LMFDB - Embedded newform 315.2.t.c.131.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("315.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.9
Character	$\chi$	$=$	315.131
Dual form			315.2.t.c.101.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.103991i q^{2} +(0.570662 + 1.63534i) q^{3} +1.98919 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.170061 + 0.0593436i) q^{6} +(-0.107447 + 2.64357i) q^{7} +0.414839i q^{8} +(-2.34869 + 1.86646i) q^{9} +O(q^{10})$	\(q+0.103991i q^{2} +(0.570662 + 1.63534i) q^{3} +1.98919 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.170061 + 0.0593436i) q^{6} +(-0.107447 + 2.64357i) q^{7} +0.414839i q^{8} +(-2.34869 + 1.86646i) q^{9} +(0.0900587 - 0.0519954i) q^{10} +(2.53457 + 1.46334i) q^{11} +(1.13515 + 3.25300i) q^{12} +(-2.40454 - 1.38826i) q^{13} +(-0.274907 - 0.0111734i) q^{14} +(1.13092 - 1.31188i) q^{15} +3.93523 q^{16} +(-3.62041 - 6.27073i) q^{17} +(-0.194094 - 0.244242i) q^{18} +(6.40301 + 3.69678i) q^{19} +(-0.994593 - 1.72269i) q^{20} +(-4.38446 + 1.33287i) q^{21} +(-0.152173 + 0.263572i) q^{22} +(-0.159465 + 0.0920672i) q^{23} +(-0.678403 + 0.236733i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.144366 - 0.250050i) q^{26} +(-4.39260 - 2.77580i) q^{27} +(-0.213731 + 5.25855i) q^{28} +(-1.84819 + 1.06705i) q^{29} +(0.136423 + 0.117605i) q^{30} -2.83342i q^{31} +1.23891i q^{32} +(-0.946671 + 4.97996i) q^{33} +(0.652098 - 0.376489i) q^{34} +(2.34312 - 1.22873i) q^{35} +(-4.67198 + 3.71273i) q^{36} +(-1.26588 + 2.19256i) q^{37} +(-0.384431 + 0.665854i) q^{38} +(0.898103 - 4.72447i) q^{39} +(0.359261 - 0.207419i) q^{40} +(3.74637 - 6.48890i) q^{41} +(-0.138606 - 0.455943i) q^{42} +(0.223536 + 0.387176i) q^{43} +(5.04173 + 2.91085i) q^{44} +(2.79074 + 1.10080i) q^{45} +(-0.00957414 - 0.0165829i) q^{46} +0.588831 q^{47} +(2.24569 + 6.43545i) q^{48} +(-6.97691 - 0.568084i) q^{49} +(-0.0900587 - 0.0519954i) q^{50} +(8.18876 - 9.49907i) q^{51} +(-4.78308 - 2.76151i) q^{52} +(6.46888 - 3.73481i) q^{53} +(0.288657 - 0.456790i) q^{54} -2.92667i q^{55} +(-1.09665 - 0.0445730i) q^{56} +(-2.39155 + 12.5807i) q^{57} +(-0.110964 - 0.192195i) q^{58} -8.14263 q^{59} +(2.24960 - 2.60957i) q^{60} -12.6412i q^{61} +0.294649 q^{62} +(-4.68175 - 6.40947i) q^{63} +7.74163 q^{64} +2.77652i q^{65} +(-0.517870 - 0.0984450i) q^{66} +3.10342 q^{67} +(-7.20166 - 12.4736i) q^{68} +(-0.241562 - 0.208241i) q^{69} +(0.127777 + 0.243663i) q^{70} -5.62459i q^{71} +(-0.774278 - 0.974327i) q^{72} +(11.3988 - 6.58111i) q^{73} +(-0.228006 - 0.131640i) q^{74} +(-1.70158 - 0.323463i) q^{75} +(12.7368 + 7.35359i) q^{76} +(-4.14076 + 6.54308i) q^{77} +(0.491302 + 0.0933945i) q^{78} -9.11435 q^{79} +(-1.96762 - 3.40801i) q^{80} +(2.03268 - 8.76745i) q^{81} +(0.674785 + 0.389587i) q^{82} +(-4.90339 - 8.49292i) q^{83} +(-8.72150 + 2.65133i) q^{84} +(-3.62041 + 6.27073i) q^{85} +(-0.0402627 + 0.0232457i) q^{86} +(-2.79969 - 2.41350i) q^{87} +(-0.607048 + 1.05144i) q^{88} +(-7.98030 + 13.8223i) q^{89} +(-0.114473 + 0.290212i) q^{90} +(3.92832 - 6.20740i) q^{91} +(-0.317206 + 0.183139i) q^{92} +(4.63361 - 1.61692i) q^{93} +0.0612330i q^{94} -7.39356i q^{95} +(-2.02603 + 0.706996i) q^{96} +(-1.69927 + 0.981074i) q^{97} +(0.0590755 - 0.725534i) q^{98} +(-8.68417 + 1.29375i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - q^{3} - 32 q^{4} - 16 q^{5} - 2 q^{6} + q^{7} + q^{9}+O(q^{10}) $ 32 * q - q^3 - 32 * q^4 - 16 * q^5 - 2 * q^6 + q^7 + q^9	$ 32 q - q^{3} - 32 q^{4} - 16 q^{5} - 2 q^{6} + q^{7} + q^{9} + 3 q^{11} + 12 q^{12} + 6 q^{13} - 15 q^{14} - q^{15} + 32 q^{16} - 3 q^{17} - 13 q^{18} + 16 q^{20} - q^{21} - 21 q^{22} - 9 q^{23} - 4 q^{24} - 16 q^{25} + 12 q^{26} + 23 q^{27} - 31 q^{28} + 18 q^{29} - 2 q^{30} + 19 q^{33} - 30 q^{34} + q^{35} + 18 q^{36} - q^{37} - 30 q^{38} + 21 q^{39} + 6 q^{41} + 19 q^{42} - 19 q^{43} + 21 q^{44} - 8 q^{45} + 6 q^{46} - 30 q^{47} - 35 q^{48} + 5 q^{49} + 36 q^{51} + 21 q^{52} - 24 q^{53} - 59 q^{54} + 30 q^{56} + 27 q^{57} + 30 q^{59} + 3 q^{60} - 32 q^{63} + 76 q^{64} + 26 q^{66} - 50 q^{67} - 3 q^{68} - 50 q^{69} + 9 q^{70} - 14 q^{72} + 12 q^{73} + 60 q^{74} + 2 q^{75} + 54 q^{76} - 27 q^{77} - 42 q^{78} + 4 q^{79} - 16 q^{80} - 23 q^{81} - 24 q^{82} - 42 q^{83} - 72 q^{84} - 3 q^{85} + 51 q^{86} + 34 q^{87} + 42 q^{88} + 30 q^{89} + 41 q^{90} - 57 q^{91} + 6 q^{92} - 33 q^{93} + 15 q^{96} - 42 q^{97} + 6 q^{98} - q^{99}+O(q^{100}) $ 32 * q - q^3 - 32 * q^4 - 16 * q^5 - 2 * q^6 + q^7 + q^9 + 3 * q^11 + 12 * q^12 + 6 * q^13 - 15 * q^14 - q^15 + 32 * q^16 - 3 * q^17 - 13 * q^18 + 16 * q^20 - q^21 - 21 * q^22 - 9 * q^23 - 4 * q^24 - 16 * q^25 + 12 * q^26 + 23 * q^27 - 31 * q^28 + 18 * q^29 - 2 * q^30 + 19 * q^33 - 30 * q^34 + q^35 + 18 * q^36 - q^37 - 30 * q^38 + 21 * q^39 + 6 * q^41 + 19 * q^42 - 19 * q^43 + 21 * q^44 - 8 * q^45 + 6 * q^46 - 30 * q^47 - 35 * q^48 + 5 * q^49 + 36 * q^51 + 21 * q^52 - 24 * q^53 - 59 * q^54 + 30 * q^56 + 27 * q^57 + 30 * q^59 + 3 * q^60 - 32 * q^63 + 76 * q^64 + 26 * q^66 - 50 * q^67 - 3 * q^68 - 50 * q^69 + 9 * q^70 - 14 * q^72 + 12 * q^73 + 60 * q^74 + 2 * q^75 + 54 * q^76 - 27 * q^77 - 42 * q^78 + 4 * q^79 - 16 * q^80 - 23 * q^81 - 24 * q^82 - 42 * q^83 - 72 * q^84 - 3 * q^85 + 51 * q^86 + 34 * q^87 + 42 * q^88 + 30 * q^89 + 41 * q^90 - 57 * q^91 + 6 * q^92 - 33 * q^93 + 15 * q^96 - 42 * q^97 + 6 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$			0.103991i			0.0735326i	0.999324	+	0.0367663i	$0.0117057\pi$
$2$			0.103991i			0.0735326i	−0.999324	+	0.0367663i	$0.988294\pi$
$3$	0.570662	+	1.63534i	0.329472	+	0.944165i
$3$	0.570662	+	1.63534i	0.329472	+	0.944165i
$4$	1.98919			0.994593
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−0.170061	+	0.0593436i	−0.0694269	+	0.0242269i
$7$	−0.107447	+	2.64357i	−0.0406110	+	0.999175i
$7$	−0.107447	+	2.64357i	−0.0406110	+	0.999175i
$8$			0.414839i			0.146668i
$9$	−2.34869	+	1.86646i	−0.782896	+	0.622152i
$10$	0.0900587	−	0.0519954i	0.0284790	−	0.0164424i
$11$	2.53457	+	1.46334i	0.764202	+	0.441212i	0.830802	−	0.556567i	$-0.187882\pi$
$11$	2.53457	+	1.46334i	0.764202	+	0.441212i	−0.0666004	+	0.997780i	$0.521215\pi$
$12$	1.13515	+	3.25300i	0.327690	+	0.939060i
$13$	−2.40454	−	1.38826i	−0.666899	−	0.385034i	0.128001	−	0.991774i	$-0.459144\pi$
$13$	−2.40454	−	1.38826i	−0.666899	−	0.385034i	−0.794901	+	0.606740i	$0.792477\pi$
$14$	−0.274907	−	0.0111734i	−0.0734719	−	0.00298623i
$15$	1.13092	−	1.31188i	0.292002	−	0.338726i
$16$	3.93523			0.983808
$17$	−3.62041	−	6.27073i	−0.878078	−	1.52088i	−0.853448	−	0.521179i	$-0.825493\pi$
$17$	−3.62041	−	6.27073i	−0.878078	−	1.52088i	−0.0246300	−	0.999697i	$-0.507841\pi$
$18$	−0.194094	−	0.244242i	−0.0457484	−	0.0575684i
$19$	6.40301	+	3.69678i	1.46895	+	0.848100i	0.999394	−	0.0348020i	$-0.0110800\pi$
$19$	6.40301	+	3.69678i	1.46895	+	0.848100i	0.469558	+	0.882902i	$0.344413\pi$
$20$	−0.994593	−	1.72269i	−0.222398	−	0.385204i
$21$	−4.38446	+	1.33287i	−0.956767	+	0.290857i
$22$	−0.152173	+	0.263572i	−0.0324435	+	0.0561938i
$23$	−0.159465	+	0.0920672i	−0.0332508	+	0.0191973i	−0.516533	−	0.856267i	$-0.672778\pi$
$23$	−0.159465	+	0.0920672i	−0.0332508	+	0.0191973i	0.483282	+	0.875464i	$0.339444\pi$
$24$	−0.678403	+	0.236733i	−0.138478	+	0.0483229i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	0.144366	−	0.250050i	0.0283126	−	0.0490388i
$27$	−4.39260	−	2.77580i	−0.845357	−	0.534202i
$28$	−0.213731	+	5.25855i	−0.0403914	+	0.993772i
$29$	−1.84819	+	1.06705i	−0.343201	+	0.198147i	−0.661686	−	0.749781i	$-0.730159\pi$
$29$	−1.84819	+	1.06705i	−0.343201	+	0.198147i	0.318486	+	0.947928i	$0.396826\pi$
$30$	0.136423	+	0.117605i	0.0249074	+	0.0214716i
$31$		−	2.83342i		−	0.508897i	−0.967086	−	0.254448i	$-0.918106\pi$
$31$		−	2.83342i		−	0.508897i	0.967086	−	0.254448i	$-0.0818939\pi$
$32$			1.23891i			0.219010i
$33$	−0.946671	+	4.97996i	−0.164794	+	0.866900i
$34$	0.652098	−	0.376489i	0.111834	−	0.0645673i
$35$	2.34312	−	1.22873i	0.396060	−	0.207694i
$36$	−4.67198	+	3.71273i	−0.778663	+	0.618788i
$37$	−1.26588	+	2.19256i	−0.208109	+	0.360455i	−0.951119	−	0.308825i	$-0.900064\pi$
$37$	−1.26588	+	2.19256i	−0.208109	+	0.360455i	0.743010	+	0.669281i	$0.233398\pi$
$38$	−0.384431	+	0.665854i	−0.0623630	+	0.108016i
$39$	0.898103	−	4.72447i	0.143812	−	0.756521i
$40$	0.359261	−	0.207419i	0.0568041	−	0.0327959i
$41$	3.74637	−	6.48890i	0.585084	−	1.01340i	−0.409781	−	0.912184i	$-0.634395\pi$
$41$	3.74637	−	6.48890i	0.585084	−	1.01340i	0.994865	−	0.101211i	$-0.0322718\pi$
$42$	−0.138606	−	0.455943i	−0.0213874	−	0.0703535i
$43$	0.223536	+	0.387176i	0.0340889	+	0.0590438i	0.882567	−	0.470188i	$-0.155814\pi$
$43$	0.223536	+	0.387176i	0.0340889	+	0.0590438i	−0.848478	+	0.529231i	$0.822480\pi$
$44$	5.04173	+	2.91085i	0.760070	+	0.438827i
$45$	2.79074	+	1.10080i	0.416019	+	0.164097i
$46$	−0.00957414	−	0.0165829i	−0.00141163	−	0.00244501i
$47$	0.588831			0.0858899			0.0429449	−	0.999077i	$-0.486326\pi$
$47$	0.588831			0.0858899			0.0429449	+	0.999077i	$0.486326\pi$
$48$	2.24569	+	6.43545i	0.324137	+	0.928878i
$49$	−6.97691	−	0.568084i	−0.996701	−	0.0811549i
$50$	−0.0900587	−	0.0519954i	−0.0127362	−	0.00735326i
$51$	8.18876	−	9.49907i	1.14666	−	1.33014i
$52$	−4.78308	−	2.76151i	−0.663293	−	0.382953i
$53$	6.46888	−	3.73481i	0.888570	−	0.513016i	0.0150952	−	0.999886i	$-0.495195\pi$
$53$	6.46888	−	3.73481i	0.888570	−	0.513016i	0.873474	+	0.486870i	$0.161862\pi$
$54$	0.288657	−	0.456790i	0.0392813	−	0.0621613i
$55$		−	2.92667i		−	0.394632i
$56$	−1.09665	−	0.0445730i	−0.146547	−	0.00595631i
$57$	−2.39155	+	12.5807i	−0.316768	+	1.66636i
$58$	−0.110964	−	0.192195i	−0.0145703	−	0.0252364i
$59$	−8.14263			−1.06008			−0.530040	−	0.847973i	$-0.677823\pi$
$59$	−8.14263			−1.06008			−0.530040	+	0.847973i	$0.677823\pi$
$60$	2.24960	−	2.60957i	0.290423	−	0.336894i
$61$		−	12.6412i		−	1.61854i	−0.587434	−	0.809272i	$-0.699862\pi$
$61$		−	12.6412i		−	1.61854i	0.587434	−	0.809272i	$-0.300138\pi$
$62$	0.294649			0.0374205
$63$	−4.68175	−	6.40947i	−0.589845	−	0.807517i
$64$	7.74163			0.967704
$65$			2.77652i			0.344385i
$66$	−0.517870	−	0.0984450i	−0.0637454	−	0.0121177i
$67$	3.10342			0.379143			0.189572	−	0.981867i	$-0.439290\pi$
$67$	3.10342			0.379143			0.189572	+	0.981867i	$0.439290\pi$
$68$	−7.20166	−	12.4736i	−0.873330	−	1.51265i
$69$	−0.241562	−	0.208241i	−0.0290806	−	0.0250692i
$70$	0.127777	+	0.243663i	0.0152723	+	0.0291233i
$71$		−	5.62459i		−	0.667516i	−0.942659	−	0.333758i	$-0.891683\pi$
$71$		−	5.62459i		−	0.667516i	0.942659	−	0.333758i	$-0.108317\pi$
$72$	−0.774278	−	0.974327i	−0.0912495	−	0.114826i
$73$	11.3988	−	6.58111i	1.33413	−	0.770261i	0.348201	−	0.937420i	$-0.386793\pi$
$73$	11.3988	−	6.58111i	1.33413	−	0.770261i	0.985930	+	0.167159i	$0.0534594\pi$
$74$	−0.228006	−	0.131640i	−0.0265052	−	0.0153028i
$75$	−1.70158	−	0.323463i	−0.196481	−	0.0373503i
$76$	12.7368	+	7.35359i	1.46101	+	0.843514i
$77$	−4.14076	+	6.54308i	−0.471883	+	0.745654i
$78$	0.491302	+	0.0933945i	0.0556290	+	0.0105748i
$79$	−9.11435			−1.02544			−0.512722	−	0.858555i	$-0.671363\pi$
$79$	−9.11435			−1.02544			−0.512722	+	0.858555i	$0.671363\pi$
$80$	−1.96762	−	3.40801i	−0.219986	−	0.381027i
$81$	2.03268	−	8.76745i	0.225854	−	0.974161i
$82$	0.674785	+	0.389587i	0.0745176	+	0.0430227i
$83$	−4.90339	−	8.49292i	−0.538217	−	0.932219i	−0.999000	−	0.0447065i	$-0.985765\pi$
$83$	−4.90339	−	8.49292i	−0.538217	−	0.932219i	0.460783	−	0.887513i	$-0.347569\pi$
$84$	−8.72150	+	2.65133i	−0.951593	+	0.289284i
$85$	−3.62041	+	6.27073i	−0.392688	+	0.680156i
$86$	−0.0402627	+	0.0232457i	−0.00434164	+	0.00250665i
$87$	−2.79969	−	2.41350i	−0.300158	−	0.258754i
$88$	−0.607048	+	1.05144i	−0.0647115	+	0.112084i
$89$	−7.98030	+	13.8223i	−0.845910	+	1.46516i	0.0389185	+	0.999242i	$0.487609\pi$
$89$	−7.98030	+	13.8223i	−0.845910	+	1.46516i	−0.884829	+	0.465917i	$0.845725\pi$
$90$	−0.114473	+	0.290212i	−0.0120665	+	0.0305910i
$91$	3.92832	−	6.20740i	0.411800	−	0.650712i
$92$	−0.317206	+	0.183139i	−0.0330710	+	0.0190935i
$93$	4.63361	−	1.61692i	0.480483	−	0.167667i
$94$			0.0612330i			0.00631571i
$95$		−	7.39356i		−	0.758564i
$96$	−2.02603	+	0.706996i	−0.206781	+	0.0721575i
$97$	−1.69927	+	0.981074i	−0.172535	+	0.0996130i	−0.583781	−	0.811912i	$-0.698427\pi$
$97$	−1.69927	+	0.981074i	−0.172535	+	0.0996130i	0.411246	+	0.911525i	$0.365094\pi$
$98$	0.0590755	−	0.725534i	0.00596753	−	0.0732900i
$99$	−8.68417	+	1.29375i	−0.872792	+	0.130026i
$100$	−0.994593	+	1.72269i	−0.0994593	+	0.172269i
$101$	−2.85272	+	4.94105i	−0.283856	+	0.491653i	−0.972331	−	0.233607i	$-0.924947\pi$
$101$	−2.85272	+	4.94105i	−0.283856	+	0.491653i	0.688475	+	0.725260i	$0.258280\pi$
$102$	0.987816	+	0.851556i	0.0978084	+	0.0843166i
$103$	−10.4398	+	6.02741i	−1.02866	+	0.593899i	−0.916601	−	0.399803i	$-0.869079\pi$
$103$	−10.4398	+	6.02741i	−1.02866	+	0.593899i	−0.112061	+	0.993701i	$0.535745\pi$
$104$	0.575904	−	0.997496i	0.0564721	−	0.0978125i
$105$	3.34653	+	3.13061i	0.326588	+	0.305517i
$106$	0.388386	+	0.672704i	0.0377234	+	0.0653388i
$107$	2.07619	+	1.19869i	0.200713	+	0.115882i	0.596988	−	0.802250i	$-0.296364\pi$
$107$	2.07619	+	1.19869i	0.200713	+	0.115882i	−0.396275	+	0.918132i	$0.629697\pi$
$108$	−8.73770	−	5.52157i	−0.840786	−	0.531314i
$109$	−5.16660	−	8.94882i	−0.494871	−	0.857141i	0.505112	−	0.863054i	$-0.331451\pi$
$109$	−5.16660	−	8.94882i	−0.494871	−	0.857141i	−0.999983	+	0.00591270i	$0.998118\pi$
$110$	0.304347			0.0290183
$111$	−4.30798	−	0.818930i	−0.408896	−	0.0777294i
$112$	−0.422827	+	10.4031i	−0.0399534	+	0.982997i
$113$	7.32912	+	4.23147i	0.689466	+	0.398063i	0.803412	−	0.595424i	$-0.203016\pi$
$113$	7.32912	+	4.23147i	0.689466	+	0.398063i	−0.113946	+	0.993487i	$0.536349\pi$
$114$	−1.30828	−	0.248699i	−0.122532	−	0.0232928i
$115$	0.159465	+	0.0920672i	0.0148702	+	0.00858531i
$116$	−3.67640	+	2.12257i	−0.341345	+	0.197076i
$117$	8.23865	−	1.22737i	0.761663	−	0.113471i
$118$		−	0.846759i		−	0.0779505i
$119$	16.9661	−	8.89703i	1.55528	−	0.815589i
$120$	0.544218	+	0.469148i	0.0496801	+	0.0428272i
$121$	−1.21730	−	2.10842i	−0.110664	−	0.191675i
$122$	1.31457			0.119016
$123$	12.7495	+	2.42362i	1.14958	+	0.218531i
$124$		−	5.63620i		−	0.506145i
$125$	1.00000			0.0894427
$126$	0.666525	−	0.486858i	0.0593788	−	0.0433728i
$127$	6.15631			0.546284			0.273142	−	0.961974i	$-0.411937\pi$
$127$	6.15631			0.546284			0.273142	+	0.961974i	$0.411937\pi$
$128$			3.28287i			0.290167i
$129$	−0.505602	+	0.586505i	−0.0445157	+	0.0516389i
$130$	−0.288733			−0.0253235
$131$	10.4097	+	18.0301i	0.909498	+	1.57530i	0.814764	+	0.579793i	$0.196867\pi$
$131$	10.4097	+	18.0301i	0.909498	+	1.57530i	0.0947339	+	0.995503i	$0.469800\pi$
$132$	−1.88310	+	9.90607i	−0.163903	+	0.862213i
$133$	−10.4607	+	16.5296i	−0.907056	+	1.43330i
$134$			0.322727i			0.0278794i
$135$	−0.207608	+	5.19200i	−0.0178681	+	0.446857i
$136$	2.60134	−	1.50188i	0.223063	−	0.128786i
$137$	4.83774	+	2.79307i	0.413316	+	0.238628i	0.692214	−	0.721693i	$-0.256636\pi$
$137$	4.83774	+	2.79307i	0.413316	+	0.238628i	−0.278897	+	0.960321i	$0.589969\pi$
$138$	0.0216551	−	0.0251202i	0.00184341	−	0.00213838i
$139$	12.4855	+	7.20849i	1.05900	+	0.611416i	0.925157	−	0.379586i	$-0.123933\pi$
$139$	12.4855	+	7.20849i	1.05900	+	0.611416i	0.133847	+	0.991002i	$0.457267\pi$
$140$	4.66090	−	2.44418i	0.393918	−	0.206571i
$141$	0.336024	+	0.962941i	0.0282983	+	0.0810943i
$142$	0.584906			0.0490842
$143$	−4.06298	−	7.03730i	−0.339764	−	0.588488i
$144$	−9.24264	+	7.34494i	−0.770220	+	0.612078i
$145$	1.84819	+	1.06705i	0.153484	+	0.0886140i
$146$	0.684375	+	1.18537i	0.0566393	+	0.0981021i
$147$	−3.05245	−	11.7338i	−0.251762	−	0.967789i
$148$	−2.51807	+	4.36142i	−0.206984	+	0.358506i
$149$	−1.34036	+	0.773860i	−0.109807	+	0.0633971i	−0.553898	−	0.832585i	$-0.686860\pi$
$149$	−1.34036	+	0.773860i	−0.109807	+	0.0633971i	0.444091	+	0.895982i	$0.353527\pi$
$150$	0.0336372	−	0.176949i	0.00274647	−	0.0144478i
$151$	7.65406	−	13.2572i	0.622878	−	1.07886i	−0.366069	−	0.930588i	$-0.619297\pi$
$151$	7.65406	−	13.2572i	0.622878	−	1.07886i	0.988947	−	0.148269i	$-0.0473701\pi$
$152$	−1.53357	+	2.65622i	−0.124389	+	0.215448i
$153$	20.2073	+	7.97066i	1.63366	+	0.644390i
$154$	−0.680420	−	0.430601i	−0.0548298	−	0.0346988i
$155$	−2.45381	+	1.41671i	−0.197095	+	0.113793i
$156$	1.78649	−	9.39786i	0.143034	−	0.752431i
$157$			4.42545i			0.353189i	0.984284	+	0.176595i	$0.0565082\pi$
$157$			4.42545i			0.353189i	−0.984284	+	0.176595i	$0.943492\pi$
$158$		−	0.947808i		−	0.0754036i
$159$	9.79924	+	8.44752i	0.777131	+	0.669932i
$160$	1.07292	−	0.619453i	0.0848220	−	0.0489720i
$161$	−0.226252	−	0.431449i	−0.0178312	−	0.0340029i
$162$	0.911734	+	0.211380i	0.0716326	+	0.0166076i
$163$	−2.67530	+	4.63375i	−0.209546	+	0.362944i	−0.951571	−	0.307428i	$-0.900532\pi$
$163$	−2.67530	+	4.63375i	−0.209546	+	0.362944i	0.742026	+	0.670371i	$0.233865\pi$
$164$	7.45222	−	12.9076i	0.581920	−	1.00792i
$165$	4.78611	−	1.67014i	0.372598	−	0.130020i
$166$	0.883186	−	0.509907i	0.0685485	−	0.0395765i
$167$	−10.2622	+	17.7747i	−0.794116	+	1.37545i	0.129284	+	0.991608i	$0.458732\pi$
$167$	−10.2622	+	17.7747i	−0.794116	+	1.37545i	−0.923399	+	0.383841i	$0.874601\pi$
$168$	−0.552927	−	1.81884i	−0.0426592	−	0.140327i
$169$	−2.64546	−	4.58207i	−0.203497	−	0.352467i
$170$	−0.652098	−	0.376489i	−0.0500136	−	0.0288754i
$171$	−21.9386	+	3.26835i	−1.67768	+	0.249937i
$172$	0.444655	+	0.770165i	0.0339046	+	0.0587245i
$173$	−21.3176			−1.62074			−0.810372	−	0.585915i	$-0.800735\pi$
$173$	−21.3176			−1.62074			−0.810372	+	0.585915i	$0.800735\pi$
$174$	0.250982	−	0.291142i	0.0190269	−	0.0220714i
$175$	−2.23567	−	1.41484i	−0.169001	−	0.106952i
$176$	9.97413	+	5.75857i	0.751828	+	0.434068i
$177$	−4.64669	−	13.3160i	−0.349267	−	1.00089i
$178$	−1.43739	−	0.829878i	−0.107737	−	0.0622020i
$179$	−2.03822	+	1.17677i	−0.152344	+	0.0879556i	−0.574234	−	0.818691i	$-0.694700\pi$
$179$	−2.03822	+	1.17677i	−0.152344	+	0.0879556i	0.421890	+	0.906647i	$0.361367\pi$
$180$	5.55131	+	2.18969i	0.413770	+	0.163210i
$181$			1.64325i			0.122142i	0.998133	+	0.0610711i	$0.0194516\pi$
$181$			1.64325i			0.122142i	−0.998133	+	0.0610711i	$0.980548\pi$
$182$	0.645513	+	0.408509i	0.0478486	+	0.0302807i
$183$	20.6728	−	7.21388i	1.52817	−	0.533265i
$184$	−0.0381930	−	0.0661522i	−0.00281563	−	0.00487681i
$185$	2.53176			0.186138
$186$	0.168145	+	0.481853i	0.0123290	+	0.0353311i
$187$		−	21.1915i		−	1.54967i
$188$	1.17130			0.0854255
$189$	7.80998	−	11.3139i	0.568092	−	0.822965i
$190$	0.768862			0.0557791
$191$			13.5068i			0.977319i	0.872475	+	0.488659i	$0.162514\pi$
$191$			13.5068i			0.977319i	−0.872475	+	0.488659i	$0.837486\pi$
$192$	4.41786	+	12.6602i	0.318831	+	0.913672i
$193$	−15.7119			−1.13097			−0.565485	−	0.824759i	$-0.691311\pi$
$193$	−15.7119			−1.13097			−0.565485	+	0.824759i	$0.691311\pi$
$194$	−0.102023	−	0.176708i	−0.00732480	−	0.0126869i
$195$	−4.54057	+	1.58446i	−0.325157	+	0.113465i
$196$	−13.8784	−	1.13003i	−0.991312	−	0.0807161i
$197$			24.6295i			1.75478i	0.479781	+	0.877388i	$0.340716\pi$
$197$			24.6295i			1.75478i	−0.479781	+	0.877388i	$0.659284\pi$
$198$	−0.134538	−	0.903074i	−0.00956117	−	0.0641787i
$199$	−14.4687	+	8.35349i	−1.02566	+	0.592163i	−0.915737	−	0.401778i	$-0.868392\pi$
$199$	−14.4687	+	8.35349i	−1.02566	+	0.592163i	−0.109919	+	0.993941i	$0.535059\pi$
$200$	−0.359261	−	0.207419i	−0.0254036	−	0.0146668i
$201$	1.77101	+	5.07516i	0.124917	+	0.357974i
$202$	−0.513824	−	0.296656i	−0.0361525	−	0.0208727i
$203$	−2.62225	−	5.00047i	−0.184046	−	0.350964i
$204$	16.2890	−	18.8954i	1.14046	−	1.32294i
$205$	−7.49273			−0.523315
$206$	−0.626795	−	1.08564i	−0.0436709	−	0.0756402i
$207$	0.202694	−	0.513872i	0.0140882	−	0.0357165i
$208$	−9.46242	−	5.46313i	−0.656101	−	0.378800i
$209$	10.8193	+	18.7395i	0.748384	+	1.29624i
$210$	−0.325555	+	0.348008i	−0.0224654	+	0.0240148i
$211$	−3.73218	+	6.46432i	−0.256934	+	0.445022i	−0.965419	−	0.260703i	$-0.916046\pi$
$211$	−3.73218	+	6.46432i	−0.256934	+	0.445022i	0.708485	+	0.705726i	$0.249379\pi$
$212$	12.8678	−	7.42923i	0.883765	−	0.510242i
$213$	9.19814	−	3.20974i	0.630246	−	0.219928i
$214$	−0.124653	+	0.215905i	−0.00852109	+	0.0147590i
$215$	0.223536	−	0.387176i	0.0152450	−	0.0264052i
$216$	1.15151	−	1.82222i	0.0783501	−	0.123986i
$217$	7.49034	+	0.304441i	0.508477	+	0.0206668i
$218$	0.930594	−	0.537279i	0.0630278	−	0.0363891i
$219$	17.2672	+	14.8854i	1.16681	+	1.00586i
$220$		−	5.82169i		−	0.392498i
$221$			20.1043i			1.35236i
$222$	0.0851612	−	0.447990i	0.00571564	−	0.0300671i
$223$	−9.35222	+	5.39951i	−0.626271	+	0.361578i	−0.779306	−	0.626643i	$-0.784428\pi$
$223$	−9.35222	+	5.39951i	−0.626271	+	0.361578i	0.153036	+	0.988221i	$0.451095\pi$
$224$	−3.27513	−	0.133116i	−0.218829	−	0.00889419i
$225$	−0.442054	−	2.96725i	−0.0294702	−	0.197817i
$226$	−0.440034	+	0.762161i	−0.0292706	+	0.0506982i
$227$	6.02014	−	10.4272i	0.399571	−	0.692077i	−0.594102	−	0.804390i	$-0.702493\pi$
$227$	6.02014	−	10.4272i	0.399571	−	0.692077i	0.993673	+	0.112313i	$0.0358259\pi$
$228$	−4.75723	+	25.0254i	−0.315055	+	1.65735i
$229$	−10.4214	+	6.01682i	−0.688668	+	0.397603i	−0.803113	−	0.595827i	$-0.796824\pi$
$229$	−10.4214	+	6.01682i	−0.688668	+	0.397603i	0.114445	+	0.993430i	$0.463491\pi$
$230$	−0.00957414	+	0.0165829i	−0.000631300	+	0.00109344i
$231$	−13.0632	−	3.03767i	−0.859493	−	0.199864i
$232$	−0.442655	−	0.766701i	−0.0290617	−	0.0503364i
$233$	20.9187	+	12.0774i	1.37043	+	0.791218i	0.990982	−	0.133995i	$-0.0427804\pi$
$233$	20.9187	+	12.0774i	1.37043	+	0.791218i	0.379448	+	0.925213i	$0.376114\pi$
$234$	0.127635	+	0.856743i	0.00834379	+	0.0560071i
$235$	−0.294416	−	0.509943i	−0.0192056	−	0.0332650i
$236$	−16.1972			−1.05435
$237$	−5.20121	−	14.9051i	−0.337855	−	0.968189i
$238$	0.925209	+	1.76432i	0.0599724	+	0.114364i
$239$	−13.7317	−	7.92802i	−0.888232	−	0.512821i	−0.0148680	−	0.999889i	$-0.504733\pi$
$239$	−13.7317	−	7.92802i	−0.888232	−	0.512821i	−0.873364	+	0.487069i	$0.838066\pi$
$240$	4.45042	−	5.16255i	0.287273	−	0.333241i
$241$	4.43827	+	2.56244i	0.285894	+	0.165061i	0.636089	−	0.771616i	$-0.280551\pi$
$241$	4.43827	+	2.56244i	0.285894	+	0.165061i	−0.350194	+	0.936677i	$0.613885\pi$
$242$	0.219257	−	0.126588i	0.0140943	−	0.00813737i
$243$	15.4978	−	1.67912i	0.994182	−	0.107715i
$244$		−	25.1458i		−	1.60979i
$245$	2.99648	+	6.32622i	0.191438	+	0.404168i
$246$	−0.252034	+	1.32583i	−0.0160691	+	0.0845317i
$247$	−10.2642	−	17.7781i	−0.653095	−	1.13119i
$248$	1.17541			0.0746387
$249$	11.0907	−	12.8653i	0.702842	−	0.815306i
$250$			0.103991i			0.00657695i
$251$	−21.3411			−1.34704			−0.673519	−	0.739170i	$-0.735218\pi$
$251$	−21.3411			−1.34704			−0.673519	+	0.739170i	$0.735218\pi$
$252$	−9.31286	−	12.7496i	−0.586655	−	0.803151i
$253$	−0.538901			−0.0338804
$254$			0.640200i			0.0401697i
$255$	−12.3208	−	2.34214i	−0.771560	−	0.146670i
$256$	15.1419			0.946367
$257$	5.32111	+	9.21643i	0.331922	+	0.574905i	0.982889	−	0.184201i	$-0.0589697\pi$
$257$	5.32111	+	9.21643i	0.331922	+	0.574905i	−0.650967	+	0.759106i	$0.725636\pi$
$258$	−0.0609911	−	0.0525779i	−0.00379714	−	0.00327336i
$259$	−5.66018	−	3.58202i	−0.351706	−	0.222576i
$260$			5.52302i			0.342523i
$261$	2.34922	−	5.95575i	0.145413	−	0.368651i
$262$	−1.87496	+	1.08251i	−0.115836	+	0.0668777i
$263$	−9.21740	−	5.32167i	−0.568369	−	0.328148i	0.188128	−	0.982144i	$-0.439758\pi$
$263$	−9.21740	−	5.32167i	−0.568369	−	0.328148i	−0.756498	+	0.653996i	$0.773091\pi$
$264$	−2.06588	−	0.392715i	−0.127146	−	0.0241700i
$265$	−6.46888	−	3.73481i	−0.397380	−	0.229428i
$266$	−1.71893	−	1.08781i	−0.105394	−	0.0666982i
$267$	−27.1582	−	5.16267i	−1.66206	−	0.315950i
$268$	6.17328			0.377093
$269$	3.88366	+	6.72670i	0.236791	+	0.410134i	0.959792	−	0.280713i	$-0.0905710\pi$
$269$	3.88366	+	6.72670i	0.236791	+	0.410134i	−0.723001	+	0.690847i	$0.757238\pi$
$270$	−0.539920	−	0.0215893i	−0.0328585	−	0.00131388i
$271$	−6.45273	−	3.72548i	−0.391975	−	0.226307i	0.291040	−	0.956711i	$-0.405999\pi$
$271$	−6.45273	−	3.72548i	−0.391975	−	0.226307i	−0.683016	+	0.730404i	$0.739332\pi$
$272$	−14.2471	−	24.6768i	−0.863860	−	1.49625i
$273$	12.3930	+	2.88183i	0.750057	+	0.174416i
$274$	−0.290454	+	0.503081i	−0.0175469	+	0.0303922i
$275$	−2.53457	+	1.46334i	−0.152840	+	0.0882424i
$276$	−0.480512	−	0.414229i	−0.0289234	−	0.0249337i
$277$	8.48617	−	14.6985i	0.509884	−	0.883146i	−0.490050	−	0.871694i	$-0.663022\pi$
$277$	8.48617	−	14.6985i	0.509884	−	0.883146i	0.999934	−	0.0114513i	$-0.00364514\pi$
$278$	−0.749617	+	1.29837i	−0.0449590	+	0.0778713i
$279$	5.28845	+	6.65482i	0.316611	+	0.398414i
$280$	0.509726	+	0.972017i	0.0304619	+	0.0580891i
$281$	21.1443	−	12.2077i	1.26136	−	0.728249i	0.288026	−	0.957623i	$-0.407001\pi$
$281$	21.1443	−	12.2077i	1.26136	−	0.728249i	0.973338	+	0.229374i	$0.0736678\pi$
$282$	−0.100137	+	0.0349434i	−0.00596307	+	0.00208085i
$283$			27.5665i			1.63866i	0.573323	+	0.819329i	$0.305654\pi$
$283$			27.5665i			1.63866i	−0.573323	+	0.819329i	$0.694346\pi$
$284$		−	11.1884i		−	0.663907i
$285$	12.0910	−	4.21923i	0.716209	−	0.249925i
$286$	0.731814	−	0.422513i	0.0432731	−	0.0249837i
$287$	16.7513	+	10.6010i	0.988798	+	0.625756i
$288$	−2.31236	−	2.90980i	−0.136257	−	0.171462i
$289$	−17.7147	+	30.6828i	−1.04204	+	1.80487i
$290$	−0.110964	+	0.192195i	−0.00651602	+	0.0112861i
$291$	−2.57410	−	2.21903i	−0.150896	−	0.130082i
$292$	22.6744	−	13.0911i	1.32692	−	0.766096i
$293$	9.60393	−	16.6345i	0.561068	−	0.971798i	−0.436336	−	0.899784i	$-0.643724\pi$
$293$	9.60393	−	16.6345i	0.561068	−	0.971798i	0.997404	−	0.0720141i	$-0.0229427\pi$
$294$	1.22021	−	0.317426i	0.0711641	−	0.0185127i
$295$	4.07132	+	7.05173i	0.237041	+	0.410567i
$296$	−0.909560	−	0.525135i	−0.0528671	−	0.0305228i
$297$	−7.07145	−	13.4633i	−0.410327	−	0.781220i
$298$	−0.0804743	−	0.139386i	−0.00466175	−	0.00807439i
$299$	0.511253			0.0295665
$300$	−3.38476	−	0.643429i	−0.195419	−	0.0371484i
$301$	−1.04754	+	0.549332i	−0.0603794	+	0.0316630i
$302$	1.37863	+	0.795951i	0.0793311	+	0.0458018i
$303$	−9.70825	−	1.84550i	−0.557724	−	0.106021i
$304$	25.1973	+	14.5477i	1.44517	+	0.834367i
$305$	−10.9476	+	6.32062i	−0.626860	+	0.361918i
$306$	−0.828876	+	2.10137i	−0.0473837	+	0.120127i
$307$		−	27.5679i		−	1.57339i	−0.617345	−	0.786693i	$-0.711792\pi$
$307$		−	27.5679i		−	1.57339i	0.617345	−	0.786693i	$-0.288208\pi$
$308$	−8.23674	+	13.0154i	−0.469332	+	0.741622i
$309$	−15.8145	−	13.6330i	−0.899654	−	0.775555i
$310$	−0.147325	−	0.255174i	−0.00836748	−	0.0144929i
$311$	13.5987			0.771112			0.385556	−	0.922684i	$-0.374010\pi$
$311$	13.5987			0.771112			0.385556	+	0.922684i	$0.374010\pi$
$312$	1.95989	+	0.372568i	0.110957	+	0.0210925i
$313$		−	13.2687i		−	0.749993i	−0.927026	−	0.374997i	$-0.877644\pi$
$313$		−	13.2687i		−	0.749993i	0.927026	−	0.374997i	$-0.122356\pi$
$314$	−0.460206			−0.0259709
$315$	−3.20989	+	7.25924i	−0.180857	+	0.409012i
$316$	−18.1301			−1.01990
$317$			25.2418i			1.41772i	0.705349	+	0.708861i	$0.250790\pi$
$317$			25.2418i			1.41772i	−0.705349	+	0.708861i	$0.749210\pi$
$318$	−0.878465	+	1.01903i	−0.0492619	+	0.0571444i
$319$	−6.24583			−0.349699
$320$	−3.87082	−	6.70445i	−0.216385	−	0.374790i
$321$	−0.775465	+	4.07933i	−0.0432822	+	0.227686i
$322$	0.0448667	−	0.0235281i	0.00250032	−	0.00131117i
$323$		−	53.5354i		−	2.97879i
$324$	4.04339	−	17.4401i	0.224633	−	0.968894i
$325$	2.40454	−	1.38826i	0.133380	−	0.0770069i
$326$	−0.481868	−	0.278207i	−0.0266882	−	0.0154084i
$327$	11.6860	−	13.5559i	0.646237	−	0.749644i
$328$	2.69184	+	1.55414i	0.148632	+	0.0858129i
$329$	−0.0632679	+	1.55662i	−0.00348807	+	0.0858190i
$330$	0.173679	+	0.497711i	0.00956073	+	0.0273981i
$331$	−8.35946			−0.459478			−0.229739	−	0.973252i	$-0.573787\pi$
$331$	−8.35946			−0.459478			−0.229739	+	0.973252i	$0.573787\pi$
$332$	−9.75376	−	16.8940i	−0.535307	−	0.927179i
$333$	−1.11917	−	7.51236i	−0.0613302	−	0.411675i
$334$	−1.84841	−	1.06718i	−0.101140	−	0.0583934i
$335$	−1.55171	−	2.68764i	−0.0847790	−	0.146842i
$336$	−17.2539	+	5.24516i	−0.941275	+	0.286147i
$337$	−6.46876	+	11.2042i	−0.352376	+	0.610333i	−0.986665	−	0.162763i	$-0.947959\pi$
$337$	−6.46876	+	11.2042i	−0.352376	+	0.610333i	0.634289	+	0.773096i	$0.281293\pi$
$338$	0.476493	−	0.275103i	0.0259178	−	0.0149637i
$339$	−2.73745	+	14.4004i	−0.148678	+	0.782120i
$340$	−7.20166	+	12.4736i	−0.390565	+	0.676478i
$341$	4.14624	−	7.18150i	0.224532	−	0.388900i
$342$	−0.339878	−	2.28141i	−0.0183785	−	0.123364i
$343$	2.25141	−	18.3829i	0.121565	−	0.992583i
$344$	−0.160615	+	0.0927314i	−0.00865981	+	0.00499974i
$345$	−0.0595607	+	0.313319i	−0.00320664	+	0.0168685i
$346$		−	2.21683i		−	0.119178i
$347$		−	23.8842i		−	1.28217i	−0.767469	−	0.641086i	$-0.778484\pi$
$347$		−	23.8842i		−	1.28217i	0.767469	−	0.641086i	$-0.221516\pi$
$348$	−5.56911	−	4.80090i	−0.298535	−	0.257355i
$349$	19.0470	−	10.9968i	1.01956	−	0.588644i	0.105585	−	0.994410i	$-0.466329\pi$
$349$	19.0470	−	10.9968i	1.01956	−	0.588644i	0.913977	+	0.405766i	$0.132995\pi$
$350$	0.147130	−	0.232490i	0.00786442	−	0.0124271i
$351$	6.70866	+	12.7726i	0.358082	+	0.681750i
$352$	−1.81293	+	3.14009i	−0.0966297	+	0.167368i
$353$	4.39642	−	7.61483i	0.233998	−	0.405296i	−0.724983	−	0.688767i	$-0.758152\pi$
$353$	4.39642	−	7.61483i	0.233998	−	0.405296i	0.958981	+	0.283470i	$0.0914858\pi$
$354$	1.38474	−	0.483213i	0.0735981	−	0.0256825i
$355$	−4.87104	+	2.81230i	−0.258528	+	0.149261i
$356$	−15.8743	+	27.4951i	−0.841336	+	1.45724i
$357$	24.2316	+	22.6682i	1.28247	+	1.19973i
$358$	−0.122373	−	0.211956i	−0.00646760	−	0.0112022i
$359$	−0.261276	−	0.150848i	−0.0137896	−	0.00796143i	0.493089	−	0.869979i	$-0.335868\pi$
$359$	−0.261276	−	0.150848i	−0.0137896	−	0.00796143i	−0.506879	+	0.862017i	$0.669201\pi$
$360$	−0.456653	+	1.15771i	−0.0240677	+	0.0610166i
$361$	17.8324	+	30.8866i	0.938547	+	1.62561i
$362$	−0.170883			−0.00898143
$363$	2.75333	−	3.19390i	0.144512	−	0.167636i
$364$	7.81417	−	12.3477i	0.409574	−	0.647194i
$365$	−11.3988	−	6.58111i	−0.596641	−	0.344471i
$366$	0.750177	+	2.14978i	0.0392124	+	0.112371i
$367$	22.8249	+	13.1780i	1.19145	+	0.687884i	0.958635	−	0.284637i	$-0.0918732\pi$
$367$	22.8249	+	13.1780i	1.19145	+	0.687884i	0.232814	+	0.972521i	$0.425207\pi$
$368$	−0.627532	+	0.362306i	−0.0327124	+	0.0188865i
$369$	3.31219	+	22.2328i	0.172426	+	1.15739i
$370$			0.263279i			0.0136872i
$371$	9.17817	+	17.5022i	0.476507	+	0.908671i
$372$	9.21711	−	3.21636i	0.477885	−	0.166761i
$373$	−18.3837	−	31.8415i	−0.951872	−	1.64869i	−0.741370	−	0.671096i	$-0.765824\pi$
$373$	−18.3837	−	31.8415i	−0.951872	−	1.64869i	−0.210501	−	0.977594i	$-0.567510\pi$
$374$	2.20372			0.113952
$375$	0.570662	+	1.63534i	0.0294689	+	0.0844487i
$376$			0.244270i			0.0125973i
$377$	5.92540			0.305174
$378$	1.17654	+	0.812166i	0.0605147	+	0.0417733i
$379$	35.0467			1.80023			0.900114	−	0.435654i	$-0.143483\pi$
$379$	35.0467			1.80023			0.900114	+	0.435654i	$0.143483\pi$
$380$		−	14.7072i		−	0.754462i
$381$	3.51317	+	10.0677i	0.179985	+	0.515783i
$382$	−1.40458			−0.0718648
$383$	9.15609	+	15.8588i	0.467855	+	0.810348i	0.999325	−	0.0367289i	$-0.0116938\pi$
$383$	9.15609	+	15.8588i	0.467855	+	0.810348i	−0.531471	+	0.847077i	$0.678360\pi$
$384$	−5.36861	+	1.87341i	−0.273966	+	0.0956020i
$385$	7.73686	+	0.314461i	0.394307	+	0.0160264i
$386$		−	1.63390i		−	0.0831632i
$387$	−1.24766	−	0.492136i	−0.0634223	−	0.0250167i
$388$	−3.38016	+	1.95154i	−0.171602	+	0.0990744i
$389$	−20.6139	−	11.9014i	−1.04516	−	0.603426i	−0.123872	−	0.992298i	$-0.539531\pi$
$389$	−20.6139	−	11.9014i	−1.04516	−	0.603426i	−0.921292	+	0.388872i	$0.872865\pi$
$390$	−0.164769	−	0.472177i	−0.00834340	−	0.0239096i
$391$	1.15466	+	0.666641i	0.0583935	+	0.0337135i
$392$	0.235663	−	2.89429i	0.0119028	−	0.146184i
$393$	−23.5450	+	27.3125i	−1.18769	+	1.37773i
$394$	−2.56124			−0.129033
$395$	4.55718	+	7.89326i	0.229296	+	0.397153i
$396$	−17.2744	+	2.57350i	−0.868073	+	0.129323i
$397$	4.81881	+	2.78214i	0.241849	+	0.139632i	0.616026	−	0.787726i	$-0.288741\pi$
$397$	4.81881	+	2.78214i	0.241849	+	0.139632i	−0.374177	+	0.927357i	$0.622075\pi$
$398$	−0.868686	−	1.50461i	−0.0435433	−	0.0754192i
$399$	−33.0011	−	7.67397i	−1.65212	−	0.384179i
$400$	−1.96762	+	3.40801i	−0.0983808	+	0.170401i
$401$	−7.30769	+	4.21910i	−0.364929	+	0.210692i	−0.671241	−	0.741240i	$-0.734238\pi$
$401$	−7.30769	+	4.21910i	−0.364929	+	0.210692i	0.306312	+	0.951931i	$0.400905\pi$
$402$	−0.527769	+	0.184168i	−0.0263227	+	0.00918548i
$403$	−3.93353	+	6.81307i	−0.195943	+	0.339383i
$404$	−5.67459	+	9.82867i	−0.282321	+	0.488995i
$405$	−8.60918	+	2.62337i	−0.427793	+	0.130356i
$406$	0.520003	−	0.272690i	0.0258073	−	0.0135334i
$407$	−6.41691	+	3.70481i	−0.318075	+	0.183640i
$408$	3.94058	+	3.39701i	0.195088	+	0.168177i
$409$			3.83286i			0.189523i	0.995500	+	0.0947614i	$0.0302088\pi$
$409$			3.83286i			0.189523i	−0.995500	+	0.0947614i	$0.969791\pi$
$410$		−	0.779175i		−	0.0384807i
$411$	−1.80691	+	9.50526i	−0.0891284	+	0.468860i
$412$	−20.7667	+	11.9896i	−1.02310	+	0.590687i
$413$	0.874897	−	21.5256i	0.0430509	−	1.05921i
$414$	0.0534379	+	0.0210784i	0.00262633	+	0.00103594i
$415$	−4.90339	+	8.49292i	−0.240698	+	0.416901i
$416$	1.71992	−	2.97900i	0.0843262	−	0.146057i
$417$	−4.66336	+	24.5316i	−0.228366	+	1.20132i
$418$	−1.94874	+	1.12510i	−0.0953158	+	0.0550306i
$419$	8.65942	−	14.9985i	0.423040	−	0.732727i	−0.573195	−	0.819419i	$-0.694296\pi$
$419$	8.65942	−	14.9985i	0.423040	−	0.732727i	0.996235	+	0.0866920i	$0.0276296\pi$
$420$	6.65687	+	6.22737i	0.324822	+	0.303865i
$421$	−10.8236	−	18.7470i	−0.527510	−	0.913673i	−0.999486	−	0.0320622i	$-0.989793\pi$
$421$	−10.8236	−	18.7470i	−0.527510	−	0.913673i	0.471976	−	0.881611i	$-0.343541\pi$
$422$	−0.672230	−	0.388112i	−0.0327236	−	0.0188930i
$423$	−1.38298	+	1.09903i	−0.0672429	+	0.0534366i
$424$	1.54934	+	2.68354i	0.0752428	+	0.130324i
$425$	7.24081			0.351231
$426$	0.333784	+	0.956521i	0.0161719	+	0.0463436i
$427$	33.4180	+	1.35826i	1.61721	+	0.0657307i
$428$	4.12993	+	2.38442i	0.199628	+	0.115255i
$429$	9.18980	−	10.6603i	0.443688	−	0.514684i
$430$	0.0402627	+	0.0232457i	0.00194164	+	0.00112101i
$431$	−26.5015	+	15.3007i	−1.27653	+	0.737008i	−0.976210	−	0.216829i	$-0.930428\pi$
$431$	−26.5015	+	15.3007i	−1.27653	+	0.737008i	−0.300325	+	0.953837i	$0.597095\pi$
$432$	−17.2859	−	10.9234i	−0.831669	−	0.525552i
$433$			33.9236i			1.63027i	0.579274	+	0.815133i	$0.303336\pi$
$433$			33.9236i			1.63027i	−0.579274	+	0.815133i	$0.696664\pi$
$434$	−0.0316590	+	0.778926i	−0.00151968	+	0.0373896i
$435$	−0.690306	+	3.63135i	−0.0330976	+	0.174110i
$436$	−10.2773	−	17.8009i	−0.492195	−	0.852507i
$437$	−1.36141			−0.0651250
$438$	−1.54794	+	1.79563i	−0.0739635	+	0.0857987i
$439$			0.196382i			0.00937278i	0.999989	+	0.00468639i	$0.00149173\pi$
$439$			0.196382i			0.00937278i	−0.999989	+	0.00468639i	$0.998508\pi$
$440$	1.21410			0.0578798
$441$	17.4469	−	11.6878i	0.830805	−	0.556564i
$442$	−2.09066			−0.0994426
$443$			6.82671i			0.324347i	0.986762	+	0.162173i	$0.0518504\pi$
$443$			6.82671i			0.324347i	−0.986762	+	0.162173i	$0.948150\pi$
$444$	−8.56938	−	1.62900i	−0.406685	−	0.0773091i
$445$	15.9606			0.756605
$446$	−0.561499	−	0.972544i	−0.0265877	−	0.0460513i
$447$	−2.03042	−	1.75034i	−0.0960357	−	0.0827884i
$448$	−0.831811	+	20.4655i	−0.0392994	+	0.966905i
$449$			1.56290i			0.0737579i	0.999320	+	0.0368789i	$0.0117416\pi$
$449$			1.56290i			0.0737579i	−0.999320	+	0.0368789i	$0.988258\pi$
$450$	0.308567	−	0.0459695i	0.0145460	−	0.00216702i
$451$	18.9909	−	10.9644i	0.894245	−	0.516292i
$452$	14.5790	+	8.41718i	0.685738	+	0.395911i
$453$	26.0480	+	4.95161i	1.22384	+	0.232647i
$454$	1.08433	+	0.626039i	0.0508902	+	0.0293815i
$455$	−7.33993	−	0.298328i	−0.344101	−	0.0139858i
$456$	−5.21897	−	0.992106i	−0.244401	−	0.0464596i
$457$	5.59317			0.261637			0.130819	−	0.991406i	$-0.458239\pi$
$457$	5.59317			0.261637			0.130819	+	0.991406i	$0.458239\pi$
$458$	−0.625694	−	1.08373i	−0.0292368	−	0.0506396i
$459$	−1.50325	+	37.5943i	−0.0701658	+	1.75475i
$460$	0.317206	+	0.183139i	0.0147898	+	0.00853889i
$461$	−3.97429	−	6.88368i	−0.185101	−	0.320605i	0.758509	−	0.651662i	$-0.225928\pi$
$461$	−3.97429	−	6.88368i	−0.185101	−	0.320605i	−0.943611	+	0.331057i	$0.892595\pi$
$462$	0.315889	−	1.35845i	0.0146965	−	0.0632007i
$463$	5.54581	−	9.60562i	0.257735	−	0.446411i	−0.707899	−	0.706313i	$-0.750357\pi$
$463$	5.54581	−	9.60562i	0.257735	−	0.446411i	0.965635	+	0.259902i	$0.0836904\pi$
$464$	−7.27306	+	4.19911i	−0.337644	+	0.194939i
$465$	−3.71710	−	3.20436i	−0.172376	−	0.148599i
$466$	−1.25594	+	2.17535i	−0.0581803	+	0.100771i
$467$	6.26534	−	10.8519i	0.289925	−	0.502165i	−0.683866	−	0.729607i	$-0.739703\pi$
$467$	6.26534	−	10.8519i	0.289925	−	0.502165i	0.973792	+	0.227442i	$0.0730362\pi$
$468$	16.3882	−	2.44147i	0.757545	−	0.112857i
$469$	−0.333452	+	8.20411i	−0.0153974	+	0.378830i
$470$	0.0530294	−	0.0306165i	0.00244606	−	0.00141223i
$471$	−7.23713	+	2.52544i	−0.333469	+	0.116366i
$472$		−	3.37788i		−	0.155479i
$473$			1.30843i			0.0601618i
$474$	1.54999	−	0.540878i	0.0711935	−	0.0248434i
$475$	−6.40301	+	3.69678i	−0.293790	+	0.169620i
$476$	33.7487	−	17.6978i	1.54687	−	0.811179i
$477$	−8.22254	+	20.8458i	−0.376484	+	0.954464i
$478$	0.824441	−	1.42797i	0.0377090	−	0.0653140i
$479$	9.12862	−	15.8112i	0.417098	−	0.722434i	−0.578549	−	0.815648i	$-0.696381\pi$
$479$	9.12862	−	15.8112i	0.417098	−	0.722434i	0.995646	+	0.0932138i	$0.0297140\pi$
$480$	1.62529	+	1.40110i	0.0741842	+	0.0639511i
$481$	6.08771	−	3.51474i	0.277575	−	0.160258i
$482$	−0.266470	+	0.461540i	−0.0121374	+	0.0210226i
$483$	0.576453	−	0.616211i	0.0262295	−	0.0280386i
$484$	−2.42143	−	4.19405i	−0.110065	−	0.190638i
$485$	1.69927	+	0.981074i	0.0771599	+	0.0445483i
$486$	0.174613	+	1.61162i	0.00792060	+	0.0731048i
$487$	−8.81372	−	15.2658i	−0.399388	−	0.691760i	0.594263	−	0.804271i	$-0.297444\pi$
$487$	−8.81372	−	15.2658i	−0.399388	−	0.691760i	−0.993650	+	0.112511i	$0.964111\pi$
$488$	5.24407			0.237388
$489$	−9.10447	−	1.73072i	−0.411718	−	0.0782660i
$490$	−0.657869	+	0.311606i	−0.0297195	+	0.0140769i
$491$	−22.4180	−	12.9430i	−1.01171	−	0.584111i	−0.100018	−	0.994986i	$-0.531890\pi$
$491$	−22.4180	−	12.9430i	−1.01171	−	0.584111i	−0.911692	+	0.410875i	$0.865223\pi$
$492$	25.3611	+	4.82104i	1.14337	+	0.217349i
$493$	13.3824	+	7.72634i	0.602714	+	0.347977i
$494$	1.84876	−	1.06738i	0.0831796	−	0.0480238i
$495$	5.46250	+	6.87384i	0.245521	+	0.308956i
$496$		−	11.1502i		−	0.500657i
$497$	14.8690	+	0.604343i	0.666966	+	0.0271085i
$498$	1.33787	+	1.15333i	0.0599516	+	0.0516818i
$499$	−8.01638	−	13.8848i	−0.358863	−	0.621568i	0.628908	−	0.777479i	$-0.283502\pi$
$499$	−8.01638	−	13.8848i	−0.358863	−	0.621568i	−0.987771	+	0.155911i	$0.950169\pi$
$500$	1.98919			0.0889591
$501$	−34.9240	−	6.63891i	−1.56029	−	0.296605i
$502$		−	2.21928i		−	0.0990512i
$503$	4.02737			0.179572			0.0897858	−	0.995961i	$-0.471382\pi$
$503$	4.02737			0.179572			0.0897858	+	0.995961i	$0.471382\pi$
$504$	2.65889	−	1.94217i	0.118437	−	0.0865111i
$505$	5.70544			0.253889
$506$		−	0.0560407i		−	0.00249131i
$507$	5.98359	−	6.94105i	0.265741	−	0.308263i
$508$	12.2460			0.543330
$509$	−12.3484	−	21.3880i	−0.547331	−	0.948006i	−0.998456	−	0.0555448i	$-0.982310\pi$
$509$	−12.3484	−	21.3880i	−0.547331	−	0.948006i	0.451125	−	0.892461i	$-0.351023\pi$
$510$	0.243561	−	1.28125i	0.0107850	−	0.0567348i
$511$	16.1729	+	30.8407i	0.715445	+	1.36431i
$512$			8.14035i			0.359756i
$513$	−17.8644	−	34.0119i	−0.788732	−	1.50166i
$514$	−0.958424	+	0.553346i	−0.0422743	+	0.0244071i
$515$	10.4398	+	6.02741i	0.460032	+	0.265600i
$516$	−1.00574	+	1.16667i	−0.0442750	+	0.0513596i
$517$	1.49244	+	0.861658i	0.0656372	+	0.0378957i
$518$	0.372497	−	0.588607i	0.0163666	−	0.0258619i
$519$	−12.1651	−	34.8615i	−0.533990	−	1.53025i
$520$	−1.15181			−0.0505102
$521$	12.5314	+	21.7049i	0.549009	+	0.950911i	0.998343	+	0.0575471i	$0.0183280\pi$
$521$	12.5314	+	21.7049i	0.549009	+	0.950911i	−0.449334	+	0.893364i	$0.648339\pi$
$522$	0.619343	+	0.244297i	0.0271079	+	0.0106926i
$523$	15.9386	+	9.20215i	0.696946	+	0.402382i	0.806209	−	0.591631i	$-0.201516\pi$
$523$	15.9386	+	9.20215i	0.696946	+	0.402382i	−0.109263	+	0.994013i	$0.534849\pi$
$524$	20.7068	+	35.8652i	0.904580	+	1.56678i
$525$	1.03793	−	4.46349i	0.0452988	−	0.194803i
$526$	0.553405	−	0.958525i	0.0241296	−	0.0417937i
$527$	−17.7676	+	10.2581i	−0.773969	+	0.446851i
$528$	−3.72537	+	19.5973i	−0.162126	+	0.852863i
$529$	−11.4830	+	19.8892i	−0.499263	+	0.864749i
$530$	0.388386	−	0.672704i	0.0168704	−	0.0292204i
$531$	19.1245	−	15.1979i	0.829933	−	0.659531i
$532$	−20.8082	+	32.8804i	−0.902151	+	1.42555i
$533$	−18.0166	+	10.4019i	−0.780384	+	0.450555i
$534$	0.536870	−	2.82420i	0.0232326	−	0.122215i
$535$		−	2.39738i		−	0.103648i
$536$			1.28742i			0.0556080i
$537$	−3.08755	−	2.66165i	−0.133238	−	0.114859i
$538$	−0.699514	+	0.403865i	−0.0301582	+	0.0174118i
$539$	−16.8522	−	11.6494i	−0.725875	−	0.501776i
$540$	−0.412971	+	10.3279i	−0.0177714	+	0.444440i
$541$	−16.3146	+	28.2578i	−0.701420	+	1.21490i	0.266548	+	0.963822i	$0.414117\pi$
$541$	−16.3146	+	28.2578i	−0.701420	+	1.21490i	−0.967968	+	0.251074i	$0.919216\pi$
$542$	0.387416	−	0.671024i	0.0166409	−	0.0288230i
$543$	−2.68728	+	0.937743i	−0.115322	+	0.0402424i
$544$	7.76884	−	4.48534i	0.333086	−	0.192307i
$545$	−5.16660	+	8.94882i	−0.221313	+	0.383325i
$546$	−0.299683	+	1.28875i	−0.0128253	+	0.0551536i
$547$	6.87713	+	11.9115i	0.294045	+	0.509300i	0.974762	−	0.223246i	$-0.0716652\pi$
$547$	6.87713	+	11.9115i	0.294045	+	0.509300i	−0.680718	+	0.732546i	$0.738332\pi$
$548$	9.62317	+	5.55594i	0.411081	+	0.237338i
$549$	23.5943	+	29.6903i	1.00698	+	1.26715i
$550$	−0.152173	−	0.263572i	−0.00648870	−	0.0112388i
$551$	−15.7787			−0.672194
$552$	0.0863863	−	0.100209i	0.00367684	−	0.00426519i
$553$	0.979305	−	24.0944i	0.0416443	−	1.02460i
$554$	1.52851	+	0.882483i	0.0649400	+	0.0374931i
$555$	1.44478	+	4.14029i	0.0613274	+	0.175745i
$556$	24.8359	+	14.3390i	1.05328	+	0.608110i
$557$	18.3957	−	10.6208i	0.779451	−	0.450016i	−0.0567848	−	0.998386i	$-0.518085\pi$
$557$	18.3957	−	10.6208i	0.779451	−	0.450016i	0.836236	+	0.548370i	$0.184752\pi$
$558$	−0.692040	+	0.549950i	−0.0292964	+	0.0232812i
$559$		−	1.24131i		−	0.0525017i
$560$	9.22073	−	4.83535i	0.389647	−	0.204331i
$561$	34.6553	−	12.0932i	1.46315	−	0.510574i
$562$	1.26949	+	2.19881i	0.0535500	+	0.0927514i
$563$	7.48251			0.315350			0.157675	−	0.987491i	$-0.449600\pi$
$563$	7.48251			0.315350			0.157675	+	0.987491i	$0.449600\pi$
$564$	0.668414	+	1.91547i	0.0281453	+	0.0806558i
$565$		−	8.46294i		−	0.356039i
$566$	−2.86666			−0.120495
$567$	22.9590	+	6.31557i	0.964185	+	0.265229i
$568$	2.33330			0.0979030
$569$		−	9.27735i		−	0.388927i	−0.980910	−	0.194463i	$-0.937703\pi$
$569$		−	9.27735i		−	0.388927i	0.980910	−	0.194463i	$-0.0622966\pi$
$570$	0.438761	+	1.25735i	0.0183777	+	0.0526647i
$571$	0.874760			0.0366076			0.0183038	−	0.999832i	$-0.494173\pi$
$571$	0.874760			0.0366076			0.0183038	+	0.999832i	$0.494173\pi$
$572$	−8.08203	−	13.9985i	−0.337927	−	0.585306i
$573$	−22.0883	+	7.70783i	−0.922750	+	0.321999i
$574$	−1.10240	+	1.74198i	−0.0460135	+	0.0727089i
$575$		−	0.184134i		−	0.00767893i
$576$	−18.1827	+	14.4494i	−0.757612	+	0.602059i
$577$	−11.3961	+	6.57956i	−0.474427	+	0.273911i	−0.718091	−	0.695949i	$-0.754984\pi$
$577$	−11.3961	+	6.57956i	−0.474427	+	0.273911i	0.243664	+	0.969860i	$0.421651\pi$
$578$	−3.19072	−	1.84216i	−0.132717	−	0.0766240i
$579$	−8.96621	−	25.6944i	−0.372623	−	1.06782i
$580$	3.67640	+	2.12257i	0.152654	+	0.0881349i
$581$	22.9785	−	12.0499i	0.953308	−	0.499915i
$582$	0.230758	−	0.267683i	0.00956524	−	0.0110958i
$583$	21.8611			0.905395
$584$	2.73010	+	4.72867i	0.112972	+	0.195674i
$585$	−5.18226	−	6.52119i	−0.214260	−	0.269618i
$586$	1.72983	+	0.998721i	0.0714588	+	0.0412568i
$587$	−9.18223	−	15.9041i	−0.378991	−	0.656432i	0.611925	−	0.790916i	$-0.290396\pi$
$587$	−9.18223	−	15.9041i	−0.378991	−	0.656432i	−0.990916	+	0.134484i	$0.957062\pi$
$588$	−6.07188	−	23.3408i	−0.250400	−	0.962556i
$589$	10.4745	−	18.1424i	0.431595	−	0.747545i
$590$	−0.733315	+	0.423379i	−0.0301901	+	0.0174303i
$591$	−40.2776	+	14.0551i	−1.65680	+	0.578150i
$592$	−4.98152	+	8.62825i	−0.204739	+	0.354619i
$593$	−14.5682	+	25.2329i	−0.598245	+	1.03619i	0.394836	+	0.918752i	$0.370802\pi$
$593$	−14.5682	+	25.2329i	−0.598245	+	1.03619i	−0.993080	+	0.117438i	$0.962532\pi$
$594$	1.40006	−	0.735365i	0.0574451	−	0.0301724i
$595$	−16.1881	−	10.2446i	−0.663647	−	0.419986i
$596$	−2.66624	+	1.53935i	−0.109213	+	0.0630543i
$597$	−21.9175	−	18.8942i	−0.897025	−	0.773288i
$598$			0.0531656i			0.00217410i
$599$			9.77430i			0.399367i	0.979860	+	0.199683i	$0.0639914\pi$
$599$			9.77430i			0.399367i	−0.979860	+	0.199683i	$0.936009\pi$
$600$	0.134185	−	0.705881i	0.00547808	−	0.0288175i
$601$	−12.0062	+	6.93177i	−0.489742	+	0.282753i	−0.724467	−	0.689309i	$-0.757914\pi$
$601$	−12.0062	+	6.93177i	−0.489742	+	0.282753i	0.234725	+	0.972062i	$0.424581\pi$
$602$	−0.0571255	−	0.108935i	−0.00232826	−	0.00443986i
$603$	−7.28897	+	5.79240i	−0.296830	+	0.235885i
$604$	15.2253	−	26.3711i	0.619510	−	1.07302i
$605$	−1.21730	+	2.10842i	−0.0494902	+	0.0857196i
$606$	0.191915	−	1.00957i	0.00779601	−	0.0410109i
$607$	3.88964	−	2.24568i	0.157876	−	0.0911495i	−0.418981	−	0.907995i	$-0.637613\pi$
$607$	3.88964	−	2.24568i	0.157876	−	0.0911495i	0.576856	+	0.816846i	$0.304279\pi$
$608$	−4.57996	+	7.93273i	−0.185742	+	0.321714i
$609$	6.68107	−	7.14185i	0.270730	−	0.289403i
$610$	−0.657286	−	1.13845i	−0.0266127	−	0.0460946i
$611$	−1.41587	−	0.817452i	−0.0572799	−	0.0330706i
$612$	40.1960	+	15.8551i	1.62483	+	0.640906i
$613$	−10.2897	−	17.8222i	−0.415596	−	0.719834i	0.579895	−	0.814692i	$-0.303094\pi$
$613$	−10.2897	−	17.8222i	−0.415596	−	0.719834i	−0.995491	+	0.0948577i	$0.969760\pi$
$614$	2.86681			0.115695
$615$	−4.27582	−	12.2532i	−0.172418	−	0.494096i
$616$	−2.71432	−	1.71775i	−0.109363	−	0.0692100i
$617$	8.84986	+	5.10947i	0.356282	+	0.205700i	0.667449	−	0.744656i	$-0.267386\pi$
$617$	8.84986	+	5.10947i	0.356282	+	0.205700i	−0.311167	+	0.950355i	$0.600720\pi$
$618$	1.41771	−	1.64456i	0.0570285	−	0.0661539i
$619$	−12.3888	−	7.15270i	−0.497949	−	0.287491i	0.229917	−	0.973210i	$-0.426155\pi$
$619$	−12.3888	−	7.15270i	−0.497949	−	0.287491i	−0.727866	+	0.685719i	$0.759488\pi$
$620$	−4.88109	+	2.81810i	−0.196029	+	0.113178i
$621$	0.956026	+	0.0382278i	0.0383640	+	0.00153403i
$622$			1.41414i			0.0567019i
$623$	−35.6827	−	22.5816i	−1.42960	−	0.904714i
$624$	3.53424	−	18.5919i	0.141483	−	0.744272i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	1.37983			0.0551490
$627$	−24.4714	+	28.3871i	−0.977293	+	1.13367i
$628$			8.80304i			0.351280i
$629$	18.3320			0.730943
$630$	−0.754894	−	0.333799i	−0.0300757	−	0.0132989i
$631$	1.77064			0.0704882			0.0352441	−	0.999379i	$-0.488779\pi$
$631$	1.77064			0.0704882			0.0352441	+	0.999379i	$0.488779\pi$
$632$		−	3.78098i		−	0.150399i
$633$	−12.7012	−	2.41444i	−0.504827	−	0.0959655i
$634$	−2.62492			−0.104249
$635$	−3.07816	−	5.33152i	−0.122153	−	0.211575i
$636$	19.4925	+	16.8037i	0.772929	+	0.666310i
$637$	15.9876	+	11.0518i	0.633452	+	0.437887i
$638$		−	0.649509i		−	0.0257143i
$639$	10.4981	+	13.2104i	0.415297	+	0.522596i
$640$	2.84305	−	1.64143i	0.112381	−	0.0648834i
$641$	−29.2397	−	16.8815i	−1.15490	−	0.666781i	−0.204822	−	0.978799i	$-0.565662\pi$
$641$	−29.2397	−	16.8815i	−1.15490	−	0.666781i	−0.950076	+	0.312018i	$0.898995\pi$
$642$	−0.424213	−	0.0806412i	−0.0167424	−	0.00318265i
$643$	19.3941	+	11.1972i	0.764827	+	0.441573i	0.831026	−	0.556233i	$-0.187754\pi$
$643$	19.3941	+	11.1972i	0.764827	+	0.441573i	−0.0661992	+	0.997806i	$0.521087\pi$
$644$	−0.450057	−	0.858232i	−0.0177347	−	0.0338191i
$645$	0.760729	+	0.144611i	0.0299537	+	0.00569407i
$646$	5.56719			0.219038
$647$	−24.0354	−	41.6305i	−0.944928	−	1.63666i	−0.755896	−	0.654692i	$-0.772798\pi$
$647$	−24.0354	−	41.6305i	−0.944928	−	1.63666i	−0.189032	−	0.981971i	$-0.560535\pi$
$648$	3.63708	+	0.843236i	0.142878	+	0.0331254i
$649$	−20.6381	−	11.9154i	−0.810116	−	0.467720i
$650$	0.144366	+	0.250050i	0.00566252	+	0.00980777i
$651$	3.77659	+	12.4230i	0.148016	+	0.486896i
$652$	−5.32167	+	9.21740i	−0.208413	+	0.360981i
$653$	−11.7614	+	6.79044i	−0.460259	+	0.265731i	−0.712153	−	0.702024i	$-0.752280\pi$
$653$	−11.7614	+	6.79044i	−0.460259	+	0.265731i	0.251894	+	0.967755i	$0.418947\pi$
$654$	1.40969	+	1.21524i	0.0551232	+	0.0475195i
$655$	10.4097	−	18.0301i	0.406740	−	0.704494i
$656$	14.7428	−	25.5353i	0.575610	−	0.996986i
$657$	−14.4889	+	36.7324i	−0.565267	+	1.43307i
$658$	−0.161874	−	0.00657928i	−0.00631050	−	0.000256487i
$659$	31.8718	−	18.4012i	1.24155	−	0.716810i	0.272141	−	0.962257i	$-0.412268\pi$
$659$	31.8718	−	18.4012i	1.24155	−	0.716810i	0.969410	+	0.245448i	$0.0789349\pi$
$660$	9.52046	−	3.32222i	0.370583	−	0.129317i
$661$		−	39.8075i		−	1.54833i	−0.632984	−	0.774165i	$-0.718170\pi$
$661$		−	39.8075i		−	1.54833i	0.632984	−	0.774165i	$-0.281830\pi$
$662$		−	0.869307i		−	0.0337866i
$663$	−32.8774	+	11.4728i	−1.27685	+	0.445565i
$664$	3.52319	−	2.03412i	0.136726	−	0.0789390i
$665$	19.5454	+	0.794412i	0.757938	+	0.0308060i
$666$	0.781216	−	0.116384i	0.0302715	−	0.00450977i
$667$	0.196481	−	0.340316i	0.00760779	−	0.0131771i
$668$	−20.4135	+	35.3572i	−0.789822	+	1.36801i
$669$	−14.1670	−	12.2128i	−0.547728	−	0.472174i
$670$	0.279490	−	0.161364i	0.0107976	−	0.00623402i
$671$	18.4984	−	32.0401i	0.714122	−	1.23690i
$672$	−1.65130	−	5.43192i	−0.0637004	−	0.209541i
$673$	−14.9975	−	25.9765i	−0.578112	−	1.00132i	−0.995696	−	0.0926811i	$-0.970456\pi$
$673$	−14.9975	−	25.9765i	−0.578112	−	1.00132i	0.417584	−	0.908638i	$-0.362877\pi$
$674$	−1.16514	−	0.672691i	−0.0448793	−	0.0259111i
$675$	4.60021	−	2.41621i	0.177062	−	0.0929999i
$676$	−5.26231	−	9.11459i	−0.202397	−	0.350561i
$677$	−10.5107			−0.403958			−0.201979	−	0.979390i	$-0.564737\pi$
$677$	−10.5107			−0.403958			−0.201979	+	0.979390i	$0.564737\pi$
$678$	−1.49750	−	0.284670i	−0.0575113	−	0.0109327i
$679$	−2.41096	−	4.59755i	−0.0925240	−	0.176438i
$680$	−2.60134	−	1.50188i	−0.0997568	−	0.0575946i
$681$	20.4875	+	3.89459i	0.785082	+	0.149241i
$682$	0.746810	+	0.431171i	0.0285968	+	0.0165104i
$683$	13.9019	−	8.02627i	0.531942	−	0.307117i	−0.209865	−	0.977730i	$-0.567302\pi$
$683$	13.9019	−	8.02627i	0.531942	−	0.307117i	0.741807	+	0.670614i	$0.233969\pi$
$684$	−43.6399	+	6.50136i	−1.66861	+	0.248586i
$685$		−	5.58614i		−	0.213436i
$686$	1.91165	+	0.234126i	0.0729872	+	0.00893899i
$687$	−15.7867	−	13.6091i	−0.602300	−	0.519218i
$688$	0.879667	+	1.52363i	0.0335370	+	0.0580877i
$689$	−20.7396			−0.790115
$690$	−0.0325823	−	0.00619376i	−0.00124039	−	0.000235793i
$691$			12.2307i			0.465278i	0.972563	+	0.232639i	$0.0747361\pi$
$691$			12.2307i			0.465278i	−0.972563	+	0.232639i	$0.925264\pi$
$692$	−42.4046			−1.61198
$693$	−2.48702	−	23.0962i	−0.0944741	−	0.877353i
$694$	2.48374			0.0942814
$695$		−	14.4170i		−	0.546867i
$696$	1.00121	−	1.16142i	0.0379509	−	0.0440235i
$697$	−54.2535			−2.05500
$698$	1.14356	+	1.98071i	0.0432845	+	0.0749710i
$699$	−7.81321	+	41.1014i	−0.295523	+	1.55460i
$700$	−4.44717	−	2.81437i	−0.168087	−	0.106373i
$701$		−	43.2427i		−	1.63325i	−0.577166	−	0.816627i	$-0.695842\pi$
$701$		−	43.2427i		−	1.63325i	0.577166	−	0.816627i	$-0.304158\pi$
$702$	−1.32823	+	0.697638i	−0.0501309	+	0.0263307i
$703$	−16.2109	+	9.35935i	−0.611404	+	0.352994i
$704$	19.6217	+	11.3286i	0.739521	+	0.426963i
$705$	0.665919	−	0.772476i	0.0250800	−	0.0290931i
$706$	0.791872	+	0.457187i	0.0298025	+	0.0172065i
$707$	−12.7555	−	8.07226i	−0.479720	−	0.303588i
$708$	−9.24313	−	26.4880i	−0.347378	−	0.995479i
$709$	5.70294			0.214178			0.107089	−	0.994249i	$-0.465847\pi$
$709$	5.70294			0.214178			0.107089	+	0.994249i	$0.465847\pi$
$710$	−0.292453	−	0.506543i	−0.0109756	−	0.0190102i
$711$	21.4068	−	17.0115i	0.802817	−	0.637982i
$712$	−5.73402	−	3.31054i	−0.214891	−	0.124068i
$713$	0.260865	+	0.451831i	0.00976946	+	0.0169212i
$714$	−2.35728	+	2.51986i	−0.0882191	+	0.0943035i
$715$	−4.06298	+	7.03730i	−0.151947	+	0.263180i
$716$	−4.05439	+	2.34080i	−0.151520	+	0.0874800i
$717$	5.12884	−	26.9803i	0.191540	−	1.00760i
$718$	0.0156868	−	0.0271703i	0.000585425	−	0.00101398i
$719$	−24.4397	+	42.3309i	−0.911448	+	1.57867i	−0.0994282	+	0.995045i	$0.531701\pi$
$719$	−24.4397	+	42.3309i	−0.911448	+	1.57867i	−0.812020	+	0.583630i	$0.801632\pi$
$720$	10.9822	+	4.33189i	0.409283	+	0.161440i
$721$	−14.8122	−	28.2459i	−0.551634	−	1.05193i
$722$	−3.21192	+	1.85440i	−0.119535	+	0.0690138i
$723$	−1.65771	+	8.72038i	−0.0616509	+	0.324315i
$724$			3.26874i			0.121482i
$725$		−	2.13411i		−	0.0792588i
$726$	0.332136	+	0.286321i	0.0123267	+	0.0106264i
$727$	−10.9887	+	6.34435i	−0.407550	+	0.235299i	−0.689736	−	0.724060i	$-0.742274\pi$
$727$	−10.9887	+	6.34435i	−0.407550	+	0.235299i	0.282187	+	0.959360i	$0.408940\pi$
$728$	2.57507	+	1.62962i	0.0954384	+	0.0603977i
$729$	11.5899	+	24.3859i	0.429256	+	0.903183i
$730$	0.684375	−	1.18537i	0.0253298	−	0.0438726i
$731$	1.61858	−	2.80347i	0.0598655	−	0.103690i
$732$	41.1220	−	14.3497i	1.51991	−	0.530382i
$733$	30.0914	−	17.3733i	1.11145	−	0.641698i	0.172248	−	0.985054i	$-0.444897\pi$
$733$	30.0914	−	17.3733i	1.11145	−	0.641698i	0.939205	+	0.343356i	$0.111564\pi$
$734$	−1.37039	+	2.37358i	−0.0505819	+	0.0876104i
$735$	−8.63556	+	8.51041i	−0.318528	+	0.313911i
$736$	−0.114062	−	0.197562i	−0.00420440	−	0.00728223i
$737$	7.86584	+	4.54135i	0.289742	+	0.167283i
$738$	−2.31201	+	0.344437i	−0.0851062	+	0.0126789i
$739$	6.28839	+	10.8918i	0.231322	+	0.400662i	0.958197	−	0.286108i	$-0.0923615\pi$
$739$	6.28839	+	10.8918i	0.231322	+	0.400662i	−0.726875	+	0.686770i	$0.759028\pi$
$740$	5.03613			0.185132
$741$	23.2159	−	26.9308i	0.852858	−	0.989327i
$742$	−1.82007	+	0.954445i	−0.0668169	+	0.0350388i
$743$	29.1685	+	16.8405i	1.07009	+	0.617817i	0.928206	−	0.372067i	$-0.121351\pi$
$743$	29.1685	+	16.8405i	1.07009	+	0.617817i	0.141884	+	0.989883i	$0.454684\pi$
$744$	0.670763	+	1.92220i	0.0245914	+	0.0704713i
$745$	1.34036	+	0.773860i	0.0491072	+	0.0283520i
$746$	3.31122	−	1.91173i	0.121232	−	0.0699936i
$747$	27.3682	+	10.7953i	1.00135	+	0.394978i
$748$		−	42.1538i		−	1.54130i
$749$	−3.39190	+	5.35976i	−0.123937	+	0.195841i
$750$	−0.170061	+	0.0593436i	−0.00620973	+	0.00216692i
$751$	26.8558	+	46.5156i	0.979981	+	1.69738i	0.662409	+	0.749143i	$0.269534\pi$
$751$	26.8558	+	46.5156i	0.979981	+	1.69738i	0.317572	+	0.948234i	$0.397132\pi$
$752$	2.31719			0.0844992
$753$	−12.1786	−	34.9000i	−0.443811	−	1.27183i
$754$			0.616187i			0.0224402i
$755$	−15.3081			−0.557119
$756$	15.5355	−	22.5054i	0.565020	−	0.818515i
$757$	16.9208			0.614998			0.307499	−	0.951548i	$-0.400508\pi$
$757$	16.9208			0.614998			0.307499	+	0.951548i	$0.400508\pi$
$758$			3.64453i			0.132375i
$759$	−0.307530	−	0.881287i	−0.0111626	−	0.0319887i
$760$	3.06713			0.111257
$761$	−8.16387	−	14.1402i	−0.295940	−	0.512583i	0.679263	−	0.733895i	$-0.262300\pi$
$761$	−8.16387	−	14.1402i	−0.295940	−	0.512583i	−0.975203	+	0.221312i	$0.928966\pi$
$762$	−1.04695	+	0.365338i	−0.0379268	+	0.0132348i
$763$	24.2119	−	12.6967i	0.876531	−	0.459653i
$764$			26.8676i			0.972034i
$765$	−3.20083	−	21.4853i	−0.115726	−	0.776804i
$766$	−1.64917	+	0.952149i	−0.0595870	+	0.0344026i
$767$	19.5793	+	11.3041i	0.706967	+	0.408168i
$768$	8.64089	+	24.7621i	0.311801	+	0.893527i
$769$	38.6374	+	22.3073i	1.39330	+	0.804423i	0.993679	−	0.112256i	$-0.0358078\pi$
$769$	38.6374	+	22.3073i	1.39330	+	0.804423i	0.399623	+	0.916680i	$0.369141\pi$
$770$	−0.0327010	+	0.804562i	−0.00117846	+	0.0289944i
$771$	−12.0355	+	13.9613i	−0.433447	+	0.502804i
$772$	−31.2540			−1.12485
$773$	6.98070	+	12.0909i	0.251078	+	0.434881i	0.963823	−	0.266543i	$-0.0858814\pi$
$773$	6.98070	+	12.0909i	0.251078	+	0.434881i	−0.712745	+	0.701424i	$0.752548\pi$
$774$	0.0511776	−	0.129746i	0.00183954	−	0.00466361i
$775$	2.45381	+	1.41671i	0.0881435	+	0.0508897i
$776$	−0.406987	−	0.704923i	−0.0146100	−	0.0253053i
$777$	2.62777	−	11.3005i	0.0942709	−	0.405402i
$778$	1.23764	−	2.14365i	0.0443715	−	0.0768536i
$779$	47.9761	−	27.6990i	1.71892	−	0.992419i
$780$	−9.03203	+	3.15178i	−0.323399	+	0.112852i
$781$	8.23067	−	14.2559i	0.294516	−	0.510117i
$782$	−0.0693245	+	0.120074i	−0.00247904	+	0.00429382i
$783$	11.0803	+	0.443058i	0.395977	+	0.0158336i
$784$	−27.4558	−	2.23554i	−0.980563	−	0.0798409i
$785$	3.83255	−	2.21273i	0.136790	−	0.0789755i
$786$	−2.84025	−	2.44846i	−0.101308	−	0.0873336i
$787$			13.1825i			0.469906i	0.972007	+	0.234953i	$0.0754935\pi$
$787$			13.1825i			0.469906i	−0.972007	+	0.234953i	$0.924506\pi$
$788$			48.9926i			1.74529i
$789$	3.44273	−	18.1105i	0.122564	−	0.644750i
$790$	−0.820826	+	0.473904i	−0.0292037	+	0.0168608i
$791$	−11.9737	+	18.9204i	−0.425735	+	0.672731i
$792$	−0.536695	−	3.60253i	−0.0190706	−	0.128010i
$793$	−17.5493	+	30.3964i	−0.623196	+	1.07941i
$794$	−0.289317	+	0.501112i	−0.0102675	+	0.0177838i
$795$	2.41615	−	12.7102i	0.0856920	−	0.450783i
$796$	−28.7809	+	16.6166i	−1.02011	+	0.588961i
$797$	14.1612	−	24.5280i	0.501617	−	0.868825i	−0.498382	−	0.866958i	$-0.666072\pi$
$797$	14.1612	−	24.5280i	0.501617	−	0.868825i	0.999998	−	0.00186773i	$-0.000594519\pi$
$798$	0.798022	−	3.43181i	0.0282497	−	0.121485i
$799$	−2.13181	−	3.69240i	−0.0754180	−	0.130628i
$800$	−1.07292	−	0.619453i	−0.0379336	−	0.0219010i
$801$	−7.05544	−	47.3591i	−0.249292	−	1.67335i
$802$	−0.438747	−	0.759932i	−0.0154927	−	0.0268341i
$803$	38.5215			1.35939
$804$	3.52286	+	10.0954i	0.124242	+	0.356038i
$805$	−0.260520	+	0.411664i	−0.00918212	+	0.0145093i
$806$	−0.708496	−	0.409050i	−0.0249557	−	0.0144082i
$807$	−8.78419	+	10.1898i	−0.309218	+	0.358697i
$808$	−2.04974	−	1.18342i	−0.0721096	−	0.0416325i
$809$	−16.5879	+	9.57704i	−0.583200	+	0.336711i	−0.762404	−	0.647101i	$-0.775981\pi$
$809$	−16.5879	+	9.57704i	−0.583200	+	0.336711i	0.179204	+	0.983812i	$0.442648\pi$
$810$	−0.272806	−	0.895275i	−0.00958543	−	0.0314568i
$811$		−	14.6454i		−	0.514269i	−0.966376	−	0.257134i	$-0.917222\pi$
$811$		−	14.6454i		−	0.514269i	0.966376	−	0.257134i	$-0.0827783\pi$
$812$	−5.21614	−	9.94687i	−0.183051	−	0.349067i
$813$	2.41011	−	12.6784i	0.0845264	−	0.444651i
$814$	−0.385266	−	0.667300i	−0.0135036	−	0.0233889i
$815$	5.35060			0.187423
$816$	32.2247	−	37.3811i	1.12809	−	1.30860i
$817$			3.30546i			0.115643i
$818$	−0.398582			−0.0139361
$819$	2.35943	+	21.9113i	0.0824451	+	0.765643i
$820$	−14.9044			−0.520485
$821$		−	4.73593i		−	0.165285i	−0.996579	−	0.0826426i	$-0.973664\pi$
$821$		−	4.73593i		−	0.165285i	0.996579	−	0.0826426i	$-0.0263360\pi$
$822$	−0.988460	−	0.187902i	−0.0344765	−	0.00655384i
$823$	−2.76948			−0.0965379			−0.0482690	−	0.998834i	$-0.515370\pi$
$823$	−2.76948			−0.0965379			−0.0482690	+	0.998834i	$0.515370\pi$
$824$	−2.50040	−	4.33083i	−0.0871057	−	0.150871i
$825$	−3.83944	−	3.30982i	−0.133672	−	0.115233i
$826$	2.23846	+	0.0909813i	0.0778862	+	0.00316564i
$827$			5.25434i			0.182711i	0.995818	+	0.0913556i	$0.0291200\pi$
$827$			5.25434i			0.182711i	−0.995818	+	0.0913556i	$0.970880\pi$
$828$	0.403197	−	1.02219i	0.0140121	−	0.0355234i
$829$	−15.3816	+	8.88058i	−0.534226	+	0.308435i	−0.742736	−	0.669585i	$-0.766472\pi$
$829$	−15.3816	+	8.88058i	−0.534226	+	0.308435i	0.208510	+	0.978020i	$0.433139\pi$
$830$	−0.883186	−	0.509907i	−0.0306558	−	0.0176991i
$831$	28.8798	+	5.48993i	1.00183	+	0.190443i
$832$	−18.6151	−	10.7474i	−0.645361	−	0.372599i
$833$	21.6970	+	45.8070i	0.751755	+	1.58712i
$834$	−2.55106	−	0.484947i	−0.0883361	−	0.0167923i
$835$	20.5245			0.710279
$836$	21.5215	+	37.2764i	0.744338	+	1.28923i
$837$	−7.86499	+	12.4461i	−0.271854	+	0.430199i
$838$	1.55971	+	0.900499i	0.0538793	+	0.0311072i
$839$	−8.51777	−	14.7532i	−0.294066	−	0.509338i	0.680701	−	0.732561i	$-0.261675\pi$
$839$	−8.51777	−	14.7532i	−0.294066	−	0.509338i	−0.974767	+	0.223224i	$0.928342\pi$
$840$	−1.29870	+	1.38827i	−0.0448094	+	0.0478998i
$841$	−12.2228	+	21.1705i	−0.421476	+	0.730017i
$842$	1.94952	−	1.12555i	0.0671848	−	0.0387891i
$843$	32.0300	+	27.6117i	1.10317	+	0.950999i
$844$	−7.42399	+	12.8587i	−0.255544	+	0.442616i
$845$	−2.64546	+	4.58207i	−0.0910066	+	0.157628i
$846$	−0.114289	−	0.143817i	−0.00392933	−	0.00494454i
$847$	5.70456	−	2.99147i	0.196011	−	0.102788i
$848$	25.4566	−	14.6974i	0.874182	−	0.504709i
$849$	−45.0807	+	15.7312i	−1.54716	+	0.539892i
$850$			0.752978i			0.0258269i
$851$		−	0.466183i		−	0.0159806i
$852$	18.2968	−	6.38477i	0.626838	−	0.218739i
$853$	−2.55801	+	1.47687i	−0.0875847	+	0.0505670i	−0.543153	−	0.839634i	$-0.682770\pi$
$853$	−2.55801	+	1.47687i	−0.0875847	+	0.0505670i	0.455568	+	0.890201i	$0.349436\pi$
$854$	−0.141246	+	3.47516i	−0.00483335	+	0.118918i
$855$	13.7998	+	17.3652i	0.471942	+	0.593877i
$856$	−0.497263	+	0.861285i	−0.0169961	+	0.0294381i
$857$	−19.1804	+	33.2214i	−0.655190	+	1.13482i	0.326656	+	0.945143i	$0.394078\pi$
$857$	−19.1804	+	33.2214i	−0.655190	+	1.13482i	−0.981846	+	0.189680i	$0.939255\pi$
$858$	1.10857	+	0.955654i	0.0378460	+	0.0326255i
$859$	−9.09692	+	5.25211i	−0.310383	+	0.179200i	−0.647098	−	0.762407i	$-0.724017\pi$
$859$	−9.09692	+	5.25211i	−0.310383	+	0.179200i	0.336715	+	0.941607i	$0.390684\pi$
$860$	0.444655	−	0.770165i	0.0151626	−	0.0262624i
$861$	−7.77690	+	33.4437i	−0.265036	+	1.13976i
$862$	−1.59113	−	2.75592i	−0.0541941	−	0.0938669i
$863$	−39.3048	−	22.6927i	−1.33795	−	0.772467i	−0.351449	−	0.936207i	$-0.614311\pi$
$863$	−39.3048	−	22.6927i	−1.33795	−	0.772467i	−0.986504	+	0.163740i	$0.947644\pi$
$864$	3.43895	−	5.44202i	0.116995	−	0.185141i
$865$	10.6588	+	18.4616i	0.362410	+	0.627712i
$866$	−3.52775			−0.119878
$867$	−60.2859	−	11.4601i	−2.04742	−	0.389206i
$868$	14.8997	+	0.605590i	0.505728	+	0.0205550i
$869$	−23.1010	−	13.3374i	−0.783647	−	0.452439i
$870$	−0.377627	−	0.0717854i	−0.0128028	−	0.00243375i
$871$	−7.46230	−	4.30836i	−0.252850	−	0.145983i
$872$	3.71231	−	2.14331i	0.125715	−	0.0725815i
$873$	2.15993	−	5.47585i	0.0731024	−	0.185329i
$874$		−	0.141574i		−	0.00478881i
$875$	−0.107447	+	2.64357i	−0.00363235	+	0.0893689i
$876$	34.3478	+	29.6098i	1.16050	+	1.00042i
$877$	−16.7656	−	29.0388i	−0.566134	−	0.980572i	−0.996943	−	0.0781294i	$-0.975105\pi$
$877$	−16.7656	−	29.0388i	−0.566134	−	0.980572i	0.430810	−	0.902443i	$-0.358228\pi$
$878$	−0.0204219			−0.000689205
$879$	32.6837	+	6.21304i	1.10239	+	0.209561i
$880$		−	11.5171i		−	0.388242i
$881$	55.1097			1.85669			0.928347	−	0.371714i	$-0.121230\pi$
$881$	55.1097			1.85669			0.928347	+	0.371714i	$0.121230\pi$
$882$	1.21543	+	1.81432i	0.0409256	+	0.0610912i
$883$	3.42725			0.115336			0.0576680	−	0.998336i	$-0.481634\pi$
$883$	3.42725			0.115336			0.0576680	+	0.998336i	$0.481634\pi$
$884$			39.9912i			1.34505i
$885$	−9.20864	+	10.6821i	−0.309545	+	0.359077i
$886$	−0.709915			−0.0238501
$887$	19.6195	+	33.9819i	0.658757	+	1.14100i	0.980938	+	0.194322i	$0.0622507\pi$
$887$	19.6195	+	33.9819i	0.658757	+	1.14100i	−0.322181	+	0.946678i	$0.604416\pi$
$888$	0.339724	−	1.78712i	0.0114004	−	0.0599717i
$889$	−0.661474	+	16.2746i	−0.0221851	+	0.545834i
$890$			1.65976i			0.0556351i
$891$	17.9817	−	19.2472i	0.602410	−	0.644807i
$892$	−18.6033	+	10.7406i	−0.622885	+	0.359623i
$893$	3.77030	+	2.17678i	0.126168	+	0.0728432i
$894$	0.182020	−	0.211145i	0.00608764	−	0.00706175i
$895$	2.03822	+	1.17677i	0.0681301	+	0.0393349i
$896$	−8.67849	−	0.352733i	−0.289928	−	0.0117840i
$897$	0.291753	+	0.836074i	0.00974135	+	0.0279157i
$898$	−0.162527			−0.00542361
$899$	3.02341	+	5.23670i	0.100836	+	0.174654i
$900$	−0.879327	−	5.90242i	−0.0293109	−	0.196747i
$901$	−46.8400	−	27.0431i	−1.56047	−	0.900936i
$902$	1.14019	+	1.97487i	0.0379643	+	0.0657561i
$903$	−1.49614	−	1.39961i	−0.0497884	−	0.0465761i
$904$	−1.75538	+	3.04040i	−0.0583830	+	0.101122i
$905$	1.42310	−	0.821627i	0.0473054	−	0.0273118i
$906$	−0.514922	+	2.70875i	−0.0171071	+	0.0899921i
$907$	5.59186	−	9.68539i	0.185675	−	0.321598i	−0.758129	−	0.652105i	$-0.773886\pi$
$907$	5.59186	−	9.68539i	0.185675	−	0.321598i	0.943804	+	0.330507i	$0.107220\pi$
$908$	11.9752	−	20.7416i	0.397410	−	0.688335i
$909$	−2.52211	−	16.9295i	−0.0836531	−	0.561515i
$910$	0.0310233	−	0.763285i	0.00102841	−	0.0253027i
$911$	−4.71312	+	2.72112i	−0.156153	+	0.0901548i	−0.576040	−	0.817421i	$-0.695403\pi$
$911$	−4.71312	+	2.72112i	−0.156153	+	0.0901548i	0.419888	+	0.907576i	$0.362070\pi$
$912$	−9.41129	+	49.5081i	−0.311639	+	1.63938i
$913$		−	28.7012i		−	0.949872i
$914$			0.581638i			0.0192389i
$915$	−16.5838	−	14.2962i	−0.548243	−	0.472618i
$916$	−20.7302	+	11.9686i	−0.684945	+	0.395453i
$917$	−48.7823	+	25.5814i	−1.61093	+	0.844773i
$918$	−3.90946	−	0.156324i	−0.129032	−	0.00515947i
$919$	−1.39443	+	2.41523i	−0.0459981	+	0.0796710i	−0.888108	−	0.459635i	$-0.847980\pi$
$919$	−1.39443	+	2.41523i	−0.0459981	+	0.0796710i	0.842110	+	0.539306i	$0.181313\pi$
$920$	−0.0381930	+	0.0661522i	−0.00125919	+	0.00218097i
$921$	45.0830	−	15.7320i	1.48554	−	0.518386i
$922$	0.715839	−	0.413290i	0.0235749	−	0.0136110i
$923$	−7.80841	+	13.5246i	−0.257017	+	0.445166i
$924$	−25.9850	−	6.04249i	−0.854845	−	0.198783i
$925$	−1.26588	−	2.19256i	−0.0416218	−	0.0720911i
$926$	0.998896	+	0.576713i	0.0328257	+	0.0189520i
$927$	13.2699	−	33.6419i	0.435841	−	1.10495i
$928$	−1.32198	−	2.28973i	−0.0433961	−	0.0751642i
$929$	−12.3464			−0.405073			−0.202536	−	0.979275i	$-0.564918\pi$
$929$	−12.3464			−0.405073			−0.202536	+	0.979275i	$0.564918\pi$
$930$	0.333224	−	0.386544i	0.0109268	−	0.0126753i
$931$	−42.5732	−	29.4296i	−1.39528	−	0.964515i
$932$	41.6112	+	24.0242i	1.36302	+	0.786940i
$933$	7.76027	+	22.2386i	0.254060	+	0.728058i
$934$	1.12850	+	0.651537i	0.0369255	+	0.0213189i
$935$	−18.3524	+	10.5957i	−0.600186	+	0.346518i
$936$	0.509161	+	3.41771i	0.0166425	+	0.111711i
$937$			12.0267i			0.392894i	0.980514	+	0.196447i	$0.0629403\pi$
$937$			12.0267i			0.392894i	−0.980514	+	0.196447i	$0.937060\pi$
$938$	−0.853152	−	0.0346759i	−0.0278564	−	0.00113221i
$939$	21.6989	−	7.57197i	0.708118	−	0.247102i
$940$	−0.585648	−	1.01437i	−0.0191017	−	0.0330851i
$941$	−13.6425			−0.444734			−0.222367	−	0.974963i	$-0.571378\pi$
$941$	−13.6425			−0.444734			−0.222367	+	0.974963i	$0.571378\pi$
$942$	−0.262622	−	0.752594i	−0.00855669	−	0.0245209i
$943$			1.37967i			0.0449282i
$944$	−32.0432			−1.04292
$945$	−13.7031	−	1.10669i	−0.445762	−	0.0360006i
$946$	−0.136065			−0.00442385
$947$		−	6.31702i		−	0.205276i	−0.994719	−	0.102638i	$-0.967272\pi$
$947$		−	6.31702i		−	0.205276i	0.994719	−	0.102638i	$-0.0327282\pi$
$948$	−10.3462	−	29.6490i	−0.336028	−	0.962954i
$949$	−36.5452			−1.18631
$950$	−0.384431	−	0.665854i	−0.0124726	−	0.0216032i
$951$	−41.2790	+	14.4045i	−1.33856	+	0.467099i
$952$	3.69083	+	7.03819i	0.119620	+	0.228109i
$953$			41.8480i			1.35559i	0.735251	+	0.677795i	$0.237064\pi$
$953$			41.8480i			1.35559i	−0.735251	+	0.677795i	$0.762936\pi$
$954$	−2.16777	−	0.855068i	−0.0701842	−	0.0276839i
$955$	11.6972	−	6.75341i	0.378514	−	0.218535i
$956$	−27.3150	−	15.7703i	−0.883429	−	0.510048i
$957$	−3.56426	−	10.2141i	−0.115216	−	0.330174i
$958$	1.64422	+	0.949293i	0.0531224	+	0.0306703i
$959$	−7.90347	+	12.4888i	−0.255217	+	0.403284i
$960$	8.75514	−	10.1561i	0.282571	−	0.327786i
$961$	22.9717			0.741024
$962$	0.365500	+	0.633065i	0.0117842	+	0.0204108i
$963$	−7.11364	+	1.05977i	−0.229234	+	0.0341506i
$964$	8.82855	+	5.09717i	0.284349	+	0.164169i
$965$	7.85597	+	13.6069i	0.252893	+	0.438023i
$966$	0.0640803	+	0.0599458i	0.00206175	+	0.00192873i
$967$	5.58321	−	9.67040i	0.179544	−	0.310979i	−0.762180	−	0.647365i	$-0.775871\pi$
$967$	5.58321	−	9.67040i	0.179544	−	0.310979i	0.941724	+	0.336385i	$0.109204\pi$
$968$	0.874655	−	0.504982i	0.0281125	−	0.0162307i
$969$	87.5487	−	30.5506i	2.81247	−	0.981428i
$970$	−0.102023	+	0.176708i	−0.00327575	+	0.00567377i
$971$	2.71987	−	4.71095i	0.0872847	−	0.151182i	−0.819078	−	0.573682i	$-0.805514\pi$
$971$	2.71987	−	4.71095i	0.0872847	−	0.151182i	0.906362	+	0.422501i	$0.138848\pi$
$972$	30.8279	−	3.34008i	0.988806	−	0.107133i
$973$	−20.3977	+	32.2317i	−0.653919	+	1.03330i
$974$	1.58750	−	0.916545i	0.0508669	−	0.0293680i
$975$	3.64246	+	3.14002i	0.116652	+	0.100561i
$976$		−	49.7462i		−	1.59234i
$977$			24.4137i			0.781064i	0.920589	+	0.390532i	$0.127709\pi$
$977$			24.4137i			0.781064i	−0.920589	+	0.390532i	$0.872291\pi$
$978$	0.179979	−	0.946781i	0.00575510	−	0.0302747i
$979$	−40.4533	+	23.3557i	−1.29289	+	0.746452i
$980$	5.96056	+	12.5840i	0.190403	+	0.401982i
$981$	28.8373	+	11.3748i	0.920705	+	0.363168i
$982$	1.34596	−	2.33126i	0.0429512	−	0.0743936i
$983$	2.29228	−	3.97034i	0.0731124	−	0.126634i	−0.827151	−	0.561979i	$-0.810040\pi$
$983$	2.29228	−	3.97034i	0.0731124	−	0.126634i	0.900264	+	0.435345i	$0.143373\pi$
$984$	−1.00541	+	5.28897i	−0.0320514	+	0.168606i
$985$	21.3297	−	12.3147i	0.679622	−	0.392380i
$986$	−0.803468	+	1.39165i	−0.0255876	+	0.0443191i
$987$	−2.58171	+	0.784837i	−0.0821766	+	0.0249816i
$988$	−20.4174	−	35.3640i	−0.649564	−	1.12508i
$989$	−0.0712924	−	0.0411607i	−0.00226697	−	0.00130883i
$990$	−0.714816	+	0.568050i	−0.0227183	+	0.0180538i
$991$	23.9244	+	41.4382i	0.759983	+	1.31633i	0.942859	+	0.333193i	$0.108126\pi$
$991$	23.9244	+	41.4382i	0.759983	+	1.31633i	−0.182876	+	0.983136i	$0.558541\pi$
$992$	3.51034			0.111453
$993$	−4.77043	−	13.6706i	−0.151385	−	0.433823i
$994$	−0.0628461	+	1.54624i	−0.00199336	+	0.0490437i
$995$	14.4687	+	8.35349i	0.458687	+	0.264823i
$996$	22.0614	−	25.5915i	0.699041	−	0.810898i
$997$	−41.1381	−	23.7511i	−1.30286	−	0.752204i	−0.321963	−	0.946752i	$-0.604343\pi$
$997$	−41.1381	−	23.7511i	−1.30286	−	0.752204i	−0.980893	+	0.194548i	$0.937676\pi$
$998$	1.44389	−	0.833630i	0.0457055	−	0.0263881i
$999$	11.6466	−	6.11725i	0.368482	−	0.193541i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.t.c.131.9	yes	32
3.2	odd	2		945.2.t.c.341.8		32
7.3	odd	6		315.2.be.c.311.8	yes	32
9.2	odd	6		315.2.be.c.236.8	yes	32
9.7	even	3		945.2.be.c.656.9		32
21.17	even	6		945.2.be.c.206.9		32
63.38	even	6	inner	315.2.t.c.101.8	✓	32
63.52	odd	6		945.2.t.c.521.9		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.t.c.101.8	✓	32	63.38	even	6	inner
315.2.t.c.131.9	yes	32	1.1	even	1	trivial
315.2.be.c.236.8	yes	32	9.2	odd	6
315.2.be.c.311.8	yes	32	7.3	odd	6
945.2.t.c.341.8		32	3.2	odd	2
945.2.t.c.521.9		32	63.52	odd	6
945.2.be.c.206.9		32	21.17	even	6
945.2.be.c.656.9		32	9.7	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.103991i q^{2} +(0.570662 + 1.63534i) q^{3} +1.98919 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.170061 + 0.0593436i) q^{6} +(-0.107447 + 2.64357i) q^{7} +0.414839i q^{8} +(-2.34869 + 1.86646i) q^{9} +O(q^{10})\)	\(q+0.103991i q^{2} +(0.570662 + 1.63534i) q^{3} +1.98919 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.170061 + 0.0593436i) q^{6} +(-0.107447 + 2.64357i) q^{7} +0.414839i q^{8} +(-2.34869 + 1.86646i) q^{9} +(0.0900587 - 0.0519954i) q^{10} +(2.53457 + 1.46334i) q^{11} +(1.13515 + 3.25300i) q^{12} +(-2.40454 - 1.38826i) q^{13} +(-0.274907 - 0.0111734i) q^{14} +(1.13092 - 1.31188i) q^{15} +3.93523 q^{16} +(-3.62041 - 6.27073i) q^{17} +(-0.194094 - 0.244242i) q^{18} +(6.40301 + 3.69678i) q^{19} +(-0.994593 - 1.72269i) q^{20} +(-4.38446 + 1.33287i) q^{21} +(-0.152173 + 0.263572i) q^{22} +(-0.159465 + 0.0920672i) q^{23} +(-0.678403 + 0.236733i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.144366 - 0.250050i) q^{26} +(-4.39260 - 2.77580i) q^{27} +(-0.213731 + 5.25855i) q^{28} +(-1.84819 + 1.06705i) q^{29} +(0.136423 + 0.117605i) q^{30} -2.83342i q^{31} +1.23891i q^{32} +(-0.946671 + 4.97996i) q^{33} +(0.652098 - 0.376489i) q^{34} +(2.34312 - 1.22873i) q^{35} +(-4.67198 + 3.71273i) q^{36} +(-1.26588 + 2.19256i) q^{37} +(-0.384431 + 0.665854i) q^{38} +(0.898103 - 4.72447i) q^{39} +(0.359261 - 0.207419i) q^{40} +(3.74637 - 6.48890i) q^{41} +(-0.138606 - 0.455943i) q^{42} +(0.223536 + 0.387176i) q^{43} +(5.04173 + 2.91085i) q^{44} +(2.79074 + 1.10080i) q^{45} +(-0.00957414 - 0.0165829i) q^{46} +0.588831 q^{47} +(2.24569 + 6.43545i) q^{48} +(-6.97691 - 0.568084i) q^{49} +(-0.0900587 - 0.0519954i) q^{50} +(8.18876 - 9.49907i) q^{51} +(-4.78308 - 2.76151i) q^{52} +(6.46888 - 3.73481i) q^{53} +(0.288657 - 0.456790i) q^{54} -2.92667i q^{55} +(-1.09665 - 0.0445730i) q^{56} +(-2.39155 + 12.5807i) q^{57} +(-0.110964 - 0.192195i) q^{58} -8.14263 q^{59} +(2.24960 - 2.60957i) q^{60} -12.6412i q^{61} +0.294649 q^{62} +(-4.68175 - 6.40947i) q^{63} +7.74163 q^{64} +2.77652i q^{65} +(-0.517870 - 0.0984450i) q^{66} +3.10342 q^{67} +(-7.20166 - 12.4736i) q^{68} +(-0.241562 - 0.208241i) q^{69} +(0.127777 + 0.243663i) q^{70} -5.62459i q^{71} +(-0.774278 - 0.974327i) q^{72} +(11.3988 - 6.58111i) q^{73} +(-0.228006 - 0.131640i) q^{74} +(-1.70158 - 0.323463i) q^{75} +(12.7368 + 7.35359i) q^{76} +(-4.14076 + 6.54308i) q^{77} +(0.491302 + 0.0933945i) q^{78} -9.11435 q^{79} +(-1.96762 - 3.40801i) q^{80} +(2.03268 - 8.76745i) q^{81} +(0.674785 + 0.389587i) q^{82} +(-4.90339 - 8.49292i) q^{83} +(-8.72150 + 2.65133i) q^{84} +(-3.62041 + 6.27073i) q^{85} +(-0.0402627 + 0.0232457i) q^{86} +(-2.79969 - 2.41350i) q^{87} +(-0.607048 + 1.05144i) q^{88} +(-7.98030 + 13.8223i) q^{89} +(-0.114473 + 0.290212i) q^{90} +(3.92832 - 6.20740i) q^{91} +(-0.317206 + 0.183139i) q^{92} +(4.63361 - 1.61692i) q^{93} +0.0612330i q^{94} -7.39356i q^{95} +(-2.02603 + 0.706996i) q^{96} +(-1.69927 + 0.981074i) q^{97} +(0.0590755 - 0.725534i) q^{98} +(-8.68417 + 1.29375i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - q^{3} - 32 q^{4} - 16 q^{5} - 2 q^{6} + q^{7} + q^{9}+O(q^{10}) \) 32 * q - q^3 - 32 * q^4 - 16 * q^5 - 2 * q^6 + q^7 + q^9	\( 32 q - q^{3} - 32 q^{4} - 16 q^{5} - 2 q^{6} + q^{7} + q^{9} + 3 q^{11} + 12 q^{12} + 6 q^{13} - 15 q^{14} - q^{15} + 32 q^{16} - 3 q^{17} - 13 q^{18} + 16 q^{20} - q^{21} - 21 q^{22} - 9 q^{23} - 4 q^{24} - 16 q^{25} + 12 q^{26} + 23 q^{27} - 31 q^{28} + 18 q^{29} - 2 q^{30} + 19 q^{33} - 30 q^{34} + q^{35} + 18 q^{36} - q^{37} - 30 q^{38} + 21 q^{39} + 6 q^{41} + 19 q^{42} - 19 q^{43} + 21 q^{44} - 8 q^{45} + 6 q^{46} - 30 q^{47} - 35 q^{48} + 5 q^{49} + 36 q^{51} + 21 q^{52} - 24 q^{53} - 59 q^{54} + 30 q^{56} + 27 q^{57} + 30 q^{59} + 3 q^{60} - 32 q^{63} + 76 q^{64} + 26 q^{66} - 50 q^{67} - 3 q^{68} - 50 q^{69} + 9 q^{70} - 14 q^{72} + 12 q^{73} + 60 q^{74} + 2 q^{75} + 54 q^{76} - 27 q^{77} - 42 q^{78} + 4 q^{79} - 16 q^{80} - 23 q^{81} - 24 q^{82} - 42 q^{83} - 72 q^{84} - 3 q^{85} + 51 q^{86} + 34 q^{87} + 42 q^{88} + 30 q^{89} + 41 q^{90} - 57 q^{91} + 6 q^{92} - 33 q^{93} + 15 q^{96} - 42 q^{97} + 6 q^{98} - q^{99}+O(q^{100}) \) 32 * q - q^3 - 32 * q^4 - 16 * q^5 - 2 * q^6 + q^7 + q^9 + 3 * q^11 + 12 * q^12 + 6 * q^13 - 15 * q^14 - q^15 + 32 * q^16 - 3 * q^17 - 13 * q^18 + 16 * q^20 - q^21 - 21 * q^22 - 9 * q^23 - 4 * q^24 - 16 * q^25 + 12 * q^26 + 23 * q^27 - 31 * q^28 + 18 * q^29 - 2 * q^30 + 19 * q^33 - 30 * q^34 + q^35 + 18 * q^36 - q^37 - 30 * q^38 + 21 * q^39 + 6 * q^41 + 19 * q^42 - 19 * q^43 + 21 * q^44 - 8 * q^45 + 6 * q^46 - 30 * q^47 - 35 * q^48 + 5 * q^49 + 36 * q^51 + 21 * q^52 - 24 * q^53 - 59 * q^54 + 30 * q^56 + 27 * q^57 + 30 * q^59 + 3 * q^60 - 32 * q^63 + 76 * q^64 + 26 * q^66 - 50 * q^67 - 3 * q^68 - 50 * q^69 + 9 * q^70 - 14 * q^72 + 12 * q^73 + 60 * q^74 + 2 * q^75 + 54 * q^76 - 27 * q^77 - 42 * q^78 + 4 * q^79 - 16 * q^80 - 23 * q^81 - 24 * q^82 - 42 * q^83 - 72 * q^84 - 3 * q^85 + 51 * q^86 + 34 * q^87 + 42 * q^88 + 30 * q^89 + 41 * q^90 - 57 * q^91 + 6 * q^92 - 33 * q^93 + 15 * q^96 - 42 * q^97 + 6 * q^98 - q^99

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