LMFDB - Embedded newform 456.2.bj.a.173.48

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [456,2,Mod(29,456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(456, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 9, 17]))

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

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

chi := DirichletCharacter("456.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 456 = 2^{3} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	456.bj (of order $18$, degree $6$, 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:	$3.64117833217$
Analytic rank:	$0$
Dimension:	$456$
Relative dimension:	$76$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			173.48
Character	$\chi$	$=$	456.173
Dual form			456.2.bj.a.29.48

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.566068 + 1.29598i) q^{2} +(-1.48828 + 0.886022i) q^{3} +(-1.35913 + 1.46723i) q^{4} +(-1.49063 + 0.542546i) q^{5} +(-1.99073 - 1.42723i) q^{6} +(2.47083 + 4.27960i) q^{7} +(-2.67086 - 0.930859i) q^{8} +(1.42993 - 2.63729i) q^{9} +O(q^{10})$	\(q+(0.566068 + 1.29598i) q^{2} +(-1.48828 + 0.886022i) q^{3} +(-1.35913 + 1.46723i) q^{4} +(-1.49063 + 0.542546i) q^{5} +(-1.99073 - 1.42723i) q^{6} +(2.47083 + 4.27960i) q^{7} +(-2.67086 - 0.930859i) q^{8} +(1.42993 - 2.63729i) q^{9} +(-1.54693 - 1.62472i) q^{10} +(-1.56878 + 2.71721i) q^{11} +(0.722769 - 3.38786i) q^{12} +(0.796665 - 0.668481i) q^{13} +(-4.14762 + 5.62469i) q^{14} +(1.73777 - 2.12819i) q^{15} +(-0.305514 - 3.98832i) q^{16} +(-4.93455 - 0.870094i) q^{17} +(4.22732 + 0.360276i) q^{18} +(0.310232 - 4.34785i) q^{19} +(1.22993 - 2.92449i) q^{20} +(-7.46909 - 4.18001i) q^{21} +(-4.40949 - 0.494985i) q^{22} +(1.04161 - 2.86179i) q^{23} +(4.79974 - 0.981066i) q^{24} +(-1.90259 + 1.59646i) q^{25} +(1.31731 + 0.654057i) q^{26} +(0.208565 + 5.19197i) q^{27} +(-9.63732 - 2.19128i) q^{28} +(1.32946 - 0.234419i) q^{29} +(3.74179 + 1.04741i) q^{30} +(4.61174 - 2.66259i) q^{31} +(4.99584 - 2.65360i) q^{32} +(-0.0727270 - 5.43394i) q^{33} +(-1.66567 - 6.88761i) q^{34} +(-6.00498 - 5.03877i) q^{35} +(1.92604 + 5.68246i) q^{36} -8.08676 q^{37} +(5.81034 - 2.05912i) q^{38} +(-0.593368 + 1.70075i) q^{39} +(4.48631 - 0.0614955i) q^{40} +(8.91543 + 7.48094i) q^{41} +(1.18921 - 12.0460i) q^{42} +(2.81235 + 7.72687i) q^{43} +(-1.85458 - 5.99482i) q^{44} +(-0.700651 + 4.70704i) q^{45} +(4.29844 - 0.270067i) q^{46} +(-9.37853 + 1.65369i) q^{47} +(3.98842 + 5.66502i) q^{48} +(-8.70996 + 15.0861i) q^{49} +(-3.14598 - 1.56201i) q^{50} +(8.11489 - 3.07718i) q^{51} +(-0.101960 + 2.07744i) q^{52} +(-1.26782 + 3.48330i) q^{53} +(-6.61063 + 3.20930i) q^{54} +(0.864268 - 4.90151i) q^{55} +(-2.61553 - 13.7302i) q^{56} +(3.39058 + 6.74567i) q^{57} +(1.05637 + 1.59025i) q^{58} +(3.60440 + 0.635553i) q^{59} +(0.760687 + 5.44220i) q^{60} +(1.34726 - 3.70157i) q^{61} +(6.06123 + 4.46952i) q^{62} +(14.8196 - 0.396759i) q^{63} +(6.26700 + 4.97239i) q^{64} +(-0.824854 + 1.42869i) q^{65} +(7.00111 - 3.17023i) q^{66} +(2.06442 + 11.7079i) q^{67} +(7.98333 - 6.05753i) q^{68} +(0.985410 + 5.18201i) q^{69} +(3.13093 - 10.6346i) q^{70} +(-0.695293 + 0.253066i) q^{71} +(-6.27409 + 5.71277i) q^{72} +(-7.47954 - 6.27608i) q^{73} +(-4.57766 - 10.4803i) q^{74} +(1.41708 - 4.06171i) q^{75} +(5.95763 + 6.36448i) q^{76} -15.5048 q^{77} +(-2.54002 + 0.193745i) q^{78} +(-0.175322 + 0.208941i) q^{79} +(2.61926 + 5.77936i) q^{80} +(-4.91060 - 7.54228i) q^{81} +(-4.64841 + 15.7890i) q^{82} +(3.47275 + 6.01499i) q^{83} +(16.2845 - 5.27765i) q^{84} +(7.82767 - 1.38023i) q^{85} +(-8.42189 + 8.01869i) q^{86} +(-1.77090 + 1.52681i) q^{87} +(6.71934 - 5.79698i) q^{88} +(-5.58323 + 4.68488i) q^{89} +(-6.49685 + 1.75648i) q^{90} +(4.82925 + 1.75770i) q^{91} +(2.78321 + 5.41782i) q^{92} +(-4.50443 + 8.04877i) q^{93} +(-7.45203 - 11.2183i) q^{94} +(1.89647 + 6.64936i) q^{95} +(-5.08404 + 8.37571i) q^{96} +(-5.62946 - 0.992626i) q^{97} +(-24.4817 - 2.74818i) q^{98} +(4.92283 + 8.02276i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 456 q - 6 q^{4} - 6 q^{6} - 12 q^{7} - 12 q^{9}+O(q^{10}) $ 456 * q - 6 * q^4 - 6 * q^6 - 12 * q^7 - 12 * q^9	$ 456 q - 6 q^{4} - 6 q^{6} - 12 q^{7} - 12 q^{9} - 6 q^{10} - 9 q^{12} - 12 q^{15} - 6 q^{16} + 6 q^{24} - 24 q^{25} + 12 q^{28} - 6 q^{30} - 36 q^{31} + 6 q^{33} + 30 q^{34} - 66 q^{36} - 24 q^{39} - 42 q^{40} + 39 q^{42} - 18 q^{46} - 15 q^{48} - 168 q^{49} - 36 q^{52} - 45 q^{54} + 36 q^{55} - 12 q^{57} - 96 q^{58} - 18 q^{60} + 30 q^{63} - 48 q^{64} - 18 q^{66} - 78 q^{70} + 60 q^{72} - 12 q^{76} + 45 q^{78} - 24 q^{79} - 156 q^{82} - 9 q^{84} - 6 q^{87} - 90 q^{88} + 84 q^{90} - 162 q^{96} - 24 q^{97}+O(q^{100}) $ 456 * q - 6 * q^4 - 6 * q^6 - 12 * q^7 - 12 * q^9 - 6 * q^10 - 9 * q^12 - 12 * q^15 - 6 * q^16 + 6 * q^24 - 24 * q^25 + 12 * q^28 - 6 * q^30 - 36 * q^31 + 6 * q^33 + 30 * q^34 - 66 * q^36 - 24 * q^39 - 42 * q^40 + 39 * q^42 - 18 * q^46 - 15 * q^48 - 168 * q^49 - 36 * q^52 - 45 * q^54 + 36 * q^55 - 12 * q^57 - 96 * q^58 - 18 * q^60 + 30 * q^63 - 48 * q^64 - 18 * q^66 - 78 * q^70 + 60 * q^72 - 12 * q^76 + 45 * q^78 - 24 * q^79 - 156 * q^82 - 9 * q^84 - 6 * q^87 - 90 * q^88 + 84 * q^90 - 162 * q^96 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/456\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.566068	+	1.29598i	0.400271	+	0.916397i
$2$	0.566068	+	1.29598i	0.400271	+	0.916397i
$3$	−1.48828	+	0.886022i	−0.859257	+	0.511545i
$3$	−1.48828	+	0.886022i	−0.859257	+	0.511545i
$4$	−1.35913	+	1.46723i	−0.679567	+	0.733614i
$5$	−1.49063	+	0.542546i	−0.666632	+	0.242634i	−0.653097	−	0.757274i	$-0.726531\pi$
$5$	−1.49063	+	0.542546i	−0.666632	+	0.242634i	−0.0135349	+	0.999908i	$0.504308\pi$
$6$	−1.99073	−	1.42723i	−0.812713	−	0.582664i
$7$	2.47083	+	4.27960i	0.933884	+	1.61754i	0.776611	+	0.629980i	$0.216937\pi$
$7$	2.47083	+	4.27960i	0.933884	+	1.61754i	0.157273	+	0.987555i	$0.449730\pi$
$8$	−2.67086	−	0.930859i	−0.944292	−	0.329109i
$9$	1.42993	−	2.63729i	0.476644	−	0.879097i
$10$	−1.54693	−	1.62472i	−0.489182	−	0.513780i
$11$	−1.56878	+	2.71721i	−0.473006	+	0.819270i	−0.999523	−	0.0308945i	$-0.990164\pi$
$11$	−1.56878	+	2.71721i	−0.473006	+	0.819270i	0.526517	+	0.850165i	$0.323498\pi$
$12$	0.722769	−	3.38786i	0.208646	−	0.977991i
$13$	0.796665	−	0.668481i	0.220955	−	0.185403i	−0.525590	−	0.850738i	$-0.676155\pi$
$13$	0.796665	−	0.668481i	0.220955	−	0.185403i	0.746545	+	0.665334i	$0.231711\pi$
$14$	−4.14762	+	5.62469i	−1.10850	+	1.50326i
$15$	1.73777	−	2.12819i	0.448690	−	0.549497i
$16$	−0.305514	−	3.98832i	−0.0763785	−	0.997079i
$17$	−4.93455	−	0.870094i	−1.19680	−	0.211029i	−0.460487	−	0.887666i	$-0.652325\pi$
$17$	−4.93455	−	0.870094i	−1.19680	−	0.211029i	−0.736316	+	0.676638i	$0.763436\pi$
$18$	4.22732	+	0.360276i	0.996388	+	0.0849180i
$19$	0.310232	−	4.34785i	0.0711720	−	0.997464i
$19$	0.310232	−	4.34785i	0.0711720	−	0.997464i
$20$	1.22993	−	2.92449i	0.275021	−	0.653936i
$21$	−7.46909	−	4.18001i	−1.62989	−	0.912154i
$22$	−4.40949	−	0.494985i	−0.940107	−	0.105531i
$23$	1.04161	−	2.86179i	0.217190	−	0.596724i	−0.782473	−	0.622684i	$-0.786042\pi$
$23$	1.04161	−	2.86179i	0.217190	−	0.596724i	0.999663	+	0.0259603i	$0.00826435\pi$
$24$	4.79974	−	0.981066i	0.979743	−	0.200259i
$25$	−1.90259	+	1.59646i	−0.380518	+	0.319292i
$26$	1.31731	+	0.654057i	0.258345	+	0.128271i
$27$	0.208565	+	5.19197i	0.0401383	+	0.999194i
$28$	−9.63732	−	2.19128i	−1.82128	−	0.414112i
$29$	1.32946	−	0.234419i	0.246874	−	0.0435305i	−0.0488417	−	0.998807i	$-0.515553\pi$
$29$	1.32946	−	0.234419i	0.246874	−	0.0435305i	0.295716	+	0.955276i	$0.404442\pi$
$30$	3.74179	+	1.04741i	0.683155	+	0.191230i
$31$	4.61174	−	2.66259i	0.828293	−	0.478215i	−0.0249746	−	0.999688i	$-0.507950\pi$
$31$	4.61174	−	2.66259i	0.828293	−	0.478215i	0.853268	+	0.521473i	$0.174617\pi$
$32$	4.99584	−	2.65360i	0.883148	−	0.469095i
$33$	−0.0727270	−	5.43394i	−0.0126601	−	0.945927i
$34$	−1.66567	−	6.88761i	−0.285659	−	1.18122i
$35$	−6.00498	−	5.03877i	−1.01503	−	0.851708i
$36$	1.92604	+	5.68246i	0.321006	+	0.947077i
$37$	−8.08676			−1.32945			−0.664727	−	0.747086i	$-0.731452\pi$
$37$	−8.08676			−1.32945			−0.664727	+	0.747086i	$0.731452\pi$
$38$	5.81034	−	2.05912i	0.942561	−	0.334034i
$39$	−0.593368	+	1.70075i	−0.0950150	+	0.272338i
$40$	4.48631	−	0.0614955i	0.709348	−	0.00972329i
$41$	8.91543	+	7.48094i	1.39236	+	1.16833i	0.964375	+	0.264539i	$0.0852197\pi$
$41$	8.91543	+	7.48094i	1.39236	+	1.16833i	0.427982	+	0.903787i	$0.359225\pi$
$42$	1.18921	−	12.0460i	0.183498	−	1.85873i
$43$	2.81235	+	7.72687i	0.428879	+	1.17834i	0.946494	+	0.322722i	$0.104598\pi$
$43$	2.81235	+	7.72687i	0.428879	+	1.17834i	−0.517614	+	0.855614i	$0.673180\pi$
$44$	−1.85458	−	5.99482i	−0.279589	−	0.903752i
$45$	−0.700651	+	4.70704i	−0.104447	+	0.701684i
$46$	4.29844	−	0.270067i	0.633771	−	0.0398191i
$47$	−9.37853	+	1.65369i	−1.36800	+	0.241215i	−0.808929	−	0.587906i	$-0.799953\pi$
$47$	−9.37853	+	1.65369i	−1.36800	+	0.241215i	−0.559069	+	0.829121i	$0.688841\pi$
$48$	3.98842	+	5.66502i	0.575679	+	0.817676i
$49$	−8.70996	+	15.0861i	−1.24428	+	2.15516i
$50$	−3.14598	−	1.56201i	−0.444909	−	0.220902i
$51$	8.11489	−	3.07718i	1.13631	−	0.430891i
$52$	−0.101960	+	2.07744i	−0.0141392	+	0.288090i
$53$	−1.26782	+	3.48330i	−0.174148	+	0.478468i	−0.995804	−	0.0915164i	$-0.970829\pi$
$53$	−1.26782	+	3.48330i	−0.174148	+	0.478468i	0.821655	+	0.569985i	$0.193051\pi$
$54$	−6.61063	+	3.20930i	−0.899592	+	0.436731i
$55$	0.864268	−	4.90151i	0.116538	−	0.660919i
$56$	−2.61553	−	13.7302i	−0.349515	−	1.83478i
$57$	3.39058	+	6.74567i	0.449093	+	0.893485i
$58$	1.05637	+	1.59025i	0.138708	+	0.208811i
$59$	3.60440	+	0.635553i	0.469253	+	0.0827419i	0.403274	−	0.915079i	$-0.367872\pi$
$59$	3.60440	+	0.635553i	0.469253	+	0.0827419i	0.0659785	+	0.997821i	$0.478983\pi$
$60$	0.760687	+	5.44220i	0.0982043	+	0.702585i
$61$	1.34726	−	3.70157i	0.172499	−	0.473938i	−0.823073	−	0.567935i	$-0.807742\pi$
$61$	1.34726	−	3.70157i	0.172499	−	0.473938i	0.995572	+	0.0939974i	$0.0299645\pi$
$62$	6.06123	+	4.46952i	0.769777	+	0.567630i
$63$	14.8196	−	0.396759i	1.86710	−	0.0499869i
$64$	6.26700	+	4.97239i	0.783375	+	0.621549i
$65$	−0.824854	+	1.42869i	−0.102311	+	0.177207i
$66$	7.00111	−	3.17023i	0.861777	−	0.390229i
$67$	2.06442	+	11.7079i	0.252209	+	1.43035i	0.803136	+	0.595796i	$0.203163\pi$
$67$	2.06442	+	11.7079i	0.252209	+	1.43035i	−0.550926	+	0.834554i	$0.685726\pi$
$68$	7.98333	−	6.05753i	0.968121	−	0.734583i
$69$	0.985410	+	5.18201i	0.118629	+	0.623841i
$70$	3.13093	−	10.6346i	0.374217	−	1.27108i
$71$	−0.695293	+	0.253066i	−0.0825161	+	0.0300334i	−0.382948	−	0.923770i	$-0.625091\pi$
$71$	−0.695293	+	0.253066i	−0.0825161	+	0.0300334i	0.300432	+	0.953803i	$0.402869\pi$
$72$	−6.27409	+	5.71277i	−0.739409	+	0.673257i
$73$	−7.47954	−	6.27608i	−0.875414	−	0.734560i	0.0898169	−	0.995958i	$-0.471372\pi$
$73$	−7.47954	−	6.27608i	−0.875414	−	0.734560i	−0.965231	+	0.261399i	$0.915816\pi$
$74$	−4.57766	−	10.4803i	−0.532142	−	1.21831i
$75$	1.41708	−	4.06171i	0.163630	−	0.469006i
$76$	5.95763	+	6.36448i	0.683387	+	0.730056i
$77$	−15.5048			−1.76693
$78$	−2.54002	+	0.193745i	−0.287601	+	0.0219373i
$79$	−0.175322	+	0.208941i	−0.0197253	+	0.0235077i	−0.775817	−	0.630958i	$-0.782662\pi$
$79$	−0.175322	+	0.208941i	−0.0197253	+	0.0235077i	0.756092	+	0.654466i	$0.227106\pi$
$80$	2.61926	+	5.77936i	0.292842	+	0.646153i
$81$	−4.91060	−	7.54228i	−0.545622	−	0.838032i
$82$	−4.64841	+	15.7890i	−0.513331	+	1.74360i
$83$	3.47275	+	6.01499i	0.381184	+	0.660231i	0.991232	−	0.132134i	$-0.0421830\pi$
$83$	3.47275	+	6.01499i	0.381184	+	0.660231i	−0.610048	+	0.792365i	$0.708850\pi$
$84$	16.2845	−	5.27765i	1.77679	−	0.575839i
$85$	7.82767	−	1.38023i	0.849030	−	0.149707i
$86$	−8.42189	+	8.01869i	−0.908156	+	0.864677i
$87$	−1.77090	+	1.52681i	−0.189860	+	0.163691i
$88$	6.71934	−	5.79698i	0.716285	−	0.617960i
$89$	−5.58323	+	4.68488i	−0.591821	+	0.496597i	−0.888805	−	0.458286i	$-0.848464\pi$
$89$	−5.58323	+	4.68488i	−0.591821	+	0.496597i	0.296984	+	0.954882i	$0.404019\pi$
$90$	−6.49685	+	1.75648i	−0.684828	+	0.185149i
$91$	4.82925	+	1.75770i	0.506243	+	0.184257i
$92$	2.78321	+	5.41782i	0.290170	+	0.564847i
$93$	−4.50443	+	8.04877i	−0.467088	+	0.834619i
$94$	−7.45203	−	11.2183i	−0.768619	−	1.15708i
$95$	1.89647	+	6.64936i	0.194573	+	0.682210i
$96$	−5.08404	+	8.37571i	−0.518888	+	0.854842i
$97$	−5.62946	−	0.992626i	−0.571585	−	0.100786i	−0.119617	−	0.992820i	$-0.538167\pi$
$97$	−5.62946	−	0.992626i	−0.571585	−	0.100786i	−0.451968	+	0.892034i	$0.649278\pi$
$98$	−24.4817	−	2.74818i	−2.47303	−	0.277608i
$99$	4.92283	+	8.02276i	0.494763	+	0.806318i
$100$	0.243499	−	4.96133i	0.0243499	−	0.496133i
$101$	13.0702	−	10.9672i	1.30053	−	1.09127i	0.310476	−	0.950581i	$-0.399512\pi$
$101$	13.0702	−	10.9672i	1.30053	−	1.09127i	0.990053	−	0.140692i	$-0.0449329\pi$
$102$	8.58154	+	8.77485i	0.849699	+	0.868840i
$103$	3.14475	+	1.81562i	0.309862	+	0.178899i	0.646865	−	0.762605i	$-0.276080\pi$
$103$	3.14475	+	1.81562i	0.309862	+	0.178899i	−0.337003	+	0.941504i	$0.609413\pi$
$104$	−2.75004	+	1.04384i	−0.269664	+	0.102357i
$105$	13.4015	+	2.17855i	1.30786	+	0.212604i
$106$	−5.23196	+	0.328719i	−0.508173	+	0.0319280i
$107$	−3.97671	+	2.29595i	−0.384443	+	0.221958i	−0.679750	−	0.733444i	$-0.737912\pi$
$107$	−3.97671	+	2.29595i	−0.384443	+	0.221958i	0.295307	+	0.955403i	$0.404578\pi$
$108$	−7.90126	−	6.75056i	−0.760299	−	0.649573i
$109$	−4.88050	+	1.77636i	−0.467467	+	0.170144i	−0.565005	−	0.825088i	$-0.691126\pi$
$109$	−4.88050	+	1.77636i	−0.467467	+	0.170144i	0.0975377	+	0.995232i	$0.468903\pi$
$110$	6.84149	−	1.65451i	0.652311	−	0.157752i
$111$	12.0353	−	7.16504i	1.14234	−	0.680076i
$112$	16.3135	−	11.1619i	1.54148	−	1.05470i
$113$	−8.63755			−0.812553			−0.406276	−	0.913750i	$-0.633173\pi$
$113$	−8.63755			−0.812553			−0.406276	+	0.913750i	$0.633173\pi$
$114$	−6.82296	+	8.21263i	−0.639028	+	0.769183i
$115$			4.83100i			0.450493i
$116$	−1.46296	+	2.26922i	−0.135833	+	0.210692i
$117$	−0.623803	−	3.05692i	−0.0576706	−	0.282612i
$118$	1.21667	+	5.03100i	0.112004	+	0.463141i
$119$	−8.46876	−	23.2677i	−0.776330	−	2.13295i
$120$	−6.62238	+	4.06649i	−0.604538	+	0.371218i
$121$	0.577839	+	1.00085i	0.0525308	+	0.0909860i
$122$	5.55981	−	0.349317i	0.503362	−	0.0316257i
$123$	−19.8969	−	3.23443i	−1.79404	−	0.291639i
$124$	−2.36135	+	10.3853i	−0.212055	+	0.932627i
$125$	5.93566	−	10.2809i	0.530901	−	0.919548i
$126$	8.90313	+	18.9814i	0.793153	+	1.69100i
$127$	5.94751	+	7.08796i	0.527756	+	0.628955i	0.962396	−	0.271649i	$-0.0875690\pi$
$127$	5.94751	+	7.08796i	0.527756	+	0.628955i	−0.434641	+	0.900604i	$0.643125\pi$
$128$	−2.89658	+	10.9366i	−0.256024	+	0.966671i
$129$	−11.0317	−	9.00791i	−0.971290	−	0.793102i
$130$	−2.31848	−	0.260259i	−0.203344	−	0.0228263i
$131$	−0.384519	+	2.18071i	−0.0335955	+	0.190530i	−0.996987	−	0.0775689i	$-0.975284\pi$
$131$	−0.384519	+	2.18071i	−0.0335955	+	0.190530i	0.963391	+	0.268099i	$0.0863953\pi$
$132$	8.07167	+	7.27874i	0.702549	+	0.633533i
$133$	19.3735	−	9.41510i	1.67990	−	0.816393i
$134$	−14.0046	+	9.30293i	−1.20982	+	0.803651i
$135$	−3.12778	−	7.62616i	−0.269196	−	0.656356i
$136$	12.3696	+	6.91727i	1.06068	+	0.593151i
$137$	2.39537	−	6.58123i	0.204650	−	0.562272i	−0.794327	−	0.607491i	$-0.792176\pi$
$137$	2.39537	−	6.58123i	0.204650	−	0.562272i	0.998977	+	0.0452186i	$0.0143984\pi$
$138$	−6.15798	+	4.21045i	−0.524202	+	0.358417i
$139$	2.96765	+	3.53671i	0.251713	+	0.299980i	0.877074	−	0.480356i	$-0.159493\pi$
$139$	2.96765	+	3.53671i	0.251713	+	0.299980i	−0.625361	+	0.780336i	$0.715048\pi$
$140$	15.5546	−	1.96230i	1.31460	−	0.165845i
$141$	12.4926	−	10.7707i	1.05207	−	0.907058i
$142$	−0.721552	−	0.757834i	−0.0605513	−	0.0635960i
$143$	0.566611	+	3.21341i	0.0473824	+	0.268719i
$144$	−10.9552	−	4.89729i	−0.912934	−	0.408107i
$145$	−1.85455	+	1.07073i	−0.154012	+	0.0889189i
$146$	3.89975	−	13.2460i	0.322745	−	1.09625i
$147$	−0.403784	−	30.1695i	−0.0333035	−	2.48834i
$148$	10.9910	−	11.8651i	0.903453	−	0.975306i
$149$	−1.80962	−	1.51845i	−0.148250	−	0.124396i	0.565646	−	0.824648i	$-0.308627\pi$
$149$	−1.80962	−	1.51845i	−0.148250	−	0.124396i	−0.713896	+	0.700252i	$0.753071\pi$
$150$	6.06606	−	0.462701i	0.495292	−	0.0377793i
$151$			14.4723i			1.17774i	0.808228	+	0.588870i	$0.200427\pi$
$151$			14.4723i			1.17774i	−0.808228	+	0.588870i	$0.799573\pi$
$152$	−4.87582	+	11.3237i	−0.395481	+	0.918474i
$153$	−9.35075	+	11.7697i	−0.755963	+	0.951520i
$154$	−8.77676	−	20.0939i	−0.707251	−	1.61921i
$155$	−5.42984	+	6.47103i	−0.436135	+	0.519766i
$156$	−1.68892	−	3.18215i	−0.135222	−	0.254776i
$157$	5.54656	+	15.2390i	0.442663	+	1.21621i	0.937734	+	0.347355i	$0.112920\pi$
$157$	5.54656	+	15.2390i	0.442663	+	1.21621i	−0.495071	+	0.868853i	$0.664858\pi$
$158$	−0.370028	−	0.108939i	−0.0294378	−	0.00866675i
$159$	−1.19942	−	6.30743i	−0.0951200	−	0.500211i
$160$	−6.00727	+	6.66602i	−0.474916	+	0.526995i
$161$	14.8209	−	2.61333i	1.16805	−	0.205959i
$162$	6.99492	−	10.6335i	0.549573	−	0.835446i
$163$	−10.3832	−	5.99477i	−0.813278	−	0.469546i	0.0348147	−	0.999394i	$-0.488916\pi$
$163$	−10.3832	−	5.99477i	−0.813278	−	0.469546i	−0.848093	+	0.529847i	$0.822249\pi$
$164$	−23.0935	+	2.91338i	−1.80330	+	0.227497i
$165$	3.05657	+	8.06056i	0.237954	+	0.627513i
$166$	−5.82949	+	7.90552i	−0.452456	+	0.613587i
$167$	3.57442	+	1.30098i	0.276597	+	0.100673i	0.476594	−	0.879123i	$-0.341871\pi$
$167$	3.57442	+	1.30098i	0.276597	+	0.100673i	−0.199997	+	0.979796i	$0.564093\pi$
$168$	16.0579	+	18.1169i	1.23889	+	1.39775i
$169$	−2.06962	+	11.7374i	−0.159201	+	0.902876i
$170$	6.21975	+	9.36321i	0.477033	+	0.718125i
$171$	−11.0229	−	7.03529i	−0.842944	−	0.538002i
$172$	−15.1594	−	6.37549i	−1.15590	−	0.486126i
$173$	23.3554	+	4.11819i	1.77568	+	0.313100i	0.962978	−	0.269581i	$-0.0868852\pi$
$173$	23.3554	+	4.11819i	1.77568	+	0.313100i	0.812701	+	0.582681i	$0.197996\pi$
$174$	−2.98116	−	1.43077i	−0.226001	−	0.108467i
$175$	−11.5332	−	4.19773i	−0.871826	−	0.317319i
$176$	11.3164	+	5.42666i	0.853005	+	0.409050i
$177$	−5.92746	+	2.24770i	−0.445535	+	0.168947i
$178$	−9.23201	−	4.58379i	−0.691968	−	0.343570i
$179$	10.2596	+	5.92337i	0.766836	+	0.442733i	0.831745	−	0.555158i	$-0.187342\pi$
$179$	10.2596	+	5.92337i	0.766836	+	0.442733i	−0.0649085	+	0.997891i	$0.520676\pi$
$180$	−5.95402	−	7.42551i	−0.443786	−	0.553465i
$181$	−2.76204	−	15.6643i	−0.205301	−	1.16432i	−0.896966	−	0.442100i	$-0.854234\pi$
$181$	−2.76204	−	15.6643i	−0.205301	−	1.16432i	0.691665	−	0.722219i	$-0.256878\pi$
$182$	0.455736	+	7.25360i	0.0337814	+	0.537672i
$183$	1.27458	+	6.70267i	0.0942194	+	0.495475i
$184$	−5.44591	+	6.67385i	−0.401478	+	0.492003i
$185$	12.0544	−	4.38744i	0.886257	−	0.322571i
$186$	−12.9809	−	1.28150i	−0.951804	−	0.0939642i
$187$	10.1055	−	12.0432i	0.738985	−	0.880688i
$188$	10.3203	−	16.0080i	0.752687	−	1.16750i
$189$	−21.7042	+	13.7210i	−1.57875	+	0.998057i
$190$	−7.54392	+	6.22178i	−0.547293	+	0.451375i
$191$			2.28623i			0.165426i	0.996573	+	0.0827130i	$0.0263585\pi$
$191$			2.28623i			0.165426i	−0.996573	+	0.0827130i	$0.973642\pi$
$192$	−13.7327	−	1.84759i	−0.991071	−	0.133339i
$193$	5.64485	−	6.72727i	0.406325	−	0.484239i	−0.523613	−	0.851956i	$-0.675416\pi$
$193$	5.64485	−	6.72727i	0.406325	−	0.484239i	0.929938	+	0.367717i	$0.119861\pi$
$194$	−1.90024	−	7.85757i	−0.136429	−	0.564141i
$195$	−0.0382393	−	2.85712i	−0.00273837	−	0.204603i
$196$	−10.2967	−	33.2835i	−0.735482	−	2.37739i
$197$	−2.03520	−	3.52507i	−0.145002	−	0.251151i	0.784372	−	0.620291i	$-0.212985\pi$
$197$	−2.03520	−	3.52507i	−0.145002	−	0.251151i	−0.929374	+	0.369140i	$0.879652\pi$
$198$	−7.61069	+	10.9213i	−0.540868	+	0.776144i
$199$	−3.39987	−	19.2816i	−0.241010	−	1.36684i	−0.829579	−	0.558390i	$-0.811419\pi$
$199$	−3.39987	−	19.2816i	−0.241010	−	1.36684i	0.588568	−	0.808447i	$-0.299692\pi$
$200$	6.56763	−	2.49288i	0.464402	−	0.176274i
$201$	−13.4459	−	15.5955i	−0.948401	−	1.10002i
$202$	21.6118	+	10.7305i	1.52060	+	0.754996i
$203$	4.28808	+	5.11033i	0.300964	+	0.358675i
$204$	−6.51430	+	16.0887i	−0.456092	+	1.12643i
$205$	−17.3484	−	6.31430i	−1.21167	−	0.441010i
$206$	−0.572869	+	5.10331i	−0.0399137	+	0.355564i
$207$	−6.05794	−	6.83917i	−0.421056	−	0.475355i
$208$	−2.90951	−	2.97312i	−0.201738	−	0.206149i
$209$	11.3273	+	7.66379i	0.783528	+	0.530116i
$210$	4.76283	+	18.6013i	0.328666	+	1.28361i
$211$	−0.998086	+	5.66043i	−0.0687111	+	0.389680i	0.930986	+	0.365056i	$0.118950\pi$
$211$	−0.998086	+	5.66043i	−0.0687111	+	0.389680i	−0.999697	+	0.0246242i	$0.992161\pi$
$212$	−3.38766	−	6.59445i	−0.232666	−	0.452908i
$213$	0.810566	−	0.992677i	0.0555391	−	0.0680171i
$214$	−5.22660	−	3.85407i	−0.357283	−	0.263459i
$215$	−8.38437	−	9.99211i	−0.571809	−	0.681456i
$216$	4.27594	−	14.0612i	0.290941	−	0.956741i
$217$	22.7896	+	13.1576i	1.54706	+	0.893196i
$218$	−5.06482	−	5.31949i	−0.343033	−	0.360282i
$219$	16.6924	+	2.71350i	1.12797	+	0.183361i
$220$	6.01697	+	7.92988i	0.405664	+	0.534632i
$221$	−4.51282	+	2.60548i	−0.303565	+	0.175263i
$222$	16.0986	+	11.5417i	1.08047	+	0.774625i
$223$	8.46432	+	23.2555i	0.566813	+	1.55730i	0.809451	+	0.587188i	$0.199765\pi$
$223$	8.46432	+	23.2555i	0.566813	+	1.55730i	−0.242638	+	0.970117i	$0.578013\pi$
$224$	23.7002	+	14.8236i	1.58354	+	0.990443i
$225$	1.48976	+	7.30051i	0.0993174	+	0.486700i
$226$	−4.88945	−	11.1941i	−0.325241	−	0.744621i
$227$			4.61503i			0.306310i	0.988202	+	0.153155i	$0.0489434\pi$
$227$			4.61503i			0.306310i	−0.988202	+	0.153155i	$0.951057\pi$
$228$	−14.5057	−	4.19351i	−0.960661	−	0.277722i
$229$		−	9.00097i		−	0.594801i	−0.954753	−	0.297400i	$-0.903880\pi$
$229$		−	9.00097i		−	0.594801i	0.954753	−	0.297400i	$-0.0961196\pi$
$230$	−6.26088	+	2.73468i	−0.412830	+	0.180319i
$231$	23.0754	−	13.7376i	1.51825	−	0.903865i
$232$	−3.76901	−	0.611437i	−0.247447	−	0.0401428i
$233$	3.51287	+	9.65154i	0.230136	+	0.632293i	0.999982	−	0.00593595i	$-0.00188948\pi$
$233$	3.51287	+	9.65154i	0.230136	+	0.632293i	−0.769847	+	0.638229i	$0.779667\pi$
$234$	3.60859	−	2.53886i	0.235901	−	0.165971i
$235$	13.0827	−	7.55333i	0.853424	−	0.492725i
$236$	−5.83136	+	4.42467i	−0.379589	+	0.288022i
$237$	0.0758016	−	0.466301i	0.00492384	−	0.0302895i
$238$	25.3606	−	24.1465i	1.64388	−	1.56518i
$239$	−11.4806	−	6.62833i	−0.742619	−	0.428751i	0.0804021	−	0.996763i	$-0.474380\pi$
$239$	−11.4806	−	6.62833i	−0.742619	−	0.428751i	−0.823021	+	0.568011i	$0.807713\pi$
$240$	−9.01882	−	6.28057i	−0.582162	−	0.405409i
$241$	−1.93482	−	2.30583i	−0.124633	−	0.148531i	0.700120	−	0.714025i	$-0.253130\pi$
$241$	−1.93482	−	2.30583i	−0.124633	−	0.148531i	−0.824752	+	0.565494i	$0.808686\pi$
$242$	−0.969981	+	1.31542i	−0.0623528	+	0.0845581i
$243$	13.9910	+	6.87410i	0.897520	+	0.440974i
$244$	3.59994	+	7.00767i	0.230463	+	0.448620i
$245$	4.79846	−	27.2134i	0.306562	−	1.73860i
$246$	−7.07125	−	27.6169i	−0.450846	−	1.76079i
$247$	−2.65930	−	3.67116i	−0.169207	−	0.233590i
$248$	−14.7958	+	2.81853i	−0.939536	+	0.178977i
$249$	−10.4978	−	5.87502i	−0.665273	−	0.372315i
$250$	16.6838	+	1.87283i	1.05518	+	0.118448i
$251$	1.09383	+	0.398123i	0.0690422	+	0.0251293i	0.376310	−	0.926494i	$-0.377193\pi$
$251$	1.09383	+	0.398123i	0.0690422	+	0.0251293i	−0.307268	+	0.951623i	$0.599415\pi$
$252$	−19.5597	+	22.2830i	−1.23215	+	1.40370i
$253$	6.14203	+	7.31979i	0.386146	+	0.460191i
$254$	−5.81917	+	11.7201i	−0.365127	+	0.735386i
$255$	−10.4268	+	8.98965i	−0.652953	+	0.562954i
$256$	−15.8133	+	2.43697i	−0.988333	+	0.152311i
$257$	−1.85042	−	10.4942i	−0.115426	−	0.654612i	−0.986538	−	0.163529i	$-0.947712\pi$
$257$	−1.85042	−	10.4942i	−0.115426	−	0.654612i	0.871113	−	0.491083i	$-0.163399\pi$
$258$	5.42937	−	19.3960i	0.338018	−	1.20754i
$259$	−19.9810	−	34.6081i	−1.24156	−	2.15044i
$260$	−0.975126	−	3.15203i	−0.0604747	−	0.195480i
$261$	1.28280	−	3.84137i	0.0794033	−	0.237775i
$262$	−3.04383	+	0.736104i	−0.188048	+	0.0454767i
$263$	12.3985	−	14.7760i	0.764525	−	0.911125i	−0.233600	−	0.972333i	$-0.575051\pi$
$263$	12.3985	−	14.7760i	0.764525	−	0.911125i	0.998125	+	0.0612074i	$0.0194951\pi$
$264$	−4.86399	+	14.5810i	−0.299358	+	0.897398i
$265$		−	5.88018i		−	0.361216i
$266$	23.1685	+	19.7782i	1.42055	+	1.21268i
$267$	4.15847	−	11.9193i	0.254494	−	0.729447i
$268$	−19.9840	−	12.8836i	−1.22072	−	0.786994i
$269$	5.05547	−	6.02488i	0.308238	−	0.367343i	−0.589581	−	0.807710i	$-0.700707\pi$
$269$	5.05547	−	6.02488i	0.308238	−	0.367343i	0.897818	+	0.440366i	$0.145151\pi$
$270$	8.11283	−	8.37047i	0.493731	−	0.509411i
$271$	−1.69615	+	0.617348i	−0.103034	+	0.0375012i	−0.393023	−	0.919529i	$-0.628571\pi$
$271$	−1.69615	+	0.617348i	−0.103034	+	0.0375012i	0.289989	+	0.957030i	$0.406348\pi$
$272$	−1.96263	+	19.9464i	−0.119002	+	1.20943i
$273$	−8.74462	+	1.66287i	−0.529249	+	0.100642i
$274$	9.88509	−	0.621070i	0.597180	−	0.0375202i
$275$	−1.35318	−	7.67424i	−0.0815995	−	0.462774i
$276$	−8.94250	−	5.59723i	−0.538275	−	0.336914i
$277$	2.41146	+	1.39226i	0.144891	+	0.0836528i	0.570693	−	0.821164i	$-0.306675\pi$
$277$	2.41146	+	1.39226i	0.144891	+	0.0836528i	−0.425802	+	0.904816i	$0.640008\pi$
$278$	−2.90362	+	5.84804i	−0.174147	+	0.350742i
$279$	−0.427552	−	15.9698i	−0.0255969	−	0.956088i
$280$	11.3481	+	19.0477i	0.678177	+	1.13832i
$281$	8.67747	+	3.15834i	0.517654	+	0.188411i	0.587618	−	0.809139i	$-0.300066\pi$
$281$	8.67747	+	3.15834i	0.517654	+	0.188411i	−0.0699633	+	0.997550i	$0.522288\pi$
$282$	21.0303	+	10.0932i	1.25234	+	0.601044i
$283$	−12.0582	−	2.12618i	−0.716785	−	0.126389i	−0.196651	−	0.980473i	$-0.563007\pi$
$283$	−12.0582	−	2.12618i	−0.716785	−	0.126389i	−0.520133	+	0.854085i	$0.674118\pi$
$284$	0.573691	−	1.36410i	0.0340423	−	0.0809447i
$285$	−8.71394	−	8.21577i	−0.516170	−	0.486660i
$286$	−3.84378	+	2.55333i	−0.227287	+	0.150981i
$287$	−9.98690	+	56.6386i	−0.589508	+	3.34327i
$288$	0.145392	−	16.9699i	0.00856728	−	0.999963i
$289$	7.61791	+	2.77269i	0.448112	+	0.163100i
$290$	−2.43744	−	1.79736i	−0.143132	−	0.105545i
$291$	9.25768	−	3.51052i	0.542695	−	0.205791i
$292$	19.3741	−	2.44416i	1.13379	−	0.143034i
$293$	−16.6288	−	9.60062i	−0.971463	−	0.560874i	−0.0717811	−	0.997420i	$-0.522868\pi$
$293$	−16.6288	−	9.60062i	−0.971463	−	0.560874i	−0.899682	+	0.436546i	$0.856202\pi$
$294$	38.8705	−	17.6013i	2.26697	−	1.02653i
$295$	−5.71766	+	1.00818i	−0.332895	+	0.0586984i
$296$	21.5986	+	7.52764i	1.25539	+	0.437535i
$297$	−14.4349	−	7.57835i	−0.837596	−	0.439741i
$298$	0.943515	−	3.20478i	0.0546563	−	0.185648i
$299$	−1.08324	−	2.97618i	−0.0626454	−	0.172117i
$300$	4.03346	+	7.59958i	0.232872	+	0.438762i
$301$	−26.1191	+	31.1275i	−1.50548	+	1.79416i
$302$	−18.7558	+	8.19232i	−1.07928	+	0.471415i
$303$	−9.73485	+	27.9026i	−0.559253	+	1.60296i
$304$	−17.4354	+	0.0910265i	−0.999986	+	0.00522073i
$305$			6.24865i			0.357796i
$306$	−20.5464	−	5.45596i	−1.17456	−	0.311897i
$307$	0.0222037	+	0.0186311i	0.00126723	+	0.00106333i	0.643421	−	0.765513i	$-0.277514\pi$
$307$	0.0222037	+	0.0186311i	0.00126723	+	0.00106333i	−0.642154	+	0.766576i	$0.721959\pi$
$308$	21.0730	−	22.7490i	1.20075	−	1.29625i
$309$	−6.28895	+	0.0841703i	−0.357766	+	0.00478828i
$310$	−11.4600	−	3.37392i	−0.650884	−	0.191626i
$311$	−3.10782	+	1.79430i	−0.176229	+	0.101746i	−0.585519	−	0.810658i	$-0.699109\pi$
$311$	−3.10782	+	1.79430i	−0.176229	+	0.101746i	0.409291	+	0.912404i	$0.365776\pi$
$312$	3.16796	−	3.99012i	0.179350	−	0.225896i
$313$	−3.11658	−	17.6750i	−0.176159	−	0.999050i	−0.936797	−	0.349873i	$-0.886225\pi$
$313$	−3.11658	−	17.6750i	−0.176159	−	0.999050i	0.760638	−	0.649177i	$-0.224886\pi$
$314$	−16.6098	+	15.8146i	−0.937344	+	0.892468i
$315$	−21.8754	+	8.63177i	−1.23254	+	0.486345i
$316$	−0.0682776	−	0.541216i	−0.00384091	−	0.0304458i
$317$	−0.416975	−	0.496931i	−0.0234196	−	0.0279104i	0.754208	−	0.656636i	$-0.228021\pi$
$317$	−0.416975	−	0.496931i	−0.0234196	−	0.0279104i	−0.777627	+	0.628726i	$0.783577\pi$
$318$	7.49535	−	5.12486i	0.420318	−	0.287388i
$319$	−1.44866	+	3.98017i	−0.0811096	+	0.222847i
$320$	−12.0396	−	4.01188i	−0.673032	−	0.224271i
$321$	3.88417	−	6.94046i	0.216793	−	0.387379i
$322$	11.7765	+	17.7283i	0.656277	+	0.987960i
$323$	−5.31388	+	21.1847i	−0.295672	+	1.17875i
$324$	17.7404	+	3.04600i	0.985578	+	0.169222i
$325$	−0.448521	+	2.54369i	−0.0248795	+	0.141099i
$326$	1.89148	−	16.8499i	0.104759	−	0.933232i
$327$	5.68964	−	6.96793i	0.314638	−	0.385328i
$328$	−16.8482	−	28.2796i	−0.930285	−	1.56148i
$329$	−30.2498	−	36.0503i	−1.66773	−	1.98752i
$330$	−8.71610	+	8.52409i	−0.479805	+	0.469235i
$331$	−11.7597	+	20.3684i	−0.646372	+	1.11955i	0.337611	+	0.941286i	$0.390381\pi$
$331$	−11.7597	+	20.3684i	−0.646372	+	1.11955i	−0.983983	+	0.178264i	$0.942952\pi$
$332$	−13.5453	−	3.07985i	−0.743394	−	0.169029i
$333$	−11.5635	+	21.3271i	−0.633676	+	1.16872i
$334$	0.337318	+	5.36883i	0.0184572	+	0.293769i
$335$	−9.42939	−	16.3322i	−0.515182	−	0.892322i
$336$	−14.3893	+	31.0661i	−0.785001	+	1.69480i
$337$	−1.16886	−	3.21143i	−0.0636721	−	0.174938i	0.903777	−	0.428004i	$-0.140783\pi$
$337$	−1.16886	−	3.21143i	−0.0636721	−	0.174938i	−0.967449	+	0.253066i	$0.918561\pi$
$338$	−16.3830	+	3.96198i	−0.891117	+	0.215503i
$339$	12.8551	−	7.65306i	0.698191	−	0.415657i
$340$	−8.61374	+	13.3609i	−0.467145	+	0.724596i
$341$			16.7081i			0.904795i
$342$	2.87787	−	18.2679i	0.155618	−	0.987817i
$343$	−51.4917			−2.78029
$344$	−0.318769	−	23.2553i	−0.0171869	−	1.25384i
$345$	−4.28037	−	7.18986i	−0.230447	−	0.387089i
$346$	7.88366	+	32.5993i	0.423828	+	1.75255i
$347$	22.3916	−	8.14989i	1.20205	−	0.437509i	0.338108	−	0.941107i	$-0.390213\pi$
$347$	22.3916	−	8.14989i	1.20205	−	0.437509i	0.863938	+	0.503598i	$0.167991\pi$
$348$	0.166711	−	4.67345i	0.00893667	−	0.250523i
$349$	3.55209	−	2.05080i	0.190139	−	0.109777i	−0.401909	−	0.915680i	$-0.631653\pi$
$349$	3.55209	−	2.05080i	0.190139	−	0.109777i	0.592048	+	0.805903i	$0.298320\pi$
$350$	−1.08838	−	17.3230i	−0.0581766	−	0.925952i
$351$	3.63689	+	3.99684i	0.194123	+	0.213335i
$352$	−0.626995	+	17.7377i	−0.0334189	+	0.945421i
$353$	20.1176	+	11.6149i	1.07075	+	0.618197i	0.928386	−	0.371617i	$-0.121197\pi$
$353$	20.1176	+	11.6149i	1.07075	+	0.618197i	0.142363	+	0.989814i	$0.454530\pi$
$354$	−6.26832	−	6.40952i	−0.333157	−	0.340662i
$355$	0.899128	−	0.754458i	0.0477207	−	0.0400425i
$356$	0.714558	−	14.5592i	0.0378715	−	0.771638i
$357$	33.2196	+	27.1253i	1.75817	+	1.43562i
$358$	−1.86895	+	16.6492i	−0.0987771	+	0.879940i
$359$	15.7015	+	2.76860i	0.828694	+	0.146121i	0.571877	−	0.820339i	$-0.306215\pi$
$359$	15.7015	+	2.76860i	0.828694	+	0.146121i	0.256816	+	0.966460i	$0.417326\pi$
$360$	6.25293	−	11.9196i	0.329559	−	0.628220i
$361$	−18.8075	−	2.69768i	−0.989869	−	0.141983i
$362$	18.7371	−	12.4466i	0.984802	−	0.654180i
$363$	−1.74676	−	0.977558i	−0.0916809	−	0.0513085i
$364$	−9.14255	+	4.69666i	−0.479200	+	0.246172i
$365$	14.5543	+	5.29734i	0.761808	+	0.277275i
$366$	−7.96503	+	5.44600i	−0.416339	+	0.284667i
$367$	3.41680	−	2.86704i	0.178355	−	0.149658i	−0.549239	−	0.835665i	$-0.685083\pi$
$367$	3.41680	−	2.86704i	0.178355	−	0.149658i	0.727595	+	0.686007i	$0.240638\pi$
$368$	−11.7319	−	3.27993i	−0.611569	−	0.170978i
$369$	32.4779	−	12.8154i	1.69073	−	0.667141i
$370$	12.5097	+	13.1387i	0.650346	+	0.683047i
$371$	−18.0397	+	3.18088i	−0.936573	+	0.165143i
$372$	−5.68726	−	17.5484i	−0.294871	−	0.909841i
$373$	12.3831	+	21.4481i	0.641172	+	1.11054i	0.985171	+	0.171573i	$0.0548848\pi$
$373$	12.3831	+	21.4481i	0.641172	+	1.11054i	−0.344000	+	0.938970i	$0.611782\pi$
$374$	21.3282	+	6.27920i	1.10285	+	0.324690i
$375$	0.275170	+	20.5599i	0.0142097	+	1.06171i
$376$	26.5881	+	4.31332i	1.37118	+	0.222443i
$377$	0.902427	−	1.07547i	0.0464774	−	0.0553896i
$378$	−30.0682	−	20.3612i	−1.54654	−	1.04727i
$379$	15.5054			0.796460			0.398230	−	0.917286i	$-0.369625\pi$
$379$	15.5054			0.796460			0.398230	+	0.917286i	$0.369625\pi$
$380$	−12.3337	−	6.25482i	−0.632704	−	0.320866i
$381$	−15.1316	−	5.27922i	−0.775216	−	0.270463i
$382$	−2.96291	+	1.29416i	−0.151596	+	0.0662152i
$383$	15.5411	+	13.0406i	0.794114	+	0.666341i	0.946760	−	0.321940i	$-0.104335\pi$
$383$	15.5411	+	13.0406i	0.794114	+	0.666341i	−0.152646	+	0.988281i	$0.548779\pi$
$384$	−5.37919	−	18.8432i	−0.274506	−	0.961586i
$385$	23.1119	−	8.41205i	1.17789	−	0.428718i
$386$	11.9138	+	3.50752i	0.606395	+	0.178528i
$387$	24.3995	+	3.63190i	1.24029	+	0.184620i
$388$	9.10760	−	6.91059i	0.462368	−	0.350832i
$389$	−1.37382	−	7.79132i	−0.0696554	−	0.395035i	−0.999625	−	0.0273980i	$-0.991278\pi$
$389$	−1.37382	−	7.79132i	−0.0696554	−	0.395035i	0.929969	−	0.367637i	$-0.119833\pi$
$390$	3.68113	−	1.66688i	0.186401	−	0.0844059i
$391$	−7.62987	+	13.2153i	−0.385859	+	0.668328i
$392$	37.3061	−	32.1851i	1.88424	−	1.62559i
$393$	−1.35989	−	3.58620i	−0.0685974	−	0.180900i
$394$	3.41636	−	4.63301i	0.172114	−	0.233408i
$395$	0.147981	−	0.406575i	0.00744574	−	0.0204570i
$396$	−18.4620	−	3.68110i	−0.927750	−	0.184982i
$397$	19.8185	+	3.49454i	0.994664	+	0.175386i	0.647211	−	0.762311i	$-0.275935\pi$
$397$	19.8185	+	3.49454i	0.994664	+	0.175386i	0.347453	+	0.937697i	$0.387047\pi$
$398$	23.0640	−	15.3209i	1.15610	−	0.767966i
$399$	−20.4912	+	31.1777i	−1.02584	+	1.56084i
$400$	6.94846	+	7.10038i	0.347423	+	0.355019i
$401$	−1.54643	+	8.77024i	−0.0772251	+	0.437965i	0.921540	+	0.388283i	$0.126932\pi$
$401$	−1.54643	+	8.77024i	−0.0772251	+	0.437965i	−0.998765	+	0.0496817i	$0.984179\pi$
$402$	12.6002	−	26.2537i	0.628439	−	1.30942i
$403$	1.89412	−	5.20406i	0.0943529	−	0.259233i
$404$	−1.67276	+	34.0827i	−0.0832228	+	1.69568i
$405$	11.4119	+	8.57856i	0.567064	+	0.426272i
$406$	−4.19555	+	8.45006i	−0.208221	+	0.419370i
$407$	12.6864	−	21.9734i	0.628840	−	1.08918i
$408$	−24.5382	+	0.664890i	−1.21482	+	0.0329170i
$409$	18.8334	−	3.32084i	0.931253	−	0.164205i	0.312614	−	0.949880i	$-0.398795\pi$
$409$	18.8334	−	3.32084i	0.931253	−	0.164205i	0.618639	+	0.785675i	$0.287684\pi$
$410$	−1.63717	−	26.0575i	−0.0808539	−	1.28689i
$411$	2.26614	+	11.9170i	0.111780	+	0.587824i
$412$	−6.93807	+	2.14639i	−0.341814	+	0.105745i
$413$	6.18593	+	16.9957i	0.304390	+	0.836305i
$414$	5.43423	−	11.7224i	0.267078	−	0.576125i
$415$	−8.44002	−	7.08202i	−0.414304	−	0.347642i
$416$	2.20613	−	5.45366i	0.108164	−	0.267387i
$417$	−7.55029	−	2.63420i	−0.369739	−	0.128997i
$418$	−3.52008	+	19.0182i	−0.172173	+	0.930212i
$419$	−28.7311			−1.40361			−0.701803	−	0.712371i	$-0.747622\pi$
$419$	−28.7311			−1.40361			−0.701803	+	0.712371i	$0.747622\pi$
$420$	−21.4109	+	16.7022i	−1.04474	+	0.814982i
$421$	5.72383	+	4.80286i	0.278962	+	0.234077i	0.771524	−	0.636200i	$-0.219495\pi$
$421$	5.72383	+	4.80286i	0.278962	+	0.234077i	−0.492561	+	0.870278i	$0.663939\pi$
$422$	−7.90079	+	1.91069i	−0.384604	+	0.0930109i
$423$	−9.04939	+	27.0985i	−0.439996	+	1.31758i
$424$	6.62863	−	8.12325i	0.321915	−	0.394500i
$425$	10.7775	−	6.22238i	0.522785	−	0.301830i
$426$	1.74533	+	0.488555i	0.0845613	+	0.0236706i
$427$	19.1701	−	3.38020i	0.927706	−	0.163580i
$428$	2.03619	−	8.95524i	0.0984229	−	0.432868i
$429$	−3.69042	−	4.28041i	−0.178175	−	0.206660i
$430$	8.20345	−	16.5222i	0.395605	−	0.796771i
$431$	25.8287	−	21.6729i	1.24413	−	1.04394i	0.246935	−	0.969032i	$-0.420577\pi$
$431$	25.8287	−	21.6729i	1.24413	−	1.04394i	0.997190	−	0.0749128i	$-0.0238679\pi$
$432$	20.6435	−	2.41804i	0.993210	−	0.116338i
$433$	9.75874	−	26.8119i	0.468975	−	1.28850i	−0.449592	−	0.893234i	$-0.648431\pi$
$433$	9.75874	−	26.8119i	0.468975	−	1.28850i	0.918567	−	0.395264i	$-0.129347\pi$
$434$	−4.15151	+	36.9830i	−0.199279	+	1.77524i
$435$	1.81140	−	3.23671i	0.0868499	−	0.155188i
$436$	4.02693	−	9.57510i	0.192855	−	0.458564i
$437$	−12.1195	−	5.41656i	−0.579753	−	0.259109i
$438$	5.93237	+	23.1690i	0.283460	+	1.10706i
$439$	34.4159	+	6.06844i	1.64258	+	0.289631i	0.917113	−	0.398627i	$-0.130513\pi$
$439$	34.4159	+	6.06844i	1.64258	+	0.289631i	0.725466	+	0.688258i	$0.241624\pi$
$440$	−6.87095	+	12.2867i	−0.327560	+	0.585747i
$441$	27.3318	+	44.5428i	1.30151	+	2.12108i
$442$	−5.93122	−	4.37365i	−0.282119	−	0.208033i
$443$	−30.7028	+	25.7627i	−1.45874	+	1.22402i	−0.532856	+	0.846206i	$0.678881\pi$
$443$	−30.7028	+	25.7627i	−1.45874	+	1.22402i	−0.925880	+	0.377818i	$0.876674\pi$
$444$	−5.84486	+	27.3968i	−0.277385	+	1.30020i
$445$	5.78078	−	10.0126i	0.274035	−	0.474643i
$446$	−25.3473	+	24.1338i	−1.20023	+	1.14277i
$447$	4.03859	+	0.656511i	0.191019	+	0.0310519i
$448$	−5.79517	+	39.1062i	−0.273796	+	1.84759i
$449$	19.3230	+	33.4685i	0.911910	+	1.57947i	0.811363	+	0.584542i	$0.198726\pi$
$449$	19.3230	+	33.4685i	0.911910	+	1.57947i	0.100547	+	0.994932i	$0.467941\pi$
$450$	−8.61801	+	6.06329i	−0.406257	+	0.285826i
$451$	−34.3137	+	12.4892i	−1.61577	+	0.588091i
$452$	11.7396	−	12.6733i	0.552184	−	0.596100i
$453$	−12.8228	−	21.5388i	−0.602467	−	1.01198i
$454$	−5.98098	+	2.61242i	−0.280702	+	0.122607i
$455$	−8.15228			−0.382185
$456$	−2.77649	−	21.1729i	−0.130021	−	0.991511i
$457$	5.71367			0.267274			0.133637	−	0.991030i	$-0.457334\pi$
$457$	5.71367			0.267274			0.133637	+	0.991030i	$0.457334\pi$
$458$	11.6651	−	5.09516i	0.545074	−	0.238081i
$459$	3.48832	−	25.8015i	0.162821	−	1.20431i
$460$	−7.08817	−	6.56597i	−0.330488	−	0.306140i
$461$	3.19194	−	1.16177i	0.148663	−	0.0541091i	−0.266617	−	0.963803i	$-0.585906\pi$
$461$	3.19194	−	1.16177i	0.148663	−	0.0541091i	0.415280	+	0.909694i	$0.363684\pi$
$462$	30.8658	+	22.1288i	1.43601	+	1.02953i
$463$	6.75896	+	11.7069i	0.314115	+	0.544064i	0.979249	−	0.202660i	$-0.0649588\pi$
$463$	6.75896	+	11.7069i	0.314115	+	0.544064i	−0.665134	+	0.746724i	$0.731625\pi$
$464$	−1.34111	−	5.23068i	−0.0622593	−	0.242828i
$465$	2.34763	−	14.4416i	0.108869	−	0.669715i
$466$	−10.5197	+	10.0160i	−0.487315	+	0.463984i
$467$	2.64523	−	4.58167i	0.122407	−	0.212014i	−0.798310	−	0.602247i	$-0.794272\pi$
$467$	2.64523	−	4.58167i	0.122407	−	0.212014i	0.920716	+	0.390233i	$0.127605\pi$
$468$	5.33303	+	3.23950i	0.246519	+	0.149746i
$469$	−45.0043	+	37.7631i	−2.07811	+	1.74374i
$470$	17.1947	+	12.6793i	0.793132	+	0.584852i
$471$	−21.7569	−	17.7655i	−1.00251	−	0.818592i
$472$	−9.03524	−	5.05266i	−0.415881	−	0.232568i
$473$	−25.4075	−	4.48003i	−1.16824	−	0.205992i
$474$	0.647226	−	0.165721i	0.0297281	−	0.00761180i
$475$	6.35092	+	8.76743i	0.291400	+	0.402277i
$476$	45.6492	+	19.1983i	2.09233	+	0.879954i
$477$	7.37358	+	8.32448i	0.337613	+	0.381152i
$478$	2.09138	−	18.6307i	0.0956576	−	0.852150i
$479$	−13.1381	+	36.0966i	−0.600295	+	1.64930i	0.150383	+	0.988628i	$0.451949\pi$
$479$	−13.1381	+	36.0966i	−0.600295	+	1.64930i	−0.750678	+	0.660669i	$0.770273\pi$
$480$	3.03423	−	15.2434i	0.138493	−	0.695765i
$481$	−6.44244	+	5.40585i	−0.293750	+	0.246485i
$482$	1.89307	−	3.81274i	0.0862269	−	0.173666i
$483$	−19.7422	+	17.0210i	−0.898299	+	0.774483i
$484$	−2.25383	−	0.512462i	−0.102447	−	0.0232937i
$485$	8.93001	−	1.57460i	0.405491	−	0.0714990i
$486$	−0.988873	+	22.0232i	−0.0448562	+	0.998993i
$487$	11.1656	−	6.44644i	0.505960	−	0.292116i	−0.225211	−	0.974310i	$-0.572307\pi$
$487$	11.1656	−	6.44644i	0.505960	−	0.292116i	0.731171	+	0.682194i	$0.238974\pi$
$488$	−7.04400	+	8.63228i	−0.318867	+	0.390765i
$489$	20.7646	−	0.277910i	0.939009	−	0.0125675i
$490$	37.9843	−	9.18594i	1.71596	−	0.414979i
$491$	4.07285	+	3.41752i	0.183805	+	0.154231i	0.730048	−	0.683396i	$-0.239498\pi$
$491$	4.07285	+	3.41752i	0.183805	+	0.154231i	−0.546243	+	0.837627i	$0.683942\pi$
$492$	31.7882	−	24.7973i	1.43312	−	1.11795i
$493$	−6.76423			−0.304646
$494$	3.25241	−	5.52453i	0.146333	−	0.248560i
$495$	−11.6909	−	9.28814i	−0.525465	−	0.417471i
$496$	−12.0282	−	17.5796i	−0.540082	−	0.789349i
$497$	−2.80097	−	2.35029i	−0.125641	−	0.105425i
$498$	1.67143	−	16.9306i	0.0748987	−	0.758681i
$499$	0.910640	+	2.50196i	0.0407659	+	0.112003i	0.958405	−	0.285411i	$-0.0921300\pi$
$499$	0.910640	+	2.50196i	0.0407659	+	0.112003i	−0.917639	+	0.397414i	$0.869908\pi$
$500$	7.01702	+	22.6820i	0.313810	+	1.01437i
$501$	−6.47243	+	1.23079i	−0.289167	+	0.0549878i
$502$	0.103225	+	1.64295i	0.00460716	+	0.0733286i
$503$	18.3604	−	3.23743i	0.818649	−	0.144350i	0.251387	−	0.967887i	$-0.419113\pi$
$503$	18.3604	−	3.23743i	0.818649	−	0.144350i	0.567263	+	0.823537i	$0.308002\pi$
$504$	−39.9505	−	12.7353i	−1.77954	−	0.567276i
$505$	−13.5326	+	23.4392i	−0.602194	+	1.04303i
$506$	−6.00949	+	12.1035i	−0.267155	+	0.538064i
$507$	−7.31942	−	19.3022i	−0.325067	−	0.857241i
$508$	−18.4831	−	0.907138i	−0.820055	−	0.0402478i
$509$	2.15766	−	5.92812i	0.0956366	−	0.262759i	−0.882645	−	0.470041i	$-0.844239\pi$
$509$	2.15766	−	5.92812i	0.0956366	−	0.262759i	0.978281	+	0.207281i	$0.0664615\pi$
$510$	−17.5527	−	8.42420i	−0.777247	−	0.373030i
$511$	8.37844	−	47.5165i	0.370641	−	2.10201i
$512$	−12.1097	−	19.1143i	−0.535178	−	0.844739i
$513$	22.6386	+	0.703903i	0.999517	+	0.0310781i
$514$	12.5529	−	8.33856i	0.553683	−	0.367798i
$515$	−5.67274	−	1.00026i	−0.249971	−	0.0440766i
$516$	28.2102	−	3.94311i	1.24189	−	0.173586i
$517$	10.2195	−	28.0777i	0.449451	−	1.23486i
$518$	33.5408	−	45.4855i	1.47370	−	1.99852i
$519$	−38.4081	+	14.5644i	−1.68593	+	0.639306i
$520$	3.53298	−	3.04801i	0.154931	−	0.133664i
$521$	7.97277	−	13.8092i	0.349293	−	0.604994i	−0.636831	−	0.771004i	$-0.719755\pi$
$521$	7.97277	−	13.8092i	0.349293	−	0.604994i	0.986124	+	0.166010i	$0.0530884\pi$
$522$	5.70449	−	0.511992i	0.249679	−	0.0224093i
$523$	−4.92892	−	27.9533i	−0.215527	−	1.22231i	−0.879990	−	0.474992i	$-0.842451\pi$
$523$	−4.92892	−	27.9533i	−0.215527	−	1.22231i	0.664463	−	0.747321i	$-0.268660\pi$
$524$	−2.67699	−	3.52806i	−0.116945	−	0.154124i
$525$	20.8838	−	3.97126i	0.911445	−	0.173320i
$526$	26.1678	+	7.70402i	1.14097	+	0.335911i
$527$	−25.0736	+	9.12603i	−1.09222	+	0.397536i
$528$	−21.6500	+	1.95020i	−0.942197	+	0.0848717i
$529$	10.5141	+	8.82241i	0.457136	+	0.383583i
$530$	7.62060	−	3.32858i	0.331018	−	0.144584i
$531$	6.83018	−	8.59705i	0.296405	−	0.373080i
$532$	−12.5171	+	41.2218i	−0.542687	+	1.78719i
$533$	12.1035			0.524260
$534$	17.8011	−	1.35781i	0.770329	−	0.0587584i
$535$	4.68216	−	5.57998i	0.202427	−	0.241243i
$536$	5.38464	−	33.1919i	0.232581	−	1.43367i
$537$	−20.5173	+	0.274600i	−0.885387	+	0.0118499i
$538$	10.6699	+	3.14130i	0.460011	+	0.135431i
$539$	−27.3281	−	47.3336i	−1.17710	−	2.03880i
$540$	15.4404	+	5.77581i	0.664448	+	0.248551i
$541$	29.8980	−	5.27183i	1.28542	−	0.226654i	0.511138	−	0.859498i	$-0.329224\pi$
$541$	29.8980	−	5.27183i	1.28542	−	0.226654i	0.774279	+	0.632845i	$0.218113\pi$
$542$	−1.76021	−	1.84872i	−0.0756074	−	0.0794091i
$543$	17.9896	+	20.8656i	0.772007	+	0.895428i
$544$	−26.9611	+	8.74746i	−1.15595	+	0.375044i
$545$	6.31128	−	5.29579i	0.270346	−	0.226847i
$546$	−7.10511	−	10.3916i	−0.304070	−	0.444718i
$547$	2.25348	+	0.820200i	0.0963519	+	0.0350692i	0.389746	−	0.920922i	$-0.372563\pi$
$547$	2.25348	+	0.820200i	0.0963519	+	0.0350692i	−0.293394	+	0.955991i	$0.594785\pi$
$548$	6.40053	+	12.4593i	0.273417	+	0.532236i
$549$	−7.83563	−	8.84612i	−0.334417	−	0.377543i
$550$	9.17968	−	6.09783i	0.391423	−	0.260012i
$551$	−0.606779	−	5.85300i	−0.0258496	−	0.249346i
$552$	2.19183	−	14.7577i	0.0932907	−	0.628130i
$553$	−1.32737	−	0.234052i	−0.0564456	−	0.00995289i
$554$	−0.439288	+	3.91333i	−0.0186636	+	0.166261i
$555$	−14.0529	+	17.2102i	−0.596512	+	0.730532i
$556$	−9.22260	−	0.452639i	−0.391125	−	0.0191962i
$557$	−31.4422	+	26.3832i	−1.33225	+	1.11789i	−0.348704	+	0.937233i	$0.613378\pi$
$557$	−31.4422	+	26.3832i	−1.33225	+	1.11789i	−0.983546	+	0.180657i	$0.942178\pi$
$558$	20.4546	−	9.59411i	0.865911	−	0.406151i
$559$	7.40577	+	4.27572i	0.313231	+	0.180844i
$560$	−18.2616	+	25.4892i	−0.771694	+	1.07711i
$561$	−4.36916	+	26.8773i	−0.184466	+	1.13476i
$562$	0.818892	+	13.0337i	0.0345429	+	0.549792i
$563$	21.1369	−	12.2034i	0.890815	−	0.514312i	0.0166060	−	0.999862i	$-0.494714\pi$
$563$	21.1369	−	12.2034i	0.890815	−	0.514312i	0.874209	+	0.485550i	$0.161381\pi$
$564$	−1.17605	+	32.9684i	−0.0495206	+	1.38822i
$565$	12.8754	−	4.68627i	0.541673	−	0.197153i
$566$	−4.07026	−	16.8307i	−0.171086	−	0.707449i
$567$	20.1447	−	39.6510i	0.845998	−	1.66519i
$568$	2.09260	−	0.0286840i	0.0878036	−	0.00120356i
$569$	−27.4674			−1.15149			−0.575747	−	0.817628i	$-0.695289\pi$
$569$	−27.4674			−1.15149			−0.575747	+	0.817628i	$0.695289\pi$
$570$	5.71480	−	15.9438i	0.239367	−	0.667812i
$571$		−	16.1889i		−	0.677484i	−0.940879	−	0.338742i	$-0.889999\pi$
$571$		−	16.1889i		−	0.677484i	0.940879	−	0.338742i	$-0.110001\pi$
$572$	−5.48490	−	3.53611i	−0.229335	−	0.147852i
$573$	−2.02565	−	3.40255i	−0.0846229	−	0.142143i
$574$	−79.0558	+	19.1185i	−3.29972	+	0.797989i
$575$	2.58699	+	7.10769i	0.107885	+	0.296411i
$576$	22.0750	−	9.41772i	0.919793	−	0.392405i
$577$	4.00268	+	6.93284i	0.166634	+	0.288618i	0.937234	−	0.348701i	$-0.113377\pi$
$577$	4.00268	+	6.93284i	0.166634	+	0.288618i	−0.770601	+	0.637318i	$0.780044\pi$
$578$	0.718901	+	11.4422i	0.0299024	+	0.475933i
$579$	−2.44058	+	15.0135i	−0.101427	+	0.623939i
$580$	0.949584	−	4.17631i	0.0394293	−	0.173412i
$581$	−17.1611	+	29.7240i	−0.711964	+	1.23316i
$582$	9.79005	+	10.0106i	0.405811	+	0.414952i
$583$	−7.47593	−	8.90947i	−0.309622	−	0.368993i
$584$	14.1347	+	23.7249i	0.584897	+	0.981745i
$585$	2.58838	+	4.21831i	0.107016	+	0.174405i
$586$	3.02921	−	26.9852i	0.125135	−	1.11475i
$587$	−8.00172	+	45.3800i	−0.330266	+	1.87303i	0.139470	+	0.990226i	$0.455460\pi$
$587$	−8.00172	+	45.3800i	−0.330266	+	1.87303i	−0.469736	+	0.882807i	$0.655651\pi$
$588$	44.8143	+	40.4119i	1.84811	+	1.66656i
$589$	−10.1458	−	20.8772i	−0.418051	−	0.860228i
$590$	−4.54316	−	6.83928i	−0.187039	−	0.281569i
$591$	6.15222	+	3.44304i	0.253069	+	0.141628i
$592$	2.47062	+	32.2525i	0.101542	+	1.32557i
$593$	−13.4454	+	36.9410i	−0.552138	+	1.51699i	0.278648	+	0.960393i	$0.410114\pi$
$593$	−13.4454	+	36.9410i	−0.552138	+	1.51699i	−0.830786	+	0.556593i	$0.812108\pi$
$594$	1.65028	−	22.9972i	0.0677118	−	0.943585i
$595$	25.2476	+	30.0890i	1.03505	+	1.23353i
$596$	4.68742	−	0.591346i	0.192004	−	0.0242225i
$597$	22.1439	+	25.6840i	0.906288	+	1.05118i
$598$	3.24388	−	3.08858i	0.132652	−	0.126301i
$599$	−0.113045	−	0.641113i	−0.00461891	−	0.0261952i	0.982411	−	0.186730i	$-0.0597891\pi$
$599$	−0.113045	−	0.641113i	−0.00461891	−	0.0261952i	−0.987030	+	0.160535i	$0.948678\pi$
$600$	−7.56570	+	9.52916i	−0.308868	+	0.389027i
$601$	41.3592	−	23.8787i	1.68708	−	0.974034i	0.730338	−	0.683086i	$-0.239362\pi$
$601$	41.3592	−	23.8787i	1.68708	−	0.974034i	0.956739	−	0.290949i	$-0.0939708\pi$
$602$	−55.1258	−	16.2295i	−2.24676	−	0.661466i
$603$	33.8292	+	11.2970i	1.37763	+	0.460051i
$604$	−21.2342	−	19.6698i	−0.864007	−	0.800353i
$605$	−1.40435	−	1.17839i	−0.0570950	−	0.0479084i
$606$	−41.6718	+	3.17860i	−1.69280	+	0.129122i
$607$		−	24.3753i		−	0.989362i	−0.869074	−	0.494681i	$-0.835285\pi$
$607$		−	24.3753i		−	0.989362i	0.869074	−	0.494681i	$-0.164715\pi$
$608$	−9.98757	−	22.5444i	−0.405050	−	0.914295i
$609$	−10.9097	−	3.80625i	−0.442084	−	0.154237i
$610$	−8.09813	+	3.53716i	−0.327884	+	0.143215i
$611$	−6.36608	+	7.58680i	−0.257544	+	0.306929i
$612$	−4.55985	−	29.7162i	−0.184321	−	1.20121i
$613$	−10.1273	−	27.8247i	−0.409040	−	1.12383i	−0.957697	−	0.287780i	$-0.907083\pi$
$613$	−10.1273	−	27.8247i	−0.409040	−	1.12383i	0.548657	−	0.836048i	$-0.315139\pi$
$614$	−0.0115768	+	0.0393221i	−0.000467200	+	0.00158691i
$615$	31.4138	−	5.97364i	1.26673	−	0.240880i
$616$	41.4111	+	14.4328i	1.66850	+	0.581512i
$617$	30.2513	−	5.33411i	1.21787	−	0.214743i	0.472461	−	0.881351i	$-0.343366\pi$
$617$	30.2513	−	5.33411i	1.21787	−	0.214743i	0.745408	+	0.666608i	$0.232255\pi$
$618$	−3.66906	−	8.10271i	−0.147591	−	0.325939i
$619$	4.92979	+	2.84621i	0.198145	+	0.114399i	0.595790	−	0.803140i	$-0.296839\pi$
$619$	4.92979	+	2.84621i	0.198145	+	0.114399i	−0.397645	+	0.917539i	$0.630172\pi$
$620$	−2.11460	−	16.7618i	−0.0849244	−	0.673171i
$621$	15.0755	+	4.81111i	0.604961	+	0.193063i
$622$	−4.08462	−	3.01198i	−0.163778	−	0.120769i
$623$	−33.8446	−	12.3184i	−1.35595	−	0.493527i
$624$	6.96440	+	1.84694i	0.278799	+	0.0739367i
$625$	−1.11364	+	6.31577i	−0.0445456	+	0.252631i
$626$	21.1423	−	14.0443i	0.845014	−	0.561322i
$627$	−23.6485	−	1.36957i	−0.944429	−	0.0546955i
$628$	−29.8976	−	12.5738i	−1.19305	−	0.501750i
$629$	39.9045	+	7.03624i	1.59110	+	0.280553i
$630$	−23.5696	−	23.4639i	−0.939035	−	0.934826i
$631$	−29.0318	−	10.5667i	−1.15574	−	0.420655i	−0.308166	−	0.951333i	$-0.599715\pi$
$631$	−29.0318	−	10.5667i	−1.15574	−	0.420655i	−0.847573	+	0.530678i	$0.821937\pi$
$632$	0.662756	−	0.394852i	0.0263630	−	0.0157064i
$633$	−3.52983	−	9.30860i	−0.140298	−	0.369984i
$634$	0.407977	−	0.821688i	0.0162028	−	0.0326334i
$635$	−12.7111	−	7.33876i	−0.504425	−	0.291230i
$636$	10.8846	+	6.81281i	0.431602	+	0.270146i
$637$	3.14585	+	17.8410i	0.124643	+	0.706887i
$638$	−5.97827	+	0.375608i	−0.236682	+	0.0148705i
$639$	−0.326813	+	2.19556i	−0.0129285	+	0.0868549i
$640$	−1.61589	−	17.8740i	−0.0638739	−	0.706533i
$641$	3.71543	−	1.35231i	0.146751	−	0.0534129i	−0.267600	−	0.963530i	$-0.586231\pi$
$641$	3.71543	−	1.35231i	0.146751	−	0.0534129i	0.414351	+	0.910117i	$0.364009\pi$
$642$	11.1934	+	1.10504i	0.441769	+	0.0436124i
$643$	−19.9809	+	23.8123i	−0.787970	+	0.939066i	−0.999264	−	0.0383568i	$-0.987788\pi$
$643$	−19.9809	+	23.8123i	−0.787970	+	0.939066i	0.211294	+	0.977422i	$0.432232\pi$
$644$	−16.3093	+	25.2975i	−0.642675	+	0.996862i
$645$	21.3315	+	7.44227i	0.839926	+	0.293039i
$646$	−30.4630	+	5.10530i	−1.19855	+	0.200865i
$647$		−	26.9237i		−	1.05848i	−0.848472	−	0.529240i	$-0.822477\pi$
$647$		−	26.9237i		−	1.05848i	0.848472	−	0.529240i	$-0.177523\pi$
$648$	6.09472	+	24.7155i	0.239423	+	0.970915i
$649$	−7.38145	+	8.79687i	−0.289747	+	0.345307i
$650$	−3.55047	+	0.858628i	−0.139261	+	0.0336781i
$651$	−45.5752	+	0.609971i	−1.78623	+	0.0239066i
$652$	22.9079	−	7.08689i	0.897143	−	0.277544i
$653$	−5.64458	−	9.77669i	−0.220889	−	0.382591i	0.734189	−	0.678945i	$-0.237563\pi$
$653$	−5.64458	−	9.77669i	−0.220889	−	0.382591i	−0.955078	+	0.296354i	$0.904229\pi$
$654$	12.2510	+	3.42933i	0.479053	+	0.134098i
$655$	−0.609962	−	3.45927i	−0.0238332	−	0.135165i
$656$	27.1125	−	37.8431i	1.05857	−	1.47752i
$657$	−27.2471	+	10.7514i	−1.06301	+	0.419450i
$658$	29.5971	−	59.6101i	1.15381	−	2.32385i
$659$	−13.9648	−	16.6426i	−0.543990	−	0.648302i	0.422087	−	0.906555i	$-0.361298\pi$
$659$	−13.9648	−	16.6426i	−0.543990	−	0.648302i	−0.966077	+	0.258253i	$0.916853\pi$
$660$	−15.9810	−	6.47068i	−0.622058	−	0.251871i
$661$	−37.9075	−	13.7972i	−1.47443	−	0.536649i	−0.525131	−	0.851022i	$-0.675984\pi$
$661$	−37.9075	−	13.7972i	−1.47443	−	0.536649i	−0.949300	+	0.314373i	$0.898206\pi$
$662$	−33.0539	−	3.71044i	−1.28468	−	0.144211i
$663$	4.40781	−	7.87613i	0.171185	−	0.305884i
$664$	−3.67614	−	19.2978i	−0.142662	−	0.748902i
$665$	−23.7707	+	24.5455i	−0.921790	+	0.951835i
$666$	−34.1853	−	2.91347i	−1.32465	−	0.112895i
$667$	0.713912	−	4.04880i	0.0276428	−	0.156770i
$668$	−6.76696	+	3.47628i	−0.261821	+	0.134501i
$669$	−33.2021	−	27.1111i	−1.28367	−	1.04817i
$670$	15.8285	−	21.4654i	0.611509	−	0.829282i
$671$	7.94440	+	9.46777i	0.306690	+	0.365499i
$672$	−48.4064	−	1.06271i	−1.86732	−	0.0409950i
$673$	−11.5761	−	6.68346i	−0.446226	−	0.257629i	0.260009	−	0.965606i	$-0.416274\pi$
$673$	−11.5761	−	6.68346i	−0.446226	−	0.257629i	−0.706235	+	0.707978i	$0.749608\pi$
$674$	3.50029	−	3.33271i	0.134826	−	0.128371i
$675$	−8.68558	−	9.54521i	−0.334308	−	0.367395i
$676$	−14.4085	−	18.9893i	−0.554174	−	0.730357i
$677$	2.02447	−	1.16883i	0.0778068	−	0.0449218i	−0.460592	−	0.887612i	$-0.652363\pi$
$677$	2.02447	−	1.16883i	0.0778068	−	0.0449218i	0.538399	+	0.842690i	$0.319029\pi$
$678$	17.1951	+	12.3278i	0.660372	+	0.473445i
$679$	−9.66138	−	26.5444i	−0.370770	−	1.01868i
$680$	−22.1914	−	3.60006i	−0.851002	−	0.138056i
$681$	−4.08901	−	6.86843i	−0.156691	−	0.263199i
$682$	−21.6534	+	9.45793i	−0.829151	+	0.362163i
$683$			39.9439i			1.52841i	0.644973	+	0.764205i	$0.276869\pi$
$683$			39.9439i			1.52841i	−0.644973	+	0.764205i	$0.723131\pi$
$684$	25.3040	−	6.61124i	0.967522	−	0.252787i
$685$			11.1098i			0.424484i
$686$	−29.1478	−	66.7322i	−1.11287	−	2.54785i
$687$	7.97505	+	13.3959i	0.304267	+	0.511086i
$688$	29.9580	−	13.5772i	1.14214	−	0.517626i
$689$	1.31850	+	3.62254i	0.0502307	+	0.138008i
$690$	6.89494	−	9.61723i	0.262486	−	0.366122i
$691$	−0.524318	+	0.302715i	−0.0199460	+	0.0115158i	−0.509940	−	0.860210i	$-0.670332\pi$
$691$	−0.524318	+	0.302715i	−0.0199460	+	0.0115158i	0.489994	+	0.871726i	$0.336999\pi$
$692$	−37.7854	+	28.6705i	−1.43639	+	1.08989i
$693$	−22.1707	+	40.8906i	−0.842197	+	1.55330i
$694$	23.2373	+	24.4057i	0.882076	+	0.926429i
$695$	−6.34251	−	3.66185i	−0.240585	−	0.138902i
$696$	6.15107	−	2.42944i	0.233156	−	0.0920875i
$697$	−37.4845	−	44.6723i	−1.41983	−	1.69208i
$698$	4.66852	+	3.44255i	0.176706	+	0.130302i
$699$	−13.7796	−	11.2517i	−0.521192	−	0.425577i
$700$	21.8342	−	11.2165i	0.825253	−	0.423944i
$701$	2.80554	−	15.9110i	0.105964	−	0.600950i	−0.884867	−	0.465843i	$-0.845751\pi$
$701$	2.80554	−	15.9110i	0.105964	−	0.600950i	0.990831	−	0.135107i	$-0.0431377\pi$
$702$	−3.12109	+	6.97582i	−0.117798	+	0.263285i
$703$	−2.50877	+	35.1600i	−0.0946200	+	1.32608i
$704$	−23.3426	+	9.22817i	−0.879758	+	0.347800i
$705$	−12.7783	+	22.8330i	−0.481260	+	0.859942i
$706$	−3.66475	+	32.6468i	−0.137925	+	1.22868i
$707$	79.2291	+	28.8370i	2.97972	+	1.08453i
$708$	4.75832	−	11.7518i	0.178828	−	0.441661i
$709$	−30.4940	−	36.3414i	−1.14523	−	1.36483i	−0.920657	−	0.390372i	$-0.872347\pi$
$709$	−30.4940	−	36.3414i	−1.14523	−	1.36483i	−0.224571	−	0.974458i	$-0.572098\pi$
$710$	1.48673	+	0.738178i	0.0557960	+	0.0277033i
$711$	0.300339	+	0.761146i	0.0112636	+	0.0285452i
$712$	19.2730	−	7.31547i	0.722286	−	0.274159i
$713$	−2.81615	−	15.9712i	−0.105466	−	0.598126i
$714$	−16.3493	+	58.4067i	−0.611858	+	2.18581i
$715$	−2.58803	−	4.48261i	−0.0967870	−	0.167640i
$716$	−22.6351	+	7.00248i	−0.845912	+	0.261695i
$717$	22.9592	−	0.307282i	0.857425	−	0.0114756i
$718$	5.30007	+	21.9161i	0.197797	+	0.817900i
$719$	−14.4221	+	17.1876i	−0.537853	+	0.640988i	−0.964705	−	0.263334i	$-0.915178\pi$
$719$	−14.4221	+	17.1876i	−0.537853	+	0.640988i	0.426852	+	0.904321i	$0.359622\pi$
$720$	18.9872	+	1.35635i	0.707612	+	0.0505482i
$721$			17.9444i			0.668283i
$722$	−7.15020	−	25.9012i	−0.266103	−	0.963945i
$723$	4.92256	+	1.71742i	0.183072	+	0.0638714i
$724$	26.7371	+	17.2373i	0.993676	+	0.640621i
$725$	−2.15517	+	2.56843i	−0.0800410	+	0.0953891i
$726$	0.278113	−	2.81713i	0.0103217	−	0.104553i
$727$	21.4453	−	7.80545i	0.795362	−	0.289488i	0.0877988	−	0.996138i	$-0.472017\pi$
$727$	21.4453	−	7.80545i	0.795362	−	0.289488i	0.707563	+	0.706650i	$0.249795\pi$
$728$	−11.2621	−	9.18994i	−0.417401	−	0.340602i
$729$	−26.9130	+	2.16572i	−0.996778	+	0.0802120i
$730$	1.37349	+	21.8608i	0.0508351	+	0.809104i
$731$	−7.15457	−	40.5756i	−0.264621	−	1.50074i
$732$	−11.5667	−	7.23972i	−0.427516	−	0.267588i
$733$	38.6718	+	22.3272i	1.42838	+	0.824673i	0.996993	−	0.0774964i	$-0.0246926\pi$
$733$	38.6718	+	22.3272i	1.42838	+	0.824673i	0.431383	+	0.902169i	$0.358026\pi$
$734$	5.64976	+	2.80517i	0.208537	+	0.103541i
$735$	16.9702	+	44.7526i	0.625957	+	1.65072i
$736$	−2.39035	−	17.0610i	−0.0881093	−	0.628878i
$737$	−35.0515	−	12.7577i	−1.29114	−	0.469936i
$738$	34.9932	+	34.8363i	1.28812	+	1.28234i
$739$	−36.4514	−	6.42737i	−1.34089	−	0.236435i	−0.543249	−	0.839571i	$-0.682806\pi$
$739$	−36.4514	−	6.42737i	−1.34089	−	0.236435i	−0.797638	+	0.603137i	$0.793917\pi$
$740$	−9.94616	+	23.6497i	−0.365628	+	0.869379i
$741$	7.21050	+	3.10750i	0.264884	+	0.114157i
$742$	−14.3341	−	21.5785i	−0.526220	−	0.792171i
$743$	−4.92350	+	27.9226i	−0.180626	+	1.02438i	0.750822	+	0.660505i	$0.229658\pi$
$743$	−4.92350	+	27.9226i	−0.180626	+	1.02438i	−0.931448	+	0.363875i	$0.881453\pi$
$744$	19.5230	−	17.3042i	0.715748	−	0.634402i
$745$	3.52131	+	1.28165i	0.129011	+	0.0469561i
$746$	−20.7867	+	28.1894i	−0.761055	+	1.03209i
$747$	20.8291	−	0.557646i	0.762096	−	0.0204032i
$748$	3.93548	+	31.1954i	0.143895	+	1.14062i
$749$	−19.6515	−	11.3458i	−0.718050	−	0.414567i
$750$	−26.4895	+	11.9949i	−0.967258	+	0.437992i
$751$	2.22513	−	0.392350i	0.0811960	−	0.0143170i	−0.132903	−	0.991129i	$-0.542430\pi$
$751$	2.22513	−	0.392350i	0.0811960	−	0.0143170i	0.214099	+	0.976812i	$0.431319\pi$
$752$	9.46070	+	36.8993i	0.344996	+	1.34558i
$753$	−1.98067	+	0.376644i	−0.0721797	+	0.0137257i
$754$	1.90463	+	0.560738i	0.0693624	+	0.0204209i
$755$	−7.85190	−	21.5729i	−0.285760	−	0.785119i
$756$	9.36702	−	50.4937i	0.340675	−	1.83644i
$757$	7.52318	−	8.96577i	0.273435	−	0.325867i	−0.611799	−	0.791013i	$-0.709554\pi$
$757$	7.52318	−	8.96577i	0.273435	−	0.325867i	0.885234	+	0.465147i	$0.153998\pi$
$758$	8.77713	+	20.0947i	0.318800	+	0.729874i
$759$	−15.6265	−	5.45189i	−0.567207	−	0.197891i
$760$	1.12442	−	19.5249i	0.0407871	−	0.708241i
$761$		−	26.7857i		−	0.970981i	−0.874242	−	0.485490i	$-0.838641\pi$
$761$		−	26.7857i		−	0.970981i	0.874242	−	0.485490i	$-0.161359\pi$
$762$	−1.72376	−	22.5987i	−0.0624452	−	0.818664i
$763$	−19.6609	−	16.4975i	−0.711774	−	0.597249i
$764$	−3.35442	−	3.10730i	−0.121359	−	0.112418i
$765$	7.55296	−	22.6175i	0.273078	−	0.817736i
$766$	−8.10297	+	27.5228i	−0.292772	+	0.994441i
$767$	3.29635	−	1.90315i	0.119024	−	0.0687188i
$768$	21.3754	−	17.6378i	0.771317	−	0.636451i
$769$	−8.33939	−	47.2950i	−0.300726	−	1.70550i	−0.642971	−	0.765891i	$-0.722298\pi$
$769$	−8.33939	−	47.2950i	−0.300726	−	1.70550i	0.342245	−	0.939611i	$-0.388813\pi$
$770$	23.9848	+	25.1908i	0.864352	+	0.907814i
$771$	12.0521	+	13.9788i	0.434044	+	0.503435i
$772$	2.19833	+	17.4255i	0.0791197	+	0.627158i
$773$	−26.6136	−	31.7168i	−0.957224	−	1.14078i	−0.989965	−	0.141312i	$-0.954868\pi$
$773$	−26.6136	−	31.7168i	−0.957224	−	1.14078i	0.0327408	−	0.999464i	$-0.489576\pi$
$774$	9.10489	+	33.6771i	0.327268	+	1.21050i
$775$	−4.52353	+	12.4283i	−0.162490	+	0.446437i
$776$	14.1115	+	7.89140i	0.506574	+	0.283285i
$777$	60.4007	+	33.8028i	2.16686	+	1.21267i
$778$	9.31972	−	6.19086i	0.334128	−	0.221953i
$779$	35.2918	−	36.4421i	1.26446	−	1.30567i
$780$	4.24402	+	3.82710i	0.151960	+	0.137032i
$781$	0.403130	−	2.28626i	0.0144251	−	0.0818090i
$782$	−21.4458	−	2.40739i	−0.766902	−	0.0860881i
$783$	1.49437	+	6.85360i	0.0534046	+	0.244928i
$784$	62.8291	+	30.1291i	2.24390	+	1.07604i
$785$	−16.5358	−	19.7066i	−0.590187	−	0.703357i
$786$	3.87785	−	3.79242i	0.138318	−	0.135271i
$787$	4.08516	−	7.07571i	0.145620	−	0.252222i	−0.783984	−	0.620781i	$-0.786816\pi$
$787$	4.08516	−	7.07571i	0.145620	−	0.252222i	0.929604	+	0.368559i	$0.120149\pi$
$788$	7.93818	+	1.80494i	0.282786	+	0.0642982i
$789$	−5.36057	+	32.9761i	−0.190842	+	1.17398i
$790$	0.610680	−	0.0383684i	0.0217270	−	0.00136509i
$791$	−21.3419	−	36.9652i	−0.758830	−	1.31433i
$792$	−5.68012	−	26.0101i	−0.201834	−	0.924230i
$793$	−1.40112	−	3.84953i	−0.0497551	−	0.136701i
$794$	6.68979	+	27.6626i	0.237412	+	0.981709i
$795$	5.20996	+	8.75133i	0.184778	+	0.310378i
$796$	32.9114	+	21.2179i	1.16651	+	0.752048i
$797$		−	37.8968i		−	1.34237i	−0.741288	−	0.671187i	$-0.765785\pi$
$797$		−	37.8968i		−	1.34237i	0.741288	−	0.671187i	$-0.234215\pi$
$798$	−52.0051	−	8.90752i	−1.84096	−	0.315323i
$799$	47.7176			1.68813
$800$	−5.26866	+	13.0244i	−0.186275	+	0.460481i
$801$	4.37177	+	21.4236i	0.154469	+	0.756967i
$802$	−12.2415	+	2.96041i	−0.432261	+	0.104536i
$803$	28.7872	−	10.4777i	1.01588	−	0.369750i
$804$	41.1569	+	1.46815i	1.45149	+	0.0517777i
$805$	−20.6747	+	11.9366i	−0.728688	+	0.420708i
$806$	7.81656	−	0.491106i	0.275327	−	0.0172985i
$807$	−2.18577	+	13.4459i	−0.0769426	+	0.473320i
$808$	−45.1175	+	17.1253i	−1.58723	+	0.602466i
$809$	−10.0287	−	5.79005i	−0.352589	−	0.203567i	0.313236	−	0.949675i	$-0.398587\pi$
$809$	−10.0287	−	5.79005i	−0.352589	−	0.203567i	−0.665825	+	0.746108i	$0.731920\pi$
$810$	−4.65771	+	19.6457i	−0.163655	+	0.690280i
$811$	21.7826	−	18.2778i	0.764890	−	0.641819i	−0.174504	−	0.984656i	$-0.555832\pi$
$811$	21.7826	−	18.2778i	0.764890	−	0.641819i	0.939395	+	0.342837i	$0.111388\pi$
$812$	−13.3261	−	0.654035i	−0.467654	−	0.0229521i
$813$	1.97735	−	2.42161i	0.0693488	−	0.0849295i
$814$	35.6585	+	4.00283i	1.24983	+	0.140299i
$815$	18.7301	+	3.30261i	0.656085	+	0.115686i
$816$	−14.7520	−	31.4246i	−0.516422	−	1.10008i
$817$	34.4677	−	9.83055i	1.20587	−	0.343927i
$818$	14.9648	+	22.5279i	0.523230	+	0.787671i
$819$	11.5411	−	10.2227i	0.403278	−	0.357211i
$820$	32.8433	−	16.8721i	1.14694	−	0.589199i
$821$	−1.34621	−	0.489981i	−0.0469832	−	0.0171005i	0.318422	−	0.947949i	$-0.396847\pi$
$821$	−1.34621	−	0.489981i	−0.0469832	−	0.0171005i	−0.365405	+	0.930849i	$0.619069\pi$
$822$	−14.1615	+	9.68272i	−0.493937	+	0.337724i
$823$	−4.52495	+	3.79688i	−0.157730	+	0.132351i	−0.718237	−	0.695799i	$-0.755051\pi$
$823$	−4.52495	+	3.79688i	−0.157730	+	0.132351i	0.560507	+	0.828149i	$0.310606\pi$
$824$	−6.70911	−	7.77661i	−0.233723	−	0.270911i
$825$	8.81344	+	10.2224i	0.306845	+	0.355900i
$826$	−18.5245	+	17.6376i	−0.644548	+	0.613690i
$827$	31.0932	−	5.48258i	1.08122	−	0.190648i	0.395464	−	0.918481i	$-0.370584\pi$
$827$	31.0932	−	5.48258i	1.08122	−	0.190648i	0.685754	+	0.727834i	$0.259473\pi$
$828$	18.2682	+	0.406970i	0.634863	+	0.0141432i
$829$	7.29724	+	12.6392i	0.253443	+	0.438977i	0.964472	−	0.264187i	$-0.0851035\pi$
$829$	7.29724	+	12.6392i	0.253443	+	0.438977i	−0.711028	+	0.703164i	$0.751770\pi$
$830$	4.40053	−	14.9470i	0.152745	−	0.518818i
$831$	−4.82250	+	0.0645435i	−0.167291	+	0.00223899i
$832$	8.31665	−	0.228042i	0.288328	−	0.00790592i
$833$	56.1060	−	66.8646i	1.94396	−	2.31672i
$834$	−0.860111	−	11.2762i	−0.0297832	−	0.390462i
$835$	−6.03400			−0.208815
$836$	−26.6399	+	6.20366i	−0.921359	+	0.214558i
$837$	14.7859	+	23.3887i	0.511076	+	0.808431i
$838$	−16.2638	−	37.2350i	−0.561823	−	1.28626i
$839$	−20.2494	−	16.9913i	−0.699088	−	0.586604i	0.222426	−	0.974950i	$-0.428602\pi$
$839$	−20.2494	−	16.9913i	−0.699088	−	0.586604i	−0.921514	+	0.388345i	$0.873047\pi$
$840$	−33.7657	−	18.2935i	−1.16503	−	0.631187i
$841$	−25.5386	+	9.29528i	−0.880641	+	0.320527i
$842$	−2.98434	+	10.1367i	−0.102847	+	0.349335i
$843$	−15.7128	+	2.98794i	−0.541178	+	0.102910i
$844$	−6.94860	−	9.15769i	−0.239181	−	0.315221i
$845$	−3.28304	−	18.6190i	−0.112940	−	0.640514i
$846$	−40.2418	+	3.61180i	−1.38354	+	0.124176i
$847$	−2.85548	+	4.94583i	−0.0981154	+	0.169941i
$848$	14.2798	+	3.99226i	0.490372	+	0.137095i
$849$	19.8298	−	7.51947i	0.680555	−	0.258067i
$850$	14.1649	+	10.4451i	0.485851	+	0.358265i
$851$	−8.42321	+	23.1426i	−0.288744	+	0.793318i
$852$	0.354816	+	2.53847i	0.0121558	+	0.0869664i
$853$	10.4867	+	1.84909i	0.359057	+	0.0633115i	0.350267	−	0.936650i	$-0.386091\pi$
$853$	10.4867	+	1.84909i	0.359057	+	0.0633115i	0.00879035	+	0.999961i	$0.497202\pi$
$854$	15.2323	+	22.9307i	0.521237	+	0.784671i
$855$	20.2481	+	4.50659i	0.692471	+	0.154122i
$856$	12.7584	−	2.43042i	0.436075	−	0.0830699i
$857$	−2.23202	+	12.6584i	−0.0762444	+	0.432404i	0.922660	+	0.385614i	$0.126010\pi$
$857$	−2.23202	+	12.6584i	−0.0762444	+	0.432404i	−0.998905	+	0.0467899i	$0.985101\pi$
$858$	3.45830	−	7.20573i	0.118064	−	0.245999i
$859$	−2.80239	+	7.69950i	−0.0956162	+	0.262703i	−0.978275	−	0.207311i	$-0.933529\pi$
$859$	−2.80239	+	7.69950i	−0.0956162	+	0.262703i	0.882659	+	0.470014i	$0.155751\pi$
$860$	26.0562	+	1.27882i	0.888508	+	0.0436074i
$861$	−35.3197	−	93.1424i	−1.20369	−	3.17428i
$862$	42.7084	+	21.2052i	1.45465	+	0.722252i
$863$	−11.7746	+	20.3942i	−0.400812	+	0.694227i	−0.993824	−	0.110966i	$-0.964605\pi$
$863$	−11.7746	+	20.3942i	−0.400812	+	0.694227i	0.593012	+	0.805194i	$0.297939\pi$
$864$	14.8194	+	25.3848i	0.504165	+	0.863608i
$865$	−37.0487	+	6.53268i	−1.25969	+	0.222118i
$866$	40.2718	−	2.53024i	1.36849	−	0.0859810i
$867$	−13.7942	+	2.62310i	−0.468476	+	0.0890853i
$868$	−50.2793	+	15.5546i	−1.70659	+	0.527959i
$869$	−0.292694	−	0.804170i	−0.00992896	−	0.0272796i
$870$	5.22009	+	0.515339i	0.176978	+	0.0174716i
$871$	9.47118	+	7.94726i	0.320919	+	0.269283i
$872$	14.6887	−	0.201343i	0.497421	−	0.00681833i
$873$	−10.6676	+	13.4271i	−0.361043	+	0.454440i
$874$	0.159305	−	18.7727i	0.00538856	−	0.634997i
$875$	58.6639			1.98320
$876$	−26.6685	+	20.8035i	−0.901044	+	0.702885i
$877$	−9.01987	−	7.56857i	−0.304579	−	0.255572i	0.477668	−	0.878540i	$-0.341482\pi$
$877$	−9.01987	−	7.56857i	−0.304579	−	0.255572i	−0.782247	+	0.622968i	$0.785927\pi$
$878$	11.6171	+	48.0375i	0.392060	+	1.62119i
$879$	33.2546	−	0.445074i	1.12165	−	0.0150120i
$880$	−19.8128	−	1.94949i	−0.667889	−	0.0657174i
$881$	−8.99408	+	5.19274i	−0.303018	+	0.174948i	−0.643798	−	0.765195i	$-0.722642\pi$
$881$	−8.99408	+	5.19274i	−0.303018	+	0.174948i	0.340780	+	0.940143i	$0.389309\pi$
$882$	−42.2549	+	60.6357i	−1.42280	+	2.04171i
$883$	37.0973	−	6.54125i	1.24842	−	0.220131i	0.489901	−	0.871778i	$-0.337033\pi$
$883$	37.0973	−	6.54125i	1.24842	−	0.220131i	0.758522	+	0.651648i	$0.225922\pi$
$884$	2.31070	−	10.1625i	0.0777171	−	0.341803i
$885$	7.61619	−	6.56642i	0.256015	−	0.220728i
$886$	−50.7679	−	25.2068i	−1.70558	−	0.846839i
$887$	−5.78784	+	4.85657i	−0.194337	+	0.163068i	−0.734764	−	0.678323i	$-0.762707\pi$
$887$	−5.78784	+	4.85657i	−0.194337	+	0.163068i	0.540427	+	0.841391i	$0.318263\pi$
$888$	−38.8143	+	7.93364i	−1.30252	+	0.266236i
$889$	−15.6384	+	42.9660i	−0.524494	+	1.44103i
$890$	16.2485	+	1.82396i	0.544650	+	0.0611393i
$891$	28.1976	−	1.51092i	0.944657	−	0.0506179i
$892$	−45.6253	−	19.1883i	−1.52765	−	0.642471i
$893$	4.28046	+	41.2894i	0.143240	+	1.38170i
$894$	1.43529	+	5.60557i	0.0480034	+	0.187478i
$895$	−18.5070	−	3.26328i	−0.618620	−	0.109079i
$896$	−53.9613	+	14.6263i	−1.80272	+	0.488632i
$897$	4.24912	+	3.46960i	0.141874	+	0.115847i
$898$	−32.4363	+	43.9877i	−1.08241	+	1.46789i
$899$	5.50695	−	4.62088i	0.183667	−	0.154115i
$900$	−12.7363	−	7.73654i	−0.424543	−	0.257885i
$901$	9.28690	−	16.0854i	0.309392	−	0.535882i
$902$	−35.6096	−	37.4002i	−1.18567	−	1.24529i
$903$	11.2927	−	69.4683i	0.375799	−	2.31176i
$904$	23.0697	+	8.04035i	0.767287	+	0.267418i
$905$	12.6158	+	21.8512i	0.419364	+	0.726359i
$906$	20.6553	−	28.8105i	0.686226	−	0.957165i
$907$	−31.3511	+	11.4109i	−1.04100	+	0.378892i	−0.805258	−	0.592925i	$-0.797973\pi$
$907$	−31.3511	+	11.4109i	−1.04100	+	0.378892i	−0.235739	+	0.971817i	$0.575751\pi$
$908$	−6.77129	−	6.27243i	−0.224713	−	0.208158i
$909$	−10.2342	−	50.1521i	−0.339446	−	1.66344i
$910$	−4.61475	−	10.5652i	−0.152977	−	0.350233i
$911$	24.0855			0.797987			0.398994	−	0.916954i	$-0.369360\pi$
$911$	24.0855			0.797987			0.398994	+	0.916954i	$0.369360\pi$
$912$	25.8680	−	15.5836i	0.856574	−	0.516024i
$913$	−21.7920			−0.721210
$914$	3.23433	+	7.40481i	0.106982	+	0.244929i
$915$	−5.53644	−	9.29971i	−0.183029	−	0.307439i
$916$	13.2065	+	12.2335i	0.436354	+	0.404207i
$917$	−10.2827	+	3.74258i	−0.339563	+	0.123591i
$918$	35.4128	−	10.0846i	1.16880	−	0.332841i
$919$	−1.70089	−	2.94603i	−0.0561072	−	0.0971805i	0.836608	−	0.547803i	$-0.184536\pi$
$919$	−1.70089	−	2.94603i	−0.0561072	−	0.0971805i	−0.892715	+	0.450622i	$0.851202\pi$
$920$	4.49698	−	12.9029i	0.148261	−	0.425397i
$921$	−0.0495528	−	0.00805528i	−0.00163282	−	0.000265431i
$922$	3.31249	+	3.47905i	0.109091	+	0.114576i
$923$	−0.384746	+	0.666399i	−0.0126641	+	0.0219348i
$924$	−11.2064	+	52.5280i	−0.368662	+	1.72804i
$925$	15.3858	−	12.9102i	0.505881	−	0.424485i
$926$	−11.3458	+	15.3864i	−0.372847	+	0.505627i
$927$	9.28511	−	5.69741i	0.304963	−	0.187128i
$928$	6.01970	−	4.69897i	0.197606	−	0.154251i
$929$	−41.1904	−	7.26297i	−1.35141	−	0.238290i	−0.549381	−	0.835572i	$-0.685136\pi$
$929$	−41.1904	−	7.26297i	−1.35141	−	0.238290i	−0.802032	+	0.597282i	$0.796247\pi$
$930$	20.0450	−	5.13248i	0.657302	−	0.168301i
$931$	62.8899	+	42.5498i	2.06113	+	1.39451i
$932$	−18.9355	−	7.96354i	−0.620252	−	0.260854i
$933$	3.03551	−	5.42402i	0.0993781	−	0.177574i
$934$	7.43513	+	0.834627i	0.243285	+	0.0273098i
$935$	−8.52954	+	23.4347i	−0.278946	+	0.766397i
$936$	−1.17947	+	8.74528i	−0.0385522	+	0.285848i
$937$	13.1297	−	11.0171i	0.428928	−	0.359913i	−0.402619	−	0.915368i	$-0.631900\pi$
$937$	13.1297	−	11.0171i	0.428928	−	0.359913i	0.831547	+	0.555454i	$0.187456\pi$
$938$	−74.4158	−	36.9483i	−2.42976	−	1.20640i
$939$	20.2988	+	23.5439i	0.662425	+	0.768326i
$940$	−6.69875	+	29.4614i	−0.218489	+	0.960923i
$941$	36.8943	−	6.50546i	1.20272	−	0.212072i	0.463846	−	0.885916i	$-0.346469\pi$
$941$	36.8943	−	6.50546i	1.20272	−	0.212072i	0.738874	+	0.673844i	$0.235358\pi$
$942$	10.7079	−	38.2531i	0.348881	−	1.24635i
$943$	30.6952	−	17.7219i	0.999574	−	0.577104i
$944$	1.43359	−	14.5697i	0.0466594	−	0.474202i
$945$	24.9087	−	32.2285i	0.810281	−	1.04839i
$946$	−8.57636	−	35.4637i	−0.278841	−	1.15302i
$947$	−21.8347	−	18.3215i	−0.709533	−	0.595369i	0.214935	−	0.976628i	$-0.431046\pi$
$947$	−21.8347	−	18.3215i	−0.709533	−	0.595369i	−0.924468	+	0.381259i	$0.875490\pi$
$948$	0.581145	+	0.744983i	0.0188747	+	0.0241959i
$949$	−10.1541			−0.329617
$950$	−7.76737	+	13.1936i	−0.252007	+	0.428058i
$951$	1.06086	+	0.370122i	0.0344009	+	0.0120020i
$952$	0.959900	+	70.0281i	0.0311105	+	2.26962i
$953$	34.0599	+	28.5796i	1.10331	+	0.925785i	0.997643	−	0.0686164i	$-0.0218585\pi$
$953$	34.0599	+	28.5796i	1.10331	+	0.925785i	0.105665	+	0.994402i	$0.466303\pi$
$954$	−6.61442	+	14.2682i	−0.214150	+	0.461952i
$955$	−1.24039	−	3.40794i	−0.0401380	−	0.110278i
$956$	25.3289	−	7.83588i	0.819196	−	0.253430i
$957$	−1.37051	−	7.20714i	−0.0443022	−	0.232974i
$958$	−54.2176	+	3.40643i	−1.75169	+	0.110057i
$959$	34.0835	−	6.00985i	1.10061	−	0.194068i
$960$	21.4728	−	4.69653i	0.693032	−	0.151580i
$961$	−1.32122	+	2.28842i	−0.0426200	+	0.0738200i
$962$	−10.6527	−	5.28920i	−0.343458	−	0.170531i
$963$	0.368678	+	13.7708i	0.0118805	+	0.443757i
$964$	6.01285	+	0.295107i	0.193661	+	0.00950474i
$965$	−4.76455	+	13.0905i	−0.153376	+	0.421398i
$966$	−33.2343	−	15.9504i	−1.06930	−	0.513196i
$967$	0.441694	−	2.50497i	0.0142039	−	0.0805544i	−0.976882	−	0.213780i	$-0.931422\pi$
$967$	0.441694	−	2.50497i	0.0142039	−	0.0805544i	0.991086	+	0.133226i	$0.0425335\pi$
$968$	−0.611680	−	3.21101i	−0.0196602	−	0.103206i
$969$	−10.8616	−	36.2369i	−0.348925	−	1.16410i
$970$	7.09565	+	10.6818i	0.227828	+	0.342972i
$971$	−32.4997	−	5.73057i	−1.04296	−	0.183903i	−0.374178	−	0.927357i	$-0.622075\pi$
$971$	−32.4997	−	5.73057i	−1.04296	−	0.183903i	−0.668787	+	0.743454i	$0.733186\pi$
$972$	−29.1014	+	11.1851i	−0.933429	+	0.358762i
$973$	−7.80314	+	21.4390i	−0.250157	+	0.687301i
$974$	14.6749	+	10.8212i	0.470215	+	0.346735i
$975$	−1.58624	−	4.18311i	−0.0508004	−	0.133967i
$976$	−15.1747	−	4.24243i	−0.485729	−	0.135797i
$977$	−5.32164	+	9.21735i	−0.170254	+	0.294889i	−0.938509	−	0.345255i	$-0.887792\pi$
$977$	−5.32164	+	9.21735i	−0.170254	+	0.294889i	0.768254	+	0.640145i	$0.221126\pi$
$978$	12.1144	+	26.7532i	0.387375	+	0.855474i
$979$	−3.97095	−	22.5204i	−0.126912	−	0.719754i
$980$	33.4065	+	44.0271i	1.06713	+	1.40639i
$981$	−2.29401	+	15.4114i	−0.0732420	+	0.492047i
$982$	−2.12354	+	7.21288i	−0.0677648	+	0.230172i
$983$	37.6897	−	13.7179i	1.20211	−	0.437534i	0.338152	−	0.941091i	$-0.390198\pi$
$983$	37.6897	−	13.7179i	1.20211	−	0.437534i	0.863962	+	0.503558i	$0.167976\pi$
$984$	50.1311	+	27.1599i	1.59812	+	0.865827i
$985$	4.94625	+	4.15040i	0.157601	+	0.132243i
$986$	−3.82902	−	8.76632i	−0.121941	−	0.279176i
$987$	76.9615	+	26.8508i	2.44971	+	0.854672i
$988$	9.00077	+	1.08779i	0.286353	+	0.0346073i
$989$	25.0420			0.796290
$990$	5.41943	−	20.4088i	0.172241	−	0.648636i
$991$	30.9064	−	36.8328i	0.981775	−	1.17003i	−0.00366215	−	0.999993i	$-0.501166\pi$
$991$	30.9064	−	36.8328i	0.981775	−	1.17003i	0.985437	−	0.170041i	$-0.0543899\pi$
$992$	15.9741	−	25.5396i	0.507177	−	0.810883i
$993$	−0.545167	−	40.7332i	−0.0173003	−	1.29263i
$994$	1.46039	−	4.96043i	0.0463209	−	0.157335i
$995$	15.5291	+	26.8972i	0.492307	+	0.852700i
$996$	22.8879	−	7.41776i	0.725232	−	0.235041i
$997$	−56.6487	+	9.98869i	−1.79408	+	0.316345i	−0.968701	−	0.248232i	$-0.920151\pi$
$997$	−56.6487	+	9.98869i	−1.79408	+	0.316345i	−0.825381	+	0.564577i	$0.809039\pi$
$998$	−2.72701	+	2.59646i	−0.0863221	+	0.0821894i
$999$	−1.68661	−	41.9862i	−0.0533621	−	1.32838i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	456.2.bj.a.173.48	yes	456
3.2	odd	2	inner	456.2.bj.a.173.29	yes	456
8.5	even	2	inner	456.2.bj.a.173.21	yes	456
19.10	odd	18	inner	456.2.bj.a.29.56	yes	456
24.5	odd	2	inner	456.2.bj.a.173.56	yes	456
57.29	even	18	inner	456.2.bj.a.29.21	✓	456
152.29	odd	18	inner	456.2.bj.a.29.29	yes	456
456.29	even	18	inner	456.2.bj.a.29.48	yes	456

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bj.a.29.21	✓	456	57.29	even	18	inner
456.2.bj.a.29.29	yes	456	152.29	odd	18	inner
456.2.bj.a.29.48	yes	456	456.29	even	18	inner
456.2.bj.a.29.56	yes	456	19.10	odd	18	inner
456.2.bj.a.173.21	yes	456	8.5	even	2	inner
456.2.bj.a.173.29	yes	456	3.2	odd	2	inner
456.2.bj.a.173.48	yes	456	1.1	even	1	trivial
456.2.bj.a.173.56	yes	456	24.5	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.bj (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.566068 + 1.29598i) q^{2} +(-1.48828 + 0.886022i) q^{3} +(-1.35913 + 1.46723i) q^{4} +(-1.49063 + 0.542546i) q^{5} +(-1.99073 - 1.42723i) q^{6} +(2.47083 + 4.27960i) q^{7} +(-2.67086 - 0.930859i) q^{8} +(1.42993 - 2.63729i) q^{9} +O(q^{10})\)	\(q+(0.566068 + 1.29598i) q^{2} +(-1.48828 + 0.886022i) q^{3} +(-1.35913 + 1.46723i) q^{4} +(-1.49063 + 0.542546i) q^{5} +(-1.99073 - 1.42723i) q^{6} +(2.47083 + 4.27960i) q^{7} +(-2.67086 - 0.930859i) q^{8} +(1.42993 - 2.63729i) q^{9} +(-1.54693 - 1.62472i) q^{10} +(-1.56878 + 2.71721i) q^{11} +(0.722769 - 3.38786i) q^{12} +(0.796665 - 0.668481i) q^{13} +(-4.14762 + 5.62469i) q^{14} +(1.73777 - 2.12819i) q^{15} +(-0.305514 - 3.98832i) q^{16} +(-4.93455 - 0.870094i) q^{17} +(4.22732 + 0.360276i) q^{18} +(0.310232 - 4.34785i) q^{19} +(1.22993 - 2.92449i) q^{20} +(-7.46909 - 4.18001i) q^{21} +(-4.40949 - 0.494985i) q^{22} +(1.04161 - 2.86179i) q^{23} +(4.79974 - 0.981066i) q^{24} +(-1.90259 + 1.59646i) q^{25} +(1.31731 + 0.654057i) q^{26} +(0.208565 + 5.19197i) q^{27} +(-9.63732 - 2.19128i) q^{28} +(1.32946 - 0.234419i) q^{29} +(3.74179 + 1.04741i) q^{30} +(4.61174 - 2.66259i) q^{31} +(4.99584 - 2.65360i) q^{32} +(-0.0727270 - 5.43394i) q^{33} +(-1.66567 - 6.88761i) q^{34} +(-6.00498 - 5.03877i) q^{35} +(1.92604 + 5.68246i) q^{36} -8.08676 q^{37} +(5.81034 - 2.05912i) q^{38} +(-0.593368 + 1.70075i) q^{39} +(4.48631 - 0.0614955i) q^{40} +(8.91543 + 7.48094i) q^{41} +(1.18921 - 12.0460i) q^{42} +(2.81235 + 7.72687i) q^{43} +(-1.85458 - 5.99482i) q^{44} +(-0.700651 + 4.70704i) q^{45} +(4.29844 - 0.270067i) q^{46} +(-9.37853 + 1.65369i) q^{47} +(3.98842 + 5.66502i) q^{48} +(-8.70996 + 15.0861i) q^{49} +(-3.14598 - 1.56201i) q^{50} +(8.11489 - 3.07718i) q^{51} +(-0.101960 + 2.07744i) q^{52} +(-1.26782 + 3.48330i) q^{53} +(-6.61063 + 3.20930i) q^{54} +(0.864268 - 4.90151i) q^{55} +(-2.61553 - 13.7302i) q^{56} +(3.39058 + 6.74567i) q^{57} +(1.05637 + 1.59025i) q^{58} +(3.60440 + 0.635553i) q^{59} +(0.760687 + 5.44220i) q^{60} +(1.34726 - 3.70157i) q^{61} +(6.06123 + 4.46952i) q^{62} +(14.8196 - 0.396759i) q^{63} +(6.26700 + 4.97239i) q^{64} +(-0.824854 + 1.42869i) q^{65} +(7.00111 - 3.17023i) q^{66} +(2.06442 + 11.7079i) q^{67} +(7.98333 - 6.05753i) q^{68} +(0.985410 + 5.18201i) q^{69} +(3.13093 - 10.6346i) q^{70} +(-0.695293 + 0.253066i) q^{71} +(-6.27409 + 5.71277i) q^{72} +(-7.47954 - 6.27608i) q^{73} +(-4.57766 - 10.4803i) q^{74} +(1.41708 - 4.06171i) q^{75} +(5.95763 + 6.36448i) q^{76} -15.5048 q^{77} +(-2.54002 + 0.193745i) q^{78} +(-0.175322 + 0.208941i) q^{79} +(2.61926 + 5.77936i) q^{80} +(-4.91060 - 7.54228i) q^{81} +(-4.64841 + 15.7890i) q^{82} +(3.47275 + 6.01499i) q^{83} +(16.2845 - 5.27765i) q^{84} +(7.82767 - 1.38023i) q^{85} +(-8.42189 + 8.01869i) q^{86} +(-1.77090 + 1.52681i) q^{87} +(6.71934 - 5.79698i) q^{88} +(-5.58323 + 4.68488i) q^{89} +(-6.49685 + 1.75648i) q^{90} +(4.82925 + 1.75770i) q^{91} +(2.78321 + 5.41782i) q^{92} +(-4.50443 + 8.04877i) q^{93} +(-7.45203 - 11.2183i) q^{94} +(1.89647 + 6.64936i) q^{95} +(-5.08404 + 8.37571i) q^{96} +(-5.62946 - 0.992626i) q^{97} +(-24.4817 - 2.74818i) q^{98} +(4.92283 + 8.02276i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 456 q - 6 q^{4} - 6 q^{6} - 12 q^{7} - 12 q^{9}+O(q^{10}) \) 456 * q - 6 * q^4 - 6 * q^6 - 12 * q^7 - 12 * q^9	\( 456 q - 6 q^{4} - 6 q^{6} - 12 q^{7} - 12 q^{9} - 6 q^{10} - 9 q^{12} - 12 q^{15} - 6 q^{16} + 6 q^{24} - 24 q^{25} + 12 q^{28} - 6 q^{30} - 36 q^{31} + 6 q^{33} + 30 q^{34} - 66 q^{36} - 24 q^{39} - 42 q^{40} + 39 q^{42} - 18 q^{46} - 15 q^{48} - 168 q^{49} - 36 q^{52} - 45 q^{54} + 36 q^{55} - 12 q^{57} - 96 q^{58} - 18 q^{60} + 30 q^{63} - 48 q^{64} - 18 q^{66} - 78 q^{70} + 60 q^{72} - 12 q^{76} + 45 q^{78} - 24 q^{79} - 156 q^{82} - 9 q^{84} - 6 q^{87} - 90 q^{88} + 84 q^{90} - 162 q^{96} - 24 q^{97}+O(q^{100}) \) 456 * q - 6 * q^4 - 6 * q^6 - 12 * q^7 - 12 * q^9 - 6 * q^10 - 9 * q^12 - 12 * q^15 - 6 * q^16 + 6 * q^24 - 24 * q^25 + 12 * q^28 - 6 * q^30 - 36 * q^31 + 6 * q^33 + 30 * q^34 - 66 * q^36 - 24 * q^39 - 42 * q^40 + 39 * q^42 - 18 * q^46 - 15 * q^48 - 168 * q^49 - 36 * q^52 - 45 * q^54 + 36 * q^55 - 12 * q^57 - 96 * q^58 - 18 * q^60 + 30 * q^63 - 48 * q^64 - 18 * q^66 - 78 * q^70 + 60 * q^72 - 12 * q^76 + 45 * q^78 - 24 * q^79 - 156 * q^82 - 9 * q^84 - 6 * q^87 - 90 * q^88 + 84 * q^90 - 162 * q^96 - 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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