LMFDB - Embedded newform 403.2.c.b.311.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(311,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("403.311");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			311.21
Character	$\chi$	$=$	403.311
Dual form			403.2.c.b.311.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.01245i q^{2} -1.05136 q^{3} +0.974950 q^{4} +3.24438i q^{5} -1.06445i q^{6} +1.79572i q^{7} +3.01198i q^{8} -1.89463 q^{9} +O(q^{10})$	\(q+1.01245i q^{2} -1.05136 q^{3} +0.974950 q^{4} +3.24438i q^{5} -1.06445i q^{6} +1.79572i q^{7} +3.01198i q^{8} -1.89463 q^{9} -3.28477 q^{10} -6.09683i q^{11} -1.02503 q^{12} +(-1.47046 + 3.29207i) q^{13} -1.81807 q^{14} -3.41103i q^{15} -1.09957 q^{16} +4.79598 q^{17} -1.91821i q^{18} +1.84875i q^{19} +3.16311i q^{20} -1.88796i q^{21} +6.17272 q^{22} -7.94273 q^{23} -3.16669i q^{24} -5.52601 q^{25} +(-3.33305 - 1.48876i) q^{26} +5.14604 q^{27} +1.75074i q^{28} -2.23287 q^{29} +3.45349 q^{30} -1.00000i q^{31} +4.91070i q^{32} +6.40999i q^{33} +4.85568i q^{34} -5.82601 q^{35} -1.84717 q^{36} +8.64644i q^{37} -1.87176 q^{38} +(1.54599 - 3.46117i) q^{39} -9.77201 q^{40} +0.0498113i q^{41} +1.91146 q^{42} +4.76573 q^{43} -5.94410i q^{44} -6.14691i q^{45} -8.04159i q^{46} -4.00376i q^{47} +1.15605 q^{48} +3.77538 q^{49} -5.59480i q^{50} -5.04233 q^{51} +(-1.43362 + 3.20961i) q^{52} +0.588394 q^{53} +5.21010i q^{54} +19.7804 q^{55} -5.40868 q^{56} -1.94371i q^{57} -2.26066i q^{58} +3.49014i q^{59} -3.32558i q^{60} +12.1590 q^{61} +1.01245 q^{62} -3.40223i q^{63} -7.17097 q^{64} +(-10.6807 - 4.77073i) q^{65} -6.48978 q^{66} -1.72095i q^{67} +4.67585 q^{68} +8.35070 q^{69} -5.89852i q^{70} +10.3643i q^{71} -5.70659i q^{72} +2.28292i q^{73} -8.75406 q^{74} +5.80985 q^{75} +1.80244i q^{76} +10.9482 q^{77} +(3.50425 + 1.56523i) q^{78} +16.1812 q^{79} -3.56743i q^{80} +0.273525 q^{81} -0.0504314 q^{82} -10.2561i q^{83} -1.84067i q^{84} +15.5600i q^{85} +4.82505i q^{86} +2.34756 q^{87} +18.3635 q^{88} -7.99914i q^{89} +6.22342 q^{90} +(-5.91165 - 2.64053i) q^{91} -7.74376 q^{92} +1.05136i q^{93} +4.05360 q^{94} -5.99805 q^{95} -5.16294i q^{96} +10.1745i q^{97} +3.82238i q^{98} +11.5512i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{3} - 36 q^{4} + 20 q^{9}+O(q^{10}) $ 32 * q - 4 * q^3 - 36 * q^4 + 20 * q^9	$ 32 q - 4 q^{3} - 36 q^{4} + 20 q^{9} + 4 q^{10} - 16 q^{12} + 10 q^{13} - 16 q^{14} + 28 q^{16} - 8 q^{17} - 16 q^{22} - 8 q^{23} + 4 q^{25} + 18 q^{26} + 20 q^{27} - 16 q^{29} + 40 q^{30} - 4 q^{35} - 44 q^{36} + 12 q^{38} + 4 q^{39} + 28 q^{40} + 28 q^{42} - 32 q^{43} - 64 q^{49} - 64 q^{52} - 12 q^{53} + 44 q^{55} + 8 q^{56} + 16 q^{61} + 8 q^{62} - 76 q^{64} - 66 q^{65} - 68 q^{66} + 64 q^{68} + 20 q^{69} + 16 q^{74} - 32 q^{77} - 20 q^{78} + 64 q^{79} - 16 q^{81} + 12 q^{82} - 72 q^{87} + 80 q^{88} + 68 q^{90} + 22 q^{91} + 28 q^{92} + 88 q^{94} + 4 q^{95}+O(q^{100}) $ 32 * q - 4 * q^3 - 36 * q^4 + 20 * q^9 + 4 * q^10 - 16 * q^12 + 10 * q^13 - 16 * q^14 + 28 * q^16 - 8 * q^17 - 16 * q^22 - 8 * q^23 + 4 * q^25 + 18 * q^26 + 20 * q^27 - 16 * q^29 + 40 * q^30 - 4 * q^35 - 44 * q^36 + 12 * q^38 + 4 * q^39 + 28 * q^40 + 28 * q^42 - 32 * q^43 - 64 * q^49 - 64 * q^52 - 12 * q^53 + 44 * q^55 + 8 * q^56 + 16 * q^61 + 8 * q^62 - 76 * q^64 - 66 * q^65 - 68 * q^66 + 64 * q^68 + 20 * q^69 + 16 * q^74 - 32 * q^77 - 20 * q^78 + 64 * q^79 - 16 * q^81 + 12 * q^82 - 72 * q^87 + 80 * q^88 + 68 * q^90 + 22 * q^91 + 28 * q^92 + 88 * q^94 + 4 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$-1$	$1$

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 $

$2$			1.01245i			0.715908i	0.933739	+	0.357954i	$0.116526\pi$
$2$			1.01245i			0.715908i	−0.933739	+	0.357954i	$0.883474\pi$
$3$	−1.05136			−0.607006			−0.303503	−	0.952831i	$-0.598156\pi$
$3$	−1.05136			−0.607006			−0.303503	+	0.952831i	$0.598156\pi$
$4$	0.974950			0.487475
$5$			3.24438i			1.45093i	0.688258	+	0.725466i	$0.258376\pi$
$5$			3.24438i			1.45093i	−0.688258	+	0.725466i	$0.741624\pi$
$6$		−	1.06445i		−	0.434561i
$7$			1.79572i			0.678719i	0.940657	+	0.339360i	$0.110210\pi$
$7$			1.79572i			0.678719i	−0.940657	+	0.339360i	$0.889790\pi$
$8$			3.01198i			1.06490i
$9$	−1.89463			−0.631544
$10$	−3.28477			−1.03873
$11$		−	6.09683i		−	1.83826i	−0.393951	−	0.919131i	$-0.628892\pi$
$11$		−	6.09683i		−	1.83826i	0.393951	−	0.919131i	$-0.371108\pi$
$12$	−1.02503			−0.295900
$13$	−1.47046	+	3.29207i	−0.407832	+	0.913057i
$13$	−1.47046	+	3.29207i	−0.407832	+	0.913057i
$14$	−1.81807			−0.485901
$15$		−	3.41103i		−	0.880724i
$16$	−1.09957			−0.274893
$17$	4.79598			1.16320			0.581598	−	0.813476i	$-0.302428\pi$
$17$	4.79598			1.16320			0.581598	+	0.813476i	$0.302428\pi$
$18$		−	1.91821i		−	0.452128i
$19$			1.84875i			0.424133i	0.977255	+	0.212066i	$0.0680193\pi$
$19$			1.84875i			0.424133i	−0.977255	+	0.212066i	$0.931981\pi$
$20$			3.16311i			0.707293i
$21$		−	1.88796i		−	0.411986i
$22$	6.17272			1.31603
$23$	−7.94273			−1.65617			−0.828086	−	0.560600i	$-0.810570\pi$
$23$	−7.94273			−1.65617			−0.828086	+	0.560600i	$0.810570\pi$
$24$		−	3.16669i		−	0.646398i
$25$	−5.52601			−1.10520
$26$	−3.33305	−	1.48876i	−0.653665	−	0.291970i
$27$	5.14604			0.990357
$28$			1.75074i			0.330859i
$29$	−2.23287			−0.414633			−0.207317	−	0.978274i	$-0.566473\pi$
$29$	−2.23287			−0.414633			−0.207317	+	0.978274i	$0.566473\pi$
$30$	3.45349			0.630518
$31$		−	1.00000i		−	0.179605i
$31$		−	1.00000i		−	0.179605i
$32$			4.91070i			0.868098i
$33$			6.40999i			1.11584i
$34$			4.85568i			0.832742i
$35$	−5.82601			−0.984775
$36$	−1.84717			−0.307862
$37$			8.64644i			1.42147i	0.703462	+	0.710733i	$0.251636\pi$
$37$			8.64644i			1.42147i	−0.703462	+	0.710733i	$0.748364\pi$
$38$	−1.87176			−0.303640
$39$	1.54599	−	3.46117i	0.247556	−	0.554231i
$40$	−9.77201			−1.54509
$41$			0.0498113i			0.00777923i	0.999992	+	0.00388961i	$0.00123811\pi$
$41$			0.0498113i			0.00777923i	−0.999992	+	0.00388961i	$0.998762\pi$
$42$	1.91146			0.294945
$43$	4.76573			0.726767			0.363384	−	0.931640i	$-0.381621\pi$
$43$	4.76573			0.726767			0.363384	+	0.931640i	$0.381621\pi$
$44$		−	5.94410i		−	0.896107i
$45$		−	6.14691i		−	0.916327i
$46$		−	8.04159i		−	1.18567i
$47$		−	4.00376i		−	0.584008i	−0.956417	−	0.292004i	$-0.905678\pi$
$47$		−	4.00376i		−	0.584008i	0.956417	−	0.292004i	$-0.0943221\pi$
$48$	1.15605			0.166862
$49$	3.77538			0.539341
$50$		−	5.59480i		−	0.791224i
$51$	−5.04233			−0.706067
$52$	−1.43362	+	3.20961i	−0.198808	+	0.445093i
$53$	0.588394			0.0808221			0.0404111	−	0.999183i	$-0.487133\pi$
$53$	0.588394			0.0808221			0.0404111	+	0.999183i	$0.487133\pi$
$54$			5.21010i			0.709005i
$55$	19.7804			2.66719
$56$	−5.40868			−0.722765
$57$		−	1.94371i		−	0.257451i
$58$		−	2.26066i		−	0.296840i
$59$			3.49014i			0.454377i	0.973851	+	0.227189i	$0.0729534\pi$
$59$			3.49014i			0.454377i	−0.973851	+	0.227189i	$0.927047\pi$
$60$		−	3.32558i		−	0.429331i
$61$	12.1590			1.55680			0.778400	−	0.627769i	$-0.216032\pi$
$61$	12.1590			1.55680			0.778400	+	0.627769i	$0.216032\pi$
$62$	1.01245			0.128581
$63$		−	3.40223i		−	0.428641i
$64$	−7.17097			−0.896371
$65$	−10.6807	−	4.77073i	−1.32478	−	0.591736i
$66$	−6.48978			−0.798836
$67$		−	1.72095i		−	0.210247i	−0.994459	−	0.105124i	$-0.966476\pi$
$67$		−	1.72095i		−	0.210247i	0.994459	−	0.105124i	$-0.0335238\pi$
$68$	4.67585			0.567029
$69$	8.35070			1.00531
$70$		−	5.89852i		−	0.705009i
$71$			10.3643i			1.23002i	0.788519	+	0.615011i	$0.210848\pi$
$71$			10.3643i			1.23002i	−0.788519	+	0.615011i	$0.789152\pi$
$72$		−	5.70659i		−	0.672529i
$73$			2.28292i			0.267196i	0.991036	+	0.133598i	$0.0426531\pi$
$73$			2.28292i			0.267196i	−0.991036	+	0.133598i	$0.957347\pi$
$74$	−8.75406			−1.01764
$75$	5.80985			0.670864
$76$			1.80244i			0.206754i
$77$	10.9482			1.24766
$78$	3.50425	+	1.56523i	0.396779	+	0.177228i
$79$	16.1812			1.82053			0.910265	−	0.414027i	$-0.135878\pi$
$79$	16.1812			1.82053			0.910265	+	0.414027i	$0.135878\pi$
$80$		−	3.56743i		−	0.398851i
$81$	0.273525			0.0303917
$82$	−0.0504314			−0.00556921
$83$		−	10.2561i		−	1.12575i	−0.826541	−	0.562877i	$-0.809694\pi$
$83$		−	10.2561i		−	1.12575i	0.826541	−	0.562877i	$-0.190306\pi$
$84$		−	1.84067i		−	0.200833i
$85$			15.5600i			1.68772i
$86$			4.82505i			0.520299i
$87$	2.34756			0.251685
$88$	18.3635			1.95756
$89$		−	7.99914i		−	0.847907i	−0.905684	−	0.423953i	$-0.860642\pi$
$89$		−	7.99914i		−	0.847907i	0.905684	−	0.423953i	$-0.139358\pi$
$90$	6.22342			0.656006
$91$	−5.91165	−	2.64053i	−0.619709	−	0.276803i
$92$	−7.74376			−0.807343
$93$			1.05136i			0.109021i
$94$	4.05360			0.418097
$95$	−5.99805			−0.615387
$96$		−	5.16294i		−	0.526940i
$97$			10.1745i			1.03307i	0.856268	+	0.516533i	$0.172777\pi$
$97$			10.1745i			1.03307i	−0.856268	+	0.516533i	$0.827223\pi$
$98$			3.82238i			0.386118i
$99$			11.5512i			1.16094i
$100$	−5.38759			−0.538759
$101$	−10.3806			−1.03291			−0.516454	−	0.856315i	$-0.672748\pi$
$101$	−10.3806			−1.03291			−0.516454	+	0.856315i	$0.672748\pi$
$102$		−	5.10509i		−	0.505479i
$103$	7.56287			0.745191			0.372596	−	0.927994i	$-0.378468\pi$
$103$	7.56287			0.745191			0.372596	+	0.927994i	$0.378468\pi$
$104$	−9.91566	−	4.42899i	−0.972311	−	0.434299i
$105$	6.12526			0.597764
$106$			0.595718i			0.0578612i
$107$	9.88355			0.955478			0.477739	−	0.878502i	$-0.341456\pi$
$107$	9.88355			0.955478			0.477739	+	0.878502i	$0.341456\pi$
$108$	5.01714			0.482774
$109$		−	5.97227i		−	0.572040i	−0.958224	−	0.286020i	$-0.907668\pi$
$109$		−	5.97227i		−	0.572040i	0.958224	−	0.286020i	$-0.0923323\pi$
$110$			20.0266i			1.90947i
$111$		−	9.09056i		−	0.862838i
$112$		−	1.97452i		−	0.186575i
$113$	5.83695			0.549094			0.274547	−	0.961574i	$-0.411472\pi$
$113$	5.83695			0.549094			0.274547	+	0.961574i	$0.411472\pi$
$114$	1.96791			0.184311
$115$		−	25.7692i		−	2.40299i
$116$	−2.17694			−0.202123
$117$	2.78598	−	6.23727i	0.257564	−	0.576636i
$118$	−3.53358			−0.325292
$119$			8.61225i			0.789484i
$120$	10.2740			0.937879
$121$	−26.1713			−2.37921
$122$			12.3103i			1.11453i
$123$		−	0.0523699i		−	0.00472204i
$124$		−	0.974950i		−	0.0875531i
$125$		−	1.70658i		−	0.152641i
$126$	3.44458			0.306868
$127$	1.76344			0.156480			0.0782399	−	0.996935i	$-0.475070\pi$
$127$	1.76344			0.156480			0.0782399	+	0.996935i	$0.475070\pi$
$128$			2.56118i			0.226378i
$129$	−5.01052			−0.441152
$130$	4.83011	−	10.8137i	0.423629	−	0.948423i
$131$	15.7996			1.38042			0.690209	−	0.723610i	$-0.257518\pi$
$131$	15.7996			1.38042			0.690209	+	0.723610i	$0.257518\pi$
$132$			6.24942i			0.543942i
$133$	−3.31984			−0.287867
$134$	1.74237			0.150518
$135$			16.6957i			1.43694i
$136$			14.4454i			1.23868i
$137$		−	14.0263i		−	1.19835i	−0.800619	−	0.599174i	$-0.795496\pi$
$137$		−	14.0263i		−	1.19835i	0.800619	−	0.599174i	$-0.204504\pi$
$138$			8.45465i			0.719707i
$139$	−8.87486			−0.752756			−0.376378	−	0.926466i	$-0.622831\pi$
$139$	−8.87486			−0.752756			−0.376378	+	0.926466i	$0.622831\pi$
$140$	−5.68007			−0.480053
$141$			4.20941i			0.354497i
$142$	−10.4934			−0.880583
$143$	20.0712	+	8.96513i	1.67844	+	0.749702i
$144$	2.08328			0.173607
$145$		−	7.24428i		−	0.601605i
$146$	−2.31134			−0.191288
$147$	−3.96931			−0.327383
$148$			8.42985i			0.692929i
$149$			0.896489i			0.0734432i	0.999326	+	0.0367216i	$0.0116915\pi$
$149$			0.896489i			0.0734432i	−0.999326	+	0.0367216i	$0.988309\pi$
$150$			5.88217i			0.480277i
$151$			0.221338i			0.0180122i	0.999959	+	0.00900611i	$0.00286677\pi$
$151$			0.221338i			0.0180122i	−0.999959	+	0.00900611i	$0.997133\pi$
$152$	−5.56840			−0.451657
$153$	−9.08662			−0.734610
$154$			11.0845i			0.893213i
$155$	3.24438			0.260595
$156$	1.50726	−	3.37447i	0.120678	−	0.270174i
$157$	8.52165			0.680102			0.340051	−	0.940407i	$-0.389556\pi$
$157$	8.52165			0.680102			0.340051	+	0.940407i	$0.389556\pi$
$158$			16.3826i			1.30333i
$159$	−0.618617			−0.0490595
$160$	−15.9322			−1.25955
$161$		−	14.2629i		−	1.12408i
$162$			0.276930i			0.0217576i
$163$		−	0.474988i		−	0.0372039i	−0.999827	−	0.0186019i	$-0.994078\pi$
$163$		−	0.474988i		−	0.0372039i	0.999827	−	0.0186019i	$-0.00592153\pi$
$164$			0.0485636i			0.00379218i
$165$	−20.7965			−1.61900
$166$	10.3838			0.805937
$167$		−	5.99300i		−	0.463752i	−0.972745	−	0.231876i	$-0.925514\pi$
$167$		−	5.99300i		−	0.463752i	0.972745	−	0.231876i	$-0.0744864\pi$
$168$	5.68650			0.438723
$169$	−8.67550	−	9.68172i	−0.667346	−	0.744748i
$170$	−15.7537			−1.20825
$171$		−	3.50270i		−	0.267858i
$172$	4.64635			0.354281
$173$	0.0189761			0.00144272			0.000721362	−	1.00000i	$-0.499770\pi$
$173$	0.0189761			0.00144272			0.000721362		1.00000i	$0.499770\pi$
$174$			2.37678i			0.180183i
$175$		−	9.92318i		−	0.750122i
$176$			6.70390i			0.505325i
$177$		−	3.66941i		−	0.275810i
$178$	8.09870			0.607024
$179$	5.66716			0.423583			0.211792	−	0.977315i	$-0.432070\pi$
$179$	5.66716			0.423583			0.211792	+	0.977315i	$0.432070\pi$
$180$		−	5.99293i		−	0.446687i
$181$	−15.5416			−1.15520			−0.577598	−	0.816322i	$-0.696010\pi$
$181$	−15.5416			−1.15520			−0.577598	+	0.816322i	$0.696010\pi$
$182$	2.67340	−	5.98523i	0.198166	−	0.443655i
$183$	−12.7835			−0.944986
$184$		−	23.9233i		−	1.76365i
$185$	−28.0523			−2.06245
$186$	−1.06445			−0.0780494
$187$		−	29.2403i		−	2.13826i
$188$		−	3.90347i		−	0.284690i
$189$			9.24086i			0.672174i
$190$		−	6.07271i		−	0.440561i
$191$	−7.38826			−0.534596			−0.267298	−	0.963614i	$-0.586131\pi$
$191$	−7.38826			−0.534596			−0.267298	+	0.963614i	$0.586131\pi$
$192$	7.53931			0.544103
$193$		−	4.22194i		−	0.303902i	−0.988388	−	0.151951i	$-0.951444\pi$
$193$		−	4.22194i		−	0.303902i	0.988388	−	0.151951i	$-0.0485556\pi$
$194$	−10.3012			−0.739580
$195$	11.2294	+	5.01578i	0.804151	+	0.359187i
$196$	3.68081			0.262915
$197$			7.13939i			0.508660i	0.967117	+	0.254330i	$0.0818550\pi$
$197$			7.13939i			0.508660i	−0.967117	+	0.254330i	$0.918145\pi$
$198$	−11.6950			−0.831129
$199$	−17.5333			−1.24290			−0.621452	−	0.783453i	$-0.713457\pi$
$199$	−17.5333			−1.24290			−0.621452	+	0.783453i	$0.713457\pi$
$200$		−	16.6442i		−	1.17693i
$201$			1.80934i			0.127621i
$202$		−	10.5098i		−	0.739467i
$203$		−	4.00961i		−	0.281420i
$204$	−4.91602			−0.344190
$205$	−0.161607			−0.0112871
$206$			7.65701i			0.533489i
$207$	15.0485			1.04595
$208$	1.61687	−	3.61987i	0.112110	−	0.250993i
$209$	11.2715			0.779667
$210$			6.20150i			0.427944i
$211$	12.5199			0.861905			0.430952	−	0.902375i	$-0.358178\pi$
$211$	12.5199			0.861905			0.430952	+	0.902375i	$0.358178\pi$
$212$	0.573655			0.0393988
$213$		−	10.8967i		−	0.746630i
$214$			10.0066i			0.684035i
$215$			15.4619i			1.05449i
$216$			15.4998i			1.05463i
$217$	1.79572			0.121902
$218$	6.04661			0.409528
$219$		−	2.40019i		−	0.162190i
$220$	19.2849			1.30019
$221$	−7.05230	+	15.7887i	−0.474389	+	1.06206i
$222$	9.20371			0.617713
$223$			13.4782i			0.902565i	0.892381	+	0.451282i	$0.149033\pi$
$223$			13.4782i			0.902565i	−0.892381	+	0.451282i	$0.850967\pi$
$224$	−8.81826			−0.589195
$225$	10.4698			0.697984
$226$			5.90961i			0.393101i
$227$		−	21.7487i		−	1.44351i	−0.692149	−	0.721755i	$-0.743336\pi$
$227$		−	21.7487i		−	1.44351i	0.692149	−	0.721755i	$-0.256664\pi$
$228$		−	1.89502i		−	0.125501i
$229$			4.82129i			0.318600i	0.987230	+	0.159300i	$0.0509237\pi$
$229$			4.82129i			0.318600i	−0.987230	+	0.159300i	$0.949076\pi$
$230$	26.0900			1.72032
$231$	−11.5106			−0.757339
$232$		−	6.72536i		−	0.441541i
$233$	−29.1203			−1.90774			−0.953868	−	0.300227i	$-0.902938\pi$
$233$	−29.1203			−1.90774			−0.953868	+	0.300227i	$0.902938\pi$
$234$	6.31491	+	2.82066i	0.412818	+	0.184392i
$235$	12.9897			0.847356
$236$			3.40271i			0.221498i
$237$	−17.0124			−1.10507
$238$	−8.71945			−0.565198
$239$			27.1826i			1.75829i	0.476552	+	0.879147i	$0.341887\pi$
$239$			27.1826i			1.75829i	−0.476552	+	0.879147i	$0.658113\pi$
$240$			3.75067i			0.242105i
$241$			21.6242i			1.39294i	0.717588	+	0.696468i	$0.245246\pi$
$241$			21.6242i			1.39294i	−0.717588	+	0.696468i	$0.754754\pi$
$242$		−	26.4971i		−	1.70330i
$243$	−15.7257			−1.00880
$244$	11.8544			0.758901
$245$			12.2488i			0.782546i
$246$	0.0530218			0.00338054
$247$	−6.08623	−	2.71851i	−0.387257	−	0.172975i
$248$	3.01198			0.191261
$249$			10.7829i			0.683339i
$250$	1.72782			0.109277
$251$	23.7774			1.50082			0.750410	−	0.660973i	$-0.229856\pi$
$251$	23.7774			1.50082			0.750410	+	0.660973i	$0.229856\pi$
$252$		−	3.31701i		−	0.208952i
$253$			48.4254i			3.04448i
$254$			1.78539i			0.112025i
$255$		−	16.3592i		−	1.02446i
$256$	−16.9350			−1.05844
$257$	3.84862			0.240070			0.120035	−	0.992770i	$-0.461699\pi$
$257$	3.84862			0.240070			0.120035	+	0.992770i	$0.461699\pi$
$258$		−	5.07289i		−	0.315824i
$259$	−15.5266			−0.964776
$260$	−10.4132	−	4.65122i	−0.645799	−	0.288457i
$261$	4.23046			0.261859
$262$			15.9963i			0.988253i
$263$	−27.4393			−1.69198			−0.845991	−	0.533198i	$-0.820990\pi$
$263$	−27.4393			−1.69198			−0.845991	+	0.533198i	$0.820990\pi$
$264$	−19.3068			−1.18825
$265$			1.90897i			0.117267i
$266$		−	3.36117i		−	0.206086i
$267$			8.41001i			0.514684i
$268$		−	1.67784i		−	0.102490i
$269$	4.99431			0.304508			0.152254	−	0.988341i	$-0.451347\pi$
$269$	4.99431			0.304508			0.152254	+	0.988341i	$0.451347\pi$
$270$	−16.9035			−1.02872
$271$		−	27.8192i		−	1.68990i	−0.534848	−	0.844948i	$-0.679631\pi$
$271$		−	27.8192i		−	1.68990i	0.534848	−	0.844948i	$-0.320369\pi$
$272$	−5.27353			−0.319754
$273$	6.21530	+	2.77617i	0.376167	+	0.168021i
$274$	14.2009			0.857908
$275$			33.6911i			2.03165i
$276$	8.14152			0.490062
$277$	19.5970			1.17747			0.588734	−	0.808327i	$-0.299627\pi$
$277$	19.5970			1.17747			0.588734	+	0.808327i	$0.299627\pi$
$278$		−	8.98533i		−	0.538904i
$279$			1.89463i			0.113429i
$280$		−	17.5478i		−	1.04868i
$281$		−	9.44497i		−	0.563440i	−0.959497	−	0.281720i	$-0.909095\pi$
$281$		−	9.44497i		−	0.563440i	0.959497	−	0.281720i	$-0.0909049\pi$
$282$	−4.26181			−0.253787
$283$	11.1656			0.663726			0.331863	−	0.943328i	$-0.392323\pi$
$283$	11.1656			0.663726			0.331863	+	0.943328i	$0.392323\pi$
$284$			10.1047i			0.599605i
$285$	6.30614			0.373544
$286$	−9.07673	+	20.3210i	−0.536718	+	1.20161i
$287$	−0.0894473			−0.00527991
$288$		−	9.30397i		−	0.548242i
$289$	6.00145			0.353027
$290$	7.33445			0.430694
$291$		−	10.6971i		−	0.627077i
$292$			2.22574i			0.130251i
$293$		−	19.3914i		−	1.13286i	−0.824110	−	0.566429i	$-0.808324\pi$
$293$		−	19.3914i		−	1.13286i	0.824110	−	0.566429i	$-0.191676\pi$
$294$		−	4.01871i		−	0.234376i
$295$	−11.3233			−0.659270
$296$	−26.0429			−1.51371
$297$		−	31.3745i		−	1.82054i
$298$	−0.907647			−0.0525786
$299$	11.6795	−	26.1480i	0.675440	−	1.51218i
$300$	5.66432			0.327030
$301$			8.55793i			0.493271i
$302$	−0.224093			−0.0128951
$303$	10.9138			0.626981
$304$		−	2.03283i		−	0.116591i
$305$			39.4484i			2.25881i
$306$		−	9.19973i		−	0.525913i
$307$			2.97843i			0.169988i	0.996381	+	0.0849939i	$0.0270871\pi$
$307$			2.97843i			0.169988i	−0.996381	+	0.0849939i	$0.972913\pi$
$308$	10.6740			0.608205
$309$	−7.95133			−0.452336
$310$			3.28477i			0.186562i
$311$	−15.2149			−0.862756			−0.431378	−	0.902171i	$-0.641972\pi$
$311$	−15.2149			−0.862756			−0.431378	+	0.902171i	$0.641972\pi$
$312$	10.4250	+	4.65649i	0.590198	+	0.263622i
$313$	−6.83949			−0.386591			−0.193295	−	0.981141i	$-0.561918\pi$
$313$	−6.83949			−0.386591			−0.193295	+	0.981141i	$0.561918\pi$
$314$			8.62773i			0.486891i
$315$	11.0381			0.621929
$316$	15.7759			0.887463
$317$			17.3492i			0.974431i	0.873282	+	0.487215i	$0.161987\pi$
$317$			17.3492i			0.974431i	−0.873282	+	0.487215i	$0.838013\pi$
$318$		−	0.626317i		−	0.0351221i
$319$			13.6134i			0.762205i
$320$		−	23.2654i		−	1.30057i
$321$	−10.3912			−0.579981
$322$	14.4405			0.804735
$323$			8.86658i			0.493350i
$324$	0.266673			0.0148152
$325$	8.12577	−	18.1920i	0.450737	−	1.00911i
$326$	0.480900			0.0266346
$327$			6.27904i			0.347231i
$328$	−0.150031			−0.00828407
$329$	7.18964			0.396378
$330$		−	21.0553i		−	1.15906i
$331$			5.82160i			0.319984i	0.987118	+	0.159992i	$0.0511469\pi$
$331$			5.82160i			0.319984i	−0.987118	+	0.159992i	$0.948853\pi$
$332$		−	9.99920i		−	0.548777i
$333$		−	16.3818i		−	0.897718i
$334$	6.06760			0.332004
$335$	5.58341			0.305054
$336$			2.07595i			0.113252i
$337$	−30.6724			−1.67083			−0.835415	−	0.549620i	$-0.814773\pi$
$337$	−30.6724			−1.67083			−0.835415	+	0.549620i	$0.814773\pi$
$338$	9.80223	−	8.78349i	0.533171	−	0.477759i
$339$	−6.13677			−0.333303
$340$			15.1702i			0.822721i
$341$	−6.09683			−0.330162
$342$	3.54630			0.191762
$343$			19.3496i			1.04478i
$344$			14.3543i			0.773932i
$345$			27.0929i			1.45863i
$346$			0.0192123i			0.00103286i
$347$	−24.5555			−1.31821			−0.659103	−	0.752053i	$-0.729064\pi$
$347$	−24.5555			−1.31821			−0.659103	+	0.752053i	$0.729064\pi$
$348$	2.28875			0.122690
$349$		−	27.8390i		−	1.49019i	−0.666959	−	0.745094i	$-0.732404\pi$
$349$		−	27.8390i		−	1.49019i	0.666959	−	0.745094i	$-0.267596\pi$
$350$	10.0467			0.537018
$351$	−7.56705	+	16.9412i	−0.403899	+	0.904252i
$352$	29.9397			1.59579
$353$		−	7.01905i		−	0.373586i	−0.982399	−	0.186793i	$-0.940191\pi$
$353$		−	7.01905i		−	0.373586i	0.982399	−	0.186793i	$-0.0598094\pi$
$354$	3.71508			0.197454
$355$	−33.6259			−1.78468
$356$		−	7.79876i		−	0.413333i
$357$		−	9.05462i		−	0.479221i
$358$			5.73770i			0.303247i
$359$		−	15.7950i		−	0.833628i	−0.908992	−	0.416814i	$-0.863147\pi$
$359$		−	15.7950i		−	0.833628i	0.908992	−	0.416814i	$-0.136853\pi$
$360$	18.5144			0.975793
$361$	15.5821			0.820112
$362$		−	15.7350i		−	0.827014i
$363$	27.5156			1.44419
$364$	−5.76356	−	2.57439i	−0.302093	−	0.134935i
$365$	−7.40667			−0.387683
$366$		−	12.9427i		−	0.676523i
$367$	10.2880			0.537029			0.268515	−	0.963276i	$-0.413467\pi$
$367$	10.2880			0.537029			0.268515	+	0.963276i	$0.413467\pi$
$368$	8.73359			0.455270
$369$		−	0.0943742i		−	0.00491292i
$370$		−	28.4015i		−	1.47652i
$371$			1.05659i			0.0548555i
$372$			1.02503i			0.0531453i
$373$	33.4821			1.73364			0.866820	−	0.498622i	$-0.166160\pi$
$373$	33.4821			1.73364			0.866820	+	0.498622i	$0.166160\pi$
$374$	29.6042			1.53080
$375$			1.79424i			0.0926541i
$376$	12.0592			0.621908
$377$	3.28334	−	7.35077i	0.169101	−	0.378584i
$378$	−9.35589			−0.481215
$379$		−	31.2200i		−	1.60367i	−0.597548	−	0.801833i	$-0.703858\pi$
$379$		−	31.2200i		−	1.60367i	0.597548	−	0.801833i	$-0.296142\pi$
$380$	−5.84781			−0.299986
$381$	−1.85402			−0.0949841
$382$		−	7.48023i		−	0.382722i
$383$		−	8.55469i		−	0.437124i	−0.975823	−	0.218562i	$-0.929863\pi$
$383$		−	8.55469i		−	0.437124i	0.975823	−	0.218562i	$-0.0701366\pi$
$384$		−	2.69273i		−	0.137413i
$385$			35.5202i			1.81027i
$386$	4.27450			0.217566
$387$	−9.02931			−0.458985
$388$			9.91964i			0.503594i
$389$	38.2805			1.94090			0.970450	−	0.241303i	$-0.0775749\pi$
$389$	38.2805			1.94090			0.970450	+	0.241303i	$0.0775749\pi$
$390$	−5.07821	+	11.3691i	−0.257145	+	0.575699i
$391$	−38.0932			−1.92645
$392$			11.3714i			0.574342i
$393$	−16.6112			−0.837922
$394$	−7.22825			−0.364154
$395$			52.4980i			2.64146i
$396$			11.2619i			0.565931i
$397$		−	18.1469i		−	0.910767i	−0.890295	−	0.455383i	$-0.849502\pi$
$397$		−	18.1469i		−	0.910767i	0.890295	−	0.455383i	$-0.150498\pi$
$398$		−	17.7515i		−	0.889805i
$399$	3.49037			0.174737
$400$	6.07624			0.303812
$401$		−	23.7338i		−	1.18521i	−0.805493	−	0.592605i	$-0.798100\pi$
$401$		−	23.7338i		−	1.18521i	0.805493	−	0.592605i	$-0.201900\pi$
$402$	−1.83187			−0.0913651
$403$	3.29207	+	1.47046i	0.163990	+	0.0732488i
$404$	−10.1206			−0.503517
$405$			0.887419i			0.0440962i
$406$	4.05952			0.201471
$407$	52.7158			2.61303
$408$		−	15.1874i		−	0.751888i
$409$		−	29.4641i		−	1.45691i	−0.685096	−	0.728453i	$-0.740240\pi$
$409$		−	29.4641i		−	1.45691i	0.685096	−	0.728453i	$-0.259760\pi$
$410$		−	0.163619i		−	0.00808055i
$411$			14.7468i			0.727404i
$412$	7.37342			0.363262
$413$	−6.26731			−0.308394
$414$			15.2359i			0.748801i
$415$	33.2747			1.63339
$416$	−16.1664	−	7.22099i	−0.792623	−	0.354038i
$417$	9.33071			0.456927
$418$			11.4118i			0.558170i
$419$	24.8096			1.21203			0.606014	−	0.795454i	$-0.292768\pi$
$419$	24.8096			1.21203			0.606014	+	0.795454i	$0.292768\pi$
$420$	5.97182			0.291395
$421$			0.191902i			0.00935275i	0.999989	+	0.00467637i	$0.00148854\pi$
$421$			0.191902i			0.00935275i	−0.999989	+	0.00467637i	$0.998511\pi$
$422$			12.6757i			0.617045i
$423$			7.58565i			0.368827i
$424$			1.77223i			0.0860672i
$425$	−26.5027			−1.28557
$426$	11.0323			0.534519
$427$			21.8342i			1.05663i
$428$	9.63597			0.465772
$429$	−21.1022	−	9.42563i	−1.01882	−	0.455074i
$430$	−15.6543			−0.754918
$431$		−	15.0633i		−	0.725574i	−0.931872	−	0.362787i	$-0.881825\pi$
$431$		−	15.0633i		−	0.725574i	0.931872	−	0.362787i	$-0.118175\pi$
$432$	−5.65844			−0.272242
$433$	12.8565			0.617844			0.308922	−	0.951087i	$-0.400032\pi$
$433$	12.8565			0.617844			0.308922	+	0.951087i	$0.400032\pi$
$434$			1.81807i			0.0872703i
$435$			7.61638i			0.365178i
$436$		−	5.82267i		−	0.278855i
$437$		−	14.6841i		−	0.702437i
$438$	2.43006			0.116113
$439$	−0.561664			−0.0268068			−0.0134034	−	0.999910i	$-0.504267\pi$
$439$	−0.561664			−0.0268068			−0.0134034	+	0.999910i	$0.504267\pi$
$440$			59.5783i			2.84028i
$441$	−7.15296			−0.340617
$442$	−15.9853	−	7.14008i	−0.760341	−	0.339619i
$443$	−10.0558			−0.477765			−0.238883	−	0.971048i	$-0.576781\pi$
$443$	−10.0558			−0.477765			−0.238883	+	0.971048i	$0.576781\pi$
$444$		−	8.86284i		−	0.420612i
$445$	25.9522			1.23025
$446$	−13.6459			−0.646154
$447$		−	0.942537i		−	0.0445805i
$448$		−	12.8771i		−	0.608384i
$449$		−	15.4936i		−	0.731187i	−0.930775	−	0.365594i	$-0.880866\pi$
$449$		−	15.4936i		−	0.731187i	0.930775	−	0.365594i	$-0.119134\pi$
$450$			10.6001i			0.499692i
$451$	0.303691			0.0143003
$452$	5.69074			0.267670
$453$		−	0.232707i		−	0.0109335i
$454$	22.0194			1.03342
$455$	8.56690	−	19.1796i	0.401623	−	0.899156i
$456$	5.85442			0.274159
$457$			22.5213i			1.05350i	0.850020	+	0.526751i	$0.176590\pi$
$457$			22.5213i			1.05350i	−0.850020	+	0.526751i	$0.823410\pi$
$458$	−4.88131			−0.228088
$459$	24.6803			1.15198
$460$		−	25.1237i		−	1.17140i
$461$			11.9714i			0.557563i	0.960354	+	0.278782i	$0.0899306\pi$
$461$			11.9714i			0.557563i	−0.960354	+	0.278782i	$0.910069\pi$
$462$		−	11.6538i		−	0.542186i
$463$		−	42.4947i		−	1.97489i	−0.157950	−	0.987447i	$-0.550489\pi$
$463$		−	42.4947i		−	1.97489i	0.157950	−	0.987447i	$-0.449511\pi$
$464$	2.45520			0.113980
$465$	−3.41103			−0.158183
$466$		−	29.4828i		−	1.36576i
$467$	35.2701			1.63211			0.816053	−	0.577977i	$-0.196158\pi$
$467$	35.2701			1.63211			0.816053	+	0.577977i	$0.196158\pi$
$468$	2.71619	−	6.08103i	0.125556	−	0.281096i
$469$	3.09034			0.142699
$470$			13.1514i			0.606629i
$471$	−8.95937			−0.412826
$472$	−10.5122			−0.483864
$473$		−	29.0558i		−	1.33599i
$474$		−	17.2241i		−	0.791130i
$475$		−	10.2162i		−	0.468752i
$476$			8.39652i			0.384854i
$477$	−1.11479			−0.0510427
$478$	−27.5209			−1.25878
$479$			17.0249i			0.777888i	0.921261	+	0.388944i	$0.127160\pi$
$479$			17.0249i			0.777888i	−0.921261	+	0.388944i	$0.872840\pi$
$480$	16.7506			0.764555
$481$	−28.4647	−	12.7142i	−1.29788	−	0.579719i
$482$	−21.8933			−0.997214
$483$			14.9955i			0.682321i
$484$	−25.5157			−1.15981
$485$	−33.0100			−1.49891
$486$		−	15.9215i		−	0.722212i
$487$			3.52549i			0.159755i	0.996805	+	0.0798776i	$0.0254529\pi$
$487$			3.52549i			0.159755i	−0.996805	+	0.0798776i	$0.974547\pi$
$488$			36.6226i			1.65783i
$489$			0.499385i			0.0225830i
$490$	−12.4012			−0.560231
$491$	−29.9606			−1.35210			−0.676051	−	0.736855i	$-0.736310\pi$
$491$	−29.9606			−1.35210			−0.676051	+	0.736855i	$0.736310\pi$
$492$		−	0.0510581i		−	0.00230187i
$493$	−10.7088			−0.482300
$494$	2.75235	−	6.16198i	0.123834	−	0.277241i
$495$	−37.4766			−1.68445
$496$			1.09957i			0.0493722i
$497$	−18.6115			−0.834839
$498$	−10.9171			−0.489208
$499$		−	9.74284i		−	0.436149i	−0.975932	−	0.218075i	$-0.930022\pi$
$499$		−	9.74284i		−	0.436149i	0.975932	−	0.218075i	$-0.0699776\pi$
$500$		−	1.66383i		−	0.0744088i
$501$			6.30083i			0.281500i
$502$			24.0734i			1.07445i
$503$	15.7364			0.701651			0.350825	−	0.936441i	$-0.385901\pi$
$503$	15.7364			0.701651			0.350825	+	0.936441i	$0.385901\pi$
$504$	10.2475			0.456458
$505$		−	33.6786i		−	1.49868i
$506$	−49.0282			−2.17957
$507$	9.12112	+	10.1790i	0.405083	+	0.452066i
$508$	1.71926			0.0762800
$509$		−	30.5793i		−	1.35541i	−0.735336	−	0.677703i	$-0.762976\pi$
$509$		−	30.5793i		−	1.35541i	0.735336	−	0.677703i	$-0.237024\pi$
$510$	16.5629			0.733416
$511$	−4.09950			−0.181351
$512$		−	12.0234i		−	0.531366i
$513$			9.51376i			0.420043i
$514$			3.89652i			0.171868i
$515$			24.5368i			1.08122i
$516$	−4.88501			−0.215051
$517$	−24.4102			−1.07356
$518$		−	15.7199i		−	0.690691i
$519$	−0.0199508			−0.000875742
$520$	14.3693	−	32.1702i	0.630137	−	1.41076i
$521$	−36.3668			−1.59326			−0.796628	−	0.604469i	$-0.793385\pi$
$521$	−36.3668			−1.59326			−0.796628	+	0.604469i	$0.793385\pi$
$522$			4.28312i			0.187467i
$523$	−12.1385			−0.530780			−0.265390	−	0.964141i	$-0.585501\pi$
$523$	−12.1385			−0.530780			−0.265390	+	0.964141i	$0.585501\pi$
$524$	15.4038			0.672920
$525$			10.4329i			0.455328i
$526$		−	27.7809i		−	1.21130i
$527$		−	4.79598i		−	0.208916i
$528$		−	7.04824i		−	0.306735i
$529$	40.0869			1.74291
$530$	−1.93274			−0.0839527
$531$		−	6.61252i		−	0.286959i
$532$	−3.23668			−0.140328
$533$	−0.163983	−	0.0732455i	−0.00710288	−	0.00317262i
$534$	−8.51469			−0.368467
$535$			32.0660i			1.38633i
$536$	5.18346			0.223891
$537$	−5.95825			−0.257118
$538$			5.05648i			0.218000i
$539$		−	23.0179i		−	0.991450i
$540$			16.2775i			0.700472i
$541$			36.2301i			1.55765i	0.627240	+	0.778826i	$0.284184\pi$
$541$			36.2301i			1.55765i	−0.627240	+	0.778826i	$0.715816\pi$
$542$	28.1655			1.20981
$543$	16.3399			0.701210
$544$			23.5516i			1.00977i
$545$	19.3763			0.829991
$546$	−2.81072	+	6.29266i	−0.120288	+	0.269301i
$547$	−4.85710			−0.207675			−0.103837	−	0.994594i	$-0.533112\pi$
$547$	−4.85710			−0.207675			−0.103837	+	0.994594i	$0.533112\pi$
$548$		−	13.6750i		−	0.584165i
$549$	−23.0368			−0.983187
$550$	−34.1105			−1.45448
$551$		−	4.12802i		−	0.175860i
$552$			25.1522i			1.07055i
$553$			29.0570i			1.23563i
$554$			19.8409i			0.842959i
$555$	29.4932			1.25192
$556$	−8.65254			−0.366950
$557$			41.4847i			1.75776i	0.477040	+	0.878882i	$0.341710\pi$
$557$			41.4847i			1.75776i	−0.477040	+	0.878882i	$0.658290\pi$
$558$	−1.91821			−0.0812045
$559$	−7.00781	+	15.6891i	−0.296399	+	0.663580i
$560$	6.40611			0.270708
$561$			30.7422i			1.29794i
$562$	9.56254			0.403371
$563$	−5.12904			−0.216163			−0.108082	−	0.994142i	$-0.534471\pi$
$563$	−5.12904			−0.216163			−0.108082	+	0.994142i	$0.534471\pi$
$564$			4.10397i			0.172808i
$565$			18.9373i			0.796698i
$566$			11.3046i			0.475167i
$567$			0.491175i			0.0206274i
$568$	−31.2172			−1.30984
$569$	−20.7637			−0.870458			−0.435229	−	0.900320i	$-0.643333\pi$
$569$	−20.7637			−0.870458			−0.435229	+	0.900320i	$0.643333\pi$
$570$			6.38464i			0.267423i
$571$	−29.8037			−1.24725			−0.623623	−	0.781726i	$-0.714340\pi$
$571$	−29.8037			−1.24725			−0.623623	+	0.781726i	$0.714340\pi$
$572$	19.5684	+	8.74056i	0.818197	+	0.365461i
$573$	7.76776			0.324503
$574$		−	0.0905607i		−	0.00377993i
$575$	43.8916			1.83041
$576$	13.5863			0.566098
$577$			31.5439i			1.31319i	0.754243	+	0.656596i	$0.228004\pi$
$577$			31.5439i			1.31319i	−0.754243	+	0.656596i	$0.771996\pi$
$578$			6.07615i			0.252735i
$579$			4.43880i			0.184470i
$580$		−	7.06281i		−	0.293267i
$581$	18.4171			0.764071
$582$	10.8303			0.448929
$583$		−	3.58734i		−	0.148572i
$584$	−6.87612			−0.284536
$585$	20.2361	+	9.03878i	0.836659	+	0.373707i
$586$	19.6328			0.811023
$587$		−	32.0469i		−	1.32272i	−0.750071	−	0.661358i	$-0.769981\pi$
$587$		−	32.0469i		−	1.32272i	0.750071	−	0.661358i	$-0.230019\pi$
$588$	−3.86988			−0.159591
$589$	1.84875			0.0761765
$590$		−	11.4643i		−	0.471977i
$591$		−	7.50610i		−	0.308760i
$592$		−	9.50737i		−	0.390751i
$593$			30.8314i			1.26609i	0.774114	+	0.633046i	$0.218196\pi$
$593$			30.8314i			1.26609i	−0.774114	+	0.633046i	$0.781804\pi$
$594$	31.7651			1.30334
$595$	−27.9414			−1.14549
$596$			0.874032i			0.0358017i
$597$	18.4339			0.754449
$598$	26.4735	+	11.8248i	1.08258	+	0.483553i
$599$	−29.6376			−1.21096			−0.605479	−	0.795861i	$-0.707018\pi$
$599$	−29.6376			−1.21096			−0.605479	+	0.795861i	$0.707018\pi$
$600$			17.4992i			0.714401i
$601$	29.7503			1.21354			0.606769	−	0.794878i	$-0.292465\pi$
$601$	29.7503			1.21354			0.606769	+	0.794878i	$0.292465\pi$
$602$	−8.66445			−0.353137
$603$			3.26056i			0.132780i
$604$			0.215793i			0.00878051i
$605$		−	84.9097i		−	3.45207i
$606$			11.0496i			0.448861i
$607$	−34.1070			−1.38436			−0.692181	−	0.721724i	$-0.743350\pi$
$607$	−34.1070			−1.38436			−0.692181	+	0.721724i	$0.743350\pi$
$608$	−9.07867			−0.368189
$609$			4.21556i			0.170823i
$610$	−39.9394			−1.61710
$611$	13.1807	+	5.88736i	0.533233	+	0.238177i
$612$	−8.85900			−0.358104
$613$		−	23.4986i		−	0.949100i	−0.880228	−	0.474550i	$-0.842611\pi$
$613$		−	23.4986i		−	0.949100i	0.880228	−	0.474550i	$-0.157389\pi$
$614$	−3.01550			−0.121696
$615$	0.169908			0.00685135
$616$			32.9758i			1.32863i
$617$		−	13.5012i		−	0.543539i	−0.962362	−	0.271770i	$-0.912391\pi$
$617$		−	13.5012i		−	0.543539i	0.962362	−	0.271770i	$-0.0876089\pi$
$618$		−	8.05031i		−	0.323831i
$619$		−	15.3528i		−	0.617080i	−0.951211	−	0.308540i	$-0.900160\pi$
$619$		−	15.3528i		−	0.617080i	0.951211	−	0.308540i	$-0.0998404\pi$
$620$	3.16311			0.127034
$621$	−40.8736			−1.64020
$622$		−	15.4043i		−	0.617654i
$623$	14.3642			0.575490
$624$	−1.69992	+	3.80580i	−0.0680515	+	0.152354i
$625$	−22.0933			−0.883730
$626$		−	6.92463i		−	0.276764i
$627$	−11.8505			−0.473263
$628$	8.30819			0.331533
$629$			41.4682i			1.65344i
$630$			11.1755i			0.445244i
$631$		−	12.9193i		−	0.514310i	−0.966370	−	0.257155i	$-0.917215\pi$
$631$		−	12.9193i		−	0.514310i	0.966370	−	0.257155i	$-0.0827850\pi$
$632$			48.7375i			1.93867i
$633$	−13.1630			−0.523181
$634$	−17.5652			−0.697603
$635$			5.72126i			0.227041i
$636$	−0.603121			−0.0239153
$637$	−5.55155	+	12.4288i	−0.219960	+	0.492449i
$638$	−13.7829			−0.545669
$639$		−	19.6366i		−	0.776813i
$640$	−8.30943			−0.328459
$641$	37.2265			1.47036			0.735180	−	0.677872i	$-0.237098\pi$
$641$	37.2265			1.47036			0.735180	+	0.677872i	$0.237098\pi$
$642$		−	10.5206i		−	0.415213i
$643$			24.3497i			0.960259i	0.877198	+	0.480130i	$0.159410\pi$
$643$			24.3497i			0.960259i	−0.877198	+	0.480130i	$0.840590\pi$
$644$		−	13.9056i		−	0.547959i
$645$		−	16.2560i		−	0.640081i
$646$	−8.97695			−0.353193
$647$	24.9639			0.981433			0.490717	−	0.871319i	$-0.336735\pi$
$647$	24.9639			0.981433			0.490717	+	0.871319i	$0.336735\pi$
$648$			0.823852i			0.0323640i
$649$	21.2788			0.835264
$650$	18.4185	+	8.22692i	0.722432	+	0.322686i
$651$	−1.88796			−0.0739949
$652$		−	0.463089i		−	0.0181360i
$653$	−2.17194			−0.0849947			−0.0424974	−	0.999097i	$-0.513531\pi$
$653$	−2.17194			−0.0849947			−0.0424974	+	0.999097i	$0.513531\pi$
$654$	−6.35719			−0.248586
$655$			51.2600i			2.00289i
$656$		−	0.0547711i		−	0.00213845i
$657$		−	4.32530i		−	0.168746i
$658$			7.27913i			0.283770i
$659$	3.53137			0.137563			0.0687814	−	0.997632i	$-0.478089\pi$
$659$	3.53137			0.137563			0.0687814	+	0.997632i	$0.478089\pi$
$660$	−20.2755			−0.789223
$661$		−	0.781774i		−	0.0304075i	−0.999884	−	0.0152037i	$-0.995160\pi$
$661$		−	0.781774i		−	0.0304075i	0.999884	−	0.0152037i	$-0.00483969\pi$
$662$	−5.89407			−0.229079
$663$	7.41454	−	16.5997i	0.287957	−	0.644680i
$664$	30.8912			1.19881
$665$		−	10.7708i		−	0.417675i
$666$	16.5857			0.642684
$667$	17.7351			0.686705
$668$		−	5.84288i		−	0.226068i
$669$		−	14.1705i		−	0.547862i
$670$			5.65291i			0.218391i
$671$		−	74.1313i		−	2.86181i
$672$	9.27121			0.357645
$673$	−39.4571			−1.52096			−0.760479	−	0.649362i	$-0.775036\pi$
$673$	−39.4571			−1.52096			−0.760479	+	0.649362i	$0.775036\pi$
$674$		−	31.0541i		−	1.19616i
$675$	−28.4371			−1.09454
$676$	−8.45818	−	9.43919i	−0.325315	−	0.363046i
$677$	44.1582			1.69714			0.848569	−	0.529085i	$-0.177465\pi$
$677$	44.1582			1.69714			0.848569	+	0.529085i	$0.177465\pi$
$678$		−	6.21315i		−	0.238615i
$679$	−18.2706			−0.701161
$680$	−46.8664			−1.79724
$681$			22.8658i			0.876219i
$682$		−	6.17272i		−	0.236366i
$683$			49.3853i			1.88967i	0.327540	+	0.944837i	$0.393781\pi$
$683$			49.3853i			1.88967i	−0.327540	+	0.944837i	$0.606219\pi$
$684$		−	3.41496i		−	0.130574i
$685$	45.5067			1.73872
$686$	−19.5904			−0.747967
$687$		−	5.06894i		−	0.193392i
$688$	−5.24026			−0.199783
$689$	−0.865209	+	1.93704i	−0.0329618	+	0.0737952i
$690$	−27.4301			−1.04425
$691$			12.4149i			0.472284i	0.971719	+	0.236142i	$0.0758831\pi$
$691$			12.4149i			0.472284i	−0.971719	+	0.236142i	$0.924117\pi$
$692$	0.0185007			0.000703292
$693$	−20.7428			−0.787955
$694$		−	24.8611i		−	0.943715i
$695$		−	28.7934i		−	1.09220i
$696$			7.07081i			0.268018i
$697$			0.238894i			0.00904877i
$698$	28.1855			1.06684
$699$	30.6161			1.15801
$700$		−	9.67461i		−	0.365666i
$701$	27.1200			1.02431			0.512155	−	0.858893i	$-0.328847\pi$
$701$	27.1200			1.02431			0.512155	+	0.858893i	$0.328847\pi$
$702$	−17.1520	−	7.66124i	−0.647362	−	0.289155i
$703$	−15.9851			−0.602890
$704$			43.7202i			1.64777i
$705$	−13.6569			−0.514350
$706$	7.10642			0.267454
$707$		−	18.6406i		−	0.701054i
$708$		−	3.57749i		−	0.134450i
$709$		−	9.01510i		−	0.338569i	−0.985567	−	0.169285i	$-0.945854\pi$
$709$		−	9.01510i		−	0.338569i	0.985567	−	0.169285i	$-0.0541457\pi$
$710$		−	34.0444i		−	1.27767i
$711$	−30.6574			−1.14974
$712$	24.0932			0.902932
$713$			7.94273i			0.297457i
$714$	9.16732			0.343078
$715$	−29.0863	+	65.1187i	−1.08777	+	2.43530i
$716$	5.52520			0.206486
$717$		−	28.5788i		−	1.06729i
$718$	15.9916			0.596801
$719$	2.03502			0.0758934			0.0379467	−	0.999280i	$-0.487918\pi$
$719$	2.03502			0.0758934			0.0379467	+	0.999280i	$0.487918\pi$
$720$			6.75896i			0.251892i
$721$			13.5808i			0.505776i
$722$			15.7761i			0.587125i
$723$		−	22.7349i		−	0.845520i
$724$	−15.1523			−0.563129
$725$	12.3389			0.458254
$726$			27.8581i			1.03391i
$727$	6.51447			0.241608			0.120804	−	0.992676i	$-0.461453\pi$
$727$	6.51447			0.241608			0.120804	+	0.992676i	$0.461453\pi$
$728$	7.95324	−	17.8058i	0.294767	−	0.659926i
$729$	15.7129			0.581959
$730$		−	7.49887i		−	0.277546i
$731$	22.8564			0.845373
$732$	−12.4633			−0.460657
$733$		−	3.11568i		−	0.115080i	−0.998343	−	0.0575402i	$-0.981674\pi$
$733$		−	3.11568i		−	0.115080i	0.998343	−	0.0575402i	$-0.0183257\pi$
$734$			10.4161i			0.384464i
$735$		−	12.8779i		−	0.475010i
$736$		−	39.0044i		−	1.43772i
$737$	−10.4923			−0.386490
$738$	0.0955489			0.00351720
$739$		−	39.1735i		−	1.44102i	−0.693444	−	0.720510i	$-0.743908\pi$
$739$		−	39.1735i		−	1.44102i	0.693444	−	0.720510i	$-0.256092\pi$
$740$	−27.3496			−1.00539
$741$	6.39884	+	2.85815i	0.235067	+	0.104997i
$742$	−1.06974			−0.0392715
$743$		−	30.6791i		−	1.12551i	−0.826625	−	0.562753i	$-0.809742\pi$
$743$		−	30.6791i		−	1.12551i	0.826625	−	0.562753i	$-0.190258\pi$
$744$	−3.16669			−0.116097
$745$	−2.90855			−0.106561
$746$			33.8989i			1.24113i
$747$			19.4315i			0.710963i
$748$		−	28.5078i		−	1.04235i
$749$			17.7481i			0.648501i
$750$	−1.81657			−0.0663318
$751$	−25.5019			−0.930578			−0.465289	−	0.885159i	$-0.654050\pi$
$751$	−25.5019			−0.930578			−0.465289	+	0.885159i	$0.654050\pi$
$752$			4.40242i			0.160540i
$753$	−24.9988			−0.911006
$754$	7.44227	+	3.32421i	0.271031	+	0.121061i
$755$	−0.718105			−0.0261345
$756$			9.00938i			0.327668i
$757$	−8.04879			−0.292538			−0.146269	−	0.989245i	$-0.546727\pi$
$757$	−8.04879			−0.292538			−0.146269	+	0.989245i	$0.546727\pi$
$758$	31.6087			1.14808
$759$		−	50.9128i		−	1.84802i
$760$		−	18.0660i		−	0.655324i
$761$			52.1296i			1.88970i	0.327508	+	0.944848i	$0.393791\pi$
$761$			52.1296i			1.88970i	−0.327508	+	0.944848i	$0.606209\pi$
$762$		−	1.87709i		−	0.0679999i
$763$	10.7245			0.388254
$764$	−7.20319			−0.260602
$765$		−	29.4805i		−	1.06587i
$766$	8.66117			0.312941
$767$	−11.4898	−	5.13210i	−0.414872	−	0.185309i
$768$	17.8049			0.642478
$769$		−	3.62057i		−	0.130561i	−0.997867	−	0.0652806i	$-0.979206\pi$
$769$		−	3.62057i		−	0.130561i	0.997867	−	0.0652806i	$-0.0207942\pi$
$770$	−35.9623			−1.29599
$771$	−4.04630			−0.145724
$772$		−	4.11619i		−	0.148145i
$773$		−	32.4020i		−	1.16542i	−0.812680	−	0.582710i	$-0.801992\pi$
$773$		−	32.4020i		−	1.16542i	0.812680	−	0.582710i	$-0.198008\pi$
$774$		−	9.14170i		−	0.328592i
$775$			5.52601i			0.198500i
$776$	−30.6454			−1.10011
$777$	16.3241			0.585624
$778$			38.7570i			1.38951i
$779$	−0.0920888			−0.00329942
$780$	10.9481	+	4.89013i	0.392004	+	0.175095i
$781$	63.1896			2.26110
$782$		−	38.5673i		−	1.37917i
$783$	−11.4904			−0.410635
$784$	−4.15130			−0.148261
$785$			27.6475i			0.986781i
$786$		−	16.8179i		−	0.599876i
$787$		−	13.0411i		−	0.464866i	−0.972612	−	0.232433i	$-0.925331\pi$
$787$		−	13.0411i		−	0.464866i	0.972612	−	0.232433i	$-0.0746686\pi$
$788$			6.96055i			0.247959i
$789$	28.8487			1.02704
$790$	−53.1515			−1.89105
$791$			10.4815i			0.372681i
$792$	−34.7921			−1.23628
$793$	−17.8793	+	40.0283i	−0.634912	+	1.42145i
$794$	18.3728			0.652026
$795$		−	2.00703i		−	0.0711820i
$796$	−17.0941			−0.605884
$797$	1.44802			0.0512914			0.0256457	−	0.999671i	$-0.491836\pi$
$797$	1.44802			0.0512914			0.0256457	+	0.999671i	$0.491836\pi$
$798$			3.53381i			0.125096i
$799$		−	19.2020i		−	0.679317i
$800$		−	27.1366i		−	0.959424i
$801$			15.1554i			0.535490i
$802$	24.0292			0.848501
$803$	13.9186			0.491176
$804$			1.76402i			0.0622122i
$805$	46.2744			1.63096
$806$	−1.48876	+	3.33305i	−0.0524394	+	0.117402i
$807$	−5.25084			−0.184838
$808$		−	31.2661i		−	1.09994i
$809$	−21.8771			−0.769156			−0.384578	−	0.923092i	$-0.625653\pi$
$809$	−21.8771			−0.769156			−0.384578	+	0.923092i	$0.625653\pi$
$810$	−0.898465			−0.0315689
$811$		−	25.9895i		−	0.912614i	−0.889822	−	0.456307i	$-0.849172\pi$
$811$		−	25.9895i		−	0.912614i	0.889822	−	0.456307i	$-0.150828\pi$
$812$		−	3.90917i		−	0.137185i
$813$			29.2481i			1.02578i
$814$			53.3720i			1.87069i
$815$	1.54104			0.0539803
$816$	5.54440			0.194093
$817$			8.81065i			0.308246i
$818$	29.8309			1.04301
$819$	11.2004	+	5.00284i	0.391374	+	0.174813i
$820$	−0.157559			−0.00550219
$821$			10.0098i			0.349345i	0.984627	+	0.174672i	$0.0558866\pi$
$821$			10.0098i			0.349345i	−0.984627	+	0.174672i	$0.944113\pi$
$822$	−14.9303			−0.520755
$823$	−27.5363			−0.959857			−0.479928	−	0.877308i	$-0.659337\pi$
$823$	−27.5363			−0.959857			−0.479928	+	0.877308i	$0.659337\pi$
$824$			22.7792i			0.793551i
$825$		−	35.4217i		−	1.23322i
$826$		−	6.34533i		−	0.220782i
$827$			6.20407i			0.215737i	0.994165	+	0.107868i	$0.0344025\pi$
$827$			6.20407i			0.215737i	−0.994165	+	0.107868i	$0.965598\pi$
$828$	14.6716			0.509873
$829$	47.6602			1.65531			0.827654	−	0.561239i	$-0.189675\pi$
$829$	47.6602			1.65531			0.827654	+	0.561239i	$0.189675\pi$
$830$			33.6889i			1.16936i
$831$	−20.6036			−0.714729
$832$	10.5446	−	23.6074i	0.365569	−	0.818438i
$833$	18.1067			0.627359
$834$			9.44686i			0.327118i
$835$	19.4436			0.672873
$836$	10.9892			0.380068
$837$		−	5.14604i		−	0.177873i
$838$			25.1184i			0.867701i
$839$			49.1966i			1.69846i	0.528026	+	0.849228i	$0.322932\pi$
$839$			49.1966i			1.69846i	−0.528026	+	0.849228i	$0.677068\pi$
$840$			18.4492i			0.636557i
$841$	−24.0143			−0.828079
$842$	−0.194291			−0.00669571
$843$			9.93011i			0.342011i
$844$	12.2063			0.420157
$845$	31.4112	−	28.1466i	1.08058	−	0.968274i
$846$	−7.68007			−0.264046
$847$		−	46.9964i		−	1.61481i
$848$	−0.646981			−0.0222174
$849$	−11.7391			−0.402885
$850$		−	26.8325i		−	0.920349i
$851$		−	68.6763i		−	2.35419i
$852$		−	10.6237i		−	0.363964i
$853$			38.1893i			1.30758i	0.756677	+	0.653789i	$0.226821\pi$
$853$			38.1893i			1.30758i	−0.756677	+	0.653789i	$0.773179\pi$
$854$	−22.1059			−0.756450
$855$	11.3641			0.388644
$856$			29.7690i			1.01749i
$857$	−18.2224			−0.622466			−0.311233	−	0.950334i	$-0.600742\pi$
$857$	−18.2224			−0.622466			−0.311233	+	0.950334i	$0.600742\pi$
$858$	9.54295	−	21.3648i	0.325791	−	0.729383i
$859$	22.2461			0.759028			0.379514	−	0.925186i	$-0.376091\pi$
$859$	22.2461			0.759028			0.379514	+	0.925186i	$0.376091\pi$
$860$			15.0745i			0.514037i
$861$	0.0940418			0.00320494
$862$	15.2508			0.519444
$863$		−	9.63571i		−	0.328003i	−0.986460	−	0.164002i	$-0.947560\pi$
$863$		−	9.63571i		−	0.328003i	0.986460	−	0.164002i	$-0.0524402\pi$
$864$			25.2707i			0.859727i
$865$			0.0615656i			0.00209329i
$866$			13.0165i			0.442319i
$867$	−6.30972			−0.214289
$868$	1.75074			0.0594240
$869$		−	98.6541i		−	3.34661i
$870$	−7.71118			−0.261434
$871$	5.66549	+	2.53058i	0.191968	+	0.0857455i
$872$	17.9884			0.609163
$873$		−	19.2770i		−	0.652426i
$874$	14.8669			0.502881
$875$	3.06454			0.103600
$876$		−	2.34006i		−	0.0790634i
$877$			29.0418i			0.980672i	0.871534	+	0.490336i	$0.163126\pi$
$877$			29.0418i			0.980672i	−0.871534	+	0.490336i	$0.836874\pi$
$878$		−	0.568656i		−	0.0191912i
$879$			20.3875i			0.687652i
$880$	−21.7500			−0.733192
$881$	24.1421			0.813368			0.406684	−	0.913569i	$-0.366685\pi$
$881$	24.1421			0.813368			0.406684	+	0.913569i	$0.366685\pi$
$882$		−	7.24200i		−	0.243851i
$883$	6.46930			0.217709			0.108855	−	0.994058i	$-0.465282\pi$
$883$	6.46930			0.217709			0.108855	+	0.994058i	$0.465282\pi$
$884$	−6.87564	+	15.3932i	−0.231253	+	0.517730i
$885$	11.9050			0.400181
$886$		−	10.1810i		−	0.342036i
$887$	−14.4837			−0.486315			−0.243158	−	0.969987i	$-0.578183\pi$
$887$	−14.4837			−0.486315			−0.243158	+	0.969987i	$0.578183\pi$
$888$	27.3806			0.918832
$889$			3.16664i			0.106206i
$890$			26.2753i			0.880750i
$891$		−	1.66763i		−	0.0558679i
$892$			13.1405i			0.439978i
$893$	7.40196			0.247697
$894$	0.954269			0.0319155
$895$			18.3864i			0.614590i
$896$	−4.59916			−0.153647
$897$	−12.2794	+	27.4911i	−0.409996	+	0.917902i
$898$	15.6864			0.523463
$899$			2.23287i			0.0744704i
$900$	10.2075			0.340250
$901$	2.82193			0.0940120
$902$			0.307471i			0.0102377i
$903$		−	8.99751i		−	0.299418i
$904$			17.5808i			0.584728i
$905$		−	50.4228i		−	1.67611i
$906$	0.235604			0.00782740
$907$	33.0392			1.09705			0.548525	−	0.836134i	$-0.315190\pi$
$907$	33.0392			1.09705			0.548525	+	0.836134i	$0.315190\pi$
$908$		−	21.2039i		−	0.703675i
$909$	19.6674			0.652326
$910$	19.4184	+	8.67354i	0.643713	+	0.287525i
$911$	−42.4959			−1.40795			−0.703975	−	0.710225i	$-0.748593\pi$
$911$	−42.4959			−1.40795			−0.703975	+	0.710225i	$0.748593\pi$
$912$			2.13725i			0.0707714i
$913$	−62.5297			−2.06943
$914$	−22.8016			−0.754211
$915$		−	41.4747i		−	1.37111i
$916$			4.70052i			0.155310i
$917$			28.3717i			0.936916i
$918$			24.9875i			0.824712i
$919$	5.17140			0.170589			0.0852944	−	0.996356i	$-0.472817\pi$
$919$	5.17140			0.170589			0.0852944	+	0.996356i	$0.472817\pi$
$920$	77.6164			2.55894
$921$		−	3.13141i		−	0.103184i
$922$	−12.1204			−0.399164
$923$	−34.1202	−	15.2403i	−1.12308	−	0.501642i
$924$	−11.2222			−0.369184
$925$		−	47.7803i		−	1.57101i
$926$	43.0236			1.41384
$927$	−14.3288			−0.470621
$928$		−	10.9650i		−	0.359942i
$929$			4.37621i			0.143579i	0.997420	+	0.0717894i	$0.0228709\pi$
$929$			4.37621i			0.143579i	−0.997420	+	0.0717894i	$0.977129\pi$
$930$		−	3.45349i		−	0.113244i
$931$			6.97975i			0.228752i
$932$	−28.3909			−0.929974
$933$	15.9964			0.523698
$934$			35.7091i			1.16844i
$935$	94.8666			3.10247
$936$	18.7865	+	8.39131i	0.614057	+	0.274279i
$937$	2.77193			0.0905550			0.0452775	−	0.998974i	$-0.485583\pi$
$937$	2.77193			0.0905550			0.0452775	+	0.998974i	$0.485583\pi$
$938$			3.12881i			0.102159i
$939$	7.19080			0.234663
$940$	12.6643			0.413065
$941$			36.3782i			1.18589i	0.805241	+	0.592947i	$0.202036\pi$
$941$			36.3782i			1.18589i	−0.805241	+	0.592947i	$0.797964\pi$
$942$		−	9.07089i		−	0.295545i
$943$		−	0.395638i		−	0.0128837i
$944$		−	3.83765i		−	0.124905i
$945$	−29.9809			−0.975278
$946$	29.4175			0.956446
$947$			28.0675i			0.912071i	0.889962	+	0.456035i	$0.150731\pi$
$947$			28.0675i			0.912071i	−0.889962	+	0.456035i	$0.849269\pi$
$948$	−16.5862			−0.538695
$949$	−7.51555	−	3.35694i	−0.243965	−	0.108971i
$950$	10.3434			0.335584
$951$		−	18.2404i		−	0.591485i
$952$	−25.9399			−0.840718
$953$	47.1931			1.52874			0.764368	−	0.644781i	$-0.223051\pi$
$953$	47.1931			1.52874			0.764368	+	0.644781i	$0.223051\pi$
$954$		−	1.12867i		−	0.0365419i
$955$		−	23.9703i		−	0.775662i
$956$			26.5016i			0.857124i
$957$		−	14.3127i		−	0.462663i
$958$	−17.2368			−0.556896
$959$	25.1873			0.813342
$960$			24.4604i			0.789456i
$961$	−1.00000			−0.0322581
$962$	12.8725	−	28.8190i	0.415026	−	0.929163i
$963$	−18.7257			−0.603427
$964$			21.0825i			0.679022i
$965$	13.6976			0.440941
$966$	−15.1822			−0.488479
$967$		−	19.0739i		−	0.613375i	−0.951810	−	0.306688i	$-0.900779\pi$
$967$		−	19.0739i		−	0.613375i	0.951810	−	0.306688i	$-0.0992207\pi$
$968$		−	78.8275i		−	2.53361i
$969$		−	9.32201i		−	0.299466i
$970$		−	33.4209i		−	1.07308i
$971$	56.9080			1.82626			0.913132	−	0.407664i	$-0.133656\pi$
$971$	56.9080			1.82626			0.913132	+	0.407664i	$0.133656\pi$
$972$	−15.3318			−0.491767
$973$		−	15.9368i		−	0.510909i
$974$	−3.56937			−0.114370
$975$	−8.54315	+	19.1265i	−0.273600	+	0.612537i
$976$	−13.3697			−0.427953
$977$			34.4785i			1.10307i	0.834153	+	0.551533i	$0.185957\pi$
$977$			34.4785i			1.10307i	−0.834153	+	0.551533i	$0.814043\pi$
$978$	−0.505601			−0.0161673
$979$	−48.7694			−1.55868
$980$			11.9420i			0.381472i
$981$			11.3153i			0.361268i
$982$		−	30.3335i		−	0.967981i
$983$		−	33.5510i		−	1.07011i	−0.844817	−	0.535056i	$-0.820291\pi$
$983$		−	33.5510i		−	1.07011i	0.844817	−	0.535056i	$-0.179709\pi$
$984$	0.157737			0.00502848
$985$	−23.1629			−0.738031
$986$		−	10.8421i		−	0.345283i
$987$	−7.55893			−0.240604
$988$	−5.93377	−	2.65041i	−0.188778	−	0.0843209i
$989$	−37.8529			−1.20365
$990$		−	37.9431i		−	1.20591i
$991$	0.204273			0.00648894			0.00324447	−	0.999995i	$-0.498967\pi$
$991$	0.204273			0.00648894			0.00324447	+	0.999995i	$0.498967\pi$
$992$	4.91070			0.155915
$993$		−	6.12063i		−	0.194232i
$994$		−	18.8431i		−	0.597668i
$995$		−	56.8847i		−	1.80337i
$996$			10.5128i			0.333111i
$997$	−36.7937			−1.16527			−0.582634	−	0.812735i	$-0.697978\pi$
$997$	−36.7937			−1.16527			−0.582634	+	0.812735i	$0.697978\pi$
$998$	9.86411			0.312243
$999$			44.4949i			1.40776i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.c.b.311.21	yes	32
13.5	odd	4		5239.2.a.l.1.10		16
13.8	odd	4		5239.2.a.k.1.7		16
13.12	even	2	inner	403.2.c.b.311.12	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.c.b.311.12	✓	32	13.12	even	2	inner
403.2.c.b.311.21	yes	32	1.1	even	1	trivial
5239.2.a.k.1.7		16	13.8	odd	4
5239.2.a.l.1.10		16	13.5	odd	4

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.01245i q^{2} -1.05136 q^{3} +0.974950 q^{4} +3.24438i q^{5} -1.06445i q^{6} +1.79572i q^{7} +3.01198i q^{8} -1.89463 q^{9} +O(q^{10})\)	\(q+1.01245i q^{2} -1.05136 q^{3} +0.974950 q^{4} +3.24438i q^{5} -1.06445i q^{6} +1.79572i q^{7} +3.01198i q^{8} -1.89463 q^{9} -3.28477 q^{10} -6.09683i q^{11} -1.02503 q^{12} +(-1.47046 + 3.29207i) q^{13} -1.81807 q^{14} -3.41103i q^{15} -1.09957 q^{16} +4.79598 q^{17} -1.91821i q^{18} +1.84875i q^{19} +3.16311i q^{20} -1.88796i q^{21} +6.17272 q^{22} -7.94273 q^{23} -3.16669i q^{24} -5.52601 q^{25} +(-3.33305 - 1.48876i) q^{26} +5.14604 q^{27} +1.75074i q^{28} -2.23287 q^{29} +3.45349 q^{30} -1.00000i q^{31} +4.91070i q^{32} +6.40999i q^{33} +4.85568i q^{34} -5.82601 q^{35} -1.84717 q^{36} +8.64644i q^{37} -1.87176 q^{38} +(1.54599 - 3.46117i) q^{39} -9.77201 q^{40} +0.0498113i q^{41} +1.91146 q^{42} +4.76573 q^{43} -5.94410i q^{44} -6.14691i q^{45} -8.04159i q^{46} -4.00376i q^{47} +1.15605 q^{48} +3.77538 q^{49} -5.59480i q^{50} -5.04233 q^{51} +(-1.43362 + 3.20961i) q^{52} +0.588394 q^{53} +5.21010i q^{54} +19.7804 q^{55} -5.40868 q^{56} -1.94371i q^{57} -2.26066i q^{58} +3.49014i q^{59} -3.32558i q^{60} +12.1590 q^{61} +1.01245 q^{62} -3.40223i q^{63} -7.17097 q^{64} +(-10.6807 - 4.77073i) q^{65} -6.48978 q^{66} -1.72095i q^{67} +4.67585 q^{68} +8.35070 q^{69} -5.89852i q^{70} +10.3643i q^{71} -5.70659i q^{72} +2.28292i q^{73} -8.75406 q^{74} +5.80985 q^{75} +1.80244i q^{76} +10.9482 q^{77} +(3.50425 + 1.56523i) q^{78} +16.1812 q^{79} -3.56743i q^{80} +0.273525 q^{81} -0.0504314 q^{82} -10.2561i q^{83} -1.84067i q^{84} +15.5600i q^{85} +4.82505i q^{86} +2.34756 q^{87} +18.3635 q^{88} -7.99914i q^{89} +6.22342 q^{90} +(-5.91165 - 2.64053i) q^{91} -7.74376 q^{92} +1.05136i q^{93} +4.05360 q^{94} -5.99805 q^{95} -5.16294i q^{96} +10.1745i q^{97} +3.82238i q^{98} +11.5512i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{3} - 36 q^{4} + 20 q^{9}+O(q^{10}) \) 32 * q - 4 * q^3 - 36 * q^4 + 20 * q^9	\( 32 q - 4 q^{3} - 36 q^{4} + 20 q^{9} + 4 q^{10} - 16 q^{12} + 10 q^{13} - 16 q^{14} + 28 q^{16} - 8 q^{17} - 16 q^{22} - 8 q^{23} + 4 q^{25} + 18 q^{26} + 20 q^{27} - 16 q^{29} + 40 q^{30} - 4 q^{35} - 44 q^{36} + 12 q^{38} + 4 q^{39} + 28 q^{40} + 28 q^{42} - 32 q^{43} - 64 q^{49} - 64 q^{52} - 12 q^{53} + 44 q^{55} + 8 q^{56} + 16 q^{61} + 8 q^{62} - 76 q^{64} - 66 q^{65} - 68 q^{66} + 64 q^{68} + 20 q^{69} + 16 q^{74} - 32 q^{77} - 20 q^{78} + 64 q^{79} - 16 q^{81} + 12 q^{82} - 72 q^{87} + 80 q^{88} + 68 q^{90} + 22 q^{91} + 28 q^{92} + 88 q^{94} + 4 q^{95}+O(q^{100}) \) 32 * q - 4 * q^3 - 36 * q^4 + 20 * q^9 + 4 * q^10 - 16 * q^12 + 10 * q^13 - 16 * q^14 + 28 * q^16 - 8 * q^17 - 16 * q^22 - 8 * q^23 + 4 * q^25 + 18 * q^26 + 20 * q^27 - 16 * q^29 + 40 * q^30 - 4 * q^35 - 44 * q^36 + 12 * q^38 + 4 * q^39 + 28 * q^40 + 28 * q^42 - 32 * q^43 - 64 * q^49 - 64 * q^52 - 12 * q^53 + 44 * q^55 + 8 * q^56 + 16 * q^61 + 8 * q^62 - 76 * q^64 - 66 * q^65 - 68 * q^66 + 64 * q^68 + 20 * q^69 + 16 * q^74 - 32 * q^77 - 20 * q^78 + 64 * q^79 - 16 * q^81 + 12 * q^82 - 72 * q^87 + 80 * q^88 + 68 * q^90 + 22 * q^91 + 28 * q^92 + 88 * q^94 + 4 * q^95

Introduction

L-functions

Modular forms

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