LMFDB - Embedded newform 429.2.bd.a.76.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(76,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 7]))

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

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

chi := DirichletCharacter("429.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bd (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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			76.8
Character	$\chi$	$=$	429.76
Dual form			429.2.bd.a.175.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.390674 + 0.104681i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.59038 - 0.918208i) q^{4} +(1.89569 + 1.89569i) q^{5} +(-0.104681 - 0.390674i) q^{6} +(1.61789 - 0.433512i) q^{7} +(-1.09719 - 1.09719i) q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.390674 + 0.104681i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.59038 - 0.918208i) q^{4} +(1.89569 + 1.89569i) q^{5} +(-0.104681 - 0.390674i) q^{6} +(1.61789 - 0.433512i) q^{7} +(-1.09719 - 1.09719i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.542154 + 0.939038i) q^{10} +(2.65409 - 1.98892i) q^{11} +1.83642i q^{12} +(1.07540 + 3.44144i) q^{13} +0.677447 q^{14} +(0.693870 - 2.58956i) q^{15} +(1.52263 + 2.63727i) q^{16} +(1.80918 - 3.13359i) q^{17} +(-0.285993 + 0.285993i) q^{18} +(-2.09025 - 7.80091i) q^{19} +(-1.27423 - 4.75551i) q^{20} +(-1.18438 - 1.18438i) q^{21} +(1.24509 - 0.499185i) q^{22} +(4.90556 - 2.83223i) q^{23} +(-0.401599 + 1.49879i) q^{24} +2.18727i q^{25} +(0.0598769 + 1.45705i) q^{26} +1.00000 q^{27} +(-2.97111 - 0.796108i) q^{28} +(-0.587414 + 0.339144i) q^{29} +(0.542154 - 0.939038i) q^{30} +(5.75152 + 5.75152i) q^{31} +(1.12198 + 4.18728i) q^{32} +(-3.04950 - 1.30405i) q^{33} +(1.03482 - 1.03482i) q^{34} +(3.88881 + 2.24521i) q^{35} +(1.59038 - 0.918208i) q^{36} +(2.99980 + 0.803794i) q^{37} -3.26642i q^{38} +(2.44268 - 2.65204i) q^{39} -4.15986i q^{40} +(-8.40565 - 2.25229i) q^{41} +(-0.338723 - 0.586686i) q^{42} +(0.971836 - 1.68327i) q^{43} +(-6.04726 + 0.726128i) q^{44} +(-2.58956 + 0.693870i) q^{45} +(2.21295 - 0.592959i) q^{46} +(-0.155263 + 0.155263i) q^{47} +(1.52263 - 2.63727i) q^{48} +(-3.63255 + 2.09725i) q^{49} +(-0.228965 + 0.854510i) q^{50} -3.61835 q^{51} +(1.44967 - 6.46065i) q^{52} -5.19243 q^{53} +(0.390674 + 0.104681i) q^{54} +(8.80170 + 1.26097i) q^{55} +(-2.25077 - 1.29948i) q^{56} +(-5.71066 + 5.71066i) q^{57} +(-0.264989 + 0.0710036i) q^{58} +(0.436706 + 1.62981i) q^{59} +(-3.48127 + 3.48127i) q^{60} +(10.2819 + 5.93624i) q^{61} +(1.64489 + 2.84904i) q^{62} +(-0.433512 + 1.61789i) q^{63} -4.33720i q^{64} +(-4.48528 + 8.56252i) q^{65} +(-1.05485 - 0.828684i) q^{66} +(-2.77821 + 10.3684i) q^{67} +(-5.75457 + 3.32240i) q^{68} +(-4.90556 - 2.83223i) q^{69} +(1.28423 + 1.28423i) q^{70} +(-10.2588 + 2.74885i) q^{71} +(1.49879 - 0.401599i) q^{72} +(0.813832 + 0.813832i) q^{73} +(1.08780 + 0.628043i) q^{74} +(1.89423 - 1.09364i) q^{75} +(-3.83856 + 14.3257i) q^{76} +(3.43181 - 4.36842i) q^{77} +(1.23191 - 0.780382i) q^{78} -0.132027i q^{79} +(-2.11301 + 7.88587i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.04810 - 1.75982i) q^{82} +(-2.46310 + 2.46310i) q^{83} +(0.796108 + 2.97111i) q^{84} +(9.36994 - 2.51067i) q^{85} +(0.555877 - 0.555877i) q^{86} +(0.587414 + 0.339144i) q^{87} +(-5.09426 - 0.729825i) q^{88} +(-9.20944 - 2.46766i) q^{89} -1.08431 q^{90} +(3.23178 + 5.10167i) q^{91} -10.4023 q^{92} +(2.10520 - 7.85672i) q^{93} +(-0.0769103 + 0.0444042i) q^{94} +(10.8256 - 18.7505i) q^{95} +(3.06530 - 3.06530i) q^{96} +(0.622187 - 0.166714i) q^{97} +(-1.63868 + 0.439084i) q^{98} +(0.395405 + 3.29297i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 28 q^{3} + 4 q^{5} - 28 q^{9}+O(q^{10}) $ 56 * q - 28 * q^3 + 4 * q^5 - 28 * q^9	$ 56 q - 28 q^{3} + 4 q^{5} - 28 q^{9} - 12 q^{11} + 24 q^{14} - 8 q^{15} + 68 q^{16} - 8 q^{20} - 10 q^{22} - 12 q^{23} - 48 q^{26} + 56 q^{27} + 4 q^{31} + 12 q^{33} + 32 q^{34} + 36 q^{37} - 12 q^{42} + 24 q^{44} + 4 q^{45} - 8 q^{47} + 68 q^{48} - 24 q^{49} - 56 q^{53} - 2 q^{55} + 72 q^{56} - 88 q^{58} + 56 q^{59} - 44 q^{60} + 20 q^{66} + 92 q^{67} + 12 q^{69} - 216 q^{70} + 72 q^{71} - 12 q^{75} - 12 q^{78} + 44 q^{80} - 28 q^{81} - 156 q^{82} - 120 q^{86} - 6 q^{88} - 56 q^{89} + 92 q^{91} + 32 q^{92} - 20 q^{93} - 44 q^{97}+O(q^{100}) $ 56 * q - 28 * q^3 + 4 * q^5 - 28 * q^9 - 12 * q^11 + 24 * q^14 - 8 * q^15 + 68 * q^16 - 8 * q^20 - 10 * q^22 - 12 * q^23 - 48 * q^26 + 56 * q^27 + 4 * q^31 + 12 * q^33 + 32 * q^34 + 36 * q^37 - 12 * q^42 + 24 * q^44 + 4 * q^45 - 8 * q^47 + 68 * q^48 - 24 * q^49 - 56 * q^53 - 2 * q^55 + 72 * q^56 - 88 * q^58 + 56 * q^59 - 44 * q^60 + 20 * q^66 + 92 * q^67 + 12 * q^69 - 216 * q^70 + 72 * q^71 - 12 * q^75 - 12 * q^78 + 44 * q^80 - 28 * q^81 - 156 * q^82 - 120 * q^86 - 6 * q^88 - 56 * q^89 + 92 * q^91 + 32 * q^92 - 20 * q^93 - 44 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.390674	+	0.104681i	0.276248	+	0.0740205i	0.394283	−	0.918989i	$-0.370993\pi$
$2$	0.390674	+	0.104681i	0.276248	+	0.0740205i	−0.118035	+	0.993009i	$0.537660\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−1.59038	−	0.918208i	−0.795191	−	0.459104i
$5$	1.89569	+	1.89569i	0.847778	+	0.847778i	0.989856	−	0.142078i	$-0.0453783\pi$
$5$	1.89569	+	1.89569i	0.847778	+	0.847778i	−0.142078	+	0.989856i	$0.545378\pi$
$6$	−0.104681	−	0.390674i	−0.0427357	−	0.159492i
$7$	1.61789	−	0.433512i	0.611504	−	0.163852i	0.0602415	−	0.998184i	$-0.480813\pi$
$7$	1.61789	−	0.433512i	0.611504	−	0.163852i	0.551263	+	0.834332i	$0.314146\pi$
$8$	−1.09719	−	1.09719i	−0.387915	−	0.387915i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.542154	+	0.939038i	0.171444	+	0.296950i
$11$	2.65409	−	1.98892i	0.800239	−	0.599681i
$11$	2.65409	−	1.98892i	0.800239	−	0.599681i
$12$			1.83642i			0.530128i
$13$	1.07540	+	3.44144i	0.298262	+	0.954484i
$13$	1.07540	+	3.44144i	0.298262	+	0.954484i
$14$	0.677447			0.181055
$15$	0.693870	−	2.58956i	0.179157	−	0.668621i
$16$	1.52263	+	2.63727i	0.380657	+	0.659317i
$17$	1.80918	−	3.13359i	0.438790	−	0.760006i	−0.558807	−	0.829298i	$-0.688741\pi$
$17$	1.80918	−	3.13359i	0.438790	−	0.760006i	0.997596	+	0.0692918i	$0.0220740\pi$
$18$	−0.285993	+	0.285993i	−0.0674092	+	0.0674092i
$19$	−2.09025	−	7.80091i	−0.479535	−	1.78965i	−0.603499	−	0.797364i	$-0.706227\pi$
$19$	−2.09025	−	7.80091i	−0.479535	−	1.78965i	0.123963	−	0.992287i	$-0.460439\pi$
$20$	−1.27423	−	4.75551i	−0.284927	−	1.06336i
$21$	−1.18438	−	1.18438i	−0.258452	−	0.258452i
$22$	1.24509	−	0.499185i	0.265453	−	0.106427i
$23$	4.90556	−	2.83223i	1.02288	−	0.590560i	0.107943	−	0.994157i	$-0.465573\pi$
$23$	4.90556	−	2.83223i	1.02288	−	0.590560i	0.914937	+	0.403597i	$0.132240\pi$
$24$	−0.401599	+	1.49879i	−0.0819760	+	0.305939i
$25$			2.18727i			0.437454i
$26$	0.0598769	+	1.45705i	0.0117428	+	0.285752i
$27$	1.00000			0.192450
$28$	−2.97111	−	0.796108i	−0.561488	−	0.150450i
$29$	−0.587414	+	0.339144i	−0.109080	+	0.0629774i	−0.553547	−	0.832818i	$-0.686726\pi$
$29$	−0.587414	+	0.339144i	−0.109080	+	0.0629774i	0.444467	+	0.895795i	$0.353393\pi$
$30$	0.542154	−	0.939038i	0.0989833	−	0.171444i
$31$	5.75152	+	5.75152i	1.03300	+	1.03300i	0.999436	+	0.0335663i	$0.0106865\pi$
$31$	5.75152	+	5.75152i	1.03300	+	1.03300i	0.0335663	+	0.999436i	$0.489314\pi$
$32$	1.12198	+	4.18728i	0.198339	+	0.740213i
$33$	−3.04950	−	1.30405i	−0.530850	−	0.227007i
$34$	1.03482	−	1.03482i	0.177471	−	0.177471i
$35$	3.88881	+	2.24521i	0.657330	+	0.379509i
$36$	1.59038	−	0.918208i	0.265064	−	0.153035i
$37$	2.99980	+	0.803794i	0.493164	+	0.132143i	0.496826	−	0.867850i	$-0.334499\pi$
$37$	2.99980	+	0.803794i	0.493164	+	0.132143i	−0.00366140	+	0.999993i	$0.501165\pi$
$38$		−	3.26642i		−	0.529883i
$39$	2.44268	−	2.65204i	0.391141	−	0.424667i
$40$		−	4.15986i		−	0.657731i
$41$	−8.40565	−	2.25229i	−1.31274	−	0.351748i	−0.466488	−	0.884527i	$-0.654481\pi$
$41$	−8.40565	−	2.25229i	−1.31274	−	0.351748i	−0.846254	+	0.532779i	$0.821148\pi$
$42$	−0.338723	−	0.586686i	−0.0522662	−	0.0905276i
$43$	0.971836	−	1.68327i	0.148204	−	0.256696i	−0.782360	−	0.622827i	$-0.785984\pi$
$43$	0.971836	−	1.68327i	0.148204	−	0.256696i	0.930564	+	0.366130i	$0.119318\pi$
$44$	−6.04726	+	0.726128i	−0.911659	+	0.109468i
$45$	−2.58956	+	0.693870i	−0.386029	+	0.103436i
$46$	2.21295	−	0.592959i	0.326282	−	0.0874271i
$47$	−0.155263	+	0.155263i	−0.0226474	+	0.0226474i	−0.718340	−	0.695692i	$-0.755098\pi$
$47$	−0.155263	+	0.155263i	−0.0226474	+	0.0226474i	0.695692	+	0.718340i	$0.255098\pi$
$48$	1.52263	−	2.63727i	0.219772	−	0.380657i
$49$	−3.63255	+	2.09725i	−0.518936	+	0.299608i
$50$	−0.228965	+	0.854510i	−0.0323806	+	0.120846i
$51$	−3.61835			−0.506671
$52$	1.44967	−	6.46065i	0.201032	−	0.895931i
$53$	−5.19243			−0.713235			−0.356618	−	0.934250i	$-0.616070\pi$
$53$	−5.19243			−0.713235			−0.356618	+	0.934250i	$0.616070\pi$
$54$	0.390674	+	0.104681i	0.0531640	+	0.0142452i
$55$	8.80170	+	1.26097i	1.18682	+	0.170029i
$56$	−2.25077	−	1.29948i	−0.300772	−	0.173651i
$57$	−5.71066	+	5.71066i	−0.756395	+	0.756395i
$58$	−0.264989	+	0.0710036i	−0.0347948	+	0.00932323i
$59$	0.436706	+	1.62981i	0.0568542	+	0.212183i	0.988509	−	0.151162i	$-0.0483014\pi$
$59$	0.436706	+	1.62981i	0.0568542	+	0.212183i	−0.931655	+	0.363345i	$0.881635\pi$
$60$	−3.48127	+	3.48127i	−0.449430	+	0.449430i
$61$	10.2819	+	5.93624i	1.31646	+	0.760057i	0.983157	−	0.182763i	$-0.0585043\pi$
$61$	10.2819	+	5.93624i	1.31646	+	0.760057i	0.333301	+	0.942821i	$0.391838\pi$
$62$	1.64489	+	2.84904i	0.208902	+	0.361829i
$63$	−0.433512	+	1.61789i	−0.0546173	+	0.203835i
$64$		−	4.33720i		−	0.542150i
$65$	−4.48528	+	8.56252i	−0.556331	+	1.06205i
$66$	−1.05485	−	0.828684i	−0.129843	−	0.102004i
$67$	−2.77821	+	10.3684i	−0.339412	+	1.26670i	0.559594	+	0.828767i	$0.310957\pi$
$67$	−2.77821	+	10.3684i	−0.339412	+	1.26670i	−0.899006	+	0.437936i	$0.855710\pi$
$68$	−5.75457	+	3.32240i	−0.697844	+	0.402900i
$69$	−4.90556	−	2.83223i	−0.590560	−	0.340960i
$70$	1.28423	+	1.28423i	0.153495	+	0.153495i
$71$	−10.2588	+	2.74885i	−1.21750	+	0.326228i	−0.809700	−	0.586844i	$-0.800370\pi$
$71$	−10.2588	+	2.74885i	−1.21750	+	0.326228i	−0.407799	+	0.913072i	$0.633704\pi$
$72$	1.49879	−	0.401599i	0.176634	−	0.0473289i
$73$	0.813832	+	0.813832i	0.0952518	+	0.0952518i	0.753127	−	0.657875i	$-0.228545\pi$
$73$	0.813832	+	0.813832i	0.0952518	+	0.0952518i	−0.657875	+	0.753127i	$0.728545\pi$
$74$	1.08780	+	0.628043i	0.126454	+	0.0730085i
$75$	1.89423	−	1.09364i	0.218727	−	0.126282i
$76$	−3.83856	+	14.3257i	−0.440313	+	1.64327i
$77$	3.43181	−	4.36842i	0.391091	−	0.497828i
$78$	1.23191	−	0.780382i	0.139486	−	0.0883609i
$79$		−	0.132027i		−	0.0148542i	−0.999972	−	0.00742708i	$-0.997636\pi$
$79$		−	0.132027i		−	0.0148542i	0.999972	−	0.00742708i	$-0.00236413\pi$
$80$	−2.11301	+	7.88587i	−0.236242	+	0.881667i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−3.04810	−	1.75982i	−0.336606	−	0.194340i
$83$	−2.46310	+	2.46310i	−0.270360	+	0.270360i	−0.829245	−	0.558885i	$-0.811229\pi$
$83$	−2.46310	+	2.46310i	−0.270360	+	0.270360i	0.558885	+	0.829245i	$0.311229\pi$
$84$	0.796108	+	2.97111i	0.0868625	+	0.324175i
$85$	9.36994	−	2.51067i	1.01631	−	0.272320i
$86$	0.555877	−	0.555877i	0.0599418	−	0.0599418i
$87$	0.587414	+	0.339144i	0.0629774	+	0.0363600i
$88$	−5.09426	−	0.729825i	−0.543050	−	0.0777997i
$89$	−9.20944	−	2.46766i	−0.976199	−	0.261572i	−0.264756	−	0.964315i	$-0.585291\pi$
$89$	−9.20944	−	2.46766i	−0.976199	−	0.261572i	−0.711443	+	0.702744i	$0.751958\pi$
$90$	−1.08431			−0.114296
$91$	3.23178	+	5.10167i	0.338782	+	0.534800i
$92$	−10.4023			−1.08451
$93$	2.10520	−	7.85672i	0.218299	−	0.814704i
$94$	−0.0769103	+	0.0444042i	−0.00793269	+	0.00457994i
$95$	10.8256	−	18.7505i	1.11069	−	1.92377i
$96$	3.06530	−	3.06530i	0.312851	−	0.312851i
$97$	0.622187	−	0.166714i	0.0631735	−	0.0169273i	−0.227094	−	0.973873i	$-0.572922\pi$
$97$	0.622187	−	0.166714i	0.0631735	−	0.0169273i	0.290267	+	0.956946i	$0.406256\pi$
$98$	−1.63868	+	0.439084i	−0.165532	+	0.0443542i
$99$	0.395405	+	3.29297i	0.0397397	+	0.330956i
$100$	2.00837	−	3.47860i	0.200837	−	0.347860i
$101$	4.27966	+	7.41259i	0.425842	+	0.737580i	0.996499	−	0.0836086i	$-0.0266446\pi$
$101$	4.27966	+	7.41259i	0.425842	+	0.737580i	−0.570657	+	0.821189i	$0.693311\pi$
$102$	−1.41360	−	0.378772i	−0.139967	−	0.0375040i
$103$			6.98396i			0.688150i	0.938942	+	0.344075i	$0.111808\pi$
$103$			6.98396i			0.688150i	−0.938942	+	0.344075i	$0.888192\pi$
$104$	2.59600	−	4.95582i	0.254558	−	0.485959i
$105$		−	4.49042i		−	0.438220i
$106$	−2.02855	−	0.543547i	−0.197030	−	0.0527940i
$107$	−13.5093	+	7.79958i	−1.30599	+	0.754014i	−0.981424	−	0.191849i	$-0.938552\pi$
$107$	−13.5093	+	7.79958i	−1.30599	+	0.754014i	−0.324566	+	0.945863i	$0.605218\pi$
$108$	−1.59038	−	0.918208i	−0.153035	−	0.0883546i
$109$	−12.1549	+	12.1549i	−1.16423	+	1.16423i	−0.180692	+	0.983540i	$0.557834\pi$
$109$	−12.1549	+	12.1549i	−1.16423	+	1.16423i	−0.983540	+	0.180692i	$0.942166\pi$
$110$	3.30660	+	1.41400i	0.315272	+	0.134819i
$111$	−0.803794	−	2.99980i	−0.0762928	−	0.284729i
$112$	3.60673	+	3.60673i	0.340804	+	0.340804i
$113$	5.81593	−	10.0735i	0.547117	−	0.947634i	−0.451354	−	0.892345i	$-0.649059\pi$
$113$	5.81593	−	10.0735i	0.547117	−	0.947634i	0.998470	−	0.0552887i	$-0.0176079\pi$
$114$	−2.82880	+	1.63321i	−0.264942	+	0.152964i
$115$	14.6684	+	3.93040i	1.36784	+	0.366511i
$116$	1.24562			0.115653
$117$	−3.51807	−	0.789399i	−0.325246	−	0.0729800i
$118$			0.682438i			0.0628235i
$119$	1.56860	−	5.85409i	0.143793	−	0.536643i
$120$	−3.60254	+	2.07993i	−0.328866	+	0.189871i
$121$	3.08843	−	10.5575i	0.280766	−	0.959776i
$122$	3.39545	+	3.39545i	0.307409	+	0.307409i
$123$	2.25229	+	8.40565i	0.203082	+	0.757912i
$124$	−3.86602	−	14.4282i	−0.347179	−	1.29569i
$125$	5.33206	−	5.33206i	0.476914	−	0.476914i
$126$	−0.338723	+	0.586686i	−0.0301759	+	0.0522662i
$127$	−4.94741	−	8.56916i	−0.439012	−	0.760390i	0.558602	−	0.829436i	$-0.311338\pi$
$127$	−4.94741	−	8.56916i	−0.439012	−	0.760390i	−0.997614	+	0.0690456i	$0.978005\pi$
$128$	2.69798	−	10.0690i	0.238470	−	0.889981i
$129$	−1.94367			−0.171131
$130$	−2.64861	+	2.87563i	−0.232299	+	0.252209i
$131$		−	8.97854i		−	0.784459i	−0.919867	−	0.392229i	$-0.871704\pi$
$131$		−	8.97854i		−	0.784459i	0.919867	−	0.392229i	$-0.128296\pi$
$132$	3.65248	+	4.87402i	0.317907	+	0.424229i
$133$	−6.76357	−	11.7148i	−0.586476	−	1.01581i
$134$	−2.17075	+	3.75984i	−0.187524	+	0.324801i
$135$	1.89569	+	1.89569i	0.163155	+	0.163155i
$136$	−5.42314	+	1.45313i	−0.465031	+	0.124605i
$137$	1.33398	+	4.97849i	0.113970	+	0.425341i	0.999208	−	0.0397973i	$-0.0126712\pi$
$137$	1.33398	+	4.97849i	0.113970	+	0.425341i	−0.885238	+	0.465138i	$0.846005\pi$
$138$	−1.62000	−	1.62000i	−0.137903	−	0.137903i
$139$	−3.01304	−	1.73958i	−0.255562	−	0.147549i	0.366746	−	0.930321i	$-0.380472\pi$
$139$	−3.01304	−	1.73958i	−0.255562	−	0.147549i	−0.622309	+	0.782772i	$0.713805\pi$
$140$	−4.12314	−	7.14148i	−0.348469	−	0.603565i
$141$	0.212093	+	0.0568302i	0.0178615	+	0.00478597i
$142$	−4.29561			−0.360479
$143$	9.69894	+	6.99503i	0.811066	+	0.584954i
$144$	−3.04525			−0.253771
$145$	−1.75646	−	0.470643i	−0.145866	−	0.0390848i
$146$	0.232750	+	0.403135i	0.0192625	+	0.0333637i
$147$	3.63255	+	2.09725i	0.299608	+	0.172979i
$148$	−4.03278	−	4.03278i	−0.331493	−	0.331493i
$149$	−4.83914	−	18.0599i	−0.396438	−	1.47952i	−0.819318	−	0.573339i	$-0.805648\pi$
$149$	−4.83914	−	18.0599i	−0.396438	−	1.47952i	0.422880	−	0.906185i	$-0.361019\pi$
$150$	0.854510	−	0.228965i	0.0697705	−	0.0186949i
$151$	15.4320	+	15.4320i	1.25584	+	1.25584i	0.953060	+	0.302782i	$0.0979155\pi$
$151$	15.4320	+	15.4320i	1.25584	+	1.25584i	0.302782	+	0.953060i	$0.402084\pi$
$152$	−6.26567	+	10.8525i	−0.508213	+	0.880251i
$153$	1.80918	+	3.13359i	0.146263	+	0.253335i
$154$	1.79801	−	1.34738i	0.144888	−	0.108575i
$155$			21.8062i			1.75151i
$156$	−6.31992	+	1.97488i	−0.505998	+	0.158117i
$157$	−9.03775			−0.721291			−0.360646	−	0.932703i	$-0.617444\pi$
$157$	−9.03775			−0.721291			−0.360646	+	0.932703i	$0.617444\pi$
$158$	0.0138206	−	0.0515793i	0.00109951	−	0.00410343i
$159$	2.59621	+	4.49678i	0.205893	+	0.356618i
$160$	−5.81085	+	10.0647i	−0.459388	+	0.795684i
$161$	6.70884	−	6.70884i	0.528731	−	0.528731i
$162$	−0.104681	−	0.390674i	−0.00822450	−	0.0306942i
$163$	−5.47429	−	20.4303i	−0.428779	−	1.60023i	−0.755529	−	0.655115i	$-0.772620\pi$
$163$	−5.47429	−	20.4303i	−0.428779	−	1.60023i	0.326750	−	0.945111i	$-0.394046\pi$
$164$	11.3001	+	11.3001i	0.882392	+	0.882392i
$165$	−3.30882	−	8.25298i	−0.257591	−	0.642494i
$166$	−1.22011	+	0.704430i	−0.0946988	+	0.0546744i
$167$	2.15286	−	8.03459i	0.166594	−	0.621736i	−0.831238	−	0.555917i	$-0.812367\pi$
$167$	2.15286	−	8.03459i	0.166594	−	0.621736i	0.997832	−	0.0658189i	$-0.0209660\pi$
$168$			2.59897i			0.200515i
$169$	−10.6870	+	7.40183i	−0.822080	+	0.569372i
$170$	3.92341			0.300912
$171$	7.80091	+	2.09025i	0.596550	+	0.159845i
$172$	−3.09118	+	1.78470i	−0.235700	+	0.136082i
$173$	−11.6057	+	20.1016i	−0.882363	+	1.52830i	−0.0336555	+	0.999433i	$0.510715\pi$
$173$	−11.6057	+	20.1016i	−0.882363	+	1.52830i	−0.848707	+	0.528863i	$0.822618\pi$
$174$	0.193986	+	0.193986i	0.0147060	+	0.0147060i
$175$	0.948208	+	3.53876i	0.0716778	+	0.267505i
$176$	9.28650	+	3.97118i	0.699996	+	0.299339i
$177$	1.19310	−	1.19310i	0.0896790	−	0.0896790i
$178$	−3.33957	−	1.92810i	−0.250312	−	0.144517i
$179$	6.62530	−	3.82512i	0.495198	−	0.285903i	−0.231530	−	0.972828i	$-0.574373\pi$
$179$	6.62530	−	3.82512i	0.495198	−	0.285903i	0.726728	+	0.686925i	$0.241040\pi$
$180$	4.75551	+	1.27423i	0.354455	+	0.0949758i
$181$			7.27824i			0.540988i	0.962722	+	0.270494i	$0.0871870\pi$
$181$			7.27824i			0.540988i	−0.962722	+	0.270494i	$0.912813\pi$
$182$	0.728525	+	2.33139i	0.0540018	+	0.172814i
$183$		−	11.8725i		−	0.877638i
$184$	−8.48981	−	2.27484i	−0.625877	−	0.167703i
$185$	4.16295	+	7.21043i	0.306066	+	0.530122i
$186$	1.64489	−	2.84904i	0.120610	−	0.208902i
$187$	−1.43071	−	11.9151i	−0.104624	−	0.871321i
$188$	0.389491	−	0.104364i	0.0284066	−	0.00761152i
$189$	1.61789	−	0.433512i	0.117684	−	0.0315333i
$190$	6.19211	−	6.19211i	0.449223	−	0.449223i
$191$	7.51583	−	13.0178i	0.543826	−	0.941935i	−0.454853	−	0.890566i	$-0.650308\pi$
$191$	7.51583	−	13.0178i	0.543826	−	0.941935i	0.998680	−	0.0513685i	$-0.0163583\pi$
$192$	−3.75613	+	2.16860i	−0.271075	+	0.156505i
$193$	−0.787102	+	2.93750i	−0.0566568	+	0.211446i	−0.988451	−	0.151541i	$-0.951576\pi$
$193$	−0.787102	+	2.93750i	−0.0566568	+	0.211446i	0.931794	+	0.362987i	$0.118243\pi$
$194$	0.260524			0.0187045
$195$	9.65800	−	0.396891i	0.691624	−	0.0284219i
$196$	7.70286			0.550204
$197$	13.6022	+	3.64470i	0.969117	+	0.259674i	0.708455	−	0.705756i	$-0.249392\pi$
$197$	13.6022	+	3.64470i	0.969117	+	0.259674i	0.260662	+	0.965430i	$0.416059\pi$
$198$	−0.190236	+	1.32787i	−0.0135195	+	0.0943675i
$199$	20.5411	+	11.8594i	1.45612	+	0.840693i	0.998818	−	0.0486166i	$-0.0154812\pi$
$199$	20.5411	+	11.8594i	1.45612	+	0.840693i	0.457306	+	0.889310i	$0.348815\pi$
$200$	2.39985	−	2.39985i	0.169695	−	0.169695i
$201$	10.3684	−	2.77821i	0.731331	−	0.195960i
$202$	0.895996	+	3.34390i	0.0630421	+	0.235276i
$203$	−0.803347	+	0.803347i	−0.0563839	+	0.0563839i
$204$	5.75457	+	3.32240i	0.402900	+	0.232615i
$205$	−11.6649	−	20.2041i	−0.814709	−	1.41112i
$206$	−0.731087	+	2.72845i	−0.0509372	+	0.190100i
$207$			5.66445i			0.393707i
$208$	−7.43857	+	8.07614i	−0.515772	+	0.559980i
$209$	−21.0631	−	16.5470i	−1.45696	−	1.14458i
$210$	0.470060	−	1.75429i	0.0324372	−	0.121057i
$211$	3.65043	−	2.10758i	0.251306	−	0.145092i	−0.369056	−	0.929407i	$-0.620319\pi$
$211$	3.65043	−	2.10758i	0.251306	−	0.145092i	0.620362	+	0.784316i	$0.286986\pi$
$212$	8.25795	+	4.76773i	0.567158	+	0.327449i
$213$	7.50999	+	7.50999i	0.514576	+	0.514576i
$214$	−6.09419	+	1.63293i	−0.416590	+	0.111625i
$215$	5.03325	−	1.34866i	0.343265	−	0.0919776i
$216$	−1.09719	−	1.09719i	−0.0746542	−	0.0746542i
$217$	11.7987	+	6.81196i	0.800945	+	0.462426i
$218$	−6.02101	+	3.47623i	−0.407794	+	0.235440i
$219$	0.297883	−	1.11171i	0.0201291	−	0.0751227i
$220$	−12.8402	−	10.0872i	−0.865689	−	0.680080i
$221$	12.7296	+	2.85633i	0.856288	+	0.192137i
$222$		−	1.25609i		−	0.0843030i
$223$	−3.74029	+	13.9589i	−0.250468	+	0.934760i	0.720088	+	0.693883i	$0.244102\pi$
$223$	−3.74029	+	13.9589i	−0.250468	+	0.934760i	−0.970556	+	0.240877i	$0.922565\pi$
$224$	3.63047	+	6.28815i	0.242571	+	0.420145i
$225$	−1.89423	−	1.09364i	−0.126282	−	0.0729091i
$226$	3.32663	−	3.32663i	0.221284	−	0.221284i
$227$	−3.81591	−	14.2412i	−0.253271	−	0.945219i	−0.969044	−	0.246887i	$-0.920592\pi$
$227$	−3.81591	−	14.2412i	−0.253271	−	0.945219i	0.715774	−	0.698332i	$-0.246074\pi$
$228$	14.3257	−	3.83856i	0.948743	−	0.254215i
$229$	6.58542	−	6.58542i	0.435177	−	0.435177i	−0.455208	−	0.890385i	$-0.650435\pi$
$229$	6.58542	−	6.58542i	0.435177	−	0.435177i	0.890385	+	0.455208i	$0.150435\pi$
$230$	5.31914	+	3.07101i	0.350734	+	0.202496i
$231$	−5.49907	−	0.787821i	−0.361812	−	0.0518348i
$232$	1.01661	+	0.272399i	0.0667436	+	0.0178839i
$233$	−23.9785			−1.57088			−0.785440	−	0.618937i	$-0.787563\pi$
$233$	−23.9785			−1.57088			−0.785440	+	0.618937i	$0.787563\pi$
$234$	−1.29179	−	0.676673i	−0.0844466	−	0.0442355i
$235$	−0.588661			−0.0384000
$236$	0.801973	−	2.99300i	0.0522040	−	0.194828i
$237$	−0.114338	+	0.0660133i	−0.00742708	+	0.00428802i
$238$	1.22562	−	2.12284i	0.0794452	−	0.137603i
$239$	−18.1215	+	18.1215i	−1.17218	+	1.17218i	−0.190495	+	0.981688i	$0.561009\pi$
$239$	−18.1215	+	18.1215i	−1.17218	+	1.17218i	−0.981688	+	0.190495i	$0.938991\pi$
$240$	7.88587	−	2.11301i	0.509031	−	0.136394i
$241$	−6.64497	+	1.78052i	−0.428040	+	0.114693i	−0.466406	−	0.884571i	$-0.654451\pi$
$241$	−6.64497	+	1.78052i	−0.428040	+	0.114693i	0.0383658	+	0.999264i	$0.487785\pi$
$242$	2.31174	−	3.80126i	0.148604	−	0.244354i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−10.9014	−	18.8818i	−0.697890	−	1.20878i
$245$	−10.8619	−	2.91044i	−0.693943	−	0.185941i
$246$			3.51964i			0.224404i
$247$	24.5985	−	15.5825i	1.56517	−	0.991493i
$248$		−	12.6210i		−	0.801434i
$249$	3.36466	+	0.901558i	0.213227	+	0.0571339i
$250$	2.64126	−	1.52493i	0.167048	−	0.0964452i
$251$	0.0968937	+	0.0559416i	0.00611588	+	0.00353100i	0.503055	−	0.864255i	$-0.332209\pi$
$251$	0.0968937	+	0.0559416i	0.00611588	+	0.00353100i	−0.496939	+	0.867786i	$0.665543\pi$
$252$	2.17501	−	2.17501i	0.137013	−	0.137013i
$253$	7.38676	−	17.2737i	0.464401	−	1.08599i
$254$	−1.03580	−	3.86565i	−0.0649917	−	0.242552i
$255$	−6.85927	−	6.85927i	−0.429544	−	0.429544i
$256$	−2.22914	+	3.86099i	−0.139321	+	0.241312i
$257$	13.0432	−	7.53047i	0.813609	−	0.469738i	−0.0345983	−	0.999401i	$-0.511015\pi$
$257$	13.0432	−	7.53047i	0.813609	−	0.469738i	0.848208	+	0.529664i	$0.177682\pi$
$258$	−0.759342	−	0.203465i	−0.0472746	−	0.0126672i
$259$	5.20180			0.323224
$260$	14.9955	−	9.49926i	0.929981	−	0.589119i
$261$		−	0.678287i		−	0.0419849i
$262$	0.939881	−	3.50768i	0.0580660	−	0.216705i
$263$	−6.53551	+	3.77328i	−0.402997	+	0.232670i	−0.687776	−	0.725923i	$-0.741413\pi$
$263$	−6.53551	+	3.77328i	−0.402997	+	0.232670i	0.284780	+	0.958593i	$0.408080\pi$
$264$	1.91508	+	4.77667i	0.117865	+	0.293984i
$265$	−9.84323	−	9.84323i	−0.604665	−	0.604665i
$266$	−1.41603	−	5.28470i	−0.0868224	−	0.324026i
$267$	2.46766	+	9.20944i	0.151019	+	0.563609i
$268$	13.9388	−	13.9388i	0.851445	−	0.851445i
$269$	−0.0706203	+	0.122318i	−0.00430580	+	0.00745786i	−0.868170	−	0.496266i	$-0.834704\pi$
$269$	−0.0706203	+	0.122318i	−0.00430580	+	0.00745786i	0.863864	+	0.503724i	$0.168037\pi$
$270$	0.542154	+	0.939038i	0.0329944	+	0.0571481i
$271$	−0.830019	+	3.09767i	−0.0504201	+	0.188170i	−0.986543	−	0.163503i	$-0.947721\pi$
$271$	−0.830019	+	3.09767i	−0.0504201	+	0.188170i	0.936123	+	0.351674i	$0.114387\pi$
$272$	11.0188			0.668113
$273$	2.80229	−	5.34964i	0.169602	−	0.323775i
$274$			2.08461i			0.125936i
$275$	4.35030	+	5.80522i	0.262333	+	0.350068i
$276$	5.20115	+	9.00865i	0.313072	+	0.542257i
$277$	−10.6138	+	18.3836i	−0.637722	+	1.10457i	0.348210	+	0.937417i	$0.386790\pi$
$277$	−10.6138	+	18.3836i	−0.637722	+	1.10457i	−0.985932	+	0.167150i	$0.946544\pi$
$278$	−0.995015	−	0.995015i	−0.0596770	−	0.0596770i
$279$	−7.85672	+	2.10520i	−0.470369	+	0.126035i
$280$	−1.80335	−	6.73018i	−0.107771	−	0.402205i
$281$	−4.52385	−	4.52385i	−0.269870	−	0.269870i	0.559178	−	0.829048i	$-0.311117\pi$
$281$	−4.52385	−	4.52385i	−0.269870	−	0.269870i	−0.829048	+	0.559178i	$0.811117\pi$
$282$	0.0769103	+	0.0444042i	0.00457994	+	0.00264423i
$283$	2.19282	+	3.79808i	0.130350	+	0.225772i	0.923811	−	0.382848i	$-0.125057\pi$
$283$	2.19282	+	3.79808i	0.130350	+	0.225772i	−0.793462	+	0.608620i	$0.791723\pi$
$284$	18.8395	+	5.04802i	1.11792	+	0.299545i
$285$	−21.6513			−1.28251
$286$	3.05688	+	3.74807i	0.180757	+	0.221628i
$287$	−14.5758			−0.860382
$288$	−4.18728	−	1.12198i	−0.246738	−	0.0661132i
$289$	1.95376	+	3.38401i	0.114927	+	0.199060i
$290$	−0.636938	−	0.367736i	−0.0374023	−	0.0215942i
$291$	−0.455472	−	0.455472i	−0.0267003	−	0.0267003i
$292$	−0.547037	−	2.04157i	−0.0320129	−	0.119474i
$293$	7.58045	−	2.03117i	0.442854	−	0.118662i	−0.0304995	−	0.999535i	$-0.509710\pi$
$293$	7.58045	−	2.03117i	0.442854	−	0.118662i	0.473354	+	0.880872i	$0.343043\pi$
$294$	1.19960	+	1.19960i	0.0699621	+	0.0699621i
$295$	−2.26175	+	3.91747i	−0.131684	+	0.228084i
$296$	−2.40943	−	4.17326i	−0.140046	−	0.242566i
$297$	2.65409	−	1.98892i	0.154006	−	0.115409i
$298$		−	7.56210i		−	0.438061i
$299$	15.0224	+	13.8364i	0.868766	+	0.800182i
$300$	−4.01674			−0.231907
$301$	0.842605	−	3.14464i	0.0485669	−	0.181254i
$302$	4.41346	+	7.64434i	0.253966	+	0.439882i
$303$	4.27966	−	7.41259i	0.245860	−	0.425842i
$304$	17.3904	−	17.3904i	0.997409	−	0.997409i
$305$	8.23795	+	30.7445i	0.471704	+	1.76042i
$306$	0.378772	+	1.41360i	0.0216529	+	0.0808099i
$307$	13.0384	+	13.0384i	0.744140	+	0.744140i	0.973372	−	0.229232i	$-0.0736214\pi$
$307$	13.0384	+	13.0384i	0.744140	+	0.744140i	−0.229232	+	0.973372i	$0.573621\pi$
$308$	−9.46901	+	3.79635i	−0.539547	+	0.216317i
$309$	6.04829	−	3.49198i	0.344075	−	0.198652i
$310$	−2.28269	+	8.51910i	−0.129648	+	0.483852i
$311$		−	5.29540i		−	0.300274i	−0.988665	−	0.150137i	$-0.952028\pi$
$311$		−	5.29540i		−	0.300274i	0.988665	−	0.150137i	$-0.0479715\pi$
$312$	−5.58987	+	0.229713i	−0.316464	+	0.0130049i
$313$	−13.5990			−0.768663			−0.384331	−	0.923195i	$-0.625568\pi$
$313$	−13.5990			−0.768663			−0.384331	+	0.923195i	$0.625568\pi$
$314$	−3.53082	−	0.946079i	−0.199255	−	0.0533903i
$315$	−3.88881	+	2.24521i	−0.219110	+	0.126503i
$316$	−0.121228	+	0.209973i	−0.00681960	+	0.0118119i
$317$	−7.14838	−	7.14838i	−0.401493	−	0.401493i	0.477266	−	0.878759i	$-0.341628\pi$
$317$	−7.14838	−	7.14838i	−0.401493	−	0.401493i	−0.878759	+	0.477266i	$0.841628\pi$
$318$	0.543547	+	2.02855i	0.0304806	+	0.113755i
$319$	−0.884524	+	2.06844i	−0.0495238	+	0.115810i
$320$	8.22198	−	8.22198i	0.459623	−	0.459623i
$321$	13.5093	+	7.79958i	0.754014	+	0.435330i
$322$	3.32326	−	1.91868i	0.185198	−	0.106924i
$323$	−28.2264	−	7.56325i	−1.57056	−	0.420830i
$324$			1.83642i			0.102023i
$325$	−7.52737	+	2.35219i	−0.417543	+	0.130476i
$326$		−	8.55464i		−	0.473798i
$327$	16.6040	+	4.44902i	0.918201	+	0.246031i
$328$	6.75140	+	11.6938i	0.372784	+	0.645681i
$329$	−0.183890	+	0.318506i	−0.0101382	+	0.0175598i
$330$	−0.428741	−	3.57059i	−0.0236014	−	0.196555i
$331$	−27.3959	+	7.34070i	−1.50581	+	0.403481i	−0.915042	−	0.403358i	$-0.867843\pi$
$331$	−27.3959	+	7.34070i	−1.50581	+	0.403481i	−0.590771	+	0.806839i	$0.701176\pi$
$332$	6.17891	−	1.65563i	0.339112	−	0.0908648i
$333$	−2.19601	+	2.19601i	−0.120340	+	0.120340i
$334$	1.68213	−	2.91354i	0.0920423	−	0.159422i
$335$	−24.9219	+	14.3887i	−1.36163	+	0.786136i
$336$	1.32015	−	4.92688i	0.0720203	−	0.268783i
$337$	−6.82969			−0.372037			−0.186019	−	0.982546i	$-0.559558\pi$
$337$	−6.82969			−0.372037			−0.186019	+	0.982546i	$0.559558\pi$
$338$	−4.94998	+	1.77298i	−0.269243	+	0.0964372i
$339$	−11.6319			−0.631756
$340$	−17.2071	−	4.61063i	−0.933186	−	0.250046i
$341$	26.7043	+	3.82578i	1.44612	+	0.207178i
$342$	2.82880	+	1.63321i	0.152964	+	0.0883139i
$343$	−13.2585	+	13.2585i	−0.715892	+	0.715892i
$344$	−2.91315	+	0.780577i	−0.157067	+	0.0420859i
$345$	−3.93040	−	14.6684i	−0.211605	−	0.789722i
$346$	−6.63828	+	6.63828i	−0.356876	+	0.356876i
$347$	5.47829	+	3.16289i	0.294090	+	0.169793i	0.639785	−	0.768554i	$-0.279023\pi$
$347$	5.47829	+	3.16289i	0.294090	+	0.169793i	−0.345695	+	0.938347i	$0.612357\pi$
$348$	−0.622809	−	1.07874i	−0.0333861	−	0.0578263i
$349$	−0.0148745	+	0.0555124i	−0.000796214	+	0.00297151i	−0.966323	−	0.257333i	$-0.917156\pi$
$349$	−0.0148745	+	0.0555124i	−0.000796214	+	0.00297151i	0.965527	+	0.260304i	$0.0838229\pi$
$350$			1.48176i			0.0792034i
$351$	1.07540	+	3.44144i	0.0574005	+	0.183691i
$352$	11.3060	+	8.88191i	0.602610	+	0.473407i
$353$	9.52664	−	35.5539i	0.507052	−	1.89234i	0.0591771	−	0.998247i	$-0.481152\pi$
$353$	9.52664	−	35.5539i	0.507052	−	1.89234i	0.447875	−	0.894096i	$-0.352181\pi$
$354$	0.591009	−	0.341219i	0.0314117	−	0.0181356i
$355$	−24.6585	−	14.2366i	−1.30874	−	0.755600i
$356$	12.3807	+	12.3807i	0.656176	+	0.656176i
$357$	−5.85409	+	1.56860i	−0.309831	+	0.0830190i
$358$	2.98875	−	0.800833i	0.157960	−	0.0423253i
$359$	14.5360	+	14.5360i	0.767183	+	0.767183i	0.977610	−	0.210427i	$-0.0674853\pi$
$359$	14.5360	+	14.5360i	0.767183	+	0.767183i	−0.210427	+	0.977610i	$0.567485\pi$
$360$	3.60254	+	2.07993i	0.189871	+	0.109622i
$361$	−40.0305	+	23.1116i	−2.10687	+	1.21640i
$362$	−0.761892	+	2.84342i	−0.0400442	+	0.149447i
$363$	−10.6873	+	2.60411i	−0.560938	+	0.136681i
$364$	−0.455370	−	11.0810i	−0.0238679	−	0.580805i
$365$			3.08554i			0.161505i
$366$	1.24282	−	4.63827i	0.0649632	−	0.242446i
$367$	−15.8180	−	27.3976i	−0.825694	−	1.43014i	−0.901388	−	0.433013i	$-0.857450\pi$
$367$	−15.8180	−	27.3976i	−0.825694	−	1.43014i	0.0756936	−	0.997131i	$-0.475883\pi$
$368$	14.9387	+	8.62485i	0.778733	+	0.449602i
$369$	6.15336	−	6.15336i	0.320331	−	0.320331i
$370$	0.871561	+	3.25271i	0.0453103	+	0.169100i
$371$	−8.40077	+	2.25098i	−0.436146	+	0.116865i
$372$	−10.5622	+	10.5622i	−0.547623	+	0.547623i
$373$	−13.4870	−	7.78673i	−0.698331	−	0.403181i	0.108395	−	0.994108i	$-0.465429\pi$
$373$	−13.4870	−	7.78673i	−0.698331	−	0.403181i	−0.806725	+	0.590926i	$0.798762\pi$
$374$	0.688342	−	4.80470i	0.0355933	−	0.248445i
$375$	−7.28373	−	1.95167i	−0.376130	−	0.100784i
$376$	0.340706			0.0175706
$377$	−1.79885	−	1.65684i	−0.0926453	−	0.0853314i
$378$	0.677447			0.0348441
$379$	1.16104	−	4.33304i	0.0596384	−	0.222573i	−0.929674	−	0.368382i	$-0.879912\pi$
$379$	1.16104	−	4.33304i	0.0596384	−	0.222573i	0.989313	+	0.145809i	$0.0465784\pi$
$380$	−34.4338	+	19.8804i	−1.76642	+	1.01984i
$381$	−4.94741	+	8.56916i	−0.253463	+	0.439012i
$382$	4.29895	−	4.29895i	0.219953	−	0.219953i
$383$	31.2419	−	8.37123i	1.59638	−	0.427750i	0.652436	−	0.757844i	$-0.273747\pi$
$383$	31.2419	−	8.37123i	1.59638	−	0.427750i	0.943948	+	0.330094i	$0.107080\pi$
$384$	−10.0690	+	2.69798i	−0.513831	+	0.137681i
$385$	14.7868	−	1.77553i	0.753606	−	0.0904895i
$386$	−0.615000	+	1.06521i	−0.0313027	+	0.0542179i
$387$	0.971836	+	1.68327i	0.0494012	+	0.0855654i
$388$	−1.14259	−	0.306157i	−0.0580064	−	0.0155428i
$389$			30.4064i			1.54167i	0.637038	+	0.770833i	$0.280160\pi$
$389$			30.4064i			1.54167i	−0.637038	+	0.770833i	$0.719840\pi$
$390$	3.81468	+	0.855952i	0.193164	+	0.0433428i
$391$		−	20.4960i		−	1.03653i
$392$	6.28668	+	1.68451i	0.317525	+	0.0850806i
$393$	−7.77565	+	4.48927i	−0.392229	+	0.226454i
$394$	4.93250	+	2.84778i	0.248496	+	0.143469i
$395$	0.250281	−	0.250281i	0.0125930	−	0.0125930i
$396$	2.39479	−	5.60015i	0.120343	−	0.281418i
$397$	3.86877	+	14.4384i	0.194168	+	0.724644i	0.992481	+	0.122401i	$0.0390595\pi$
$397$	3.86877	+	14.4384i	0.194168	+	0.724644i	−0.798313	+	0.602243i	$0.794274\pi$
$398$	6.78343	+	6.78343i	0.340023	+	0.340023i
$399$	−6.76357	+	11.7148i	−0.338602	+	0.586476i
$400$	−5.76842	+	3.33040i	−0.288421	+	0.166520i
$401$	4.38695	+	1.17548i	0.219074	+	0.0587007i	0.366686	−	0.930345i	$-0.380492\pi$
$401$	4.38695	+	1.17548i	0.219074	+	0.0587007i	−0.147612	+	0.989045i	$0.547159\pi$
$402$	4.34149			0.216534
$403$	−13.6083	+	25.9787i	−0.677880	+	1.29409i
$404$		−	15.7185i		−	0.782023i
$405$	0.693870	−	2.58956i	0.0344787	−	0.128676i
$406$	−0.397942	+	0.229752i	−0.0197495	+	0.0114024i
$407$	9.56043	−	3.83301i	0.473893	−	0.189995i
$408$	3.97002	+	3.97002i	0.196545	+	0.196545i
$409$	5.21908	+	19.4779i	0.258067	+	0.963119i	0.966358	+	0.257199i	$0.0827996\pi$
$409$	5.21908	+	19.4779i	0.258067	+	0.963119i	−0.708291	+	0.705920i	$0.750534\pi$
$410$	−2.44217	−	9.11432i	−0.120610	−	0.450124i
$411$	3.64451	−	3.64451i	0.179770	−	0.179770i
$412$	6.41273	−	11.1072i	0.315933	−	0.547211i
$413$	1.41308	+	2.44753i	0.0695332	+	0.120435i
$414$	−0.592959	+	2.21295i	−0.0291424	+	0.108761i
$415$	−9.33855			−0.458411
$416$	−13.2037	+	8.36421i	−0.647365	+	0.410089i
$417$			3.47916i			0.170375i
$418$	−6.49663	−	8.66938i	−0.317761	−	0.424033i
$419$	−1.99817	−	3.46094i	−0.0976171	−	0.169078i	0.813081	−	0.582151i	$-0.197789\pi$
$419$	−1.99817	−	3.46094i	−0.0976171	−	0.169078i	−0.910698	+	0.413073i	$0.864455\pi$
$420$	−4.12314	+	7.14148i	−0.201188	+	0.348469i
$421$	24.1748	+	24.1748i	1.17821	+	1.17821i	0.980201	+	0.198007i	$0.0634468\pi$
$421$	24.1748	+	24.1748i	1.17821	+	1.17821i	0.198007	+	0.980201i	$0.436553\pi$
$422$	1.64675	−	0.441246i	0.0801626	−	0.0214795i
$423$	−0.0568302	−	0.212093i	−0.00276318	−	0.0103123i
$424$	5.69707	+	5.69707i	0.276674	+	0.276674i
$425$	6.85400	+	3.95716i	0.332468	+	0.191950i
$426$	2.14780	+	3.72011i	0.104061	+	0.180240i
$427$	19.2083	+	5.14686i	0.929556	+	0.249074i
$428$	28.6466			1.38468
$429$	1.20841	−	11.8970i	0.0583424	−	0.574395i
$430$	2.10754			0.101635
$431$	−8.41673	−	2.25526i	−0.405420	−	0.108632i	0.0503456	−	0.998732i	$-0.483968\pi$
$431$	−8.41673	−	2.25526i	−0.405420	−	0.108632i	−0.455765	+	0.890100i	$0.650634\pi$
$432$	1.52263	+	2.63727i	0.0732574	+	0.126886i
$433$	−28.0868	−	16.2159i	−1.34976	−	0.779286i	−0.361547	−	0.932354i	$-0.617751\pi$
$433$	−28.0868	−	16.2159i	−1.34976	−	0.779286i	−0.988216	+	0.153068i	$0.951085\pi$
$434$	3.89635	+	3.89635i	0.187031	+	0.187031i
$435$	0.470643	+	1.75646i	0.0225656	+	0.0842160i
$436$	30.4918	−	8.17024i	1.46029	−	0.391284i
$437$	−32.3478	−	32.3478i	−1.54740	−	1.54740i
$438$	0.232750	−	0.403135i	0.0111212	−	0.0192625i
$439$	−5.47998	−	9.49160i	−0.261545	−	0.453009i	0.705108	−	0.709100i	$-0.250899\pi$
$439$	−5.47998	−	9.49160i	−0.261545	−	0.453009i	−0.966653	+	0.256091i	$0.917565\pi$
$440$	−8.27361	−	11.0406i	−0.394429	−	0.526342i
$441$		−	4.19451i		−	0.199738i
$442$	4.67413	+	2.44844i	0.222326	+	0.116460i
$443$	−0.681483			−0.0323783			−0.0161891	−	0.999869i	$-0.505153\pi$
$443$	−0.681483			−0.0323783			−0.0161891	+	0.999869i	$0.505153\pi$
$444$	−1.47610	+	5.50888i	−0.0700526	+	0.261440i
$445$	−12.7803	−	22.1362i	−0.605845	−	1.04935i
$446$	−2.92247	+	5.06186i	−0.138383	+	0.239686i
$447$	−13.2208	+	13.2208i	−0.625321	+	0.625321i
$448$	−1.88023	−	7.01710i	−0.0888324	−	0.331527i
$449$	−7.99676	−	29.8443i	−0.377391	−	1.40844i	−0.849820	−	0.527072i	$-0.823290\pi$
$449$	−7.99676	−	29.8443i	−0.377391	−	1.40844i	0.472430	−	0.881368i	$-0.343377\pi$
$450$	−0.625545	−	0.625545i	−0.0294885	−	0.0294885i
$451$	−26.7890	+	10.7404i	−1.26144	+	0.505743i
$452$	−18.4991	+	10.6805i	−0.870125	+	0.502367i
$453$	5.64852	−	21.0806i	0.265391	−	0.990451i
$454$		−	5.96310i		−	0.279862i
$455$	−3.54473	+	15.7976i	−0.166180	+	0.740604i
$456$	12.5313			0.586834
$457$	6.77167	+	1.81446i	0.316765	+	0.0848770i	0.413699	−	0.910414i	$-0.364237\pi$
$457$	6.77167	+	1.81446i	0.316765	+	0.0848770i	−0.0969334	+	0.995291i	$0.530903\pi$
$458$	3.26212	−	1.88339i	0.152429	−	0.0880048i
$459$	1.80918	−	3.13359i	0.0844451	−	0.146263i
$460$	−19.7195	−	19.7195i	−0.919427	−	0.919427i
$461$	4.61606	+	17.2274i	0.214991	+	0.802358i	0.986170	+	0.165739i	$0.0530010\pi$
$461$	4.61606	+	17.2274i	0.214991	+	0.802358i	−0.771178	+	0.636619i	$0.780332\pi$
$462$	−2.06587	−	0.883428i	−0.0961131	−	0.0411008i
$463$	7.74346	−	7.74346i	0.359869	−	0.359869i	−0.503895	−	0.863765i	$-0.668100\pi$
$463$	7.74346	−	7.74346i	0.359869	−	0.359869i	0.863765	+	0.503895i	$0.168100\pi$
$464$	−1.78883	−	1.03278i	−0.0830441	−	0.0479455i
$465$	18.8847	−	10.9031i	0.875757	−	0.505618i
$466$	−9.36776	−	2.51008i	−0.433953	−	0.116277i
$467$		−	21.1094i		−	0.976828i	−0.872612	−	0.488414i	$-0.837576\pi$
$467$		−	21.1094i		−	0.976828i	0.872612	−	0.488414i	$-0.162424\pi$
$468$	4.87025	+	4.48577i	0.225127	+	0.207355i
$469$			17.9793i			0.830207i
$470$	−0.229974	−	0.0616214i	−0.0106079	−	0.00284239i
$471$	4.51888	+	7.82693i	0.208219	+	0.360646i
$472$	1.30906	−	2.26735i	0.0602543	−	0.104363i
$473$	−0.768538	−	6.40046i	−0.0353374	−	0.294293i
$474$	−0.0515793	+	0.0138206i	−0.00236912	+	0.000634803i
$475$	17.0627	−	4.57194i	0.782891	−	0.209775i
$476$	−7.86994	+	7.86994i	−0.360718	+	0.360718i
$477$	2.59621	−	4.49678i	0.118873	−	0.205893i
$478$	−8.97657	+	5.18263i	−0.410579	+	0.237048i
$479$	−0.379596	+	1.41667i	−0.0173442	+	0.0647293i	−0.974056	−	0.226309i	$-0.927334\pi$
$479$	−0.379596	+	1.41667i	−0.0173442	+	0.0647293i	0.956711	+	0.291038i	$0.0940007\pi$
$480$	11.6217			0.530456
$481$	0.459767	+	11.1880i	0.0209636	+	0.510131i
$482$	−2.78240			−0.126735
$483$	−9.16445	−	2.45561i	−0.416997	−	0.111734i
$484$	−14.6058	+	13.9547i	−0.663900	+	0.634305i
$485$	1.49551	+	0.863434i	0.0679077	+	0.0392065i
$486$	−0.285993	+	0.285993i	−0.0129729	+	0.0129729i
$487$	−17.2632	+	4.62566i	−0.782271	+	0.209609i	−0.627786	−	0.778386i	$-0.716039\pi$
$487$	−17.2632	+	4.62566i	−0.782271	+	0.209609i	−0.154485	+	0.987995i	$0.549372\pi$
$488$	−4.76797	−	17.7943i	−0.215836	−	0.805511i
$489$	−14.9560	+	14.9560i	−0.676335	+	0.676335i
$490$	−3.93880	−	2.27407i	−0.177937	−	0.102732i
$491$	13.2775	+	22.9973i	0.599204	+	1.03785i	0.992939	+	0.118628i	$0.0378495\pi$
$491$	13.2775	+	22.9973i	0.599204	+	1.03785i	−0.393735	+	0.919224i	$0.628817\pi$
$492$	4.13614	−	15.4363i	0.186471	−	0.695921i
$493$			2.45428i			0.110535i
$494$	11.2412	−	3.51270i	0.505765	−	0.158044i
$495$	−5.49288	+	6.99201i	−0.246887	+	0.314268i
$496$	−6.41087	+	23.9257i	−0.287857	+	1.07430i
$497$	−15.4060	+	8.89465i	−0.691053	+	0.398979i
$498$	1.22011	+	0.704430i	0.0546744	+	0.0315663i
$499$	27.3736	+	27.3736i	1.22541	+	1.22541i	0.965682	+	0.259728i	$0.0836328\pi$
$499$	27.3736	+	27.3736i	1.22541	+	1.22541i	0.259728	+	0.965682i	$0.416367\pi$
$500$	−13.3759	+	3.58407i	−0.598191	+	0.160285i
$501$	−8.03459	+	2.15286i	−0.358959	+	0.0961828i
$502$	0.0319978	+	0.0319978i	0.00142813	+	0.00142813i
$503$	−33.3675	−	19.2647i	−1.48778	−	0.858972i	−0.487880	−	0.872911i	$-0.662230\pi$
$503$	−33.3675	−	19.2647i	−1.48778	−	0.858972i	−0.999903	+	0.0139388i	$0.995563\pi$
$504$	2.25077	−	1.29948i	0.100257	−	0.0578836i
$505$	−5.93906	+	22.1649i	−0.264285	+	0.986324i
$506$	4.69404	−	5.97515i	0.208676	−	0.265628i
$507$	11.7537	+	5.55433i	0.522000	+	0.246677i
$508$			18.1710i			0.806208i
$509$	−8.47727	+	31.6376i	−0.375749	+	1.40231i	0.476500	+	0.879175i	$0.341905\pi$
$509$	−8.47727	+	31.6376i	−0.375749	+	1.40231i	−0.852248	+	0.523138i	$0.824761\pi$
$510$	−1.96170	−	3.39777i	−0.0868657	−	0.150456i
$511$	1.66949	+	0.963883i	0.0738540	+	0.0426397i
$512$	−16.0171	+	16.0171i	−0.707861	+	0.707861i
$513$	−2.09025	−	7.80091i	−0.0922866	−	0.344418i
$514$	5.88391	−	1.57659i	0.259528	−	0.0695404i
$515$	−13.2394	+	13.2394i	−0.583399	+	0.583399i
$516$	3.09118	+	1.78470i	0.136082	+	0.0785668i
$517$	−0.103277	+	0.720888i	−0.00454214	+	0.0317046i
$518$	2.03221	+	0.544528i	0.0892900	+	0.0239252i
$519$	23.2113			1.01886
$520$	14.3159	−	4.47350i	0.627794	−	0.196176i
$521$	36.0330			1.57863			0.789317	−	0.613986i	$-0.210435\pi$
$521$	36.0330			1.57863			0.789317	+	0.613986i	$0.210435\pi$
$522$	0.0710036	−	0.264989i	0.00310774	−	0.0115983i
$523$	29.7731	−	17.1895i	1.30189	−	0.751645i	0.321159	−	0.947025i	$-0.395928\pi$
$523$	29.7731	−	17.1895i	1.30189	−	0.751645i	0.980727	+	0.195381i	$0.0625942\pi$
$524$	−8.24417	+	14.2793i	−0.360148	+	0.623795i
$525$	2.59055	−	2.59055i	0.113061	−	0.113061i
$526$	−2.94824	+	0.789979i	−0.128549	+	0.0344447i
$527$	28.4284	−	7.61736i	1.23836	−	0.331817i
$528$	−1.20411	−	10.0279i	−0.0524021	−	0.436410i
$529$	4.54302	−	7.86874i	0.197523	−	0.342119i
$530$	−2.81510	−	4.87589i	−0.122280	−	0.211795i
$531$	−1.62981	−	0.436706i	−0.0707276	−	0.0189514i
$532$			24.8414i			1.07701i
$533$	−1.28830	−	31.3497i	−0.0558024	−	1.35790i
$534$			3.85621i			0.166874i
$535$	−40.3950	−	10.8238i	−1.74643	−	0.467954i
$536$	14.4243	−	8.32788i	0.623035	−	0.359710i
$537$	−6.62530	−	3.82512i	−0.285903	−	0.165066i
$538$	−0.0403939	+	0.0403939i	−0.00174150	+	0.00174150i
$539$	−5.46987	+	12.7911i	−0.235604	+	0.550954i
$540$	−1.27423	−	4.75551i	−0.0548343	−	0.204644i
$541$	12.0368	+	12.0368i	0.517501	+	0.517501i	0.916814	−	0.399314i	$-0.130752\pi$
$541$	12.0368	+	12.0368i	0.517501	+	0.517501i	−0.399314	+	0.916814i	$0.630752\pi$
$542$	−0.648534	+	1.12329i	−0.0278569	+	0.0482496i
$543$	6.30314	−	3.63912i	0.270494	−	0.156170i
$544$	15.1510	+	4.05971i	0.649596	+	0.174059i
$545$	−46.0840			−1.97402
$546$	1.65478	−	1.79662i	0.0708182	−	0.0768881i
$547$		−	17.0234i		−	0.727870i	−0.931424	−	0.363935i	$-0.881433\pi$
$547$		−	17.0234i		−	0.727870i	0.931424	−	0.363935i	$-0.118567\pi$
$548$	2.44975	−	9.14258i	0.104648	−	0.390552i
$549$	−10.2819	+	5.93624i	−0.438819	+	0.253352i
$550$	1.09185	+	2.72334i	0.0465568	+	0.116124i
$551$	3.87347	+	3.87347i	0.165015	+	0.165015i
$552$	2.27484	+	8.48981i	0.0968236	+	0.361350i
$553$	−0.0572351	−	0.213604i	−0.00243388	−	0.00908337i
$554$	−6.07095	+	6.07095i	−0.257930	+	0.257930i
$555$	4.16295	−	7.21043i	0.176707	−	0.306066i
$556$	3.19459	+	5.53319i	0.135481	+	0.234659i
$557$	−5.51320	+	20.5756i	−0.233602	+	0.871814i	0.745172	+	0.666872i	$0.232367\pi$
$557$	−5.51320	+	20.5756i	−0.233602	+	0.871814i	−0.978774	+	0.204942i	$0.934299\pi$
$558$	−3.28979			−0.139268
$559$	6.83798	+	1.53433i	0.289216	+	0.0648954i
$560$			13.6745i			0.577852i
$561$	−9.60345	+	7.19660i	−0.405458	+	0.303841i
$562$	−1.29379	−	2.24091i	−0.0545752	−	0.0945271i
$563$	14.2799	−	24.7335i	0.601827	−	1.04239i	−0.390718	−	0.920511i	$-0.627773\pi$
$563$	14.2799	−	24.7335i	0.601827	−	1.04239i	0.992544	−	0.121884i	$-0.0388936\pi$
$564$	−0.285127	−	0.285127i	−0.0120060	−	0.0120060i
$565$	30.1214	−	8.07100i	1.26722	−	0.339550i
$566$	0.459092	+	1.71335i	0.0192971	+	0.0720177i
$567$	−1.18438	−	1.18438i	−0.0497391	−	0.0497391i
$568$	14.2719	+	8.23987i	0.598835	+	0.345737i
$569$	−2.51335	−	4.35326i	−0.105365	−	0.182498i	0.808522	−	0.588466i	$-0.200268\pi$
$569$	−2.51335	−	4.35326i	−0.105365	−	0.182498i	−0.913887	+	0.405968i	$0.866935\pi$
$570$	−8.45859	−	2.26647i	−0.354291	−	0.0949320i
$571$	29.9518			1.25345			0.626723	−	0.779242i	$-0.284396\pi$
$571$	29.9518			1.25345			0.626723	+	0.779242i	$0.284396\pi$
$572$	−9.00214	−	20.0304i	−0.376398	−	0.837514i
$573$	−15.0317			−0.627957
$574$	−5.69438	−	1.52581i	−0.237679	−	0.0636859i
$575$	6.19485	+	10.7298i	0.258343	+	0.447463i
$576$	3.75613	+	2.16860i	0.156505	+	0.0903583i
$577$	3.71062	+	3.71062i	0.154475	+	0.154475i	0.780113	−	0.625638i	$-0.215161\pi$
$577$	3.71062	+	3.71062i	0.154475	+	0.154475i	−0.625638	+	0.780113i	$0.715161\pi$
$578$	0.409042	+	1.52657i	0.0170139	+	0.0634968i
$579$	2.93750	−	0.787102i	0.122078	−	0.0327108i
$580$	2.36130	+	2.36130i	0.0980478	+	0.0980478i
$581$	−2.91724	+	5.05280i	−0.121027	+	0.209626i
$582$	−0.130262	−	0.225620i	−0.00539953	−	0.00935226i
$583$	−13.7812	+	10.3273i	−0.570759	+	0.427713i
$584$		−	1.78585i		−	0.0738991i
$585$	−5.17272	−	8.16563i	−0.213866	−	0.337607i
$586$	3.17411			0.131121
$587$	−7.01152	+	26.1674i	−0.289396	+	1.08004i	0.656170	+	0.754613i	$0.272175\pi$
$587$	−7.01152	+	26.1674i	−0.289396	+	1.08004i	−0.945566	+	0.325429i	$0.894491\pi$
$588$	−3.85143	−	6.67087i	−0.158830	−	0.275102i
$589$	32.8450	−	56.8891i	1.35335	−	2.34408i
$590$	−1.29369	+	1.29369i	−0.0532604	+	0.0532604i
$591$	−3.64470	−	13.6022i	−0.149923	−	0.559520i
$592$	2.44776	+	9.13516i	0.100602	+	0.375453i
$593$	−34.3167	−	34.3167i	−1.40922	−	1.40922i	−0.763994	−	0.645223i	$-0.776764\pi$
$593$	−34.3167	−	34.3167i	−1.40922	−	1.40922i	−0.645223	−	0.763994i	$-0.723236\pi$
$594$	1.24509	−	0.499185i	0.0510865	−	0.0204818i
$595$	14.0711	−	8.12396i	0.576859	−	0.333050i
$596$	−8.88667	+	33.1655i	−0.364012	+	1.35851i
$597$		−	23.7189i		−	0.970749i
$598$	4.42044	+	6.97809i	0.180765	+	0.285355i
$599$	8.42231			0.344126			0.172063	−	0.985086i	$-0.444957\pi$
$599$	8.42231			0.344126			0.172063	+	0.985086i	$0.444957\pi$
$600$	−3.27826	−	0.878406i	−0.133834	−	0.0358608i
$601$	23.1855	−	13.3861i	0.945756	−	0.546032i	0.0539959	−	0.998541i	$-0.482804\pi$
$601$	23.1855	−	13.3861i	0.945756	−	0.546032i	0.891760	+	0.452509i	$0.149471\pi$
$602$	0.658367	−	1.14033i	0.0268330	−	0.0464762i
$603$	−7.59020	−	7.59020i	−0.309097	−	0.309097i
$604$	−10.3730	−	38.7127i	−0.422073	−	1.57520i
$605$	25.8685	−	14.1591i	1.05170	−	0.575650i
$606$	2.44791	−	2.44791i	0.0994394	−	0.0994394i
$607$	−34.8274	−	20.1076i	−1.41360	−	0.816144i	−0.417876	−	0.908504i	$-0.637225\pi$
$607$	−34.8274	−	20.1076i	−1.41360	−	0.816144i	−0.995726	+	0.0923604i	$0.970559\pi$
$608$	30.3193	−	17.5049i	1.22961	−	0.709917i
$609$	1.09739	+	0.294045i	0.0444686	+	0.0119153i
$610$			12.8734i			0.521229i
$611$	−0.701298	−	0.367359i	−0.0283715	−	0.0148618i
$612$		−	6.64480i		−	0.268600i
$613$	29.7806	+	7.97969i	1.20283	+	0.322296i	0.803944	−	0.594705i	$-0.202731\pi$
$613$	29.7806	+	7.97969i	1.20283	+	0.322296i	0.398883	+	0.917002i	$0.369398\pi$
$614$	3.72889	+	6.45862i	0.150486	+	0.260649i
$615$	−11.6649	+	20.2041i	−0.470373	+	0.814709i
$616$	−8.55832	+	1.02764i	−0.344825	+	0.0414050i
$617$	1.79709	−	0.481529i	0.0723482	−	0.0193856i	−0.222463	−	0.974941i	$-0.571410\pi$
$617$	1.79709	−	0.481529i	0.0723482	−	0.0193856i	0.294812	+	0.955555i	$0.404743\pi$
$618$	2.72845	−	0.731087i	0.109754	−	0.0294086i
$619$	25.6040	−	25.6040i	1.02911	−	1.02911i	0.0295501	−	0.999563i	$-0.490593\pi$
$619$	25.6040	−	25.6040i	1.02911	−	1.02911i	0.999563	−	0.0295501i	$-0.00940745\pi$
$620$	20.0226	−	34.6802i	0.804127	−	1.39279i
$621$	4.90556	−	2.83223i	0.196853	−	0.113653i
$622$	0.554326	−	2.06877i	0.0222265	−	0.0829503i
$623$	−15.9696			−0.639809
$624$	10.7134	+	2.40392i	0.428881	+	0.0962339i
$625$	31.1522			1.24609
$626$	−5.31279	−	1.42356i	−0.212342	−	0.0568968i
$627$	−3.79860	+	26.5146i	−0.151702	+	1.05889i
$628$	14.3735	+	8.29854i	0.573565	+	0.331148i
$629$	7.94593	−	7.94593i	0.316825	−	0.316825i
$630$	−1.75429	+	0.470060i	−0.0698925	+	0.0187276i
$631$	0.437466	+	1.63265i	0.0174152	+	0.0649946i	0.974087	−	0.226175i	$-0.0726222\pi$
$631$	0.437466	+	1.63265i	0.0174152	+	0.0649946i	−0.956671	+	0.291170i	$0.905956\pi$
$632$	−0.144858	+	0.144858i	−0.00576214	+	0.00576214i
$633$	−3.65043	−	2.10758i	−0.145092	−	0.0837687i
$634$	−2.04439	−	3.54098i	−0.0811930	−	0.140630i
$635$	6.86572	−	25.6232i	0.272458	−	1.01683i
$636$		−	9.53546i		−	0.378106i
$637$	−11.1240	−	10.2458i	−0.440749	−	0.405954i
$638$	−0.562086	+	0.715491i	−0.0222532	+	0.0283266i
$639$	2.74885	−	10.2588i	0.108743	−	0.405833i
$640$	24.2022	−	13.9731i	0.956675	−	0.552337i
$641$	−30.6849	−	17.7160i	−1.21198	−	0.699738i	−0.248791	−	0.968557i	$-0.580033\pi$
$641$	−30.6849	−	17.7160i	−1.21198	−	0.699738i	−0.963191	+	0.268819i	$0.913367\pi$
$642$	4.46125	+	4.46125i	0.176072	+	0.176072i
$643$	19.4342	−	5.20737i	0.766409	−	0.205359i	0.145624	−	0.989340i	$-0.453481\pi$
$643$	19.4342	−	5.20737i	0.766409	−	0.205359i	0.620784	+	0.783981i	$0.286814\pi$
$644$	−16.8297	+	4.50952i	−0.663185	+	0.177700i
$645$	−3.68460	−	3.68460i	−0.145081	−	0.145081i
$646$	−10.2356	−	5.90953i	−0.402714	−	0.232507i
$647$	12.7550	−	7.36410i	0.501451	−	0.289513i	−0.227862	−	0.973693i	$-0.573173\pi$
$647$	12.7550	−	7.36410i	0.501451	−	0.289513i	0.729312	+	0.684181i	$0.239840\pi$
$648$	−0.401599	+	1.49879i	−0.0157763	+	0.0588779i
$649$	4.40061	+	3.45709i	0.172739	+	0.135703i
$650$	−3.18698	+	0.130967i	−0.125003	+	0.00513695i
$651$		−	13.6239i		−	0.533963i
$652$	−10.0531	+	37.5185i	−0.393708	+	1.46934i
$653$	−11.6544	−	20.1859i	−0.456070	−	0.789937i	0.542679	−	0.839940i	$-0.317410\pi$
$653$	−11.6544	−	20.1859i	−0.456070	−	0.789937i	−0.998749	+	0.0500032i	$0.984077\pi$
$654$	6.02101	+	3.47623i	0.235440	+	0.135931i
$655$	17.0205	−	17.0205i	0.665047	−	0.665047i
$656$	−6.85879	−	25.5974i	−0.267791	−	0.999409i
$657$	−1.11171	+	0.297883i	−0.0433721	+	0.0116215i
$658$	−0.105182	+	0.105182i	−0.00410044	+	0.00410044i
$659$	37.8244	+	21.8379i	1.47343	+	0.850684i	0.999553	−	0.0299081i	$-0.00952147\pi$
$659$	37.8244	+	21.8379i	1.47343	+	0.850684i	0.473875	+	0.880592i	$0.342855\pi$
$660$	−2.31567	+	16.1636i	−0.0901371	+	0.629167i
$661$	4.29823	+	1.15171i	0.167182	+	0.0447962i	0.341439	−	0.939904i	$-0.389086\pi$
$661$	4.29823	+	1.15171i	0.167182	+	0.0447962i	−0.174257	+	0.984700i	$0.555752\pi$
$662$	−11.4713			−0.445844
$663$	−3.89117	−	12.4524i	−0.151120	−	0.483609i
$664$	5.40497			0.209754
$665$	9.38608	−	35.0293i	0.363976	−	1.35838i
$666$	−1.08780	+	0.628043i	−0.0421515	+	0.0243362i
$667$	−1.92106	+	3.32738i	−0.0743839	+	0.128837i
$668$	−10.8013	+	10.8013i	−0.417915	+	0.417915i
$669$	13.9589	−	3.74029i	0.539684	−	0.144608i
$670$	−11.2425	+	3.01243i	−0.434337	+	0.116380i
$671$	39.0957	−	4.69443i	1.50927	−	0.181227i
$672$	3.63047	−	6.28815i	0.140048	−	0.242571i
$673$	10.3959	+	18.0063i	0.400733	+	0.694091i	0.993815	−	0.111052i	$-0.0354220\pi$
$673$	10.3959	+	18.0063i	0.400733	+	0.694091i	−0.593081	+	0.805143i	$0.702089\pi$
$674$	−2.66818	−	0.714937i	−0.102775	−	0.0275384i
$675$			2.18727i			0.0841881i
$676$	23.7929	−	1.95882i	0.915112	−	0.0753394i
$677$		−	1.33288i		−	0.0512269i	−0.999672	−	0.0256135i	$-0.991846\pi$
$677$		−	1.33288i		−	0.0512269i	0.999672	−	0.0256135i	$-0.00815391\pi$
$678$	−4.54426	−	1.21763i	−0.174521	−	0.0467629i
$679$	0.934356	−	0.539450i	0.0358573	−	0.0207022i
$680$	−13.0353	−	7.52591i	−0.499880	−	0.288606i
$681$	−10.4253	+	10.4253i	−0.399496	+	0.399496i
$682$	10.0322	+	4.29006i	0.384153	+	0.164275i
$683$	11.8554	+	44.2450i	0.453635	+	1.69299i	0.692071	+	0.721829i	$0.256698\pi$
$683$	11.8554	+	44.2450i	0.453635	+	1.69299i	−0.238437	+	0.971158i	$0.576635\pi$
$684$	−10.4871	−	10.4871i	−0.400986	−	0.400986i
$685$	−6.90885	+	11.9665i	−0.263974	+	0.457216i
$686$	−6.56766	+	3.79184i	−0.250755	+	0.144773i
$687$	−8.99585	−	2.41043i	−0.343213	−	0.0919637i
$688$	5.91898			0.225659
$689$	−5.58392	−	17.8694i	−0.212731	−	0.680772i
$690$		−	6.14201i		−	0.233822i
$691$	−3.81168	+	14.2254i	−0.145003	+	0.541159i	0.854752	+	0.519036i	$0.173709\pi$
$691$	−3.81168	+	14.2254i	−0.145003	+	0.541159i	−0.999755	+	0.0221227i	$0.992958\pi$
$692$	36.9149	−	21.3128i	1.40329	−	0.810192i
$693$	2.06726	+	5.15624i	0.0785288	+	0.195870i
$694$	1.80913	+	1.80913i	0.0686737	+	0.0686737i
$695$	−2.41408	−	9.00948i	−0.0915714	−	0.341749i
$696$	−0.272399	−	1.01661i	−0.0103253	−	0.0385344i
$697$	−22.2650	+	22.2650i	−0.843349	+	0.843349i
$698$	−0.0116222	+	0.0201302i	−0.000439905	+	0.000761938i
$699$	11.9892	+	20.7660i	0.453474	+	0.785440i
$700$	1.74130	−	6.49864i	0.0658151	−	0.245625i
$701$	−25.5168			−0.963756			−0.481878	−	0.876238i	$-0.660045\pi$
$701$	−25.5168			−0.963756			−0.481878	+	0.876238i	$0.660045\pi$
$702$	0.0598769	+	1.45705i	0.00225991	+	0.0549930i
$703$		−	25.0813i		−	0.945959i
$704$	−8.62633	−	11.5113i	−0.325117	−	0.433850i
$705$	0.294330	+	0.509795i	0.0110851	+	0.0192000i
$706$	7.44362	−	12.8927i	0.280144	−	0.485224i
$707$	10.1375	+	10.1375i	0.381258	+	0.381258i
$708$	−2.99300	+	0.801973i	−0.112484	+	0.0301400i
$709$	7.93191	+	29.6023i	0.297889	+	1.11174i	0.938896	+	0.344202i	$0.111851\pi$
$709$	7.93191	+	29.6023i	0.297889	+	1.11174i	−0.641006	+	0.767536i	$0.721483\pi$
$710$	−8.14314	−	8.14314i	−0.305606	−	0.305606i
$711$	0.114338	+	0.0660133i	0.00428802	+	0.00247569i
$712$	7.39700	+	12.8120i	0.277214	+	0.480150i
$713$	44.5040	+	11.9248i	1.66669	+	0.446588i
$714$	−2.45124			−0.0917354
$715$	5.12577	+	31.6466i	0.191693	+	1.18352i
$716$	−14.0490			−0.525036
$717$	24.7544	+	6.63293i	0.924472	+	0.247711i
$718$	4.15721	+	7.20050i	0.155146	+	0.268720i
$719$	−7.14293	−	4.12397i	−0.266386	−	0.153798i	0.360858	−	0.932621i	$-0.382484\pi$
$719$	−7.14293	−	4.12397i	−0.266386	−	0.153798i	−0.627244	+	0.778823i	$0.715817\pi$
$720$	−5.77286	−	5.77286i	−0.215142	−	0.215142i
$721$	3.02763	+	11.2993i	0.112755	+	0.420807i
$722$	−18.0582	+	4.83869i	−0.672058	+	0.180077i
$723$	4.86446	+	4.86446i	0.180911	+	0.180911i
$724$	6.68294	−	11.5752i	0.248370	−	0.430189i
$725$	−0.741799	−	1.28483i	−0.0275497	−	0.0477175i
$726$	−4.44785	−	0.101397i	−0.165075	−	0.00376318i
$727$		−	31.2638i		−	1.15951i	−0.814791	−	0.579755i	$-0.803148\pi$
$727$		−	31.2638i		−	1.15951i	0.814791	−	0.579755i	$-0.196852\pi$
$728$	2.05162	−	9.14336i	0.0760382	−	0.338876i
$729$	1.00000			0.0370370
$730$	−0.322997	+	1.20544i	−0.0119547	+	0.0446154i
$731$	−3.51645	−	6.09066i	−0.130060	−	0.225271i
$732$	−10.9014	+	18.8818i	−0.402927	+	0.697890i
$733$	−24.2186	+	24.2186i	−0.894535	+	0.894535i	−0.994946	−	0.100411i	$-0.967984\pi$
$733$	−24.2186	+	24.2186i	−0.894535	+	0.894535i	0.100411	+	0.994946i	$0.467984\pi$
$734$	−3.31169	−	12.3594i	−0.122237	−	0.456193i
$735$	2.91044	+	10.8619i	0.107353	+	0.400648i
$736$	17.3632	+	17.3632i	0.640018	+	0.640018i
$737$	13.2483	+	33.0443i	0.488006	+	1.21720i
$738$	3.04810	−	1.75982i	0.112202	−	0.0647799i
$739$	11.8588	−	44.2575i	0.436232	−	1.62804i	−0.301869	−	0.953349i	$-0.597610\pi$
$739$	11.8588	−	44.2575i	0.436232	−	1.62804i	0.738101	−	0.674690i	$-0.235723\pi$
$740$		−	15.2898i		−	0.562064i
$741$	−25.7941	−	13.5117i	−0.947571	−	0.496364i
$742$	−3.51760			−0.129135
$743$	24.3346	+	6.52043i	0.892749	+	0.239211i	0.675900	−	0.736994i	$-0.263755\pi$
$743$	24.3346	+	6.52043i	0.892749	+	0.239211i	0.216850	+	0.976205i	$0.430422\pi$
$744$	−10.9301	+	6.31050i	−0.400717	+	0.231354i
$745$	25.0625	−	43.4095i	0.918217	−	1.59040i
$746$	−4.45390	−	4.45390i	−0.163069	−	0.163069i
$747$	−0.901558	−	3.36466i	−0.0329863	−	0.123106i
$748$	−8.66518	+	20.2633i	−0.316830	+	0.740900i
$749$	−18.4753	+	18.4753i	−0.675072	+	0.675072i
$750$	−2.64126	−	1.52493i	−0.0964452	−	0.0556826i
$751$	17.8207	−	10.2888i	0.650287	−	0.375443i	−0.138279	−	0.990393i	$-0.544157\pi$
$751$	17.8207	−	10.2888i	0.650287	−	0.375443i	0.788566	+	0.614950i	$0.210824\pi$
$752$	−0.645878	−	0.173062i	−0.0235527	−	0.00631094i
$753$		−	0.111883i		−	0.00407725i
$754$	−0.529323	−	0.835588i	−0.0192768	−	0.0304303i
$755$			58.5087i			2.12935i
$756$	−2.97111	−	0.796108i	−0.108058	−	0.0289542i
$757$	5.89879	+	10.2170i	0.214395	+	0.371343i	0.953085	−	0.302702i	$-0.0978887\pi$
$757$	5.89879	+	10.2170i	0.214395	+	0.371343i	−0.738690	+	0.674045i	$0.764555\pi$
$758$	0.907173	−	1.57127i	0.0329500	−	0.0570711i
$759$	−18.6529	+	2.23975i	−0.677057	+	0.0812979i
$760$	−32.4507	+	8.69513i	−1.17711	+	0.315405i
$761$	−11.4872	+	3.07798i	−0.416410	+	0.111577i	−0.460940	−	0.887431i	$-0.652488\pi$
$761$	−11.4872	+	3.07798i	−0.416410	+	0.111577i	0.0445297	+	0.999008i	$0.485821\pi$
$762$	−2.82985	+	2.82985i	−0.102515	+	0.102515i
$763$	−14.3960	+	24.9346i	−0.521171	+	0.902694i
$764$	−23.9061	+	13.8022i	−0.864892	+	0.499346i
$765$	−2.51067	+	9.36994i	−0.0907734	+	0.338771i
$766$	13.0817			0.472661
$767$	−5.13925	+	3.25559i	−0.185568	+	0.117552i
$768$	4.45828			0.160874
$769$	3.72302	+	0.997579i	0.134255	+	0.0359736i	0.325321	−	0.945604i	$-0.394528\pi$
$769$	3.72302	+	0.997579i	0.134255	+	0.0359736i	−0.191066	+	0.981577i	$0.561194\pi$
$770$	5.96269	+	0.854240i	0.214880	+	0.0307847i
$771$	−13.0432	−	7.53047i	−0.469738	−	0.271203i
$772$	3.94903	−	3.94903i	0.142129	−	0.142129i
$773$	2.87366	−	0.769994i	0.103358	−	0.0276947i	−0.206769	−	0.978390i	$-0.566295\pi$
$773$	2.87366	−	0.769994i	0.103358	−	0.0276947i	0.310127	+	0.950695i	$0.399628\pi$
$774$	0.203465	+	0.759342i	0.00731340	+	0.0272940i
$775$	−12.5801	+	12.5801i	−0.451892	+	0.451892i
$776$	−0.865573	−	0.499739i	−0.0310723	−	0.0179396i
$777$	−2.60090	−	4.50489i	−0.0933067	−	0.161612i
$778$	−3.18296	+	11.8790i	−0.114115	+	0.425882i
$779$			70.2795i			2.51803i
$780$	−15.7243	−	8.23685i	−0.563022	−	0.294926i
$781$	−21.7607	+	27.6996i	−0.778658	+	0.991171i
$782$	2.14554	−	8.00725i	0.0767242	−	0.286339i
$783$	−0.587414	+	0.339144i	−0.0209925	+	0.0121200i
$784$	−11.0620	−	6.38667i	−0.395073	−	0.228095i
$785$	−17.1328	−	17.1328i	−0.611495	−	0.611495i
$786$	−3.50768	+	0.939881i	−0.125115	+	0.0335244i
$787$	−2.38600	+	0.639326i	−0.0850517	+	0.0227895i	−0.301094	−	0.953594i	$-0.597352\pi$
$787$	−2.38600	+	0.639326i	−0.0850517	+	0.0227895i	0.216042	+	0.976384i	$0.430685\pi$
$788$	−18.2861	−	18.2861i	−0.651416	−	0.651416i
$789$	6.53551	+	3.77328i	0.232670	+	0.134332i
$790$	0.123978	−	0.0715787i	0.00441094	−	0.00254666i
$791$	5.04255	−	18.8190i	0.179292	−	0.669128i
$792$	3.17918	−	4.04684i	0.112967	−	0.143798i
$793$	−9.37212	+	41.7682i	−0.332814	+	1.48323i
$794$			6.04570i			0.214554i
$795$	−3.60287	+	13.4461i	−0.127781	+	0.476884i
$796$	−21.7789	−	37.7221i	−0.771931	−	1.33702i
$797$	10.9194	+	6.30431i	0.386784	+	0.223310i	0.680766	−	0.732501i	$-0.261647\pi$
$797$	10.9194	+	6.30431i	0.386784	+	0.223310i	−0.293981	+	0.955811i	$0.594980\pi$
$798$	−3.86867	+	3.86867i	−0.136949	+	0.136949i
$799$	0.205632	+	0.767428i	0.00727473	+	0.0271497i
$800$	−9.15871	+	2.45407i	−0.323809	+	0.0867645i
$801$	6.74178	−	6.74178i	0.238209	−	0.238209i
$802$	1.59082	+	0.918459i	0.0561737	+	0.0324319i
$803$	3.77863	+	0.541343i	0.133345	+	0.0191036i
$804$	−19.0407	−	5.10194i	−0.671514	−	0.179932i
$805$	25.4358			0.896493
$806$	−8.03589	+	8.72466i	−0.283052	+	0.307313i
$807$	0.141241			0.00497191
$808$	3.43741	−	12.8286i	0.120928	−	0.451309i
$809$	−25.5426	+	14.7470i	−0.898030	+	0.518478i	−0.876560	−	0.481292i	$-0.840168\pi$
$809$	−25.5426	+	14.7470i	−0.898030	+	0.518478i	−0.0214693	+	0.999770i	$0.506834\pi$
$810$	0.542154	−	0.939038i	0.0190494	−	0.0329944i
$811$	−4.38933	+	4.38933i	−0.154130	+	0.154130i	−0.779960	−	0.625830i	$-0.784761\pi$
$811$	−4.38933	+	4.38933i	−0.154130	+	0.154130i	0.625830	+	0.779960i	$0.284761\pi$
$812$	2.01527	−	0.539990i	0.0707221	−	0.0189499i
$813$	3.09767	−	0.830019i	0.108640	−	0.0291101i
$814$	4.13625	−	0.496663i	0.144976	−	0.0174080i
$815$	28.3520	−	49.1071i	0.993126	−	1.72015i
$816$	−5.50940	−	9.54257i	−0.192868	−	0.334057i
$817$	−15.1624	−	4.06275i	−0.530465	−	0.142138i
$818$			8.15584i			0.285162i
$819$	−6.03406	+	0.247967i	−0.210847	+	0.00866466i
$820$			42.8431i			1.49615i
$821$	22.5588	+	6.04462i	0.787309	+	0.210959i	0.630004	−	0.776591i	$-0.283053\pi$
$821$	22.5588	+	6.04462i	0.787309	+	0.210959i	0.157304	+	0.987550i	$0.449720\pi$
$822$	1.80532	−	1.04230i	0.0629679	−	0.0363545i
$823$	−35.5873	−	20.5464i	−1.24050	−	0.716201i	−0.271302	−	0.962494i	$-0.587454\pi$
$823$	−35.5873	−	20.5464i	−1.24050	−	0.716201i	−0.969195	+	0.246293i	$0.920787\pi$
$824$	7.66273	−	7.66273i	0.266944	−	0.266944i
$825$	2.85232	−	6.67008i	0.0993051	−	0.232222i
$826$	0.295845	+	1.10411i	0.0102938	+	0.0384168i
$827$	−24.0377	−	24.0377i	−0.835874	−	0.835874i	0.152439	−	0.988313i	$-0.451287\pi$
$827$	−24.0377	−	24.0377i	−0.835874	−	0.835874i	−0.988313	+	0.152439i	$0.951287\pi$
$828$	5.20115	−	9.00865i	0.180752	−	0.313072i
$829$	30.4153	−	17.5603i	1.05637	−	0.609893i	0.131941	−	0.991258i	$-0.457879\pi$
$829$	30.4153	−	17.5603i	1.05637	−	0.609893i	0.924425	+	0.381364i	$0.124546\pi$
$830$	−3.64833	−	0.977566i	−0.126635	−	0.0339318i
$831$	21.2276			0.736377
$832$	14.9262	−	4.66421i	0.517474	−	0.161702i
$833$			15.1772i			0.525859i
$834$	−0.364201	+	1.35922i	−0.0126112	+	0.0470658i
$835$	19.3122	−	11.1499i	0.668328	−	0.385859i
$836$	18.3047	+	45.6563i	0.633082	+	1.57906i
$837$	5.75152	+	5.75152i	0.198801	+	0.198801i
$838$	−0.418340	−	1.56127i	−0.0144513	−	0.0539331i
$839$	−0.0564528	−	0.210685i	−0.00194897	−	0.00727365i	0.964944	−	0.262454i	$-0.0845318\pi$
$839$	−0.0564528	−	0.210685i	−0.00194897	−	0.00727365i	−0.966893	+	0.255180i	$0.917865\pi$
$840$	−4.92683	+	4.92683i	−0.169992	+	0.169992i
$841$	−14.2700	+	24.7163i	−0.492068	+	0.852286i
$842$	6.91383	+	11.9751i	0.238266	+	0.412689i
$843$	−1.65584	+	6.17969i	−0.0570303	+	0.212840i
$844$	−7.74078			−0.266448
$845$	−34.2909	−	6.22773i	−1.17964	−	0.214240i
$846$		−	0.0888083i		−	0.00305329i
$847$	0.419911	−	18.4198i	0.0144283	−	0.632911i
$848$	−7.90613	−	13.6938i	−0.271498	−	0.470248i
$849$	2.19282	−	3.79808i	0.0752574	−	0.130350i
$850$	2.26344	+	2.26344i	0.0776354	+	0.0776354i
$851$	16.9922	−	4.55306i	0.582487	−	0.156077i
$852$	−5.04802	−	18.8395i	−0.172942	−	0.645430i
$853$	10.4753	+	10.4753i	0.358669	+	0.358669i	0.863322	−	0.504653i	$-0.168380\pi$
$853$	10.4753	+	10.4753i	0.358669	+	0.358669i	−0.504653	+	0.863322i	$0.668380\pi$
$854$	6.96542	+	4.02148i	0.238352	+	0.137612i
$855$	10.8256	+	18.7505i	0.370229	+	0.641255i
$856$	23.3798	+	6.26461i	0.799106	+	0.214120i
$857$	29.2067			0.997681			0.498841	−	0.866694i	$-0.333759\pi$
$857$	29.2067			0.997681			0.498841	+	0.866694i	$0.333759\pi$
$858$	1.71748	−	4.52137i	0.0586340	−	0.154357i
$859$	23.8171			0.812628			0.406314	−	0.913733i	$-0.366814\pi$
$859$	23.8171			0.812628			0.406314	+	0.913733i	$0.366814\pi$
$860$	−9.24315	−	2.47669i	−0.315189	−	0.0844546i
$861$	7.28790	+	12.6230i	0.248371	+	0.430191i
$862$	−3.05212	−	1.76214i	−0.103955	−	0.0600187i
$863$	9.15875	+	9.15875i	0.311767	+	0.311767i	0.845594	−	0.533827i	$-0.179246\pi$
$863$	9.15875	+	9.15875i	0.311767	+	0.311767i	−0.533827	+	0.845594i	$0.679246\pi$
$864$	1.12198	+	4.18728i	0.0381704	+	0.142454i
$865$	−60.1071	+	16.1057i	−2.04370	+	0.547609i
$866$	−9.27527	−	9.27527i	−0.315186	−	0.315186i
$867$	1.95376	−	3.38401i	0.0663532	−	0.114927i
$868$	−12.5096	−	21.6672i	−0.424603	−	0.735434i
$869$	−0.262590	−	0.350411i	−0.00890775	−	0.0118869i
$870$			0.735472i			0.0249348i
$871$	−38.6699	+	1.58912i	−1.31028	+	0.0538453i
$872$	26.6725			0.903246
$873$	−0.166714	+	0.622187i	−0.00564243	+	0.0210578i
$874$	−9.25124	−	16.0236i	−0.312928	−	0.542007i
$875$	6.31516	−	10.9382i	0.213491	−	0.369778i
$876$	−1.49453	+	1.49453i	−0.0504956	+	0.0504956i
$877$	0.293055	+	1.09369i	0.00989575	+	0.0369314i	0.970697	−	0.240306i	$-0.0772478\pi$
$877$	0.293055	+	1.09369i	0.00989575	+	0.0369314i	−0.960801	+	0.277237i	$0.910581\pi$
$878$	−1.14730	−	4.28177i	−0.0387194	−	0.144503i
$879$	−5.54927	−	5.54927i	−0.187172	−	0.187172i
$880$	10.0762	+	25.1324i	0.339668	+	0.847214i
$881$	6.00046	−	3.46437i	0.202161	−	0.116718i	−0.395502	−	0.918465i	$-0.629429\pi$
$881$	6.00046	−	3.46437i	0.202161	−	0.116718i	0.597663	+	0.801747i	$0.296096\pi$
$882$	0.439084	−	1.63868i	0.0147847	−	0.0551774i
$883$		−	52.7494i		−	1.77516i	−0.460655	−	0.887580i	$-0.652385\pi$
$883$		−	52.7494i		−	1.77516i	0.460655	−	0.887580i	$-0.347615\pi$
$884$	−17.6223	−	16.2311i	−0.592702	−	0.545911i
$885$	4.52350			0.152056
$886$	−0.266238	−	0.0713382i	−0.00894443	−	0.00239665i
$887$	−7.93782	+	4.58290i	−0.266526	+	0.153879i	−0.627308	−	0.778771i	$-0.715843\pi$
$887$	−7.93782	+	4.58290i	−0.266526	+	0.153879i	0.360782	+	0.932650i	$0.382510\pi$
$888$	−2.40943	+	4.17326i	−0.0808553	+	0.140046i
$889$	−11.7192	−	11.7192i	−0.393049	−	0.393049i
$890$	−2.67571	−	9.98587i	−0.0896899	−	0.334727i
$891$	−3.04950	−	1.30405i	−0.102162	−	0.0436875i
$892$	18.7657	−	18.7657i	0.628322	−	0.628322i
$893$	1.53573	+	0.886654i	0.0513912	+	0.0296707i
$894$	−6.54897	+	3.78105i	−0.219030	+	0.126457i
$895$	19.8107	+	5.30827i	0.662200	+	0.177436i
$896$		−	17.4601i		−	0.583301i
$897$	4.47152	−	19.9280i	0.149300	−	0.665376i
$898$		−	12.4965i		−	0.417014i
$899$	−5.32911	−	1.42793i	−0.177736	−	0.0476242i
$900$	2.00837	+	3.47860i	0.0669457	+	0.115953i
$901$	−9.39402	+	16.2709i	−0.312960	+	0.542063i
$902$	−11.5901	+	1.39168i	−0.385907	+	0.0463380i
$903$	−3.14464	+	0.842605i	−0.104647	+	0.0280401i
$904$	−17.4337	+	4.67134i	−0.579836	+	0.155367i
$905$	−13.7973	+	13.7973i	−0.458637	+	0.458637i
$906$	4.41346	−	7.64434i	0.146627	−	0.253966i
$907$	−21.4347	+	12.3753i	−0.711727	+	0.410916i	−0.811700	−	0.584074i	$-0.801458\pi$
$907$	−21.4347	+	12.3753i	−0.711727	+	0.410916i	0.0999731	+	0.994990i	$0.468124\pi$
$908$	−7.00759	+	26.1527i	−0.232555	+	0.867907i
$909$	−8.55932			−0.283895
$910$	−3.03854	+	5.80065i	−0.100727	+	0.192290i
$911$	−40.2246			−1.33270			−0.666350	−	0.745639i	$-0.732144\pi$
$911$	−40.2246			−1.33270			−0.666350	+	0.745639i	$0.732144\pi$
$912$	−23.7557	−	6.36533i	−0.786631	−	0.210777i
$913$	−1.63840	+	11.4362i	−0.0542231	+	0.378483i
$914$	2.45557	+	1.41773i	0.0812232	+	0.0468942i
$915$	22.5065	−	22.5065i	0.744042	−	0.744042i
$916$	−16.5201	+	4.42655i	−0.545840	+	0.146257i
$917$	−3.89230	−	14.5263i	−0.128535	−	0.479700i
$918$	1.03482	−	1.03482i	0.0341543	−	0.0341543i
$919$	−21.1606	−	12.2171i	−0.698024	−	0.403004i	0.108587	−	0.994087i	$-0.465367\pi$
$919$	−21.1606	−	12.2171i	−0.698024	−	0.403004i	−0.806611	+	0.591083i	$0.798701\pi$
$920$	−11.7817	−	20.4064i	−0.388430	−	0.672780i
$921$	4.77238	−	17.8108i	0.157255	−	0.586885i
$922$			7.21349i			0.237564i
$923$	−20.4923	−	32.3491i	−0.674513	−	1.06478i
$924$	8.02224	+	6.30223i	0.263912	+	0.207328i
$925$	−1.75812	+	6.56138i	−0.0578065	+	0.215737i
$926$	3.83576	−	2.21458i	0.126051	−	0.0727755i
$927$	−6.04829	−	3.49198i	−0.198652	−	0.114692i
$928$	−2.07915	−	2.07915i	−0.0682516	−	0.0682516i
$929$	5.95611	−	1.59594i	0.195414	−	0.0523610i	−0.159785	−	0.987152i	$-0.551080\pi$
$929$	5.95611	−	1.59594i	0.195414	−	0.0523610i	0.355198	+	0.934791i	$0.384413\pi$
$930$	8.51910	−	2.28269i	0.279352	−	0.0748522i
$931$	23.9534	+	23.9534i	0.785041	+	0.785041i
$932$	38.1349	+	22.0172i	1.24915	+	0.721198i
$933$	−4.58595	+	2.64770i	−0.150137	+	0.0866818i
$934$	2.20975	−	8.24691i	0.0723053	−	0.269847i
$935$	19.8752	−	25.2996i	0.649988	−	0.827384i
$936$	2.99387	+	4.72611i	0.0978577	+	0.154478i
$937$		−	28.2464i		−	0.922769i	−0.887200	−	0.461385i	$-0.847353\pi$
$937$		−	28.2464i		−	0.922769i	0.887200	−	0.461385i	$-0.152647\pi$
$938$	−1.88209	+	7.02404i	−0.0614523	+	0.229343i
$939$	6.79952	+	11.7771i	0.221894	+	0.384331i
$940$	0.936196	+	0.540513i	0.0305353	+	0.0176296i
$941$	−2.59800	+	2.59800i	−0.0846924	+	0.0846924i	−0.748184	−	0.663491i	$-0.769074\pi$
$941$	−2.59800	+	2.59800i	−0.0846924	+	0.0846924i	0.663491	+	0.748184i	$0.269074\pi$
$942$	0.946079	+	3.53082i	0.0308249	+	0.115040i
$943$	−47.6134	+	12.7580i	−1.55051	+	0.415457i
$944$	−3.63330	+	3.63330i	−0.118254	+	0.118254i
$945$	3.88881	+	2.24521i	0.126503	+	0.0730366i
$946$	0.369757	−	2.58094i	0.0120218	−	0.0839137i
$947$	−36.1416	−	9.68412i	−1.17444	−	0.314691i	−0.381724	−	0.924276i	$-0.624669\pi$
$947$	−36.1416	−	9.68412i	−1.17444	−	0.314691i	−0.792721	+	0.609585i	$0.791336\pi$
$948$	0.242456			0.00787460
$949$	−1.92556	+	3.67595i	−0.0625064	+	0.119326i
$950$	7.14455			0.231800
$951$	−2.61649	+	9.76487i	−0.0848454	+	0.316648i
$952$	−8.14409	+	4.70199i	−0.263951	+	0.152392i
$953$	−10.8988	+	18.8772i	−0.353046	+	0.611494i	−0.986782	−	0.162056i	$-0.948187\pi$
$953$	−10.8988	+	18.8772i	−0.353046	+	0.611494i	0.633735	+	0.773550i	$0.281521\pi$
$954$	1.48500	−	1.48500i	0.0480786	−	0.0480786i
$955$	38.9254	−	10.4300i	1.25960	−	0.337508i
$956$	45.4594	−	12.1808i	1.47026	−	0.393956i
$957$	2.23358	−	0.268198i	0.0722014	−	0.00866961i
$958$	−0.296596	+	0.513720i	−0.00958259	+	0.0165975i
$959$	4.31647	+	7.47634i	0.139386	+	0.241424i
$960$	−11.2314	−	3.00945i	−0.362493	−	0.0971297i
$961$			35.1599i			1.13419i
$962$	−0.991554	+	4.41900i	−0.0319690	+	0.142474i
$963$		−	15.5992i		−	0.502676i
$964$	12.2029	+	3.26977i	0.393030	+	0.105312i
$965$	−7.06069	+	4.07649i	−0.227292	+	0.131227i
$966$	−3.32326	−	1.91868i	−0.106924	−	0.0617326i
$967$	27.6248	−	27.6248i	0.888352	−	0.888352i	−0.106012	−	0.994365i	$-0.533808\pi$
$967$	27.6248	−	27.6248i	0.888352	−	0.888352i	0.994365	+	0.106012i	$0.0338083\pi$
$968$	−14.9722	+	8.19503i	−0.481225	+	0.263398i
$969$	7.56325	+	28.2264i	0.242967	+	0.906764i
$970$	0.493872	+	0.493872i	0.0158573	+	0.0158573i
$971$	−8.58197	+	14.8644i	−0.275409	+	0.477022i	−0.970238	−	0.242153i	$-0.922146\pi$
$971$	−8.58197	+	14.8644i	−0.275409	+	0.477022i	0.694829	+	0.719175i	$0.255480\pi$
$972$	1.59038	−	0.918208i	0.0510116	−	0.0294515i
$973$	−5.62888	−	1.50825i	−0.180454	−	0.0483524i
$974$	−7.22850			−0.231616
$975$	5.80074	+	5.34280i	0.185772	+	0.171107i
$976$			36.1547i			1.15728i
$977$	12.8667	−	48.0192i	0.411642	−	1.53627i	−0.379825	−	0.925058i	$-0.624016\pi$
$977$	12.8667	−	48.0192i	0.411642	−	1.53627i	0.791467	−	0.611211i	$-0.209317\pi$
$978$	−7.40854	+	4.27732i	−0.236899	+	0.136774i
$979$	−29.3507	+	11.7674i	−0.938052	+	0.376088i
$980$	14.6022	+	14.6022i	0.466451	+	0.466451i
$981$	−4.44902	−	16.6040i	−0.142046	−	0.530123i
$982$	2.77979	+	10.3743i	0.0887068	+	0.331058i
$983$	−3.72735	+	3.72735i	−0.118884	+	0.118884i	−0.764046	−	0.645162i	$-0.776790\pi$
$983$	−3.72735	+	3.72735i	−0.118884	+	0.118884i	0.645162	+	0.764046i	$0.276790\pi$
$984$	6.75140	−	11.6938i	0.215227	−	0.372784i
$985$	18.8763	+	32.6948i	0.601450	+	1.04174i
$986$	−0.256916	+	0.958824i	−0.00818188	+	0.0305352i
$987$	0.367780			0.0117066
$988$	−53.4291	+	2.19564i	−1.69981	+	0.0698526i
$989$		−	11.0098i		−	0.350093i
$990$	−2.87786	+	2.15660i	−0.0914642	+	0.0685412i
$991$	−22.8006	−	39.4918i	−0.724284	−	1.25450i	−0.959268	−	0.282498i	$-0.908837\pi$
$991$	−22.8006	−	39.4918i	−0.724284	−	1.25450i	0.234984	−	0.971999i	$-0.424496\pi$
$992$	−17.6301	+	30.5363i	−0.559757	+	0.969527i
$993$	20.0552	+	20.0552i	0.636432	+	0.636432i
$994$	−6.94981	+	1.86220i	−0.220435	+	0.0590653i
$995$	16.4578	+	61.4214i	0.521748	+	1.94719i
$996$	−4.52328	−	4.52328i	−0.143326	−	0.143326i
$997$	−40.1547	−	23.1833i	−1.27171	−	0.734223i	−0.296401	−	0.955063i	$-0.595787\pi$
$997$	−40.1547	−	23.1833i	−1.27171	−	0.734223i	−0.975310	+	0.220841i	$0.929120\pi$
$998$	7.82866	+	13.5596i	0.247812	+	0.429223i
$999$	2.99980	+	0.803794i	0.0949095	+	0.0254309i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bd.a.76.8	yes	56
11.10	odd	2	inner	429.2.bd.a.76.7	✓	56
13.6	odd	12	inner	429.2.bd.a.175.7	yes	56
143.32	even	12	inner	429.2.bd.a.175.8	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bd.a.76.7	✓	56	11.10	odd	2	inner
429.2.bd.a.76.8	yes	56	1.1	even	1	trivial
429.2.bd.a.175.7	yes	56	13.6	odd	12	inner
429.2.bd.a.175.8	yes	56	143.32	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.390674 + 0.104681i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.59038 - 0.918208i) q^{4} +(1.89569 + 1.89569i) q^{5} +(-0.104681 - 0.390674i) q^{6} +(1.61789 - 0.433512i) q^{7} +(-1.09719 - 1.09719i) q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.390674 + 0.104681i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.59038 - 0.918208i) q^{4} +(1.89569 + 1.89569i) q^{5} +(-0.104681 - 0.390674i) q^{6} +(1.61789 - 0.433512i) q^{7} +(-1.09719 - 1.09719i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.542154 + 0.939038i) q^{10} +(2.65409 - 1.98892i) q^{11} +1.83642i q^{12} +(1.07540 + 3.44144i) q^{13} +0.677447 q^{14} +(0.693870 - 2.58956i) q^{15} +(1.52263 + 2.63727i) q^{16} +(1.80918 - 3.13359i) q^{17} +(-0.285993 + 0.285993i) q^{18} +(-2.09025 - 7.80091i) q^{19} +(-1.27423 - 4.75551i) q^{20} +(-1.18438 - 1.18438i) q^{21} +(1.24509 - 0.499185i) q^{22} +(4.90556 - 2.83223i) q^{23} +(-0.401599 + 1.49879i) q^{24} +2.18727i q^{25} +(0.0598769 + 1.45705i) q^{26} +1.00000 q^{27} +(-2.97111 - 0.796108i) q^{28} +(-0.587414 + 0.339144i) q^{29} +(0.542154 - 0.939038i) q^{30} +(5.75152 + 5.75152i) q^{31} +(1.12198 + 4.18728i) q^{32} +(-3.04950 - 1.30405i) q^{33} +(1.03482 - 1.03482i) q^{34} +(3.88881 + 2.24521i) q^{35} +(1.59038 - 0.918208i) q^{36} +(2.99980 + 0.803794i) q^{37} -3.26642i q^{38} +(2.44268 - 2.65204i) q^{39} -4.15986i q^{40} +(-8.40565 - 2.25229i) q^{41} +(-0.338723 - 0.586686i) q^{42} +(0.971836 - 1.68327i) q^{43} +(-6.04726 + 0.726128i) q^{44} +(-2.58956 + 0.693870i) q^{45} +(2.21295 - 0.592959i) q^{46} +(-0.155263 + 0.155263i) q^{47} +(1.52263 - 2.63727i) q^{48} +(-3.63255 + 2.09725i) q^{49} +(-0.228965 + 0.854510i) q^{50} -3.61835 q^{51} +(1.44967 - 6.46065i) q^{52} -5.19243 q^{53} +(0.390674 + 0.104681i) q^{54} +(8.80170 + 1.26097i) q^{55} +(-2.25077 - 1.29948i) q^{56} +(-5.71066 + 5.71066i) q^{57} +(-0.264989 + 0.0710036i) q^{58} +(0.436706 + 1.62981i) q^{59} +(-3.48127 + 3.48127i) q^{60} +(10.2819 + 5.93624i) q^{61} +(1.64489 + 2.84904i) q^{62} +(-0.433512 + 1.61789i) q^{63} -4.33720i q^{64} +(-4.48528 + 8.56252i) q^{65} +(-1.05485 - 0.828684i) q^{66} +(-2.77821 + 10.3684i) q^{67} +(-5.75457 + 3.32240i) q^{68} +(-4.90556 - 2.83223i) q^{69} +(1.28423 + 1.28423i) q^{70} +(-10.2588 + 2.74885i) q^{71} +(1.49879 - 0.401599i) q^{72} +(0.813832 + 0.813832i) q^{73} +(1.08780 + 0.628043i) q^{74} +(1.89423 - 1.09364i) q^{75} +(-3.83856 + 14.3257i) q^{76} +(3.43181 - 4.36842i) q^{77} +(1.23191 - 0.780382i) q^{78} -0.132027i q^{79} +(-2.11301 + 7.88587i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.04810 - 1.75982i) q^{82} +(-2.46310 + 2.46310i) q^{83} +(0.796108 + 2.97111i) q^{84} +(9.36994 - 2.51067i) q^{85} +(0.555877 - 0.555877i) q^{86} +(0.587414 + 0.339144i) q^{87} +(-5.09426 - 0.729825i) q^{88} +(-9.20944 - 2.46766i) q^{89} -1.08431 q^{90} +(3.23178 + 5.10167i) q^{91} -10.4023 q^{92} +(2.10520 - 7.85672i) q^{93} +(-0.0769103 + 0.0444042i) q^{94} +(10.8256 - 18.7505i) q^{95} +(3.06530 - 3.06530i) q^{96} +(0.622187 - 0.166714i) q^{97} +(-1.63868 + 0.439084i) q^{98} +(0.395405 + 3.29297i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 28 q^{3} + 4 q^{5} - 28 q^{9}+O(q^{10}) \) 56 * q - 28 * q^3 + 4 * q^5 - 28 * q^9	\( 56 q - 28 q^{3} + 4 q^{5} - 28 q^{9} - 12 q^{11} + 24 q^{14} - 8 q^{15} + 68 q^{16} - 8 q^{20} - 10 q^{22} - 12 q^{23} - 48 q^{26} + 56 q^{27} + 4 q^{31} + 12 q^{33} + 32 q^{34} + 36 q^{37} - 12 q^{42} + 24 q^{44} + 4 q^{45} - 8 q^{47} + 68 q^{48} - 24 q^{49} - 56 q^{53} - 2 q^{55} + 72 q^{56} - 88 q^{58} + 56 q^{59} - 44 q^{60} + 20 q^{66} + 92 q^{67} + 12 q^{69} - 216 q^{70} + 72 q^{71} - 12 q^{75} - 12 q^{78} + 44 q^{80} - 28 q^{81} - 156 q^{82} - 120 q^{86} - 6 q^{88} - 56 q^{89} + 92 q^{91} + 32 q^{92} - 20 q^{93} - 44 q^{97}+O(q^{100}) \) 56 * q - 28 * q^3 + 4 * q^5 - 28 * q^9 - 12 * q^11 + 24 * q^14 - 8 * q^15 + 68 * q^16 - 8 * q^20 - 10 * q^22 - 12 * q^23 - 48 * q^26 + 56 * q^27 + 4 * q^31 + 12 * q^33 + 32 * q^34 + 36 * q^37 - 12 * q^42 + 24 * q^44 + 4 * q^45 - 8 * q^47 + 68 * q^48 - 24 * q^49 - 56 * q^53 - 2 * q^55 + 72 * q^56 - 88 * q^58 + 56 * q^59 - 44 * q^60 + 20 * q^66 + 92 * q^67 + 12 * q^69 - 216 * q^70 + 72 * q^71 - 12 * q^75 - 12 * q^78 + 44 * q^80 - 28 * q^81 - 156 * q^82 - 120 * q^86 - 6 * q^88 - 56 * q^89 + 92 * q^91 + 32 * q^92 - 20 * q^93 - 44 * q^97

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