LMFDB - Embedded newform 92.4.e.a.13.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [92,4,Mod(9,92)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(92, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 10]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("92.9");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 92 = 2^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	92.e (of order $11$, degree $10$, 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:	$5.42817572053$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$6$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			13.2
Character	$\chi$	$=$	92.13
Dual form			92.4.e.a.85.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.98530 - 2.56119i) q^{3} +(-3.66438 + 8.02386i) q^{5} +(26.9581 + 7.91560i) q^{7} +(-1.89333 - 4.14582i) q^{9} +O(q^{10})$	\(q+(-3.98530 - 2.56119i) q^{3} +(-3.66438 + 8.02386i) q^{5} +(26.9581 + 7.91560i) q^{7} +(-1.89333 - 4.14582i) q^{9} +(28.7886 - 33.2238i) q^{11} +(70.8452 - 20.8020i) q^{13} +(35.1543 - 22.5923i) q^{15} +(-7.49450 - 52.1254i) q^{17} +(-19.1590 + 133.254i) q^{19} +(-87.1625 - 100.591i) q^{21} +(101.165 + 43.9623i) q^{23} +(30.9029 + 35.6638i) q^{25} +(-21.2760 + 147.978i) q^{27} +(-21.3173 - 148.265i) q^{29} +(35.8072 - 23.0119i) q^{31} +(-199.824 + 58.6736i) q^{33} +(-162.298 + 187.302i) q^{35} +(19.4108 + 42.5037i) q^{37} +(-335.617 - 98.5461i) q^{39} +(66.4549 - 145.516i) q^{41} +(-356.023 - 228.802i) q^{43} +40.2034 q^{45} +427.204 q^{47} +(375.531 + 241.339i) q^{49} +(-103.635 + 226.930i) q^{51} +(-675.469 - 198.336i) q^{53} +(161.091 + 352.740i) q^{55} +(417.644 - 481.986i) q^{57} +(-161.456 + 47.4076i) q^{59} +(-367.622 + 236.256i) q^{61} +(-18.2239 - 126.750i) q^{63} +(-92.6908 + 644.678i) q^{65} +(65.8013 + 75.9387i) q^{67} +(-290.576 - 434.306i) q^{69} +(351.821 + 406.023i) q^{71} +(45.2458 - 314.692i) q^{73} +(-31.8151 - 221.279i) q^{75} +(1039.07 - 667.771i) q^{77} +(870.892 - 255.717i) q^{79} +(383.205 - 442.242i) q^{81} +(66.0359 + 144.598i) q^{83} +(445.710 + 130.872i) q^{85} +(-294.780 + 645.477i) q^{87} +(-373.937 - 240.315i) q^{89} +2074.51 q^{91} -201.640 q^{93} +(-999.005 - 642.022i) q^{95} +(-224.258 + 491.056i) q^{97} +(-192.247 - 56.4487i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 4 q^{3} + 10 q^{5} + 4 q^{7} - 50 q^{9}+O(q^{10}) $ 60 * q - 4 * q^3 + 10 * q^5 + 4 * q^7 - 50 * q^9	$ 60 q - 4 q^{3} + 10 q^{5} + 4 q^{7} - 50 q^{9} + 58 q^{11} - 56 q^{13} - 246 q^{15} + 28 q^{17} + 84 q^{19} + 560 q^{21} + 484 q^{23} + 274 q^{25} - 358 q^{27} - 400 q^{29} - 334 q^{31} - 668 q^{33} + 1510 q^{35} + 1374 q^{37} - 420 q^{39} - 554 q^{41} - 1218 q^{43} - 2812 q^{45} - 1468 q^{47} - 2704 q^{49} - 668 q^{51} + 8 q^{53} - 304 q^{55} + 1732 q^{57} + 1270 q^{59} + 1242 q^{61} + 38 q^{63} + 4984 q^{65} + 3018 q^{67} + 3464 q^{69} + 2162 q^{71} + 932 q^{73} + 5748 q^{75} + 1052 q^{77} - 1238 q^{79} - 4130 q^{81} - 4154 q^{83} - 5282 q^{85} - 4862 q^{87} - 1594 q^{89} - 4700 q^{91} + 4044 q^{93} - 5714 q^{95} - 9698 q^{97} - 4566 q^{99}+O(q^{100}) $ 60 * q - 4 * q^3 + 10 * q^5 + 4 * q^7 - 50 * q^9 + 58 * q^11 - 56 * q^13 - 246 * q^15 + 28 * q^17 + 84 * q^19 + 560 * q^21 + 484 * q^23 + 274 * q^25 - 358 * q^27 - 400 * q^29 - 334 * q^31 - 668 * q^33 + 1510 * q^35 + 1374 * q^37 - 420 * q^39 - 554 * q^41 - 1218 * q^43 - 2812 * q^45 - 1468 * q^47 - 2704 * q^49 - 668 * q^51 + 8 * q^53 - 304 * q^55 + 1732 * q^57 + 1270 * q^59 + 1242 * q^61 + 38 * q^63 + 4984 * q^65 + 3018 * q^67 + 3464 * q^69 + 2162 * q^71 + 932 * q^73 + 5748 * q^75 + 1052 * q^77 - 1238 * q^79 - 4130 * q^81 - 4154 * q^83 - 5282 * q^85 - 4862 * q^87 - 1594 * q^89 - 4700 * q^91 + 4044 * q^93 - 5714 * q^95 - 9698 * q^97 - 4566 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/92\mathbb{Z}\right)^\times$.

$n$	$5$	$47$
$\chi(n)$	$e\left(\frac{7}{11}\right)$	$1$

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			0
$2$		0			0
$3$	−3.98530	−	2.56119i	−0.766971	−	0.492902i	0.0977156	−	0.995214i	$-0.468846\pi$
$3$	−3.98530	−	2.56119i	−0.766971	−	0.492902i	−0.864686	+	0.502312i	$0.832483\pi$
$4$		0			0
$5$	−3.66438	+	8.02386i	−0.327752	+	0.717676i	−0.999738	−	0.0228875i	$-0.992714\pi$
$5$	−3.66438	+	8.02386i	−0.327752	+	0.717676i	0.671986	+	0.740564i	$0.265441\pi$
$6$		0			0
$7$	26.9581	+	7.91560i	1.45560	+	0.427402i	0.911389	−	0.411546i	$-0.135011\pi$
$7$	26.9581	+	7.91560i	1.45560	+	0.427402i	0.544210	+	0.838949i	$0.316829\pi$
$8$		0			0
$9$	−1.89333	−	4.14582i	−0.0701235	−	0.153549i
$10$		0			0
$11$	28.7886	−	33.2238i	0.789099	−	0.910669i	−0.208632	−	0.977994i	$-0.566901\pi$
$11$	28.7886	−	33.2238i	0.789099	−	0.910669i	0.997731	+	0.0673249i	$0.0214464\pi$
$12$		0			0
$13$	70.8452	−	20.8020i	1.51146	−	0.443803i	0.582140	−	0.813089i	$-0.302216\pi$
$13$	70.8452	−	20.8020i	1.51146	−	0.443803i	0.929316	+	0.369286i	$0.120398\pi$
$14$		0			0
$15$	35.1543	−	22.5923i	0.605120	−	0.388887i
$16$		0			0
$17$	−7.49450	−	52.1254i	−0.106923	−	0.743663i	−0.970788	−	0.239940i	$-0.922872\pi$
$17$	−7.49450	−	52.1254i	−0.106923	−	0.743663i	0.863865	−	0.503723i	$-0.168037\pi$
$18$		0			0
$19$	−19.1590	+	133.254i	−0.231336	+	1.60898i	0.461000	+	0.887400i	$0.347491\pi$
$19$	−19.1590	+	133.254i	−0.231336	+	1.60898i	−0.692336	+	0.721576i	$0.743418\pi$
$20$		0			0
$21$	−87.1625	−	100.591i	−0.905734	−	1.04527i
$22$		0			0
$23$	101.165	+	43.9623i	0.917144	+	0.398555i
$23$	101.165	+	43.9623i	0.917144	+	0.398555i
$24$		0			0
$25$	30.9029	+	35.6638i	0.247223	+	0.285311i
$26$		0			0
$27$	−21.2760	+	147.978i	−0.151650	+	1.05475i
$28$		0			0
$29$	−21.3173	−	148.265i	−0.136501	−	0.949383i	−0.936821	−	0.349810i	$-0.886246\pi$
$29$	−21.3173	−	148.265i	−0.136501	−	0.949383i	0.800320	−	0.599573i	$-0.204663\pi$
$30$		0			0
$31$	35.8072	−	23.0119i	0.207457	−	0.133324i	−0.432787	−	0.901496i	$-0.642470\pi$
$31$	35.8072	−	23.0119i	0.207457	−	0.133324i	0.640244	+	0.768172i	$0.278833\pi$
$32$		0			0
$33$	−199.824	+	58.6736i	−1.05409	+	0.309508i
$34$		0			0
$35$	−162.298	+	187.302i	−0.783812	+	0.904567i
$36$		0			0
$37$	19.4108	+	42.5037i	0.0862464	+	0.188853i	0.947841	−	0.318744i	$-0.103261\pi$
$37$	19.4108	+	42.5037i	0.0862464	+	0.188853i	−0.861594	+	0.507597i	$0.830534\pi$
$38$		0			0
$39$	−335.617	−	98.5461i	−1.37799	−	0.404615i
$40$		0			0
$41$	66.4549	−	145.516i	0.253135	−	0.554287i	−0.739817	−	0.672808i	$-0.765088\pi$
$41$	66.4549	−	145.516i	0.253135	−	0.554287i	0.992952	+	0.118521i	$0.0378152\pi$
$42$		0			0
$43$	−356.023	−	228.802i	−1.26263	−	0.811442i	−0.273986	−	0.961734i	$-0.588342\pi$
$43$	−356.023	−	228.802i	−1.26263	−	0.811442i	−0.988642	+	0.150292i	$0.951979\pi$
$44$		0			0
$45$	40.2034			0.133182
$46$		0			0
$47$	427.204			1.32583			0.662915	−	0.748694i	$-0.269319\pi$
$47$	427.204			1.32583			0.662915	+	0.748694i	$0.269319\pi$
$48$		0			0
$49$	375.531	+	241.339i	1.09484	+	0.703613i
$50$		0			0
$51$	−103.635	+	226.930i	−0.284546	+	0.623070i
$52$		0			0
$53$	−675.469	−	198.336i	−1.75062	−	0.514028i	−0.759910	−	0.650028i	$-0.774757\pi$
$53$	−675.469	−	198.336i	−1.75062	−	0.514028i	−0.990709	+	0.136000i	$0.956575\pi$
$54$		0			0
$55$	161.091	+	352.740i	0.394937	+	0.864791i
$56$		0			0
$57$	417.644	−	481.986i	0.970495	−	1.12001i
$58$		0			0
$59$	−161.456	+	47.4076i	−0.356266	+	0.104609i	−0.454968	−	0.890508i	$-0.650349\pi$
$59$	−161.456	+	47.4076i	−0.356266	+	0.104609i	0.0987015	+	0.995117i	$0.468531\pi$
$60$		0			0
$61$	−367.622	+	236.256i	−0.771625	+	0.495893i	−0.866244	−	0.499620i	$-0.833473\pi$
$61$	−367.622	+	236.256i	−0.771625	+	0.495893i	0.0946197	+	0.995513i	$0.469836\pi$
$62$		0			0
$63$	−18.2239	−	126.750i	−0.0364445	−	0.253477i
$64$		0			0
$65$	−92.6908	+	644.678i	−0.176875	+	1.23019i
$66$		0			0
$67$	65.8013	+	75.9387i	0.119984	+	0.138469i	0.812563	−	0.582873i	$-0.198071\pi$
$67$	65.8013	+	75.9387i	0.119984	+	0.138469i	−0.692580	+	0.721341i	$0.743526\pi$
$68$		0			0
$69$	−290.576	−	434.306i	−0.506974	−	0.757743i
$70$		0			0
$71$	351.821	+	406.023i	0.588077	+	0.678677i	0.969321	−	0.245797i	$-0.0790498\pi$
$71$	351.821	+	406.023i	0.588077	+	0.678677i	−0.381244	+	0.924474i	$0.624504\pi$
$72$		0			0
$73$	45.2458	−	314.692i	0.0725428	−	0.504546i	−0.920862	−	0.389888i	$-0.872514\pi$
$73$	45.2458	−	314.692i	0.0725428	−	0.504546i	0.993405	−	0.114658i	$-0.0365772\pi$
$74$		0			0
$75$	−31.8151	−	221.279i	−0.0489826	−	0.340682i
$76$		0			0
$77$	1039.07	−	667.771i	1.53783	−	0.988307i
$78$		0			0
$79$	870.892	−	255.717i	1.24029	−	0.364183i	0.405167	−	0.914243i	$-0.367213\pi$
$79$	870.892	−	255.717i	1.24029	−	0.364183i	0.835125	+	0.550060i	$0.185395\pi$
$80$		0			0
$81$	383.205	−	442.242i	0.525658	−	0.606642i
$82$		0			0
$83$	66.0359	+	144.598i	0.0873299	+	0.191226i	0.948258	−	0.317501i	$-0.102844\pi$
$83$	66.0359	+	144.598i	0.0873299	+	0.191226i	−0.860928	+	0.508727i	$0.830116\pi$
$84$		0			0
$85$	445.710	+	130.872i	0.568753	+	0.167001i
$86$		0			0
$87$	−294.780	+	645.477i	−0.363261	+	0.795430i
$88$		0			0
$89$	−373.937	−	240.315i	−0.445362	−	0.286217i	0.298675	−	0.954355i	$-0.403455\pi$
$89$	−373.937	−	240.315i	−0.445362	−	0.286217i	−0.744037	+	0.668138i	$0.767092\pi$
$90$		0			0
$91$	2074.51			2.38976
$92$		0			0
$93$	−201.640			−0.224829
$94$		0			0
$95$	−999.005	−	642.022i	−1.07890	−	0.693369i
$96$		0			0
$97$	−224.258	+	491.056i	−0.234741	+	0.514012i	−0.989941	−	0.141484i	$-0.954813\pi$
$97$	−224.258	+	491.056i	−0.234741	+	0.514012i	0.755199	+	0.655495i	$0.227540\pi$
$98$		0			0
$99$	−192.247	−	56.4487i	−0.195167	−	0.0573062i
$100$		0			0
$101$	−179.510	−	393.071i	−0.176850	−	0.387248i	0.800361	−	0.599519i	$-0.204641\pi$
$101$	−179.510	−	393.071i	−0.176850	−	0.387248i	−0.977211	+	0.212271i	$0.931914\pi$
$102$		0			0
$103$	−271.463	+	313.285i	−0.259689	+	0.299697i	−0.870589	−	0.492010i	$-0.836262\pi$
$103$	−271.463	+	313.285i	−0.259689	+	0.299697i	0.610900	+	0.791708i	$0.290808\pi$
$104$		0			0
$105$	1126.52	−	330.777i	1.04702	−	0.307434i
$106$		0			0
$107$	−1080.12	+	694.152i	−0.975882	+	0.627161i	−0.928349	−	0.371709i	$-0.878772\pi$
$107$	−1080.12	+	694.152i	−0.975882	+	0.627161i	−0.0475322	+	0.998870i	$0.515136\pi$
$108$		0			0
$109$	188.102	+	1308.28i	0.165293	+	1.14964i	0.888457	+	0.458960i	$0.151778\pi$
$109$	188.102	+	1308.28i	0.165293	+	1.14964i	−0.723165	+	0.690676i	$0.757313\pi$
$110$		0			0
$111$	31.5025	−	219.105i	0.0269377	−	0.187356i
$112$		0			0
$113$	−1016.22	−	1172.78i	−0.845998	−	0.976333i	0.153933	−	0.988081i	$-0.450806\pi$
$113$	−1016.22	−	1172.78i	−0.845998	−	0.976333i	−0.999931	+	0.0117480i	$0.996260\pi$
$114$		0			0
$115$	−723.453	+	650.638i	−0.586629	+	0.527585i
$116$		0			0
$117$	−220.375	−	254.327i	−0.174134	−	0.200962i
$118$		0			0
$119$	210.567	−	1464.52i	0.162207	−	1.12817i
$120$		0			0
$121$	−85.6177	−	595.484i	−0.0643258	−	0.447396i
$122$		0			0
$123$	−637.537	+	409.720i	−0.467356	+	0.300352i
$124$		0			0
$125$	−1457.36	+	427.920i	−1.04280	+	0.306195i
$126$		0			0
$127$	−982.616	+	1134.00i	−0.686560	+	0.792332i	−0.986871	−	0.161509i	$-0.948364\pi$
$127$	−982.616	+	1134.00i	−0.686560	+	0.792332i	0.300312	+	0.953841i	$0.402909\pi$
$128$		0			0
$129$	832.851	+	1823.69i	0.568437	+	1.24470i
$130$		0			0
$131$	199.856	+	58.6830i	0.133294	+	0.0391386i	0.347699	−	0.937606i	$-0.386963\pi$
$131$	199.856	+	58.6830i	0.133294	+	0.0391386i	−0.214405	+	0.976745i	$0.568781\pi$
$132$		0			0
$133$	−1571.28	+	3440.61i	−1.02441	+	2.24315i
$134$		0			0
$135$	−1109.39	−	712.961i	−0.707266	−	0.454532i
$136$		0			0
$137$	−699.802			−0.436410			−0.218205	−	0.975903i	$-0.570020\pi$
$137$	−699.802			−0.436410			−0.218205	+	0.975903i	$0.570020\pi$
$138$		0			0
$139$	2659.14			1.62263			0.811313	−	0.584612i	$-0.198753\pi$
$139$	2659.14			1.62263			0.811313	+	0.584612i	$0.198753\pi$
$140$		0			0
$141$	−1702.53	−	1094.15i	−1.01687	−	0.653505i
$142$		0			0
$143$	1348.41	−	2952.61i	0.788531	−	1.72664i
$144$		0			0
$145$	1267.77	+	372.251i	0.726088	+	0.213199i
$146$		0			0
$147$	−878.486	−	1923.62i	−0.492900	−	1.07930i
$148$		0			0
$149$	−24.0792	+	27.7889i	−0.0132393	+	0.0152789i	−0.762331	−	0.647188i	$-0.775945\pi$
$149$	−24.0792	+	27.7889i	−0.0132393	+	0.0152789i	0.749091	+	0.662467i	$0.230490\pi$
$150$		0			0
$151$	−1804.68	+	529.902i	−0.972601	+	0.285581i	−0.729167	−	0.684336i	$-0.760092\pi$
$151$	−1804.68	+	529.902i	−0.972601	+	0.285581i	−0.243434	+	0.969917i	$0.578274\pi$
$152$		0			0
$153$	−201.913	+	129.762i	−0.106691	+	0.0685661i
$154$		0			0
$155$	53.4332	+	371.636i	0.0276894	+	0.192584i
$156$		0			0
$157$	199.166	−	1385.23i	0.101243	−	0.704162i	−0.874465	−	0.485088i	$-0.838787\pi$
$157$	199.166	−	1385.23i	0.101243	−	0.704162i	0.975708	−	0.219074i	$-0.0703035\pi$
$158$		0			0
$159$	2183.97	+	2520.43i	1.08931	+	1.25713i
$160$		0			0
$161$	2379.22	+	1985.92i	1.16465	+	0.972127i
$162$		0			0
$163$	−2590.95	−	2990.11i	−1.24502	−	1.43683i	−0.857107	−	0.515138i	$-0.827741\pi$
$163$	−2590.95	−	2990.11i	−1.24502	−	1.43683i	−0.387915	−	0.921695i	$-0.626805\pi$
$164$		0			0
$165$	261.441	−	1818.36i	0.123352	−	0.857935i
$166$		0			0
$167$	−143.050	−	994.936i	−0.0662848	−	0.461021i	−0.995749	−	0.0921084i	$-0.970639\pi$
$167$	−143.050	−	994.936i	−0.0662848	−	0.461021i	0.929464	−	0.368912i	$-0.120270\pi$
$168$		0			0
$169$	2738.08	−	1759.66i	1.24628	−	0.800937i
$170$		0			0
$171$	588.722	−	172.864i	0.263279	−	0.0773056i
$172$		0			0
$173$	−2373.99	+	2739.73i	−1.04330	+	1.20404i	−0.0647793	+	0.997900i	$0.520634\pi$
$173$	−2373.99	+	2739.73i	−1.04330	+	1.20404i	−0.978523	+	0.206136i	$0.933911\pi$
$174$		0			0
$175$	550.781	+	1206.04i	0.237915	+	0.520962i
$176$		0			0
$177$	764.868	+	224.586i	0.324808	+	0.0953722i
$178$		0			0
$179$	−519.437	+	1137.41i	−0.216897	+	0.474938i	−0.986537	−	0.163541i	$-0.947709\pi$
$179$	−519.437	+	1137.41i	−0.216897	+	0.474938i	0.769640	+	0.638478i	$0.220436\pi$
$180$		0			0
$181$	808.858	+	519.821i	0.332165	+	0.213470i	0.696083	−	0.717961i	$-0.254925\pi$
$181$	808.858	+	519.821i	0.332165	+	0.213470i	−0.363917	+	0.931431i	$0.618561\pi$
$182$		0			0
$183$	2070.18			0.836240
$184$		0			0
$185$	−412.172			−0.163803
$186$		0			0
$187$	−1947.56	−	1251.62i	−0.761603	−	0.489453i
$188$		0			0
$189$	−1744.89	+	3820.78i	−0.671546	+	1.47048i
$190$		0			0
$191$	−1908.80	−	560.475i	−0.723121	−	0.212328i	−0.100596	−	0.994927i	$-0.532075\pi$
$191$	−1908.80	−	560.475i	−0.723121	−	0.212328i	−0.622525	+	0.782600i	$0.713893\pi$
$192$		0			0
$193$	1369.91	+	2999.68i	0.510923	+	1.11877i	0.972763	+	0.231802i	$0.0744621\pi$
$193$	1369.91	+	2999.68i	0.510923	+	1.11877i	−0.461840	+	0.886963i	$0.652811\pi$
$194$		0			0
$195$	2020.55	−	2331.84i	0.742023	−	0.856340i
$196$		0			0
$197$	3489.03	−	1024.47i	1.26184	−	0.370510i	0.418662	−	0.908142i	$-0.362499\pi$
$197$	3489.03	−	1024.47i	1.26184	−	0.370510i	0.843180	+	0.537632i	$0.180681\pi$
$198$		0			0
$199$	1840.82	−	1183.02i	0.655739	−	0.421418i	−0.170020	−	0.985441i	$-0.554383\pi$
$199$	1840.82	−	1183.02i	0.655739	−	0.421418i	0.825759	+	0.564022i	$0.190747\pi$
$200$		0			0
$201$	−67.7438	−	471.168i	−0.0237725	−	0.165342i
$202$		0			0
$203$	598.934	−	4165.68i	0.207078	−	1.44026i
$204$		0			0
$205$	924.084	+	1066.45i	0.314833	+	0.363337i
$206$		0			0
$207$	−9.27878	−	502.647i	−0.00311555	−	0.168775i
$208$		0			0
$209$	3875.64	+	4472.73i	1.28270	+	1.48031i
$210$		0			0
$211$	32.0481	−	222.900i	0.0104563	−	0.0727254i	−0.983925	−	0.178581i	$-0.942849\pi$
$211$	32.0481	−	222.900i	0.0104563	−	0.0727254i	0.994381	+	0.105856i	$0.0337583\pi$
$212$		0			0
$213$	−362.207	−	2519.20i	−0.116516	−	0.810390i
$214$		0			0
$215$	3140.48	−	2018.26i	0.996181	−	0.640206i
$216$		0			0
$217$	1147.45	−	336.921i	0.358957	−	0.105399i
$218$		0			0
$219$	−986.304	+	1138.26i	−0.304330	+	0.351216i
$220$		0			0
$221$	−1615.26	−	3536.93i	−0.491649	−	1.07656i
$222$		0			0
$223$	−475.540	−	139.631i	−0.142801	−	0.0419300i	0.209551	−	0.977798i	$-0.432800\pi$
$223$	−475.540	−	139.631i	−0.142801	−	0.0419300i	−0.352352	+	0.935868i	$0.614618\pi$
$224$		0			0
$225$	89.3464	−	195.641i	0.0264730	−	0.0579678i
$226$		0			0
$227$	1737.12	+	1116.38i	0.507914	+	0.326416i	0.769375	−	0.638798i	$-0.220568\pi$
$227$	1737.12	+	1116.38i	0.507914	+	0.326416i	−0.261461	+	0.965214i	$0.584204\pi$
$228$		0			0
$229$	−913.635			−0.263645			−0.131823	−	0.991273i	$-0.542083\pi$
$229$	−913.635			−0.263645			−0.131823	+	0.991273i	$0.542083\pi$
$230$		0			0
$231$	−5851.30			−1.66661
$232$		0			0
$233$	−3837.58	−	2466.26i	−1.07901	−	0.693435i	−0.124678	−	0.992197i	$-0.539790\pi$
$233$	−3837.58	−	2466.26i	−1.07901	−	0.693435i	−0.954327	+	0.298763i	$0.903426\pi$
$234$		0			0
$235$	−1565.43	+	3427.82i	−0.434543	+	0.951517i
$236$		0			0
$237$	−4125.71	−	1211.42i	−1.13077	−	0.332025i
$238$		0			0
$239$	−320.978	−	702.843i	−0.0868716	−	0.190222i	0.861210	−	0.508249i	$-0.169707\pi$
$239$	−320.978	−	702.843i	−0.0868716	−	0.190222i	−0.948082	+	0.318027i	$0.896980\pi$
$240$		0			0
$241$	3685.62	−	4253.43i	0.985110	−	1.13688i	−0.00547601	−	0.999985i	$-0.501743\pi$
$241$	3685.62	−	4253.43i	0.985110	−	1.13688i	0.990586	−	0.136892i	$-0.0437115\pi$
$242$		0			0
$243$	1213.12	−	356.205i	0.320255	−	0.0940352i
$244$		0			0
$245$	−3312.56	+	2128.85i	−0.863802	+	0.555132i
$246$		0			0
$247$	1414.63	+	9838.94i	0.364415	+	2.53456i
$248$		0			0
$249$	107.172	−	745.398i	0.0272761	−	0.189710i
$250$		0			0
$251$	3679.57	+	4246.45i	0.925307	+	1.06786i	0.997514	+	0.0704720i	$0.0224506\pi$
$251$	3679.57	+	4246.45i	0.925307	+	1.06786i	−0.0722063	+	0.997390i	$0.523004\pi$
$252$		0			0
$253$	4372.99	−	2095.47i	1.08667	−	0.520715i
$254$		0			0
$255$	−1441.10	−	1663.11i	−0.353902	−	0.408424i
$256$		0			0
$257$	−418.473	+	2910.54i	−0.101571	+	0.706439i	0.873867	+	0.486164i	$0.161604\pi$
$257$	−418.473	+	2910.54i	−0.101571	+	0.706439i	−0.975438	+	0.220274i	$0.929305\pi$
$258$		0			0
$259$	186.835	+	1299.47i	0.0448238	+	0.311757i
$260$		0			0
$261$	−574.320	+	369.093i	−0.136205	+	0.0875336i
$262$		0			0
$263$	−6678.40	+	1960.95i	−1.56581	+	0.459763i	−0.945778	−	0.324814i	$-0.894698\pi$
$263$	−6678.40	+	1960.95i	−1.56581	+	0.459763i	−0.620031	+	0.784577i	$0.712880\pi$
$264$		0			0
$265$	4066.59	−	4693.09i	0.942674	−	1.08790i
$266$		0			0
$267$	874.756	+	1915.45i	0.200503	+	0.439040i
$268$		0			0
$269$	−6083.27	−	1786.21i	−1.37882	−	0.404859i	−0.493464	−	0.869766i	$-0.664270\pi$
$269$	−6083.27	−	1786.21i	−1.37882	−	0.404859i	−0.885360	+	0.464907i	$0.846088\pi$
$270$		0			0
$271$	−622.781	+	1363.70i	−0.139599	+	0.305679i	−0.966499	−	0.256670i	$-0.917375\pi$
$271$	−622.781	+	1363.70i	−0.139599	+	0.305679i	0.826900	+	0.562348i	$0.190102\pi$
$272$		0			0
$273$	−8267.54	−	5313.23i	−1.83287	−	1.17792i
$274$		0			0
$275$	2074.54			0.454907
$276$		0			0
$277$	−9056.94			−1.96454			−0.982272	−	0.187459i	$-0.939975\pi$
$277$	−9056.94			−1.96454			−0.982272	+	0.187459i	$0.939975\pi$
$278$		0			0
$279$	−163.198	−	104.881i	−0.0350195	−	0.0225056i
$280$		0			0
$281$	−3480.96	+	7622.23i	−0.738991	+	1.61816i	0.0462157	+	0.998931i	$0.485284\pi$
$281$	−3480.96	+	7622.23i	−0.738991	+	1.61816i	−0.785207	+	0.619234i	$0.787443\pi$
$282$		0			0
$283$	−6703.40	−	1968.30i	−1.40804	−	0.413438i	−0.512604	−	0.858625i	$-0.671319\pi$
$283$	−6703.40	−	1968.30i	−1.40804	−	0.413438i	−0.895438	+	0.445187i	$0.853137\pi$
$284$		0			0
$285$	2336.99	+	5117.29i	0.485724	+	1.06359i
$286$		0			0
$287$	2943.34	−	3396.80i	0.605366	−	0.698630i
$288$		0			0
$289$	2053.10	−	602.844i	0.417891	−	0.122704i
$290$		0			0
$291$	2151.42	−	1382.63i	0.433397	−	0.278527i
$292$		0			0
$293$	443.311	+	3083.30i	0.0883908	+	0.614772i	0.985078	+	0.172107i	$0.0550576\pi$
$293$	443.311	+	3083.30i	0.0883908	+	0.614772i	−0.896687	+	0.442664i	$0.854033\pi$
$294$		0			0
$295$	211.241	−	1469.22i	0.0416914	−	0.289970i
$296$		0			0
$297$	4303.88	+	4966.94i	0.840863	+	0.970407i
$298$		0			0
$299$	8081.54	+	1010.09i	1.56310	+	0.195367i
$300$		0			0
$301$	−7786.59	−	8986.20i	−1.49107	−	1.72078i
$302$		0			0
$303$	−291.333	+	2026.26i	−0.0552364	+	0.384178i
$304$		0			0
$305$	−548.582	−	3815.47i	−0.102989	−	0.716306i
$306$		0			0
$307$	2182.03	−	1402.31i	0.405652	−	0.260697i	−0.321866	−	0.946785i	$-0.604310\pi$
$307$	2182.03	−	1402.31i	0.405652	−	0.260697i	0.727518	+	0.686089i	$0.240674\pi$
$308$		0			0
$309$	1884.24	−	553.263i	0.346896	−	0.101858i
$310$		0			0
$311$	−6215.24	+	7172.77i	−1.13323	+	1.30782i	−0.187718	+	0.982223i	$0.560109\pi$
$311$	−6215.24	+	7172.77i	−1.13323	+	1.30782i	−0.945510	+	0.325592i	$0.894436\pi$
$312$		0			0
$313$	554.087	+	1213.28i	0.100060	+	0.219101i	0.953041	−	0.302841i	$-0.0979350\pi$
$313$	554.087	+	1213.28i	0.100060	+	0.219101i	−0.852981	+	0.521942i	$0.825208\pi$
$314$		0			0
$315$	1083.81	+	318.234i	0.193859	+	0.0569221i
$316$		0			0
$317$	3744.25	−	8198.77i	0.663401	−	1.45265i	−0.215917	−	0.976412i	$-0.569274\pi$
$317$	3744.25	−	8198.77i	0.663401	−	1.45265i	0.879319	−	0.476234i	$-0.157999\pi$
$318$		0			0
$319$	−5539.62	−	3560.10i	−0.972287	−	0.624851i
$320$		0			0
$321$	6082.47			1.05760
$322$		0			0
$323$	7089.50			1.22127
$324$		0			0
$325$	2931.20	+	1883.77i	0.500288	+	0.321516i
$326$		0			0
$327$	2601.11	−	5695.64i	0.439883	−	0.963210i
$328$		0			0
$329$	11516.6	+	3381.57i	1.92988	+	0.566663i
$330$		0			0
$331$	−3338.38	−	7310.04i	−0.554363	−	1.21389i	−0.954714	−	0.297524i	$-0.903839\pi$
$331$	−3338.38	−	7310.04i	−0.554363	−	1.21389i	0.400351	−	0.916362i	$-0.368888\pi$
$332$		0			0
$333$	139.462	−	160.948i	0.0229503	−	0.0264861i
$334$		0			0
$335$	−850.442	+	249.712i	−0.138700	+	0.0407261i
$336$		0			0
$337$	104.348	−	67.0607i	0.0168671	−	0.0108398i	−0.532180	−	0.846631i	$-0.678627\pi$
$337$	104.348	−	67.0607i	0.0168671	−	0.0108398i	0.549047	+	0.835791i	$0.314991\pi$
$338$		0			0
$339$	1046.22	+	7276.60i	0.167619	+	1.16581i
$340$		0			0
$341$	266.297	−	1852.13i	0.0422896	−	0.294131i
$342$		0			0
$343$	1902.37	+	2195.45i	0.299470	+	0.345606i
$344$		0			0
$345$	4549.59	−	740.081i	0.709975	−	0.115492i
$346$		0			0
$347$	2461.25	+	2840.44i	0.380769	+	0.439431i	0.913491	−	0.406859i	$-0.133376\pi$
$347$	2461.25	+	2840.44i	0.380769	+	0.439431i	−0.532721	+	0.846291i	$0.678831\pi$
$348$		0			0
$349$	1116.15	−	7763.02i	0.171193	−	1.19067i	−0.705176	−	0.709032i	$-0.749132\pi$
$349$	1116.15	−	7763.02i	0.171193	−	1.19067i	0.876369	−	0.481641i	$-0.159959\pi$
$350$		0			0
$351$	1570.93	+	10926.1i	0.238890	+	1.66151i
$352$		0			0
$353$	7178.10	−	4613.09i	1.08230	−	0.695552i	0.127212	−	0.991875i	$-0.459397\pi$
$353$	7178.10	−	4613.09i	1.08230	−	0.695552i	0.955088	+	0.296323i	$0.0957606\pi$
$354$		0			0
$355$	−4547.08	+	1335.14i	−0.679813	+	0.199611i
$356$		0			0
$357$	−4590.10	+	5297.26i	−0.680487	+	0.785324i
$358$		0			0
$359$	528.990	+	1158.33i	0.0777689	+	0.170290i	0.944523	−	0.328446i	$-0.106525\pi$
$359$	528.990	+	1158.33i	0.0777689	+	0.170290i	−0.866754	+	0.498736i	$0.833798\pi$
$360$		0			0
$361$	−10808.4	−	3173.62i	−1.57579	−	0.462695i
$362$		0			0
$363$	−1183.94	+	2592.46i	−0.171186	+	0.374846i
$364$		0			0
$365$	2359.24	+	1516.19i	0.338325	+	0.217428i
$366$		0			0
$367$	2001.39			0.284663			0.142332	−	0.989819i	$-0.454540\pi$
$367$	2001.39			0.284663			0.142332	+	0.989819i	$0.454540\pi$
$368$		0			0
$369$	−729.105			−0.102861
$370$		0			0
$371$	−16639.4	−	10693.5i	−2.32850	−	1.49644i
$372$		0			0
$373$	−572.534	+	1253.67i	−0.0794763	+	0.174029i	−0.945199	−	0.326496i	$-0.894132\pi$
$373$	−572.534	+	1253.67i	−0.0794763	+	0.174029i	0.865722	+	0.500524i	$0.166859\pi$
$374$		0			0
$375$	6904.01	+	2027.20i	0.950724	+	0.279158i
$376$		0			0
$377$	−4594.44	−	10060.4i	−0.627654	−	1.37437i
$378$		0			0
$379$	−2737.14	+	3158.83i	−0.370970	+	0.428122i	−0.910285	−	0.413982i	$-0.864138\pi$
$379$	−2737.14	+	3158.83i	−0.370970	+	0.428122i	0.539315	+	0.842104i	$0.318683\pi$
$380$		0			0
$381$	6820.41	−	2002.65i	0.917113	−	0.269289i
$382$		0			0
$383$	6449.28	−	4144.70i	0.860425	−	0.552962i	−0.0343848	−	0.999409i	$-0.510947\pi$
$383$	6449.28	−	4144.70i	0.860425	−	0.552962i	0.894810	+	0.446447i	$0.147311\pi$
$384$		0			0
$385$	1550.55	+	10784.3i	0.205256	+	1.42759i
$386$		0			0
$387$	−274.503	+	1909.21i	−0.0360562	+	0.250776i
$388$		0			0
$389$	7647.16	+	8825.29i	0.996726	+	1.15028i	0.988638	+	0.150315i	$0.0480289\pi$
$389$	7647.16	+	8825.29i	0.996726	+	1.15028i	0.00808764	+	0.999967i	$0.497426\pi$
$390$		0			0
$391$	1533.37	−	5602.73i	0.198327	−	0.724660i
$392$		0			0
$393$	−646.187	−	745.740i	−0.0829410	−	0.0957191i
$394$		0			0
$395$	−1139.44	+	7924.96i	−0.145143	+	1.00949i
$396$		0			0
$397$	−1359.91	−	9458.35i	−0.171919	−	1.19572i	−0.874825	−	0.484439i	$-0.839024\pi$
$397$	−1359.91	−	9458.35i	−0.171919	−	1.19572i	0.702907	−	0.711282i	$-0.251885\pi$
$398$		0			0
$399$	15074.1	−	9687.52i	1.89135	−	1.21550i
$400$		0			0
$401$	−2673.83	+	785.108i	−0.332980	+	0.0977716i	−0.443949	−	0.896052i	$-0.646423\pi$
$401$	−2673.83	+	785.108i	−0.332980	+	0.0977716i	0.110969	+	0.993824i	$0.464605\pi$
$402$		0			0
$403$	2058.07	−	2375.14i	0.254392	−	0.293584i
$404$		0			0
$405$	2144.28	+	4695.32i	0.263087	+	0.576080i
$406$		0			0
$407$	1970.95	+	578.722i	0.240040	+	0.0704820i
$408$		0			0
$409$	−1214.95	+	2660.38i	−0.146884	+	0.321631i	−0.968746	−	0.248056i	$-0.920208\pi$
$409$	−1214.95	+	2660.38i	−0.146884	+	0.321631i	0.821862	+	0.569687i	$0.192936\pi$
$410$		0			0
$411$	2788.92	+	1792.33i	0.334713	+	0.215107i
$412$		0			0
$413$	−4727.79			−0.563291
$414$		0			0
$415$	−1402.22			−0.165861
$416$		0			0
$417$	−10597.4	−	6810.57i	−1.24451	−	0.799796i
$418$		0			0
$419$	−5624.68	+	12316.3i	−0.655808	+	1.43602i	0.230569	+	0.973056i	$0.425941\pi$
$419$	−5624.68	+	12316.3i	−0.655808	+	1.43602i	−0.886377	+	0.462964i	$0.846786\pi$
$420$		0			0
$421$	3617.77	+	1062.27i	0.418810	+	0.122974i	0.484346	−	0.874876i	$-0.339058\pi$
$421$	3617.77	+	1062.27i	0.418810	+	0.122974i	−0.0655359	+	0.997850i	$0.520876\pi$
$422$		0			0
$423$	−808.839	−	1771.11i	−0.0929719	−	0.203580i
$424$		0			0
$425$	1627.39	−	1878.11i	0.185741	−	0.214357i
$426$		0			0
$427$	−11780.5	+	3459.06i	−1.33512	+	0.392027i
$428$		0			0
$429$	−12936.0	+	8313.48i	−1.45585	+	0.935615i
$430$		0			0
$431$	−990.410	−	6888.45i	−0.110688	−	0.769850i	−0.967254	−	0.253812i	$-0.918316\pi$
$431$	−990.410	−	6888.45i	−0.110688	−	0.769850i	0.856566	−	0.516038i	$-0.172594\pi$
$432$		0			0
$433$	1270.62	−	8837.34i	0.141021	−	0.980821i	−0.789283	−	0.614030i	$-0.789547\pi$
$433$	1270.62	−	8837.34i	0.141021	−	0.980821i	0.930303	−	0.366791i	$-0.119544\pi$
$434$		0			0
$435$	−4099.04	−	4730.54i	−0.451802	−	0.521407i
$436$		0			0
$437$	−7796.37	+	12638.3i	−0.853434	+	1.38346i
$438$		0			0
$439$	2331.99	+	2691.26i	0.253530	+	0.292589i	0.868220	−	0.496180i	$-0.165264\pi$
$439$	2331.99	+	2691.26i	0.253530	+	0.292589i	−0.614690	+	0.788769i	$0.710719\pi$
$440$		0			0
$441$	289.544	−	2013.82i	0.0312649	−	0.217452i
$442$		0			0
$443$	−1335.01	−	9285.20i	−0.143179	−	0.995831i	−0.927058	−	0.374918i	$-0.877671\pi$
$443$	−1335.01	−	9285.20i	−0.143179	−	0.995831i	0.783879	−	0.620914i	$-0.213238\pi$
$444$		0			0
$445$	3298.49	−	2119.81i	0.351379	−	0.225818i
$446$		0			0
$447$	167.136	−	49.0755i	0.0176851	−	0.00519282i
$448$		0			0
$449$	357.985	−	413.136i	0.0376266	−	0.0434234i	−0.736624	−	0.676302i	$-0.763581\pi$
$449$	357.985	−	413.136i	0.0376266	−	0.0434234i	0.774251	+	0.632879i	$0.218127\pi$
$450$		0			0
$451$	−2921.45	−	6397.09i	−0.305024	−	0.667910i
$452$		0			0
$453$	8549.36	+	2510.32i	0.886720	+	0.260364i
$454$		0			0
$455$	−7601.79	+	16645.6i	−0.783247	+	1.71507i
$456$		0			0
$457$	−10959.5	−	7043.24i	−1.12180	−	0.720938i	−0.157968	−	0.987444i	$-0.550494\pi$
$457$	−10959.5	−	7043.24i	−1.12180	−	0.720938i	−0.963833	+	0.266506i	$0.914131\pi$
$458$		0			0
$459$	7872.84			0.800594
$460$		0			0
$461$	4888.31			0.493864			0.246932	−	0.969033i	$-0.420578\pi$
$461$	4888.31			0.493864			0.246932	+	0.969033i	$0.420578\pi$
$462$		0			0
$463$	−4815.06	−	3094.45i	−0.483314	−	0.310607i	0.276197	−	0.961101i	$-0.410926\pi$
$463$	−4815.06	−	3094.45i	−0.483314	−	0.310607i	−0.759512	+	0.650494i	$0.774562\pi$
$464$		0			0
$465$	738.886	−	1617.93i	0.0736882	−	0.161355i
$466$		0			0
$467$	6625.95	+	1945.55i	0.656558	+	0.192783i	0.593009	−	0.805196i	$-0.297940\pi$
$467$	6625.95	+	1945.55i	0.656558	+	0.192783i	0.0635488	+	0.997979i	$0.479758\pi$
$468$		0			0
$469$	1172.77	+	2568.02i	0.115466	+	0.252836i
$470$		0			0
$471$	−4341.58	+	5010.45i	−0.424734	+	0.490169i
$472$		0			0
$473$	−17851.1	+	5241.55i	−1.73529	+	0.509528i
$474$		0			0
$475$	−5344.41	+	3434.64i	−0.516249	+	0.331773i
$476$		0			0
$477$	456.624	+	3175.89i	0.0438310	+	0.304851i
$478$		0			0
$479$	1629.22	−	11331.5i	0.155409	−	1.08089i	−0.751551	−	0.659675i	$-0.770694\pi$
$479$	1629.22	−	11331.5i	0.155409	−	1.08089i	0.906960	−	0.421218i	$-0.138397\pi$
$480$		0			0
$481$	2259.33	+	2607.40i	0.214171	+	0.247167i
$482$		0			0
$483$	−4395.57	−	14008.1i	−0.414090	−	1.31965i
$484$		0			0
$485$	−3118.40	−	3598.82i	−0.291957	−	0.336936i
$486$		0			0
$487$	33.7609	−	234.812i	0.00314138	−	0.0218488i	−0.988190	−	0.153231i	$-0.951032\pi$
$487$	33.7609	−	234.812i	0.00314138	−	0.0218488i	0.991332	+	0.131382i	$0.0419414\pi$
$488$		0			0
$489$	2667.43	+	18552.4i	0.246678	+	1.71568i
$490$		0			0
$491$	−3403.72	+	2187.44i	−0.312847	+	0.201055i	−0.687636	−	0.726056i	$-0.741352\pi$
$491$	−3403.72	+	2187.44i	−0.312847	+	0.201055i	0.374789	+	0.927110i	$0.377715\pi$
$492$		0			0
$493$	−7568.61	+	2222.34i	−0.691426	+	0.203021i
$494$		0			0
$495$	1157.40	−	1335.71i	0.105094	−	0.121284i
$496$		0			0
$497$	6270.50	+	13730.5i	0.565936	+	1.23923i
$498$		0			0
$499$	11244.6	+	3301.71i	1.00877	+	0.296202i	0.744051	−	0.668123i	$-0.232902\pi$
$499$	11244.6	+	3301.71i	1.00877	+	0.296202i	0.264721	+	0.964325i	$0.414720\pi$
$500$		0			0
$501$	−1978.13	+	4331.49i	−0.176400	+	0.386261i
$502$		0			0
$503$	789.832	+	507.594i	0.0700137	+	0.0449951i	0.575179	−	0.818027i	$-0.304932\pi$
$503$	789.832	+	507.594i	0.0700137	+	0.0449951i	−0.505166	+	0.863022i	$0.668569\pi$
$504$		0			0
$505$	3811.74			0.335882
$506$		0			0
$507$	−15418.9			−1.35065
$508$		0			0
$509$	13643.2	+	8767.97i	1.18807	+	0.763524i	0.976852	−	0.213916i	$-0.0686219\pi$
$509$	13643.2	+	8767.97i	1.18807	+	0.763524i	0.211214	+	0.977440i	$0.432258\pi$
$510$		0			0
$511$	3710.71	−	8125.33i	0.321237	−	0.703412i
$512$		0			0
$513$	−19311.0	−	5670.21i	−1.66199	−	0.488004i
$514$		0			0
$515$	−1519.01	−	3326.17i	−0.129972	−	0.284599i
$516$		0			0
$517$	12298.6	−	14193.3i	1.04621	−	1.20739i
$518$		0			0
$519$	16478.1	−	4838.39i	1.39365	−	0.409214i
$520$		0			0
$521$	−3378.90	+	2171.49i	−0.284131	+	0.182600i	−0.674941	−	0.737871i	$-0.735831\pi$
$521$	−3378.90	+	2171.49i	−0.284131	+	0.182600i	0.390811	+	0.920471i	$0.372195\pi$
$522$		0			0
$523$	2591.80	+	18026.4i	0.216695	+	1.50715i	0.750120	+	0.661302i	$0.229996\pi$
$523$	2591.80	+	18026.4i	0.216695	+	1.50715i	−0.533425	+	0.845847i	$0.679095\pi$
$524$		0			0
$525$	893.883	−	6217.10i	0.0743091	−	0.516831i
$526$		0			0
$527$	−1467.86	−	1694.00i	−0.121330	−	0.140023i
$528$		0			0
$529$	8301.63	+	8894.88i	0.682307	+	0.731066i
$530$		0			0
$531$	502.233	+	579.608i	0.0410453	+	0.0473688i
$532$		0			0
$533$	1680.98	−	11691.5i	0.136607	−	0.950123i
$534$		0			0
$535$	−1611.81	−	11210.4i	−0.130252	−	0.905920i
$536$		0			0
$537$	4983.23	−	3202.53i	0.400451	−	0.257354i
$538$		0			0
$539$	18829.2	−	5528.76i	1.50470	−	0.441819i
$540$		0			0
$541$	1540.74	−	1778.10i	0.122443	−	0.141306i	−0.691218	−	0.722646i	$-0.742926\pi$
$541$	1540.74	−	1778.10i	0.122443	−	0.141306i	0.813661	+	0.581340i	$0.197471\pi$
$542$		0			0
$543$	−1892.17	−	4143.28i	−0.149541	−	0.327450i
$544$		0			0
$545$	−11186.7	−	3284.72i	−0.879241	−	0.258168i
$546$		0			0
$547$	2173.18	−	4758.60i	0.169869	−	0.371962i	−0.805482	−	0.592620i	$-0.798093\pi$
$547$	2173.18	−	4758.60i	0.169869	−	0.371962i	0.975351	+	0.220659i	$0.0708207\pi$
$548$		0			0
$549$	1675.51	+	1076.78i	0.130253	+	0.0837085i
$550$		0			0
$551$	20165.3			1.55911
$552$		0			0
$553$	25501.7			1.96102
$554$		0			0
$555$	1642.63	+	1055.65i	0.125632	+	0.0807388i
$556$		0			0
$557$	2544.11	−	5570.82i	0.193532	−	0.423776i	−0.787844	−	0.615875i	$-0.788802\pi$
$557$	2544.11	−	5570.82i	0.193532	−	0.423776i	0.981375	+	0.192100i	$0.0615297\pi$
$558$		0			0
$559$	−29982.1	−	8803.53i	−2.26853	−	0.666099i
$560$		0			0
$561$	4555.96	+	9976.17i	0.342875	+	0.750792i
$562$		0			0
$563$	7389.64	−	8528.10i	0.553173	−	0.638395i	−0.408447	−	0.912782i	$-0.633929\pi$
$563$	7389.64	−	8528.10i	0.553173	−	0.638395i	0.961619	+	0.274387i	$0.0884748\pi$
$564$		0			0
$565$	13134.0	−	3856.49i	0.977968	−	0.287157i
$566$		0			0
$567$	13831.1	−	8888.69i	1.02443	−	0.658360i
$568$		0			0
$569$	−3376.70	−	23485.5i	−0.248785	−	1.73034i	−0.605255	−	0.796032i	$-0.706929\pi$
$569$	−3376.70	−	23485.5i	−0.248785	−	1.73034i	0.356470	−	0.934307i	$-0.383980\pi$
$570$		0			0
$571$	−2258.27	+	15706.6i	−0.165509	+	1.15114i	0.722519	+	0.691351i	$0.242984\pi$
$571$	−2258.27	+	15706.6i	−0.165509	+	1.15114i	−0.888028	+	0.459789i	$0.847925\pi$
$572$		0			0
$573$	6171.66	+	7122.47i	0.449956	+	0.519277i
$574$		0			0
$575$	1558.42	+	4966.48i	0.113027	+	0.360203i
$576$		0			0
$577$	2881.64	+	3325.59i	0.207910	+	0.239941i	0.850122	−	0.526586i	$-0.176528\pi$
$577$	2881.64	+	3325.59i	0.207910	+	0.239941i	−0.642212	+	0.766527i	$0.721983\pi$
$578$		0			0
$579$	2223.27	−	15463.2i	0.159579	−	1.10989i
$580$		0			0
$581$	635.616	+	4420.81i	0.0453869	+	0.315673i
$582$		0			0
$583$	−26035.3	+	16731.9i	−1.84952	+	1.18862i
$584$		0			0
$585$	2848.22	−	836.312i	0.201298	−	0.0591064i
$586$		0			0
$587$	−9447.39	+	10902.9i	−0.664285	+	0.766626i	−0.983471	−	0.181066i	$-0.942045\pi$
$587$	−9447.39	+	10902.9i	−0.664285	+	0.766626i	0.319186	+	0.947692i	$0.396591\pi$
$588$		0			0
$589$	2380.39	+	5212.34i	0.166524	+	0.364636i
$590$		0			0
$591$	−16528.7	−	4853.26i	−1.15042	−	0.337794i
$592$		0			0
$593$	−2489.40	+	5451.03i	−0.172390	+	0.377482i	−0.976031	−	0.217633i	$-0.930166\pi$
$593$	−2489.40	+	5451.03i	−0.172390	+	0.377482i	0.803640	+	0.595115i	$0.202894\pi$
$594$		0			0
$595$	10979.5	+	7056.12i	0.756500	+	0.486173i
$596$		0			0
$597$	−10366.2			−0.710651
$598$		0			0
$599$	464.556			0.0316882			0.0158441	−	0.999874i	$-0.494956\pi$
$599$	464.556			0.0316882			0.0158441	+	0.999874i	$0.494956\pi$
$600$		0			0
$601$	6087.44	+	3912.16i	0.413164	+	0.265525i	0.730669	−	0.682732i	$-0.239208\pi$
$601$	6087.44	+	3912.16i	0.413164	+	0.265525i	−0.317504	+	0.948257i	$0.602845\pi$
$602$		0			0
$603$	190.245	−	416.578i	0.0128480	−	0.0281333i
$604$		0			0
$605$	5091.82	+	1495.09i	0.342168	+	0.100470i
$606$		0			0
$607$	7768.61	+	17010.9i	0.519470	+	1.13748i	0.969640	+	0.244537i	$0.0786360\pi$
$607$	7768.61	+	17010.9i	0.519470	+	1.13748i	−0.450170	+	0.892943i	$0.648637\pi$
$608$		0			0
$609$	−13056.0	+	15067.5i	−0.868731	+	1.00257i
$610$		0			0
$611$	30265.3	−	8886.70i	2.00393	−	0.588408i
$612$		0			0
$613$	−6056.83	+	3892.49i	−0.399075	+	0.256470i	−0.724750	−	0.689012i	$-0.758045\pi$
$613$	−6056.83	+	3892.49i	−0.399075	+	0.256470i	0.325675	+	0.945482i	$0.394408\pi$
$614$		0			0
$615$	−951.364	−	6616.88i	−0.0623784	−	0.433851i
$616$		0			0
$617$	−4163.62	+	28958.6i	−0.271671	+	1.88951i	0.159428	+	0.987210i	$0.449035\pi$
$617$	−4163.62	+	28958.6i	−0.271671	+	1.88951i	−0.431099	+	0.902305i	$0.641874\pi$
$618$		0			0
$619$	−13969.2	−	16121.3i	−0.907059	−	1.04680i	−0.998698	−	0.0510100i	$-0.983756\pi$
$619$	−13969.2	−	16121.3i	−0.907059	−	1.04680i	0.0916388	−	0.995792i	$-0.470789\pi$
$620$		0			0
$621$	−8657.81	+	14034.8i	−0.559462	+	0.906918i
$622$		0			0
$623$	−8178.38	−	9438.35i	−0.525939	−	0.606966i
$624$		0			0
$625$	1067.27	−	7423.02i	0.0683053	−	0.475073i
$626$		0			0
$627$	−3990.05	−	27751.4i	−0.254143	−	1.76760i
$628$		0			0
$629$	2070.05	−	1330.34i	0.131221	−	0.0843309i
$630$		0			0
$631$	−4616.20	+	1355.44i	−0.291233	+	0.0855137i	−0.424086	−	0.905622i	$-0.639404\pi$
$631$	−4616.20	+	1355.44i	−0.291233	+	0.0855137i	0.132853	+	0.991136i	$0.457586\pi$
$632$		0			0
$633$	−698.611	+	806.240i	−0.0438662	+	0.0506243i
$634$		0			0
$635$	−5498.38	−	12039.8i	−0.343617	−	0.752416i
$636$		0			0
$637$	31624.9	+	9285.91i	1.96707	+	0.577584i
$638$		0			0
$639$	1017.19	−	2227.33i	0.0629722	−	0.137890i
$640$		0			0
$641$	−14037.8	−	9021.57i	−0.864994	−	0.555898i	0.0312234	−	0.999512i	$-0.490060\pi$
$641$	−14037.8	−	9021.57i	−0.864994	−	0.555898i	−0.896218	+	0.443614i	$0.853696\pi$
$642$		0			0
$643$	−4851.02			−0.297520			−0.148760	−	0.988873i	$-0.547528\pi$
$643$	−4851.02			−0.297520			−0.148760	+	0.988873i	$0.547528\pi$
$644$		0			0
$645$	−17684.9			−1.07960
$646$		0			0
$647$	2220.77	+	1427.20i	0.134942	+	0.0867218i	0.606370	−	0.795183i	$-0.292625\pi$
$647$	2220.77	+	1427.20i	0.134942	+	0.0867218i	−0.471428	+	0.881904i	$0.656261\pi$
$648$		0			0
$649$	−3073.02	+	6728.97i	−0.185865	+	0.406988i
$650$		0			0
$651$	−5435.83	−	1596.10i	−0.327261	−	0.0960926i
$652$		0			0
$653$	2294.31	+	5023.83i	0.137493	+	0.301068i	0.965836	−	0.259153i	$-0.0834434\pi$
$653$	2294.31	+	5023.83i	0.137493	+	0.301068i	−0.828343	+	0.560221i	$0.810716\pi$
$654$		0			0
$655$	−1203.21	+	1388.58i	−0.0717762	+	0.0828341i
$656$		0			0
$657$	−1390.32	+	408.235i	−0.0825595	+	0.0242417i
$658$		0			0
$659$	−2051.33	+	1318.31i	−0.121257	+	0.0779271i	−0.599863	−	0.800102i	$-0.704778\pi$
$659$	−2051.33	+	1318.31i	−0.121257	+	0.0779271i	0.478607	+	0.878029i	$0.341142\pi$
$660$		0			0
$661$	−1145.10	−	7964.35i	−0.0673816	−	0.468649i	−0.995376	−	0.0960552i	$-0.969377\pi$
$661$	−1145.10	−	7964.35i	−0.0673816	−	0.468649i	0.927994	−	0.372594i	$-0.121532\pi$
$662$		0			0
$663$	−2621.47	+	18232.7i	−0.153559	+	1.06802i
$664$		0			0
$665$	−21849.3	−	25215.4i	−1.27410	−	1.47039i
$666$		0			0
$667$	4361.51	−	15936.3i	0.253191	−	0.925124i
$668$		0			0
$669$	1537.55	+	1774.42i	0.0888564	+	0.102546i
$670$		0			0
$671$	−2733.98	+	19015.3i	−0.157294	+	1.09400i
$672$		0			0
$673$	1130.94	+	7865.86i	0.0647764	+	0.450530i	0.996236	+	0.0866846i	$0.0276273\pi$
$673$	1130.94	+	7865.86i	0.0647764	+	0.450530i	−0.931459	+	0.363845i	$0.881464\pi$
$674$		0			0
$675$	−5934.93	+	3814.15i	−0.338423	+	0.217491i
$676$		0			0
$677$	13587.4	−	3989.61i	0.771352	−	0.226489i	0.127705	−	0.991812i	$-0.459239\pi$
$677$	13587.4	−	3989.61i	0.771352	−	0.226489i	0.643647	+	0.765323i	$0.277421\pi$
$678$		0			0
$679$	−9932.55	+	11462.8i	−0.561379	+	0.647866i
$680$		0			0
$681$	−4063.66	−	8898.18i	−0.228664	−	0.500703i
$682$		0			0
$683$	1138.99	+	334.436i	0.0638097	+	0.0187362i	0.313482	−	0.949594i	$-0.398505\pi$
$683$	1138.99	+	334.436i	0.0638097	+	0.0187362i	−0.249672	+	0.968330i	$0.580323\pi$
$684$		0			0
$685$	2564.34	−	5615.11i	0.143034	−	0.313201i
$686$		0			0
$687$	3641.11	+	2340.00i	0.202208	+	0.129951i
$688$		0			0
$689$	−51979.5			−2.87411
$690$		0			0
$691$	16829.8			0.926535			0.463268	−	0.886218i	$-0.346677\pi$
$691$	16829.8			0.926535			0.463268	+	0.886218i	$0.346677\pi$
$692$		0			0
$693$	−4735.77	−	3043.50i	−0.259592	−	0.166830i
$694$		0			0
$695$	−9744.07	+	21336.5i	−0.531818	+	1.16452i
$696$		0			0
$697$	−8083.12	−	2373.42i	−0.439269	−	0.128981i
$698$		0			0
$699$	8977.32	+	19657.6i	0.485770	+	1.06369i
$700$		0			0
$701$	16155.2	−	18644.1i	0.870435	−	1.00454i	−0.129481	−	0.991582i	$-0.541331\pi$
$701$	16155.2	−	18644.1i	0.870435	−	1.00454i	0.999916	−	0.0129534i	$-0.00412331\pi$
$702$		0			0
$703$	−6035.68	+	1772.24i	−0.323812	+	0.0950798i
$704$		0			0
$705$	15018.0	−	9651.51i	0.802287	−	0.515598i
$706$		0			0
$707$	−1727.84	−	12017.4i	−0.0919123	−	0.639264i
$708$		0			0
$709$	1993.72	−	13866.6i	0.105608	−	0.734517i	−0.866363	−	0.499415i	$-0.833548\pi$
$709$	1993.72	−	13866.6i	0.105608	−	0.734517i	0.971971	−	0.235102i	$-0.0755425\pi$
$710$		0			0
$711$	−2709.05	−	3126.41i	−0.142893	−	0.164908i
$712$		0			0
$713$	4634.08	−	753.826i	0.243405	−	0.0395947i
$714$		0			0
$715$	18750.3	+	21638.9i	0.980727	+	1.13182i
$716$		0			0
$717$	−520.927	+	3623.12i	−0.0271330	+	0.188714i
$718$		0			0
$719$	−3412.19	−	23732.3i	−0.176986	−	1.23097i	−0.863688	−	0.504027i	$-0.831851\pi$
$719$	−3412.19	−	23732.3i	−0.176986	−	1.23097i	0.686702	−	0.726939i	$-0.259058\pi$
$720$		0			0
$721$	−9797.95	+	6296.76i	−0.506095	+	0.325248i
$722$		0			0
$723$	−25582.1	+	7511.59i	−1.31592	+	0.386389i
$724$		0			0
$725$	4628.93	−	5342.07i	0.237123	−	0.273654i
$726$		0			0
$727$	14318.9	+	31354.0i	0.730479	+	1.59953i	0.798610	+	0.601849i	$0.205569\pi$
$727$	14318.9	+	31354.0i	0.730479	+	1.59953i	−0.0681312	+	0.997676i	$0.521704\pi$
$728$		0			0
$729$	−20906.6	−	6138.72i	−1.06216	−	0.311879i
$730$		0			0
$731$	−9258.18	+	20272.6i	−0.468435	+	1.02573i
$732$		0			0
$733$	13151.8	+	8452.15i	0.662719	+	0.425903i	0.828294	−	0.560294i	$-0.189312\pi$
$733$	13151.8	+	8452.15i	0.662719	+	0.425903i	−0.165575	+	0.986197i	$0.552948\pi$
$734$		0			0
$735$	18653.9			0.936137
$736$		0			0
$737$	4417.30			0.220778
$738$		0			0
$739$	22678.3	+	14574.4i	1.12887	+	0.725480i	0.965324	−	0.261056i	$-0.0840708\pi$
$739$	22678.3	+	14574.4i	1.12887	+	0.725480i	0.163545	+	0.986536i	$0.447707\pi$
$740$		0			0
$741$	19561.7	−	42834.2i	0.969796	−	2.12356i
$742$		0			0
$743$	6904.05	+	2027.21i	0.340895	+	0.100096i	0.447699	−	0.894184i	$-0.352244\pi$
$743$	6904.05	+	2027.21i	0.340895	+	0.100096i	−0.106804	+	0.994280i	$0.534062\pi$
$744$		0			0
$745$	−134.739	−	295.038i	−0.00662612	−	0.0145092i
$746$		0			0
$747$	474.452	−	547.546i	0.0232387	−	0.0268188i
$748$		0			0
$749$	−34612.6	+	10163.2i	−1.68854	+	0.495801i
$750$		0			0
$751$	−7957.13	+	5113.74i	−0.386631	+	0.248473i	−0.719488	−	0.694505i	$-0.755624\pi$
$751$	−7957.13	+	5113.74i	−0.386631	+	0.248473i	0.332857	+	0.942977i	$0.391987\pi$
$752$		0			0
$753$	−3788.19	−	26347.4i	−0.183332	−	1.27510i
$754$		0			0
$755$	2361.16	−	16422.3i	0.113817	−	0.791612i
$756$		0			0
$757$	864.732	+	997.954i	0.0415181	+	0.0479145i	0.776129	−	0.630574i	$-0.217181\pi$
$757$	864.732	+	997.954i	0.0415181	+	0.0479145i	−0.734611	+	0.678489i	$0.762635\pi$
$758$		0			0
$759$	−22794.6	−	2849.02i	−1.09011	−	0.136249i
$760$		0			0
$761$	6492.66	+	7492.93i	0.309276	+	0.356923i	0.889014	−	0.457879i	$-0.151391\pi$
$761$	6492.66	+	7492.93i	0.309276	+	0.356923i	−0.579739	+	0.814803i	$0.696845\pi$
$762$		0			0
$763$	−5284.94	+	36757.6i	−0.250757	+	1.74405i
$764$		0			0
$765$	−301.304	−	2095.62i	−0.0142401	−	0.0990422i
$766$		0			0
$767$	−10452.2	+	6717.20i	−0.492055	+	0.316224i
$768$		0			0
$769$	7370.30	−	2164.12i	0.345618	−	0.101482i	−0.104317	−	0.994544i	$-0.533266\pi$
$769$	7370.30	−	2164.12i	0.345618	−	0.101482i	0.449934	+	0.893062i	$0.351447\pi$
$770$		0			0
$771$	9122.21	−	10527.6i	0.426107	−	0.491753i
$772$		0			0
$773$	−8869.76	−	19422.1i	−0.412708	−	0.903704i	−0.995822	−	0.0913137i	$-0.970893\pi$
$773$	−8869.76	−	19422.1i	−0.412708	−	0.903704i	0.583115	−	0.812390i	$-0.301834\pi$
$774$		0			0
$775$	1927.24	+	565.888i	0.0893270	+	0.0262288i
$776$		0			0
$777$	2583.59	−	5657.28i	0.119287	−	0.261202i
$778$		0			0
$779$	18117.4	+	11643.3i	0.833276	+	0.535514i
$780$		0			0
$781$	23618.1			1.08210
$782$		0			0
$783$	22393.4			1.02206
$784$		0			0
$785$	10385.1	+	6674.09i	0.472178	+	0.303450i
$786$		0			0
$787$	−1057.39	+	2315.36i	−0.0478930	+	0.104871i	−0.932066	−	0.362289i	$-0.881995\pi$
$787$	−1057.39	+	2315.36i	−0.0478930	+	0.104871i	0.884173	+	0.467160i	$0.154723\pi$
$788$		0			0
$789$	31637.8	+	9289.69i	1.42755	+	0.419166i
$790$		0			0
$791$	−18112.0	−	39659.8i	−0.814146	−	1.78273i
$792$		0			0
$793$	−21129.6	+	24384.9i	−0.946197	+	1.09197i
$794$		0			0
$795$	−28226.5	+	8288.04i	−1.25923	+	0.369744i
$796$		0			0
$797$	−16713.8	+	10741.3i	−0.742825	+	0.477385i	−0.856509	−	0.516132i	$-0.827371\pi$
$797$	−16713.8	+	10741.3i	−0.742825	+	0.477385i	0.113684	+	0.993517i	$0.463735\pi$
$798$		0			0
$799$	−3201.68	−	22268.2i	−0.141761	−	0.985971i
$800$		0			0
$801$	−288.315	+	2005.27i	−0.0127180	+	0.0884554i
$802$		0			0
$803$	−9152.70	−	10562.8i	−0.402231	−	0.464200i
$804$		0			0
$805$	−24653.1	+	11813.4i	−1.07939	+	0.517226i
$806$		0			0
$807$	19668.8	+	22699.0i	0.857962	+	0.990140i
$808$		0			0
$809$	4938.99	−	34351.4i	0.214642	−	1.49287i	−0.542742	−	0.839900i	$-0.682614\pi$
$809$	4938.99	−	34351.4i	0.214642	−	1.49287i	0.757384	−	0.652970i	$-0.226477\pi$
$810$		0			0
$811$	5141.53	+	35760.1i	0.222619	+	1.54835i	0.728077	+	0.685495i	$0.240414\pi$
$811$	5141.53	+	35760.1i	0.222619	+	1.54835i	−0.505459	+	0.862851i	$0.668677\pi$
$812$		0			0
$813$	5974.67	−	3839.69i	0.257738	−	0.165638i
$814$		0			0
$815$	33486.5	−	9832.51i	1.43924	−	0.422599i
$816$		0			0
$817$	37309.8	−	43057.8i	1.59768	−	1.84382i
$818$		0			0
$819$	−3927.74	−	8600.56i	−0.167578	−	0.366945i
$820$		0			0
$821$	33085.1	+	9714.67i	1.40643	+	0.412965i	0.894887	−	0.446293i	$-0.147256\pi$
$821$	33085.1	+	9714.67i	1.40643	+	0.412965i	0.511543	+	0.859258i	$0.329074\pi$
$822$		0			0
$823$	17538.5	−	38404.0i	0.742837	−	1.62659i	−0.0359943	−	0.999352i	$-0.511460\pi$
$823$	17538.5	−	38404.0i	0.742837	−	1.62659i	0.778831	−	0.627234i	$-0.215813\pi$
$824$		0			0
$825$	−8267.66	−	5313.30i	−0.348900	−	0.224225i
$826$		0			0
$827$	−5257.27			−0.221056			−0.110528	−	0.993873i	$-0.535254\pi$
$827$	−5257.27			−0.221056			−0.110528	+	0.993873i	$0.535254\pi$
$828$		0			0
$829$	17578.0			0.736439			0.368220	−	0.929739i	$-0.379967\pi$
$829$	17578.0			0.736439			0.368220	+	0.929739i	$0.379967\pi$
$830$		0			0
$831$	36094.6	+	23196.6i	1.50675	+	0.968328i
$832$		0			0
$833$	9765.48	−	21383.4i	0.406187	−	0.889426i
$834$		0			0
$835$	8507.42	+	2498.00i	0.352588	+	0.103529i
$836$		0			0
$837$	2643.41	+	5788.26i	0.109163	+	0.239034i
$838$		0			0
$839$	−16408.9	+	18936.9i	−0.675207	+	0.779231i	−0.985182	−	0.171514i	$-0.945134\pi$
$839$	−16408.9	+	18936.9i	−0.675207	+	0.779231i	0.309974	+	0.950745i	$0.399680\pi$
$840$		0			0
$841$	1873.01	−	549.965i	0.0767973	−	0.0225497i
$842$		0			0
$843$	33394.7	−	21461.5i	1.36438	−	0.876835i
$844$		0			0
$845$	4085.90	+	28418.1i	0.166342	+	1.15694i
$846$		0			0
$847$	2405.53	−	16730.8i	0.0975855	−	0.678722i
$848$		0			0
$849$	21673.8	+	25012.9i	0.876142	+	1.01112i
$850$		0			0
$851$	95.1277	+	5153.22i	0.00383189	+	0.207580i
$852$		0			0
$853$	−18287.2	−	21104.6i	−0.734048	−	0.847137i	0.258873	−	0.965911i	$-0.416649\pi$
$853$	−18287.2	−	21104.6i	−0.734048	−	0.847137i	−0.992921	+	0.118774i	$0.962103\pi$
$854$		0			0
$855$	−770.258	+	5357.26i	−0.0308097	+	0.214286i
$856$		0			0
$857$	6123.32	+	42588.6i	0.244071	+	1.69755i	0.631278	+	0.775557i	$0.282531\pi$
$857$	6123.32	+	42588.6i	0.244071	+	1.69755i	−0.387207	+	0.921993i	$0.626560\pi$
$858$		0			0
$859$	7747.97	−	4979.32i	0.307750	−	0.197779i	−0.377645	−	0.925951i	$-0.623266\pi$
$859$	7747.97	−	4979.32i	0.307750	−	0.197779i	0.685395	+	0.728172i	$0.259630\pi$
$860$		0			0
$861$	−20430.0	+	5998.78i	−0.808654	+	0.237442i
$862$		0			0
$863$	−4230.54	+	4882.30i	−0.166870	+	0.192579i	−0.833026	−	0.553234i	$-0.813393\pi$
$863$	−4230.54	+	4882.30i	−0.166870	+	0.192579i	0.666155	+	0.745813i	$0.267939\pi$
$864$		0			0
$865$	−13284.0	−	29088.0i	−0.522163	−	1.14338i
$866$		0			0
$867$	−9726.21	−	2855.87i	−0.380991	−	0.111869i
$868$		0			0
$869$	16575.9	−	36296.1i	0.647064	−	1.41687i
$870$		0			0
$871$	6241.38	+	4011.09i	0.242803	+	0.156040i
$872$		0			0
$873$	2460.42			0.0953869
$874$		0			0
$875$	−42674.9			−1.64877
$876$		0			0
$877$	−32573.6	−	20933.8i	−1.25420	−	0.806025i	−0.266721	−	0.963774i	$-0.585940\pi$
$877$	−32573.6	−	20933.8i	−1.25420	−	0.806025i	−0.987479	+	0.157749i	$0.949576\pi$
$878$		0			0
$879$	6130.20	−	13423.3i	0.235229	−	0.515080i
$880$		0			0
$881$	22751.4	+	6680.42i	0.870051	+	0.255470i	0.686137	−	0.727472i	$-0.259305\pi$
$881$	22751.4	+	6680.42i	0.870051	+	0.255470i	0.183914	+	0.982942i	$0.441123\pi$
$882$		0			0
$883$	−16837.9	−	36869.8i	−0.641721	−	1.40517i	−0.898617	−	0.438735i	$-0.855427\pi$
$883$	−16837.9	−	36869.8i	−0.641721	−	1.40517i	0.256895	−	0.966439i	$-0.417300\pi$
$884$		0			0
$885$	−4604.81	+	5314.23i	−0.174903	+	0.201849i
$886$		0			0
$887$	−30917.9	+	9078.32i	−1.17037	+	0.343653i	−0.808456	−	0.588557i	$-0.799696\pi$
$887$	−30917.9	+	9078.32i	−1.17037	+	0.343653i	−0.361919	+	0.932210i	$0.617878\pi$
$888$		0			0
$889$	−35465.7	+	22792.4i	−1.33800	+	0.859881i
$890$		0			0
$891$	−3661.03	−	25463.1i	−0.137654	−	0.957401i
$892$		0			0
$893$	−8184.80	+	56926.5i	−0.306712	+	2.13323i
$894$		0			0
$895$	−7222.99	−	8335.78i	−0.269763	−	0.311323i
$896$		0			0
$897$	−29620.3	−	24723.9i	−1.10256	−	0.920298i
$898$		0			0
$899$	−4175.17	−	4818.40i	−0.154894	−	0.178757i
$900$		0			0
$901$	−5276.02	+	36695.5i	−0.195083	+	1.35683i
$902$		0			0
$903$	8016.45	+	55755.6i	0.295427	+	2.05474i
$904$		0			0
$905$	−7134.93	+	4585.34i	−0.262070	+	0.168422i
$906$		0			0
$907$	8471.30	−	2487.40i	0.310127	−	0.0910614i	−0.122966	−	0.992411i	$-0.539241\pi$
$907$	8471.30	−	2487.40i	0.310127	−	0.0910614i	0.433092	+	0.901349i	$0.357422\pi$
$908$		0			0
$909$	−1289.73	+	1488.43i	−0.0470602	+	0.0543104i
$910$		0			0
$911$	−4086.74	−	8948.70i	−0.148627	−	0.325449i	0.820645	−	0.571438i	$-0.193614\pi$
$911$	−4086.74	−	8948.70i	−0.148627	−	0.325449i	−0.969272	+	0.245990i	$0.920887\pi$
$912$		0			0
$913$	6705.20	+	1968.82i	0.243055	+	0.0713675i
$914$		0			0
$915$	−7585.91	+	16610.8i	−0.274079	+	0.600150i
$916$		0			0
$917$	4923.22	+	3163.96i	0.177295	+	0.113940i
$918$		0			0
$919$	−36234.6			−1.30062			−0.650309	−	0.759670i	$-0.725361\pi$
$919$	−36234.6			−1.30062			−0.650309	+	0.759670i	$0.725361\pi$
$920$		0			0
$921$	−12287.6			−0.439621
$922$		0			0
$923$	33370.9	+	21446.2i	1.19005	+	0.764800i
$924$		0			0
$925$	−915.995	+	2005.75i	−0.0325597	+	0.0712959i
$926$		0			0
$927$	1812.79	+	532.284i	0.0642286	+	0.0188592i
$928$		0			0
$929$	4468.90	+	9785.52i	0.157825	+	0.345589i	0.971982	−	0.235056i	$-0.0755275\pi$
$929$	4468.90	+	9785.52i	0.157825	+	0.345589i	−0.814156	+	0.580646i	$0.802800\pi$
$930$		0			0
$931$	−39354.2	+	45417.2i	−1.38537	+	1.59880i
$932$		0			0
$933$	43140.4	−	12667.2i	1.51378	−	0.444485i
$934$		0			0
$935$	17179.4	−	11040.6i	0.600885	−	0.386166i
$936$		0			0
$937$	−1137.56	−	7911.88i	−0.0396610	−	0.275848i	0.960335	−	0.278851i	$-0.0899534\pi$
$937$	−1137.56	−	7911.88i	−0.0396610	−	0.275848i	−0.999995	+	0.00300237i	$0.999044\pi$
$938$		0			0
$939$	899.249	−	6254.41i	0.0312523	−	0.217364i
$940$		0			0
$941$	−17593.9	−	20304.5i	−0.609507	−	0.703408i	0.364172	−	0.931332i	$-0.381352\pi$
$941$	−17593.9	−	20304.5i	−0.609507	−	0.703408i	−0.973679	+	0.227923i	$0.926806\pi$
$942$		0			0
$943$	13120.1	−	11799.6i	0.453075	−	0.407473i
$944$		0			0
$945$	−24263.5	−	28001.5i	−0.835228	−	0.963904i
$946$		0			0
$947$	4097.43	−	28498.3i	0.140601	−	0.977898i	−0.790325	−	0.612688i	$-0.790088\pi$
$947$	4097.43	−	28498.3i	0.140601	−	0.977898i	0.930925	−	0.365210i	$-0.119003\pi$
$948$		0			0
$949$	−3340.77	−	23235.6i	−0.114274	−	0.794794i
$950$		0			0
$951$	−35920.6	+	23084.8i	−1.22482	+	0.787145i
$952$		0			0
$953$	20434.2	−	6000.04i	0.694575	−	0.203946i	0.0846571	−	0.996410i	$-0.473021\pi$
$953$	20434.2	−	6000.04i	0.694575	−	0.203946i	0.609918	+	0.792464i	$0.291202\pi$
$954$		0			0
$955$	11491.7	−	13262.2i	0.389386	−	0.449376i
$956$		0			0
$957$	12958.9	+	28376.1i	0.437725	+	0.958484i
$958$		0			0
$959$	−18865.3	−	5539.36i	−0.635237	−	0.186523i
$960$		0			0
$961$	−11623.0	+	25450.9i	−0.390152	+	0.854314i
$962$		0			0
$963$	4922.87	+	3163.73i	0.164732	+	0.105867i
$964$		0			0
$965$	−29088.9			−0.970367
$966$		0			0
$967$	19497.6			0.648397			0.324198	−	0.945989i	$-0.394905\pi$
$967$	19497.6			0.648397			0.324198	+	0.945989i	$0.394905\pi$
$968$		0			0
$969$	−28253.8	−	18157.6i	−0.936678	−	0.601967i
$970$		0			0
$971$	−6126.08	+	13414.2i	−0.202467	+	0.443340i	−0.983442	−	0.181221i	$-0.941995\pi$
$971$	−6126.08	+	13414.2i	−0.202467	+	0.443340i	0.780976	+	0.624562i	$0.214722\pi$
$972$		0			0
$973$	71685.2	+	21048.7i	2.36189	+	0.693514i
$974$		0			0
$975$	−6857.00	−	15014.7i	−0.225231	−	0.493186i
$976$		0			0
$977$	−36619.3	+	42260.9i	−1.19914	+	1.38388i	−0.295628	+	0.955303i	$0.595529\pi$
$977$	−36619.3	+	42260.9i	−1.19914	+	1.38388i	−0.903507	+	0.428572i	$0.859017\pi$
$978$		0			0
$979$	−18749.3	+	5505.29i	−0.612084	+	0.179724i
$980$		0			0
$981$	5067.75	−	3256.84i	0.164935	−	0.105997i
$982$		0			0
$983$	5433.02	+	37787.5i	0.176283	+	1.22608i	0.865271	+	0.501304i	$0.167146\pi$
$983$	5433.02	+	37787.5i	0.176283	+	1.22608i	−0.688988	+	0.724773i	$0.741945\pi$
$984$		0			0
$985$	−4564.89	+	31749.5i	−0.147665	+	1.02703i
$986$		0			0
$987$	−37236.1	−	42972.8i	−1.20085	−	1.38586i
$988$		0			0
$989$	−25958.3	−	38798.3i	−0.834607	−	1.24744i
$990$		0			0
$991$	−17450.5	−	20139.0i	−0.559369	−	0.645546i	0.403671	−	0.914904i	$-0.367734\pi$
$991$	−17450.5	−	20139.0i	−0.559369	−	0.645546i	−0.963040	+	0.269358i	$0.913188\pi$
$992$		0			0
$993$	−5417.99	+	37682.9i	−0.173147	+	1.20426i
$994$		0			0
$995$	2746.96	+	19105.5i	0.0875220	+	0.608729i
$996$		0			0
$997$	−47250.6	+	30366.1i	−1.50094	+	0.964598i	−0.506176	+	0.862430i	$0.668941\pi$
$997$	−47250.6	+	30366.1i	−1.50094	+	0.964598i	−0.994767	+	0.102168i	$0.967422\pi$
$998$		0			0
$999$	−6702.58	+	1968.06i	−0.212273	+	0.0623288i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	92.4.e.a.13.2	✓	60
23.4	even	11		2116.4.a.i.1.8		30
23.16	even	11	inner	92.4.e.a.85.2	yes	60
23.19	odd	22		2116.4.a.j.1.8		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
92.4.e.a.13.2	✓	60	1.1	even	1	trivial
92.4.e.a.85.2	yes	60	23.16	even	11	inner
2116.4.a.i.1.8		30	23.4	even	11
2116.4.a.j.1.8		30	23.19	odd	22

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:	\( N \)	\(=\)	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	92.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.98530 - 2.56119i) q^{3} +(-3.66438 + 8.02386i) q^{5} +(26.9581 + 7.91560i) q^{7} +(-1.89333 - 4.14582i) q^{9} +O(q^{10})\)	\(q+(-3.98530 - 2.56119i) q^{3} +(-3.66438 + 8.02386i) q^{5} +(26.9581 + 7.91560i) q^{7} +(-1.89333 - 4.14582i) q^{9} +(28.7886 - 33.2238i) q^{11} +(70.8452 - 20.8020i) q^{13} +(35.1543 - 22.5923i) q^{15} +(-7.49450 - 52.1254i) q^{17} +(-19.1590 + 133.254i) q^{19} +(-87.1625 - 100.591i) q^{21} +(101.165 + 43.9623i) q^{23} +(30.9029 + 35.6638i) q^{25} +(-21.2760 + 147.978i) q^{27} +(-21.3173 - 148.265i) q^{29} +(35.8072 - 23.0119i) q^{31} +(-199.824 + 58.6736i) q^{33} +(-162.298 + 187.302i) q^{35} +(19.4108 + 42.5037i) q^{37} +(-335.617 - 98.5461i) q^{39} +(66.4549 - 145.516i) q^{41} +(-356.023 - 228.802i) q^{43} +40.2034 q^{45} +427.204 q^{47} +(375.531 + 241.339i) q^{49} +(-103.635 + 226.930i) q^{51} +(-675.469 - 198.336i) q^{53} +(161.091 + 352.740i) q^{55} +(417.644 - 481.986i) q^{57} +(-161.456 + 47.4076i) q^{59} +(-367.622 + 236.256i) q^{61} +(-18.2239 - 126.750i) q^{63} +(-92.6908 + 644.678i) q^{65} +(65.8013 + 75.9387i) q^{67} +(-290.576 - 434.306i) q^{69} +(351.821 + 406.023i) q^{71} +(45.2458 - 314.692i) q^{73} +(-31.8151 - 221.279i) q^{75} +(1039.07 - 667.771i) q^{77} +(870.892 - 255.717i) q^{79} +(383.205 - 442.242i) q^{81} +(66.0359 + 144.598i) q^{83} +(445.710 + 130.872i) q^{85} +(-294.780 + 645.477i) q^{87} +(-373.937 - 240.315i) q^{89} +2074.51 q^{91} -201.640 q^{93} +(-999.005 - 642.022i) q^{95} +(-224.258 + 491.056i) q^{97} +(-192.247 - 56.4487i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 4 q^{3} + 10 q^{5} + 4 q^{7} - 50 q^{9}+O(q^{10}) \) 60 * q - 4 * q^3 + 10 * q^5 + 4 * q^7 - 50 * q^9	\( 60 q - 4 q^{3} + 10 q^{5} + 4 q^{7} - 50 q^{9} + 58 q^{11} - 56 q^{13} - 246 q^{15} + 28 q^{17} + 84 q^{19} + 560 q^{21} + 484 q^{23} + 274 q^{25} - 358 q^{27} - 400 q^{29} - 334 q^{31} - 668 q^{33} + 1510 q^{35} + 1374 q^{37} - 420 q^{39} - 554 q^{41} - 1218 q^{43} - 2812 q^{45} - 1468 q^{47} - 2704 q^{49} - 668 q^{51} + 8 q^{53} - 304 q^{55} + 1732 q^{57} + 1270 q^{59} + 1242 q^{61} + 38 q^{63} + 4984 q^{65} + 3018 q^{67} + 3464 q^{69} + 2162 q^{71} + 932 q^{73} + 5748 q^{75} + 1052 q^{77} - 1238 q^{79} - 4130 q^{81} - 4154 q^{83} - 5282 q^{85} - 4862 q^{87} - 1594 q^{89} - 4700 q^{91} + 4044 q^{93} - 5714 q^{95} - 9698 q^{97} - 4566 q^{99}+O(q^{100}) \) 60 * q - 4 * q^3 + 10 * q^5 + 4 * q^7 - 50 * q^9 + 58 * q^11 - 56 * q^13 - 246 * q^15 + 28 * q^17 + 84 * q^19 + 560 * q^21 + 484 * q^23 + 274 * q^25 - 358 * q^27 - 400 * q^29 - 334 * q^31 - 668 * q^33 + 1510 * q^35 + 1374 * q^37 - 420 * q^39 - 554 * q^41 - 1218 * q^43 - 2812 * q^45 - 1468 * q^47 - 2704 * q^49 - 668 * q^51 + 8 * q^53 - 304 * q^55 + 1732 * q^57 + 1270 * q^59 + 1242 * q^61 + 38 * q^63 + 4984 * q^65 + 3018 * q^67 + 3464 * q^69 + 2162 * q^71 + 932 * q^73 + 5748 * q^75 + 1052 * q^77 - 1238 * q^79 - 4130 * q^81 - 4154 * q^83 - 5282 * q^85 - 4862 * q^87 - 1594 * q^89 - 4700 * q^91 + 4044 * q^93 - 5714 * q^95 - 9698 * q^97 - 4566 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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