LMFDB - Embedded newform 273.2.bz.b.31.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(31,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 9]))

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

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

chi := DirichletCharacter("273.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bz (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			31.6
Character	$\chi$	$=$	273.31
Dual form			273.2.bz.b.229.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.612438 + 0.164102i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-1.38390 - 0.798995i) q^{4} +(0.690032 - 2.57523i) q^{5} +(0.448336 + 0.448336i) q^{6} +(-1.89836 - 1.84289i) q^{7} +(-1.61311 - 1.61311i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.612438 + 0.164102i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-1.38390 - 0.798995i) q^{4} +(0.690032 - 2.57523i) q^{5} +(0.448336 + 0.448336i) q^{6} +(-1.89836 - 1.84289i) q^{7} +(-1.61311 - 1.61311i) q^{8} +(0.500000 + 0.866025i) q^{9} +(0.845203 - 1.46393i) q^{10} +(4.30328 - 1.15306i) q^{11} +(-0.798995 - 1.38390i) q^{12} +(2.17576 - 2.87507i) q^{13} +(-0.860206 - 1.44018i) q^{14} +(1.88520 - 1.88520i) q^{15} +(0.874777 + 1.51516i) q^{16} +(-2.00699 + 3.47620i) q^{17} +(0.164102 + 0.612438i) q^{18} +(-1.13380 + 4.23139i) q^{19} +(-3.01253 + 3.01253i) q^{20} +(-0.722584 - 2.54517i) q^{21} +2.82471 q^{22} +(-3.04951 + 1.76064i) q^{23} +(-0.590438 - 2.20355i) q^{24} +(-1.82556 - 1.05399i) q^{25} +(1.80433 - 1.40376i) q^{26} +1.00000i q^{27} +(1.15468 + 4.06715i) q^{28} +0.379497 q^{29} +(1.46393 - 0.845203i) q^{30} +(10.1442 - 2.71812i) q^{31} +(1.46798 + 5.47858i) q^{32} +(4.30328 + 1.15306i) q^{33} +(-1.79961 + 1.79961i) q^{34} +(-6.05579 + 3.61707i) q^{35} -1.59799i q^{36} +(-0.0661642 + 0.246928i) q^{37} +(-1.38876 + 2.40541i) q^{38} +(3.32180 - 1.40200i) q^{39} +(-5.26722 + 3.04103i) q^{40} +(-7.78577 - 7.78577i) q^{41} +(-0.0248706 - 1.67733i) q^{42} -3.61181i q^{43} +(-6.87660 - 1.84258i) q^{44} +(2.57523 - 0.690032i) q^{45} +(-2.15656 + 0.577848i) q^{46} +(4.20803 + 1.12754i) q^{47} +1.74955i q^{48} +(0.207539 + 6.99692i) q^{49} +(-0.945080 - 0.945080i) q^{50} +(-3.47620 + 2.00699i) q^{51} +(-5.30821 + 2.24039i) q^{52} +(-5.54550 + 9.60509i) q^{53} +(-0.164102 + 0.612438i) q^{54} -11.8776i q^{55} +(0.0894843 + 6.03503i) q^{56} +(-3.09759 + 3.09759i) q^{57} +(0.232418 + 0.0622763i) q^{58} +(0.924065 + 3.44866i) q^{59} +(-4.11520 + 1.10266i) q^{60} +(12.0879 - 6.97894i) q^{61} +6.65872 q^{62} +(0.646807 - 2.56547i) q^{63} +0.0970831i q^{64} +(-5.90264 - 7.58699i) q^{65} +(2.44627 + 1.41236i) q^{66} +(3.38708 + 12.6408i) q^{67} +(5.55494 - 3.20714i) q^{68} -3.52127 q^{69} +(-4.30237 + 1.22146i) q^{70} +(-5.43926 + 5.43926i) q^{71} +(0.590438 - 2.20355i) q^{72} +(-2.09027 - 7.80100i) q^{73} +(-0.0810429 + 0.140370i) q^{74} +(-1.05399 - 1.82556i) q^{75} +(4.94993 - 4.94993i) q^{76} +(-10.2941 - 5.74153i) q^{77} +(2.26447 - 0.313525i) q^{78} +(1.48371 + 2.56986i) q^{79} +(4.50551 - 1.20725i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.49064 - 6.04596i) q^{82} +(8.78402 + 8.78402i) q^{83} +(-1.03359 + 4.09960i) q^{84} +(7.56715 + 7.56715i) q^{85} +(0.592706 - 2.21201i) q^{86} +(0.328654 + 0.189749i) q^{87} +(-8.80166 - 5.08164i) q^{88} +(-0.621191 - 0.166448i) q^{89} +1.69041 q^{90} +(-9.42882 + 1.44824i) q^{91} +5.62696 q^{92} +(10.1442 + 2.71812i) q^{93} +(2.39212 + 1.38109i) q^{94} +(10.1145 + 5.83959i) q^{95} +(-1.46798 + 5.47858i) q^{96} +(-7.39070 - 7.39070i) q^{97} +(-1.02111 + 4.31924i) q^{98} +(3.15022 + 3.15022i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{7} + 18 q^{9}+O(q^{10}) $ 36 * q + 4 * q^7 + 18 * q^9	$ 36 q + 4 q^{7} + 18 q^{9} + 4 q^{11} + 16 q^{12} - 36 q^{14} + 12 q^{16} - 4 q^{17} - 12 q^{19} - 44 q^{20} + 6 q^{21} - 8 q^{22} + 12 q^{23} - 18 q^{24} + 48 q^{25} - 28 q^{26} + 12 q^{28} - 16 q^{29} - 56 q^{32} + 4 q^{33} + 48 q^{34} + 8 q^{35} + 22 q^{37} - 16 q^{38} - 8 q^{39} + 60 q^{40} + 32 q^{41} + 12 q^{42} + 4 q^{44} - 44 q^{46} - 14 q^{47} - 6 q^{49} - 68 q^{50} + 12 q^{51} - 82 q^{52} - 8 q^{53} + 8 q^{56} - 6 q^{57} - 84 q^{58} + 70 q^{59} + 2 q^{60} + 36 q^{61} - 48 q^{62} + 2 q^{63} - 8 q^{65} + 38 q^{67} + 36 q^{68} + 8 q^{69} - 40 q^{70} - 36 q^{71} + 18 q^{72} - 46 q^{73} + 40 q^{74} - 10 q^{75} + 60 q^{76} - 60 q^{77} + 32 q^{78} - 38 q^{80} - 18 q^{81} - 24 q^{83} + 38 q^{84} + 44 q^{85} - 24 q^{86} + 36 q^{87} - 168 q^{88} + 38 q^{89} - 14 q^{91} - 40 q^{92} + 56 q^{96} - 36 q^{97} + 58 q^{98} + 8 q^{99}+O(q^{100}) $ 36 * q + 4 * q^7 + 18 * q^9 + 4 * q^11 + 16 * q^12 - 36 * q^14 + 12 * q^16 - 4 * q^17 - 12 * q^19 - 44 * q^20 + 6 * q^21 - 8 * q^22 + 12 * q^23 - 18 * q^24 + 48 * q^25 - 28 * q^26 + 12 * q^28 - 16 * q^29 - 56 * q^32 + 4 * q^33 + 48 * q^34 + 8 * q^35 + 22 * q^37 - 16 * q^38 - 8 * q^39 + 60 * q^40 + 32 * q^41 + 12 * q^42 + 4 * q^44 - 44 * q^46 - 14 * q^47 - 6 * q^49 - 68 * q^50 + 12 * q^51 - 82 * q^52 - 8 * q^53 + 8 * q^56 - 6 * q^57 - 84 * q^58 + 70 * q^59 + 2 * q^60 + 36 * q^61 - 48 * q^62 + 2 * q^63 - 8 * q^65 + 38 * q^67 + 36 * q^68 + 8 * q^69 - 40 * q^70 - 36 * q^71 + 18 * q^72 - 46 * q^73 + 40 * q^74 - 10 * q^75 + 60 * q^76 - 60 * q^77 + 32 * q^78 - 38 * q^80 - 18 * q^81 - 24 * q^83 + 38 * q^84 + 44 * q^85 - 24 * q^86 + 36 * q^87 - 168 * q^88 + 38 * q^89 - 14 * q^91 - 40 * q^92 + 56 * q^96 - 36 * q^97 + 58 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.612438	+	0.164102i	0.433059	+	0.116038i	0.468762	−	0.883325i	$-0.344700\pi$
$2$	0.612438	+	0.164102i	0.433059	+	0.116038i	−0.0357028	+	0.999362i	$0.511367\pi$
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	−1.38390	−	0.798995i	−0.691950	−	0.399498i
$5$	0.690032	−	2.57523i	0.308592	−	1.15168i	−0.621218	−	0.783638i	$-0.713362\pi$
$5$	0.690032	−	2.57523i	0.308592	−	1.15168i	0.929809	−	0.368042i	$-0.119972\pi$
$6$	0.448336	+	0.448336i	0.183032	+	0.183032i
$7$	−1.89836	−	1.84289i	−0.717513	−	0.696546i
$7$	−1.89836	−	1.84289i	−0.717513	−	0.696546i
$8$	−1.61311	−	1.61311i	−0.570320	−	0.570320i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	0.845203	−	1.46393i	0.267277	−	0.462937i
$11$	4.30328	−	1.15306i	1.29749	−	0.347661i	0.456988	−	0.889473i	$-0.348928\pi$
$11$	4.30328	−	1.15306i	1.29749	−	0.347661i	0.840500	+	0.541812i	$0.182262\pi$
$12$	−0.798995	−	1.38390i	−0.230650	−	0.399498i
$13$	2.17576	−	2.87507i	0.603448	−	0.797402i
$13$	2.17576	−	2.87507i	0.603448	−	0.797402i
$14$	−0.860206	−	1.44018i	−0.229900	−	0.384904i
$15$	1.88520	−	1.88520i	0.486757	−	0.486757i
$16$	0.874777	+	1.51516i	0.218694	+	0.378790i
$17$	−2.00699	+	3.47620i	−0.486766	+	0.843103i	−0.999884	−	0.0152149i	$-0.995157\pi$
$17$	−2.00699	+	3.47620i	−0.486766	+	0.843103i	0.513119	+	0.858318i	$0.328490\pi$
$18$	0.164102	+	0.612438i	0.0386793	+	0.144353i
$19$	−1.13380	+	4.23139i	−0.260111	+	0.970748i	0.705064	+	0.709144i	$0.250918\pi$
$19$	−1.13380	+	4.23139i	−0.260111	+	0.970748i	−0.965175	+	0.261604i	$0.915748\pi$
$20$	−3.01253	+	3.01253i	−0.673623	+	0.673623i
$21$	−0.722584	−	2.54517i	−0.157681	−	0.555401i
$22$	2.82471			0.602231
$23$	−3.04951	+	1.76064i	−0.635867	+	0.367118i	−0.783021	−	0.621996i	$-0.786322\pi$
$23$	−3.04951	+	1.76064i	−0.635867	+	0.367118i	0.147154	+	0.989114i	$0.452989\pi$
$24$	−0.590438	−	2.20355i	−0.120523	−	0.449797i
$25$	−1.82556	−	1.05399i	−0.365112	−	0.210797i
$26$	1.80433	−	1.40376i	0.353858	−	0.275299i
$27$			1.00000i			0.192450i
$28$	1.15468	+	4.06715i	0.218215	+	0.768619i
$29$	0.379497			0.0704709			0.0352354	−	0.999379i	$-0.488782\pi$
$29$	0.379497			0.0704709			0.0352354	+	0.999379i	$0.488782\pi$
$30$	1.46393	−	0.845203i	0.267277	−	0.154312i
$31$	10.1442	−	2.71812i	1.82195	−	0.488189i	0.824920	−	0.565250i	$-0.191220\pi$
$31$	10.1442	−	2.71812i	1.82195	−	0.488189i	0.997026	+	0.0770611i	$0.0245536\pi$
$32$	1.46798	+	5.47858i	0.259505	+	0.968486i
$33$	4.30328	+	1.15306i	0.749105	+	0.200722i
$34$	−1.79961	+	1.79961i	−0.308630	+	0.308630i
$35$	−6.05579	+	3.61707i	−1.02362	+	0.611396i
$36$		−	1.59799i		−	0.266332i
$37$	−0.0661642	+	0.246928i	−0.0108773	+	0.0405947i	−0.971151	−	0.238465i	$-0.923356\pi$
$37$	−0.0661642	+	0.246928i	−0.0108773	+	0.0405947i	0.960274	+	0.279059i	$0.0900226\pi$
$38$	−1.38876	+	2.40541i	−0.225287	+	0.390208i
$39$	3.32180	−	1.40200i	0.531914	−	0.224500i
$40$	−5.26722	+	3.04103i	−0.832821	+	0.480830i
$41$	−7.78577	−	7.78577i	−1.21593	−	1.21593i	−0.969044	−	0.246889i	$-0.920592\pi$
$41$	−7.78577	−	7.78577i	−1.21593	−	1.21593i	−0.246889	−	0.969044i	$-0.579408\pi$
$42$	−0.0248706	−	1.67733i	−0.00383762	−	0.258818i
$43$		−	3.61181i		−	0.550796i	−0.961330	−	0.275398i	$-0.911190\pi$
$43$		−	3.61181i		−	0.550796i	0.961330	−	0.275398i	$-0.0888096\pi$
$44$	−6.87660	−	1.84258i	−1.03669	−	0.277779i
$45$	2.57523	−	0.690032i	0.383893	−	0.102864i
$46$	−2.15656	+	0.577848i	−0.317967	+	0.0851991i
$47$	4.20803	+	1.12754i	0.613804	+	0.164468i	0.552310	−	0.833639i	$-0.313747\pi$
$47$	4.20803	+	1.12754i	0.613804	+	0.164468i	0.0614946	+	0.998107i	$0.480413\pi$
$48$			1.74955i			0.252526i
$49$	0.207539	+	6.99692i	0.0296484	+	0.999560i
$50$	−0.945080	−	0.945080i	−0.133654	−	0.133654i
$51$	−3.47620	+	2.00699i	−0.486766	+	0.281034i
$52$	−5.30821	+	2.24039i	−0.736116	+	0.310686i
$53$	−5.54550	+	9.60509i	−0.761733	+	1.31936i	0.180223	+	0.983626i	$0.442318\pi$
$53$	−5.54550	+	9.60509i	−0.761733	+	1.31936i	−0.941957	+	0.335735i	$0.891015\pi$
$54$	−0.164102	+	0.612438i	−0.0223315	+	0.0833422i
$55$		−	11.8776i		−	1.60158i
$56$	0.0894843	+	6.03503i	0.0119578	+	0.806465i
$57$	−3.09759	+	3.09759i	−0.410286	+	0.410286i
$58$	0.232418	+	0.0622763i	0.0305180	+	0.00817728i
$59$	0.924065	+	3.44866i	0.120303	+	0.448977i	0.999629	−	0.0272437i	$-0.00867302\pi$
$59$	0.924065	+	3.44866i	0.120303	+	0.448977i	−0.879326	+	0.476221i	$0.842006\pi$
$60$	−4.11520	+	1.10266i	−0.531270	+	0.142353i
$61$	12.0879	−	6.97894i	1.54769	−	0.893561i	0.549377	−	0.835575i	$-0.314865\pi$
$61$	12.0879	−	6.97894i	1.54769	−	0.893561i	0.998317	−	0.0579866i	$-0.0184681\pi$
$62$	6.65872			0.845658
$63$	0.646807	−	2.56547i	0.0814900	−	0.323219i
$64$			0.0970831i			0.0121354i
$65$	−5.90264	−	7.58699i	−0.732133	−	0.941051i
$66$	2.44627	+	1.41236i	0.301115	+	0.173849i
$67$	3.38708	+	12.6408i	0.413798	+	1.54431i	0.787231	+	0.616658i	$0.211514\pi$
$67$	3.38708	+	12.6408i	0.413798	+	1.54431i	−0.373434	+	0.927657i	$0.621820\pi$
$68$	5.55494	−	3.20714i	0.673635	−	0.388923i
$69$	−3.52127			−0.423911
$70$	−4.30237	+	1.22146i	−0.514231	+	0.145993i
$71$	−5.43926	+	5.43926i	−0.645522	+	0.645522i	−0.951907	−	0.306386i	$-0.900880\pi$
$71$	−5.43926	+	5.43926i	−0.645522	+	0.645522i	0.306386	+	0.951907i	$0.400880\pi$
$72$	0.590438	−	2.20355i	0.0695838	−	0.259690i
$73$	−2.09027	−	7.80100i	−0.244648	−	0.913038i	−0.973560	−	0.228431i	$-0.926640\pi$
$73$	−2.09027	−	7.80100i	−0.244648	−	0.913038i	0.728912	−	0.684607i	$-0.240026\pi$
$74$	−0.0810429	+	0.140370i	−0.00942105	+	0.0163177i
$75$	−1.05399	−	1.82556i	−0.121704	−	0.210797i
$76$	4.94993	−	4.94993i	0.567795	−	0.567795i
$77$	−10.2941	−	5.74153i	−1.17313	−	0.654308i
$78$	2.26447	−	0.313525i	0.256401	−	0.0354998i
$79$	1.48371	+	2.56986i	0.166931	+	0.289132i	0.937339	−	0.348418i	$-0.113281\pi$
$79$	1.48371	+	2.56986i	0.166931	+	0.289132i	−0.770409	+	0.637551i	$0.779948\pi$
$80$	4.50551	−	1.20725i	0.503731	−	0.134974i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−3.49064	−	6.04596i	−0.385476	−	0.667665i
$83$	8.78402	+	8.78402i	0.964171	+	0.964171i	0.999380	−	0.0352090i	$-0.0112097\pi$
$83$	8.78402	+	8.78402i	0.964171	+	0.964171i	−0.0352090	+	0.999380i	$0.511210\pi$
$84$	−1.03359	+	4.09960i	−0.112774	+	0.447303i
$85$	7.56715	+	7.56715i	0.820773	+	0.820773i
$86$	0.592706	−	2.21201i	0.0639131	−	0.238527i
$87$	0.328654	+	0.189749i	0.0352354	+	0.0203432i
$88$	−8.80166	−	5.08164i	−0.938260	−	0.541705i
$89$	−0.621191	−	0.166448i	−0.0658461	−	0.0176434i	0.225746	−	0.974186i	$-0.427518\pi$
$89$	−0.621191	−	0.166448i	−0.0658461	−	0.0176434i	−0.291592	+	0.956543i	$0.594185\pi$
$90$	1.69041			0.178184
$91$	−9.42882	+	1.44824i	−0.988409	+	0.151817i
$92$	5.62696			0.586651
$93$	10.1442	+	2.71812i	1.05190	+	0.281856i
$94$	2.39212	+	1.38109i	0.246729	+	0.142449i
$95$	10.1145	+	5.83959i	1.03772	+	0.599129i
$96$	−1.46798	+	5.47858i	−0.149825	+	0.559156i
$97$	−7.39070	−	7.39070i	−0.750412	−	0.750412i	0.224144	−	0.974556i	$-0.428041\pi$
$97$	−7.39070	−	7.39070i	−0.750412	−	0.750412i	−0.974556	+	0.224144i	$0.928041\pi$
$98$	−1.02111	+	4.31924i	−0.103147	+	0.436309i
$99$	3.15022	+	3.15022i	0.316609	+	0.316609i
$100$	1.68426	+	2.91723i	0.168426	+	0.291723i
$101$	0.273020	−	0.472884i	0.0271665	−	0.0470537i	−0.852123	−	0.523342i	$-0.824685\pi$
$101$	0.273020	−	0.472884i	0.0271665	−	0.0470537i	0.879289	+	0.476289i	$0.158018\pi$
$102$	−2.45831	+	0.658702i	−0.243409	+	0.0652212i
$103$	1.32112	+	2.28824i	0.130173	+	0.225467i	0.923743	−	0.383012i	$-0.125113\pi$
$103$	1.32112	+	2.28824i	0.130173	+	0.225467i	−0.793570	+	0.608479i	$0.791780\pi$
$104$	−8.14754	+	1.12806i	−0.798932	+	0.110616i
$105$	−7.05301	+	0.104578i	−0.688303	+	0.0102058i
$106$	−4.97249	+	4.97249i	−0.482971	+	0.482971i
$107$	−2.75251	−	4.76749i	−0.266096	−	0.460891i	0.701755	−	0.712419i	$-0.252400\pi$
$107$	−2.75251	−	4.76749i	−0.266096	−	0.460891i	−0.967850	+	0.251528i	$0.919067\pi$
$108$	0.798995	−	1.38390i	0.0768833	−	0.133166i
$109$	3.27311	+	12.2154i	0.313507	+	1.17002i	0.925372	+	0.379061i	$0.123753\pi$
$109$	3.27311	+	12.2154i	0.313507	+	1.17002i	−0.611865	+	0.790962i	$0.709580\pi$
$110$	1.94914	−	7.27429i	0.185843	−	0.693577i
$111$	−0.180764	+	0.180764i	−0.0171574	+	0.0171574i
$112$	1.13162	−	4.48843i	0.106928	−	0.424117i
$113$	−7.54675			−0.709939			−0.354969	−	0.934878i	$-0.615509\pi$
$113$	−7.54675			−0.709939			−0.354969	+	0.934878i	$0.615509\pi$
$114$	−2.40541	+	1.38876i	−0.225287	+	0.130069i
$115$	2.42979	+	9.06809i	0.226579	+	0.845604i
$116$	−0.525186	−	0.303216i	−0.0487623	−	0.0281529i
$117$	3.57777	+	0.446730i	0.330765	+	0.0413002i
$118$			2.26373i			0.208393i
$119$	10.2162	−	2.90043i	0.936520	−	0.265882i
$120$	−6.08207			−0.555214
$121$	7.66239	−	4.42389i	0.696581	−	0.402171i
$122$	8.54833	−	2.29052i	0.773930	−	0.207374i
$123$	−2.84979	−	10.6356i	−0.256957	−	0.958976i
$124$	−16.2103	−	4.34353i	−1.45573	−	0.390061i
$125$	5.45205	−	5.45205i	0.487646	−	0.487646i
$126$	0.817128	−	1.46505i	0.0727956	−	0.130517i
$127$		−	8.81008i		−	0.781768i	−0.920440	−	0.390884i	$-0.872169\pi$
$127$		−	8.81008i		−	0.781768i	0.920440	−	0.390884i	$-0.127831\pi$
$128$	2.92003	−	10.8977i	0.258097	−	0.963231i
$129$	1.80591	−	3.12792i	0.159001	−	0.275398i
$130$	−2.36996	−	5.61520i	−0.207859	−	0.492486i
$131$	4.36467	−	2.51994i	0.381343	−	0.220168i	−0.297059	−	0.954859i	$-0.596006\pi$
$131$	4.36467	−	2.51994i	0.381343	−	0.220168i	0.678402	+	0.734691i	$0.262673\pi$
$132$	−5.03402	−	5.03402i	−0.438155	−	0.438155i
$133$	9.95033	−	5.94324i	0.862803	−	0.515344i
$134$			8.29751i			0.716795i
$135$	2.57523	+	0.690032i	0.221641	+	0.0593885i
$136$	8.84497	−	2.37000i	0.758450	−	0.203226i
$137$	−21.6500	+	5.80111i	−1.84969	+	0.495622i	−0.999523	−	0.0308968i	$-0.990164\pi$
$137$	−21.6500	+	5.80111i	−1.84969	+	0.495622i	−0.850164	+	0.526519i	$0.823497\pi$
$138$	−2.15656	−	0.577848i	−0.183578	−	0.0491897i
$139$		−	2.70096i		−	0.229092i	−0.993418	−	0.114546i	$-0.963459\pi$
$139$		−	2.70096i		−	0.229092i	0.993418	−	0.114546i	$-0.0365413\pi$
$140$	11.2706	−	0.167115i	0.952542	−	0.0141238i
$141$	3.08049	+	3.08049i	0.259424	+	0.259424i
$142$	−4.22380	+	2.43861i	−0.354454	+	0.204644i
$143$	6.04779	−	14.8810i	0.505742	−	1.24441i
$144$	−0.874777	+	1.51516i	−0.0728981	+	0.126263i
$145$	0.261865	−	0.977294i	0.0217467	−	0.0811598i
$146$		−	5.12065i		−	0.423788i
$147$	−3.31873	+	6.16328i	−0.273724	+	0.508339i
$148$	0.288859	−	0.288859i	0.0237441	−	0.0237441i
$149$	3.62891	+	0.972364i	0.297292	+	0.0796592i	0.404382	−	0.914590i	$-0.367487\pi$
$149$	3.62891	+	0.972364i	0.297292	+	0.0796592i	−0.107090	+	0.994249i	$0.534153\pi$
$150$	−0.345923	−	1.29100i	−0.0282445	−	0.105410i
$151$	2.30870	−	0.618613i	0.187879	−	0.0503420i	−0.163653	−	0.986518i	$-0.552328\pi$
$151$	2.30870	−	0.618613i	0.187879	−	0.0503420i	0.351532	+	0.936176i	$0.385661\pi$
$152$	8.65463	−	4.99675i	0.701983	−	0.405290i
$153$	−4.01397			−0.324510
$154$	−5.36232	−	5.20562i	−0.432108	−	0.419481i
$155$		−	27.9992i		−	2.24895i
$156$	−5.71724	−	0.713870i	−0.457746	−	0.0571554i
$157$	5.15461	+	2.97601i	0.411382	+	0.237512i	0.691384	−	0.722488i	$-0.257002\pi$
$157$	5.15461	+	2.97601i	0.411382	+	0.237512i	−0.280001	+	0.960000i	$0.590335\pi$
$158$	0.486961	+	1.81736i	0.0387405	+	0.144582i
$159$	−9.60509	+	5.54550i	−0.761733	+	0.439787i
$160$	15.1216			1.19547
$161$	9.03372	+	2.27758i	0.711957	+	0.179499i
$162$	−0.448336	+	0.448336i	−0.0352246	+	0.0352246i
$163$	−1.16232	+	4.33782i	−0.0910396	+	0.339764i	−0.996389	−	0.0849025i	$-0.972942\pi$
$163$	−1.16232	+	4.33782i	−0.0910396	+	0.339764i	0.905350	+	0.424667i	$0.139609\pi$
$164$	4.55393	+	16.9955i	0.355603	+	1.32713i
$165$	5.93880	−	10.2863i	0.462335	−	0.800788i
$166$	3.93819	+	6.82114i	0.305663	+	0.529423i
$167$	3.94806	−	3.94806i	0.305510	−	0.305510i	−0.537655	−	0.843165i	$-0.680690\pi$
$167$	3.94806	−	3.94806i	0.305510	−	0.305510i	0.843165	+	0.537655i	$0.180690\pi$
$168$	−2.94002	+	5.27123i	−0.226827	+	0.406684i
$169$	−3.53210	−	12.5110i	−0.271700	−	0.962382i
$170$	3.39262	+	5.87619i	0.260202	+	0.450684i
$171$	−4.23139	+	1.13380i	−0.323583	+	0.0867037i
$172$	−2.88582	+	4.99839i	−0.220042	+	0.381123i
$173$	−4.34592	−	7.52735i	−0.330414	−	0.572294i	0.652179	−	0.758065i	$-0.273855\pi$
$173$	−4.34592	−	7.52735i	−0.330414	−	0.572294i	−0.982593	+	0.185771i	$0.940522\pi$
$174$	0.170142	+	0.170142i	0.0128984	+	0.0128984i
$175$	1.52319	+	5.36514i	0.115142	+	0.405567i
$176$	5.51148	+	5.51148i	0.415443	+	0.415443i
$177$	−0.924065	+	3.44866i	−0.0694570	+	0.259217i
$178$	−0.353126	−	0.203878i	−0.0264679	−	0.0152813i
$179$	2.57505	+	1.48671i	0.192469	+	0.111122i	0.593138	−	0.805101i	$-0.297889\pi$
$179$	2.57505	+	1.48671i	0.192469	+	0.111122i	−0.400669	+	0.916223i	$0.631222\pi$
$180$	−4.11520	−	1.10266i	−0.306729	−	0.0821877i
$181$	−14.0519			−1.04447			−0.522235	−	0.852802i	$-0.674902\pi$
$181$	−14.0519			−1.04447			−0.522235	+	0.852802i	$0.674902\pi$
$182$	−6.01222	−	0.660334i	−0.445656	−	0.0489472i
$183$	13.9579			1.03180
$184$	7.75928	+	2.07909i	0.572022	+	0.153273i
$185$	0.590242	+	0.340777i	0.0433955	+	0.0250544i
$186$	5.76662	+	3.32936i	0.422829	+	0.244121i
$187$	−4.62835	+	17.2732i	−0.338459	+	1.26314i
$188$	−4.92260	−	4.92260i	−0.359017	−	0.359017i
$189$	1.84289	−	1.89836i	0.134050	−	0.138085i
$190$	5.23619	+	5.23619i	0.379873	+	0.379873i
$191$	−2.73812	−	4.74256i	−0.198123	−	0.343160i	0.749797	−	0.661668i	$-0.230151\pi$
$191$	−2.73812	−	4.74256i	−0.198123	−	0.343160i	−0.947920	+	0.318509i	$0.896818\pi$
$192$	−0.0485415	+	0.0840764i	−0.00350318	+	0.00606769i
$193$	16.8047	−	4.50280i	1.20963	−	0.324119i	0.403012	−	0.915195i	$-0.367963\pi$
$193$	16.8047	−	4.50280i	1.20963	−	0.324119i	0.806616	+	0.591076i	$0.201297\pi$
$194$	−3.31351	−	5.73917i	−0.237896	−	0.412049i
$195$	−1.31834	−	9.52185i	−0.0944083	−	0.681874i
$196$	5.30329	−	9.84887i	0.378807	−	0.703490i
$197$	−0.527316	+	0.527316i	−0.0375697	+	0.0375697i	−0.725642	−	0.688072i	$-0.758457\pi$
$197$	−0.527316	+	0.527316i	−0.0375697	+	0.0375697i	0.688072	+	0.725642i	$0.258457\pi$
$198$	1.41236	+	2.44627i	0.100372	+	0.173849i
$199$	−5.40687	+	9.36497i	−0.383283	+	0.663865i	−0.991529	−	0.129883i	$-0.958540\pi$
$199$	−5.40687	+	9.36497i	−0.383283	+	0.663865i	0.608247	+	0.793748i	$0.291873\pi$
$200$	1.24463	+	4.64502i	0.0880085	+	0.328452i
$201$	−3.38708	+	12.6408i	−0.238906	+	0.891610i
$202$	0.244809	−	0.244809i	0.0172247	−	0.0172247i
$203$	−0.720422	−	0.699370i	−0.0505637	−	0.0490862i
$204$	6.41429			0.449090
$205$	−25.4226	+	14.6777i	−1.77559	+	1.02514i
$206$	0.433596	+	1.61820i	0.0302101	+	0.112746i
$207$	−3.04951	−	1.76064i	−0.211956	−	0.122373i
$208$	6.25950	+	0.781578i	0.434018	+	0.0541927i
$209$			19.5162i			1.34996i
$210$	−4.33669	−	1.09337i	−0.299260	−	0.0754494i
$211$	−18.0930			−1.24557			−0.622786	−	0.782392i	$-0.713999\pi$
$211$	−18.0930			−1.24557			−0.622786	+	0.782392i	$0.713999\pi$
$212$	15.3488	−	8.86166i	1.05416	−	0.608621i
$213$	−7.43017	+	1.99091i	−0.509107	+	0.136415i
$214$	−0.903387	−	3.37149i	−0.0617543	−	0.230470i
$215$	−9.30126	−	2.49226i	−0.634340	−	0.169971i
$216$	1.61311	−	1.61311i	0.109758	−	0.109758i
$217$	−24.2665	−	13.5346i	−1.64731	−	0.918787i
$218$			8.01830i			0.543068i
$219$	2.09027	−	7.80100i	0.141248	−	0.527143i
$220$	−9.49015	+	16.4374i	−0.639826	+	1.10821i
$221$	5.62761	+	13.3336i	0.378554	+	0.896917i
$222$	−0.140370	+	0.0810429i	−0.00942105	+	0.00543924i
$223$	−1.88034	−	1.88034i	−0.125917	−	0.125917i	0.641340	−	0.767257i	$-0.278379\pi$
$223$	−1.88034	−	1.88034i	−0.125917	−	0.125917i	−0.767257	+	0.641340i	$0.778379\pi$
$224$	7.30965	−	13.1056i	0.488397	−	0.875658i
$225$		−	2.10797i		−	0.140532i
$226$	−4.62192	−	1.23844i	−0.307445	−	0.0823797i
$227$	15.0796	−	4.04057i	1.00087	−	0.268182i	0.279059	−	0.960274i	$-0.409977\pi$
$227$	15.0796	−	4.04057i	1.00087	−	0.268182i	0.721809	+	0.692092i	$0.243311\pi$
$228$	6.76172	−	1.81180i	0.447806	−	0.119989i
$229$	−18.1364	−	4.85963i	−1.19849	−	0.321133i	−0.396251	−	0.918142i	$-0.629689\pi$
$229$	−18.1364	−	4.85963i	−1.19849	−	0.321133i	−0.802235	+	0.597009i	$0.796356\pi$
$230$			5.95238i			0.392488i
$231$	−6.04421	−	10.1194i	−0.397680	−	0.665806i
$232$	−0.612170	−	0.612170i	−0.0401909	−	0.0401909i
$233$	−18.1975	+	10.5063i	−1.19216	+	0.688293i	−0.958796	−	0.284097i	$-0.908306\pi$
$233$	−18.1975	+	10.5063i	−1.19216	+	0.688293i	−0.233363	+	0.972390i	$0.574973\pi$
$234$	2.11785	+	0.860714i	0.138448	+	0.0562667i
$235$	5.80735	−	10.0586i	0.378830	−	0.656152i
$236$	1.47665	−	5.51092i	0.0961215	−	0.358730i
$237$			2.96742i			0.192755i
$238$	6.73277	−	0.0998300i	0.436421	−	0.00647102i
$239$	2.72859	−	2.72859i	0.176498	−	0.176498i	−0.613329	−	0.789827i	$-0.710170\pi$
$239$	2.72859	−	2.72859i	0.176498	−	0.176498i	0.789827	+	0.613329i	$0.210170\pi$
$240$	4.50551	+	1.20725i	0.290829	+	0.0779275i
$241$	1.30249	+	4.86096i	0.0839008	+	0.313122i	0.995104	−	0.0988356i	$-0.0315118\pi$
$241$	1.30249	+	4.86096i	0.0839008	+	0.313122i	−0.911203	+	0.411958i	$0.864845\pi$
$242$	5.41871	−	1.45194i	0.348328	−	0.0933342i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−22.3046			−1.42790
$245$	18.1619	+	4.29364i	1.16032	+	0.274310i
$246$		−	6.98127i		−	0.445110i
$247$	9.69869	+	12.4663i	0.617113	+	0.793209i
$248$	−20.7482	−	11.9790i	−1.31752	−	0.760668i
$249$	3.21517	+	11.9992i	0.203753	+	0.760418i
$250$	4.23374	−	2.44435i	0.267765	−	0.154594i
$251$	0.125710			0.00793476			0.00396738	−	0.999992i	$-0.498737\pi$
$251$	0.125710			0.00793476			0.00396738	+	0.999992i	$0.498737\pi$
$252$	−2.94491	+	3.03356i	−0.185512	+	0.191096i
$253$	−11.0928	+	11.0928i	−0.697397	+	0.697397i
$254$	1.44575	−	5.39563i	0.0907146	−	0.338552i
$255$	2.76977	+	10.3369i	0.173450	+	0.647323i
$256$	3.67376	−	6.36314i	0.229610	−	0.397696i
$257$	3.34108	+	5.78691i	0.208411	+	0.360978i	0.951214	−	0.308532i	$-0.0998376\pi$
$257$	3.34108	+	5.78691i	0.208411	+	0.360978i	−0.742803	+	0.669510i	$0.766504\pi$
$258$	1.61930	−	1.61930i	0.100813	−	0.100813i
$259$	0.580664	−	0.346825i	0.0360807	−	0.0215507i
$260$	2.10669	+	15.2158i	0.130652	+	0.943645i
$261$	0.189749	+	0.328654i	0.0117451	+	0.0203432i
$262$	3.08662	−	0.827057i	0.190692	−	0.0510957i
$263$	−5.65684	+	9.79794i	−0.348816	+	0.604167i	−0.986039	−	0.166512i	$-0.946749\pi$
$263$	−5.65684	+	9.79794i	−0.348816	+	0.604167i	0.637223	+	0.770679i	$0.280083\pi$
$264$	−5.08164	−	8.80166i	−0.312753	−	0.541705i
$265$	20.9088	+	20.9088i	1.28442	+	1.28442i
$266$	7.06926	−	2.00700i	0.433444	−	0.123057i
$267$	−0.454743	−	0.454743i	−0.0278298	−	0.0278298i
$268$	5.41252	−	20.1998i	0.330623	−	1.23390i
$269$	−23.7129	−	13.6907i	−1.44580	−	0.834735i	−0.447575	−	0.894246i	$-0.647712\pi$
$269$	−23.7129	−	13.6907i	−1.44580	−	0.834735i	−0.998228	+	0.0595114i	$0.981046\pi$
$270$	1.46393	+	0.845203i	0.0890922	+	0.0514374i
$271$	16.8431	+	4.51309i	1.02315	+	0.274151i	0.731112	−	0.682257i	$-0.239002\pi$
$271$	16.8431	+	4.51309i	1.02315	+	0.274151i	0.292033	+	0.956408i	$0.405668\pi$
$272$	−7.02266			−0.425811
$273$	−8.88971	−	3.46020i	−0.538030	−	0.209421i
$274$	−14.2113			−0.858534
$275$	−9.07120	−	2.43062i	−0.547014	−	0.146572i
$276$	4.87309	+	2.81348i	0.293325	+	0.169351i
$277$	−18.8085	−	10.8591i	−1.13009	−	0.652460i	−0.186136	−	0.982524i	$-0.559596\pi$
$277$	−18.8085	−	10.8591i	−1.13009	−	0.652460i	−0.943959	+	0.330064i	$0.892930\pi$
$278$	0.443233	−	1.65417i	0.0265833	−	0.0992103i
$279$	7.42604	+	7.42604i	0.444586	+	0.444586i
$280$	15.6034	+	3.93392i	0.932479	+	0.235097i
$281$	14.1780	+	14.1780i	0.845786	+	0.845786i	0.989604	−	0.143818i	$-0.0459380\pi$
$281$	14.1780	+	14.1780i	0.845786	+	0.845786i	−0.143818	+	0.989604i	$0.545938\pi$
$282$	1.38109	+	2.39212i	0.0822430	+	0.142449i
$283$	11.7397	−	20.3338i	0.697853	−	1.20872i	−0.271356	−	0.962479i	$-0.587472\pi$
$283$	11.7397	−	20.3338i	0.697853	−	1.20872i	0.969209	−	0.246238i	$-0.0791945\pi$
$284$	11.8733	−	3.18145i	0.704553	−	0.188784i
$285$	5.83959	+	10.1145i	0.345907	+	0.599129i
$286$	6.14591	−	8.12125i	0.363415	−	0.480220i
$287$	0.431902	+	29.1285i	0.0254943	+	1.71940i
$288$	−4.01060	+	4.01060i	−0.236327	+	0.236327i
$289$	0.444014	+	0.769054i	0.0261184	+	0.0452385i
$290$	0.320752	−	0.555559i	0.0188352	−	0.0326236i
$291$	−2.70518	−	10.0959i	−0.158581	−	0.591831i
$292$	−3.34024	+	12.4659i	−0.195472	+	0.729513i
$293$	−9.60223	+	9.60223i	−0.560968	+	0.560968i	−0.929583	−	0.368614i	$-0.879832\pi$
$293$	−9.60223	+	9.60223i	−0.560968	+	0.560968i	0.368614	+	0.929583i	$0.379832\pi$
$294$	−3.04392	+	3.23002i	−0.177525	+	0.188378i
$295$	9.51873			0.554202
$296$	0.505052	−	0.291592i	0.0293555	−	0.0169484i
$297$	1.15306	+	4.30328i	0.0669074	+	0.249702i
$298$	2.06292	+	1.19103i	0.119502	+	0.0689942i
$299$	−1.57306	+	12.5983i	−0.0909723	+	0.728578i
$300$			3.36852i			0.194482i
$301$	−6.65616	+	6.85652i	−0.383654	+	0.395203i
$302$	1.51545			0.0872043
$303$	0.472884	−	0.273020i	0.0271665	−	0.0156846i
$304$	−7.40305	+	1.98364i	−0.424594	+	0.113770i
$305$	−9.63138	−	35.9448i	−0.551491	−	2.05819i
$306$	−2.45831	−	0.658702i	−0.140532	−	0.0376555i
$307$	−19.5360	+	19.5360i	−1.11498	+	1.11498i	−0.122511	+	0.992467i	$0.539095\pi$
$307$	−19.5360	+	19.5360i	−1.11498	+	1.11498i	−0.992467	+	0.122511i	$0.960905\pi$
$308$	9.65860	+	16.1707i	0.550350	+	0.921410i
$309$			2.64223i			0.150311i
$310$	4.59473	−	17.1478i	0.260963	−	0.973928i
$311$	−5.24697	+	9.08801i	−0.297528	+	0.515334i	−0.975570	−	0.219690i	$-0.929496\pi$
$311$	−5.24697	+	9.08801i	−0.297528	+	0.515334i	0.678042	+	0.735023i	$0.262829\pi$
$312$	−7.62001	−	3.09684i	−0.431398	−	0.175324i
$313$	−6.19124	+	3.57452i	−0.349950	+	0.202044i	−0.664663	−	0.747143i	$-0.731425\pi$
$313$	−6.19124	+	3.57452i	−0.349950	+	0.202044i	0.314713	+	0.949187i	$0.398092\pi$
$314$	2.66851	+	2.66851i	0.150593	+	0.150593i
$315$	−6.16037	−	3.43594i	−0.347098	−	0.193593i
$316$		−	4.74192i		−	0.266754i
$317$	−31.0094	−	8.30895i	−1.74166	−	0.466677i	−0.758847	−	0.651269i	$-0.774237\pi$
$317$	−31.0094	−	8.30895i	−1.74166	−	0.466677i	−0.982815	+	0.184593i	$0.940903\pi$
$318$	−6.79255	+	1.82006i	−0.380907	+	0.102064i
$319$	1.63308	−	0.437583i	0.0914351	−	0.0245000i
$320$	0.250012	+	0.0669904i	0.0139761	+	0.00374488i
$321$		−	5.50503i		−	0.307261i
$322$	5.15883	+	2.87733i	0.287491	+	0.160347i
$323$	−12.4337	−	12.4337i	−0.691827	−	0.691827i
$324$	1.38390	−	0.798995i	0.0768833	−	0.0443886i
$325$	−7.00228	+	2.95539i	−0.388416	+	0.163936i
$326$	−1.42369	+	2.46591i	−0.0788510	+	0.136574i
$327$	−3.27311	+	12.2154i	−0.181003	+	0.675513i
$328$			25.1186i			1.38694i
$329$	−5.91043	−	9.89539i	−0.325852	−	0.545551i
$330$	5.32515	−	5.32515i	0.293140	−	0.293140i
$331$	9.40856	+	2.52102i	0.517141	+	0.138568i	0.507944	−	0.861390i	$-0.330406\pi$
$331$	9.40856	+	2.52102i	0.517141	+	0.138568i	0.00919731	+	0.999958i	$0.497072\pi$
$332$	−5.13782	−	19.1746i	−0.281974	−	1.05234i
$333$	−0.246928	+	0.0661642i	−0.0135316	+	0.00362578i
$334$	3.06583	−	1.77006i	0.167755	−	0.0968532i
$335$	34.8901			1.90625
$336$	3.22423	−	3.32128i	0.175896	−	0.181191i
$337$		−	10.0099i		−	0.545275i	−0.962117	−	0.272637i	$-0.912104\pi$
$337$		−	10.0099i		−	0.545275i	0.962117	−	0.272637i	$-0.0878959\pi$
$338$	−0.110114	−	8.24181i	−0.00598943	−	0.448296i
$339$	−6.53568	−	3.77338i	−0.354969	−	0.204942i
$340$	−4.42606	−	16.5183i	−0.240037	−	0.895830i
$341$	40.5190	−	23.3937i	2.19423	−	1.26684i
$342$	−2.77752			−0.150191
$343$	12.5006	−	13.6651i	0.674966	−	0.737849i
$344$	−5.82624	+	5.82624i	−0.314130	+	0.314130i
$345$	−2.42979	+	9.06809i	−0.130815	+	0.488210i
$346$	−1.42635	−	5.32321i	−0.0766810	−	0.286177i
$347$	−14.1695	+	24.5424i	−0.760661	+	1.31750i	0.181849	+	0.983326i	$0.441792\pi$
$347$	−14.1695	+	24.5424i	−0.760661	+	1.31750i	−0.942510	+	0.334177i	$0.891542\pi$
$348$	−0.303216	−	0.525186i	−0.0162541	−	0.0281529i
$349$	−1.32859	+	1.32859i	−0.0711180	+	0.0711180i	−0.741771	−	0.670653i	$-0.766014\pi$
$349$	−1.32859	+	1.32859i	−0.0711180	+	0.0711180i	0.670653	+	0.741771i	$0.266014\pi$
$350$	0.0524266	+	3.53578i	0.00280232	+	0.188995i
$351$	2.87507	+	2.17576i	0.153460	+	0.116134i
$352$	12.6343	+	21.8832i	0.673409	+	1.16638i
$353$	−34.8954	+	9.35019i	−1.85729	+	0.497660i	−0.999857	−	0.0169280i	$-0.994611\pi$
$353$	−34.8954	+	9.35019i	−1.85729	+	0.497660i	−0.857437	+	0.514588i	$0.827945\pi$
$354$	−1.13186	+	1.96045i	−0.0601579	+	0.104197i
$355$	10.2541	+	17.7606i	0.544231	+	0.942637i
$356$	0.726675	+	0.726675i	0.0385137	+	0.0385137i
$357$	10.2977	+	2.59626i	0.545014	+	0.137409i
$358$	1.33309	+	1.33309i	0.0704559	+	0.0704559i
$359$	1.60246	−	5.98046i	0.0845746	−	0.315637i	−0.910659	−	0.413159i	$-0.864425\pi$
$359$	1.60246	−	5.98046i	0.0845746	−	0.315637i	0.995233	+	0.0975229i	$0.0310919\pi$
$360$	−5.26722	−	3.04103i	−0.277607	−	0.160277i
$361$	−0.164696	−	0.0950875i	−0.00866823	−	0.00500461i
$362$	−8.60592	−	2.30595i	−0.452317	−	0.121198i
$363$	8.84777			0.464388
$364$	14.2057	+	5.52936i	0.744580	+	0.289817i
$365$	−21.5318			−1.12702
$366$	8.54833	+	2.29052i	0.446828	+	0.119727i
$367$	−12.7879	−	7.38308i	−0.667521	−	0.385394i	0.127615	−	0.991824i	$-0.459268\pi$
$367$	−12.7879	−	7.38308i	−0.667521	−	0.385394i	−0.795137	+	0.606430i	$0.792601\pi$
$368$	−5.33528	−	3.08033i	−0.278121	−	0.160573i
$369$	2.84979	−	10.6356i	0.148354	−	0.553665i
$370$	0.305565	+	0.305565i	0.0158855	+	0.0158855i
$371$	28.2284	−	8.01419i	1.46555	−	0.416076i
$372$	−11.8667	−	11.8667i	−0.615262	−	0.615262i
$373$	9.31901	+	16.1410i	0.482520	+	0.835749i	0.999799	−	0.0200681i	$-0.00638831\pi$
$373$	9.31901	+	16.1410i	0.482520	+	0.835749i	−0.517279	+	0.855817i	$0.673055\pi$
$374$	−5.66916	+	9.81927i	−0.293145	+	0.507742i
$375$	7.44764	−	1.99559i	0.384595	−	0.103052i
$376$	−4.96916	−	8.60684i	−0.256265	−	0.443864i
$377$	0.825696	−	1.09108i	0.0425255	−	0.0561936i
$378$	1.44018	−	0.860206i	0.0740748	−	0.0442442i
$379$	25.7884	−	25.7884i	1.32466	−	1.32466i	0.414703	−	0.909957i	$-0.363886\pi$
$379$	25.7884	−	25.7884i	1.32466	−	1.32466i	0.909957	−	0.414703i	$-0.136114\pi$
$380$	−9.33161	−	16.1628i	−0.478701	−	0.829135i
$381$	4.40504	−	7.62975i	0.225677	−	0.390884i
$382$	−0.898662	−	3.35385i	−0.0459796	−	0.171598i
$383$	−2.28945	+	8.54436i	−0.116986	+	0.436596i	−0.999428	−	0.0338247i	$-0.989231\pi$
$383$	−2.28945	+	8.54436i	−0.116986	+	0.436596i	0.882442	+	0.470421i	$0.155898\pi$
$384$	7.97768	−	7.97768i	0.407109	−	0.407109i
$385$	−21.8891	+	22.5480i	−1.11557	+	1.14915i
$386$	11.0307			0.561450
$387$	3.12792	−	1.80591i	0.159001	−	0.0917993i
$388$	4.32286	+	16.1331i	0.219460	+	0.819035i
$389$	−3.76516	−	2.17382i	−0.190901	−	0.110217i	0.401503	−	0.915858i	$-0.368488\pi$
$389$	−3.76516	−	2.17382i	−0.190901	−	0.110217i	−0.592404	+	0.805641i	$0.701821\pi$
$390$	0.755155	−	6.04788i	0.0382388	−	0.306247i
$391$		−	14.1343i		−	0.714801i
$392$	10.9520	−	11.6216i	0.553160	−	0.586978i
$393$	5.03989			0.254229
$394$	−0.409482	+	0.236415i	−0.0206294	+	0.0119104i
$395$	7.64181	−	2.04762i	0.384501	−	0.103027i
$396$	−1.84258	−	6.87660i	−0.0925931	−	0.345562i
$397$	4.71695	+	1.26390i	0.236737	+	0.0634334i	0.375237	−	0.926929i	$-0.377561\pi$
$397$	4.71695	+	1.26390i	0.236737	+	0.0634334i	−0.138500	+	0.990362i	$0.544228\pi$
$398$	−4.84818	+	4.84818i	−0.243017	+	0.243017i
$399$	11.5889	−	0.171834i	0.580169	−	0.00860244i
$400$		−	3.68801i		−	0.184401i
$401$	−4.78185	+	17.8461i	−0.238794	+	0.891192i	0.737608	+	0.675230i	$0.235955\pi$
$401$	−4.78185	+	17.8461i	−0.238794	+	0.891192i	−0.976402	+	0.215962i	$0.930711\pi$
$402$	−4.14875	+	7.18585i	−0.206921	+	0.358398i
$403$	14.2565	−	35.0792i	0.710168	−	1.74742i
$404$	−0.755664	+	0.436283i	−0.0375957	+	0.0217059i
$405$	1.88520	+	1.88520i	0.0936764	+	0.0936764i
$406$	−0.326446	−	0.546544i	−0.0162012	−	0.0271245i
$407$			1.13889i			0.0564528i
$408$	8.84497	+	2.37000i	0.437891	+	0.117333i
$409$	23.7087	−	6.35274i	1.17232	−	0.314123i	0.380445	−	0.924804i	$-0.375771\pi$
$409$	23.7087	−	6.35274i	1.17232	−	0.314123i	0.791877	+	0.610681i	$0.209104\pi$
$410$	−17.9784	+	4.81730i	−0.887890	+	0.237910i
$411$	−21.6500	−	5.80111i	−1.06792	−	0.286147i
$412$		−	4.22226i		−	0.208016i
$413$	4.60128	−	8.24974i	0.226414	−	0.405943i
$414$	−1.57871	−	1.57871i	−0.0775894	−	0.0775894i
$415$	28.6821	−	16.5596i	1.40795	−	0.812881i
$416$	18.9453	+	7.69955i	0.928871	+	0.377501i
$417$	1.35048	−	2.33910i	0.0661332	−	0.114546i
$418$	−3.20265	+	11.9525i	−0.156647	+	0.584614i
$419$			5.88805i			0.287650i	0.989603	+	0.143825i	$0.0459402\pi$
$419$			5.88805i			0.287650i	−0.989603	+	0.143825i	$0.954060\pi$
$420$	9.84421	+	5.49059i	0.480348	+	0.267913i
$421$	14.9037	−	14.9037i	0.726360	−	0.726360i	−0.243533	−	0.969893i	$-0.578306\pi$
$421$	14.9037	−	14.9037i	0.726360	−	0.726360i	0.969893	+	0.243533i	$0.0783063\pi$
$422$	−11.0808	−	2.96910i	−0.539406	−	0.144534i
$423$	1.12754	+	4.20803i	0.0548228	+	0.204601i
$424$	24.4395	−	6.54855i	1.18689	−	0.318026i
$425$	7.32774	−	4.23067i	0.355448	−	0.205218i
$426$	−4.87723			−0.236302
$427$	−35.8085	−	9.02805i	−1.73290	−	0.436898i
$428$			8.79698i			0.425218i
$429$	12.6781	−	9.86346i	0.612102	−	0.476212i
$430$	−5.28746	−	3.05271i	−0.254984	−	0.147215i
$431$	−3.29583	−	12.3002i	−0.158755	−	0.592481i	−0.998755	−	0.0498939i	$-0.984112\pi$
$431$	−3.29583	−	12.3002i	−0.158755	−	0.592481i	0.840000	−	0.542587i	$-0.182555\pi$
$432$	−1.51516	+	0.874777i	−0.0728981	+	0.0420877i
$433$	24.9932			1.20109			0.600547	−	0.799589i	$-0.294949\pi$
$433$	24.9932			1.20109			0.600547	+	0.799589i	$0.294949\pi$
$434$	−12.6406	−	12.2713i	−0.606770	−	0.589040i
$435$	0.715429	−	0.715429i	0.0343022	−	0.0343022i
$436$	5.23039	−	19.5201i	0.250490	−	0.934843i
$437$	−3.99241	−	14.8999i	−0.190983	−	0.712758i
$438$	2.56032	−	4.43461i	0.122337	−	0.211894i
$439$	−13.6949	−	23.7203i	−0.653624	−	1.13211i	−0.982237	−	0.187645i	$-0.939915\pi$
$439$	−13.6949	−	23.7203i	−0.653624	−	1.13211i	0.328613	−	0.944465i	$-0.393419\pi$
$440$	−19.1598	+	19.1598i	−0.913410	+	0.913410i
$441$	−5.95574	+	3.67820i	−0.283607	+	0.175152i
$442$	1.25848	+	9.08952i	0.0598599	+	0.432344i
$443$	3.27445	+	5.67152i	0.155574	+	0.269462i	0.933268	−	0.359181i	$-0.116944\pi$
$443$	3.27445	+	5.67152i	0.155574	+	0.269462i	−0.777694	+	0.628643i	$0.783611\pi$
$444$	0.394589	−	0.105730i	0.0187264	−	0.00501771i
$445$	−0.857283	+	1.48486i	−0.0406391	+	0.0703890i
$446$	−0.843024	−	1.46016i	−0.0399183	−	0.0691406i
$447$	2.65655	+	2.65655i	0.125650	+	0.125650i
$448$	0.178913	−	0.184299i	0.00845285	−	0.00870729i
$449$	−13.3279	−	13.3279i	−0.628980	−	0.628980i	0.318831	−	0.947812i	$-0.396710\pi$
$449$	−13.3279	−	13.3279i	−0.628980	−	0.628980i	−0.947812	+	0.318831i	$0.896710\pi$
$450$	0.345923	−	1.29100i	0.0163070	−	0.0608585i
$451$	−42.4818	−	24.5269i	−2.00039	−	1.15493i
$452$	10.4440	+	6.02982i	0.491242	+	0.283619i
$453$	2.30870	+	0.618613i	0.108472	+	0.0290650i
$454$	9.89838			0.464554
$455$	−2.77663	+	25.2807i	−0.130171	+	1.18518i
$456$	9.99350			0.467989
$457$	−13.5314	−	3.62574i	−0.632974	−	0.169605i	−0.0719554	−	0.997408i	$-0.522924\pi$
$457$	−13.5314	−	3.62574i	−0.632974	−	0.169605i	−0.561019	+	0.827803i	$0.689591\pi$
$458$	−10.3099	−	5.95244i	−0.481751	−	0.278139i
$459$	−3.47620	−	2.00699i	−0.162255	−	0.0936781i
$460$	3.88278	−	14.4907i	0.181035	−	0.675634i
$461$	4.95593	+	4.95593i	0.230821	+	0.230821i	0.813035	−	0.582215i	$-0.197814\pi$
$461$	4.95593	+	4.95593i	0.230821	+	0.230821i	−0.582215	+	0.813035i	$0.697814\pi$
$462$	−2.04109	−	7.18936i	−0.0949602	−	0.334479i
$463$	21.9607	+	21.9607i	1.02060	+	1.02060i	0.999783	+	0.0208179i	$0.00662701\pi$
$463$	21.9607	+	21.9607i	1.02060	+	1.02060i	0.0208179	+	0.999783i	$0.493373\pi$
$464$	0.331975	+	0.574998i	0.0154116	+	0.0266936i
$465$	13.9996	−	24.2480i	0.649216	−	1.12447i
$466$	−12.8690	+	3.44823i	−0.596143	+	0.159736i
$467$	9.68386	+	16.7729i	0.448116	+	0.776159i	0.998263	−	0.0589081i	$-0.0187619\pi$
$467$	9.68386	+	16.7729i	0.448116	+	0.776159i	−0.550148	+	0.835067i	$0.685429\pi$
$468$	−4.59434	−	3.47685i	−0.212373	−	0.160717i
$469$	16.8656	−	30.2387i	0.778780	−	1.39629i
$470$	5.20728	−	5.20728i	0.240194	−	0.240194i
$471$	2.97601	+	5.15461i	0.137127	+	0.237512i
$472$	4.07244	−	7.05367i	0.187449	−	0.324671i
$473$	−4.16464	−	15.5426i	−0.191490	−	0.714651i
$474$	−0.486961	+	1.81736i	−0.0223669	+	0.0834742i
$475$	6.52965	−	6.52965i	0.299601	−	0.299601i
$476$	−16.4557	−	4.14880i	−0.754244	−	0.190160i
$477$	−11.0910			−0.507822
$478$	2.11886	−	1.22333i	0.0969145	−	0.0559536i
$479$	0.0710447	+	0.265142i	0.00324612	+	0.0121147i	0.967530	−	0.252757i	$-0.0813372\pi$
$479$	0.0710447	+	0.265142i	0.00324612	+	0.0121147i	−0.964284	+	0.264871i	$0.914671\pi$
$480$	13.0957	+	7.56079i	0.597733	+	0.345101i
$481$	0.565979	+	0.727484i	0.0258064	+	0.0331704i
$482$			3.19078i			0.145336i
$483$	6.68464	+	6.48930i	0.304162	+	0.295273i
$484$	−14.1387			−0.642666
$485$	−24.1326	+	13.9330i	−1.09580	+	0.632663i
$486$	−0.612438	+	0.164102i	−0.0277807	+	0.00744383i
$487$	−0.788208	−	2.94163i	−0.0357171	−	0.133298i	0.945765	−	0.324851i	$-0.105314\pi$
$487$	−0.788208	−	2.94163i	−0.0357171	−	0.133298i	−0.981482	+	0.191553i	$0.938648\pi$
$488$	−30.7568	−	8.24126i	−1.39230	−	0.373064i
$489$	−3.17551	+	3.17551i	−0.143601	+	0.143601i
$490$	10.4185	+	5.61000i	0.470658	+	0.253434i
$491$			41.7528i			1.88428i	0.335221	+	0.942140i	$0.391189\pi$
$491$			41.7528i			1.88428i	−0.335221	+	0.942140i	$0.608811\pi$
$492$	−4.55393	+	16.9955i	−0.205307	+	0.766217i
$493$	−0.761646	+	1.31921i	−0.0343028	+	0.0594142i
$494$	3.89410	+	9.22639i	0.175204	+	0.415115i
$495$	10.2863	−	5.93880i	0.462335	−	0.266929i
$496$	12.9923	+	12.9923i	0.583370	+	0.583370i
$497$	20.3496	−	0.301733i	0.912805	−	0.0135346i
$498$			7.87637i			0.352949i
$499$	1.19936	+	0.321369i	0.0536909	+	0.0143864i	0.285565	−	0.958359i	$-0.407819\pi$
$499$	1.19936	+	0.321369i	0.0536909	+	0.0143864i	−0.231874	+	0.972746i	$0.574486\pi$
$500$	−11.9013	+	3.18893i	−0.532241	+	0.142613i
$501$	5.39315	−	1.44509i	0.240948	−	0.0645619i
$502$	0.0769897	+	0.0206293i	0.00343622	+	0.000920732i
$503$		−	7.14012i		−	0.318362i	−0.987249	−	0.159181i	$-0.949115\pi$
$503$		−	7.14012i		−	0.318362i	0.987249	−	0.159181i	$-0.0508854\pi$
$504$	−5.18175	+	3.09501i	−0.230813	+	0.137863i
$505$	−1.02939	−	1.02939i	−0.0458075	−	0.0458075i
$506$	−8.61398	+	4.97329i	−0.382938	+	0.221090i
$507$	3.19659	−	12.6009i	0.141966	−	0.559624i
$508$	−7.03921	+	12.1923i	−0.312314	+	0.540945i
$509$	4.50433	−	16.8104i	0.199651	−	0.745108i	−0.791363	−	0.611347i	$-0.790628\pi$
$509$	4.50433	−	16.8104i	0.199651	−	0.745108i	0.991014	−	0.133761i	$-0.0427054\pi$
$510$			6.78524i			0.300456i
$511$	−10.4083	+	18.6612i	−0.460435	+	0.825525i
$512$	−12.6612	+	12.6612i	−0.559551	+	0.559551i
$513$	−4.23139	−	1.13380i	−0.186821	−	0.0500584i
$514$	1.09656	+	4.09240i	0.0483670	+	0.180508i
$515$	6.80437	−	1.82322i	0.299836	−	0.0803409i
$516$	−4.99839	+	2.88582i	−0.220042	+	0.127041i
$517$	19.4085			0.853583
$518$	0.412535	−	0.117121i	0.0181258	−	0.00514599i
$519$		−	8.69183i		−	0.381529i
$520$	−2.71704	+	21.7602i	−0.119150	+	0.954249i
$521$	4.93163	+	2.84728i	0.216059	+	0.124742i	0.604124	−	0.796890i	$-0.293523\pi$
$521$	4.93163	+	2.84728i	0.216059	+	0.124742i	−0.388065	+	0.921632i	$0.626856\pi$
$522$	0.0622763	+	0.232418i	0.00272576	+	0.0101727i
$523$	−19.5332	+	11.2775i	−0.854128	+	0.493131i	−0.862042	−	0.506838i	$-0.830814\pi$
$523$	−19.5332	+	11.2775i	−0.854128	+	0.493131i	0.00791352	+	0.999969i	$0.497481\pi$
$524$	−8.05369			−0.351827
$525$	−1.36345	+	5.40795i	−0.0595059	+	0.236022i
$526$	−5.07233	+	5.07233i	−0.221164	+	0.221164i
$527$	−10.9105	+	40.7184i	−0.475267	+	1.77372i
$528$	2.01734	+	7.52882i	0.0877935	+	0.327650i
$529$	−5.30033	+	9.18044i	−0.230449	+	0.399149i
$530$	9.37415	+	16.2365i	0.407187	+	0.705269i
$531$	−2.52459	+	2.52459i	−0.109558	+	0.109558i
$532$	−18.5189	+	0.274588i	−0.802896	+	0.0119049i
$533$	−39.3246	+	5.44466i	−1.70334	+	0.235835i
$534$	−0.203878	−	0.353126i	−0.00882264	−	0.0152813i
$535$	−14.1767	+	3.79864i	−0.612914	+	0.164230i
$536$	14.9272	−	25.8546i	0.644756	−	1.11675i
$537$	1.48671	+	2.57505i	0.0641562	+	0.111122i
$538$	−12.2760	−	12.2760i	−0.529257	−	0.529257i
$539$	8.96097	+	29.8704i	0.385976	+	1.28661i
$540$	−3.01253	−	3.01253i	−0.129639	−	0.129639i
$541$	3.79928	−	14.1791i	0.163344	−	0.609607i	−0.834902	−	0.550399i	$-0.814476\pi$
$541$	3.79928	−	14.1791i	0.163344	−	0.609607i	0.998246	−	0.0592081i	$-0.0188576\pi$
$542$	9.57474	+	5.52798i	0.411270	+	0.237447i
$543$	−12.1693	−	7.02595i	−0.522235	−	0.301513i
$544$	−21.9909	−	5.89244i	−0.942851	−	0.252636i
$545$	33.7161			1.44424
$546$	−4.87657	−	3.57798i	−0.208698	−	0.153123i
$547$	−12.7838			−0.546598			−0.273299	−	0.961929i	$-0.588115\pi$
$547$	−12.7838			−0.546598			−0.273299	+	0.961929i	$0.588115\pi$
$548$	34.5965	+	9.27011i	1.47789	+	0.396000i
$549$	12.0879	+	6.97894i	0.515898	+	0.297854i
$550$	−5.15668	−	2.97721i	−0.219881	−	0.126949i
$551$	−0.430273	+	1.60580i	−0.0183303	+	0.0684094i
$552$	5.68019	+	5.68019i	0.241765	+	0.241765i
$553$	1.91935	−	7.61284i	0.0816191	−	0.323731i
$554$	−9.73705	−	9.73705i	−0.413687	−	0.413687i
$555$	0.340777	+	0.590242i	0.0144652	+	0.0250544i
$556$	−2.15805	+	3.73785i	−0.0915217	+	0.158520i
$557$	25.1801	−	6.74698i	1.06691	−	0.285879i	0.317690	−	0.948195i	$-0.397093\pi$
$557$	25.1801	−	6.74698i	1.06691	−	0.285879i	0.749225	+	0.662316i	$0.230426\pi$
$558$	3.32936	+	5.76662i	0.140943	+	0.244121i
$559$	−10.3842	−	7.85845i	−0.439206	−	0.332377i
$560$	−10.7779	−	6.01135i	−0.455449	−	0.254026i
$561$	−12.6449	+	12.6449i	−0.533868	+	0.533868i
$562$	6.35648	+	11.0098i	0.268132	+	0.464418i
$563$	3.53955	−	6.13068i	0.149174	−	0.258377i	−0.781748	−	0.623594i	$-0.785672\pi$
$563$	3.53955	−	6.13068i	0.149174	−	0.258377i	0.930923	+	0.365217i	$0.119005\pi$
$564$	−1.80180	−	6.72439i	−0.0758693	−	0.283148i
$565$	−5.20750	+	19.4347i	−0.219081	+	0.817622i
$566$	10.5267	−	10.5267i	0.442468	−	0.442468i
$567$	2.54517	−	0.722584i	0.106887	−	0.0303457i
$568$	17.5482			0.736307
$569$	31.3701	−	18.1116i	1.31510	−	0.759276i	0.332168	−	0.943220i	$-0.392220\pi$
$569$	31.3701	−	18.1116i	1.31510	−	0.759276i	0.982937	+	0.183944i	$0.0588866\pi$
$570$	1.91658	+	7.15277i	0.0802767	+	0.299597i
$571$	27.5222	+	15.8899i	1.15177	+	0.664974i	0.949317	−	0.314319i	$-0.101776\pi$
$571$	27.5222	+	15.8899i	1.15177	+	0.664974i	0.202451	+	0.979292i	$0.435109\pi$
$572$	−20.2594	+	15.7617i	−0.847089	+	0.659030i
$573$		−	5.47624i		−	0.228773i
$574$	−4.51553	+	17.9103i	−0.188475	+	0.747560i
$575$	7.42275			0.309550
$576$	−0.0840764	+	0.0485415i	−0.00350318	+	0.00202256i
$577$	−7.88022	+	2.11150i	−0.328058	+	0.0879029i	−0.419089	−	0.907945i	$-0.637650\pi$
$577$	−7.88022	+	2.11150i	−0.328058	+	0.0879029i	0.0910309	+	0.995848i	$0.470984\pi$
$578$	0.145727	+	0.543861i	0.00606145	+	0.0226217i
$579$	16.8047	+	4.50280i	0.698379	+	0.187130i
$580$	−1.14325	+	1.14325i	−0.0474708	+	0.0474708i
$581$	−0.487278	−	32.8632i	−0.0202157	−	1.36339i
$582$		−	6.62702i		−	0.274699i
$583$	−12.7886	+	47.7277i	−0.529650	+	1.97668i
$584$	−9.21202	+	15.9557i	−0.381196	+	0.660251i
$585$	3.61921	−	8.90533i	0.149636	−	0.368190i
$586$	−7.45652	+	4.30502i	−0.308026	+	0.177839i
$587$	−25.4365	−	25.4365i	−1.04988	−	1.04988i	−0.998689	−	0.0511873i	$-0.983699\pi$
$587$	−25.4365	−	25.4365i	−1.04988	−	1.04988i	−0.0511873	−	0.998689i	$-0.516301\pi$
$588$	9.51722	−	5.87772i	0.392484	−	0.242393i
$589$			46.0057i			1.89563i
$590$	5.82963	+	1.56205i	0.240002	+	0.0643084i
$591$	−0.720327	+	0.193011i	−0.0296303	+	0.00793942i
$592$	−0.432014	+	0.115758i	−0.0177557	+	0.00475762i
$593$	35.0090	+	9.38063i	1.43765	+	0.385216i	0.891709	−	0.452610i	$-0.149507\pi$
$593$	35.0090	+	9.38063i	1.43765	+	0.385216i	0.545937	+	0.837826i	$0.316174\pi$
$594$			2.82471i			0.115899i
$595$	−0.419774	−	28.3106i	−0.0172091	−	1.16062i
$596$	−4.24514	−	4.24514i	−0.173888	−	0.173888i
$597$	−9.36497	+	5.40687i	−0.383283	+	0.221288i
$598$	−3.03081	+	7.45753i	−0.123939	+	0.304961i
$599$	19.1999	−	33.2553i	0.784488	−	1.35877i	−0.144816	−	0.989459i	$-0.546259\pi$
$599$	19.1999	−	33.2553i	0.784488	−	1.35877i	0.929304	−	0.369315i	$-0.120408\pi$
$600$	−1.24463	+	4.64502i	−0.0508117	+	0.189632i
$601$			11.4894i			0.468662i	0.972157	+	0.234331i	$0.0752900\pi$
$601$			11.4894i			0.468662i	−0.972157	+	0.234331i	$0.924710\pi$
$602$	−5.20165	+	3.10690i	−0.212003	+	0.126628i
$603$	−9.25368	+	9.25368i	−0.376839	+	0.376839i
$604$	−3.68927	−	0.988538i	−0.150114	−	0.0402230i
$605$	−6.10524	−	22.7851i	−0.248213	−	0.926345i
$606$	0.334415	−	0.0896063i	0.0135847	−	0.00364001i
$607$	6.82222	−	3.93881i	0.276906	−	0.159871i	−0.355116	−	0.934822i	$-0.615559\pi$
$607$	6.82222	−	3.93881i	0.276906	−	0.159871i	0.632022	+	0.774951i	$0.282225\pi$
$608$	−24.8464			−1.00766
$609$	−0.274219	−	0.965883i	−0.0111119	−	0.0391396i
$610$		−	23.5945i		−	0.955313i
$611$	12.3974	−	9.64514i	0.501547	−	0.390201i
$612$	5.55494	+	3.20714i	0.224545	+	0.129641i
$613$	4.93561	+	18.4199i	0.199347	+	0.743974i	0.991099	+	0.133131i	$0.0425030\pi$
$613$	4.93561	+	18.4199i	0.199347	+	0.743974i	−0.791751	+	0.610844i	$0.790830\pi$
$614$	−15.1705	+	8.75868i	−0.612231	+	0.353472i
$615$	−29.3555			−1.18373
$616$	7.34383	+	25.8673i	0.295891	+	1.04222i
$617$	15.5811	−	15.5811i	0.627271	−	0.627271i	−0.320109	−	0.947381i	$-0.603720\pi$
$617$	15.5811	−	15.5811i	0.627271	−	0.627271i	0.947381	+	0.320109i	$0.103720\pi$
$618$	−0.433596	+	1.61820i	−0.0174418	+	0.0650937i
$619$	3.91524	+	14.6119i	0.157367	+	0.587300i	0.998891	+	0.0470813i	$0.0149920\pi$
$619$	3.91524	+	14.6119i	0.157367	+	0.587300i	−0.841524	+	0.540219i	$0.818341\pi$
$620$	−22.3712	+	38.7481i	−0.898450	+	1.55616i
$621$	−1.76064	−	3.04951i	−0.0706519	−	0.122373i
$622$	−4.70480	+	4.70480i	−0.188645	+	0.188645i
$623$	0.872499	+	1.46076i	0.0349559	+	0.0585242i
$624$	5.03010	+	3.80662i	0.201365	+	0.152387i
$625$	−15.5482	−	26.9302i	−0.621926	−	1.07721i
$626$	−4.37834	+	1.17317i	−0.174994	+	0.0468894i
$627$	−9.75810	+	16.9015i	−0.389701	+	0.674982i
$628$	−4.75564	−	8.23701i	−0.189771	−	0.328693i
$629$	−0.725582	−	0.725582i	−0.0289308	−	0.0289308i
$630$	−3.20900	−	3.11523i	−0.127850	−	0.124114i
$631$	33.3285	+	33.3285i	1.32679	+	1.32679i	0.908157	+	0.418630i	$0.137490\pi$
$631$	33.3285	+	33.3285i	1.32679	+	1.32679i	0.418630	+	0.908157i	$0.362510\pi$
$632$	1.75208	−	6.53885i	0.0696940	−	0.260102i
$633$	−15.6690	−	9.04650i	−0.622786	−	0.359566i
$634$	−17.6278	−	10.1774i	−0.700090	−	0.404197i
$635$	−22.6880	−	6.07924i	−0.900346	−	0.241247i
$636$	17.7233			0.702775
$637$	20.5682	+	14.6270i	0.814943	+	0.579541i
$638$	1.07197			0.0424397
$639$	−7.43017	−	1.99091i	−0.293933	−	0.0787591i
$640$	−26.0492	−	15.0395i	−1.02969	−	0.594490i
$641$	−4.68848	−	2.70690i	−0.185184	−	0.106916i	0.404542	−	0.914519i	$-0.367431\pi$
$641$	−4.68848	−	2.70690i	−0.185184	−	0.106916i	−0.589726	+	0.807603i	$0.700764\pi$
$642$	0.903387	−	3.37149i	0.0356538	−	0.133062i
$643$	−28.8484	−	28.8484i	−1.13767	−	1.13767i	−0.988867	−	0.148804i	$-0.952458\pi$
$643$	−28.8484	−	28.8484i	−1.13767	−	1.13767i	−0.148804	−	0.988867i	$-0.547542\pi$
$644$	−10.6820	−	10.3698i	−0.420929	−	0.408629i
$645$	−6.80899	−	6.80899i	−0.268104	−	0.268104i
$646$	−5.57445	−	9.65523i	−0.219324	−	0.379880i
$647$	−10.6093	+	18.3758i	−0.417094	+	0.722428i	−0.995646	−	0.0932180i	$-0.970285\pi$
$647$	−10.6093	+	18.3758i	−0.417094	+	0.722428i	0.578552	+	0.815646i	$0.303618\pi$
$648$	2.20355	−	0.590438i	0.0865634	−	0.0231946i
$649$	7.95302	+	13.7750i	0.312183	+	0.540717i
$650$	−4.77345	+	0.660903i	−0.187230	+	0.0259228i
$651$	−14.2481	−	23.8545i	−0.558427	−	0.934932i
$652$	5.07443	−	5.07443i	0.198730	−	0.198730i
$653$	0.627139	+	1.08624i	0.0245418	+	0.0425077i	0.878035	−	0.478596i	$-0.158854\pi$
$653$	0.627139	+	1.08624i	0.0245418	+	0.0425077i	−0.853494	+	0.521103i	$0.825521\pi$
$654$	−4.00915	+	6.94405i	−0.156770	+	0.271534i
$655$	−3.47768	−	12.9789i	−0.135884	−	0.507127i
$656$	4.98586	−	18.6075i	0.194665	−	0.726500i
$657$	5.71073	−	5.71073i	0.222797	−	0.222797i
$658$	−1.99591	−	7.03023i	−0.0778088	−	0.274067i
$659$	7.07902			0.275760			0.137880	−	0.990449i	$-0.455971\pi$
$659$	7.07902			0.275760			0.137880	+	0.990449i	$0.455971\pi$
$660$	−16.4374	+	9.49015i	−0.639826	+	0.369403i
$661$	−4.81618	−	17.9742i	−0.187328	−	0.699117i	−0.994120	−	0.108282i	$-0.965465\pi$
$661$	−4.81618	−	17.9742i	−0.187328	−	0.699117i	0.806792	−	0.590835i	$-0.201202\pi$
$662$	5.34845	+	3.08793i	0.207874	+	0.120016i
$663$	−1.79316	+	14.3611i	−0.0696407	+	0.557738i
$664$		−	28.3391i		−	1.09977i
$665$	−8.43919	−	29.7255i	−0.327258	−	1.15270i
$666$	−0.162086			−0.00628070
$667$	−1.15728	+	0.668156i	−0.0448101	+	0.0258711i
$668$	−8.61820	+	2.30924i	−0.333448	+	0.0893472i
$669$	−0.688253	−	2.56859i	−0.0266094	−	0.0993076i
$670$	21.3680	+	5.72554i	0.825519	+	0.221197i
$671$	43.9704	−	43.9704i	1.69746	−	1.69746i
$672$	12.8832	−	7.69500i	0.496979	−	0.296841i
$673$			13.2257i			0.509814i	0.966966	+	0.254907i	$0.0820449\pi$
$673$			13.2257i			0.509814i	−0.966966	+	0.254907i	$0.917955\pi$
$674$	1.64265	−	6.13045i	0.0632725	−	0.236136i
$675$	1.05399	−	1.82556i	0.0405680	−	0.0702658i
$676$	−5.10813	+	20.1361i	−0.196466	+	0.774464i
$677$	17.3206	−	10.0001i	0.665686	−	0.384334i	−0.128754	−	0.991677i	$-0.541098\pi$
$677$	17.3206	−	10.0001i	0.665686	−	0.384334i	0.794440	+	0.607343i	$0.207764\pi$
$678$	−3.38348	−	3.38348i	−0.129942	−	0.129942i
$679$	0.409986	+	27.6504i	0.0157338	+	1.06113i
$680$		−	24.4132i		−	0.936205i
$681$	15.0796	+	4.04057i	0.577852	+	0.154835i
$682$	28.6543	−	7.67791i	1.09723	−	0.294002i
$683$	−14.1596	+	3.79406i	−0.541804	+	0.145176i	−0.519333	−	0.854572i	$-0.673820\pi$
$683$	−14.1596	+	3.79406i	−0.541804	+	0.145176i	−0.0224701	+	0.999748i	$0.507153\pi$
$684$	6.76172	+	1.81180i	0.258541	+	0.0692758i
$685$			59.7568i			2.28319i
$686$	9.89829	−	6.31768i	0.377919	−	0.241210i
$687$	−13.2768	−	13.2768i	−0.506540	−	0.506540i
$688$	5.47246	−	3.15953i	0.208636	−	0.120456i
$689$	15.5496	+	36.8421i	0.592394	+	1.40357i
$690$	−2.97619	+	5.15491i	−0.113302	+	0.196244i
$691$	2.51149	−	9.37299i	0.0955414	−	0.356565i	−0.901560	−	0.432655i	$-0.857577\pi$
$691$	2.51149	−	9.37299i	0.0955414	−	0.356565i	0.997101	+	0.0760896i	$0.0242435\pi$
$692$			13.8895i			0.527998i
$693$	−0.174753	−	11.7857i	−0.00663831	−	0.447704i
$694$	−12.7054	+	12.7054i	−0.482291	+	0.482291i
$695$	−6.95559	−	1.86375i	−0.263841	−	0.0706959i
$696$	−0.224070	−	0.836239i	−0.00849334	−	0.0316976i
$697$	42.6908	−	11.4390i	1.61703	−	0.433282i
$698$	−1.03171	+	0.595656i	−0.0390507	+	0.0225459i
$699$	−21.0127			−0.794772
$700$	2.17878	−	8.64185i	0.0823502	−	0.326631i
$701$		−	36.6271i		−	1.38339i	−0.722191	−	0.691693i	$-0.756865\pi$
$701$		−	36.6271i		−	1.38339i	0.722191	−	0.691693i	$-0.243135\pi$
$702$	1.40376	+	1.80433i	0.0529814	+	0.0680999i
$703$	−0.969833	−	0.559933i	−0.0365779	−	0.0211183i
$704$	0.111943	+	0.417776i	0.00421900	+	0.0157455i
$705$	10.0586	−	5.80735i	0.378830	−	0.218717i
$706$	−22.9056			−0.862065
$707$	−1.38976	+	0.394560i	−0.0522673	+	0.0148389i
$708$	4.03427	−	4.03427i	0.151617	−	0.151617i
$709$	−0.595933	+	2.22405i	−0.0223807	+	0.0835260i	−0.976213	−	0.216814i	$-0.930433\pi$
$709$	−0.595933	+	2.22405i	−0.0223807	+	0.0835260i	0.953832	+	0.300340i	$0.0971001\pi$
$710$	3.36544	+	12.5600i	0.126303	+	0.471369i
$711$	−1.48371	+	2.56986i	−0.0556436	+	0.0963775i
$712$	0.733549	+	1.27054i	0.0274909	+	0.0476157i
$713$	−26.1491	+	26.1491i	−0.979292	+	0.979292i
$714$	5.88067	+	3.27993i	0.220078	+	0.122748i
$715$	−34.1490	−	25.8429i	−1.27710	−	0.966468i
$716$	−2.37575	−	4.11491i	−0.0887858	−	0.153781i
$717$	3.72733	−	0.998734i	0.139200	−	0.0372984i
$718$	1.96281	−	3.39969i	0.0732515	−	0.126875i
$719$	11.6951	+	20.2565i	0.436153	+	0.755438i	0.997389	−	0.0722171i	$-0.0230075\pi$
$719$	11.6951	+	20.2565i	0.436153	+	0.755438i	−0.561236	+	0.827656i	$0.689674\pi$
$720$	3.29826	+	3.29826i	0.122919	+	0.122919i
$721$	1.70901	−	6.77857i	0.0636470	−	0.252447i
$722$	−0.0852623	−	0.0852623i	−0.00317313	−	0.00317313i
$723$	−1.30249	+	4.86096i	−0.0484402	+	0.180781i
$724$	19.4464	+	11.2274i	0.722721	+	0.417263i
$725$	−0.692794	−	0.399985i	−0.0257297	−	0.0148551i
$726$	5.41871	+	1.45194i	0.201107	+	0.0538865i
$727$	−12.6815			−0.470329			−0.235165	−	0.971956i	$-0.575563\pi$
$727$	−12.6815			−0.470329			−0.235165	+	0.971956i	$0.575563\pi$
$728$	17.5459	+	12.8735i	0.650293	+	0.477125i
$729$	−1.00000			−0.0370370
$730$	−13.1869	−	3.53341i	−0.488068	−	0.130777i
$731$	12.5554	+	7.24885i	0.464378	+	0.268109i
$732$	−19.3163	−	11.1523i	−0.713951	−	0.412200i
$733$	0.0590689	−	0.220448i	0.00218176	−	0.00814244i	−0.964826	−	0.262888i	$-0.915325\pi$
$733$	0.0590689	−	0.220448i	0.00218176	−	0.00814244i	0.967008	+	0.254746i	$0.0819917\pi$
$734$	−6.62020	−	6.62020i	−0.244356	−	0.244356i
$735$	13.5819	+	12.7994i	0.500975	+	0.472112i
$736$	−14.1224	−	14.1224i	−0.520559	−	0.520559i
$737$	29.1511	+	50.4912i	1.07380	+	1.85987i
$738$	3.49064	−	6.04596i	0.128492	−	0.222555i
$739$	−24.6895	+	6.61553i	−0.908218	+	0.243356i	−0.682542	−	0.730846i	$-0.739126\pi$
$739$	−24.6895	+	6.61553i	−0.908218	+	0.243356i	−0.225676	+	0.974202i	$0.572459\pi$
$740$	−0.544558	−	0.943202i	−0.0200183	−	0.0346728i
$741$	2.16618	+	15.6454i	0.0795765	+	0.574750i
$742$	18.6033	−	0.275840i	0.682949	−	0.0101264i
$743$	20.2576	−	20.2576i	0.743179	−	0.743179i	−0.230010	−	0.973188i	$-0.573876\pi$
$743$	20.2576	−	20.2576i	0.743179	−	0.743179i	0.973188	+	0.230010i	$0.0738758\pi$
$744$	−11.9790	−	20.7482i	−0.439172	−	0.760668i
$745$	5.00813	−	8.67434i	0.183484	−	0.317803i
$746$	3.05854	+	11.4146i	0.111981	+	0.417919i
$747$	−3.21517	+	11.9992i	−0.117637	+	0.439027i
$748$	20.2064	−	20.2064i	0.738820	−	0.738820i
$749$	−3.56069	+	14.1230i	−0.130105	+	0.516043i
$750$	4.88870			0.178510
$751$	−20.7644	+	11.9883i	−0.757705	+	0.437461i	−0.828471	−	0.560032i	$-0.810789\pi$
$751$	−20.7644	+	11.9883i	−0.757705	+	0.437461i	0.0707663	+	0.997493i	$0.477456\pi$
$752$	1.97269	+	7.36217i	0.0719366	+	0.268471i
$753$	0.108868	+	0.0628551i	0.00396738	+	0.00229057i
$754$	0.684737	−	0.532722i	0.0249366	−	0.0194006i
$755$		−	6.37230i		−	0.231912i
$756$	−4.06715	+	1.15468i	−0.147921	+	0.0419954i
$757$	26.4959			0.963009			0.481504	−	0.876444i	$-0.340091\pi$
$757$	26.4959			0.963009			0.481504	+	0.876444i	$0.340091\pi$
$758$	20.0257	−	11.5618i	0.727366	−	0.419945i
$759$	−15.1530	+	4.06024i	−0.550020	+	0.147377i
$760$	−6.89583	−	25.7356i	−0.250138	−	0.933529i
$761$	6.67547	+	1.78869i	0.241986	+	0.0648399i	0.377773	−	0.925898i	$-0.376690\pi$
$761$	6.67547	+	1.78869i	0.241986	+	0.0648399i	−0.135788	+	0.990738i	$0.543357\pi$
$762$	3.94987	−	3.94987i	0.143089	−	0.143089i
$763$	16.2981	−	29.2212i	0.590029	−	1.05788i
$764$			8.75097i			0.316599i
$765$	−2.76977	+	10.3369i	−0.100141	+	0.373732i
$766$	−2.80430	+	4.85718i	−0.101323	+	0.175497i
$767$	11.9257	+	4.84671i	0.430612	+	0.175005i
$768$	6.36314	−	3.67376i	0.229610	−	0.132565i
$769$	16.0449	+	16.0449i	0.578594	+	0.578594i	0.934516	−	0.355922i	$-0.115833\pi$
$769$	16.0449	+	16.0449i	0.578594	+	0.578594i	−0.355922	+	0.934516i	$0.615833\pi$
$770$	−17.1059	+	10.2172i	−0.616453	+	0.368202i
$771$			6.68215i			0.240652i
$772$	−26.8537	−	7.19544i	−0.966487	−	0.258969i
$773$	39.1653	−	10.4943i	1.40868	−	0.377454i	0.527224	−	0.849726i	$-0.323233\pi$
$773$	39.1653	−	10.4943i	1.40868	−	0.377454i	0.881453	+	0.472273i	$0.156566\pi$
$774$	2.21201	−	0.592706i	0.0795090	−	0.0213044i
$775$	−21.3836	−	5.72973i	−0.768123	−	0.205818i
$776$			23.8440i			0.855949i
$777$	0.676282	−	0.0100276i	0.0242615	−	0.000359737i
$778$	−1.94920	−	1.94920i	−0.0698822	−	0.0698822i
$779$	41.7721	−	24.1171i	1.49664	−	0.864086i
$780$	−5.78346	+	14.2306i	−0.207081	+	0.509539i
$781$	−17.1349	+	29.6785i	−0.613134	+	1.06198i
$782$	2.31947	−	8.65637i	0.0829440	−	0.309551i
$783$			0.379497i			0.0135621i
$784$	−10.4199	+	6.43520i	−0.372139	+	0.229829i
$785$	11.2208	−	11.2208i	0.400487	−	0.400487i
$786$	3.08662	+	0.827057i	0.110096	+	0.0295001i
$787$	−10.1123	−	37.7395i	−0.360463	−	1.34527i	−0.873468	−	0.486881i	$-0.838135\pi$
$787$	−10.1123	−	37.7395i	−0.360463	−	1.34527i	0.513005	−	0.858385i	$-0.328532\pi$
$788$	1.15108	−	0.308430i	0.0410054	−	0.0109874i
$789$	−9.79794	+	5.65684i	−0.348816	+	0.201389i
$790$	5.01615			0.178467
$791$	14.3264	+	13.9078i	0.509390	+	0.494505i
$792$		−	10.1633i		−	0.361137i
$793$	6.23540	−	49.9381i	0.221426	−	1.77335i
$794$	2.68143	+	1.54812i	0.0951603	+	0.0549408i
$795$	7.65314	+	28.5619i	0.271429	+	1.01299i
$796$	14.9651	−	8.64012i	0.530425	−	0.306241i
$797$	32.6956			1.15814			0.579069	−	0.815278i	$-0.303416\pi$
$797$	32.6956			1.15814			0.579069	+	0.815278i	$0.303416\pi$
$798$	7.12566	+	1.79652i	0.252245	+	0.0635961i
$799$	−12.3650	+	12.3650i	−0.437443	+	0.437443i
$800$	3.09447	−	11.5487i	0.109406	−	0.408309i
$801$	−0.166448	−	0.621191i	−0.00588113	−	0.0219487i
$802$	−5.85717	+	10.1449i	−0.206824	+	0.358229i
$803$	−17.9901	−	31.1597i	−0.634855	−	1.09960i
$804$	14.7873	−	14.7873i	0.521507	−	0.521507i
$805$	12.0989	−	21.6923i	0.426429	−	0.764554i
$806$	14.4878	−	19.1443i	0.510311	−	0.674330i
$807$	−13.6907	−	23.7129i	−0.481934	−	0.834735i
$808$	−1.20322	+	0.322402i	−0.0423292	+	0.0113421i
$809$	−22.8560	+	39.5878i	−0.803574	+	1.39183i	0.113675	+	0.993518i	$0.463738\pi$
$809$	−22.8560	+	39.5878i	−0.803574	+	1.39183i	−0.917249	+	0.398314i	$0.869596\pi$
$810$	0.845203	+	1.46393i	0.0296974	+	0.0514374i
$811$	−28.8393	−	28.8393i	−1.01268	−	1.01268i	−0.999919	−	0.0127654i	$-0.995937\pi$
$811$	−28.8393	−	28.8393i	−1.01268	−	1.01268i	−0.0127654	−	0.999919i	$-0.504063\pi$
$812$	0.438199	+	1.54347i	0.0153778	+	0.0541653i
$813$	12.3300	+	12.3300i	0.432432	+	0.432432i
$814$	−0.186895	+	0.697501i	−0.00655066	+	0.0244474i
$815$	10.3689	+	5.98647i	0.363206	+	0.209697i
$816$	−6.08180	−	3.51133i	−0.212906	−	0.122921i
$817$	15.2830	+	4.09506i	0.534684	+	0.143268i
$818$	15.5626			0.544134
$819$	−5.96862	−	7.44148i	−0.208560	−	0.260026i
$820$	46.9098			1.63816
$821$	−17.8485	−	4.78248i	−0.622916	−	0.166910i	−0.0664629	−	0.997789i	$-0.521171\pi$
$821$	−17.8485	−	4.78248i	−0.622916	−	0.166910i	−0.556453	+	0.830879i	$0.687838\pi$
$822$	−12.3073	−	7.10563i	−0.429267	−	0.247837i
$823$	−27.6431	−	15.9598i	−0.963579	−	0.556322i	−0.0663061	−	0.997799i	$-0.521121\pi$
$823$	−27.6431	−	15.9598i	−0.963579	−	0.556322i	−0.897273	+	0.441477i	$0.854455\pi$
$824$	1.56008	−	5.82228i	0.0543478	−	0.202829i
$825$	−6.64058	−	6.64058i	−0.231195	−	0.231195i
$826$	4.17180	−	4.29737i	0.145155	−	0.149525i
$827$	−36.1938	−	36.1938i	−1.25858	−	1.25858i	−0.951770	−	0.306814i	$-0.900737\pi$
$827$	−36.1938	−	36.1938i	−1.25858	−	1.25858i	−0.306814	−	0.951770i	$-0.599263\pi$
$828$	2.81348	+	4.87309i	0.0977751	+	0.169351i
$829$	4.66716	−	8.08376i	0.162097	−	0.280761i	−0.773523	−	0.633768i	$-0.781508\pi$
$829$	4.66716	−	8.08376i	0.162097	−	0.280761i	0.935621	+	0.353007i	$0.114841\pi$
$830$	20.2835	−	5.43495i	0.704051	−	0.188650i
$831$	−10.8591	−	18.8085i	−0.376698	−	0.652460i
$832$	0.279121	+	0.211230i	0.00967678	+	0.00732308i
$833$	−24.7392	−	13.3213i	−0.857164	−	0.461555i
$834$	1.21093	−	1.21093i	0.0419312	−	0.0419312i
$835$	−7.44289	−	12.8915i	−0.257572	−	0.446128i
$836$	15.5934	−	27.0085i	0.539307	−	0.934108i
$837$	2.71812	+	10.1442i	0.0939520	+	0.350634i
$838$	−0.966242	+	3.60606i	−0.0333783	+	0.124569i
$839$	−12.5740	+	12.5740i	−0.434102	+	0.434102i	−0.890021	−	0.455919i	$-0.849311\pi$
$839$	−12.5740	+	12.5740i	−0.434102	+	0.434102i	0.455919	+	0.890021i	$0.349311\pi$
$840$	11.5459	+	11.2086i	0.398373	+	0.386732i
$841$	−28.8560			−0.995034
$842$	11.5733	−	6.68184i	0.398842	−	0.230272i
$843$	5.18949	+	19.3675i	0.178736	+	0.667050i
$844$	25.0389	+	14.4562i	0.861874	+	0.497603i
$845$	−34.6559	+	0.463019i	−1.19220	+	0.0159283i
$846$			2.76219i			0.0949660i
$847$	−22.6987	−	5.72280i	−0.779937	−	0.196638i
$848$	−19.4043			−0.666347
$849$	20.3338	−	11.7397i	0.697853	−	0.402906i
$850$	5.18205	−	1.38853i	0.177743	−	0.0476261i
$851$	−0.232982	−	0.869501i	−0.00798652	−	0.0298061i
$852$	11.8733	+	3.18145i	0.406774	+	0.108995i
$853$	−15.0336	+	15.0336i	−0.514741	+	0.514741i	−0.915975	−	0.401234i	$-0.868581\pi$
$853$	−15.0336	+	15.0336i	−0.514741	+	0.514741i	0.401234	+	0.915975i	$0.368581\pi$
$854$	−20.4490	−	11.4054i	−0.699749	−	0.390284i
$855$			11.6792i			0.399420i
$856$	−3.25038	+	12.1306i	−0.111096	+	0.414615i
$857$	2.16516	−	3.75017i	0.0739605	−	0.128103i	−0.826673	−	0.562682i	$-0.809769\pi$
$857$	2.16516	−	3.75017i	0.0739605	−	0.128103i	0.900634	+	0.434579i	$0.143103\pi$
$858$	9.38314	−	3.96026i	0.320335	−	0.135201i
$859$	24.0746	−	13.8995i	0.821415	−	0.474244i	−0.0294890	−	0.999565i	$-0.509388\pi$
$859$	24.0746	−	13.8995i	0.821415	−	0.474244i	0.850904	+	0.525321i	$0.176055\pi$
$860$	10.8807	+	10.8807i	0.371029	+	0.371029i
$861$	−14.1902	+	25.4419i	−0.483601	+	0.867059i
$862$		−	8.07397i		−	0.275001i
$863$	−21.2044	−	5.68171i	−0.721807	−	0.193408i	−0.120829	−	0.992673i	$-0.538555\pi$
$863$	−21.2044	−	5.68171i	−0.721807	−	0.193408i	−0.600978	+	0.799266i	$0.705222\pi$
$864$	−5.47858	+	1.46798i	−0.186385	+	0.0499418i
$865$	−22.3835	+	5.99764i	−0.761062	+	0.203926i
$866$	15.3068	+	4.10143i	0.520145	+	0.139372i
$867$			0.888027i			0.0301590i
$868$	22.7683	+	38.1193i	0.772807	+	1.29385i
$869$	9.34804	+	9.34804i	0.317111	+	0.317111i
$870$	0.555559	−	0.320752i	0.0188352	−	0.0108745i
$871$	43.7126	+	17.7652i	1.48115	+	0.601951i
$872$	14.4249	−	24.9846i	0.488488	−	0.846086i
$873$	2.70518	−	10.0959i	0.0915566	−	0.341694i
$874$		−	9.78041i		−	0.330827i
$875$	−20.3975	+	0.302443i	−0.689560	+	0.0102244i
$876$	−9.12569	+	9.12569i	−0.308329	+	0.308329i
$877$	−13.5828	−	3.63951i	−0.458660	−	0.122898i	0.0220888	−	0.999756i	$-0.492968\pi$
$877$	−13.5828	−	3.63951i	−0.458660	−	0.122898i	−0.480749	+	0.876859i	$0.659635\pi$
$878$	−4.49474	−	16.7746i	−0.151690	−	0.566115i
$879$	−13.1169	+	3.51466i	−0.442422	+	0.118547i
$880$	17.9964	−	10.3903i	0.606660	−	0.350255i
$881$	−5.27268			−0.177641			−0.0888205	−	0.996048i	$-0.528310\pi$
$881$	−5.27268			−0.177641			−0.0888205	+	0.996048i	$0.528310\pi$
$882$	−4.25112	+	1.27532i	−0.143143	+	0.0429421i
$883$			43.5789i			1.46655i	0.679934	+	0.733274i	$0.262009\pi$
$883$			43.5789i			1.46655i	−0.679934	+	0.733274i	$0.737991\pi$
$884$	2.86546	−	22.9488i	0.0963757	−	0.771853i
$885$	8.24346	+	4.75937i	0.277101	+	0.159984i
$886$	1.07469	+	4.01080i	0.0361049	+	0.134745i
$887$	0.278768	−	0.160947i	0.00936011	−	0.00540406i	−0.495313	−	0.868715i	$-0.664946\pi$
$887$	0.278768	−	0.160947i	0.00936011	−	0.00540406i	0.504673	+	0.863311i	$0.331613\pi$
$888$	0.583183			0.0195703
$889$	−16.2360	+	16.7247i	−0.544537	+	0.560928i
$890$	−0.768701	+	0.768701i	−0.0257669	+	0.0257669i
$891$	−1.15306	+	4.30328i	−0.0386290	+	0.144165i
$892$	1.09982	+	4.10459i	0.0368247	+	0.137432i
$893$	−9.54211	+	16.5274i	−0.319315	+	0.553069i
$894$	1.19103	+	2.06292i	0.0398338	+	0.0689942i
$895$	5.60549	−	5.60549i	0.187371	−	0.187371i
$896$	−25.6265	+	15.3065i	−0.856122	+	0.511354i
$897$	−7.66145	+	10.1239i	−0.255808	+	0.338028i
$898$	−5.97535	−	10.3496i	−0.199400	−	0.345371i
$899$	3.84968	−	1.03152i	0.128394	−	0.0344031i
$900$	−1.68426	+	2.91723i	−0.0561420	+	0.0972409i
$901$	−22.2595	−	38.5546i	−0.741571	−	1.28444i
$902$	−21.9925	−	21.9925i	−0.732272	−	0.732272i
$903$	−9.19266	+	2.60984i	−0.305913	+	0.0868500i
$904$	12.1737	+	12.1737i	0.404892	+	0.404892i
$905$	−9.69626	+	36.1870i	−0.322315	+	1.20289i
$906$	1.31242	+	0.757724i	0.0436021	+	0.0251737i
$907$	19.6998	+	11.3737i	0.654121	+	0.377657i	0.790033	−	0.613064i	$-0.210063\pi$
$907$	19.6998	+	11.3737i	0.654121	+	0.377657i	−0.135912	+	0.990721i	$0.543397\pi$
$908$	−24.0971	−	6.45679i	−0.799689	−	0.214276i
$909$	0.546039			0.0181110
$910$	−5.84914	+	15.0272i	−0.193897	+	0.498148i
$911$	32.2846			1.06964			0.534818	−	0.844967i	$-0.320380\pi$
$911$	32.2846			1.06964			0.534818	+	0.844967i	$0.320380\pi$
$912$	−7.40305	−	1.98364i	−0.245139	−	0.0656849i
$913$	47.9286	+	27.6716i	1.58620	+	0.915796i
$914$	−7.69218	−	4.44108i	−0.254435	−	0.146898i
$915$	9.63138	−	35.9448i	0.318404	−	1.18830i
$916$	21.2161	+	21.2161i	0.701000	+	0.701000i
$917$	−12.9297	−	3.25983i	−0.426976	−	0.107649i
$918$	−1.79961	−	1.79961i	−0.0593959	−	0.0593959i
$919$	−17.5929	−	30.4718i	−0.580337	−	1.00517i	−0.995439	−	0.0953985i	$-0.969587\pi$
$919$	−17.5929	−	30.4718i	−0.580337	−	1.00517i	0.415102	−	0.909775i	$-0.363746\pi$
$920$	10.7083	−	18.5473i	0.353042	−	0.611487i
$921$	−26.6867	+	7.15067i	−0.879356	+	0.235623i
$922$	2.22192	+	3.84848i	0.0731750	+	0.126743i
$923$	3.80373	+	27.4728i	0.125201	+	0.904279i
$924$	0.279253	+	18.8335i	0.00918676	+	0.619577i
$925$	0.381046	−	0.381046i	0.0125287	−	0.0125287i
$926$	9.84577	+	17.0534i	0.323552	+	0.560409i
$927$	−1.32112	+	2.28824i	−0.0433912	+	0.0751557i
$928$	0.557095	+	2.07911i	0.0182875	+	0.0682500i
$929$	−3.77515	+	14.0891i	−0.123859	+	0.462247i	−0.999796	−	0.0201774i	$-0.993577\pi$
$929$	−3.77515	+	14.0891i	−0.123859	+	0.462247i	0.875938	+	0.482424i	$0.160244\pi$
$930$	12.5530	−	12.5530i	0.411630	−	0.411630i
$931$	−29.8420	−	7.05492i	−0.978033	−	0.231216i
$932$	33.5780			1.09989
$933$	−9.08801	+	5.24697i	−0.297528	+	0.171778i
$934$	3.17829	+	11.8615i	0.103997	+	0.388121i
$935$	41.2889	+	23.8382i	1.35029	+	0.779592i
$936$	−5.05070	−	6.49195i	−0.165087	−	0.212196i
$937$			3.02803i			0.0989214i	0.998776	+	0.0494607i	$0.0157503\pi$
$937$			3.02803i			0.0989214i	−0.998776	+	0.0494607i	$0.984250\pi$
$938$	15.2914	−	15.7517i	0.499281	−	0.514310i
$939$	−7.14903			−0.233300
$940$	−16.0736	+	9.28009i	−0.524262	+	0.302683i
$941$	55.1297	−	14.7719i	1.79718	−	0.481552i	0.803644	−	0.595110i	$-0.202892\pi$
$941$	55.1297	−	14.7719i	1.79718	−	0.481552i	0.993531	+	0.113559i	$0.0362250\pi$
$942$	0.976741	+	3.64525i	0.0318239	+	0.118769i
$943$	37.4507	+	10.0349i	1.21956	+	0.326780i
$944$	−4.41691	+	4.41691i	−0.143758	+	0.143758i
$945$	−3.61707	−	6.05579i	−0.117663	−	0.196995i
$946$		−	10.2023i		−	0.331706i
$947$	9.96185	−	37.1781i	0.323717	−	1.20813i	−0.591879	−	0.806027i	$-0.701614\pi$
$947$	9.96185	−	37.1781i	0.323717	−	1.20813i	0.915596	−	0.402100i	$-0.131720\pi$
$948$	2.37096	−	4.10662i	0.0770051	−	0.133377i
$949$	−26.9764	−	10.9635i	−0.875691	−	0.355889i
$950$	5.07053	−	2.92747i	0.164510	−	0.0949798i
$951$	−22.7005	−	22.7005i	−0.736113	−	0.736113i
$952$	−21.1586	−	11.8012i	−0.685754	−	0.382478i
$953$		−	0.863851i		−	0.0279829i	−0.999902	−	0.0139914i	$-0.995546\pi$
$953$		−	0.863851i		−	0.0279829i	0.999902	−	0.0139914i	$-0.00445376\pi$
$954$	−6.79255	−	1.82006i	−0.219917	−	0.0589266i
$955$	−14.1026	+	3.77878i	−0.456349	+	0.122278i
$956$	−5.95623	+	1.59597i	−0.192638	+	0.0516173i
$957$	1.63308	+	0.437583i	0.0527901	+	0.0141451i
$958$			0.174042i			0.00562304i
$959$	51.7903	+	28.8859i	1.67240	+	0.932776i
$960$	0.183021	+	0.183021i	0.00590698	+	0.00590698i
$961$	68.6691	−	39.6461i	2.21513	−	1.27891i
$962$	0.227245	+	0.538417i	0.00732668	+	0.0173593i
$963$	2.75251	−	4.76749i	0.0886985	−	0.153630i
$964$	2.08137	−	7.76777i	0.0670364	−	0.250183i
$965$		−	46.3831i		−	1.49312i
$966$	3.02902	+	5.07126i	0.0974570	+	0.163165i
$967$	12.9900	−	12.9900i	0.417731	−	0.417731i	−0.466690	−	0.884421i	$-0.654554\pi$
$967$	12.9900	−	12.9900i	0.417731	−	0.417731i	0.884421	+	0.466690i	$0.154554\pi$
$968$	−19.4965	−	5.22406i	−0.626640	−	0.167908i
$969$	−4.55103	−	16.9847i	−0.146200	−	0.545627i
$970$	−17.0661	+	4.57286i	−0.547961	+	0.146826i
$971$	−44.9692	+	25.9630i	−1.44313	+	0.833191i	−0.998057	−	0.0623033i	$-0.980155\pi$
$971$	−44.9692	+	25.9630i	−1.44313	+	0.833191i	−0.445072	+	0.895495i	$0.646822\pi$
$972$	1.59799			0.0512556
$973$	−4.97755	+	5.12738i	−0.159573	+	0.164376i
$974$		−	1.93091i		−	0.0618704i
$975$	−7.54184	−	0.941696i	−0.241532	−	0.0301584i
$976$	21.1484	+	12.2100i	0.676944	+	0.390834i
$977$	−6.91585	−	25.8103i	−0.221258	−	0.825745i	−0.983869	−	0.178889i	$-0.942750\pi$
$977$	−6.91585	−	25.8103i	−0.221258	−	0.825745i	0.762612	−	0.646857i	$-0.223917\pi$
$978$	−2.46591	+	1.42369i	−0.0788510	+	0.0455247i
$979$	−2.86508			−0.0915684
$980$	−21.7037	−	20.4533i	−0.693299	−	0.653355i
$981$	−8.94229	+	8.94229i	−0.285505	+	0.285505i
$982$	−6.85173	+	25.5710i	−0.218648	+	0.816004i
$983$	6.10538	+	22.7856i	0.194731	+	0.726747i	0.992336	+	0.123567i	$0.0394334\pi$
$983$	6.10538	+	22.7856i	0.194731	+	0.726747i	−0.797605	+	0.603180i	$0.793900\pi$
$984$	−12.5593	+	21.7533i	−0.400375	+	0.693470i
$985$	0.994097	+	1.72183i	0.0316746	+	0.0548620i
$986$	−0.682946	+	0.682946i	−0.0217494	+	0.0217494i
$987$	−0.170885	−	11.5249i	−0.00543932	−	0.366841i
$988$	−3.46153	−	25.0013i	−0.110126	−	0.795396i
$989$	6.35908	+	11.0142i	0.202207	+	0.350233i
$990$	7.27429	−	1.94914i	0.231192	−	0.0619478i
$991$	−25.9147	+	44.8856i	−0.823208	+	1.42584i	0.0800739	+	0.996789i	$0.474484\pi$
$991$	−25.9147	+	44.8856i	−0.823208	+	1.42584i	−0.903281	+	0.429048i	$0.858849\pi$
$992$	29.7829	+	51.5855i	0.945608	+	1.63784i
$993$	6.88754	+	6.88754i	0.218570	+	0.218570i
$994$	12.5124	+	3.15462i	0.396869	+	0.100059i
$995$	20.3861	+	20.3861i	0.646282	+	0.646282i
$996$	5.13782	−	19.1746i	0.162798	−	0.607570i
$997$	9.83406	+	5.67770i	0.311448	+	0.179814i	0.647574	−	0.762002i	$-0.275784\pi$
$997$	9.83406	+	5.67770i	0.311448	+	0.179814i	−0.336126	+	0.941817i	$0.609117\pi$
$998$	0.681798	+	0.393636i	0.0215819	+	0.0124603i
$999$	−0.246928	−	0.0661642i	−0.00781246	−	0.00209334i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bz.b.31.6	yes	36
3.2	odd	2		819.2.fn.g.577.4		36
7.5	odd	6		273.2.bz.a.187.4	yes	36
13.8	odd	4		273.2.bz.a.73.4	✓	36
21.5	even	6		819.2.fn.f.460.6		36
39.8	even	4		819.2.fn.f.73.6		36
91.47	even	12	inner	273.2.bz.b.229.6	yes	36
273.47	odd	12		819.2.fn.g.775.4		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bz.a.73.4	✓	36	13.8	odd	4
273.2.bz.a.187.4	yes	36	7.5	odd	6
273.2.bz.b.31.6	yes	36	1.1	even	1	trivial
273.2.bz.b.229.6	yes	36	91.47	even	12	inner
819.2.fn.f.73.6		36	39.8	even	4
819.2.fn.f.460.6		36	21.5	even	6
819.2.fn.g.577.4		36	3.2	odd	2
819.2.fn.g.775.4		36	273.47	odd	12

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bz (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.612438 + 0.164102i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-1.38390 - 0.798995i) q^{4} +(0.690032 - 2.57523i) q^{5} +(0.448336 + 0.448336i) q^{6} +(-1.89836 - 1.84289i) q^{7} +(-1.61311 - 1.61311i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.612438 + 0.164102i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-1.38390 - 0.798995i) q^{4} +(0.690032 - 2.57523i) q^{5} +(0.448336 + 0.448336i) q^{6} +(-1.89836 - 1.84289i) q^{7} +(-1.61311 - 1.61311i) q^{8} +(0.500000 + 0.866025i) q^{9} +(0.845203 - 1.46393i) q^{10} +(4.30328 - 1.15306i) q^{11} +(-0.798995 - 1.38390i) q^{12} +(2.17576 - 2.87507i) q^{13} +(-0.860206 - 1.44018i) q^{14} +(1.88520 - 1.88520i) q^{15} +(0.874777 + 1.51516i) q^{16} +(-2.00699 + 3.47620i) q^{17} +(0.164102 + 0.612438i) q^{18} +(-1.13380 + 4.23139i) q^{19} +(-3.01253 + 3.01253i) q^{20} +(-0.722584 - 2.54517i) q^{21} +2.82471 q^{22} +(-3.04951 + 1.76064i) q^{23} +(-0.590438 - 2.20355i) q^{24} +(-1.82556 - 1.05399i) q^{25} +(1.80433 - 1.40376i) q^{26} +1.00000i q^{27} +(1.15468 + 4.06715i) q^{28} +0.379497 q^{29} +(1.46393 - 0.845203i) q^{30} +(10.1442 - 2.71812i) q^{31} +(1.46798 + 5.47858i) q^{32} +(4.30328 + 1.15306i) q^{33} +(-1.79961 + 1.79961i) q^{34} +(-6.05579 + 3.61707i) q^{35} -1.59799i q^{36} +(-0.0661642 + 0.246928i) q^{37} +(-1.38876 + 2.40541i) q^{38} +(3.32180 - 1.40200i) q^{39} +(-5.26722 + 3.04103i) q^{40} +(-7.78577 - 7.78577i) q^{41} +(-0.0248706 - 1.67733i) q^{42} -3.61181i q^{43} +(-6.87660 - 1.84258i) q^{44} +(2.57523 - 0.690032i) q^{45} +(-2.15656 + 0.577848i) q^{46} +(4.20803 + 1.12754i) q^{47} +1.74955i q^{48} +(0.207539 + 6.99692i) q^{49} +(-0.945080 - 0.945080i) q^{50} +(-3.47620 + 2.00699i) q^{51} +(-5.30821 + 2.24039i) q^{52} +(-5.54550 + 9.60509i) q^{53} +(-0.164102 + 0.612438i) q^{54} -11.8776i q^{55} +(0.0894843 + 6.03503i) q^{56} +(-3.09759 + 3.09759i) q^{57} +(0.232418 + 0.0622763i) q^{58} +(0.924065 + 3.44866i) q^{59} +(-4.11520 + 1.10266i) q^{60} +(12.0879 - 6.97894i) q^{61} +6.65872 q^{62} +(0.646807 - 2.56547i) q^{63} +0.0970831i q^{64} +(-5.90264 - 7.58699i) q^{65} +(2.44627 + 1.41236i) q^{66} +(3.38708 + 12.6408i) q^{67} +(5.55494 - 3.20714i) q^{68} -3.52127 q^{69} +(-4.30237 + 1.22146i) q^{70} +(-5.43926 + 5.43926i) q^{71} +(0.590438 - 2.20355i) q^{72} +(-2.09027 - 7.80100i) q^{73} +(-0.0810429 + 0.140370i) q^{74} +(-1.05399 - 1.82556i) q^{75} +(4.94993 - 4.94993i) q^{76} +(-10.2941 - 5.74153i) q^{77} +(2.26447 - 0.313525i) q^{78} +(1.48371 + 2.56986i) q^{79} +(4.50551 - 1.20725i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.49064 - 6.04596i) q^{82} +(8.78402 + 8.78402i) q^{83} +(-1.03359 + 4.09960i) q^{84} +(7.56715 + 7.56715i) q^{85} +(0.592706 - 2.21201i) q^{86} +(0.328654 + 0.189749i) q^{87} +(-8.80166 - 5.08164i) q^{88} +(-0.621191 - 0.166448i) q^{89} +1.69041 q^{90} +(-9.42882 + 1.44824i) q^{91} +5.62696 q^{92} +(10.1442 + 2.71812i) q^{93} +(2.39212 + 1.38109i) q^{94} +(10.1145 + 5.83959i) q^{95} +(-1.46798 + 5.47858i) q^{96} +(-7.39070 - 7.39070i) q^{97} +(-1.02111 + 4.31924i) q^{98} +(3.15022 + 3.15022i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{7} + 18 q^{9}+O(q^{10}) \) 36 * q + 4 * q^7 + 18 * q^9	\( 36 q + 4 q^{7} + 18 q^{9} + 4 q^{11} + 16 q^{12} - 36 q^{14} + 12 q^{16} - 4 q^{17} - 12 q^{19} - 44 q^{20} + 6 q^{21} - 8 q^{22} + 12 q^{23} - 18 q^{24} + 48 q^{25} - 28 q^{26} + 12 q^{28} - 16 q^{29} - 56 q^{32} + 4 q^{33} + 48 q^{34} + 8 q^{35} + 22 q^{37} - 16 q^{38} - 8 q^{39} + 60 q^{40} + 32 q^{41} + 12 q^{42} + 4 q^{44} - 44 q^{46} - 14 q^{47} - 6 q^{49} - 68 q^{50} + 12 q^{51} - 82 q^{52} - 8 q^{53} + 8 q^{56} - 6 q^{57} - 84 q^{58} + 70 q^{59} + 2 q^{60} + 36 q^{61} - 48 q^{62} + 2 q^{63} - 8 q^{65} + 38 q^{67} + 36 q^{68} + 8 q^{69} - 40 q^{70} - 36 q^{71} + 18 q^{72} - 46 q^{73} + 40 q^{74} - 10 q^{75} + 60 q^{76} - 60 q^{77} + 32 q^{78} - 38 q^{80} - 18 q^{81} - 24 q^{83} + 38 q^{84} + 44 q^{85} - 24 q^{86} + 36 q^{87} - 168 q^{88} + 38 q^{89} - 14 q^{91} - 40 q^{92} + 56 q^{96} - 36 q^{97} + 58 q^{98} + 8 q^{99}+O(q^{100}) \) 36 * q + 4 * q^7 + 18 * q^9 + 4 * q^11 + 16 * q^12 - 36 * q^14 + 12 * q^16 - 4 * q^17 - 12 * q^19 - 44 * q^20 + 6 * q^21 - 8 * q^22 + 12 * q^23 - 18 * q^24 + 48 * q^25 - 28 * q^26 + 12 * q^28 - 16 * q^29 - 56 * q^32 + 4 * q^33 + 48 * q^34 + 8 * q^35 + 22 * q^37 - 16 * q^38 - 8 * q^39 + 60 * q^40 + 32 * q^41 + 12 * q^42 + 4 * q^44 - 44 * q^46 - 14 * q^47 - 6 * q^49 - 68 * q^50 + 12 * q^51 - 82 * q^52 - 8 * q^53 + 8 * q^56 - 6 * q^57 - 84 * q^58 + 70 * q^59 + 2 * q^60 + 36 * q^61 - 48 * q^62 + 2 * q^63 - 8 * q^65 + 38 * q^67 + 36 * q^68 + 8 * q^69 - 40 * q^70 - 36 * q^71 + 18 * q^72 - 46 * q^73 + 40 * q^74 - 10 * q^75 + 60 * q^76 - 60 * q^77 + 32 * q^78 - 38 * q^80 - 18 * q^81 - 24 * q^83 + 38 * q^84 + 44 * q^85 - 24 * q^86 + 36 * q^87 - 168 * q^88 + 38 * q^89 - 14 * q^91 - 40 * q^92 + 56 * q^96 - 36 * q^97 + 58 * q^98 + 8 * q^99

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