LMFDB - Embedded newform 168.2.ba.c.5.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,2,Mod(5,168)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 3, 5]))

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

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

chi := DirichletCharacter("168.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	168.ba (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:	$1.34148675396$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.13
Character	$\chi$	$=$	168.5
Dual form			168.2.ba.c.101.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0857242 + 1.41161i) q^{2} +(1.69273 + 0.366975i) q^{3} +(-1.98530 + 0.242019i) q^{4} +(2.66818 + 1.54047i) q^{5} +(-0.372919 + 2.42094i) q^{6} +(-1.46307 - 2.20441i) q^{7} +(-0.511826 - 2.78173i) q^{8} +(2.73066 + 1.24238i) q^{9} +(-1.94583 + 3.89849i) q^{10} +(-0.621780 - 1.07696i) q^{11} +(-3.44939 - 0.318884i) q^{12} -5.98957 q^{13} +(2.98636 - 2.25426i) q^{14} +(3.95119 + 3.58676i) q^{15} +(3.88285 - 0.960961i) q^{16} +(0.595854 + 1.03205i) q^{17} +(-1.51967 + 3.96114i) q^{18} +(0.614126 - 1.06370i) q^{19} +(-5.66997 - 2.41256i) q^{20} +(-1.66761 - 4.26838i) q^{21} +(1.46694 - 0.970035i) q^{22} +(-2.56956 - 1.48354i) q^{23} +(0.154445 - 4.89654i) q^{24} +(2.24612 + 3.89040i) q^{25} +(-0.513451 - 8.45496i) q^{26} +(4.16634 + 3.10509i) q^{27} +(3.43814 + 4.02234i) q^{28} -3.19900 q^{29} +(-4.72441 + 5.88502i) q^{30} +(1.33987 - 0.773574i) q^{31} +(1.68936 + 5.39871i) q^{32} +(-0.657290 - 2.05117i) q^{33} +(-1.40578 + 0.929587i) q^{34} +(-0.507883 - 8.13559i) q^{35} +(-5.72186 - 1.80563i) q^{36} +(-0.334978 - 0.193399i) q^{37} +(1.55417 + 0.775723i) q^{38} +(-10.1387 - 2.19802i) q^{39} +(2.91955 - 8.21062i) q^{40} +9.44060 q^{41} +(5.88235 - 2.71992i) q^{42} -8.29057i q^{43} +(1.49507 + 1.98760i) q^{44} +(5.37204 + 7.52140i) q^{45} +(1.87391 - 3.75440i) q^{46} +(3.34244 - 5.78928i) q^{47} +(6.92527 - 0.201736i) q^{48} +(-2.71887 + 6.45041i) q^{49} +(-5.29919 + 3.50416i) q^{50} +(0.629882 + 1.96564i) q^{51} +(11.8911 - 1.44959i) q^{52} +(5.25317 + 9.09875i) q^{53} +(-4.02603 + 6.14744i) q^{54} -3.83135i q^{55} +(-5.38325 + 5.19813i) q^{56} +(1.42990 - 1.57518i) q^{57} +(-0.274232 - 4.51576i) q^{58} +(-3.22898 + 1.86425i) q^{59} +(-8.71237 - 6.16454i) q^{60} +(3.16493 - 5.48181i) q^{61} +(1.20685 + 1.82506i) q^{62} +(-1.25642 - 7.83718i) q^{63} +(-7.47607 + 2.84752i) q^{64} +(-15.9813 - 9.22678i) q^{65} +(2.83911 - 1.10367i) q^{66} +(-10.7324 + 6.19634i) q^{67} +(-1.43273 - 1.90472i) q^{68} +(-3.80515 - 3.45419i) q^{69} +(11.4408 - 1.41435i) q^{70} +6.21100i q^{71} +(2.05834 - 8.23184i) q^{72} +(-8.92963 + 5.15552i) q^{73} +(0.244290 - 0.489438i) q^{74} +(2.37440 + 7.40966i) q^{75} +(-0.961791 + 2.26039i) q^{76} +(-1.46435 + 2.94632i) q^{77} +(2.23362 - 14.5004i) q^{78} +(-6.41425 + 11.1098i) q^{79} +(11.8405 + 3.41742i) q^{80} +(5.91299 + 6.78502i) q^{81} +(0.809288 + 13.3265i) q^{82} -5.22882i q^{83} +(4.34374 + 8.07044i) q^{84} +3.67159i q^{85} +(11.7031 - 0.710702i) q^{86} +(-5.41505 - 1.17396i) q^{87} +(-2.67756 + 2.28084i) q^{88} +(-6.94090 + 12.0220i) q^{89} +(-10.1568 + 8.22800i) q^{90} +(8.76314 + 13.2035i) q^{91} +(5.46040 + 2.32339i) q^{92} +(2.55192 - 0.817752i) q^{93} +(8.45876 + 4.22196i) q^{94} +(3.27720 - 1.89209i) q^{95} +(0.878436 + 9.75850i) q^{96} -17.1489i q^{97} +(-9.33855 - 3.28504i) q^{98} +(-0.359884 - 3.71328i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9} - 30 q^{10} - 18 q^{12} + 4 q^{15} + 6 q^{16} - 36 q^{22} - 12 q^{24} - 8 q^{25} - 10 q^{28} + 22 q^{30} + 48 q^{31} - 42 q^{33} + 52 q^{36} - 8 q^{39} - 18 q^{40} + 12 q^{42}+ \cdots + 90 q^{96}+O(q^{100}) $ 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9 - 30 * q^10 - 18 * q^12 + 4 * q^15 + 6 * q^16 - 36 * q^22 - 12 * q^24 - 8 * q^25 - 10 * q^28 + 22 * q^30 + 48 * q^31 - 42 * q^33 + 52 * q^36 - 8 * q^39 - 18 * q^40 + 12 * q^42 - 8 * q^46 - 36 * q^49 - 48 * q^52 + 60 * q^54 + 4 * q^57 + 30 * q^58 - 32 * q^60 - 6 * q^63 - 60 * q^64 + 54 * q^66 + 42 * q^70 + 42 * q^72 - 36 * q^73 - 68 * q^78 - 56 * q^79 + 42 * q^81 + 48 * q^82 + 48 * q^84 - 132 * q^87 + 6 * q^88 + 48 * q^94 + 90 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.0857242	+	1.41161i	0.0606162	+	0.998161i
$2$	0.0857242	+	1.41161i	0.0606162	+	0.998161i
$3$	1.69273	+	0.366975i	0.977297	+	0.211873i
$3$	1.69273	+	0.366975i	0.977297	+	0.211873i
$4$	−1.98530	+	0.242019i	−0.992651	+	0.121009i
$5$	2.66818	+	1.54047i	1.19325	+	0.688921i	0.959041	−	0.283266i	$-0.0914180\pi$
$5$	2.66818	+	1.54047i	1.19325	+	0.688921i	0.234205	+	0.972187i	$0.424751\pi$
$6$	−0.372919	+	2.42094i	−0.152244	+	0.988343i
$7$	−1.46307	−	2.20441i	−0.552987	−	0.833190i
$7$	−1.46307	−	2.20441i	−0.552987	−	0.833190i
$8$	−0.511826	−	2.78173i	−0.180958	−	0.983491i
$9$	2.73066	+	1.24238i	0.910220	+	0.414126i
$10$	−1.94583	+	3.89849i	−0.615324	+	1.23281i
$11$	−0.621780	−	1.07696i	−0.187474	−	0.324714i	0.756933	−	0.653492i	$-0.226697\pi$
$11$	−0.621780	−	1.07696i	−0.187474	−	0.324714i	−0.944407	+	0.328778i	$0.893363\pi$
$12$	−3.44939	−	0.318884i	−0.995754	−	0.0920540i
$13$	−5.98957			−1.66121			−0.830604	−	0.556864i	$-0.812005\pi$
$13$	−5.98957			−1.66121			−0.830604	+	0.556864i	$0.812005\pi$
$14$	2.98636	−	2.25426i	0.798138	−	0.602475i
$15$	3.95119	+	3.58676i	1.02019	+	0.926098i
$16$	3.88285	−	0.960961i	0.970713	−	0.240240i
$17$	0.595854	+	1.03205i	0.144516	+	0.250309i	0.929192	−	0.369597i	$-0.120504\pi$
$17$	0.595854	+	1.03205i	0.144516	+	0.250309i	−0.784676	+	0.619906i	$0.787171\pi$
$18$	−1.51967	+	3.96114i	−0.358191	+	0.933649i
$19$	0.614126	−	1.06370i	0.140890	−	0.244029i	−0.786942	−	0.617027i	$-0.788337\pi$
$19$	0.614126	−	1.06370i	0.140890	−	0.244029i	0.927832	+	0.372998i	$0.121670\pi$
$20$	−5.66997	−	2.41256i	−1.26784	−	0.539464i
$21$	−1.66761	−	4.26838i	−0.363902	−	0.931437i
$22$	1.46694	−	0.970035i	0.312753	−	0.206812i
$23$	−2.56956	−	1.48354i	−0.535791	−	0.309339i	0.207581	−	0.978218i	$-0.433441\pi$
$23$	−2.56956	−	1.48354i	−0.535791	−	0.309339i	−0.743371	+	0.668879i	$0.766774\pi$
$24$	0.154445	−	4.89654i	0.0315259	−	0.999503i
$25$	2.24612	+	3.89040i	0.449225	+	0.778080i
$26$	−0.513451	−	8.45496i	−0.100696	−	1.65815i
$27$	4.16634	+	3.10509i	0.801813	+	0.597575i
$28$	3.43814	+	4.02234i	0.649747	+	0.760150i
$29$	−3.19900			−0.594040			−0.297020	−	0.954871i	$-0.595993\pi$
$29$	−3.19900			−0.594040			−0.297020	+	0.954871i	$0.595993\pi$
$30$	−4.72441	+	5.88502i	−0.862554	+	1.07445i
$31$	1.33987	−	0.773574i	0.240648	−	0.138938i	−0.374827	−	0.927095i	$-0.622298\pi$
$31$	1.33987	−	0.773574i	0.240648	−	0.138938i	0.615474	+	0.788157i	$0.288964\pi$
$32$	1.68936	+	5.39871i	0.298640	+	0.954366i
$33$	−0.657290	−	2.05117i	−0.114419	−	0.357063i
$34$	−1.40578	+	0.929587i	−0.241088	+	0.159423i
$35$	−0.507883	−	8.13559i	−0.0858478	−	1.37517i
$36$	−5.72186	−	1.80563i	−0.953644	−	0.300938i
$37$	−0.334978	−	0.193399i	−0.0550700	−	0.0317947i	0.472212	−	0.881485i	$-0.343456\pi$
$37$	−0.334978	−	0.193399i	−0.0550700	−	0.0317947i	−0.527282	+	0.849690i	$0.676789\pi$
$38$	1.55417	+	0.775723i	0.252120	+	0.125839i
$39$	−10.1387	−	2.19802i	−1.62349	−	0.351965i
$40$	2.91955	−	8.21062i	0.461621	−	1.29821i
$41$	9.44060			1.47437			0.737187	−	0.675689i	$-0.236154\pi$
$41$	9.44060			1.47437			0.737187	+	0.675689i	$0.236154\pi$
$42$	5.88235	−	2.71992i	0.907666	−	0.419693i
$43$		−	8.29057i		−	1.26430i	−0.774846	−	0.632150i	$-0.782173\pi$
$43$		−	8.29057i		−	1.26430i	0.774846	−	0.632150i	$-0.217827\pi$
$44$	1.49507	+	1.98760i	0.225390	+	0.299642i
$45$	5.37204	+	7.52140i	0.800816	+	1.12122i
$46$	1.87391	−	3.75440i	0.276292	−	0.553556i
$47$	3.34244	−	5.78928i	0.487546	−	0.844454i	−0.512352	−	0.858776i	$-0.671226\pi$
$47$	3.34244	−	5.78928i	0.487546	−	0.844454i	0.999897	+	0.0143219i	$0.00455895\pi$
$48$	6.92527	−	0.201736i	0.999576	−	0.0291181i
$49$	−2.71887	+	6.45041i	−0.388410	+	0.921486i
$50$	−5.29919	+	3.50416i	−0.749419	+	0.495563i
$51$	0.629882	+	1.96564i	0.0882012	+	0.275245i
$52$	11.8911	−	1.44959i	1.64900	−	0.201022i
$53$	5.25317	+	9.09875i	0.721578	+	1.24981i	0.960367	+	0.278738i	$0.0899162\pi$
$53$	5.25317	+	9.09875i	0.721578	+	1.24981i	−0.238789	+	0.971071i	$0.576750\pi$
$54$	−4.02603	+	6.14744i	−0.547874	+	0.836561i
$55$		−	3.83135i		−	0.516619i
$56$	−5.38325	+	5.19813i	−0.719367	+	0.694630i
$57$	1.42990	−	1.57518i	0.189395	−	0.208638i
$58$	−0.274232	−	4.51576i	−0.0360084	−	0.592948i
$59$	−3.22898	+	1.86425i	−0.420377	+	0.242705i	−0.695238	−	0.718779i	$-0.744701\pi$
$59$	−3.22898	+	1.86425i	−0.420377	+	0.242705i	0.274862	+	0.961484i	$0.411368\pi$
$60$	−8.71237	−	6.16454i	−1.12476	−	0.795839i
$61$	3.16493	−	5.48181i	0.405227	−	0.701874i	−0.589121	−	0.808045i	$-0.700526\pi$
$61$	3.16493	−	5.48181i	0.405227	−	0.701874i	0.994348	+	0.106171i	$0.0338590\pi$
$62$	1.20685	+	1.82506i	0.153270	+	0.231783i
$63$	−1.25642	−	7.83718i	−0.158294	−	0.987392i
$64$	−7.47607	+	2.84752i	−0.934509	+	0.355940i
$65$	−15.9813	−	9.22678i	−1.98223	−	1.14444i
$66$	2.83911	−	1.10367i	0.349471	−	0.135853i
$67$	−10.7324	+	6.19634i	−1.31117	+	0.757003i	−0.982290	−	0.187369i	$-0.940004\pi$
$67$	−10.7324	+	6.19634i	−1.31117	+	0.757003i	−0.328878	+	0.944372i	$0.606671\pi$
$68$	−1.43273	−	1.90472i	−0.173744	−	0.230982i
$69$	−3.80515	−	3.45419i	−0.458086	−	0.415836i
$70$	11.4408	−	1.41435i	1.36743	−	0.169047i
$71$			6.21100i			0.737110i	0.929606	+	0.368555i	$0.120147\pi$
$71$			6.21100i			0.737110i	−0.929606	+	0.368555i	$0.879853\pi$
$72$	2.05834	−	8.23184i	0.242578	−	0.970132i
$73$	−8.92963	+	5.15552i	−1.04513	+	0.603408i	−0.921283	−	0.388893i	$-0.872858\pi$
$73$	−8.92963	+	5.15552i	−1.04513	+	0.603408i	−0.123851	+	0.992301i	$0.539524\pi$
$74$	0.244290	−	0.489438i	0.0283981	−	0.0568960i
$75$	2.37440	+	7.40966i	0.274172	+	0.855594i
$76$	−0.961791	+	2.26039i	−0.110325	+	0.259285i
$77$	−1.46435	+	2.94632i	−0.166878	+	0.335764i
$78$	2.23362	−	14.5004i	0.252908	−	1.64184i
$79$	−6.41425	+	11.1098i	−0.721660	+	1.24995i	0.238674	+	0.971100i	$0.423287\pi$
$79$	−6.41425	+	11.1098i	−0.721660	+	1.24995i	−0.960334	+	0.278852i	$0.910046\pi$
$80$	11.8405	+	3.41742i	1.32381	+	0.382079i
$81$	5.91299	+	6.78502i	0.656999	+	0.753891i
$82$	0.809288	+	13.3265i	0.0893709	+	1.47166i
$83$		−	5.22882i		−	0.573938i	−0.957940	−	0.286969i	$-0.907352\pi$
$83$		−	5.22882i		−	0.573938i	0.957940	−	0.286969i	$-0.0926476\pi$
$84$	4.34374	+	8.07044i	0.473941	+	0.880557i
$85$			3.67159i			0.398240i
$86$	11.7031	−	0.710702i	1.26197	−	0.0766370i
$87$	−5.41505	−	1.17396i	−0.580554	−	0.125861i
$88$	−2.67756	+	2.28084i	−0.285429	+	0.243138i
$89$	−6.94090	+	12.0220i	−0.735734	+	1.27433i	0.218666	+	0.975800i	$0.429829\pi$
$89$	−6.94090	+	12.0220i	−0.735734	+	1.27433i	−0.954400	+	0.298529i	$0.903504\pi$
$90$	−10.1568	+	8.22800i	−1.07062	+	0.867308i
$91$	8.76314	+	13.2035i	0.918627	+	1.38410i
$92$	5.46040	+	2.32339i	0.569286	+	0.242230i
$93$	2.55192	−	0.817752i	0.264621	−	0.0847969i
$94$	8.45876	+	4.22196i	0.872454	+	0.435462i
$95$	3.27720	−	1.89209i	0.336233	−	0.194124i
$96$	0.878436	+	9.75850i	0.0896550	+	0.995973i
$97$		−	17.1489i		−	1.74120i	−0.491989	−	0.870601i	$-0.663730\pi$
$97$		−	17.1489i		−	1.74120i	0.491989	−	0.870601i	$-0.336270\pi$
$98$	−9.33855	−	3.28504i	−0.943336	−	0.331839i
$99$	−0.359884	−	3.71328i	−0.0361697	−	0.373199i
$100$	−5.40078	−	7.18002i	−0.540078	−	0.718002i
$101$	2.87413	−	1.65938i	0.285986	−	0.165114i	−0.350144	−	0.936696i	$-0.613867\pi$
$101$	2.87413	−	1.65938i	0.285986	−	0.165114i	0.636130	+	0.771582i	$0.280534\pi$
$102$	−2.72073	+	1.05765i	−0.269392	+	0.104723i
$103$	10.7667	+	6.21615i	1.06087	+	0.612496i	0.925674	−	0.378322i	$-0.123499\pi$
$103$	10.7667	+	6.21615i	1.06087	+	0.612496i	0.135200	+	0.990818i	$0.456832\pi$
$104$	3.06561	+	16.6614i	0.300608	+	1.63378i
$105$	2.12585	−	13.9577i	0.207462	−	1.36213i
$106$	−12.3936	+	8.19542i	−1.20377	+	0.796010i
$107$	−4.79031	+	8.29706i	−0.463097	+	0.802107i	−0.999113	−	0.0421002i	$-0.986595\pi$
$107$	−4.79031	+	8.29706i	−0.463097	+	0.802107i	0.536017	+	0.844207i	$0.319928\pi$
$108$	−9.02294	−	5.15622i	−0.868233	−	0.496157i
$109$	−0.510424	+	0.294693i	−0.0488898	+	0.0282265i	−0.524246	−	0.851567i	$-0.675653\pi$
$109$	−0.510424	+	0.294693i	−0.0488898	+	0.0282265i	0.475356	+	0.879794i	$0.342319\pi$
$110$	5.40838	−	0.328439i	0.515669	−	0.0313155i
$111$	−0.496053	−	0.450301i	−0.0470833	−	0.0427407i
$112$	−7.79923	−	7.15346i	−0.736958	−	0.675939i
$113$			7.02041i			0.660425i	0.943907	+	0.330212i	$0.107120\pi$
$113$			7.02041i			0.660425i	−0.943907	+	0.330212i	$0.892880\pi$
$114$	2.34612	+	1.88343i	0.219735	+	0.176400i
$115$	−4.57070	−	7.91669i	−0.426220	−	0.738235i
$116$	6.35099	−	0.774219i	0.589675	−	0.0718845i
$117$	−16.3555	−	7.44131i	−1.51206	−	0.687950i
$118$	−2.90840	−	4.39825i	−0.267740	−	0.404892i
$119$	1.40329	−	2.82346i	0.128639	−	0.258827i
$120$	7.95509	−	12.8269i	0.726197	−	1.17093i
$121$	4.72678	−	8.18702i	0.429707	−	0.744275i
$122$	8.00951	+	3.99773i	0.725147	+	0.361937i
$123$	15.9804	+	3.46446i	1.44090	+	0.312380i
$124$	−2.47283	+	1.86005i	−0.222066	+	0.167038i
$125$		−	1.56436i		−	0.139921i
$126$	10.9554	−	2.44542i	0.975981	−	0.217855i
$127$	−5.88744			−0.522426			−0.261213	−	0.965281i	$-0.584123\pi$
$127$	−5.88744			−0.522426			−0.261213	+	0.965281i	$0.584123\pi$
$128$	−4.66048	−	10.3092i	−0.411932	−	0.911214i
$129$	3.04243	−	14.0337i	0.267871	−	1.23560i
$130$	11.6547	−	23.3503i	1.02218	−	2.04796i
$131$	−3.67922	−	2.12420i	−0.321455	−	0.185592i	0.330586	−	0.943776i	$-0.392754\pi$
$131$	−3.67922	−	2.12420i	−0.321455	−	0.185592i	−0.652041	+	0.758184i	$0.726087\pi$
$132$	1.80134	+	3.91312i	0.156787	+	0.340593i
$133$	−3.24333	+	0.202473i	−0.281233	+	0.0175566i
$134$	−9.66685	−	14.6188i	−0.835089	−	1.26287i
$135$	6.33323	+	14.7031i	0.545078	+	1.26544i
$136$	2.56591	−	2.18574i	0.220025	−	0.187425i
$137$	−0.674838	+	0.389618i	−0.0576553	+	0.0332873i	−0.528551	−	0.848902i	$-0.677264\pi$
$137$	−0.674838	+	0.389618i	−0.0576553	+	0.0332873i	0.470895	+	0.882189i	$0.343931\pi$
$138$	4.54979	−	5.66750i	0.387304	−	0.482450i
$139$	5.54714			0.470502			0.235251	−	0.971935i	$-0.424409\pi$
$139$	5.54714			0.470502			0.235251	+	0.971935i	$0.424409\pi$
$140$	2.97727	+	16.0287i	0.251625	+	1.35467i
$141$	7.78237	−	8.57309i	0.655394	−	0.721984i
$142$	−8.76752	+	0.532433i	−0.735754	+	0.0446808i
$143$	3.72420	+	6.45050i	0.311433	+	0.539418i
$144$	11.7966	+	2.19992i	0.983052	+	0.183326i
$145$	−8.53552	−	4.92798i	−0.708836	−	0.409247i
$146$	−8.04309	−	12.1632i	−0.665651	−	1.00664i
$147$	−6.96945	+	9.92102i	−0.574831	+	0.818272i
$148$	0.711838	+	0.302886i	0.0585128	+	0.0248970i
$149$	2.07219	−	3.58914i	0.169761	−	0.294034i	−0.768575	−	0.639760i	$-0.779034\pi$
$149$	2.07219	−	3.58914i	0.169761	−	0.294034i	0.938336	+	0.345726i	$0.112367\pi$
$150$	−10.2560	+	3.98692i	−0.837401	+	0.325530i
$151$	2.16486	+	3.74965i	0.176174	+	0.305142i	0.940567	−	0.339608i	$-0.110295\pi$
$151$	2.16486	+	3.74965i	0.176174	+	0.305142i	−0.764393	+	0.644751i	$0.776961\pi$
$152$	−3.27325	−	1.16391i	−0.265495	−	0.0944052i
$153$	0.344878	+	3.55845i	0.0278817	+	0.287684i
$154$	−4.28459	−	1.81452i	−0.345262	−	0.146218i
$155$	4.76668			0.382869
$156$	20.6604	+	1.90998i	1.65415	+	0.152921i
$157$	−3.21017	−	5.56018i	−0.256200	−	0.443751i	0.709021	−	0.705187i	$-0.249137\pi$
$157$	−3.21017	−	5.56018i	−0.256200	−	0.443751i	−0.965221	+	0.261437i	$0.915804\pi$
$158$	−16.2326	−	8.10207i	−1.29140	−	0.644566i
$159$	5.55317	+	17.3295i	0.440395	+	1.37432i
$160$	−3.80906	+	17.0071i	−0.301132	+	1.34453i
$161$	0.489111	+	7.83489i	0.0385473	+	0.617476i
$162$	−9.07094	+	8.92850i	−0.712680	+	0.701489i
$163$	−9.18195	−	5.30120i	−0.719186	−	0.415222i	0.0952672	−	0.995452i	$-0.469629\pi$
$163$	−9.18195	−	5.30120i	−0.719186	−	0.415222i	−0.814453	+	0.580230i	$0.802963\pi$
$164$	−18.7424	+	2.28480i	−1.46354	+	0.178413i
$165$	1.40601	−	6.48543i	0.109458	−	0.504890i
$166$	7.38107	−	0.448237i	0.572882	−	0.0347899i
$167$	15.5718			1.20498			0.602492	−	0.798125i	$-0.294175\pi$
$167$	15.5718			1.20498			0.602492	+	0.798125i	$0.294175\pi$
$168$	−11.0200	+	6.82351i	−0.850209	+	0.526445i
$169$	22.8750			1.75961
$170$	−5.18287	+	0.314744i	−0.397508	+	0.0241398i
$171$	2.99848	−	2.14162i	0.229300	−	0.163774i
$172$	2.00647	+	16.4593i	0.152992	+	1.25501i
$173$	−1.61807	−	0.934192i	−0.123019	−	0.0710253i	0.437228	−	0.899351i	$-0.355960\pi$
$173$	−1.61807	−	0.934192i	−0.123019	−	0.0710253i	−0.560247	+	0.828326i	$0.689294\pi$
$174$	1.19297	−	7.74459i	0.0904388	−	0.587116i
$175$	5.28982	−	10.6433i	0.399873	−	0.804558i
$176$	−3.44920	−	3.58415i	−0.259993	−	0.270166i
$177$	−6.14991	+	1.97071i	−0.462256	+	0.148128i
$178$	−17.5654	−	8.76729i	−1.31658	−	0.657136i
$179$	−7.73124	−	13.3909i	−0.577860	−	1.00088i	−0.995724	−	0.0923734i	$-0.970555\pi$
$179$	−7.73124	−	13.3909i	−0.577860	−	1.00088i	0.417864	−	0.908509i	$-0.362779\pi$
$180$	−12.4854	−	13.6321i	−0.930610	−	1.01608i
$181$	16.6129			1.23483			0.617415	−	0.786638i	$-0.288180\pi$
$181$	16.6129			1.23483			0.617415	+	0.786638i	$0.288180\pi$
$182$	−17.8870	+	13.5020i	−1.32587	+	1.00084i
$183$	7.36905	−	8.11777i	0.544736	−	0.600083i
$184$	−2.81164	+	7.90714i	−0.207277	+	0.582922i
$185$	−0.595854	−	1.03205i	−0.0438081	−	0.0758778i
$186$	1.37311	+	3.53222i	0.100681	+	0.258995i
$187$	0.740981	−	1.28342i	0.0541859	−	0.0938527i
$188$	−5.23465	+	12.3024i	−0.381776	+	0.897246i
$189$	0.749273	−	13.7273i	0.0545016	−	0.998514i
$190$	2.95183	+	4.46393i	0.214149	+	0.323848i
$191$	0.391130	+	0.225819i	0.0283012	+	0.0163397i	0.514084	−	0.857740i	$-0.328132\pi$
$191$	0.391130	+	0.225819i	0.0283012	+	0.0163397i	−0.485783	+	0.874080i	$0.661465\pi$
$192$	−13.6999	+	2.07655i	−0.988707	+	0.149862i
$193$	0.859277	+	1.48831i	0.0618521	+	0.107131i	0.895293	−	0.445477i	$-0.146966\pi$
$193$	0.859277	+	1.48831i	0.0618521	+	0.107131i	−0.833441	+	0.552608i	$0.813633\pi$
$194$	24.2076	−	1.47007i	1.73800	−	0.105545i
$195$	−23.6659	−	21.4832i	−1.69475	−	1.53844i
$196$	3.83667	−	13.4640i	0.274048	−	0.961716i
$197$	16.4222			1.17003			0.585017	−	0.811021i	$-0.301088\pi$
$197$	16.4222			1.17003			0.585017	+	0.811021i	$0.301088\pi$
$198$	5.21087	−	0.826336i	0.370320	−	0.0587251i
$199$	0.839396	−	0.484625i	0.0595032	−	0.0343542i	−0.469953	−	0.882691i	$-0.655729\pi$
$199$	0.839396	−	0.484625i	0.0595032	−	0.0343542i	0.529456	+	0.848337i	$0.322396\pi$
$200$	9.67243	−	8.23932i	0.683944	−	0.582608i
$201$	−20.4409	+	6.55020i	−1.44179	+	0.462016i
$202$	2.58878	+	3.91491i	0.182146	+	0.275452i
$203$	4.68036	+	7.05193i	0.328497	+	0.494948i
$204$	−1.72623	−	3.74995i	−0.120860	−	0.262549i
$205$	25.1892	+	14.5430i	1.75929	+	1.01573i
$206$	−7.85184	+	15.7313i	−0.547063	+	1.09605i
$207$	−5.17348	−	7.24340i	−0.359582	−	0.503451i
$208$	−23.2566	+	5.75575i	−1.61256	+	0.399089i
$209$	−1.52741			−0.105653
$210$	19.8851	+	1.80436i	1.37220	+	0.124513i
$211$			9.99340i			0.687974i	0.938974	+	0.343987i	$0.111778\pi$
$211$			9.99340i			0.687974i	−0.938974	+	0.343987i	$0.888222\pi$
$212$	−12.6312	−	16.7924i	−0.867514	−	1.15331i
$213$	−2.27928	+	10.5135i	−0.156174	+	0.720375i
$214$	−12.1229	−	6.05081i	−0.828703	−	0.413625i
$215$	12.7714	−	22.1207i	0.871003	−	1.50862i
$216$	6.50510	−	13.1789i	0.442616	−	0.896711i
$217$	−3.66559	−	1.82184i	−0.248837	−	0.123674i
$218$	−0.459749	−	0.695259i	−0.0311381	−	0.0470889i
$219$	−17.0074	+	5.44995i	−1.14925	+	0.368273i
$220$	0.927258	+	7.60639i	0.0625158	+	0.512822i
$221$	−3.56891	−	6.18153i	−0.240071	−	0.415815i
$222$	0.593127	−	0.738837i	0.0398081	−	0.0495875i
$223$		−	13.7534i		−	0.920996i	−0.887661	−	0.460498i	$-0.847671\pi$
$223$		−	13.7534i		−	0.920996i	0.887661	−	0.460498i	$-0.152329\pi$
$224$	9.42934	−	11.6227i	0.630024	−	0.776576i
$225$	1.30005	+	13.4139i	0.0866699	+	0.894259i
$226$	−9.91010	+	0.601819i	−0.659210	+	0.0400324i
$227$	4.13075	−	2.38489i	0.274167	−	0.158291i	−0.356613	−	0.934252i	$-0.616068\pi$
$227$	4.13075	−	2.38489i	0.274167	−	0.158291i	0.630780	+	0.775962i	$0.282735\pi$
$228$	−2.45756	+	3.47327i	−0.162756	+	0.230023i
$229$	0.743202	−	1.28726i	0.0491122	−	0.0850648i	−0.840424	−	0.541929i	$-0.817694\pi$
$229$	0.743202	−	1.28726i	0.0491122	−	0.0850648i	0.889536	+	0.456864i	$0.151027\pi$
$230$	10.7835	−	7.13071i	0.711042	−	0.470185i
$231$	−3.55997	+	4.44994i	−0.234229	+	0.292784i
$232$	1.63733	+	8.89877i	0.107496	+	0.584233i
$233$	−2.00188	−	1.15579i	−0.131148	−	0.0757182i	0.432991	−	0.901398i	$-0.357458\pi$
$233$	−2.00188	−	1.15579i	−0.131148	−	0.0757182i	−0.564139	+	0.825680i	$0.690792\pi$
$234$	9.10219	−	23.7255i	0.595029	−	1.55098i
$235$	17.8365	−	10.2979i	1.16352	−	0.671761i
$236$	5.95931	−	4.48257i	0.387918	−	0.291791i
$237$	−14.9346	+	16.4520i	−0.970108	+	1.06867i
$238$	4.10594	+	1.73886i	0.266148	+	0.112714i
$239$			21.6031i			1.39739i	0.715420	+	0.698695i	$0.246235\pi$
$239$			21.6031i			1.39739i	−0.715420	+	0.698695i	$0.753765\pi$
$240$	18.7886	+	10.1299i	1.21280	+	0.653884i
$241$	3.38489	−	1.95427i	0.218040	−	0.125885i	−0.387002	−	0.922079i	$-0.626489\pi$
$241$	3.38489	−	1.95427i	0.218040	−	0.125885i	0.605042	+	0.796193i	$0.293156\pi$
$242$	11.9621	+	5.97056i	0.768953	+	0.383802i
$243$	7.51916	+	13.6551i	0.482354	+	0.875976i
$244$	−4.95663	+	11.6490i	−0.317316	+	0.745753i
$245$	−17.1911	+	13.0225i	−1.09830	+	0.831976i
$246$	−3.52058	+	22.8551i	−0.224464	+	1.45719i
$247$	−3.67835	+	6.37109i	−0.234048	+	0.405383i
$248$	−2.83766	−	3.33122i	−0.180191	−	0.211533i
$249$	1.91885	−	8.85097i	0.121602	−	0.560908i
$250$	2.20827	−	0.134104i	0.139664	−	0.00848147i
$251$			15.6528i			0.987995i	0.869463	+	0.493997i	$0.164465\pi$
$251$			15.6528i			0.987995i	−0.869463	+	0.493997i	$0.835535\pi$
$252$	4.39112	+	15.2551i	0.276615	+	0.960981i
$253$			3.68974i			0.231972i
$254$	−0.504696	−	8.31079i	−0.0316675	−	0.521465i
$255$	−1.34738	+	6.21501i	−0.0843764	+	0.389199i
$256$	14.1531	−	7.46255i	0.884569	−	0.466409i
$257$	6.53148	−	11.3128i	0.407422	−	0.705676i	−0.587178	−	0.809458i	$-0.699761\pi$
$257$	6.53148	−	11.3128i	0.407422	−	0.705676i	0.994600	+	0.103782i	$0.0330944\pi$
$258$	20.0709	+	3.09171i	1.24956	+	0.192481i
$259$	0.0637623	+	1.02139i	0.00396200	+	0.0634658i
$260$	33.9607	+	14.4502i	2.10615	+	0.896163i
$261$	−8.73539	−	3.97437i	−0.540707	−	0.246008i
$262$	2.68315	−	5.37573i	0.165766	−	0.332114i
$263$	−26.2857	+	15.1761i	−1.62085	+	0.935796i	−0.634151	+	0.773209i	$0.718650\pi$
$263$	−26.2857	+	15.1761i	−1.62085	+	0.935796i	−0.986694	+	0.162586i	$0.948016\pi$
$264$	−5.36939	+	2.87825i	−0.330463	+	0.177144i
$265$			32.3695i			1.98844i
$266$	−0.563845	−	4.56098i	−0.0345716	−	0.279651i
$267$	−16.1608	+	17.8028i	−0.989027	+	1.08952i
$268$	19.8074	−	14.8990i	1.20993	−	0.910104i
$269$	0.684713	−	0.395319i	0.0417477	−	0.0241030i	−0.478981	−	0.877825i	$-0.658994\pi$
$269$	0.684713	−	0.395319i	0.0417477	−	0.0241030i	0.520729	+	0.853722i	$0.325660\pi$
$270$	−20.2122	+	10.2005i	−1.23007	+	0.620782i
$271$	−4.95134	−	2.85866i	−0.300773	−	0.173651i	0.342017	−	0.939694i	$-0.388890\pi$
$271$	−4.95134	−	2.85866i	−0.300773	−	0.173651i	−0.642790	+	0.766043i	$0.722223\pi$
$272$	3.30537	+	3.43470i	0.200418	+	0.208259i
$273$	9.98826	+	25.5658i	0.604517	+	1.54731i
$274$	−0.607840	−	0.919211i	−0.0367209	−	0.0555315i
$275$	2.79319	−	4.83795i	0.168436	−	0.291739i
$276$	8.39035	+	5.93670i	0.505040	+	0.357347i
$277$	−15.4143	+	8.89945i	−0.926156	+	0.534716i	−0.885594	−	0.464461i	$-0.846248\pi$
$277$	−15.4143	+	8.89945i	−0.926156	+	0.534716i	−0.0405619	+	0.999177i	$0.512915\pi$
$278$	0.475524	+	7.83041i	0.0285200	+	0.469637i
$279$	4.61980	−	0.447742i	0.276580	−	0.0268056i
$280$	−22.3711	+	5.57679i	−1.33693	+	0.333277i
$281$		−	27.9140i		−	1.66521i	−0.553866	−	0.832606i	$-0.686848\pi$
$281$		−	27.9140i		−	1.66521i	0.553866	−	0.832606i	$-0.313152\pi$
$282$	12.7690	+	10.2508i	0.760384	+	0.610425i
$283$	1.81190	+	3.13830i	0.107706	+	0.186552i	0.914841	−	0.403815i	$-0.132316\pi$
$283$	1.81190	+	3.13830i	0.107706	+	0.186552i	−0.807134	+	0.590368i	$0.798983\pi$
$284$	−1.50318	−	12.3307i	−0.0891972	−	0.731693i
$285$	6.24175	−	2.00015i	0.369729	−	0.118478i
$286$	−8.78636	+	5.81009i	−0.519548	+	0.343558i
$287$	−13.8122	−	20.8110i	−0.815309	−	1.22843i
$288$	−2.09417	+	16.8409i	−0.123400	+	0.992357i
$289$	7.78992	−	13.4925i	0.458230	−	0.793678i
$290$	6.22471	−	12.4713i	0.365527	−	0.732340i
$291$	6.29320	−	29.0284i	0.368914	−	1.70167i
$292$	16.4803	−	12.3964i	0.964435	−	0.725445i
$293$		−	9.77037i		−	0.570791i	−0.958410	−	0.285396i	$-0.907875\pi$
$293$		−	9.77037i		−	0.570791i	0.958410	−	0.285396i	$-0.0921250\pi$
$294$	−14.6021	−	8.98770i	−0.851612	−	0.524173i
$295$	−11.4873			−0.668817
$296$	−0.366535	+	1.03081i	−0.0213044	+	0.0599143i
$297$	0.753496	−	6.41765i	0.0437223	−	0.372390i
$298$	5.24411	+	2.61746i	0.303783	+	0.151625i
$299$	15.3906	+	8.88575i	0.890059	+	0.513876i
$300$	−6.50717	−	14.1358i	−0.375692	−	0.816129i
$301$	−18.2758	+	12.1296i	−1.05340	+	0.699141i
$302$	−5.10747	+	3.37738i	−0.293902	+	0.194347i
$303$	5.47407	−	1.75414i	0.314477	−	0.100773i
$304$	1.36239	−	4.72033i	0.0781383	−	0.270730i
$305$	16.8892	−	9.75098i	0.967072	−	0.558339i
$306$	−4.99359	+	0.791880i	−0.285465	+	0.0452687i
$307$	9.56907			0.546136			0.273068	−	0.961995i	$-0.411962\pi$
$307$	9.56907			0.546136			0.273068	+	0.961995i	$0.411962\pi$
$308$	2.19411	−	6.20373i	0.125021	−	0.353491i
$309$	15.9439	+	14.4734i	0.907018	+	0.823361i
$310$	0.408620	+	6.72871i	0.0232081	+	0.382165i
$311$	−8.85168	−	15.3316i	−0.501933	−	0.869373i	−0.999998	−	0.00223345i	$-0.999289\pi$
$311$	−8.85168	−	15.3316i	−0.501933	−	0.869373i	0.498065	−	0.867140i	$-0.334044\pi$
$312$	−0.925059	+	29.3282i	−0.0523711	+	1.66038i
$313$	−9.93451	−	5.73569i	−0.561532	−	0.324200i	0.192228	−	0.981350i	$-0.438429\pi$
$313$	−9.93451	−	5.73569i	−0.561532	−	0.324200i	−0.753760	+	0.657150i	$0.771762\pi$
$314$	7.57363	−	5.00816i	0.427405	−	0.282627i
$315$	8.72062	−	22.8465i	0.491351	−	1.28725i
$316$	10.0455	−	23.6087i	0.565101	−	1.32809i
$317$	1.15640	−	2.00294i	0.0649499	−	0.112497i	−0.831722	−	0.555193i	$-0.812645\pi$
$317$	1.15640	−	2.00294i	0.0649499	−	0.112497i	0.896672	+	0.442696i	$0.145978\pi$
$318$	−23.9865	+	9.32448i	−1.34510	+	0.522891i
$319$	1.98908	+	3.44519i	0.111367	+	0.192893i
$320$	−24.3340	−	3.91899i	−1.36031	−	0.219078i
$321$	−11.1535	+	12.2867i	−0.622528	+	0.685779i
$322$	−11.0179	+	1.36207i	−0.614004	+	0.0759055i
$323$	1.46372			0.0814434
$324$	−13.3812	−	12.0393i	−0.743399	−	0.668848i
$325$	−13.4533	−	23.3018i	−0.746256	−	1.29255i
$326$	6.69613	−	13.4158i	0.370864	−	0.743032i
$327$	−0.972154	+	0.311523i	−0.0537603	+	0.0172273i
$328$	−4.83194	−	26.2612i	−0.266799	−	1.45003i
$329$	−17.6522	+	1.10198i	−0.973197	+	0.0607540i
$330$	9.27545	+	1.42878i	0.510597	+	0.0786519i
$331$	20.7165	+	11.9607i	1.13868	+	0.657418i	0.946104	−	0.323863i	$-0.104982\pi$
$331$	20.7165	+	11.9607i	1.13868	+	0.657418i	0.192578	+	0.981282i	$0.438315\pi$
$332$	1.26547	+	10.3808i	0.0694519	+	0.569720i
$333$	−0.674434	−	0.944277i	−0.0369588	−	0.0517461i
$334$	1.33488	+	21.9814i	0.0730415	+	1.20277i
$335$	−38.1812			−2.08606
$336$	−10.5768	−	14.9710i	−0.577014	−	0.816735i
$337$	−25.6463			−1.39704			−0.698522	−	0.715589i	$-0.746159\pi$
$337$	−25.6463			−1.39704			−0.698522	+	0.715589i	$0.746159\pi$
$338$	1.96094	+	32.2906i	0.106661	+	1.75638i
$339$	−2.57632	+	11.8836i	−0.139926	+	0.645431i
$340$	−0.888594	−	7.28922i	−0.0481908	−	0.395313i
$341$	−1.66621	−	0.961986i	−0.0902303	−	0.0520945i
$342$	3.28018	+	4.04911i	0.177372	+	0.218951i
$343$	18.1972	−	3.44385i	0.982559	−	0.185950i
$344$	−23.0621	+	4.24332i	−1.24343	+	0.228785i
$345$	−4.83173	−	15.0781i	−0.260132	−	0.811779i
$346$	1.18001	−	2.36417i	0.0634377	−	0.127099i
$347$	−0.473950	−	0.820906i	−0.0254430	−	0.0440686i	0.853024	−	0.521872i	$-0.174766\pi$
$347$	−0.473950	−	0.820906i	−0.0254430	−	0.0440686i	−0.878467	+	0.477804i	$0.841433\pi$
$348$	11.0346	+	1.02011i	0.591518	+	0.0546838i
$349$	14.1965			0.759919			0.379960	−	0.925003i	$-0.375938\pi$
$349$	14.1965			0.759919			0.379960	+	0.925003i	$0.375938\pi$
$350$	15.4777	+	6.55479i	0.827317	+	0.350368i
$351$	−24.9546	−	18.5982i	−1.33198	−	0.992697i
$352$	4.76376	−	5.17618i	0.253909	−	0.275891i
$353$	7.75978	+	13.4403i	0.413011	+	0.715356i	0.995217	−	0.0976847i	$-0.0311437\pi$
$353$	7.75978	+	13.4403i	0.413011	+	0.715356i	−0.582206	+	0.813041i	$0.697810\pi$
$354$	−3.30908	−	8.51236i	−0.175876	−	0.452427i
$355$	−9.56788	+	16.5721i	−0.507810	+	0.879553i
$356$	10.8702	−	25.5471i	0.576122	−	1.35400i
$357$	3.41153	−	4.26439i	0.180557	−	0.225695i
$358$	18.2400	−	12.0614i	0.964015	−	0.637467i
$359$	12.2735	+	7.08613i	0.647772	+	0.373991i	0.787602	−	0.616184i	$-0.211322\pi$
$359$	12.2735	+	7.08613i	0.647772	+	0.373991i	−0.139830	+	0.990176i	$0.544656\pi$
$360$	18.1730	−	18.7932i	0.957800	−	0.990489i
$361$	8.74570	+	15.1480i	0.460300	+	0.797263i
$362$	1.42413	+	23.4510i	0.0748507	+	1.23256i
$363$	11.0056	−	12.1238i	0.577643	−	0.636334i
$364$	−20.5930	−	24.0921i	−1.07937	−	1.26277i
$365$	−31.7678			−1.66280
$366$	12.0909	+	9.70636i	0.631999	+	0.507359i
$367$	−11.5602	+	6.67430i	−0.603439	+	0.348396i	−0.770393	−	0.637569i	$-0.779940\pi$
$367$	−11.5602	+	6.67430i	−0.603439	+	0.348396i	0.166954	+	0.985965i	$0.446607\pi$
$368$	−11.4029	−	3.29111i	−0.594415	−	0.171561i
$369$	25.7790	+	11.7288i	1.34200	+	0.610576i
$370$	1.40578	−	0.929587i	0.0730828	−	0.0483269i
$371$	12.3717	−	24.8922i	0.642305	−	1.29234i
$372$	−4.86842	+	2.24110i	−0.252416	+	0.116195i
$373$	−4.56967	−	2.63830i	−0.236609	−	0.136606i	0.377008	−	0.926210i	$-0.376953\pi$
$373$	−4.56967	−	2.63830i	−0.236609	−	0.136606i	−0.613617	+	0.789604i	$0.710286\pi$
$374$	1.87521	+	0.935958i	0.0969646	+	0.0483972i
$375$	0.574082	−	2.64804i	0.0296455	−	0.136744i
$376$	−17.8150	−	6.33468i	−0.918738	−	0.326686i
$377$	19.1607			0.986824
$378$	19.4419	−	0.119079i	0.999981	−	0.00612475i
$379$		−	15.3619i		−	0.789086i	−0.918877	−	0.394543i	$-0.870903\pi$
$379$		−	15.3619i		−	0.789086i	0.918877	−	0.394543i	$-0.129097\pi$
$380$	−6.04830	+	4.54951i	−0.310271	+	0.233385i
$381$	−9.96584	−	2.16054i	−0.510565	−	0.110688i
$382$	−0.285240	+	0.571482i	−0.0145941	+	0.0292396i
$383$	1.35424	−	2.34561i	0.0691983	−	0.119855i	−0.829350	−	0.558729i	$-0.811289\pi$
$383$	1.35424	−	2.34561i	0.0691983	−	0.119855i	0.898549	+	0.438874i	$0.144623\pi$
$384$	−4.10570	−	19.1610i	−0.209518	−	0.977805i
$385$	−8.44587	+	5.60552i	−0.430442	+	0.285684i
$386$	−2.02726	+	1.34055i	−0.103185	+	0.0682323i
$387$	10.3000	−	22.6387i	0.523579	−	1.15079i
$388$	4.15035	+	34.0457i	0.210702	+	1.72841i
$389$	6.35306	+	11.0038i	0.322113	+	0.557916i	0.980924	−	0.194393i	$-0.0622736\pi$
$389$	6.35306	+	11.0038i	0.322113	+	0.557916i	−0.658811	+	0.752308i	$0.728940\pi$
$390$	28.2972	−	35.2487i	1.43288	−	1.78489i
$391$		−	3.53589i		−	0.178817i
$392$	19.3349	+	4.26170i	0.976559	+	0.215248i
$393$	−5.44840	−	4.94588i	−0.274835	−	0.249487i
$394$	1.40778	+	23.1818i	0.0709229	+	1.16788i
$395$	−34.2288	+	19.7620i	−1.72224	+	0.994334i
$396$	1.61316	+	7.28489i	0.0810645	+	0.366080i
$397$	11.9617	−	20.7184i	0.600343	−	1.03982i	−0.392426	−	0.919784i	$-0.628364\pi$
$397$	11.9617	−	20.7184i	0.600343	−	1.03982i	0.992769	−	0.120041i	$-0.0383026\pi$
$398$	0.756060	+	1.14336i	0.0378979	+	0.0573113i
$399$	−5.56439	−	0.847492i	−0.278568	−	0.0424277i
$400$	12.4599	+	12.9474i	0.622995	+	0.647371i
$401$	23.5968	+	13.6236i	1.17837	+	0.680331i	0.955636	−	0.294549i	$-0.0951694\pi$
$401$	23.5968	+	13.6236i	1.17837	+	0.680331i	0.222731	+	0.974880i	$0.428503\pi$
$402$	−10.9986	−	28.2931i	−0.548562	−	1.41113i
$403$	−8.02524	+	4.63338i	−0.399766	+	0.230805i
$404$	−5.30441	+	3.98996i	−0.263904	+	0.198508i
$405$	5.32478	+	27.2125i	0.264590	+	1.35220i
$406$	−9.55337	+	7.21137i	−0.474126	+	0.357894i
$407$			0.481008i			0.0238427i
$408$	5.14550	−	2.75823i	0.254740	−	0.136553i
$409$	6.82328	−	3.93942i	0.337390	−	0.194792i	−0.321727	−	0.946832i	$-0.604263\pi$
$409$	6.82328	−	3.93942i	0.337390	−	0.194792i	0.659117	+	0.752040i	$0.270930\pi$
$410$	−18.3698	+	36.8041i	−0.907218	+	1.81763i
$411$	−1.28530	+	0.411869i	−0.0633991	+	0.0203160i
$412$	−22.8796	−	9.73520i	−1.12720	−	0.479619i
$413$	8.83378	+	4.39047i	0.434682	+	0.216041i
$414$	9.78138	−	7.92389i	0.480729	−	0.389438i
$415$	8.05487	−	13.9514i	0.395398	−	0.684849i
$416$	−10.1185	−	32.3359i	−0.496102	−	1.58540i
$417$	9.38980	+	2.03566i	0.459820	+	0.0996868i
$418$	−0.130936	−	2.15611i	−0.00640427	−	0.105459i
$419$			19.8589i			0.970173i	0.874466	+	0.485086i	$0.161212\pi$
$419$			19.8589i			0.970173i	−0.874466	+	0.485086i	$0.838788\pi$
$420$	−0.842425	+	28.2248i	−0.0411062	+	1.37723i
$421$		−	16.6507i		−	0.811505i	−0.913983	−	0.405753i	$-0.867009\pi$
$421$		−	16.6507i		−	0.811505i	0.913983	−	0.405753i	$-0.132991\pi$
$422$	−14.1068	+	0.856676i	−0.686709	+	0.0417024i
$423$	16.3196	−	11.6560i	0.793484	−	0.566733i
$424$	22.6216	−	19.2699i	1.09860	−	0.935828i
$425$	−2.67672	+	4.63622i	−0.129840	+	0.224890i
$426$	−15.0364	−	2.31620i	−0.728517	−	0.112220i
$427$	−16.7147	+	1.04345i	−0.808880	+	0.0504962i
$428$	7.50217	−	17.6315i	0.362631	−	0.852252i
$429$	3.93688	+	12.2856i	0.190074	+	0.593156i
$430$	32.3207	+	16.1320i	1.55864	+	0.777954i
$431$	19.8541	−	11.4628i	0.956339	−	0.552142i	0.0612944	−	0.998120i	$-0.480477\pi$
$431$	19.8541	−	11.4628i	0.956339	−	0.552142i	0.895044	+	0.445977i	$0.147144\pi$
$432$	19.1612	+	8.05293i	0.921892	+	0.387447i
$433$		−	10.5825i		−	0.508564i	−0.967130	−	0.254282i	$-0.918161\pi$
$433$		−	10.5825i		−	0.508564i	0.967130	−	0.254282i	$-0.0818392\pi$
$434$	2.25750	−	5.33058i	0.108363	−	0.255876i
$435$	−12.6399	−	11.4741i	−0.606035	−	0.550139i
$436$	0.942025	−	0.708588i	0.0451148	−	0.0339352i
$437$	−3.15607	+	1.82216i	−0.150975	+	0.0871656i
$438$	−9.15116	−	23.5406i	−0.437259	−	1.12482i
$439$	−6.69332	−	3.86439i	−0.319455	−	0.184437i	0.331695	−	0.943387i	$-0.392380\pi$
$439$	−6.69332	−	3.86439i	−0.319455	−	0.184437i	−0.651150	+	0.758949i	$0.725713\pi$
$440$	−10.6578	+	1.96098i	−0.508090	+	0.0934861i
$441$	−15.4382	+	14.2360i	−0.735150	+	0.677904i
$442$	8.41999	−	5.56783i	0.400498	−	0.264834i
$443$	2.28548	−	3.95856i	0.108586	−	0.188077i	−0.806611	−	0.591082i	$-0.798701\pi$
$443$	2.28548	−	3.95856i	0.108586	−	0.188077i	0.915198	+	0.403005i	$0.132034\pi$
$444$	1.09380	+	0.773930i	0.0519093	+	0.0367291i
$445$	−37.0392	+	21.3846i	−1.75582	+	1.01373i
$446$	19.4145	−	1.17900i	0.919303	−	0.0558273i
$447$	4.82478	−	5.31500i	0.228204	−	0.251391i
$448$	17.2151	+	12.3142i	0.813337	+	0.581793i
$449$		−	4.33700i		−	0.204676i	−0.994750	−	0.102338i	$-0.967368\pi$
$449$		−	4.33700i		−	0.204676i	0.994750	−	0.102338i	$-0.0326323\pi$
$450$	−18.8238	+	2.98506i	−0.887361	+	0.140717i
$451$	−5.86998	−	10.1671i	−0.276406	−	0.478750i
$452$	−1.69907	−	13.9376i	−0.0799176	−	0.655572i
$453$	2.28849	+	7.14159i	0.107523	+	0.335541i
$454$	3.72065	+	5.62658i	0.174619	+	0.264068i
$455$	3.04200	+	48.7287i	0.142611	+	2.28444i
$456$	−5.11359	−	3.17138i	−0.239466	−	0.148513i
$457$	−9.88462	+	17.1207i	−0.462383	+	0.800871i	−0.999079	−	0.0429048i	$-0.986339\pi$
$457$	−9.88462	+	17.1207i	−0.462383	+	0.800871i	0.536696	+	0.843776i	$0.319672\pi$
$458$	1.88083	+	0.938764i	0.0878853	+	0.0438656i
$459$	−0.722078	+	6.15005i	−0.0337037	+	0.287060i
$460$	10.9902	+	14.6108i	0.512421	+	0.681233i
$461$		−	25.3326i		−	1.17986i	−0.807455	−	0.589929i	$-0.799156\pi$
$461$		−	25.3326i		−	1.17986i	0.807455	−	0.589929i	$-0.200844\pi$
$462$	−6.58676	−	4.64383i	−0.306444	−	0.216051i
$463$	20.9574			0.973975			0.486988	−	0.873409i	$-0.338096\pi$
$463$	20.9574			0.973975			0.486988	+	0.873409i	$0.338096\pi$
$464$	−12.4213	+	3.07412i	−0.576643	+	0.142712i
$465$	8.06870	+	1.74925i	0.374177	+	0.0811197i
$466$	1.45992	−	2.92497i	0.0676293	−	0.135496i
$467$	−26.9170	−	15.5406i	−1.24557	−	0.719131i	−0.275348	−	0.961345i	$-0.588793\pi$
$467$	−26.9170	−	15.5406i	−1.24557	−	0.719131i	−0.970223	+	0.242214i	$0.922127\pi$
$468$	34.2715	+	10.8149i	1.58420	+	0.499920i
$469$	29.3615	+	14.5929i	1.35579	+	0.673839i
$470$	16.0657	+	24.2954i	0.741054	+	1.12066i
$471$	−3.39350	−	10.5899i	−0.156364	−	0.487958i
$472$	6.83852	+	8.02797i	0.314768	+	0.369517i
$473$	−8.92857	+	5.15491i	−0.410536	+	0.237023i
$474$	−24.5042	−	19.6716i	−1.12551	−	0.903545i
$475$	5.51761			0.253165
$476$	−2.10262	+	5.94505i	−0.0963735	+	0.272491i
$477$	3.04051	+	31.3720i	0.139216	+	1.43643i
$478$	−30.4952	+	1.85191i	−1.39482	+	0.0847044i
$479$	17.0894	+	29.5997i	0.780835	+	1.35245i	0.931456	+	0.363855i	$0.118540\pi$
$479$	17.0894	+	29.5997i	0.780835	+	1.35245i	−0.150620	+	0.988592i	$0.548127\pi$
$480$	−12.6889	+	27.3906i	−0.579166	+	1.25021i
$481$	2.00637	+	1.15838i	0.0914827	+	0.0528176i
$482$	3.04884	+	4.61063i	0.138871	+	0.210008i
$483$	−2.04728	+	13.4418i	−0.0931543	+	0.611624i
$484$	−7.40267	+	17.3977i	−0.336485	+	0.790804i
$485$	26.4174	−	45.7562i	1.19955	−	2.07768i
$486$	−18.6312	+	11.7847i	−0.845127	+	0.534565i
$487$	−12.3371	−	21.3684i	−0.559046	−	0.968296i	−0.997576	−	0.0695795i	$-0.977834\pi$
$487$	−12.3371	−	21.3684i	−0.559046	−	0.968296i	0.438531	−	0.898716i	$-0.355499\pi$
$488$	−16.8688	−	5.99825i	−0.763616	−	0.271528i
$489$	−13.5971	−	12.3430i	−0.614884	−	0.558171i
$490$	−19.8564	−	23.1509i	−0.897021	−	1.04585i
$491$	43.3064			1.95439			0.977196	−	0.212339i	$-0.0681079\pi$
$491$	43.3064			1.95439			0.977196	+	0.212339i	$0.0681079\pi$
$492$	−32.5643	−	3.01046i	−1.46811	−	0.135722i
$493$	−1.90614	−	3.30153i	−0.0858482	−	0.148693i
$494$	−9.30883	−	4.64625i	−0.418824	−	0.209045i
$495$	4.75998	−	10.4621i	0.213945	−	0.470237i
$496$	4.45914	−	4.29124i	0.200221	−	0.192682i
$497$	13.6916	−	9.08710i	0.614152	−	0.407612i
$498$	12.6586	+	1.94993i	0.567247	+	0.0873783i
$499$	−32.3258	−	18.6633i	−1.44710	−	0.835485i	−0.448795	−	0.893635i	$-0.648147\pi$
$499$	−32.3258	−	18.6633i	−1.44710	−	0.835485i	−0.998308	+	0.0581497i	$0.981480\pi$
$500$	0.378605	+	3.10573i	0.0169317	+	0.138893i
$501$	26.3589	+	5.71447i	1.17763	+	0.255304i
$502$	−22.0957	+	1.34182i	−0.986178	+	0.0598885i
$503$	−34.2432			−1.52683			−0.763414	−	0.645910i	$-0.776478\pi$
$503$	−34.2432			−1.52683			−0.763414	+	0.645910i	$0.776478\pi$
$504$	−21.1579	+	7.50629i	−0.942447	+	0.334357i
$505$	10.2249			0.455003
$506$	−5.20848	+	0.316300i	−0.231545	+	0.0140612i
$507$	38.7211	+	8.39454i	1.71966	+	0.372814i
$508$	11.6884	−	1.42487i	0.518587	−	0.0632185i
$509$	24.1054	+	13.9173i	1.06845	+	0.616871i	0.927758	−	0.373182i	$-0.121733\pi$
$509$	24.1054	+	13.9173i	1.06845	+	0.616871i	0.140694	+	0.990053i	$0.455067\pi$
$510$	−8.88869	−	1.36921i	−0.393598	−	0.0606295i
$511$	24.4295	+	12.1417i	1.08070	+	0.537118i
$512$	11.7475	+	19.3390i	0.519171	+	0.854671i
$513$	5.86153	−	2.52481i	0.258793	−	0.111473i
$514$	16.5293	+	8.25013i	0.729075	+	0.363898i
$515$	19.1517	+	33.1716i	0.843923	+	1.46172i
$516$	−2.64373	+	28.5974i	−0.116384	+	1.25893i
$517$	−8.31307			−0.365608
$518$	−1.43634	+	0.177565i	−0.0631089	+	0.00780177i
$519$	−2.39612	−	2.17512i	−0.105178	−	0.0954774i
$520$	−17.4868	+	49.1781i	−0.766848	+	2.15660i
$521$	8.13261	+	14.0861i	0.356296	+	0.617123i	0.987339	−	0.158625i	$-0.0507061\pi$
$521$	8.13261	+	14.0861i	0.356296	+	0.617123i	−0.631043	+	0.775748i	$0.717373\pi$
$522$	4.86144	−	12.6717i	0.212780	−	0.554625i
$523$	6.98922	−	12.1057i	0.305617	−	0.529345i	−0.671781	−	0.740750i	$-0.734470\pi$
$523$	6.98922	−	12.1057i	0.305617	−	0.529345i	0.977399	+	0.211405i	$0.0678038\pi$
$524$	7.81847	+	3.32674i	0.341551	+	0.145329i
$525$	12.8601	−	16.0750i	0.561259	−	0.701570i
$526$	−23.6760	−	35.8043i	−1.03232	−	1.56114i
$527$	1.59673	+	0.921874i	0.0695548	+	0.0401575i
$528$	−4.52326	−	7.33277i	−0.196849	−	0.319118i
$529$	−7.09824	−	12.2945i	−0.308619	−	0.534544i
$530$	−45.6932	+	2.77485i	−1.98478	+	0.120532i
$531$	−11.1333	+	1.07902i	−0.483145	+	0.0468255i
$532$	6.39000	−	1.18692i	0.277042	−	0.0514594i
$533$	−56.5451			−2.44924
$534$	−26.5161	−	21.2867i	−1.14746	−	0.921166i
$535$	−25.5628	+	14.7587i	−1.10518	+	0.638074i
$536$	22.7297	+	26.6831i	0.981771	+	1.15254i
$537$	−8.17276	−	25.5043i	−0.352681	−	1.10059i
$538$	0.616734	+	0.932661i	0.0265893	+	0.0402099i
$539$	8.63734	−	1.08263i	0.372037	−	0.0466322i
$540$	−16.1318	−	27.6573i	−0.694203	−	1.19018i
$541$	−18.9287	−	10.9285i	−0.813810	−	0.469853i	0.0344673	−	0.999406i	$-0.489027\pi$
$541$	−18.9287	−	10.9285i	−0.813810	−	0.469853i	−0.848277	+	0.529552i	$0.822360\pi$
$542$	3.61087	−	7.23443i	0.155100	−	0.310746i
$543$	28.1212	+	6.09653i	1.20680	+	0.261627i
$544$	−4.56512	+	4.96034i	−0.195728	+	0.212673i
$545$	−1.81587			−0.0777834
$546$	−35.2327	+	16.2912i	−1.50782	+	0.697198i
$547$		−	9.11111i		−	0.389563i	−0.980847	−	0.194782i	$-0.937600\pi$
$547$		−	9.11111i		−	0.389563i	0.980847	−	0.194782i	$-0.0623998\pi$
$548$	1.24546	−	0.936833i	0.0532035	−	0.0400195i
$549$	15.4528	−	11.0369i	0.659510	−	0.471044i
$550$	7.06876	+	3.52818i	0.301413	+	0.150442i
$551$	−1.96459	+	3.40277i	−0.0836944	+	0.144963i
$552$	−7.66106	+	12.3528i	−0.326076	+	0.525772i
$553$	33.8751	−	2.11473i	1.44052	−	0.0899275i
$554$	−13.8840	−	20.9961i	−0.589873	−	0.892040i
$555$	−0.629882	−	1.96564i	−0.0267370	−	0.0834369i
$556$	−11.0127	+	1.34251i	−0.467044	+	0.0569352i
$557$	−2.14436	−	3.71415i	−0.0908596	−	0.157373i	0.817013	−	0.576619i	$-0.195628\pi$
$557$	−2.14436	−	3.71415i	−0.0908596	−	0.157373i	−0.907873	+	0.419245i	$0.862295\pi$
$558$	1.02807	+	6.48298i	0.0435215	+	0.274447i
$559$			49.6569i			2.10026i
$560$	−9.79002	−	31.1012i	−0.413704	−	1.31427i
$561$	1.72526	−	1.90055i	0.0728406	−	0.0802414i
$562$	39.4038	−	2.39291i	1.66215	−	0.100939i
$563$	27.2512	−	15.7335i	1.14850	−	0.663087i	0.199979	−	0.979800i	$-0.435913\pi$
$563$	27.2512	−	15.7335i	1.14850	−	0.663087i	0.948521	+	0.316713i	$0.102579\pi$
$564$	−13.3755	+	18.9037i	−0.563211	+	0.795988i
$565$	−10.8148	+	18.7317i	−0.454981	+	0.788049i
$566$	−4.27474	+	2.82673i	−0.179681	+	0.118816i
$567$	6.30589	−	22.9616i	0.264822	−	0.964297i
$568$	17.2773	−	3.17895i	0.724941	−	0.133386i
$569$	−8.62592	−	4.98018i	−0.361617	−	0.208780i	0.308173	−	0.951330i	$-0.400283\pi$
$569$	−8.62592	−	4.98018i	−0.361617	−	0.208780i	−0.669790	+	0.742551i	$0.733616\pi$
$570$	3.35850	+	8.63948i	0.140672	+	0.361868i
$571$	−29.5465	+	17.0587i	−1.23648	+	0.713883i	−0.968373	−	0.249506i	$-0.919732\pi$
$571$	−29.5465	+	17.0587i	−1.23648	+	0.713883i	−0.268108	+	0.963389i	$0.586399\pi$
$572$	−8.95480	−	11.9049i	−0.374419	−	0.497768i
$573$	0.579206	+	0.525785i	0.0241967	+	0.0219650i
$574$	28.1930	−	21.2815i	1.17675	−	0.888273i
$575$		−	13.3288i		−	0.555851i
$576$	−23.9523	−	1.51249i	−0.998012	−	0.0630205i
$577$	0.843668	−	0.487092i	0.0351224	−	0.0202779i	−0.482336	−	0.875986i	$-0.660212\pi$
$577$	0.843668	−	0.487092i	0.0351224	−	0.0202779i	0.517458	+	0.855708i	$0.326878\pi$
$578$	19.7140	+	9.83971i	0.819995	+	0.409278i
$579$	0.908350	+	2.83464i	0.0377497	+	0.117804i
$580$	18.1383	+	7.71779i	0.753150	+	0.320464i
$581$	−11.5265	+	7.65011i	−0.478199	+	0.317380i
$582$	41.5163	+	6.39514i	1.72091	+	0.265087i
$583$	6.53263	−	11.3149i	0.270554	−	0.468613i
$584$	18.9117	+	22.2011i	0.782571	+	0.918688i
$585$	−32.1762	−	45.0499i	−1.33032	−	1.86259i
$586$	13.7920	−	0.837557i	0.569741	−	0.0345992i
$587$			25.9212i			1.06988i	0.844890	+	0.534940i	$0.179666\pi$
$587$			25.9212i			1.06988i	−0.844890	+	0.534940i	$0.820334\pi$
$588$	11.4354	−	21.3830i	0.471588	−	0.881819i
$589$		−	1.90029i		−	0.0782999i
$590$	−0.984741	−	16.2156i	−0.0405412	−	0.667588i
$591$	27.7983	+	6.02654i	1.14347	+	0.247899i
$592$	−1.48652	−	0.429041i	−0.0610956	−	0.0176335i
$593$	−22.1118	+	38.2987i	−0.908022	+	1.57274i	−0.0912135	+	0.995831i	$0.529075\pi$
$593$	−22.1118	+	38.2987i	−0.908022	+	1.57274i	−0.816808	+	0.576909i	$0.804259\pi$
$594$	9.12383	+	0.513497i	0.374355	+	0.0210691i
$595$	8.09370	−	5.37178i	0.331809	−	0.220222i
$596$	−3.24529	+	7.62704i	−0.132932	+	0.312416i
$597$	1.59871	−	0.512302i	0.0654310	−	0.0209671i
$598$	−11.2239	+	22.4872i	−0.458979	+	0.919572i
$599$	8.58632	−	4.95731i	0.350827	−	0.202550i	−0.314222	−	0.949349i	$-0.601744\pi$
$599$	8.58632	−	4.95731i	0.350827	−	0.202550i	0.665050	+	0.746799i	$0.268410\pi$
$600$	19.3964	−	10.3974i	0.791855	−	0.424472i
$601$			11.8235i			0.482292i	0.970489	+	0.241146i	$0.0775233\pi$
$601$			11.8235i			0.482292i	−0.970489	+	0.241146i	$0.922477\pi$
$602$	−18.6890	−	24.7586i	−0.761709	−	1.00908i
$603$	−37.0046	+	3.58642i	−1.50695	+	0.146050i
$604$	−5.20539	−	6.92025i	−0.211804	−	0.281581i
$605$	25.2238	−	14.5630i	1.02549	−	0.592069i
$606$	2.94543	+	7.57689i	0.119650	+	0.307790i
$607$	5.56281	+	3.21169i	0.225788	+	0.130359i	0.608627	−	0.793456i	$-0.291721\pi$
$607$	5.56281	+	3.21169i	0.225788	+	0.130359i	−0.382840	+	0.923815i	$0.625054\pi$
$608$	6.78007	+	1.51852i	0.274968	+	0.0615841i
$609$	5.33469	+	13.6546i	0.216173	+	0.553311i
$610$	15.2124	+	23.0051i	0.615933	+	0.931449i
$611$	−20.0198	+	34.6753i	−0.809915	+	1.40281i
$612$	−1.54590	−	6.98113i	−0.0624893	−	0.282196i
$613$	17.5740	−	10.1463i	0.709805	−	0.409806i	−0.101184	−	0.994868i	$-0.532263\pi$
$613$	17.5740	−	10.1463i	0.709805	−	0.409806i	0.810989	+	0.585061i	$0.198930\pi$
$614$	0.820301	+	13.5078i	0.0331047	+	0.545131i
$615$	37.3016	+	33.8612i	1.50414	+	1.36541i
$616$	8.94536	+	2.56542i	0.360419	+	0.103364i
$617$		−	26.7202i		−	1.07571i	−0.843036	−	0.537856i	$-0.819234\pi$
$617$		−	26.7202i		−	1.07571i	0.843036	−	0.537856i	$-0.180766\pi$
$618$	−19.0640	+	23.7474i	−0.766867	+	0.955259i
$619$	−7.12358	−	12.3384i	−0.286321	−	0.495922i	0.686608	−	0.727028i	$-0.259099\pi$
$619$	−7.12358	−	12.3384i	−0.286321	−	0.495922i	−0.972929	+	0.231106i	$0.925766\pi$
$620$	−9.46331	+	1.15363i	−0.380056	+	0.0463308i
$621$	−6.09915	−	14.1596i	−0.244750	−	0.568207i
$622$	20.8834	−	13.8094i	0.837350	−	0.553708i
$623$	36.6564	−	2.28836i	1.46861	−	0.0916813i
$624$	−41.4794	+	1.20831i	−1.66050	+	0.0483712i
$625$	13.6405	−	23.6260i	0.545619	−	0.945040i
$626$	7.24495	−	14.5154i	0.289566	−	0.580151i
$627$	−2.58548	−	0.560520i	−0.103254	−	0.0223850i
$628$	7.71883	+	10.2617i	0.308015	+	0.409487i
$629$		−	0.460951i		−	0.0183793i
$630$	32.9980	+	10.3516i	1.31467	+	0.412419i
$631$	−13.9775			−0.556436			−0.278218	−	0.960518i	$-0.589744\pi$
$631$	−13.9775			−0.556436			−0.278218	+	0.960518i	$0.589744\pi$
$632$	34.1875	+	12.1565i	1.35991	+	0.483558i
$633$	−3.66733	+	16.9161i	−0.145763	+	0.672355i
$634$	2.92651	+	1.46069i	0.116227	+	0.0580113i
$635$	−15.7088	−	9.06945i	−0.623383	−	0.359910i
$636$	−15.2188	−	33.0603i	−0.603464	−	1.31093i
$637$	16.2849	−	38.6352i	0.645231	−	1.53078i
$638$	−4.69276	+	3.10315i	−0.185788	+	0.122855i
$639$	−7.71641	+	16.9601i	−0.305256	+	0.670932i
$640$	3.44608	−	34.6862i	0.136218	−	1.37109i
$641$	−6.31225	+	3.64438i	−0.249319	+	0.143944i	−0.619452	−	0.785034i	$-0.712645\pi$
$641$	−6.31225	+	3.64438i	−0.249319	+	0.143944i	0.370133	+	0.928979i	$0.379312\pi$
$642$	−18.3003	−	14.6912i	−0.722254	−	0.579814i
$643$	25.1189			0.990594			0.495297	−	0.868724i	$-0.335059\pi$
$643$	25.1189			0.990594			0.495297	+	0.868724i	$0.335059\pi$
$644$	−2.86722	−	15.4362i	−0.112984	−	0.608273i
$645$	29.7363	−	32.7576i	1.17086	−	1.28983i
$646$	0.125476	+	2.06620i	0.00493679	+	0.0812936i
$647$	−20.2246	−	35.0301i	−0.795112	−	1.37717i	−0.922768	−	0.385355i	$-0.874079\pi$
$647$	−20.2246	−	35.0301i	−0.795112	−	1.37717i	0.127657	−	0.991818i	$-0.459254\pi$
$648$	15.8477	−	19.9211i	0.622556	−	0.782575i
$649$	4.01543	+	2.31831i	0.157619	+	0.0910016i
$650$	31.7399	−	20.9884i	1.24494	−	0.823233i
$651$	−5.53629	−	4.42905i	−0.216984	−	0.173588i
$652$	19.5119	+	8.30228i	0.764146	+	0.325142i
$653$	−22.0316	+	38.1599i	−0.862164	+	1.49331i	0.00767187	+	0.999971i	$0.497558\pi$
$653$	−22.0316	+	38.1599i	−0.862164	+	1.49331i	−0.869836	+	0.493341i	$0.835775\pi$
$654$	−0.523087	−	1.34560i	−0.0204543	−	0.0526172i
$655$	−6.54455	−	11.3355i	−0.255717	−	0.442915i
$656$	36.6565	−	9.07205i	1.43119	−	0.354204i
$657$	−30.7889	+	2.98400i	−1.20119	+	0.116417i
$658$	−3.06879	−	24.8236i	−0.119634	−	0.967724i
$659$	−5.89051			−0.229462			−0.114731	−	0.993397i	$-0.536601\pi$
$659$	−5.89051			−0.229462			−0.114731	+	0.993397i	$0.536601\pi$
$660$	−1.22176	+	13.2158i	−0.0475568	+	0.514425i
$661$	21.0993	+	36.5450i	0.820667	+	1.42144i	0.905186	+	0.425015i	$0.139731\pi$
$661$	21.0993	+	36.5450i	0.820667	+	1.42144i	−0.0845192	+	0.996422i	$0.526935\pi$
$662$	−15.1079	+	30.2690i	−0.587187	+	1.17644i
$663$	−3.77273	−	11.7734i	−0.146521	−	0.457239i
$664$	−14.5452	+	2.67624i	−0.564462	+	0.103858i
$665$	−8.96570	−	4.45604i	−0.347675	−	0.172798i
$666$	1.27514	−	1.03299i	0.0494106	−	0.0400275i
$667$	8.22004	+	4.74584i	0.318281	+	0.183760i
$668$	−30.9148	+	3.76868i	−1.19613	+	0.145814i
$669$	5.04716	−	23.2808i	0.195134	−	0.900087i
$670$	−3.27305	−	53.8971i	−0.126449	−	2.08223i
$671$	−7.87156			−0.303878
$672$	20.2266	−	16.2138i	0.780256	−	0.625460i
$673$	−46.7729			−1.80296			−0.901481	−	0.432818i	$-0.857519\pi$
$673$	−46.7729			−1.80296			−0.901481	+	0.432818i	$0.857519\pi$
$674$	−2.19851	−	36.2027i	−0.0846834	−	1.39447i
$675$	−2.72193	+	23.1832i	−0.104767	+	0.892320i
$676$	−45.4137	+	5.53617i	−1.74668	+	0.212930i
$677$	−35.7518	−	20.6413i	−1.37405	−	0.793310i	−0.382618	−	0.923907i	$-0.624977\pi$
$677$	−35.7518	−	20.6413i	−1.37405	−	0.793310i	−0.991436	+	0.130596i	$0.958311\pi$
$678$	−16.9960	−	2.61804i	−0.652726	−	0.100545i
$679$	−37.8032	+	25.0899i	−1.45075	+	0.962863i
$680$	10.2134	−	1.87921i	0.391665	−	0.0720646i
$681$	7.86743	−	2.52109i	0.301481	−	0.0966083i
$682$	1.21512	−	2.43451i	0.0465293	−	0.0932221i
$683$	−17.1346	−	29.6781i	−0.655638	−	1.13560i	−0.981733	−	0.190262i	$-0.939066\pi$
$683$	−17.1346	−	29.6781i	−0.655638	−	1.13560i	0.326095	−	0.945337i	$-0.394267\pi$
$684$	−5.43458	+	4.97745i	−0.207796	+	0.190317i
$685$	−2.40079			−0.0917293
$686$	6.42133	+	25.3923i	0.245168	+	0.969481i
$687$	1.73043	−	1.90625i	0.0660201	−	0.0727280i
$688$	−7.96691	−	32.1911i	−0.303736	−	1.22727i
$689$	−31.4642	−	54.4976i	−1.19869	−	2.07619i
$690$	20.8703	−	8.11309i	0.794519	−	0.308860i
$691$	−3.57575	+	6.19338i	−0.136028	+	0.235607i	−0.925990	−	0.377549i	$-0.876767\pi$
$691$	−3.57575	+	6.19338i	−0.136028	+	0.235607i	0.789962	+	0.613156i	$0.210100\pi$
$692$	3.43845	+	1.46305i	0.130710	+	0.0556169i
$693$	−7.65908	+	6.22611i	−0.290944	+	0.236511i
$694$	1.11817	−	0.739406i	0.0424453	−	0.0280675i
$695$	14.8008	+	8.54522i	0.561425	+	0.324139i
$696$	−0.494070	+	15.6641i	−0.0187277	+	0.593745i
$697$	5.62522	+	9.74316i	0.213070	+	0.369048i
$698$	1.21698	+	20.0399i	0.0460634	+	0.758522i
$699$	−2.96450	−	2.69108i	−0.112128	−	0.101786i
$700$	−7.92602	+	22.4104i	−0.299575	+	0.847034i
$701$	12.4116			0.468778			0.234389	−	0.972143i	$-0.424691\pi$
$701$	12.4116			0.468778			0.234389	+	0.972143i	$0.424691\pi$
$702$	24.1142	−	36.8205i	0.910132	−	1.38970i
$703$	−0.411437	+	0.237543i	−0.0155176	+	0.00895911i
$704$	7.71513	+	6.28086i	0.290775	+	0.236719i
$705$	33.9714	−	10.8860i	1.27944	−	0.409991i
$706$	−18.3073	+	12.1060i	−0.689006	+	0.455614i
$707$	−7.86299	−	3.90798i	−0.295718	−	0.146975i
$708$	11.7325	−	5.40086i	0.440934	−	0.202977i
$709$	−30.5908	−	17.6616i	−1.14886	−	0.663295i	−0.200251	−	0.979745i	$-0.564176\pi$
$709$	−30.5908	−	17.6616i	−1.14886	−	0.663295i	−0.948609	+	0.316450i	$0.897509\pi$
$710$	−24.2135	−	12.0855i	−0.908718	−	0.453561i
$711$	−31.3177	+	22.3682i	−1.17451	+	0.838872i
$712$	36.9945	+	13.1546i	1.38643	+	0.492988i
$713$	−4.59050			−0.171916
$714$	6.31211	+	4.45020i	0.236225	+	0.166544i
$715$			22.9481i			0.858211i
$716$	18.5897	+	24.7139i	0.694730	+	0.923601i
$717$	−7.92780	+	36.5682i	−0.296069	+	1.36566i
$718$	−8.95073	+	17.9329i	−0.334038	+	0.669251i
$719$	−12.1803	+	21.0969i	−0.454250	+	0.786783i	−0.998645	−	0.0520455i	$-0.983426\pi$
$719$	−12.1803	+	21.0969i	−0.454250	+	0.786783i	0.544395	+	0.838829i	$0.316759\pi$
$720$	28.0866	+	24.0422i	1.04673	+	0.895999i
$721$	−2.04942	−	32.8289i	−0.0763243	−	1.22261i
$722$	−20.6334	+	13.6441i	−0.767895	+	0.507781i
$723$	6.44687	−	2.06587i	0.239762	−	0.0768307i
$724$	−32.9817	+	4.02064i	−1.22576	+	0.149426i
$725$	−7.18536	−	12.4454i	−0.266858	−	0.462211i
$726$	18.0575	+	14.4963i	0.670178	+	0.538009i
$727$		−	5.15142i		−	0.191055i	−0.995427	−	0.0955277i	$-0.969546\pi$
$727$		−	5.15142i		−	0.191055i	0.995427	−	0.0955277i	$-0.0304539\pi$
$728$	32.2434	−	31.1346i	1.19502	−	1.15392i
$729$	7.71680	+	25.8738i	0.285807	+	0.958287i
$730$	−2.72327	−	44.8438i	−0.100793	−	1.65975i
$731$	8.55627	−	4.93997i	0.316465	−	0.182711i
$732$	−12.6651	+	17.8997i	−0.468117	+	0.661591i
$733$	3.74171	−	6.48083i	0.138203	−	0.239375i	−0.788613	−	0.614889i	$-0.789201\pi$
$733$	3.74171	−	6.48083i	0.138203	−	0.239375i	0.926817	+	0.375514i	$0.122534\pi$
$734$	−10.4125	−	15.7464i	−0.384333	−	0.581211i
$735$	−33.8788	+	15.7348i	−1.24964	+	0.580388i
$736$	3.66827	−	16.3785i	0.135214	−	0.603721i
$737$	13.3464	+	7.70552i	0.491619	+	0.283837i
$738$	−14.3466	+	37.3955i	−0.528107	+	1.37655i
$739$	2.26360	−	1.30689i	0.0832679	−	0.0480747i	−0.457788	−	0.889061i	$-0.651358\pi$
$739$	2.26360	−	1.30689i	0.0832679	−	0.0480747i	0.541056	+	0.840987i	$0.318025\pi$
$740$	1.43273	+	1.90472i	0.0526680	+	0.0700190i
$741$	−8.56448	+	9.43466i	−0.314624	+	0.346591i
$742$	36.1987	+	15.3302i	1.32890	+	0.562788i
$743$		−	23.6093i		−	0.866140i	−0.901360	−	0.433070i	$-0.857430\pi$
$743$		−	23.6093i		−	0.866140i	0.901360	−	0.433070i	$-0.142570\pi$
$744$	−3.58090	−	6.68020i	−0.131282	−	0.244908i
$745$	11.0580	−	6.38431i	0.405132	−	0.233903i
$746$	3.33253	−	6.67677i	0.122012	−	0.244454i
$747$	6.49617	−	14.2781i	0.237683	−	0.522409i
$748$	−1.16046	+	2.72730i	−0.0424306	+	0.0997200i
$749$	25.2987	−	1.57933i	0.924394	−	0.0577074i
$750$	3.78722	+	0.583380i	0.138290	+	0.0213020i
$751$	0.504993	−	0.874673i	0.0184275	−	0.0319173i	−0.856665	−	0.515874i	$-0.827467\pi$
$751$	0.504993	−	0.874673i	0.0184275	−	0.0319173i	0.875092	+	0.483956i	$0.160801\pi$
$752$	7.41494	−	25.6909i	0.270395	−	0.936851i
$753$	−5.74418	+	26.4959i	−0.209330	+	0.965564i
$754$	1.64253	+	27.0474i	0.0598175	+	0.985010i
$755$			13.3397i			0.485480i
$756$	1.83473	+	27.4342i	0.0667285	+	0.997771i
$757$			11.1837i			0.406478i	0.979129	+	0.203239i	$0.0651469\pi$
$757$			11.1837i			0.406478i	−0.979129	+	0.203239i	$0.934853\pi$
$758$	21.6850	−	1.31688i	0.787635	−	0.0478314i
$759$	−1.35404	+	6.24572i	−0.0491486	+	0.226705i
$760$	−6.94064	−	8.14786i	−0.251763	−	0.295554i
$761$	3.99009	−	6.91104i	0.144641	−	0.250525i	−0.784598	−	0.620005i	$-0.787131\pi$
$761$	3.99009	−	6.91104i	0.144641	−	0.250525i	0.929239	+	0.369480i	$0.120464\pi$
$762$	2.19554	−	14.2531i	0.0795360	−	0.516336i
$763$	1.39641	+	0.694029i	0.0505534	+	0.0251255i
$764$	−0.831163	−	0.353658i	−0.0300704	−	0.0127949i
$765$	−4.56150	+	10.0259i	−0.164922	+	0.362486i
$766$	3.42718	+	1.71058i	0.123829	+	0.0618059i
$767$	19.3402	−	11.1661i	0.698333	−	0.403183i
$768$	26.6959	−	7.43822i	0.963306	−	0.268404i
$769$		−	11.8900i		−	0.428766i	−0.976750	−	0.214383i	$-0.931226\pi$
$769$		−	11.8900i		−	0.428766i	0.976750	−	0.214383i	$-0.0687740\pi$
$770$	−8.63684	−	11.4418i	−0.311250	−	0.412333i
$771$	15.2075	−	16.7527i	0.547686	−	0.603333i
$772$	−2.06613	−	2.74679i	−0.0743615	−	0.0988591i
$773$	31.4449	−	18.1547i	1.13099	−	0.652979i	0.186809	−	0.982396i	$-0.440186\pi$
$773$	31.4449	−	18.1547i	1.13099	−	0.652979i	0.944185	+	0.329417i	$0.106852\pi$
$774$	32.8400	+	12.5990i	1.18041	+	0.452860i
$775$	6.01902	+	3.47508i	0.216210	+	0.124829i
$776$	−47.7035	+	8.77722i	−1.71246	+	0.315084i
$777$	−0.266891	+	1.75233i	−0.00957465	+	0.0628644i
$778$	−14.9885	+	9.91135i	−0.537364	+	0.355339i
$779$	5.79771	−	10.0419i	0.207725	−	0.359790i
$780$	52.1833	+	36.9230i	1.86846	+	1.32205i
$781$	6.68897	−	3.86188i	0.239350	−	0.138189i
$782$	4.99130	−	0.303111i	0.178489	−	0.0108392i
$783$	−13.3281	−	9.93321i	−0.476309	−	0.354984i
$784$	−4.35840	+	27.6587i	−0.155657	+	0.987811i
$785$		−	19.7807i		−	0.706005i
$786$	6.51461	−	8.11501i	0.232368	−	0.289453i
$787$	−6.73055	−	11.6577i	−0.239918	−	0.415551i	0.720772	−	0.693172i	$-0.243787\pi$
$787$	−6.73055	−	11.6577i	−0.239918	−	0.415551i	−0.960691	+	0.277621i	$0.910454\pi$
$788$	−32.6030	+	3.97448i	−1.16143	+	0.141585i
$789$	−50.0638	+	16.0427i	−1.78232	+	0.571137i
$790$	−30.8305	−	46.6237i	−1.09690	−	1.65880i
$791$	15.4759	−	10.2713i	0.550259	−	0.365206i
$792$	−10.1452	+	2.90166i	−0.360493	+	0.103106i
$793$	−18.9565	+	32.8337i	−0.673167	+	1.16596i
$794$	30.2717	+	15.1093i	1.07430	+	0.536209i
$795$	−11.8788	+	54.7927i	−0.421297	+	1.94330i
$796$	−1.54917	+	1.16528i	−0.0549087	+	0.0413022i
$797$		−	13.9811i		−	0.495236i	−0.968858	−	0.247618i	$-0.920352\pi$
$797$		−	13.9811i		−	0.495236i	0.968858	−	0.247618i	$-0.0796479\pi$
$798$	0.719328	−	7.92741i	0.0254639	−	0.280627i
$799$	7.96643			0.281832
$800$	−17.2086	+	18.6985i	−0.608417	+	0.661090i
$801$	−33.8891	+	24.2047i	−1.19741	+	0.855232i
$802$	−17.2085	+	34.4774i	−0.607652	+	1.21744i
$803$	11.1045	+	6.41121i	0.391871	+	0.226247i
$804$	38.9961	−	17.9512i	1.37529	−	0.633091i
$805$	−10.7644	+	21.6584i	−0.379396	+	0.763357i
$806$	−7.22849	−	10.9313i	−0.254613	−	0.385040i
$807$	1.30411	−	0.417895i	0.0459067	−	0.0147106i
$808$	−6.08700	−	7.14574i	−0.214140	−	0.251386i
$809$	2.99316	−	1.72810i	0.105234	−	0.0607569i	−0.446459	−	0.894804i	$-0.647315\pi$
$809$	2.99316	−	1.72810i	0.105234	−	0.0607569i	0.551693	+	0.834047i	$0.313982\pi$
$810$	−37.9570	+	9.84929i	−1.33367	+	0.346069i
$811$	−45.3167			−1.59129			−0.795643	−	0.605766i	$-0.792867\pi$
$811$	−45.3167			−1.59129			−0.795643	+	0.605766i	$0.792867\pi$
$812$	−10.9986	−	12.8675i	−0.385976	−	0.451560i
$813$	−7.33222	−	6.65595i	−0.257152	−	0.233434i
$814$	−0.678997	+	0.0412340i	−0.0237988	+	0.00144525i
$815$	−16.3327	−	28.2891i	−0.572111	−	0.990924i
$816$	4.33465	+	7.02701i	0.151743	+	0.245995i
$817$	−8.81865	−	5.09145i	−0.308525	−	0.178127i
$818$	6.14586	+	9.29413i	0.214885	+	0.324962i
$819$	7.52542	+	46.9413i	0.262959	+	1.64026i
$820$	−53.5279	−	22.7760i	−1.86927	−	0.795372i
$821$	−22.3394	+	38.6931i	−0.779652	+	1.35040i	0.152490	+	0.988305i	$0.451271\pi$
$821$	−22.3394	+	38.6931i	−0.779652	+	1.35040i	−0.932142	+	0.362092i	$0.882063\pi$
$822$	−0.691580	−	1.77904i	−0.0241216	−	0.0620510i
$823$	21.1932	+	36.7076i	0.738747	+	1.27955i	0.953060	+	0.302783i	$0.0979157\pi$
$823$	21.1932	+	36.7076i	0.738747	+	1.27955i	−0.214312	+	0.976765i	$0.568751\pi$
$824$	11.7810	−	33.1316i	0.410411	−	1.15420i
$825$	6.50352	−	7.16430i	0.226424	−	0.249429i
$826$	−5.44038	+	12.8463i	−0.189295	+	0.446978i
$827$	−9.18843			−0.319513			−0.159757	−	0.987156i	$-0.551071\pi$
$827$	−9.18843			−0.319513			−0.159757	+	0.987156i	$0.551071\pi$
$828$	12.0240	+	13.1283i	0.417862	+	0.456239i
$829$	13.0225	+	22.5556i	0.452290	+	0.783389i	0.998528	−	0.0542413i	$-0.0172740\pi$
$829$	13.0225	+	22.5556i	0.452290	+	0.783389i	−0.546238	+	0.837630i	$0.683941\pi$
$830$	20.3845	+	10.1744i	0.707557	+	0.353158i
$831$	−29.3581	+	9.40769i	−1.01842	+	0.326349i
$832$	44.7784	−	17.0554i	1.55241	−	0.591291i
$833$	−8.27719	+	1.03749i	−0.286788	+	0.0359468i
$834$	−2.06863	+	13.4293i	−0.0716309	+	0.465017i
$835$	41.5484	+	23.9880i	1.43784	+	0.830139i
$836$	3.03236	−	0.369661i	0.104876	−	0.0127850i
$837$	7.98437	+	0.937445i	0.275980	+	0.0324029i
$838$	−28.0331	+	1.70239i	−0.968389	+	0.0588082i
$839$	31.2096			1.07748			0.538738	−	0.842473i	$-0.318901\pi$
$839$	31.2096			1.07748			0.538738	+	0.842473i	$0.318901\pi$
$840$	−39.9147	+	1.23037i	−1.37719	+	0.0424518i
$841$	−18.7664			−0.647116
$842$	23.5043	−	1.42737i	0.810013	−	0.0491903i
$843$	10.2438	−	47.2509i	0.352814	−	1.62741i
$844$	−2.41859	−	19.8399i	−0.0832513	−	0.682918i
$845$	61.0345	+	35.2383i	2.09965	+	1.21223i
$846$	17.8527	+	22.0377i	0.613789	+	0.757672i
$847$	−24.9632	+	1.55838i	−0.857744	+	0.0535467i
$848$	29.1408	+	30.2810i	1.00070	+	1.03985i
$849$	1.91537	+	5.97721i	0.0657354	+	0.205137i
$850$	−6.77401	−	3.38106i	−0.232347	−	0.115969i
$851$	0.573831	+	0.993904i	0.0196707	+	0.0340706i
$852$	1.98059	−	21.4242i	0.0678539	−	0.733980i
$853$	4.78201			0.163733			0.0818665	−	0.996643i	$-0.473912\pi$
$853$	4.78201			0.163733			0.0818665	+	0.996643i	$0.473912\pi$
$854$	−2.90580	−	23.5052i	−0.0994345	−	0.804332i
$855$	11.2996	−	1.09513i	0.386438	−	0.0374528i
$856$	25.5320	+	9.07872i	0.872666	+	0.310304i
$857$	15.2965	+	26.4944i	0.522520	+	0.905031i	0.999657	+	0.0262016i	$0.00834119\pi$
$857$	15.2965	+	26.4944i	0.522520	+	0.905031i	−0.477137	+	0.878829i	$0.658325\pi$
$858$	−17.0051	+	6.61053i	−0.580544	+	0.225680i
$859$	12.2711	−	21.2542i	0.418684	−	0.725183i	−0.577123	−	0.816657i	$-0.695825\pi$
$859$	12.2711	−	21.2542i	0.418684	−	0.725183i	0.995807	+	0.0914746i	$0.0291580\pi$
$860$	−20.0015	+	47.0072i	−0.682045	+	1.60293i
$861$	−15.7432	−	40.2961i	−0.536528	−	1.37329i
$862$	17.8830	+	27.0437i	0.609097	+	0.921111i
$863$	−32.1415	−	18.5569i	−1.09411	−	0.631684i	−0.159441	−	0.987207i	$-0.550969\pi$
$863$	−32.1415	−	18.5569i	−1.09411	−	0.631684i	−0.934667	+	0.355523i	$0.884303\pi$
$864$	−9.72504	+	27.7385i	−0.330853	+	0.943682i
$865$	−2.87820	−	4.98519i	−0.0978617	−	0.169501i
$866$	14.9384	−	0.907180i	0.507629	−	0.0308272i
$867$	18.1376	−	19.9805i	0.615986	−	0.678573i
$868$	7.71823	+	2.72975i	0.261974	+	0.0926538i
$869$	15.9530			0.541170
$870$	15.1134	−	18.8262i	0.512392	−	0.638268i
$871$	64.2823	−	37.1134i	2.17812	−	1.25754i
$872$	1.08101	+	1.26903i	0.0366075	+	0.0429748i
$873$	21.3054	−	46.8277i	0.721078	−	1.58488i
$874$	−2.84273	−	4.29894i	−0.0961568	−	0.145414i
$875$	−3.44850	+	2.28877i	−0.116581	+	0.0773744i
$876$	32.4458	−	14.9359i	1.09624	−	0.504637i
$877$	28.4107	+	16.4029i	0.959360	+	0.553887i	0.895976	−	0.444103i	$-0.146477\pi$
$877$	28.4107	+	16.4029i	0.959360	+	0.553887i	0.0633837	+	0.997989i	$0.479811\pi$
$878$	4.88125	−	9.77965i	0.164734	−	0.330047i
$879$	3.58548	−	16.5386i	0.120935	−	0.557832i
$880$	−3.68178	−	14.8766i	−0.124113	−	0.501489i
$881$	−27.1405			−0.914385			−0.457193	−	0.889368i	$-0.651145\pi$
$881$	−27.1405			−0.914385			−0.457193	+	0.889368i	$0.651145\pi$
$882$	−21.4191	−	20.5723i	−0.721219	−	0.692707i
$883$			47.9537i			1.61377i	0.590709	+	0.806884i	$0.298848\pi$
$883$			47.9537i			1.61377i	−0.590709	+	0.806884i	$0.701152\pi$
$884$	8.58141	+	11.4085i	0.288624	+	0.383708i
$885$	−19.4449	−	4.21556i	−0.653633	−	0.141704i
$886$	5.78388	+	2.88686i	0.194313	+	0.0969861i
$887$	−14.5502	+	25.2017i	−0.488548	+	0.846190i	−0.999913	−	0.0131735i	$-0.995807\pi$
$887$	−14.5502	+	25.2017i	−0.488548	+	0.846190i	0.511365	+	0.859364i	$0.329140\pi$
$888$	−0.998725	+	1.61036i	−0.0335150	+	0.0540403i
$889$	8.61372	+	12.9784i	0.288895	+	0.435280i
$890$	−33.3619	−	50.4518i	−1.11829	−	1.69115i
$891$	3.63058	−	10.5868i	0.121629	−	0.354672i
$892$	3.32858	+	27.3047i	0.111449	+	0.914228i
$893$	−4.10536	−	7.11070i	−0.137381	−	0.237950i
$894$	7.91632	+	6.35510i	0.264761	+	0.212546i
$895$		−	47.6391i		−	1.59240i
$896$	−15.9072	+	25.3567i	−0.531421	+	0.847108i
$897$	22.7912	+	20.6891i	0.760976	+	0.690789i
$898$	6.12216	−	0.371786i	0.204299	−	0.0124066i
$899$	−4.28625	+	2.47467i	−0.142954	+	0.0825348i
$900$	−5.82740	−	26.3160i	−0.194247	−	0.877200i
$901$	−6.26024	+	10.8431i	−0.208559	+	0.361235i
$902$	13.8488	−	9.15770i	0.461115	−	0.304918i
$903$	−35.3873	+	13.8254i	−1.17762	+	0.460081i
$904$	19.5289	−	3.59323i	0.649522	−	0.119509i
$905$	44.3263	+	25.5918i	1.47346	+	0.850700i
$906$	−9.88498	+	3.84268i	−0.328407	+	0.127664i
$907$	1.60692	−	0.927757i	0.0533570	−	0.0308057i	−0.473084	−	0.881017i	$-0.656859\pi$
$907$	1.60692	−	0.927757i	0.0533570	−	0.0308057i	0.526441	+	0.850212i	$0.323526\pi$
$908$	−7.62360	+	5.73445i	−0.252998	+	0.190304i
$909$	9.90984	−	0.960442i	0.328688	−	0.0318558i
$910$	−68.5253	+	8.47135i	−2.27159	+	0.280823i
$911$			12.2209i			0.404896i	0.979293	+	0.202448i	$0.0648897\pi$
$911$			12.2209i			0.404896i	−0.979293	+	0.202448i	$0.935110\pi$
$912$	4.03840	−	7.49027i	0.133725	−	0.248028i
$913$	−5.63121	+	3.25118i	−0.186366	+	0.107598i
$914$	−25.0151	−	12.4856i	−0.827426	−	0.412987i
$915$	32.1672	−	10.3078i	1.06341	−	0.340767i
$916$	−1.16394	+	2.73548i	−0.0384576	+	0.0903827i
$917$	0.700333	+	11.2184i	0.0231270	+	0.370463i
$918$	−8.74339	−	0.492086i	−0.288575	−	0.0162413i
$919$	14.5126	−	25.1365i	0.478726	−	0.829177i	−0.520977	−	0.853571i	$-0.674432\pi$
$919$	14.5126	−	25.1365i	0.478726	−	0.829177i	0.999702	+	0.0243939i	$0.00776558\pi$
$920$	−19.6827	+	16.7664i	−0.648919	+	0.552773i
$921$	16.1978	+	3.51161i	0.533737	+	0.115712i
$922$	35.7599	−	2.17162i	1.17769	−	0.0715185i
$923$		−	37.2012i		−	1.22449i
$924$	5.99065	−	9.69605i	0.197078	−	0.318977i
$925$		−	1.73760i		−	0.0571318i
$926$	1.79656	+	29.5838i	0.0590387	+	0.972184i
$927$	21.6774	+	30.3505i	0.711978	+	0.996841i
$928$	−5.40427	−	17.2705i	−0.177404	−	0.566932i
$929$	14.7335	−	25.5191i	0.483390	−	0.837255i	−0.516428	−	0.856330i	$-0.672739\pi$
$929$	14.7335	−	25.5191i	0.483390	−	0.837255i	0.999818	+	0.0190749i	$0.00607211\pi$
$930$	−1.77759	+	11.5398i	−0.0582894	+	0.378406i
$931$	5.19155	+	6.85342i	0.170146	+	0.224612i
$932$	4.25407	+	1.81010i	0.139347	+	0.0592917i
$933$	−9.35719	−	29.2005i	−0.306341	−	0.955982i
$934$	19.6298	−	39.3286i	0.642307	−	1.28687i
$935$	3.95414	−	2.28292i	0.129314	−	0.0746596i
$936$	−12.3286	+	49.3052i	−0.402973	+	1.61159i
$937$		−	23.9964i		−	0.783929i	−0.919980	−	0.391965i	$-0.871796\pi$
$937$		−	23.9964i		−	0.783929i	0.919980	−	0.391965i	$-0.128204\pi$
$938$	−18.0826	+	42.6980i	−0.590417	+	1.39414i
$939$	−14.7116	−	13.3547i	−0.480094	−	0.435814i
$940$	−32.9185	+	24.7612i	−1.07368	+	0.807622i
$941$	−37.8505	+	21.8530i	−1.23389	+	0.712387i	−0.967839	−	0.251571i	$-0.919053\pi$
$941$	−37.8505	+	21.8530i	−1.23389	+	0.712387i	−0.266052	+	0.963959i	$0.585719\pi$
$942$	14.6580	−	5.69812i	0.477583	−	0.185655i
$943$	−24.2582	−	14.0055i	−0.789955	−	0.456081i
$944$	−10.7462	+	10.3415i	−0.349758	+	0.336588i
$945$	23.1457	−	35.4727i	0.752931	−	1.15393i
$946$	−8.04214	−	12.1618i	−0.261472	−	0.395414i
$947$	15.9345	−	27.5994i	0.517802	−	0.896859i	−0.481984	−	0.876180i	$-0.660084\pi$
$947$	15.9345	−	27.5994i	0.517802	−	0.896859i	0.999786	−	0.0206793i	$-0.00658291\pi$
$948$	25.6680	−	36.2767i	0.833659	−	1.17821i
$949$	53.4846	−	30.8794i	1.73618	−	1.00239i
$950$	0.472993	+	7.78873i	0.0153459	+	0.252700i
$951$	2.69250	−	2.96607i	0.0873103	−	0.0961814i
$952$	−8.57236	−	2.45845i	−0.277832	−	0.0796789i
$953$			49.4699i			1.60249i	0.598338	+	0.801243i	$0.295828\pi$
$953$			49.4699i			1.60249i	−0.598338	+	0.801243i	$0.704172\pi$
$954$	−44.0245	+	6.98137i	−1.42535	+	0.226030i
$955$	0.695736	+	1.20505i	0.0225135	+	0.0389945i
$956$	−5.22836	−	42.8887i	−0.169097	−	1.38712i
$957$	2.10267	+	6.56171i	0.0679698	+	0.212110i
$958$	−40.3184	+	26.6611i	−1.30263	+	0.861380i
$959$	1.84621	+	0.917585i	0.0596173	+	0.0296304i
$960$	−39.7527	−	15.5638i	−1.28301	−	0.502319i
$961$	−14.3032	+	24.7738i	−0.461392	+	0.799155i
$962$	−1.46319	+	2.93152i	−0.0471751	+	0.0945161i
$963$	−23.3888	+	16.7051i	−0.753693	+	0.538313i
$964$	−6.24706	+	4.69902i	−0.201204	+	0.151345i
$965$			5.29478i			0.170445i
$966$	−19.1502	−	1.73767i	−0.616146	−	0.0559087i
$967$	18.5748			0.597324			0.298662	−	0.954359i	$-0.403460\pi$
$967$	18.5748			0.597324			0.298662	+	0.954359i	$0.403460\pi$
$968$	−25.1934	−	8.95831i	−0.809746	−	0.287931i
$969$	2.47767	+	0.537148i	0.0795944	+	0.0172557i
$970$	66.8547	+	33.3687i	2.14658	+	1.07140i
$971$	−41.9333	−	24.2102i	−1.34570	−	0.776943i	−0.358067	−	0.933696i	$-0.616564\pi$
$971$	−41.9333	−	24.2102i	−1.34570	−	0.776943i	−0.987638	+	0.156753i	$0.949897\pi$
$972$	−18.2326	−	25.2898i	−0.584811	−	0.811170i
$973$	−8.11583	−	12.2282i	−0.260182	−	0.392018i
$974$	29.1064	−	19.2470i	0.932628	−	0.616712i
$975$	−14.2216	−	44.3807i	−0.455456	−	1.42132i
$976$	7.02114	−	24.3265i	0.224741	−	0.778671i
$977$	−46.0630	+	26.5945i	−1.47369	+	0.850833i	−0.999561	−	0.0296250i	$-0.990569\pi$
$977$	−46.0630	+	26.5945i	−1.47369	+	0.850833i	−0.474125	+	0.880458i	$0.657235\pi$
$978$	16.2580	−	20.2520i	0.519873	−	0.647587i
$979$	17.2629			0.551724
$980$	30.9779	−	30.0142i	0.989553	−	0.958767i
$981$	−1.75991	+	0.170567i	−0.0561897	+	0.00544580i
$982$	3.71241	+	61.1319i	0.118468	+	1.95080i
$983$	7.97962	+	13.8211i	0.254510	+	0.440825i	0.964762	−	0.263123i	$-0.0847524\pi$
$983$	7.97962	+	13.8211i	0.254510	+	0.440825i	−0.710252	+	0.703947i	$0.751419\pi$
$984$	1.45805	−	46.2263i	0.0464810	−	1.47364i
$985$	43.8174	+	25.2980i	1.39614	+	0.806061i
$986$	4.49708	−	2.97375i	0.143216	−	0.0947036i
$987$	−30.2848	−	4.61256i	−0.963975	−	0.146820i
$988$	5.76071	−	13.5388i	0.183273	−	0.430726i
$989$	−12.2994	+	21.3031i	−0.391097	+	0.677400i
$990$	15.1765	+	5.82240i	0.482340	+	0.185048i
$991$	−4.26387	−	7.38524i	−0.135446	−	0.234600i	0.790322	−	0.612692i	$-0.209914\pi$
$991$	−4.26387	−	7.38524i	−0.135446	−	0.234600i	−0.925768	+	0.378092i	$0.876580\pi$
$992$	6.43982	+	5.92672i	0.204465	+	0.188174i
$993$	30.6781	+	27.8486i	0.973541	+	0.883749i
$994$	14.0012	+	18.5483i	0.444090	+	0.588315i
$995$	2.98621			0.0946693
$996$	−1.66739	+	18.0363i	−0.0528333	+	0.571501i
$997$	−13.8974	−	24.0710i	−0.440136	−	0.762337i	0.557564	−	0.830134i	$-0.311736\pi$
$997$	−13.8974	−	24.0710i	−0.440136	−	0.762337i	−0.997699	+	0.0677970i	$0.978403\pi$
$998$	23.5743	−	47.2315i	0.746231	−	1.49509i
$999$	−0.795108	−	1.84591i	−0.0251561	−	0.0584019i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.2.ba.c.5.13	yes	48
3.2	odd	2	inner	168.2.ba.c.5.12	yes	48
4.3	odd	2		672.2.bi.c.593.3		48
7.3	odd	6	inner	168.2.ba.c.101.5	yes	48
8.3	odd	2		672.2.bi.c.593.22		48
8.5	even	2	inner	168.2.ba.c.5.20	yes	48
12.11	even	2		672.2.bi.c.593.15		48
21.17	even	6	inner	168.2.ba.c.101.20	yes	48
24.5	odd	2	inner	168.2.ba.c.5.5	✓	48
24.11	even	2		672.2.bi.c.593.10		48
28.3	even	6		672.2.bi.c.17.10		48
56.3	even	6		672.2.bi.c.17.15		48
56.45	odd	6	inner	168.2.ba.c.101.12	yes	48
84.59	odd	6		672.2.bi.c.17.22		48
168.59	odd	6		672.2.bi.c.17.3		48
168.101	even	6	inner	168.2.ba.c.101.13	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.ba.c.5.5	✓	48	24.5	odd	2	inner
168.2.ba.c.5.12	yes	48	3.2	odd	2	inner
168.2.ba.c.5.13	yes	48	1.1	even	1	trivial
168.2.ba.c.5.20	yes	48	8.5	even	2	inner
168.2.ba.c.101.5	yes	48	7.3	odd	6	inner
168.2.ba.c.101.12	yes	48	56.45	odd	6	inner
168.2.ba.c.101.13	yes	48	168.101	even	6	inner
168.2.ba.c.101.20	yes	48	21.17	even	6	inner
672.2.bi.c.17.3		48	168.59	odd	6
672.2.bi.c.17.10		48	28.3	even	6
672.2.bi.c.17.15		48	56.3	even	6
672.2.bi.c.17.22		48	84.59	odd	6
672.2.bi.c.593.3		48	4.3	odd	2
672.2.bi.c.593.10		48	24.11	even	2
672.2.bi.c.593.15		48	12.11	even	2
672.2.bi.c.593.22		48	8.3	odd	2

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:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	168.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0857242 + 1.41161i) q^{2} +(1.69273 + 0.366975i) q^{3} +(-1.98530 + 0.242019i) q^{4} +(2.66818 + 1.54047i) q^{5} +(-0.372919 + 2.42094i) q^{6} +(-1.46307 - 2.20441i) q^{7} +(-0.511826 - 2.78173i) q^{8} +(2.73066 + 1.24238i) q^{9} +(-1.94583 + 3.89849i) q^{10} +(-0.621780 - 1.07696i) q^{11} +(-3.44939 - 0.318884i) q^{12} -5.98957 q^{13} +(2.98636 - 2.25426i) q^{14} +(3.95119 + 3.58676i) q^{15} +(3.88285 - 0.960961i) q^{16} +(0.595854 + 1.03205i) q^{17} +(-1.51967 + 3.96114i) q^{18} +(0.614126 - 1.06370i) q^{19} +(-5.66997 - 2.41256i) q^{20} +(-1.66761 - 4.26838i) q^{21} +(1.46694 - 0.970035i) q^{22} +(-2.56956 - 1.48354i) q^{23} +(0.154445 - 4.89654i) q^{24} +(2.24612 + 3.89040i) q^{25} +(-0.513451 - 8.45496i) q^{26} +(4.16634 + 3.10509i) q^{27} +(3.43814 + 4.02234i) q^{28} -3.19900 q^{29} +(-4.72441 + 5.88502i) q^{30} +(1.33987 - 0.773574i) q^{31} +(1.68936 + 5.39871i) q^{32} +(-0.657290 - 2.05117i) q^{33} +(-1.40578 + 0.929587i) q^{34} +(-0.507883 - 8.13559i) q^{35} +(-5.72186 - 1.80563i) q^{36} +(-0.334978 - 0.193399i) q^{37} +(1.55417 + 0.775723i) q^{38} +(-10.1387 - 2.19802i) q^{39} +(2.91955 - 8.21062i) q^{40} +9.44060 q^{41} +(5.88235 - 2.71992i) q^{42} -8.29057i q^{43} +(1.49507 + 1.98760i) q^{44} +(5.37204 + 7.52140i) q^{45} +(1.87391 - 3.75440i) q^{46} +(3.34244 - 5.78928i) q^{47} +(6.92527 - 0.201736i) q^{48} +(-2.71887 + 6.45041i) q^{49} +(-5.29919 + 3.50416i) q^{50} +(0.629882 + 1.96564i) q^{51} +(11.8911 - 1.44959i) q^{52} +(5.25317 + 9.09875i) q^{53} +(-4.02603 + 6.14744i) q^{54} -3.83135i q^{55} +(-5.38325 + 5.19813i) q^{56} +(1.42990 - 1.57518i) q^{57} +(-0.274232 - 4.51576i) q^{58} +(-3.22898 + 1.86425i) q^{59} +(-8.71237 - 6.16454i) q^{60} +(3.16493 - 5.48181i) q^{61} +(1.20685 + 1.82506i) q^{62} +(-1.25642 - 7.83718i) q^{63} +(-7.47607 + 2.84752i) q^{64} +(-15.9813 - 9.22678i) q^{65} +(2.83911 - 1.10367i) q^{66} +(-10.7324 + 6.19634i) q^{67} +(-1.43273 - 1.90472i) q^{68} +(-3.80515 - 3.45419i) q^{69} +(11.4408 - 1.41435i) q^{70} +6.21100i q^{71} +(2.05834 - 8.23184i) q^{72} +(-8.92963 + 5.15552i) q^{73} +(0.244290 - 0.489438i) q^{74} +(2.37440 + 7.40966i) q^{75} +(-0.961791 + 2.26039i) q^{76} +(-1.46435 + 2.94632i) q^{77} +(2.23362 - 14.5004i) q^{78} +(-6.41425 + 11.1098i) q^{79} +(11.8405 + 3.41742i) q^{80} +(5.91299 + 6.78502i) q^{81} +(0.809288 + 13.3265i) q^{82} -5.22882i q^{83} +(4.34374 + 8.07044i) q^{84} +3.67159i q^{85} +(11.7031 - 0.710702i) q^{86} +(-5.41505 - 1.17396i) q^{87} +(-2.67756 + 2.28084i) q^{88} +(-6.94090 + 12.0220i) q^{89} +(-10.1568 + 8.22800i) q^{90} +(8.76314 + 13.2035i) q^{91} +(5.46040 + 2.32339i) q^{92} +(2.55192 - 0.817752i) q^{93} +(8.45876 + 4.22196i) q^{94} +(3.27720 - 1.89209i) q^{95} +(0.878436 + 9.75850i) q^{96} -17.1489i q^{97} +(-9.33855 - 3.28504i) q^{98} +(-0.359884 - 3.71328i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9} - 30 q^{10} - 18 q^{12} + 4 q^{15} + 6 q^{16} - 36 q^{22} - 12 q^{24} - 8 q^{25} - 10 q^{28} + 22 q^{30} + 48 q^{31} - 42 q^{33} + 52 q^{36} - 8 q^{39} - 18 q^{40} + 12 q^{42}+ \cdots + 90 q^{96}+O(q^{100}) \) 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9 - 30 * q^10 - 18 * q^12 + 4 * q^15 + 6 * q^16 - 36 * q^22 - 12 * q^24 - 8 * q^25 - 10 * q^28 + 22 * q^30 + 48 * q^31 - 42 * q^33 + 52 * q^36 - 8 * q^39 - 18 * q^40 + 12 * q^42 - 8 * q^46 - 36 * q^49 - 48 * q^52 + 60 * q^54 + 4 * q^57 + 30 * q^58 - 32 * q^60 - 6 * q^63 - 60 * q^64 + 54 * q^66 + 42 * q^70 + 42 * q^72 - 36 * q^73 - 68 * q^78 - 56 * q^79 + 42 * q^81 + 48 * q^82 + 48 * q^84 - 132 * q^87 + 6 * q^88 + 48 * q^94 + 90 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more