	0.970499	+	0.241106i	$0.0775101\pi$
$542$	5.92704	−	10.2659i	0.254588	−	0.440960i
$543$	7.65036	+	0.758056i	0.328308	+	0.0325313i
$544$	−11.0335	+	6.37018i	−0.473056	+	0.273119i
$545$	−2.05801	+	3.56458i	−0.0881555	+	0.152690i
$546$	−23.1745	+	4.61728i	−0.991778	+	0.197601i
$547$	2.84645	+	4.93020i	0.121705	+	0.210800i	0.920440	−	0.390883i	$-0.127830\pi$
$547$	2.84645	+	4.93020i	0.121705	+	0.210800i	−0.798735	+	0.601683i	$0.794497\pi$
$548$	82.6386	+	47.7114i	3.53015	+	2.03813i
$549$	−4.31705	+	21.5701i	−0.184247	+	0.920590i
$550$	−8.09635	−	14.0233i	−0.345230	−	0.597955i
$551$	25.7525			1.09709
$552$	26.7349	−	12.0944i	1.13791	−	0.514772i
$553$	−6.95672	+	7.44110i	−0.295830	+	0.316428i
$554$	23.0752	+	13.3225i	0.980372	+	0.566018i
$555$	−0.449217	+	4.53353i	−0.0190682	+	0.192438i
$556$	33.6777	+	19.4438i	1.42825	+	0.824601i
$557$	−4.62341	+	2.66932i	−0.195900	+	0.113103i	−0.594742	−	0.803917i	$-0.702746\pi$
$557$	−4.62341	+	2.66932i	−0.195900	+	0.113103i	0.398842	+	0.917020i	$0.369412\pi$
$558$	7.15374	+	1.43175i	0.302842	+	0.0606109i
$559$		−	3.22807i		−	0.136533i
$560$	−15.9479	−	3.70331i	−0.673921	−	0.156493i
$561$	−37.4019	−	3.70607i	−1.57911	−	0.156470i
$562$	8.55204	+	14.8126i	0.360746	+	0.624830i
$563$	28.4309			1.19822			0.599110	−	0.800667i	$-0.295521\pi$
$563$	28.4309			1.19822			0.599110	+	0.800667i	$0.295521\pi$
$564$	−4.48978	+	45.3112i	−0.189054	+	1.90795i
$565$			3.05995i			0.128733i
$566$	0.763142			0.0320773
$567$	21.7036	−	9.79567i	0.911464	−	0.411379i
$568$	30.3074			1.27167
$569$			38.5156i			1.61466i	0.590101	+	0.807329i	$0.299088\pi$
$569$			38.5156i			1.61466i	−0.590101	+	0.807329i	$0.700912\pi$
$570$	1.74648	−	17.6256i	0.0731520	−	0.738256i
$571$	12.3259			0.515824			0.257912	−	0.966168i	$-0.416966\pi$
$571$	12.3259			0.515824			0.257912	+	0.966168i	$0.416966\pi$
$572$	−28.5889	−	49.5174i	−1.19536	−	2.07043i
$573$	4.85721	+	0.481289i	0.202913	+	0.0201061i
$574$	−44.6782	+	13.5971i	−1.86483	+	0.567534i
$575$		−	2.86827i		−	0.119615i
$576$	−8.44012	−	1.68921i	−0.351672	−	0.0703837i
$577$	12.2658	−	7.08167i	0.510632	−	0.294814i	−0.222461	−	0.974942i	$-0.571409\pi$
$577$	12.2658	−	7.08167i	0.510632	−	0.294814i	0.733094	+	0.680128i	$0.238076\pi$
$578$	−12.2281	−	7.05992i	−0.508624	−	0.293654i
$579$	1.52333	−	15.3735i	0.0633073	−	0.638902i
$580$	23.8689	+	13.7807i	0.991101	+	0.572212i
$581$	2.83195	+	0.657617i	0.117489	+	0.0272826i
$582$	−13.6151	+	6.15925i	−0.564366	+	0.255309i
$583$	23.9595			0.992302
$584$	−32.7941	−	56.8011i	−1.35703	−	2.35045i
$585$	1.20523	−	6.02194i	0.0498302	−	0.248976i
$586$	44.3348	+	25.5967i	1.83145	+	1.05739i
$587$	19.7385	+	34.1880i	0.814694	+	1.41109i	0.909548	+	0.415600i	$0.136428\pi$
$587$	19.7385	+	34.1880i	0.814694	+	1.41109i	−0.0948539	+	0.995491i	$0.530238\pi$
$588$	−52.6525	−	1.65940i	−2.17135	−	0.0684324i
$589$	1.95972	−	3.39433i	0.0807487	−	0.139861i
$590$	−31.2057	+	18.0166i	−1.28472	+	0.741731i
$591$	−37.6254	−	3.72822i	−1.54770	−	0.153358i
$592$	−8.13816	+	14.0957i	−0.334476	+	0.579330i
$593$	−2.13494	+	3.69782i	−0.0876714	+	0.151851i	−0.906526	−	0.422149i	$-0.861276\pi$
$593$	−2.13494	+	3.69782i	−0.0876714	+	0.151851i	0.818855	+	0.574000i	$0.194609\pi$
$594$	57.4084	+	61.5124i	2.35550	+	2.52388i
$595$	2.60024	+	8.54400i	0.106599	+	0.350270i
$596$	87.1171	−	50.2971i	3.56846	−	2.06025i
$597$	5.28195	+	11.6758i	0.216176	+	0.477860i
$598$		−	14.7902i		−	0.604817i
$599$		−	31.7088i		−	1.29559i	−0.761816	−	0.647793i	$-0.775692\pi$
$599$		−	31.7088i		−	1.29559i	0.761816	−	0.647793i	$-0.224308\pi$
$600$	5.96385	−	8.31217i	0.243473	−	0.339343i
$601$	6.58474	−	3.80170i	0.268597	−	0.155075i	−0.359653	−	0.933086i	$-0.617105\pi$
$601$	6.58474	−	3.80170i	0.268597	−	0.155075i	0.628250	+	0.778012i	$0.283772\pi$
$602$	2.37707	−	10.2366i	0.0968823	−	0.417212i
$603$	−45.2538	−	9.05711i	−1.84288	−	0.368834i
$604$	17.2596	−	29.8944i	0.702282	−	1.21639i
$605$	15.1627	−	26.2625i	0.616450	−	1.06772i
$606$	17.4489	−	24.3195i	0.708812	−	0.987913i
$607$	25.6693	−	14.8202i	1.04188	−	0.601532i	0.121518	−	0.992589i	$-0.461224\pi$
$607$	25.6693	−	14.8202i	1.04188	−	0.601532i	0.920367	+	0.391057i	$0.127890\pi$
$608$	7.66125	−	13.2697i	0.310705	−	0.538156i
$609$	27.5295	+	9.33537i	1.11555	+	0.378288i
$610$	9.23508	+	15.9956i	0.373918	+	0.647644i
$611$	10.7267	+	6.19304i	0.433954	+	0.250544i
$612$	−14.0938	−	41.6808i	−0.569710	−	1.68485i
$613$	−3.84128	−	6.65328i	−0.155148	−	0.268724i	0.777965	−	0.628307i	$-0.216252\pi$
$613$	−3.84128	−	6.65328i	−0.155148	−	0.268724i	−0.933113	+	0.359584i	$0.882919\pi$
$614$	−47.0815			−1.90006
$615$	1.19682	−	12.0784i	0.0482604	−	0.487048i
$616$	−29.2485	−	96.1062i	−1.17846	−	3.87223i
$617$	−34.1625	−	19.7237i	−1.37533	−	0.794047i	−0.383736	−	0.923443i	$-0.625363\pi$
$617$	−34.1625	−	19.7237i	−1.37533	−	0.794047i	−0.991593	+	0.129396i	$0.958696\pi$
$618$	57.8166	−	26.1552i	2.32572	−	1.05212i
$619$	17.6369	+	10.1827i	0.708888	+	0.409277i	0.810649	−	0.585532i	$-0.199114\pi$
$619$	17.6369	+	10.1827i	0.708888	+	0.409277i	−0.101761	+	0.994809i	$0.532448\pi$
$620$	3.63275	−	2.09737i	0.145895	−	0.0842324i
$621$	3.35862	+	14.5206i	0.134777	+	0.582692i
$622$		−	25.6831i		−	1.02980i
$623$	0.652199	+	2.14303i	0.0261298	+	0.0858586i
$624$	12.7908	−	17.8274i	0.512044	−	0.713666i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	10.9295			0.436830
$627$	41.1844	−	18.6311i	1.64475	−	0.744054i
$628$			53.0273i			2.11602i
$629$	8.87859			0.354013
$630$	8.25634	−	18.2088i	0.328941	−	0.725455i
$631$	−21.1304			−0.841188			−0.420594	−	0.907249i	$-0.638178\pi$
$631$	−21.1304			−0.841188			−0.420594	+	0.907249i	$0.638178\pi$
$632$		−	22.7409i		−	0.904583i
$633$	−1.01290	−	0.726737i	−0.0402590	−	0.0288852i
$634$	31.8886			1.26646
$635$	1.19225	+	2.06504i	0.0473130	+	0.0819485i
$636$	11.5606	+	25.5550i	0.458410	+	1.01332i
$637$	−6.31466	+	12.8635i	−0.250196	+	0.509670i
$638$			102.717i			4.06662i
$639$	−3.02098	+	15.0943i	−0.119508	+	0.597122i
$640$	−12.7962	+	7.38786i	−0.505812	+	0.292031i
$641$	−8.71481	−	5.03150i	−0.344214	−	0.198732i	0.317920	−	0.948118i	$-0.397016\pi$
$641$	−8.71481	−	5.03150i	−0.344214	−	0.198732i	−0.662134	+	0.749385i	$0.730349\pi$
$642$	21.8932	+	15.7080i	0.864055	+	0.619946i
$643$	−11.3765	−	6.56823i	−0.448646	−	0.259026i	0.258612	−	0.965981i	$-0.416735\pi$
$643$	−11.3765	−	6.56823i	−0.448646	−	0.259026i	−0.707258	+	0.706955i	$0.750068\pi$
$644$	7.45810	−	32.1174i	0.293890	−	1.26560i
$645$	2.21914	+	1.59220i	0.0873786	+	0.0626928i
$646$	−34.5185			−1.35811
$647$	−0.895105	−	1.55037i	−0.0351902	−	0.0609512i	0.847894	−	0.530166i	$-0.177870\pi$
$647$	−0.895105	−	1.55037i	−0.0351902	−	0.0609512i	−0.883084	+	0.469215i	$0.844537\pi$
$648$	−20.4588	+	49.0637i	−0.803696	+	1.92740i
$649$	−79.6398	−	45.9801i	−3.12614	−	1.80488i
$650$	−2.57825	−	4.46565i	−0.101127	−	0.175157i
$651$	3.32540	−	2.91815i	0.130333	−	0.114371i
$652$	10.4211	−	18.0499i	0.408123	−	0.706891i
$653$	11.8440	−	6.83813i	0.463491	−	0.267597i	−0.250020	−	0.968241i	$-0.580437\pi$
$653$	11.8440	−	6.83813i	0.463491	−	0.267597i	0.713511	+	0.700644i	$0.247104\pi$
$654$	−7.40158	−	16.3613i	−0.289425	−	0.639779i
$655$	3.70602	−	6.41901i	0.144806	−	0.250812i
$656$	21.6820	−	37.5543i	0.846538	−	1.46625i
$657$	31.5581	−	10.6710i	1.23120	−	0.416314i
$658$	29.4551	+	27.5377i	1.14828	+	1.07353i
$659$	24.3549	−	14.0613i	0.948733	−	0.547751i	0.0560458	−	0.998428i	$-0.482151\pi$
$659$	24.3549	−	14.0613i	0.948733	−	0.547751i	0.892687	+	0.450677i	$0.148817\pi$
$660$	48.1419	+	4.77027i	1.87392	+	0.185682i
$661$			17.8742i			0.695225i	0.937638	+	0.347612i	$0.113008\pi$
$661$			17.8742i			0.695225i	−0.937638	+	0.347612i	$0.886992\pi$
$662$			6.37522i			0.247780i
$663$	−11.9105	−	1.18018i	−0.462564	−	0.0458344i
$664$	−5.62084	+	3.24519i	−0.218131	+	0.125938i
$665$	−7.84608	−	7.33534i	−0.304258	−	0.284452i
$666$	−14.9281	−	13.1228i	−0.578453	−	0.508499i
$667$	−9.09735	+	15.7571i	−0.352251	+	0.610117i
$668$	−0.617461	+	1.06947i	−0.0238903	+	0.0413792i
$669$	13.9046	+	30.7365i	0.537585	+	1.18834i
$670$	−33.5586	+	19.3751i	−1.29648	+	0.748524i
$671$	−23.5688	+	40.8224i	−0.909864	+	1.57593i
$672$	13.0002	−	11.4081i	0.501494	−	0.440078i
$673$	17.5144	+	30.3358i	0.675129	+	1.16936i	0.976431	+	0.215829i	$0.0692455\pi$
$673$	17.5144	+	30.3358i	0.675129	+	1.16936i	−0.301302	+	0.953529i	$0.597421\pi$
$674$	−33.5146	−	19.3497i	−1.29094	−	0.745322i
$675$	3.54533	+	3.79877i	0.136460	+	0.146215i
$676$	19.1376	+	33.1473i	0.736062	+	1.27490i
$677$	23.8409			0.916281			0.458141	−	0.888880i	$-0.348516\pi$
$677$	23.8409			0.916281			0.458141	+	0.888880i	$0.348516\pi$
$678$	−10.8470	−	7.78258i	−0.416578	−	0.298888i
$679$	−2.04981	+	8.82725i	−0.0786643	+	0.338759i
$680$	−17.2666	−	9.96886i	−0.662143	−	0.382288i
$681$	−5.37032	−	3.85312i	−0.205791	−	0.147652i
$682$	13.5388	+	7.81660i	0.518426	+	0.299313i
$683$	−15.9666	+	9.21834i	−0.610947	+	0.352730i	−0.773336	−	0.633997i	$-0.781413\pi$
$683$	−15.9666	+	9.21834i	−0.610947	+	0.352730i	0.162389	+	0.986727i	$0.448080\pi$
$684$	39.7435	+	34.9373i	1.51963	+	1.33586i
$685$			21.9622i			0.839133i
$686$	−29.4969	+	36.1417i	−1.12620	+	1.37990i
$687$	11.8844	+	26.2707i	0.453419	+	1.00229i
$688$	4.87897	+	8.45062i	0.186009	+	0.322177i
$689$	7.62980			0.290672
$690$	10.1676	+	7.29506i	0.387072	+	0.277718i
$691$		−	38.1309i		−	1.45057i	−0.688451	−	0.725283i	$-0.741709\pi$
$691$		−	38.1309i		−	1.45057i	0.688451	−	0.725283i	$-0.258291\pi$
$692$	−54.4059			−2.06820
$693$	50.7801	−	4.98725i	1.92898	−	0.189450i
$694$	53.1984			2.01938
$695$			8.95025i			0.339502i
$696$	−59.1268	+	26.7479i	−2.24119	+	1.01388i
$697$	−23.6547			−0.895984
$698$	−42.0357	−	72.8080i	−1.59108	−	2.75582i
$699$	11.4551	−	15.9657i	0.433273	−	0.603878i
$700$	−3.34690	−	10.9974i	−0.126501	−	0.415663i
$701$		−	0.559500i		−	0.0211320i	−0.999944	−	0.0105660i	$-0.996637\pi$
$701$		−	0.559500i		−	0.0211320i	0.999944	−	0.0105660i	$-0.00336333\pi$
$702$	18.2814	+	19.5883i	0.689989	+	0.739314i
$703$	−9.24746	+	5.33902i	−0.348775	+	0.201365i
$704$	−15.9733	−	9.22218i	−0.602016	−	0.347574i
$705$	−9.54818	+	4.31943i	−0.359605	+	0.162679i
$706$	33.8713	+	19.5556i	1.27476	+	0.735984i
$707$	−5.28476	−	17.3649i	−0.198754	−	0.653075i
$708$	10.6152	−	107.129i	0.398942	−	4.02615i
$709$	−34.5554			−1.29776			−0.648878	−	0.760893i	$-0.724761\pi$
$709$	−34.5554			−1.29776			−0.648878	+	0.760893i	$0.724761\pi$
$710$	6.46251	+	11.1934i	0.242534	+	0.420081i
$711$	11.3259	+	2.26676i	0.424753	+	0.0850102i
$712$	−4.33085	−	2.50041i	−0.162305	−	0.0937070i
$713$	1.38458	+	2.39817i	0.0518530	+	0.0898121i
$714$	−36.9004	−	12.5131i	−1.38096	−	0.468290i
$715$	6.57993	−	11.3968i	0.246076	−	0.426215i
$716$	−52.8751	+	30.5274i	−1.97603	+	1.14086i
$717$	13.2845	−	18.5154i	0.496120	−	0.691472i
$718$	9.74453	−	16.8780i	0.363663	−	0.629882i
$719$	4.86201	−	8.42124i	0.181322	−	0.314059i	−0.761009	−	0.648742i	$-0.775296\pi$
$719$	4.86201	−	8.42124i	0.181322	−	0.314059i	0.942331	+	0.334682i	$0.108629\pi$
$720$	5.94655	+	17.5862i	0.221615	+	0.655398i
$721$	8.70448	−	37.4848i	0.324172	−	1.39601i
$722$	−5.49463	+	3.17233i	−0.204489	+	0.118062i
$723$	16.7297	−	23.3172i	0.622184	−	0.867175i
$724$			19.2850i			0.716720i
$725$			6.34344i			0.235590i
$726$	54.5321	+	120.544i	2.02388	+	4.47382i
$727$	−32.9183	+	19.0054i	−1.22087	+	0.704870i	−0.965104	−	0.261868i	$-0.915662\pi$
$727$	−32.9183	+	19.0054i	−1.22087	+	0.704870i	−0.255768	+	0.966738i	$0.582328\pi$
$728$	−9.31405	−	30.6046i	−0.345202	−	1.13428i
$729$	−22.3964	−	15.0798i	−0.829496	−	0.558513i
$730$	13.9855	−	24.2236i	0.517627	−	0.896557i
$731$	2.66144	−	4.60974i	0.0984368	−	0.170498i
$732$	−54.9130	−	5.44120i	−2.02964	−	0.201112i
$733$	−38.9571	+	22.4919i	−1.43891	+	0.830757i	−0.997774	−	0.0666812i	$-0.978759\pi$
$733$	−38.9571	+	22.4919i	−1.43891	+	0.830757i	−0.441140	+	0.897439i	$0.645426\pi$
$734$	−11.6685	+	20.2105i	−0.430693	+	0.745982i
$735$	−5.72842	−	10.6858i	−0.211296	−	0.394150i
$736$	5.41284	+	9.37532i	0.199520	+	0.345579i
$737$	−85.6448	−	49.4470i	−3.15477	−	1.82140i
$738$	39.7720	+	34.9623i	1.46403	+	1.28698i
$739$	6.67946	+	11.5692i	0.245708	+	0.425578i	0.962330	−	0.271883i	$-0.0876463\pi$
$739$	6.67946	+	11.5692i	0.245708	+	0.425578i	−0.716623	+	0.697461i	$0.754313\pi$
$740$	−11.4281			−0.420105
$741$	13.1150	−	5.93299i	0.481791	−	0.217954i
$742$	24.1950	+	5.61840i	0.888227	+	0.206258i
$743$	−24.6039	−	14.2051i	−0.902629	−	0.521133i	−0.0245769	−	0.999698i	$-0.507824\pi$
$743$	−24.6039	−	14.2051i	−0.902629	−	0.521133i	−0.878052	+	0.478565i	$0.841157\pi$
$744$	−0.973904	+	9.82871i	−0.0357051	+	0.360338i
$745$	20.0506	+	11.5762i	0.734597	+	0.424120i
$746$	−10.6515	+	6.14966i	−0.389980	+	0.225155i
$747$	−1.05596	−	3.12287i	−0.0386356	−	0.114260i
$748$		−	94.2824i		−	3.44731i
$749$	15.6324	−	4.75750i	0.571197	−	0.173835i
$750$	4.34160	+	0.430199i	0.158533	+	0.0157087i
$751$	14.5813	+	25.2556i	0.532079	+	0.921589i	0.999299	+	0.0374471i	$0.0119226\pi$
$751$	14.5813	+	25.2556i	0.532079	+	0.921589i	−0.467219	+	0.884142i	$0.654744\pi$
$752$	−37.4411			−1.36534
$753$	−3.60845	+	36.4167i	−0.131499	+	1.32710i
$754$			32.7099i			1.19123i
$755$	7.94481			0.289141
$756$	29.8212	+	51.7553i	1.08459	+	1.88232i
$757$	29.7991			1.08307			0.541534	−	0.840679i	$-0.317844\pi$
$757$	29.7991			1.08307			0.541534	+	0.840679i	$0.317844\pi$
$758$			3.92413i			0.142531i
$759$	−3.14910	+	31.7810i	−0.114305	+	1.15358i
$760$	23.9786			0.869794
$761$	−7.22627	−	12.5163i	−0.261952	−	0.453714i	0.704808	−	0.709398i	$-0.251033\pi$
$761$	−7.22627	−	12.5163i	−0.261952	−	0.453714i	−0.966761	+	0.255683i	$0.917700\pi$
$762$	−10.3526	−	1.02581i	−0.375033	−	0.0371612i
$763$	−10.6077	−	2.46325i	−0.384025	−	0.0891758i
$764$			12.2440i			0.442973i
$765$	6.68598	−	7.60576i	0.241732	−	0.274987i
$766$	61.4303	−	35.4668i	2.21957	−	1.28147i
$767$	−25.3609	−	14.6421i	−0.915731	−	0.528697i
$768$	5.37647	−	54.2597i	0.194007	−	1.95793i
$769$	18.6200	+	10.7503i	0.671456	+	0.387665i	0.796628	−	0.604470i	$-0.206615\pi$
$769$	18.6200	+	10.7503i	0.671456	+	0.387665i	−0.125172	+	0.992135i	$0.539948\pi$
$770$	29.2581	−	31.2952i	1.05439	−	1.12780i
$771$	−2.81567	+	1.27376i	−0.101404	+	0.0458733i
$772$	38.7535			1.39477
$773$	−16.9972	−	29.4400i	−0.611347	−	1.05888i	−0.991014	−	0.133761i	$-0.957295\pi$
$773$	−16.9972	−	29.4400i	−0.611347	−	1.05888i	0.379667	−	0.925123i	$-0.376039\pi$
$774$	−11.2882	+	3.81696i	−0.405745	+	0.137198i
$775$	0.836103	+	0.482724i	0.0300337	+	0.0173400i
$776$	−10.1153	−	17.5202i	−0.363119	−	0.628940i
$777$	−11.8210	+	2.35521i	−0.424076	+	0.0844926i
$778$	26.3887	−	45.7065i	0.946080	−	1.63866i
$779$	24.6374	−	14.2244i	0.882727	−	0.509642i
$780$	15.3306	+	1.51907i	0.548923	+	0.0543915i
$781$	−16.4930	+	28.5666i	−0.590164	+	1.02219i
$782$	12.1940	−	21.1207i	0.436058	−	0.755275i
$783$	−7.42790	−	32.1137i	−0.265451	−	1.14765i
$784$	−2.91128	−	43.2189i	−0.103974	−	1.54353i
$785$	−10.5695	+	6.10230i	−0.377241	+	0.217800i
$786$	13.3286	+	29.4631i	0.475416	+	1.05091i
$787$			41.8219i			1.49079i	0.666622	+	0.745396i	$0.267739\pi$
$787$			41.8219i			1.49079i	−0.666622	+	0.745396i	$0.732261\pi$
$788$		−	94.8459i		−	3.37875i
$789$	23.0601	−	32.1402i	0.820960	−	1.14422i
$790$	8.39885	−	4.84908i	0.298818	−	0.172523i
$791$	−7.74514	+	2.35712i	−0.275385	+	0.0838095i
$792$	−75.2065	+	85.5526i	−2.67235	+	3.03998i
$793$	−7.50539	+	12.9997i	−0.266524	+	0.461633i
$794$	−28.4016	+	49.1930i	−1.00794	+	1.74579i
$795$	−3.76329	+	5.24512i	−0.133470	+	0.186025i
$796$	−27.8397	+	16.0733i	−0.986752	+	0.569702i
$797$	24.2721	−	42.0406i	0.859763	−	1.48915i	−0.0123919	−	0.999923i	$-0.503945\pi$
$797$	24.2721	−	42.0406i	0.859763	−	1.48915i	0.872155	−	0.489230i	$-0.162722\pi$
$798$	45.9581	−	9.15665i	1.62690	−	0.324142i
$799$	10.2119	+	17.6875i	0.361271	+	0.625740i
$800$	3.26863	+	1.88715i	0.115564	+	0.0667207i
$801$	1.67700	−	1.90770i	0.0592537	−	0.0674052i
$802$	−47.5098	−	82.2893i	−1.67763	−	2.90574i
$803$	71.3848			2.51911
$804$	11.4156	−	115.207i	0.402595	−	4.06302i
$805$	7.25996	−	2.20946i	0.255880	−	0.0778733i
$806$	4.31136	+	2.48916i	0.151861	+	0.0876770i
$807$	28.4720	−	12.8802i	1.00226	−	0.453405i
$808$	35.0928	+	20.2608i	1.23456	+	0.712774i
$809$	11.9261	−	6.88553i	0.419299	−	0.242082i	−0.275478	−	0.961307i	$-0.588836\pi$
$809$	11.9261	−	6.88553i	0.419299	−	0.242082i	0.694777	+	0.719225i	$0.255503\pi$
$810$	−22.4831	+	2.90595i	−0.789975	+	0.102105i
$811$			27.8470i			0.977841i	0.872328	+	0.488920i	$0.162609\pi$
$811$			27.8470i			0.977841i	−0.872328	+	0.488920i	$0.837391\pi$
$812$	−16.4943	+	71.0307i	−0.578835	+	2.49269i
$813$	−4.75176	+	6.62281i	−0.166652	+	0.232272i
$814$	−21.2955	−	36.8848i	−0.746405	−	1.29281i
$815$	4.79699			0.168031
$816$	32.9636	−	14.9122i	1.15396	−	0.522031i
$817$			6.40168i			0.223966i
$818$	−32.3861			−1.13235
$819$	16.1707	−	1.58817i	0.565050	−	0.0554951i
$820$	30.4471			1.06326
$821$		−	38.8646i		−	1.35638i	−0.734885	−	0.678191i	$-0.762764\pi$
$821$		−	38.8646i		−	1.35638i	0.734885	−	0.678191i	$-0.237236\pi$
$822$	−77.8525	−	55.8579i	−2.71542	−	1.94827i
$823$	−23.5055			−0.819349			−0.409674	−	0.912232i	$-0.634358\pi$
$823$	−23.5055			−0.819349			−0.409674	+	0.912232i	$0.634358\pi$
$824$	42.9546	+	74.3996i	1.49640	+	2.59183i
$825$	4.58928	+	10.1447i	0.159778	+	0.353192i
$826$	−69.6404	−	65.1072i	−2.42310	−	2.26537i
$827$			29.5187i			1.02647i	0.858249	+	0.513233i	$0.171552\pi$
$827$			29.5187i			1.02647i	−0.858249	+	0.513233i	$0.828448\pi$
$828$	−35.4168	+	11.9757i	−1.23082	+	0.416186i
$829$	18.3249	−	10.5799i	0.636451	−	0.367455i	−0.146795	−	0.989167i	$-0.546896\pi$
$829$	18.3249	−	10.5799i	0.636451	−	0.367455i	0.783246	+	0.621712i	$0.213562\pi$
$830$	−2.39708	−	1.38396i	−0.0832040	−	0.0480378i
$831$	−14.8864	−	10.6807i	−0.516403	−	0.370511i
$832$	−5.08662	−	2.93676i	−0.176347	−	0.101814i
$833$	−19.6230	+	13.1631i	−0.679896	+	0.456074i
$834$	−31.7272	−	22.7637i	−1.09862	−	0.788244i
$835$	−0.284226			−0.00983603
$836$	56.6955	+	98.1995i	1.96085	+	3.39630i
$837$	−4.79801	−	1.46475i	−0.165844	−	0.0506291i
$838$	25.4352	+	14.6850i	0.878645	+	0.507286i
$839$	14.3192	+	24.8016i	0.494353	+	0.856245i	0.999979	−	0.00650811i	$-0.00207161\pi$
$839$	14.3192	+	24.8016i	0.494353	+	0.856245i	−0.505626	+	0.862753i	$0.668738\pi$
$840$	25.6332	+	8.69231i	0.884429	+	0.299913i
$841$	5.61964	−	9.73351i	0.193781	−	0.335638i
$842$	42.1601	−	24.3411i	1.45293	−	0.838851i
$843$	−4.84758	−	10.7157i	−0.166959	−	0.369067i
$844$	1.56360	−	2.70824i	0.0538214	−	0.0932214i
$845$	−4.40465	+	7.62908i	−0.151525	+	0.262448i
$846$	8.97282	−	44.8327i	0.308492	−	1.54138i
$847$	78.1538	+	18.1484i	2.68540	+	0.623585i
$848$	−19.9737	+	11.5318i	−0.685901	+	0.396005i
$849$	−0.522196	−	0.0517432i	−0.0179217	−	0.00177582i
$850$		−	8.50272i		−	0.291641i
$851$		−	7.54428i		−	0.258614i
$852$	−38.4269	−	3.80763i	−1.31648	−	0.130447i
$853$	30.6183	−	17.6775i	1.04835	−	0.605266i	0.126164	−	0.992009i	$-0.459733\pi$
$853$	30.6183	−	17.6775i	1.04835	−	0.605266i	0.922187	+	0.386743i	$0.126400\pi$
$854$	−33.3731	+	35.6968i	−1.14201	+	1.22152i
$855$	−2.39013	+	11.9423i	−0.0817408	+	0.408417i
$856$	−18.2394	+	31.5916i	−0.623411	+	1.07978i
$857$	25.4164	−	44.0225i	0.868209	−	1.50378i	0.00438311	−	0.999990i	$-0.498605\pi$
$857$	25.4164	−	44.0225i	0.868209	−	1.50378i	0.863826	−	0.503791i	$-0.168062\pi$
$858$	23.6646	+	52.3110i	0.807895	+	1.78587i
$859$	−21.7062	+	12.5321i	−0.740606	+	0.427589i	−0.822290	−	0.569069i	$-0.807304\pi$
$859$	−21.7062	+	12.5321i	−0.740606	+	0.427589i	0.0816834	+	0.996658i	$0.473970\pi$
$860$	−3.42567	+	5.93344i	−0.116814	+	0.202329i
$861$	31.4939	−	6.27482i	1.07331	−	0.213845i
$862$	−38.9230	−	67.4165i	−1.32572	−	2.29622i
$863$	18.6022	+	10.7400i	0.633226	+	0.365593i	0.782000	−	0.623278i	$-0.214199\pi$
$863$	18.6022	+	10.7400i	0.633226	+	0.365593i	−0.148774	+	0.988871i	$0.547533\pi$
$864$	−18.7572	−	5.72624i	−0.638133	−	0.194811i
$865$	−6.26094	−	10.8443i	−0.212878	−	0.368716i
$866$	13.7722			0.467999
$867$	7.88868	+	5.66000i	0.267914	+	0.192224i
$868$	8.10707	+	7.57934i	0.275172	+	0.257260i
$869$	21.4347	+	12.3753i	0.727122	+	0.419804i
$870$	−22.4865	−	16.1337i	−0.762363	−	0.546984i
$871$	−27.2732	−	15.7462i	−0.924117	−	0.533539i
$872$	21.0541	−	12.1556i	0.712982	−	0.411640i
$873$	9.73405	−	3.29145i	0.329448	−	0.111399i
$874$			29.3309i			0.992132i
$875$	1.80687	−	1.93267i	0.0610833	−	0.0653363i
$876$	34.4437	+	76.1384i	1.16374	+	2.57248i
$877$	−25.0124	−	43.3227i	−0.844607	−	1.46290i	−0.885962	−	0.463758i	$-0.846501\pi$
$877$	−25.0124	−	43.3227i	−0.844607	−	1.46290i	0.0413545	−	0.999145i	$-0.486833\pi$
$878$	−42.0997			−1.42080
$879$	−28.6015	−	20.5211i	−0.964704	−	0.692160i
$880$			39.7802i			1.34099i
$881$	17.7239			0.597133			0.298566	−	0.954389i	$-0.403492\pi$
$881$	17.7239			0.597133			0.298566	+	0.954389i	$0.403492\pi$
$882$	52.4487	+	6.87145i	1.76604	+	0.231374i
$883$	−36.8397			−1.23975			−0.619877	−	0.784699i	$-0.712818\pi$
$883$	−36.8397			−1.23975			−0.619877	+	0.784699i	$0.712818\pi$
$884$		−	30.0238i		−	1.00981i
$885$	22.5747	−	10.2124i	0.758840	−	0.343286i
$886$	81.1545			2.72644
$887$	−3.02943	−	5.24713i	−0.101718	−	0.176181i	0.810674	−	0.585497i	$-0.199101\pi$
$887$	−3.02943	−	5.24713i	−0.101718	−	0.176181i	−0.912393	+	0.409316i	$0.865767\pi$
$888$	15.6864	−	21.8631i	0.526402	−	0.733678i
$889$	−4.30847	+	4.60846i	−0.144502	+	0.154563i
$890$		−	2.13267i		−	0.0714874i
$891$	−35.1122	−	45.9835i	−1.17630	−	1.54051i
$892$	−73.2877	+	42.3126i	−2.45385	+	1.41673i
$893$	−21.2723	−	12.2816i	−0.711852	−	0.410988i
$894$	−92.0318	+	41.6336i	−3.07800	+	1.39244i
$895$	−12.1696	−	7.02610i	−0.406783	−	0.234857i
$896$	−28.5567	−	26.6978i	−0.954012	−	0.891910i
$897$	−1.00282	+	10.1205i	−0.0334831	+	0.337914i
$898$	−14.1828			−0.473287
$899$	−3.06213	−	5.30377i	−0.102128	−	0.176891i
$900$	−8.60587	+	9.78977i	−0.286862	+	0.326326i
$901$	10.8955	+	6.29052i	0.362982	+	0.209568i
$902$	56.7361	+	98.2698i	1.88911	+	3.27203i
$903$	−2.32063	+	6.84343i	−0.0772258	+	0.227735i
$904$	9.03678	−	15.6522i	0.300559	−	0.520583i
$905$	−3.84391	+	2.21928i	−0.127776	+	0.0737715i
$906$	−20.2066	+	28.1631i	−0.671318	+	0.935656i
$907$	−13.6426	+	23.6297i	−0.452996	+	0.784613i	−0.998571	−	0.0534498i	$-0.982978\pi$
$907$	−13.6426	+	23.6297i	−0.452996	+	0.784613i	0.545574	+	0.838063i	$0.316312\pi$
$908$	8.29013	−	14.3589i	0.275118	−	0.476518i
$909$	−13.5887	+	15.4580i	−0.450708	+	0.512711i
$910$	9.31710	−	9.96582i	0.308859	−	0.330364i
$911$	−23.6495	+	13.6541i	−0.783544	+	0.452379i	−0.837685	−	0.546154i	$-0.816091\pi$
$911$	−23.6495	+	13.6541i	−0.783544	+	0.452379i	0.0541409	+	0.998533i	$0.482758\pi$
$912$	−25.3659	+	35.3540i	−0.839949	+	1.17069i
$913$		−	7.06398i		−	0.233784i
$914$		−	66.7390i		−	2.20753i
$915$	−5.23475	−	11.5715i	−0.173055	−	0.382542i
$916$	−62.6396	+	36.1650i	−2.06967	+	1.19492i
$917$	19.1021	+	4.43577i	0.630808	+	0.146482i
$918$	9.95631	+	43.0450i	0.328607	+	1.42070i
$919$	−29.8925	+	51.7753i	−0.986061	+	1.70791i	−0.348939	+	0.937145i	$0.613458\pi$
$919$	−29.8925	+	51.7753i	−0.986061	+	1.70791i	−0.637122	+	0.770763i	$0.719875\pi$
$920$	−8.47069	+	14.6717i	−0.279270	+	0.483710i
$921$	32.2165	+	3.19226i	1.06157	+	0.105189i
$922$	−26.0625	+	15.0472i	−0.858323	+	0.495553i
$923$	−5.25211	+	9.09692i	−0.172875	+	0.299429i
$924$	25.0101	+	125.528i	0.822772	+	4.12957i
$925$	−1.31513	−	2.27787i	−0.0432411	−	0.0748958i
$926$	−47.8077	−	27.6018i	−1.57106	−	0.907050i
$927$	−41.3356	+	13.9771i	−1.35764	+	0.459069i
$928$	−11.9710	−	20.7344i	−0.392967	−	0.680639i
$929$	−8.45306			−0.277336			−0.138668	−	0.990339i	$-0.544282\pi$
$929$	−8.45306			−0.277336			−0.138668	+	0.990339i	$0.544282\pi$
$930$	−3.83769	+	1.73611i	−0.125843	+	0.0569291i
$931$	12.5228	−	25.5100i	0.410417	−	0.836055i
$932$	42.6884	+	24.6461i	1.39830	+	0.807311i
$933$	−1.74138	+	17.5742i	−0.0570104	+	0.575353i
$934$	0.828829	+	0.478524i	0.0271201	+	0.0156578i
$935$	18.7925	−	10.8499i	0.614581	−	0.354829i
$936$	−23.9492	+	27.2438i	−0.782804	+	0.890493i
$937$			22.6449i			0.739778i	0.929076	+	0.369889i	$0.120604\pi$
$937$			22.6449i			0.739778i	−0.929076	+	0.369889i	$0.879396\pi$
$938$	−74.8914	−	70.0164i	−2.44529	−	2.28612i
$939$	−7.47872	−	0.741049i	−0.244059	−	0.0241832i
$940$	−13.1443	−	22.7666i	−0.428719	−	0.742563i
$941$	22.8055			0.743438			0.371719	−	0.928345i	$-0.378769\pi$
$941$	22.8055			0.743438			0.371719	+	0.928345i	$0.378769\pi$
$942$	5.25041	−	52.9875i	0.171068	−	1.72643i
$943$			20.0997i			0.654537i
$944$	88.5217			2.88114
$945$	−6.88418	+	11.8999i	−0.223942	+	0.387104i
$946$	−25.5340			−0.830182
$947$		−	32.8664i		−	1.06801i	−0.845480	−	0.534007i	$-0.820686\pi$
$947$		−	32.8664i		−	1.06801i	0.845480	−	0.534007i	$-0.179314\pi$
$948$	−2.85702	+	28.8332i	−0.0927916	+	0.936460i
$949$	22.7322			0.737917
$950$	5.11299	+	8.85597i	0.165887	+	0.287325i
$951$	−21.8204	−	2.16214i	−0.707576	−	0.0701121i
$952$	11.9318	−	51.3831i	0.386713	−	1.66533i
$953$		−	17.8442i		−	0.578030i	−0.957325	−	0.289015i	$-0.906672\pi$
$953$		−	17.8442i		−	0.578030i	0.957325	−	0.289015i	$-0.0933277\pi$
$954$	−9.02169	−	26.6805i	−0.292088	−	0.863813i
$955$	−2.44050	+	1.40902i	−0.0789726	+	0.0455949i
$956$	49.5057	+	28.5821i	1.60113	+	0.924413i
$957$	6.96453	−	70.2866i	0.225131	−	2.27204i
$958$	45.8464	+	26.4694i	1.48123	+	0.855188i
$959$	−55.5892	+	16.9178i	−1.79507	+	0.546303i
$960$	4.52779	−	2.04829i	0.146134	−	0.0661083i
$961$	30.0679			0.969933
$962$	−6.78144	−	11.7458i	−0.218642	−	0.378700i
$963$	−13.9158	−	12.2329i	−0.448431	−	0.394201i
$964$	62.3444	+	35.9945i	2.00798	+	1.15931i
$965$	4.45969	+	7.72440i	0.143562	+	0.248657i
$966$	−10.6326	+	31.3549i	−0.342097	+	1.00883i
$967$	2.76048	−	4.78130i	0.0887712	−	0.153756i	−0.818221	−	0.574904i	$-0.805039\pi$
$967$	2.76048	−	4.78130i	0.0887712	−	0.153756i	0.906992	+	0.421148i	$0.138373\pi$
$968$	−155.119	+	89.5580i	−4.98571	+	2.87850i
$969$	23.6200	+	2.34045i	0.758783	+	0.0751861i
$970$	4.31382	−	7.47175i	0.138508	−	0.239904i
$971$	−16.1932	+	28.0474i	−0.519664	+	0.900084i	0.480075	+	0.877228i	$0.340610\pi$
$971$	−16.1932	+	28.0474i	−0.519664	+	0.900084i	−0.999739	+	0.0228569i	$0.992724\pi$
$972$	32.1038	−	59.6378i	1.02973	−	1.91288i
$973$	−22.6542	+	6.89448i	−0.726262	+	0.221027i
$974$	22.7475	−	13.1333i	0.728878	−	0.420818i
$975$	1.46143	+	3.23053i	0.0468034	+	0.103460i
$976$		−	45.3752i		−	1.45242i
$977$			21.0030i			0.671945i	0.941872	+	0.335972i	$0.109065\pi$
$977$			21.0030i			0.671945i	−0.941872	+	0.335972i	$0.890935\pi$
$978$	−12.2005	+	17.0046i	−0.390129	+	0.543746i
$979$	4.71359	−	2.72139i	0.150647	−	0.0869761i
$980$	25.2577	−	16.9429i	0.806829	−	0.541220i
$981$	3.95534	+	11.6974i	0.126284	+	0.373470i
$982$	−3.41423	+	5.91361i	−0.108952	+	0.188711i
$983$	10.3888	−	17.9939i	0.331351	−	0.573918i	−0.651426	−	0.758712i	$-0.725829\pi$
$983$	10.3888	−	17.9939i	0.331351	−	0.573918i	0.982777	+	0.184795i	$0.0591621\pi$
$984$	−41.7923	+	58.2484i	−1.33229	+	1.85689i
$985$	18.9048	−	10.9147i	0.602358	−	0.347772i
$986$	−26.9683	+	46.7104i	−0.858844	+	1.48756i
$987$	−18.2881	−	20.8404i	−0.582117	−	0.663357i
$988$	18.0544	+	31.2712i	0.574388	+	0.994869i
$989$	−3.91697	−	2.26146i	−0.124552	−	0.0719104i
$990$	−47.6335	−	9.53338i	−1.51389	−	0.302991i
$991$	4.77749	+	8.27485i	0.151762	+	0.262859i	0.931875	−	0.362779i	$-0.118172\pi$
$991$	4.77749	+	8.27485i	0.151762	+	0.262859i	−0.780113	+	0.625638i	$0.784839\pi$
$992$	−3.64388			−0.115693
$993$	0.432258	−	4.36238i	0.0137173	−	0.138436i
$994$	−23.3538	+	24.9799i	−0.740738	+	0.792313i
$995$	−6.40750	−	3.69937i	−0.203131	−	0.117278i
$996$	7.53438	−	3.40842i	0.238736	−	0.108000i
$997$	−41.5478	−	23.9876i	−1.31583	−	0.759696i	−0.332777	−	0.943005i	$-0.607986\pi$
$997$	−41.5478	−	23.9876i	−1.31583	−	0.759696i	−0.983055	+	0.183309i	$0.941319\pi$
$998$	1.21337	−	0.700541i	0.0384086	−	0.0221752i
$999$	9.32511	+	9.99173i	0.295033	+	0.316124i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.t.c.131.1	yes	32
3.2	odd	2		945.2.t.c.341.16		32
7.3	odd	6		315.2.be.c.311.16	yes	32
9.2	odd	6		315.2.be.c.236.16	yes	32
9.7	even	3		945.2.be.c.656.1		32
21.17	even	6		945.2.be.c.206.1		32
63.38	even	6	inner	315.2.t.c.101.16	✓	32
63.52	odd	6		945.2.t.c.521.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.t.c.101.16	✓	32	63.38	even	6	inner
315.2.t.c.131.1	yes	32	1.1	even	1	trivial
315.2.be.c.236.16	yes	32	9.2	odd	6
315.2.be.c.311.16	yes	32	7.3	odd	6
945.2.t.c.341.16		32	3.2	odd	2
945.2.t.c.521.1		32	63.52	odd	6
945.2.be.c.206.1		32	21.17	even	6
945.2.be.c.656.1		32	9.7	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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.51890i q^{2} +(-0.170788 + 1.72361i) q^{3} -4.34486 q^{4} +(-0.500000 - 0.866025i) q^{5} +(4.34160 + 0.430199i) q^{6} +(1.80687 - 1.93267i) q^{7} +5.90648i q^{8} +(-2.94166 - 0.588745i) q^{9} +O(q^{10})\)	\(q-2.51890i q^{2} +(-0.170788 + 1.72361i) q^{3} -4.34486 q^{4} +(-0.500000 - 0.866025i) q^{5} +(4.34160 + 0.430199i) q^{6} +(1.80687 - 1.93267i) q^{7} +5.90648i q^{8} +(-2.94166 - 0.588745i) q^{9} +(-2.18143 + 1.25945i) q^{10} +(-5.56722 - 3.21424i) q^{11} +(0.742053 - 7.48885i) q^{12} +(-1.77286 - 1.02356i) q^{13} +(-4.86822 - 4.55132i) q^{14} +(1.57808 - 0.713898i) q^{15} +6.18812 q^{16} +(-1.68778 - 2.92333i) q^{17} +(-1.48299 + 7.40976i) q^{18} +(3.51581 + 2.02985i) q^{19} +(2.17243 + 3.76276i) q^{20} +(3.02259 + 3.44441i) q^{21} +(-8.09635 + 14.0233i) q^{22} +(-2.48399 + 1.43413i) q^{23} +(-10.1805 - 1.00876i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-2.57825 + 4.46565i) q^{26} +(1.51717 - 4.96973i) q^{27} +(-7.85059 + 8.39721i) q^{28} +(5.49358 - 3.17172i) q^{29} +(-1.79824 - 3.97504i) q^{30} -0.965448i q^{31} -3.77429i q^{32} +(6.49091 - 9.04677i) q^{33} +(-7.36357 + 4.25136i) q^{34} +(-2.57718 - 0.598455i) q^{35} +(12.7811 + 2.55802i) q^{36} +(-1.31513 + 2.27787i) q^{37} +(5.11299 - 8.85597i) q^{38} +(2.06700 - 2.88090i) q^{39} +(5.11516 - 2.95324i) q^{40} +(3.50381 - 6.06877i) q^{41} +(8.67614 - 7.61359i) q^{42} +(0.788442 + 1.36562i) q^{43} +(24.1888 + 13.9654i) q^{44} +(0.960963 + 2.84193i) q^{45} +(3.61244 + 6.25694i) q^{46} -6.05049 q^{47} +(-1.05686 + 10.6659i) q^{48} +(-0.470463 - 6.98417i) q^{49} +(2.18143 + 1.25945i) q^{50} +(5.32693 - 2.40981i) q^{51} +(7.70283 + 4.44723i) q^{52} +(-3.22776 + 1.86355i) q^{53} +(-12.5183 - 3.82160i) q^{54} +6.42848i q^{55} +(11.4153 + 10.6722i) q^{56} +(-4.09913 + 5.71320i) q^{57} +(-7.98926 - 13.8378i) q^{58} +14.3051 q^{59} +(-6.85656 + 3.10179i) q^{60} -7.33263i q^{61} -2.43187 q^{62} +(-6.45305 + 4.62149i) q^{63} +2.86917 q^{64} +2.04712i q^{65} +(-22.7879 - 16.3500i) q^{66} +15.3837 q^{67} +(7.33319 + 12.7015i) q^{68} +(-2.04765 - 4.52637i) q^{69} +(-1.50745 + 6.49166i) q^{70} -5.13122i q^{71} +(3.47741 - 17.3749i) q^{72} +(-9.61674 + 5.55223i) q^{73} +(5.73772 + 3.31267i) q^{74} +(-1.40730 - 1.00971i) q^{75} +(-15.2757 - 8.81943i) q^{76} +(-16.2713 + 4.95193i) q^{77} +(-7.25671 - 5.20657i) q^{78} -3.85016 q^{79} +(-3.09406 - 5.35907i) q^{80} +(8.30676 + 3.46378i) q^{81} +(-15.2866 - 8.82574i) q^{82} +(0.549429 + 0.951639i) q^{83} +(-13.1327 - 14.9655i) q^{84} +(-1.68778 + 2.92333i) q^{85} +(3.43987 - 1.98601i) q^{86} +(4.52857 + 10.0105i) q^{87} +(18.9848 - 32.8827i) q^{88} +(-0.423334 + 0.733236i) q^{89} +(7.15853 - 2.42057i) q^{90} +(-5.18153 + 1.57692i) q^{91} +(10.7926 - 6.23112i) q^{92} +(1.66406 + 0.164887i) q^{93} +15.2406i q^{94} -4.05970i q^{95} +(6.50540 + 0.644605i) q^{96} +(-2.96628 + 1.71258i) q^{97} +(-17.5924 + 1.18505i) q^{98} +(14.4845 + 12.7329i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - q^{3} - 32 q^{4} - 16 q^{5} - 2 q^{6} + q^{7} + q^{9}+O(q^{10}) \) 32 * q - q^3 - 32 * q^4 - 16 * q^5 - 2 * q^6 + q^7 + q^9	\( 32 q - q^{3} - 32 q^{4} - 16 q^{5} - 2 q^{6} + q^{7} + q^{9} + 3 q^{11} + 12 q^{12} + 6 q^{13} - 15 q^{14} - q^{15} + 32 q^{16} - 3 q^{17} - 13 q^{18} + 16 q^{20} - q^{21} - 21 q^{22} - 9 q^{23} - 4 q^{24} - 16 q^{25} + 12 q^{26} + 23 q^{27} - 31 q^{28} + 18 q^{29} - 2 q^{30} + 19 q^{33} - 30 q^{34} + q^{35} + 18 q^{36} - q^{37} - 30 q^{38} + 21 q^{39} + 6 q^{41} + 19 q^{42} - 19 q^{43} + 21 q^{44} - 8 q^{45} + 6 q^{46} - 30 q^{47} - 35 q^{48} + 5 q^{49} + 36 q^{51} + 21 q^{52} - 24 q^{53} - 59 q^{54} + 30 q^{56} + 27 q^{57} + 30 q^{59} + 3 q^{60} - 32 q^{63} + 76 q^{64} + 26 q^{66} - 50 q^{67} - 3 q^{68} - 50 q^{69} + 9 q^{70} - 14 q^{72} + 12 q^{73} + 60 q^{74} + 2 q^{75} + 54 q^{76} - 27 q^{77} - 42 q^{78} + 4 q^{79} - 16 q^{80} - 23 q^{81} - 24 q^{82} - 42 q^{83} - 72 q^{84} - 3 q^{85} + 51 q^{86} + 34 q^{87} + 42 q^{88} + 30 q^{89} + 41 q^{90} - 57 q^{91} + 6 q^{92} - 33 q^{93} + 15 q^{96} - 42 q^{97} + 6 q^{98} - q^{99}+O(q^{100}) \) 32 * q - q^3 - 32 * q^4 - 16 * q^5 - 2 * q^6 + q^7 + q^9 + 3 * q^11 + 12 * q^12 + 6 * q^13 - 15 * q^14 - q^15 + 32 * q^16 - 3 * q^17 - 13 * q^18 + 16 * q^20 - q^21 - 21 * q^22 - 9 * q^23 - 4 * q^24 - 16 * q^25 + 12 * q^26 + 23 * q^27 - 31 * q^28 + 18 * q^29 - 2 * q^30 + 19 * q^33 - 30 * q^34 + q^35 + 18 * q^36 - q^37 - 30 * q^38 + 21 * q^39 + 6 * q^41 + 19 * q^42 - 19 * q^43 + 21 * q^44 - 8 * q^45 + 6 * q^46 - 30 * q^47 - 35 * q^48 + 5 * q^49 + 36 * q^51 + 21 * q^52 - 24 * q^53 - 59 * q^54 + 30 * q^56 + 27 * q^57 + 30 * q^59 + 3 * q^60 - 32 * q^63 + 76 * q^64 + 26 * q^66 - 50 * q^67 - 3 * q^68 - 50 * q^69 + 9 * q^70 - 14 * q^72 + 12 * q^73 + 60 * q^74 + 2 * q^75 + 54 * q^76 - 27 * q^77 - 42 * q^78 + 4 * q^79 - 16 * q^80 - 23 * q^81 - 24 * q^82 - 42 * q^83 - 72 * q^84 - 3 * q^85 + 51 * q^86 + 34 * q^87 + 42 * q^88 + 30 * q^89 + 41 * q^90 - 57 * q^91 + 6 * q^92 - 33 * q^93 + 15 * q^96 - 42 * q^97 + 6 * q^98 - q^99

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