LMFDB - Embedded newform 310.2.b.a.249.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [310,2,Mod(249,310)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(310, 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("310.249");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 310 = 2 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	310.b (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:	$2.47536246266$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.619810816.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{5} + 14x^{4} - 8x^{3} + 2x^{2} + 2x + 1 $ x^8 - 2x^5 + 14x^4 - 8x^3 + 2x^2 + 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			249.2
Root			$1.18254 + 1.18254i$ of defining polynomial
Character	$\chi$	$=$	310.249
Dual form			310.2.b.a.249.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.79682i q^{3} -1.00000 q^{4} +(1.60536 + 1.55654i) q^{5} -1.79682 q^{6} -3.47817i q^{7} +1.00000i q^{8} -0.228545 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -1.79682i q^{3} -1.00000 q^{4} +(1.60536 + 1.55654i) q^{5} -1.79682 q^{6} -3.47817i q^{7} +1.00000i q^{8} -0.228545 q^{9} +(1.55654 - 1.60536i) q^{10} -2.47063 q^{11} +1.79682i q^{12} -7.00754i q^{13} -3.47817 q^{14} +(2.79682 - 2.88454i) q^{15} +1.00000 q^{16} +5.40399i q^{17} +0.228545i q^{18} -0.480550 q^{19} +(-1.60536 - 1.55654i) q^{20} -6.24962 q^{21} +2.47063i q^{22} +0.365086i q^{23} +1.79682 q^{24} +(0.154365 + 4.99762i) q^{25} -7.00754 q^{26} -4.97979i q^{27} +3.47817i q^{28} +0.00991953 q^{29} +(-2.88454 - 2.79682i) q^{30} -1.00000 q^{31} -1.00000i q^{32} +4.43927i q^{33} +5.40399 q^{34} +(5.41391 - 5.58371i) q^{35} +0.228545 q^{36} +10.5270i q^{37} +0.480550i q^{38} -12.5912 q^{39} +(-1.55654 + 1.60536i) q^{40} +9.63015 q^{41} +6.24962i q^{42} -5.72264i q^{43} +2.47063 q^{44} +(-0.366896 - 0.355739i) q^{45} +0.365086 q^{46} +2.94328i q^{47} -1.79682i q^{48} -5.09764 q^{49} +(4.99762 - 0.154365i) q^{50} +9.70996 q^{51} +7.00754i q^{52} -6.60117i q^{53} -4.97979 q^{54} +(-3.96625 - 3.84564i) q^{55} +3.47817 q^{56} +0.863459i q^{57} -0.00991953i q^{58} +10.9563 q^{59} +(-2.79682 + 2.88454i) q^{60} +8.31388 q^{61} +1.00000i q^{62} +0.794916i q^{63} -1.00000 q^{64} +(10.9075 - 11.2496i) q^{65} +4.43927 q^{66} +7.01544i q^{67} -5.40399i q^{68} +0.655991 q^{69} +(-5.58371 - 5.41391i) q^{70} +0.632531 q^{71} -0.228545i q^{72} -3.20871i q^{73} +10.5270 q^{74} +(8.97979 - 0.277365i) q^{75} +0.480550 q^{76} +8.59326i q^{77} +12.5912i q^{78} +13.5111 q^{79} +(1.60536 + 1.55654i) q^{80} -9.63340 q^{81} -9.63015i q^{82} +9.56589i q^{83} +6.24962 q^{84} +(-8.41152 + 8.67535i) q^{85} -5.72264 q^{86} -0.0178236i q^{87} -2.47063i q^{88} -15.1516 q^{89} +(-0.355739 + 0.366896i) q^{90} -24.3734 q^{91} -0.365086i q^{92} +1.79682i q^{93} +2.94328 q^{94} +(-0.771455 - 0.747995i) q^{95} -1.79682 q^{96} +5.32981i q^{97} +5.09764i q^{98} +0.564649 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 2 q^{5} - 8 q^{6} - 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^4 - 2 * q^5 - 8 * q^6 - 8 * q^9	$ 8 q - 8 q^{4} - 2 q^{5} - 8 q^{6} - 8 q^{9} + 2 q^{10} - 16 q^{11} + 12 q^{14} + 16 q^{15} + 8 q^{16} - 12 q^{19} + 2 q^{20} - 4 q^{21} + 8 q^{24} + 12 q^{25} - 20 q^{26} + 12 q^{29} + 4 q^{30} - 8 q^{31} + 8 q^{34} + 20 q^{35} + 8 q^{36} - 40 q^{39} - 2 q^{40} + 16 q^{44} + 30 q^{45} - 16 q^{46} - 32 q^{49} - 8 q^{50} - 44 q^{51} + 44 q^{54} + 36 q^{55} - 12 q^{56} + 8 q^{59} - 16 q^{60} + 4 q^{61} - 8 q^{64} + 12 q^{65} + 12 q^{66} - 28 q^{69} - 20 q^{70} - 24 q^{71} + 40 q^{74} - 12 q^{75} + 12 q^{76} + 32 q^{79} - 2 q^{80} + 88 q^{81} + 4 q^{84} + 4 q^{85} - 44 q^{86} - 24 q^{89} - 34 q^{90} - 20 q^{91} + 4 q^{94} - 8 q^{96} + 20 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 - 2 * q^5 - 8 * q^6 - 8 * q^9 + 2 * q^10 - 16 * q^11 + 12 * q^14 + 16 * q^15 + 8 * q^16 - 12 * q^19 + 2 * q^20 - 4 * q^21 + 8 * q^24 + 12 * q^25 - 20 * q^26 + 12 * q^29 + 4 * q^30 - 8 * q^31 + 8 * q^34 + 20 * q^35 + 8 * q^36 - 40 * q^39 - 2 * q^40 + 16 * q^44 + 30 * q^45 - 16 * q^46 - 32 * q^49 - 8 * q^50 - 44 * q^51 + 44 * q^54 + 36 * q^55 - 12 * q^56 + 8 * q^59 - 16 * q^60 + 4 * q^61 - 8 * q^64 + 12 * q^65 + 12 * q^66 - 28 * q^69 - 20 * q^70 - 24 * q^71 + 40 * q^74 - 12 * q^75 + 12 * q^76 + 32 * q^79 - 2 * q^80 + 88 * q^81 + 4 * q^84 + 4 * q^85 - 44 * q^86 - 24 * q^89 - 34 * q^90 - 20 * q^91 + 4 * q^94 - 8 * q^96 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/310\mathbb{Z}\right)^\times$.

$n$	$187$	$251$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		−	1.79682i		−	1.03739i	−0.854959	−	0.518696i	$-0.826418\pi$
$3$		−	1.79682i		−	1.03739i	0.854959	−	0.518696i	$-0.173582\pi$
$4$	−1.00000			−0.500000
$5$	1.60536	+	1.55654i	0.717939	+	0.696106i
$5$	1.60536	+	1.55654i	0.717939	+	0.696106i
$6$	−1.79682			−0.733547
$7$		−	3.47817i		−	1.31462i	−0.753619	−	0.657312i	$-0.771694\pi$
$7$		−	3.47817i		−	1.31462i	0.753619	−	0.657312i	$-0.228306\pi$
$8$			1.00000i			0.353553i
$9$	−0.228545			−0.0761815
$10$	1.55654	−	1.60536i	0.492221	−	0.507660i
$11$	−2.47063			−0.744923			−0.372462	−	0.928048i	$-0.621486\pi$
$11$	−2.47063			−0.744923			−0.372462	+	0.928048i	$0.621486\pi$
$12$			1.79682i			0.518696i
$13$		−	7.00754i		−	1.94354i	−0.235929	−	0.971770i	$-0.575813\pi$
$13$		−	7.00754i		−	1.94354i	0.235929	−	0.971770i	$-0.424187\pi$
$14$	−3.47817			−0.929579
$15$	2.79682	−	2.88454i	0.722135	−	0.744784i
$16$	1.00000			0.250000
$17$			5.40399i			1.31066i	0.755343	+	0.655330i	$0.227470\pi$
$17$			5.40399i			1.31066i	−0.755343	+	0.655330i	$0.772530\pi$
$18$			0.228545i			0.0538685i
$19$	−0.480550			−0.110246			−0.0551228	−	0.998480i	$-0.517555\pi$
$19$	−0.480550			−0.110246			−0.0551228	+	0.998480i	$0.517555\pi$
$20$	−1.60536	−	1.55654i	−0.358970	−	0.348053i
$21$	−6.24962			−1.36378
$22$			2.47063i			0.526740i
$23$			0.365086i			0.0761256i	0.999275	+	0.0380628i	$0.0121187\pi$
$23$			0.365086i			0.0761256i	−0.999275	+	0.0380628i	$0.987881\pi$
$24$	1.79682			0.366773
$25$	0.154365	+	4.99762i	0.0308729	+	0.999523i
$26$	−7.00754			−1.37429
$27$		−	4.97979i		−	0.958362i
$28$			3.47817i			0.657312i
$29$	0.00991953			0.00184201			0.000921005	−	1.00000i	$-0.499707\pi$
$29$	0.00991953			0.00184201			0.000921005		1.00000i	$0.499707\pi$
$30$	−2.88454	−	2.79682i	−0.526642	−	0.510626i
$31$	−1.00000			−0.179605
$31$	−1.00000			−0.179605
$32$		−	1.00000i		−	0.176777i
$33$			4.43927i			0.772777i
$34$	5.40399			0.926776
$35$	5.41391	−	5.58371i	0.915117	−	0.943819i
$36$	0.228545			0.0380908
$37$			10.5270i			1.73063i	0.501232	+	0.865313i	$0.332880\pi$
$37$			10.5270i			1.73063i	−0.501232	+	0.865313i	$0.667120\pi$
$38$			0.480550i			0.0779554i
$39$	−12.5912			−2.01621
$40$	−1.55654	+	1.60536i	−0.246111	+	0.253830i
$41$	9.63015			1.50398			0.751988	−	0.659177i	$-0.229095\pi$
$41$	9.63015			1.50398			0.751988	+	0.659177i	$0.229095\pi$
$42$			6.24962i			0.964338i
$43$		−	5.72264i		−	0.872694i	−0.899779	−	0.436347i	$-0.856272\pi$
$43$		−	5.72264i		−	0.872694i	0.899779	−	0.436347i	$-0.143728\pi$
$44$	2.47063			0.372462
$45$	−0.366896	−	0.355739i	−0.0546937	−	0.0530304i
$46$	0.365086			0.0538289
$47$			2.94328i			0.429321i	0.976689	+	0.214660i	$0.0688645\pi$
$47$			2.94328i			0.429321i	−0.976689	+	0.214660i	$0.931136\pi$
$48$		−	1.79682i		−	0.259348i
$49$	−5.09764			−0.728234
$50$	4.99762	−	0.154365i	0.706770	−	0.0218305i
$51$	9.70996			1.35967
$52$			7.00754i			0.971770i
$53$		−	6.60117i		−	0.906740i	−0.891322	−	0.453370i	$-0.850222\pi$
$53$		−	6.60117i		−	0.906740i	0.891322	−	0.453370i	$-0.149778\pi$
$54$	−4.97979			−0.677664
$55$	−3.96625	−	3.84564i	−0.534809	−	0.518545i
$56$	3.47817			0.464790
$57$			0.863459i			0.114368i
$58$		−	0.00991953i		−	0.00130250i
$59$	10.9563			1.42639			0.713196	−	0.700964i	$-0.247247\pi$
$59$	10.9563			1.42639			0.713196	+	0.700964i	$0.247247\pi$
$60$	−2.79682	+	2.88454i	−0.361067	+	0.372392i
$61$	8.31388			1.06448			0.532242	−	0.846592i	$-0.321350\pi$
$61$	8.31388			1.06448			0.532242	+	0.846592i	$0.321350\pi$
$62$			1.00000i			0.127000i
$63$			0.794916i			0.100150i
$64$	−1.00000			−0.125000
$65$	10.9075	−	11.2496i	1.35291	−	1.39534i
$66$	4.43927			0.546436
$67$			7.01544i			0.857072i	0.903525	+	0.428536i	$0.140971\pi$
$67$			7.01544i			0.857072i	−0.903525	+	0.428536i	$0.859029\pi$
$68$		−	5.40399i		−	0.655330i
$69$	0.655991			0.0789721
$70$	−5.58371	−	5.41391i	−0.667381	−	0.647086i
$71$	0.632531			0.0750676			0.0375338	−	0.999295i	$-0.488050\pi$
$71$	0.632531			0.0750676			0.0375338	+	0.999295i	$0.488050\pi$
$72$		−	0.228545i		−	0.0269342i
$73$		−	3.20871i		−	0.375551i	−0.982212	−	0.187775i	$-0.939872\pi$
$73$		−	3.20871i		−	0.375551i	0.982212	−	0.187775i	$-0.0601277\pi$
$74$	10.5270			1.22374
$75$	8.97979	−	0.277365i	1.03690	−	0.0320273i
$76$	0.480550			0.0551228
$77$			8.59326i			0.979293i
$78$			12.5912i			1.42568i
$79$	13.5111			1.52011			0.760057	−	0.649857i	$-0.225171\pi$
$79$	13.5111			1.52011			0.760057	+	0.649857i	$0.225171\pi$
$80$	1.60536	+	1.55654i	0.179485	+	0.174026i
$81$	−9.63340			−1.07038
$82$		−	9.63015i		−	1.06347i
$83$			9.56589i			1.04999i	0.851105	+	0.524996i	$0.175933\pi$
$83$			9.56589i			1.04999i	−0.851105	+	0.524996i	$0.824067\pi$
$84$	6.24962			0.681890
$85$	−8.41152	+	8.67535i	−0.912358	+	0.940973i
$86$	−5.72264			−0.617088
$87$		−	0.0178236i		−	0.00191089i
$88$		−	2.47063i		−	0.263370i
$89$	−15.1516			−1.60607			−0.803034	−	0.595933i	$-0.796782\pi$
$89$	−15.1516			−1.60607			−0.803034	+	0.595933i	$0.796782\pi$
$90$	−0.355739	+	0.366896i	−0.0374982	+	0.0386743i
$91$	−24.3734			−2.55502
$92$		−	0.365086i		−	0.0380628i
$93$			1.79682i			0.186321i
$94$	2.94328			0.303576
$95$	−0.771455	−	0.747995i	−0.0791497	−	0.0767427i
$96$	−1.79682			−0.183387
$97$			5.32981i			0.541160i	0.962698	+	0.270580i	$0.0872154\pi$
$97$			5.32981i			0.541160i	−0.962698	+	0.270580i	$0.912785\pi$
$98$			5.09764i			0.514939i
$99$	0.564649			0.0567494
$100$	−0.154365	−	4.99762i	−0.0154365	−	0.499762i
$101$	−0.300341			−0.0298851			−0.0149425	−	0.999888i	$-0.504757\pi$
$101$	−0.300341			−0.0298851			−0.0149425	+	0.999888i	$0.504757\pi$
$102$		−	9.70996i		−	0.961430i
$103$		−	2.50401i		−	0.246727i	−0.992362	−	0.123364i	$-0.960632\pi$
$103$		−	2.50401i		−	0.246727i	0.992362	−	0.123364i	$-0.0393682\pi$
$104$	7.00754			0.687145
$105$	−10.0329	−	9.72779i	−0.979110	−	0.949335i
$106$	−6.60117			−0.641162
$107$			13.4369i			1.29899i	0.760365	+	0.649496i	$0.225020\pi$
$107$			13.4369i			1.29899i	−0.760365	+	0.649496i	$0.774980\pi$
$108$			4.97979i			0.479181i
$109$	0.706711			0.0676906			0.0338453	−	0.999427i	$-0.489225\pi$
$109$	0.706711			0.0676906			0.0338453	+	0.999427i	$0.489225\pi$
$110$	−3.84564	+	3.96625i	−0.366667	+	0.378167i
$111$	18.9150			1.79534
$112$		−	3.47817i		−	0.328656i
$113$			7.55597i			0.710806i	0.934713	+	0.355403i	$0.115656\pi$
$113$			7.55597i			0.710806i	−0.934713	+	0.355403i	$0.884344\pi$
$114$	0.863459			0.0808703
$115$	−0.568271	+	0.586094i	−0.0529915	+	0.0546536i
$116$	−0.00991953			−0.000921005
$117$			1.60153i			0.148062i
$118$		−	10.9563i		−	1.00861i
$119$	18.7960			1.72302
$120$	2.88454	+	2.79682i	0.263321	+	0.255313i
$121$	−4.89599			−0.445090
$122$		−	8.31388i		−	0.752704i
$123$		−	17.3036i		−	1.56021i
$124$	1.00000			0.0898027
$125$	−7.53118	+	8.26325i	−0.673609	+	0.739088i
$126$	0.794916			0.0708167
$127$			17.9389i			1.59182i	0.605416	+	0.795909i	$0.293007\pi$
$127$			17.9389i			1.59182i	−0.605416	+	0.795909i	$0.706993\pi$
$128$			1.00000i			0.0883883i
$129$	−10.2825			−0.905325
$130$	−11.2496	−	10.9075i	−0.986657	−	0.956652i
$131$	2.15198			0.188019			0.0940097	−	0.995571i	$-0.470032\pi$
$131$	2.15198			0.188019			0.0940097	+	0.995571i	$0.470032\pi$
$132$		−	4.43927i		−	0.386388i
$133$			1.67143i			0.144932i
$134$	7.01544			0.606042
$135$	7.75125	−	7.99436i	0.667121	−	0.688045i
$136$	−5.40399			−0.463388
$137$		−	10.3651i		−	0.885549i	−0.896633	−	0.442775i	$-0.853994\pi$
$137$		−	10.3651i		−	0.885549i	0.896633	−	0.442775i	$-0.146006\pi$
$138$		−	0.655991i		−	0.0558417i
$139$	−14.0250			−1.18958			−0.594792	−	0.803880i	$-0.702766\pi$
$139$	−14.0250			−1.18958			−0.594792	+	0.803880i	$0.702766\pi$
$140$	−5.41391	+	5.58371i	−0.457559	+	0.471910i
$141$	5.28852			0.445374
$142$		−	0.632531i		−	0.0530808i
$143$			17.3130i			1.44779i
$144$	−0.228545			−0.0190454
$145$	0.0159244	+	0.0154401i	0.00132245	+	0.00128223i
$146$	−3.20871			−0.265554
$147$			9.15952i			0.755464i
$148$		−	10.5270i		−	0.865313i
$149$	20.5301			1.68189			0.840947	−	0.541118i	$-0.181999\pi$
$149$	20.5301			1.68189			0.840947	+	0.541118i	$0.181999\pi$
$150$	−0.277365	−	8.97979i	−0.0226467	−	0.733197i
$151$	−11.0849			−0.902073			−0.451036	−	0.892506i	$-0.648946\pi$
$151$	−11.0849			−0.902073			−0.451036	+	0.892506i	$0.648946\pi$
$152$		−	0.480550i		−	0.0389777i
$153$		−	1.23505i		−	0.0998480i
$154$	8.59326			0.692465
$155$	−1.60536	−	1.55654i	−0.128946	−	0.125024i
$156$	12.5912			1.00811
$157$		−	15.3976i		−	1.22886i	−0.788970	−	0.614432i	$-0.789385\pi$
$157$		−	15.3976i		−	1.22886i	0.788970	−	0.614432i	$-0.210615\pi$
$158$		−	13.5111i		−	1.07488i
$159$	−11.8611			−0.940644
$160$	1.55654	−	1.60536i	0.123055	−	0.126915i
$161$	1.26983			0.100077
$162$			9.63340i			0.756871i
$163$		−	17.9325i		−	1.40458i	−0.711890	−	0.702291i	$-0.752161\pi$
$163$		−	17.9325i		−	1.40458i	0.711890	−	0.702291i	$-0.247839\pi$
$164$	−9.63015			−0.751988
$165$	−6.90990	+	7.12662i	−0.537935	+	0.554807i
$166$	9.56589			0.742457
$167$		−	12.9658i		−	1.00332i	−0.865065	−	0.501661i	$-0.832723\pi$
$167$		−	12.9658i		−	1.00332i	0.865065	−	0.501661i	$-0.167277\pi$
$168$		−	6.24962i		−	0.482169i
$169$	−36.1056			−2.77735
$170$	8.67535	+	8.41152i	0.665369	+	0.645134i
$171$	0.109827			0.00839868
$172$			5.72264i			0.436347i
$173$			6.51908i			0.495637i	0.968807	+	0.247818i	$0.0797136\pi$
$173$			6.51908i			0.495637i	−0.968807	+	0.247818i	$0.920286\pi$
$174$	−0.0178236			−0.00135120
$175$	17.3825	−	0.536906i	1.31400	−	0.0405863i
$176$	−2.47063			−0.186231
$177$		−	19.6865i		−	1.47973i
$178$			15.1516i			1.13566i
$179$	−14.2820			−1.06749			−0.533745	−	0.845646i	$-0.679216\pi$
$179$	−14.2820			−1.06749			−0.533745	+	0.845646i	$0.679216\pi$
$180$	0.366896	+	0.355739i	0.0273468	+	0.0265152i
$181$	−6.92295			−0.514579			−0.257290	−	0.966334i	$-0.582829\pi$
$181$	−6.92295			−0.514579			−0.257290	+	0.966334i	$0.582829\pi$
$182$			24.3734i			1.80667i
$183$		−	14.9385i		−	1.10429i
$184$	−0.365086			−0.0269145
$185$	−16.3857	+	16.8996i	−1.20470	+	1.24248i
$186$	1.79682			0.131749
$187$		−	13.3513i		−	0.976340i
$188$		−	2.94328i		−	0.214660i
$189$	−17.3205			−1.25988
$190$	−0.747995	+	0.771455i	−0.0542653	+	0.0559673i
$191$	−7.17783			−0.519369			−0.259685	−	0.965693i	$-0.583619\pi$
$191$	−7.17783			−0.519369			−0.259685	+	0.965693i	$0.583619\pi$
$192$			1.79682i			0.129674i
$193$			9.63958i			0.693872i	0.937889	+	0.346936i	$0.112778\pi$
$193$			9.63958i			0.693872i	−0.937889	+	0.346936i	$0.887222\pi$
$194$	5.32981			0.382658
$195$	−20.2135	−	19.5988i	−1.44752	−	1.40350i
$196$	5.09764			0.364117
$197$		−	14.8309i		−	1.05666i	−0.849039	−	0.528331i	$-0.822818\pi$
$197$		−	14.8309i		−	1.05666i	0.849039	−	0.528331i	$-0.177182\pi$
$198$		−	0.564649i		−	0.0401279i
$199$	−9.18726			−0.651268			−0.325634	−	0.945496i	$-0.605578\pi$
$199$	−9.18726			−0.651268			−0.325634	+	0.945496i	$0.605578\pi$
$200$	−4.99762	+	0.154365i	−0.353385	+	0.0109152i
$201$	12.6054			0.889120
$202$			0.300341i			0.0211319i
$203$		−	0.0345018i		−	0.00242155i
$204$	−9.70996			−0.679833
$205$	15.4599	+	14.9897i	1.07976	+	1.04693i
$206$	−2.50401			−0.174463
$207$		−	0.0834383i		−	0.00579937i
$208$		−	7.00754i		−	0.485885i
$209$	1.18726			0.0821245
$210$	−9.72779	+	10.0329i	−0.671281	+	0.692336i
$211$	7.97177			0.548799			0.274400	−	0.961616i	$-0.411521\pi$
$211$	7.97177			0.548799			0.274400	+	0.961616i	$0.411521\pi$
$212$			6.60117i			0.453370i
$213$		−	1.13654i		−	0.0778745i
$214$	13.4369			0.918526
$215$	8.90751	−	9.18689i	0.607487	−	0.626541i
$216$	4.97979			0.338832
$217$			3.47817i			0.236113i
$218$		−	0.706711i		−	0.0478645i
$219$	−5.76545			−0.389593
$220$	3.96625	+	3.84564i	0.267405	+	0.259273i
$221$	37.8686			2.54732
$222$		−	18.9150i		−	1.26949i
$223$			23.2190i			1.55486i	0.628969	+	0.777430i	$0.283477\pi$
$223$			23.2190i			1.55486i	−0.628969	+	0.777430i	$0.716523\pi$
$224$	−3.47817			−0.232395
$225$	−0.0352792	−	1.14218i	−0.00235195	−	0.0761452i
$226$	7.55597			0.502615
$227$		−	1.88252i		−	0.124947i	−0.998047	−	0.0624736i	$-0.980101\pi$
$227$		−	1.88252i		−	0.124947i	0.998047	−	0.0624736i	$-0.0198989\pi$
$228$		−	0.863459i		−	0.0571840i
$229$	11.9472			0.789493			0.394746	−	0.918790i	$-0.370832\pi$
$229$	11.9472			0.789493			0.394746	+	0.918790i	$0.370832\pi$
$230$	0.586094	+	0.568271i	0.0386459	+	0.0374707i
$231$	15.4405			1.01591
$232$			0.00991953i			0.000651249i
$233$			10.4393i			0.683899i	0.939718	+	0.341950i	$0.111087\pi$
$233$			10.4393i			0.683899i	−0.939718	+	0.341950i	$0.888913\pi$
$234$	1.60153			0.104696
$235$	−4.58133	+	4.72502i	−0.298853	+	0.308226i
$236$	−10.9563			−0.713196
$237$		−	24.2769i		−	1.57695i
$238$		−	18.7960i		−	1.21836i
$239$	−5.47615			−0.354223			−0.177111	−	0.984191i	$-0.556675\pi$
$239$	−5.47615			−0.354223			−0.177111	+	0.984191i	$0.556675\pi$
$240$	2.79682	−	2.88454i	0.180534	−	0.186196i
$241$	5.73722			0.369567			0.184784	−	0.982779i	$-0.440842\pi$
$241$	5.73722			0.369567			0.184784	+	0.982779i	$0.440842\pi$
$242$			4.89599i			0.314726i
$243$			2.37006i			0.152040i
$244$	−8.31388			−0.532242
$245$	−8.18355	−	7.93468i	−0.522828	−	0.506928i
$246$	−17.3036			−1.10324
$247$			3.36747i			0.214267i
$248$		−	1.00000i		−	0.0635001i
$249$	17.1881			1.08925
$250$	8.26325	+	7.53118i	0.522614	+	0.476314i
$251$	0.881767			0.0556566			0.0278283	−	0.999613i	$-0.491141\pi$
$251$	0.881767			0.0556566			0.0278283	+	0.999613i	$0.491141\pi$
$252$		−	0.794916i		−	0.0500750i
$253$		−	0.901992i		−	0.0567077i
$254$	17.9389			1.12559
$255$	15.5880	+	15.1140i	0.976158	+	0.946472i
$256$	1.00000			0.0625000
$257$			24.6079i			1.53500i	0.641049	+	0.767500i	$0.278500\pi$
$257$			24.6079i			1.53500i	−0.641049	+	0.767500i	$0.721500\pi$
$258$			10.2825i			0.640162i
$259$	36.6146			2.27512
$260$	−10.9075	+	11.2496i	−0.676455	+	0.697672i
$261$	−0.00226705			−0.000140327
$262$		−	2.15198i		−	0.132950i
$263$			12.9818i			0.800493i	0.916408	+	0.400246i	$0.131075\pi$
$263$			12.9818i			0.800493i	−0.916408	+	0.400246i	$0.868925\pi$
$264$	−4.43927			−0.273218
$265$	10.2750	−	10.5973i	0.631187	−	0.650984i
$266$	1.67143			0.102482
$267$			27.2246i			1.66612i
$268$		−	7.01544i		−	0.428536i
$269$	−12.6611			−0.771964			−0.385982	−	0.922506i	$-0.626137\pi$
$269$	−12.6611			−0.771964			−0.385982	+	0.922506i	$0.626137\pi$
$270$	−7.99436	−	7.75125i	−0.486521	−	0.471726i
$271$	−4.60165			−0.279530			−0.139765	−	0.990185i	$-0.544635\pi$
$271$	−4.60165			−0.279530			−0.139765	+	0.990185i	$0.544635\pi$
$272$			5.40399i			0.327665i
$273$			43.7944i			2.65056i
$274$	−10.3651			−0.626178
$275$	−0.381378	−	12.3473i	−0.0229980	−	0.744568i
$276$	−0.655991			−0.0394860
$277$		−	11.7734i		−	0.707392i	−0.935360	−	0.353696i	$-0.884925\pi$
$277$		−	11.7734i		−	0.707392i	0.935360	−	0.353696i	$-0.115075\pi$
$278$			14.0250i			0.841163i
$279$	0.228545			0.0136826
$280$	5.58371	+	5.41391i	0.333691	+	0.323543i
$281$	−28.3293			−1.68999			−0.844993	−	0.534777i	$-0.820396\pi$
$281$	−28.3293			−1.68999			−0.844993	+	0.534777i	$0.820396\pi$
$282$		−	5.28852i		−	0.314927i
$283$		−	22.2992i		−	1.32555i	−0.748819	−	0.662775i	$-0.769379\pi$
$283$		−	22.2992i		−	1.32555i	0.748819	−	0.662775i	$-0.230621\pi$
$284$	−0.632531			−0.0375338
$285$	−1.34401	+	1.38616i	−0.0796122	+	0.0821092i
$286$	17.3130			1.02374
$287$		−	33.4953i		−	1.97716i
$288$			0.228545i			0.0134671i
$289$	−12.2031			−0.717828
$290$	0.0154401	−	0.0159244i	0.000906677	−	0.000935114i
$291$	9.57668			0.561395
$292$			3.20871i			0.187775i
$293$		−	10.5227i		−	0.614743i	−0.951590	−	0.307371i	$-0.900551\pi$
$293$		−	10.5227i		−	0.614743i	0.951590	−	0.307371i	$-0.0994494\pi$
$294$	9.15952			0.534194
$295$	17.5889	+	17.0540i	1.02406	+	0.992921i
$296$	−10.5270			−0.611869
$297$			12.3032i			0.713906i
$298$		−	20.5301i		−	1.18928i
$299$	2.55835			0.147953
$300$	−8.97979	+	0.277365i	−0.518449	+	0.0160137i
$301$	−19.9043			−1.14726
$302$			11.0849i			0.637862i
$303$			0.539657i			0.0310025i
$304$	−0.480550			−0.0275614
$305$	13.3468	+	12.9409i	0.764234	+	0.740993i
$306$	−1.23505			−0.0706032
$307$			25.5955i			1.46082i	0.683012	+	0.730408i	$0.260670\pi$
$307$			25.5955i			1.46082i	−0.683012	+	0.730408i	$0.739330\pi$
$308$		−	8.59326i		−	0.489647i
$309$	−4.49924			−0.255953
$310$	−1.55654	+	1.60536i	−0.0884055	+	0.0911783i
$311$	21.0492			1.19359			0.596795	−	0.802393i	$-0.296440\pi$
$311$	21.0492			1.19359			0.596795	+	0.802393i	$0.296440\pi$
$312$		−	12.5912i		−	0.712839i
$313$		−	15.6658i		−	0.885483i	−0.896649	−	0.442742i	$-0.854006\pi$
$313$		−	15.6658i		−	0.885483i	0.896649	−	0.442742i	$-0.145994\pi$
$314$	−15.3976			−0.868938
$315$	−1.23732	+	1.27613i	−0.0697150	+	0.0719016i
$316$	−13.5111			−0.760057
$317$		−	23.8928i		−	1.34195i	−0.741478	−	0.670977i	$-0.765875\pi$
$317$		−	23.8928i		−	1.34195i	0.741478	−	0.670977i	$-0.234125\pi$
$318$			11.8611i			0.665136i
$319$	−0.0245075			−0.00137216
$320$	−1.60536	−	1.55654i	−0.0897424	−	0.0870132i
$321$	24.1436			1.34756
$322$		−	1.26983i		−	0.0707648i
$323$		−	2.59688i		−	0.144494i
$324$	9.63340			0.535189
$325$	35.0210	−	1.08172i	1.94261	−	0.0600028i
$326$	−17.9325			−0.993190
$327$		−	1.26983i		−	0.0702217i
$328$			9.63015i			0.531736i
$329$	10.2372			0.564395
$330$	7.12662	+	6.90990i	0.392308	+	0.380377i
$331$	0.617845			0.0339598			0.0169799	−	0.999856i	$-0.494595\pi$
$331$	0.617845			0.0339598			0.0169799	+	0.999856i	$0.494595\pi$
$332$		−	9.56589i		−	0.524996i
$333$		−	2.40589i		−	0.131842i
$334$	−12.9658			−0.709455
$335$	−10.9198	+	11.2623i	−0.596613	+	0.615326i
$336$	−6.24962			−0.340945
$337$		−	20.6992i		−	1.12756i	−0.825926	−	0.563778i	$-0.809347\pi$
$337$		−	20.6992i		−	1.12756i	0.825926	−	0.563778i	$-0.190653\pi$
$338$			36.1056i			1.96388i
$339$	13.5767			0.737384
$340$	8.41152	−	8.67535i	0.456179	−	0.470487i
$341$	2.47063			0.133792
$342$		−	0.109827i		−	0.00593876i
$343$		−	6.61672i		−	0.357269i
$344$	5.72264			0.308544
$345$	1.05310	+	1.02108i	0.0566971	+	0.0549729i
$346$	6.51908			0.350468
$347$		−	33.0611i		−	1.77482i	−0.460986	−	0.887408i	$-0.652504\pi$
$347$		−	33.0611i		−	1.77482i	0.460986	−	0.887408i	$-0.347496\pi$
$348$			0.0178236i			0.000955443i
$349$	−7.31198			−0.391401			−0.195701	−	0.980664i	$-0.562698\pi$
$349$	−7.31198			−0.391401			−0.195701	+	0.980664i	$0.562698\pi$
$350$	−0.536906	−	17.3825i	−0.0286988	−	0.929136i
$351$	−34.8961			−1.86261
$352$			2.47063i			0.131685i
$353$			21.7429i			1.15726i	0.815592	+	0.578628i	$0.196412\pi$
$353$			21.7429i			1.15726i	−0.815592	+	0.578628i	$0.803588\pi$
$354$	−19.6865			−1.04633
$355$	1.01544	+	0.984560i	0.0538940	+	0.0522550i
$356$	15.1516			0.803034
$357$		−	33.7729i		−	1.78745i
$358$			14.2820i			0.754829i
$359$	7.72054			0.407475			0.203737	−	0.979026i	$-0.434691\pi$
$359$	7.72054			0.407475			0.203737	+	0.979026i	$0.434691\pi$
$360$	0.355739	−	0.366896i	0.0187491	−	0.0193371i
$361$	−18.7691			−0.987846
$362$			6.92295i			0.363862i
$363$			8.79718i			0.461732i
$364$	24.3734			1.27751
$365$	4.99448	−	5.15113i	0.261423	−	0.269622i
$366$	−14.9385			−0.780848
$367$			23.0325i			1.20229i	0.799141	+	0.601144i	$0.205288\pi$
$367$			23.0325i			1.20229i	−0.799141	+	0.601144i	$0.794712\pi$
$368$			0.365086i			0.0190314i
$369$	−2.20092			−0.114575
$370$	16.8996	+	16.3857i	0.878569	+	0.851851i
$371$	−22.9600			−1.19202
$372$		−	1.79682i		−	0.0931605i
$373$			7.35528i			0.380842i	0.981703	+	0.190421i	$0.0609853\pi$
$373$			7.35528i			0.380842i	−0.981703	+	0.190421i	$0.939015\pi$
$374$	−13.3513			−0.690377
$375$	14.8475	+	13.5321i	0.766723	+	0.698797i
$376$	−2.94328			−0.151788
$377$		−	0.0695115i		−	0.00358002i
$378$			17.3205i			0.890873i
$379$	−19.3928			−0.996144			−0.498072	−	0.867136i	$-0.665958\pi$
$379$	−19.3928			−0.996144			−0.498072	+	0.867136i	$0.665958\pi$
$380$	0.771455	+	0.747995i	0.0395748	+	0.0383713i
$381$	32.2328			1.65134
$382$			7.17783i			0.367249i
$383$			13.1111i			0.669944i	0.942228	+	0.334972i	$0.108727\pi$
$383$			13.1111i			0.669944i	−0.942228	+	0.334972i	$0.891273\pi$
$384$	1.79682			0.0916933
$385$	−13.3758	+	13.7953i	−0.681692	+	0.703073i
$386$	9.63958			0.490642
$387$			1.30788i			0.0664831i
$388$		−	5.32981i		−	0.270580i
$389$	8.76355			0.444330			0.222165	−	0.975009i	$-0.428688\pi$
$389$	8.76355			0.444330			0.222165	+	0.975009i	$0.428688\pi$
$390$	−19.5988	+	20.2135i	−0.992423	+	1.02355i
$391$	−1.97292			−0.0997748
$392$		−	5.09764i		−	0.257470i
$393$		−	3.86671i		−	0.195050i
$394$	−14.8309			−0.747172
$395$	21.6901	+	21.0305i	1.09135	+	1.05816i
$396$	−0.564649			−0.0283747
$397$			22.2056i			1.11447i	0.830356	+	0.557233i	$0.188137\pi$
$397$			22.2056i			1.11447i	−0.830356	+	0.557233i	$0.811863\pi$
$398$			9.18726i			0.460516i
$399$	3.00325			0.150351
$400$	0.154365	+	4.99762i	0.00771823	+	0.249881i
$401$	−5.65942			−0.282618			−0.141309	−	0.989966i	$-0.545131\pi$
$401$	−5.65942			−0.282618			−0.141309	+	0.989966i	$0.545131\pi$
$402$		−	12.6054i		−	0.628703i
$403$			7.00754i			0.349070i
$404$	0.300341			0.0149425
$405$	−15.4651	−	14.9948i	−0.768466	−	0.745096i
$406$	−0.0345018			−0.00171229
$407$		−	26.0083i		−	1.28918i
$408$			9.70996i			0.480715i
$409$	13.2801			0.656660			0.328330	−	0.944563i	$-0.393514\pi$
$409$	13.2801			0.656660			0.328330	+	0.944563i	$0.393514\pi$
$410$	14.9897	−	15.4599i	0.740289	−	0.763508i
$411$	−18.6241			−0.918661
$412$			2.50401i			0.123364i
$413$		−	38.1079i		−	1.87517i
$414$	−0.0834383			−0.00410077
$415$	−14.8897	+	15.3567i	−0.730906	+	0.753831i
$416$	−7.00754			−0.343573
$417$			25.2003i			1.23406i
$418$		−	1.18726i		−	0.0580708i
$419$	−18.8268			−0.919751			−0.459876	−	0.887983i	$-0.652106\pi$
$419$	−18.8268			−0.919751			−0.459876	+	0.887983i	$0.652106\pi$
$420$	10.0329	+	9.72779i	0.489555	+	0.474667i
$421$	16.6627			0.812089			0.406045	−	0.913853i	$-0.366908\pi$
$421$	16.6627			0.812089			0.406045	+	0.913853i	$0.366908\pi$
$422$		−	7.97177i		−	0.388060i
$423$		−	0.672670i		−	0.0327063i
$424$	6.60117			0.320581
$425$	−27.0071	+	0.834185i	−1.31003	+	0.0404639i
$426$	−1.13654			−0.0550656
$427$		−	28.9171i		−	1.39939i
$428$		−	13.4369i		−	0.649496i
$429$	31.1083			1.50192
$430$	−9.18689	−	8.90751i	−0.443031	−	0.429558i
$431$	−30.2936			−1.45919			−0.729595	−	0.683880i	$-0.760291\pi$
$431$	−30.2936			−1.45919			−0.729595	+	0.683880i	$0.760291\pi$
$432$		−	4.97979i		−	0.239590i
$433$		−	10.7913i		−	0.518597i	−0.965797	−	0.259298i	$-0.916509\pi$
$433$		−	10.7913i		−	0.518597i	0.965797	−	0.259298i	$-0.0834913\pi$
$434$	3.47817			0.166957
$435$	0.0277431	−	0.0286132i	0.00133018	−	0.00137190i
$436$	−0.706711			−0.0338453
$437$		−	0.175442i		−	0.00839252i
$438$			5.76545i			0.275484i
$439$	−8.47303			−0.404396			−0.202198	−	0.979345i	$-0.564808\pi$
$439$	−8.47303			−0.404396			−0.202198	+	0.979345i	$0.564808\pi$
$440$	3.84564	−	3.96625i	0.183333	−	0.189084i
$441$	1.16504			0.0554780
$442$		−	37.8686i		−	1.80123i
$443$		−	35.8921i		−	1.70528i	−0.522495	−	0.852642i	$-0.674999\pi$
$443$		−	35.8921i		−	1.70528i	0.522495	−	0.852642i	$-0.325001\pi$
$444$	−18.9150			−0.897668
$445$	−24.3238	−	23.5841i	−1.15306	−	1.11799i
$446$	23.2190			1.09945
$447$		−	36.8888i		−	1.74478i
$448$			3.47817i			0.164328i
$449$	17.3271			0.817714			0.408857	−	0.912598i	$-0.365927\pi$
$449$	17.3271			0.817714			0.408857	+	0.912598i	$0.365927\pi$
$450$	−1.14218	+	0.0352792i	−0.0538428	+	0.00166308i
$451$	−23.7925			−1.12035
$452$		−	7.55597i		−	0.355403i
$453$			19.9174i			0.935803i
$454$	−1.88252			−0.0883511
$455$	−39.1281	−	37.9381i	−1.83435	−	1.77857i
$456$	−0.863459			−0.0404352
$457$		−	20.0674i		−	0.938713i	−0.883009	−	0.469357i	$-0.844486\pi$
$457$		−	20.0674i		−	0.938713i	0.883009	−	0.469357i	$-0.155514\pi$
$458$		−	11.9472i		−	0.558256i
$459$	26.9107			1.25609
$460$	0.568271	−	0.586094i	0.0264958	−	0.0273268i
$461$	−10.2586			−0.477789			−0.238895	−	0.971045i	$-0.576785\pi$
$461$	−10.2586			−0.477789			−0.238895	+	0.971045i	$0.576785\pi$
$462$		−	15.4405i		−	0.718357i
$463$			0.766689i			0.0356310i	0.999841	+	0.0178155i	$0.00567116\pi$
$463$			0.766689i			0.0356310i	−0.999841	+	0.0178155i	$0.994329\pi$
$464$	0.00991953			0.000460503
$465$	−2.79682	+	2.88454i	−0.129699	+	0.133767i
$466$	10.4393			0.483590
$467$			21.4273i			0.991539i	0.868454	+	0.495770i	$0.165114\pi$
$467$			21.4273i			0.991539i	−0.868454	+	0.495770i	$0.834886\pi$
$468$		−	1.60153i		−	0.0740309i
$469$	24.4009			1.12673
$470$	4.72502	+	4.58133i	0.217949	+	0.211321i
$471$	−27.6667			−1.27481
$472$			10.9563i			0.504306i
$473$			14.1385i			0.650090i
$474$	−24.2769			−1.11507
$475$	−0.0741799	−	2.40160i	−0.00340361	−	0.110193i
$476$	−18.7960			−0.861512
$477$			1.50866i			0.0690768i
$478$			5.47615i			0.250473i
$479$	29.6667			1.35550			0.677752	−	0.735290i	$-0.262954\pi$
$479$	29.6667			1.35550			0.677752	+	0.735290i	$0.262954\pi$
$480$	−2.88454	−	2.79682i	−0.131660	−	0.127657i
$481$	73.7682			3.36354
$482$		−	5.73722i		−	0.261323i
$483$		−	2.28165i		−	0.103819i
$484$	4.89599			0.222545
$485$	−8.29606	+	8.55626i	−0.376705	+	0.388520i
$486$	2.37006			0.107508
$487$		−	25.8096i		−	1.16955i	−0.811197	−	0.584773i	$-0.801184\pi$
$487$		−	25.8096i		−	1.16955i	0.811197	−	0.584773i	$-0.198816\pi$
$488$			8.31388i			0.376352i
$489$	−32.2214			−1.45710
$490$	−7.93468	+	8.18355i	−0.358452	+	0.369695i
$491$	−18.7250			−0.845048			−0.422524	−	0.906352i	$-0.638856\pi$
$491$	−18.7250			−0.845048			−0.422524	+	0.906352i	$0.638856\pi$
$492$			17.3036i			0.780106i
$493$			0.0536050i			0.00241425i
$494$	3.36747			0.151510
$495$	0.906465	+	0.878899i	0.0407426	+	0.0395036i
$496$	−1.00000			−0.0449013
$497$		−	2.20005i		−	0.0986856i
$498$		−	17.1881i		−	0.770219i
$499$	−41.9722			−1.87893			−0.939466	−	0.342642i	$-0.888678\pi$
$499$	−41.9722			−1.87893			−0.939466	+	0.342642i	$0.888678\pi$
$500$	7.53118	−	8.26325i	0.336805	−	0.369544i
$501$	−23.2971			−1.04084
$502$		−	0.881767i		−	0.0393552i
$503$			30.3436i			1.35296i	0.736463	+	0.676478i	$0.236495\pi$
$503$			30.3436i			1.35296i	−0.736463	+	0.676478i	$0.763505\pi$
$504$	−0.794916			−0.0354084
$505$	−0.482156	−	0.467493i	−0.0214556	−	0.0208032i
$506$	−0.901992			−0.0400984
$507$			64.8750i			2.88120i
$508$		−	17.9389i		−	0.795909i
$509$	25.3183			1.12221			0.561107	−	0.827744i	$-0.310376\pi$
$509$	25.3183			1.12221			0.561107	+	0.827744i	$0.310376\pi$
$510$	15.1140	−	15.5880i	0.669257	−	0.690248i
$511$	−11.1604			−0.493708
$512$		−	1.00000i		−	0.0441942i
$513$			2.39304i			0.105655i
$514$	24.6079			1.08541
$515$	3.89759	−	4.01984i	0.171748	−	0.177135i
$516$	10.2825			0.452663
$517$		−	7.27175i		−	0.319811i
$518$		−	36.6146i		−	1.60875i
$519$	11.7136			0.514169
$520$	11.2496	+	10.9075i	0.493329	+	0.478326i
$521$	7.15235			0.313350			0.156675	−	0.987650i	$-0.449922\pi$
$521$	7.15235			0.313350			0.156675	+	0.987650i	$0.449922\pi$
$522$			0.00226705i			9.92263e-5i
$523$		−	20.5035i		−	0.896557i	−0.893894	−	0.448278i	$-0.852037\pi$
$523$		−	20.5035i		−	0.896557i	0.893894	−	0.448278i	$-0.147963\pi$
$524$	−2.15198			−0.0940097
$525$	−0.964721	−	31.2332i	−0.0421039	−	1.36313i
$526$	12.9818			0.566034
$527$		−	5.40399i		−	0.235401i
$528$			4.43927i			0.193194i
$529$	22.8667			0.994205
$530$	−10.5973	−	10.2750i	−0.460315	−	0.446317i
$531$	−2.50401			−0.108665
$532$		−	1.67143i		−	0.0724658i
$533$		−	67.4836i		−	2.92304i
$534$	27.2246			1.17813
$535$	−20.9150	+	21.5710i	−0.904236	+	0.932597i
$536$	−7.01544			−0.303021
$537$			25.6622i			1.10740i
$538$			12.6611i			0.545861i
$539$	12.5944			0.542479
$540$	−7.75125	+	7.99436i	−0.333561	+	0.344023i
$541$	17.0504			0.733052			0.366526	−	0.930408i	$-0.380547\pi$
$541$	17.0504			0.733052			0.366526	+	0.930408i	$0.380547\pi$
$542$			4.60165i			0.197658i
$543$			12.4393i			0.533820i
$544$	5.40399			0.231694
$545$	1.13453	+	1.10002i	0.0485977	+	0.0471198i
$546$	43.7944			1.87423
$547$			19.3000i			0.825207i	0.910911	+	0.412604i	$0.135381\pi$
$547$			19.3000i			0.825207i	−0.910911	+	0.412604i	$0.864619\pi$
$548$			10.3651i			0.442775i
$549$	−1.90009			−0.0810940
$550$	−12.3473	+	0.381378i	−0.526489	+	0.0162620i
$551$	−0.00476683			−0.000203074
$552$			0.655991i			0.0279209i
$553$		−	46.9937i		−	1.99838i
$554$	−11.7734			−0.500202
$555$	30.3655	+	29.4420i	1.28894	+	1.24974i
$556$	14.0250			0.594792
$557$			12.9913i			0.550460i	0.961378	+	0.275230i	$0.0887540\pi$
$557$			12.9913i			0.550460i	−0.961378	+	0.275230i	$0.911246\pi$
$558$		−	0.228545i		−	0.00967506i
$559$	−40.1016			−1.69612
$560$	5.41391	−	5.58371i	0.228779	−	0.235955i
$561$	−23.9897			−1.01285
$562$			28.3293i			1.19500i
$563$		−	17.6480i		−	0.743773i	−0.928278	−	0.371887i	$-0.878711\pi$
$563$		−	17.6480i		−	0.743773i	0.928278	−	0.371887i	$-0.121289\pi$
$564$	−5.28852			−0.222687
$565$	−11.7612	+	12.1301i	−0.494796	+	0.510315i
$566$	−22.2992			−0.937305
$567$			33.5066i			1.40714i
$568$			0.632531i			0.0265404i
$569$	−16.5151			−0.692347			−0.346173	−	0.938171i	$-0.612519\pi$
$569$	−16.5151			−0.692347			−0.346173	+	0.938171i	$0.612519\pi$
$570$	1.38616	+	1.34401i	0.0580600	+	0.0562943i
$571$	−34.8517			−1.45850			−0.729248	−	0.684249i	$-0.760130\pi$
$571$	−34.8517			−1.45850			−0.729248	+	0.684249i	$0.760130\pi$
$572$		−	17.3130i		−	0.723894i
$573$			12.8972i			0.538789i
$574$	−33.4953			−1.39806
$575$	−1.82456	+	0.0563563i	−0.0760893	+	0.00235022i
$576$	0.228545			0.00952269
$577$		−	14.2440i		−	0.592985i	−0.955035	−	0.296492i	$-0.904183\pi$
$577$		−	14.2440i		−	0.592985i	0.955035	−	0.296492i	$-0.0958170\pi$
$578$			12.2031i			0.507581i
$579$	17.3205			0.719817
$580$	−0.0159244	−	0.0154401i	−0.000661226	−	0.000641117i
$581$	33.2717			1.38034
$582$		−	9.57668i		−	0.396966i
$583$			16.3090i			0.675451i
$584$	3.20871			0.132777
$585$	−2.49285	+	2.57104i	−0.103067	+	0.106299i
$586$	−10.5227			−0.434689
$587$		−	12.2766i		−	0.506711i	−0.967373	−	0.253355i	$-0.918466\pi$
$587$		−	12.2766i		−	0.506711i	0.967373	−	0.253355i	$-0.0815342\pi$
$588$		−	9.15952i		−	0.377732i
$589$	0.480550			0.0198007
$590$	17.0540	−	17.5889i	0.702101	−	0.724122i
$591$	−26.6485			−1.09617
$592$			10.5270i			0.432656i
$593$			42.1988i			1.73290i	0.499266	+	0.866449i	$0.333603\pi$
$593$			42.1988i			1.73290i	−0.499266	+	0.866449i	$0.666397\pi$
$594$	12.3032			0.504808
$595$	30.1743	+	29.2567i	1.23703	+	1.19941i
$596$	−20.5301			−0.840947
$597$			16.5078i			0.675620i
$598$		−	2.55835i		−	0.104619i
$599$	8.14997			0.332999			0.166499	−	0.986042i	$-0.446754\pi$
$599$	8.14997			0.332999			0.166499	+	0.986042i	$0.446754\pi$
$600$	0.277365	+	8.97979i	0.0113234	+	0.366599i
$601$	14.6953			0.599432			0.299716	−	0.954028i	$-0.403108\pi$
$601$	14.6953			0.599432			0.299716	+	0.954028i	$0.403108\pi$
$602$			19.9043i			0.811238i
$603$		−	1.60334i		−	0.0652931i
$604$	11.0849			0.451036
$605$	−7.85982	−	7.62080i	−0.319547	−	0.309830i
$606$	0.539657			0.0219221
$607$			7.18249i			0.291528i	0.989319	+	0.145764i	$0.0465641\pi$
$607$			7.18249i			0.291528i	−0.989319	+	0.145764i	$0.953436\pi$
$608$			0.480550i			0.0194889i
$609$	−0.0619933			−0.00251210
$610$	12.9409	−	13.3468i	0.523961	−	0.540395i
$611$	20.6251			0.834403
$612$			1.23505i			0.0499240i
$613$			4.55787i			0.184091i	0.995755	+	0.0920453i	$0.0293404\pi$
$613$			4.55787i			0.184091i	−0.995755	+	0.0920453i	$0.970660\pi$
$614$	25.5955			1.03295
$615$	26.9337	−	27.7785i	1.08607	−	1.12014i
$616$	−8.59326			−0.346232
$617$			12.5698i			0.506041i	0.967461	+	0.253021i	$0.0814240\pi$
$617$			12.5698i			0.506041i	−0.967461	+	0.253021i	$0.918576\pi$
$618$			4.49924i			0.180986i
$619$	12.3888			0.497948			0.248974	−	0.968510i	$-0.419907\pi$
$619$	12.3888			0.497948			0.248974	+	0.968510i	$0.419907\pi$
$620$	1.60536	+	1.55654i	0.0644728	+	0.0625122i
$621$	1.81805			0.0729559
$622$		−	21.0492i		−	0.843996i
$623$			52.6998i			2.11137i
$624$	−12.5912			−0.504053
$625$	−24.9523	+	1.54291i	−0.998094	+	0.0617164i
$626$	−15.6658			−0.626131
$627$		−	2.13329i		−	0.0851953i
$628$			15.3976i			0.614432i
$629$	−56.8877			−2.26826
$630$	1.27613	+	1.23732i	0.0508421	+	0.0492960i
$631$	24.3238			0.968315			0.484158	−	0.874981i	$-0.339126\pi$
$631$	24.3238			0.968315			0.484158	+	0.874981i	$0.339126\pi$
$632$			13.5111i			0.537441i
$633$		−	14.3238i		−	0.569320i
$634$	−23.8928			−0.948905
$635$	−27.9226	+	28.7984i	−1.10807	+	1.14283i
$636$	11.8611			0.470322
$637$			35.7219i			1.41535i
$638$			0.0245075i			0.000970261i
$639$	−0.144562			−0.00571876
$640$	−1.55654	+	1.60536i	−0.0615277	+	0.0634574i
$641$	−20.1238			−0.794840			−0.397420	−	0.917637i	$-0.630094\pi$
$641$	−20.1238			−0.794840			−0.397420	+	0.917637i	$0.630094\pi$
$642$		−	24.1436i		−	0.952872i
$643$			14.7682i			0.582402i	0.956662	+	0.291201i	$0.0940548\pi$
$643$			14.7682i			0.582402i	−0.956662	+	0.291201i	$0.905945\pi$
$644$	−1.26983			−0.0500383
$645$	−16.5071	−	16.0052i	−0.649968	−	0.630202i
$646$	−2.59688			−0.102173
$647$			11.4557i			0.450369i	0.974316	+	0.225185i	$0.0722985\pi$
$647$			11.4557i			0.450369i	−0.974316	+	0.225185i	$0.927702\pi$
$648$		−	9.63340i		−	0.378436i
$649$	−27.0690			−1.06255
$650$	−1.08172	−	35.0210i	−0.0424284	−	1.37364i
$651$	6.24962			0.244942
$652$			17.9325i			0.702291i
$653$			6.14168i			0.240342i	0.992753	+	0.120171i	$0.0383443\pi$
$653$			6.14168i			0.240342i	−0.992753	+	0.120171i	$0.961656\pi$
$654$	−1.26983			−0.0496542
$655$	3.45471	+	3.34965i	0.134987	+	0.130881i
$656$	9.63015			0.375994
$657$			0.733332i			0.0286100i
$658$		−	10.2372i		−	0.399088i
$659$	23.6164			0.919963			0.459981	−	0.887929i	$-0.347856\pi$
$659$	23.6164			0.919963			0.459981	+	0.887929i	$0.347856\pi$
$660$	6.90990	−	7.12662i	0.268967	−	0.277403i
$661$	36.5330			1.42097			0.710485	−	0.703713i	$-0.248476\pi$
$661$	36.5330			1.42097			0.710485	+	0.703713i	$0.248476\pi$
$662$		−	0.617845i		−	0.0240132i
$663$		−	68.0429i		−	2.64257i
$664$	−9.56589			−0.371228
$665$	−2.60165	+	2.68325i	−0.100888	+	0.104052i
$666$	−2.40589			−0.0932262
$667$			0.00362148i			0.000140224i
$668$			12.9658i			0.501661i
$669$	41.7203			1.61300
$670$	11.2623	+	10.9198i	0.435101	+	0.421869i
$671$	−20.5405			−0.792958
$672$			6.24962i			0.241084i
$673$			11.1721i			0.430652i	0.976542	+	0.215326i	$0.0690815\pi$
$673$			11.1721i			0.430652i	−0.976542	+	0.215326i	$0.930919\pi$
$674$	−20.6992			−0.797303
$675$	24.8871	−	0.768704i	0.957905	−	0.0295874i
$676$	36.1056			1.38868
$677$			14.4172i			0.554096i	0.960856	+	0.277048i	$0.0893562\pi$
$677$			14.4172i			0.554096i	−0.960856	+	0.277048i	$0.910644\pi$
$678$		−	13.5767i		−	0.521409i
$679$	18.5380			0.711421
$680$	−8.67535	−	8.41152i	−0.332684	−	0.322567i
$681$	−3.38254			−0.129619
$682$		−	2.47063i		−	0.0946053i
$683$			42.5368i			1.62763i	0.581127	+	0.813813i	$0.302612\pi$
$683$			42.5368i			1.62763i	−0.581127	+	0.813813i	$0.697388\pi$
$684$	−0.109827			−0.00419934
$685$	16.1337	−	16.6397i	0.616436	−	0.635770i
$686$	−6.61672			−0.252628
$687$		−	21.4669i		−	0.819013i
$688$		−	5.72264i		−	0.218173i
$689$	−46.2579			−1.76229
$690$	1.02108	−	1.05310i	0.0388717	−	0.0400909i
$691$	−44.3143			−1.68579			−0.842897	−	0.538075i	$-0.819152\pi$
$691$	−44.3143			−1.68579			−0.842897	+	0.538075i	$0.819152\pi$
$692$		−	6.51908i		−	0.247818i
$693$		−	1.96394i		−	0.0746040i
$694$	−33.0611			−1.25498
$695$	−22.5152	−	21.8305i	−0.854049	−	0.828077i
$696$	0.0178236			0.000675600
$697$			52.0412i			1.97120i
$698$			7.31198i			0.276763i
$699$	18.7574			0.709471
$700$	−17.3825	+	0.536906i	−0.656998	+	0.0202931i
$701$	23.8627			0.901281			0.450641	−	0.892706i	$-0.351196\pi$
$701$	23.8627			0.901281			0.450641	+	0.892706i	$0.351196\pi$
$702$			34.8961i			1.31707i
$703$		−	5.05874i		−	0.190794i
$704$	2.47063			0.0931154
$705$	8.48998	+	8.23180i	0.319751	+	0.310027i
$706$	21.7429			0.818303
$707$			1.04464i			0.0392876i
$708$			19.6865i			0.739864i
$709$	46.3627			1.74119			0.870594	−	0.492002i	$-0.163735\pi$
$709$	46.3627			1.74119			0.870594	+	0.492002i	$0.163735\pi$
$710$	0.984560	−	1.01544i	0.0369499	−	0.0381088i
$711$	−3.08788			−0.115805
$712$		−	15.1516i		−	0.567831i
$713$		−	0.365086i		−	0.0136726i
$714$	−33.7729			−1.26392
$715$	−26.9484	+	27.7937i	−1.00781	+	1.03942i
$716$	14.2820			0.533745
$717$			9.83963i			0.367468i
$718$		−	7.72054i		−	0.288128i
$719$	6.20252			0.231315			0.115658	−	0.993289i	$-0.463102\pi$
$719$	6.20252			0.231315			0.115658	+	0.993289i	$0.463102\pi$
$720$	−0.366896	−	0.355739i	−0.0136734	−	0.0132576i
$721$	−8.70936			−0.324354
$722$			18.7691i			0.698513i
$723$		−	10.3087i		−	0.383386i
$724$	6.92295			0.257290
$725$	0.00153122	+	0.0495740i	5.68683e−5	+	0.00184113i
$726$	8.79718			0.326494
$727$			19.6556i			0.728987i	0.931206	+	0.364493i	$0.118758\pi$
$727$			19.6556i			0.728987i	−0.931206	+	0.364493i	$0.881242\pi$
$728$		−	24.3734i		−	0.903337i
$729$	−24.6416			−0.912653
$730$	−5.15113	−	4.99448i	−0.190652	−	0.184854i
$731$	30.9250			1.14380
$732$			14.9385i			0.552143i
$733$			26.8898i			0.993198i	0.867980	+	0.496599i	$0.165418\pi$
$733$			26.8898i			0.993198i	−0.867980	+	0.496599i	$0.834582\pi$
$734$	23.0325			0.850146
$735$	−14.2572	+	14.7043i	−0.525883	+	0.542377i
$736$	0.365086			0.0134572
$737$		−	17.3326i		−	0.638453i
$738$			2.20092i			0.0810169i
$739$	31.8249			1.17070			0.585350	−	0.810781i	$-0.300957\pi$
$739$	31.8249			1.17070			0.585350	+	0.810781i	$0.300957\pi$
$740$	16.3857	−	16.8996i	0.602350	−	0.621242i
$741$	6.05072			0.222279
$742$			22.9600i			0.842886i
$743$		−	11.7373i		−	0.430601i	−0.976548	−	0.215300i	$-0.930927\pi$
$743$		−	11.7373i		−	0.430601i	0.976548	−	0.215300i	$-0.0690730\pi$
$744$	−1.79682			−0.0658744
$745$	32.9582	+	31.9560i	1.20750	+	1.17078i
$746$	7.35528			0.269296
$747$		−	2.18623i		−	0.0799900i
$748$			13.3513i			0.488170i
$749$	46.7357			1.70769
$750$	13.5321	−	14.8475i	0.494124	−	0.542155i
$751$	0.486363			0.0177477			0.00887383	−	0.999961i	$-0.497175\pi$
$751$	0.486363			0.0177477			0.00887383	+	0.999961i	$0.497175\pi$
$752$			2.94328i			0.107330i
$753$		−	1.58437i		−	0.0577377i
$754$	−0.0695115			−0.00253146
$755$	−17.7952	−	17.2540i	−0.647633	−	0.627938i
$756$	17.3205			0.629942
$757$		−	30.9080i		−	1.12337i	−0.827351	−	0.561685i	$-0.810153\pi$
$757$		−	30.9080i		−	1.12337i	0.827351	−	0.561685i	$-0.189847\pi$
$758$			19.3928i			0.704380i
$759$	−1.62071			−0.0588281
$760$	0.747995	−	0.771455i	0.0271326	−	0.0279836i
$761$	22.4602			0.814180			0.407090	−	0.913388i	$-0.366544\pi$
$761$	22.4602			0.814180			0.407090	+	0.913388i	$0.366544\pi$
$762$		−	32.2328i		−	1.16767i
$763$		−	2.45806i		−	0.0889877i
$764$	7.17783			0.259685
$765$	1.92241	−	1.98270i	0.0695048	−	0.0716848i
$766$	13.1111			0.473722
$767$		−	76.7769i		−	2.77225i
$768$		−	1.79682i		−	0.0648370i
$769$	−4.70873			−0.169801			−0.0849005	−	0.996389i	$-0.527057\pi$
$769$	−4.70873			−0.169801			−0.0849005	+	0.996389i	$0.527057\pi$
$770$	13.7953	+	13.3758i	0.497148	+	0.482029i
$771$	44.2159			1.59240
$772$		−	9.63958i		−	0.346936i
$773$		−	23.9122i		−	0.860061i	−0.902814	−	0.430031i	$-0.858503\pi$
$773$		−	23.9122i		−	0.860061i	0.902814	−	0.430031i	$-0.141497\pi$
$774$	1.30788			0.0470107
$775$	−0.154365	−	4.99762i	−0.00554494	−	0.179520i
$776$	−5.32981			−0.191329
$777$		−	65.7897i		−	2.36019i
$778$		−	8.76355i		−	0.314189i
$779$	−4.62776			−0.165807
$780$	20.2135	+	19.5988i	0.723759	+	0.701749i
$781$	−1.56275			−0.0559196
$782$			1.97292i			0.0705514i
$783$		−	0.0493972i		−	0.00176531i
$784$	−5.09764			−0.182059
$785$	23.9670	−	24.7187i	0.855419	−	0.882249i
$786$	−3.86671			−0.137921
$787$			12.6874i			0.452255i	0.974098	+	0.226128i	$0.0726067\pi$
$787$			12.6874i			0.452255i	−0.974098	+	0.226128i	$0.927393\pi$
$788$			14.8309i			0.528331i
$789$	23.3259			0.830424
$790$	21.0305	−	21.6901i	0.748232	−	0.771700i
$791$	26.2809			0.934442
$792$			0.564649i			0.0200639i
$793$		−	58.2598i		−	2.06887i
$794$	22.2056			0.788047
$795$	−19.0413	−	18.4622i	−0.675325	−	0.654788i
$796$	9.18726			0.325634
$797$			30.6460i			1.08554i	0.839883	+	0.542768i	$0.182624\pi$
$797$			30.6460i			1.08554i	−0.839883	+	0.542768i	$0.817376\pi$
$798$		−	3.00325i		−	0.106314i
$799$	−15.9054			−0.562693
$800$	4.99762	−	0.154365i	0.176692	−	0.00545762i
$801$	3.46282			0.122353
$802$			5.65942i			0.199841i
$803$			7.92752i			0.279756i
$804$	−12.6054			−0.444560
$805$	2.03853	+	1.97654i	0.0718488	+	0.0696639i
$806$	7.00754			0.246830
$807$			22.7497i			0.800829i
$808$		−	0.300341i		−	0.0105660i
$809$	−53.8848			−1.89449			−0.947245	−	0.320510i	$-0.896146\pi$
$809$	−53.8848			−1.89449			−0.947245	+	0.320510i	$0.896146\pi$
$810$	−14.9948	+	15.4651i	−0.526863	+	0.543388i
$811$	−6.42547			−0.225629			−0.112814	−	0.993616i	$-0.535987\pi$
$811$	−6.42547			−0.225629			−0.112814	+	0.993616i	$0.535987\pi$
$812$			0.0345018i			0.00121077i
$813$			8.26832i			0.289982i
$814$	−26.0083			−0.911590
$815$	27.9127	−	28.7881i	0.977738	−	1.00840i
$816$	9.70996			0.339917
$817$			2.75001i			0.0962107i
$818$		−	13.2801i		−	0.464329i
$819$	5.57040			0.194646
$820$	−15.4599	−	14.9897i	−0.539882	−	0.523463i
$821$	−12.2283			−0.426769			−0.213384	−	0.976968i	$-0.568449\pi$
$821$	−12.2283			−0.426769			−0.213384	+	0.976968i	$0.568449\pi$
$822$			18.6241i			0.649592i
$823$		−	33.0905i		−	1.15346i	−0.816934	−	0.576731i	$-0.804328\pi$
$823$		−	33.0905i		−	1.15346i	0.816934	−	0.576731i	$-0.195672\pi$
$824$	2.50401			0.0872313
$825$	−22.1857	+	0.685266i	−0.772409	+	0.0238579i
$826$	−38.1079			−1.32595
$827$			21.6099i			0.751451i	0.926731	+	0.375725i	$0.122606\pi$
$827$			21.6099i			0.751451i	−0.926731	+	0.375725i	$0.877394\pi$
$828$			0.0834383i			0.00289968i
$829$	2.19681			0.0762984			0.0381492	−	0.999272i	$-0.487854\pi$
$829$	2.19681			0.0762984			0.0381492	+	0.999272i	$0.487854\pi$
$830$	15.3567	+	14.8897i	0.533039	+	0.516829i
$831$	−21.1545			−0.733843
$832$			7.00754i			0.242943i
$833$		−	27.5476i		−	0.954467i
$834$	25.2003			0.872616
$835$	20.1817	−	20.8147i	0.698418	−	0.720323i
$836$	−1.18726			−0.0410623
$837$			4.97979i			0.172127i
$838$			18.8268i			0.650363i
$839$	−23.3786			−0.807120			−0.403560	−	0.914953i	$-0.632227\pi$
$839$	−23.3786			−0.807120			−0.403560	+	0.914953i	$0.632227\pi$
$840$	9.72779	−	10.0329i	0.335641	−	0.346168i
$841$	−28.9999			−0.999997
$842$		−	16.6627i		−	0.574234i
$843$			50.9026i			1.75318i
$844$	−7.97177			−0.274400
$845$	−57.9624	−	56.1998i	−1.99397	−	1.93333i
$846$	−0.672670			−0.0231269
$847$			17.0291i			0.585125i
$848$		−	6.60117i		−	0.226685i
$849$	−40.0675			−1.37511
$850$	0.834185	+	27.0071i	0.0286123	+	0.926334i
$851$	−3.84325			−0.131745
$852$			1.13654i			0.0389373i
$853$			13.8395i			0.473854i	0.971527	+	0.236927i	$0.0761402\pi$
$853$			13.8395i			0.473854i	−0.971527	+	0.236927i	$0.923860\pi$
$854$	−28.9171			−0.989522
$855$	0.176312	+	0.170950i	0.00602974	+	0.00584637i
$856$	−13.4369			−0.459263
$857$			4.45306i			0.152114i	0.997103	+	0.0760568i	$0.0242330\pi$
$857$			4.45306i			0.152114i	−0.997103	+	0.0760568i	$0.975767\pi$
$858$		−	31.1083i		−	1.06202i
$859$	−39.0357			−1.33188			−0.665940	−	0.746005i	$-0.731969\pi$
$859$	−39.0357			−1.33188			−0.665940	+	0.746005i	$0.731969\pi$
$860$	−8.90751	+	9.18689i	−0.303744	+	0.313270i
$861$	−60.1848			−2.05109
$862$			30.2936i			1.03180i
$863$			2.85709i			0.0972563i	0.998817	+	0.0486282i	$0.0154849\pi$
$863$			2.85709i			0.0972563i	−0.998817	+	0.0486282i	$0.984515\pi$
$864$	−4.97979			−0.169416
$865$	−10.1472	+	10.4655i	−0.345016	+	0.355837i
$866$	−10.7913			−0.366703
$867$			21.9267i			0.744668i
$868$		−	3.47817i		−	0.118057i
$869$	−33.3808			−1.13237
$870$	−0.0286132	−	0.0277431i	−0.000970080	−	0.000940579i
$871$	49.1610			1.66576
$872$			0.706711i			0.0239322i
$873$		−	1.21810i		−	0.0412264i
$874$	−0.175442			−0.00593441
$875$	28.7410	+	26.1947i	0.971622	+	0.885542i
$876$	5.76545			0.194797
$877$			8.39130i			0.283354i	0.989913	+	0.141677i	$0.0452494\pi$
$877$			8.39130i			0.283354i	−0.989913	+	0.141677i	$0.954751\pi$
$878$			8.47303i			0.285951i
$879$	−18.9074			−0.637729
$880$	−3.96625	−	3.84564i	−0.133702	−	0.129636i
$881$	11.8276			0.398483			0.199241	−	0.979950i	$-0.436152\pi$
$881$	11.8276			0.398483			0.199241	+	0.979950i	$0.436152\pi$
$882$		−	1.16504i		−	0.0392289i
$883$		−	13.6326i		−	0.458775i	−0.973335	−	0.229388i	$-0.926328\pi$
$883$		−	13.6326i		−	0.458775i	0.973335	−	0.229388i	$-0.0736723\pi$
$884$	−37.8686			−1.27366
$885$	30.6428	−	31.6039i	1.03005	−	1.06235i
$886$	−35.8921			−1.20582
$887$			0.478944i			0.0160814i	0.999968	+	0.00804068i	$0.00255945\pi$
$887$			0.478944i			0.0160814i	−0.999968	+	0.00804068i	$0.997441\pi$
$888$			18.9150i			0.634747i
$889$	62.3944			2.09264
$890$	−23.5841	+	24.3238i	−0.790541	+	0.815336i
$891$	23.8006			0.797349
$892$		−	23.2190i		−	0.777430i
$893$		−	1.41439i		−	0.0473308i
$894$	−36.8888			−1.23375
$895$	−22.9278	−	22.2306i	−0.766392	−	0.743086i
$896$	3.47817			0.116197
$897$		−	4.59688i		−	0.153485i
$898$		−	17.3271i		−	0.578211i
$899$	−0.00991953			−0.000330835
$900$	0.0352792	+	1.14218i	0.00117597	+	0.0380726i
$901$	35.6726			1.18843
$902$			23.7925i			0.792205i
$903$			35.7643i			1.19016i
$904$	−7.55597			−0.251308
$905$	−11.1138	−	10.7759i	−0.369436	−	0.358202i
$906$	19.9174			0.661712
$907$			18.7958i			0.624104i	0.950065	+	0.312052i	$0.101016\pi$
$907$			18.7958i			0.624104i	−0.950065	+	0.312052i	$0.898984\pi$
$908$			1.88252i			0.0624736i
$909$	0.0686413			0.00227669
$910$	−37.9381	+	39.1281i	−1.25764	+	1.29708i
$911$	9.54043			0.316089			0.158044	−	0.987432i	$-0.449481\pi$
$911$	9.54043			0.316089			0.158044	+	0.987432i	$0.449481\pi$
$912$			0.863459i			0.0285920i
$913$		−	23.6338i		−	0.782164i
$914$	−20.0674			−0.663771
$915$	23.2524	−	23.9817i	0.768700	−	0.792810i
$916$	−11.9472			−0.394746
$917$		−	7.48495i		−	0.247175i
$918$		−	26.9107i		−	0.888187i
$919$	−0.788134			−0.0259981			−0.0129991	−	0.999916i	$-0.504138\pi$
$919$	−0.788134			−0.0259981			−0.0129991	+	0.999916i	$0.504138\pi$
$920$	−0.586094	−	0.568271i	−0.0193230	−	0.0187353i
$921$	45.9905			1.51544
$922$			10.2586i			0.337848i
$923$		−	4.43248i		−	0.145897i
$924$	−15.4405			−0.507955
$925$	−52.6098	+	1.62499i	−1.72980	+	0.0534295i
$926$	0.766689			0.0251950
$927$			0.572278i			0.0187961i
$928$		−	0.00991953i		−	0.000325625i
$929$	25.3062			0.830271			0.415136	−	0.909760i	$-0.363734\pi$
$929$	25.3062			0.830271			0.415136	+	0.909760i	$0.363734\pi$
$930$	2.88454	+	2.79682i	0.0945877	+	0.0917112i
$931$	2.44967			0.0802847
$932$		−	10.4393i		−	0.341950i
$933$		−	37.8215i		−	1.23822i
$934$	21.4273			0.701124
$935$	20.7818	−	21.4336i	0.679636	−	0.700953i
$936$	−1.60153			−0.0523478
$937$			51.1730i			1.67175i	0.548922	+	0.835874i	$0.315039\pi$
$937$			51.1730i			1.67175i	−0.548922	+	0.835874i	$0.684961\pi$
$938$		−	24.4009i		−	0.796717i
$939$	−28.1485			−0.918593
$940$	4.58133	−	4.72502i	0.149426	−	0.154113i
$941$	−37.4102			−1.21954			−0.609769	−	0.792579i	$-0.708738\pi$
$941$	−37.4102			−1.21954			−0.609769	+	0.792579i	$0.708738\pi$
$942$			27.6667i			0.901429i
$943$			3.51583i			0.114491i
$944$	10.9563			0.356598
$945$	−27.8057	−	26.9601i	−0.904520	−	0.877013i
$946$	14.1385			0.459683
$947$			38.3159i			1.24510i	0.782580	+	0.622550i	$0.213903\pi$
$947$			38.3159i			1.24510i	−0.782580	+	0.622550i	$0.786097\pi$
$948$			24.2769i			0.788476i
$949$	−22.4851			−0.729898
$950$	−2.40160	+	0.0741799i	−0.0779183	+	0.00240671i
$951$	−42.9310			−1.39213
$952$			18.7960i			0.609181i
$953$			7.42383i			0.240481i	0.992745	+	0.120241i	$0.0383666\pi$
$953$			7.42383i			0.240481i	−0.992745	+	0.120241i	$0.961633\pi$
$954$	1.50866			0.0488447
$955$	−11.5230	−	11.1726i	−0.372875	−	0.361536i
$956$	5.47615			0.177111
$957$			0.0440354i			0.00142346i
$958$		−	29.6667i		−	0.958486i
$959$	−36.0515			−1.16416
$960$	−2.79682	+	2.88454i	−0.0902668	+	0.0930980i
$961$	1.00000			0.0322581
$962$		−	73.7682i		−	2.37838i
$963$		−	3.07093i		−	0.0989592i
$964$	−5.73722			−0.184784
$965$	−15.0044	+	15.4750i	−0.483009	+	0.498158i
$966$	−2.28165			−0.0734108
$967$		−	7.13090i		−	0.229314i	−0.993405	−	0.114657i	$-0.963423\pi$
$967$		−	7.13090i		−	0.229314i	0.993405	−	0.114657i	$-0.0365770\pi$
$968$		−	4.89599i		−	0.157363i
$969$	−4.66612			−0.149897
$970$	8.55626	+	8.29606i	0.274725	+	0.266370i
$971$	28.9403			0.928738			0.464369	−	0.885642i	$-0.346281\pi$
$971$	28.9403			0.928738			0.464369	+	0.885642i	$0.346281\pi$
$972$		−	2.37006i		−	0.0760198i
$973$			48.7813i			1.56386i
$974$	−25.8096			−0.826994
$975$	−1.94364	−	62.9262i	−0.0622464	−	2.01525i
$976$	8.31388			0.266121
$977$		−	33.7944i		−	1.08118i	−0.841286	−	0.540590i	$-0.818201\pi$
$977$		−	33.7944i		−	1.08118i	0.841286	−	0.540590i	$-0.181799\pi$
$978$			32.2214i			1.03033i
$979$	37.4340			1.19640
$980$	8.18355	+	7.93468i	0.261414	+	0.253464i
$981$	−0.161515			−0.00515677
$982$			18.7250i			0.597539i
$983$			19.8142i			0.631973i	0.948764	+	0.315987i	$0.102335\pi$
$983$			19.8142i			0.631973i	−0.948764	+	0.315987i	$0.897665\pi$
$984$	17.3036			0.551618
$985$	23.0850	−	23.8090i	0.735548	−	0.758618i
$986$	0.0536050			0.00170713
$987$		−	18.3944i		−	0.585499i
$988$		−	3.36747i		−	0.107133i
$989$	2.08925			0.0664344
$990$	0.878899	−	0.906465i	0.0279332	−	0.0288094i
$991$	−60.3261			−1.91632			−0.958161	−	0.286229i	$-0.907598\pi$
$991$	−60.3261			−1.91632			−0.958161	+	0.286229i	$0.907598\pi$
$992$			1.00000i			0.0317500i
$993$		−	1.11015i		−	0.0352296i
$994$	−2.20005			−0.0697813
$995$	−14.7489	−	14.3003i	−0.467570	−	0.453351i
$996$	−17.1881			−0.544627
$997$		−	21.3759i		−	0.676980i	−0.940970	−	0.338490i	$-0.890084\pi$
$997$		−	21.3759i		−	0.676980i	0.940970	−	0.338490i	$-0.109916\pi$
$998$			41.9722i			1.32861i
$999$	52.4222			1.65857

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	310.2.b.a.249.2	✓	8
3.2	odd	2		2790.2.d.m.559.5		8
4.3	odd	2		2480.2.d.d.1489.7		8
5.2	odd	4		1550.2.a.p.1.2		4
5.3	odd	4		1550.2.a.o.1.3		4
5.4	even	2	inner	310.2.b.a.249.7	yes	8
15.14	odd	2		2790.2.d.m.559.1		8
20.19	odd	2		2480.2.d.d.1489.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
310.2.b.a.249.2	✓	8	1.1	even	1	trivial
310.2.b.a.249.7	yes	8	5.4	even	2	inner
1550.2.a.o.1.3		4	5.3	odd	4
1550.2.a.p.1.2		4	5.2	odd	4
2480.2.d.d.1489.2		8	20.19	odd	2
2480.2.d.d.1489.7		8	4.3	odd	2
2790.2.d.m.559.1		8	15.14	odd	2
2790.2.d.m.559.5		8	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 310 = 2 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	310.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.79682i q^{3} -1.00000 q^{4} +(1.60536 + 1.55654i) q^{5} -1.79682 q^{6} -3.47817i q^{7} +1.00000i q^{8} -0.228545 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -1.79682i q^{3} -1.00000 q^{4} +(1.60536 + 1.55654i) q^{5} -1.79682 q^{6} -3.47817i q^{7} +1.00000i q^{8} -0.228545 q^{9} +(1.55654 - 1.60536i) q^{10} -2.47063 q^{11} +1.79682i q^{12} -7.00754i q^{13} -3.47817 q^{14} +(2.79682 - 2.88454i) q^{15} +1.00000 q^{16} +5.40399i q^{17} +0.228545i q^{18} -0.480550 q^{19} +(-1.60536 - 1.55654i) q^{20} -6.24962 q^{21} +2.47063i q^{22} +0.365086i q^{23} +1.79682 q^{24} +(0.154365 + 4.99762i) q^{25} -7.00754 q^{26} -4.97979i q^{27} +3.47817i q^{28} +0.00991953 q^{29} +(-2.88454 - 2.79682i) q^{30} -1.00000 q^{31} -1.00000i q^{32} +4.43927i q^{33} +5.40399 q^{34} +(5.41391 - 5.58371i) q^{35} +0.228545 q^{36} +10.5270i q^{37} +0.480550i q^{38} -12.5912 q^{39} +(-1.55654 + 1.60536i) q^{40} +9.63015 q^{41} +6.24962i q^{42} -5.72264i q^{43} +2.47063 q^{44} +(-0.366896 - 0.355739i) q^{45} +0.365086 q^{46} +2.94328i q^{47} -1.79682i q^{48} -5.09764 q^{49} +(4.99762 - 0.154365i) q^{50} +9.70996 q^{51} +7.00754i q^{52} -6.60117i q^{53} -4.97979 q^{54} +(-3.96625 - 3.84564i) q^{55} +3.47817 q^{56} +0.863459i q^{57} -0.00991953i q^{58} +10.9563 q^{59} +(-2.79682 + 2.88454i) q^{60} +8.31388 q^{61} +1.00000i q^{62} +0.794916i q^{63} -1.00000 q^{64} +(10.9075 - 11.2496i) q^{65} +4.43927 q^{66} +7.01544i q^{67} -5.40399i q^{68} +0.655991 q^{69} +(-5.58371 - 5.41391i) q^{70} +0.632531 q^{71} -0.228545i q^{72} -3.20871i q^{73} +10.5270 q^{74} +(8.97979 - 0.277365i) q^{75} +0.480550 q^{76} +8.59326i q^{77} +12.5912i q^{78} +13.5111 q^{79} +(1.60536 + 1.55654i) q^{80} -9.63340 q^{81} -9.63015i q^{82} +9.56589i q^{83} +6.24962 q^{84} +(-8.41152 + 8.67535i) q^{85} -5.72264 q^{86} -0.0178236i q^{87} -2.47063i q^{88} -15.1516 q^{89} +(-0.355739 + 0.366896i) q^{90} -24.3734 q^{91} -0.365086i q^{92} +1.79682i q^{93} +2.94328 q^{94} +(-0.771455 - 0.747995i) q^{95} -1.79682 q^{96} +5.32981i q^{97} +5.09764i q^{98} +0.564649 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 2 q^{5} - 8 q^{6} - 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^4 - 2 * q^5 - 8 * q^6 - 8 * q^9	\( 8 q - 8 q^{4} - 2 q^{5} - 8 q^{6} - 8 q^{9} + 2 q^{10} - 16 q^{11} + 12 q^{14} + 16 q^{15} + 8 q^{16} - 12 q^{19} + 2 q^{20} - 4 q^{21} + 8 q^{24} + 12 q^{25} - 20 q^{26} + 12 q^{29} + 4 q^{30} - 8 q^{31} + 8 q^{34} + 20 q^{35} + 8 q^{36} - 40 q^{39} - 2 q^{40} + 16 q^{44} + 30 q^{45} - 16 q^{46} - 32 q^{49} - 8 q^{50} - 44 q^{51} + 44 q^{54} + 36 q^{55} - 12 q^{56} + 8 q^{59} - 16 q^{60} + 4 q^{61} - 8 q^{64} + 12 q^{65} + 12 q^{66} - 28 q^{69} - 20 q^{70} - 24 q^{71} + 40 q^{74} - 12 q^{75} + 12 q^{76} + 32 q^{79} - 2 q^{80} + 88 q^{81} + 4 q^{84} + 4 q^{85} - 44 q^{86} - 24 q^{89} - 34 q^{90} - 20 q^{91} + 4 q^{94} - 8 q^{96} + 20 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 - 2 * q^5 - 8 * q^6 - 8 * q^9 + 2 * q^10 - 16 * q^11 + 12 * q^14 + 16 * q^15 + 8 * q^16 - 12 * q^19 + 2 * q^20 - 4 * q^21 + 8 * q^24 + 12 * q^25 - 20 * q^26 + 12 * q^29 + 4 * q^30 - 8 * q^31 + 8 * q^34 + 20 * q^35 + 8 * q^36 - 40 * q^39 - 2 * q^40 + 16 * q^44 + 30 * q^45 - 16 * q^46 - 32 * q^49 - 8 * q^50 - 44 * q^51 + 44 * q^54 + 36 * q^55 - 12 * q^56 + 8 * q^59 - 16 * q^60 + 4 * q^61 - 8 * q^64 + 12 * q^65 + 12 * q^66 - 28 * q^69 - 20 * q^70 - 24 * q^71 + 40 * q^74 - 12 * q^75 + 12 * q^76 + 32 * q^79 - 2 * q^80 + 88 * q^81 + 4 * q^84 + 4 * q^85 - 44 * q^86 - 24 * q^89 - 34 * q^90 - 20 * q^91 + 4 * q^94 - 8 * q^96 + 20 * q^99

Introduction

L-functions

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