LMFDB - Embedded newform 310.2.b.b.249.6

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:	8.0.2058981376.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 2x^{6} + 18x^{4} - 34x^{3} + 32x^{2} - 8x + 1 $ x^8 - 2x^7 + 2x^6 + 18x^4 - 34x^3 + 32x^2 - 8x + 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			249.6
Root			$-1.43917 + 1.43917i$ of defining polynomial
Character	$\chi$	$=$	310.249
Dual form			310.2.b.b.249.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.55241i q^{3} -1.00000 q^{4} +(-2.23418 + 0.0917505i) q^{5} +1.55241 q^{6} +4.87834i q^{7} -1.00000i q^{8} +0.590025 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -1.55241i q^{3} -1.00000 q^{4} +(-2.23418 + 0.0917505i) q^{5} +1.55241 q^{6} +4.87834i q^{7} -1.00000i q^{8} +0.590025 q^{9} +(-0.0917505 - 2.23418i) q^{10} +3.14243 q^{11} +1.55241i q^{12} +4.02078i q^{13} -4.87834 q^{14} +(0.142434 + 3.46837i) q^{15} +1.00000 q^{16} +1.59002i q^{17} +0.590025i q^{18} -3.28832 q^{19} +(2.23418 - 0.0917505i) q^{20} +7.57319 q^{21} +3.14243i q^{22} +6.16666i q^{23} -1.55241 q^{24} +(4.98316 - 0.409975i) q^{25} -4.02078 q^{26} -5.57319i q^{27} -4.87834i q^{28} +2.14589 q^{29} +(-3.46837 + 0.142434i) q^{30} +1.00000 q^{31} +1.00000i q^{32} -4.87834i q^{33} -1.59002 q^{34} +(-0.447591 - 10.8991i) q^{35} -0.590025 q^{36} +5.55241i q^{37} -3.28832i q^{38} +6.24190 q^{39} +(0.0917505 + 2.23418i) q^{40} -10.4515 q^{41} +7.57319i q^{42} -1.81114i q^{43} -3.14243 q^{44} +(-1.31822 + 0.0541351i) q^{45} -6.16666 q^{46} -6.26803i q^{47} -1.55241i q^{48} -16.7982 q^{49} +(0.409975 + 4.98316i) q^{50} +2.46837 q^{51} -4.02078i q^{52} -12.9575i q^{53} +5.57319 q^{54} +(-7.02078 + 0.288320i) q^{55} +4.87834 q^{56} +5.10482i q^{57} +2.14589i q^{58} +14.6934 q^{59} +(-0.142434 - 3.46837i) q^{60} -6.79085 q^{61} +1.00000i q^{62} +2.87834i q^{63} -1.00000 q^{64} +(-0.368908 - 8.98316i) q^{65} +4.87834 q^{66} -2.67801i q^{67} -1.59002i q^{68} +9.57319 q^{69} +(10.8991 - 0.447591i) q^{70} +14.4086 q^{71} -0.590025i q^{72} +4.15976i q^{73} -5.55241 q^{74} +(-0.636449 - 7.73591i) q^{75} +3.28832 q^{76} +15.3299i q^{77} +6.24190i q^{78} +5.10482 q^{79} +(-2.23418 + 0.0917505i) q^{80} -6.88180 q^{81} -10.4515i q^{82} +2.73936i q^{83} -7.57319 q^{84} +(-0.145886 - 3.55241i) q^{85} +1.81114 q^{86} -3.33129i q^{87} -3.14243i q^{88} +2.00690 q^{89} +(-0.0541351 - 1.31822i) q^{90} -19.6147 q^{91} -6.16666i q^{92} -1.55241i q^{93} +6.26803 q^{94} +(7.34671 - 0.301705i) q^{95} +1.55241 q^{96} +15.9010i q^{97} -16.7982i q^{98} +1.85411 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 2 q^{5} + 4 q^{6}+O(q^{10}) $ 8 * q - 8 * q^4 - 2 * q^5 + 4 * q^6	$ 8 q - 8 q^{4} - 2 q^{5} + 4 q^{6} + 2 q^{10} + 12 q^{11} - 12 q^{14} - 12 q^{15} + 8 q^{16} - 4 q^{19} + 2 q^{20} + 12 q^{21} - 4 q^{24} - 4 q^{25} + 8 q^{26} + 8 q^{29} + 4 q^{30} + 8 q^{31} - 8 q^{34} - 12 q^{35} + 8 q^{39} - 2 q^{40} - 8 q^{41} - 12 q^{44} - 18 q^{45} + 8 q^{50} - 12 q^{51} - 4 q^{54} - 16 q^{55} + 12 q^{56} + 12 q^{60} - 8 q^{64} + 12 q^{66} + 28 q^{69} + 20 q^{70} + 24 q^{71} - 36 q^{74} - 20 q^{75} + 4 q^{76} + 24 q^{79} - 2 q^{80} - 32 q^{81} - 12 q^{84} + 8 q^{85} + 8 q^{86} + 24 q^{89} + 6 q^{90} - 28 q^{91} - 20 q^{94} + 4 q^{96} + 24 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 - 2 * q^5 + 4 * q^6 + 2 * q^10 + 12 * q^11 - 12 * q^14 - 12 * q^15 + 8 * q^16 - 4 * q^19 + 2 * q^20 + 12 * q^21 - 4 * q^24 - 4 * q^25 + 8 * q^26 + 8 * q^29 + 4 * q^30 + 8 * q^31 - 8 * q^34 - 12 * q^35 + 8 * q^39 - 2 * q^40 - 8 * q^41 - 12 * q^44 - 18 * q^45 + 8 * q^50 - 12 * q^51 - 4 * q^54 - 16 * q^55 + 12 * q^56 + 12 * q^60 - 8 * q^64 + 12 * q^66 + 28 * q^69 + 20 * q^70 + 24 * q^71 - 36 * q^74 - 20 * q^75 + 4 * q^76 + 24 * q^79 - 2 * q^80 - 32 * q^81 - 12 * q^84 + 8 * q^85 + 8 * q^86 + 24 * q^89 + 6 * q^90 - 28 * q^91 - 20 * q^94 + 4 * q^96 + 24 * 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
$3$		−	1.55241i		−	0.896284i	−0.893962	−	0.448142i	$-0.852086\pi$
$3$		−	1.55241i		−	0.896284i	0.893962	−	0.448142i	$-0.147914\pi$
$4$	−1.00000			−0.500000
$5$	−2.23418	+	0.0917505i	−0.999158	+	0.0410321i
$5$	−2.23418	+	0.0917505i	−0.999158	+	0.0410321i
$6$	1.55241			0.633769
$7$			4.87834i			1.84384i	0.387379	+	0.921921i	$0.373380\pi$
$7$			4.87834i			1.84384i	−0.387379	+	0.921921i	$0.626620\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.590025			0.196675
$10$	−0.0917505	−	2.23418i	−0.0290141	−	0.706511i
$11$	3.14243			0.947480			0.473740	−	0.880665i	$-0.342904\pi$
$11$	3.14243			0.947480			0.473740	+	0.880665i	$0.342904\pi$
$12$			1.55241i			0.448142i
$13$			4.02078i			1.11516i	0.830122	+	0.557582i	$0.188271\pi$
$13$			4.02078i			1.11516i	−0.830122	+	0.557582i	$0.811729\pi$
$14$	−4.87834			−1.30379
$15$	0.142434	+	3.46837i	0.0367764	+	0.895529i
$16$	1.00000			0.250000
$17$			1.59002i			0.385638i	0.981234	+	0.192819i	$0.0617630\pi$
$17$			1.59002i			0.385638i	−0.981234	+	0.192819i	$0.938237\pi$
$18$			0.590025i			0.139070i
$19$	−3.28832			−0.754392			−0.377196	−	0.926133i	$-0.623112\pi$
$19$	−3.28832			−0.754392			−0.377196	+	0.926133i	$0.623112\pi$
$20$	2.23418	−	0.0917505i	0.499579	−	0.0205160i
$21$	7.57319			1.65261
$22$			3.14243i			0.669969i
$23$			6.16666i			1.28584i	0.765934	+	0.642919i	$0.222277\pi$
$23$			6.16666i			1.28584i	−0.765934	+	0.642919i	$0.777723\pi$
$24$	−1.55241			−0.316884
$25$	4.98316	−	0.409975i	0.996633	−	0.0819950i
$26$	−4.02078			−0.788540
$27$		−	5.57319i		−	1.07256i
$28$		−	4.87834i		−	0.921921i
$29$	2.14589			0.398481			0.199240	−	0.979951i	$-0.436153\pi$
$29$	2.14589			0.398481			0.199240	+	0.979951i	$0.436153\pi$
$30$	−3.46837	+	0.142434i	−0.633235	+	0.0260048i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$			1.00000i			0.176777i
$33$		−	4.87834i		−	0.849211i
$34$	−1.59002			−0.272687
$35$	−0.447591	−	10.8991i	−0.0756566	−	1.84229i
$36$	−0.590025			−0.0983375
$37$			5.55241i			0.912810i	0.889772	+	0.456405i	$0.150863\pi$
$37$			5.55241i			0.912810i	−0.889772	+	0.456405i	$0.849137\pi$
$38$		−	3.28832i		−	0.533436i
$39$	6.24190			0.999503
$40$	0.0917505	+	2.23418i	0.0145070	+	0.353256i
$41$	−10.4515			−1.63226			−0.816128	−	0.577872i	$-0.803883\pi$
$41$	−10.4515			−1.63226			−0.816128	+	0.577872i	$0.803883\pi$
$42$			7.57319i			1.16857i
$43$		−	1.81114i		−	0.276196i	−0.990419	−	0.138098i	$-0.955901\pi$
$43$		−	1.81114i		−	0.276196i	0.990419	−	0.138098i	$-0.0440990\pi$
$44$	−3.14243			−0.473740
$45$	−1.31822	+	0.0541351i	−0.196509	+	0.00806998i
$46$	−6.16666			−0.909225
$47$		−	6.26803i		−	0.914286i	−0.889393	−	0.457143i	$-0.848873\pi$
$47$		−	6.26803i		−	0.914286i	0.889393	−	0.457143i	$-0.151127\pi$
$48$		−	1.55241i		−	0.224071i
$49$	−16.7982			−2.39975
$50$	0.409975	+	4.98316i	0.0579792	+	0.704726i
$51$	2.46837			0.345641
$52$		−	4.02078i		−	0.557582i
$53$		−	12.9575i		−	1.77985i	−0.456105	−	0.889926i	$-0.650756\pi$
$53$		−	12.9575i		−	1.77985i	0.456105	−	0.889926i	$-0.349244\pi$
$54$	5.57319			0.758415
$55$	−7.02078	+	0.288320i	−0.946682	+	0.0388770i
$56$	4.87834			0.651896
$57$			5.10482i			0.676150i
$58$			2.14589i			0.281769i
$59$	14.6934			1.91292			0.956461	−	0.291861i	$-0.0942745\pi$
$59$	14.6934			1.91292			0.956461	+	0.291861i	$0.0942745\pi$
$60$	−0.142434	−	3.46837i	−0.0183882	−	0.447765i
$61$	−6.79085			−0.869480			−0.434740	−	0.900556i	$-0.643160\pi$
$61$	−6.79085			−0.869480			−0.434740	+	0.900556i	$0.643160\pi$
$62$			1.00000i			0.127000i
$63$			2.87834i			0.362637i
$64$	−1.00000			−0.125000
$65$	−0.368908	−	8.98316i	−0.0457575	−	1.11422i
$66$	4.87834			0.600483
$67$		−	2.67801i		−	0.327171i	−0.986529	−	0.163585i	$-0.947694\pi$
$67$		−	2.67801i		−	0.327171i	0.986529	−	0.163585i	$-0.0523059\pi$
$68$		−	1.59002i		−	0.192819i
$69$	9.57319			1.15248
$70$	10.8991	−	0.447591i	1.30269	−	0.0534973i
$71$	14.4086			1.70998			0.854991	−	0.518643i	$-0.173563\pi$
$71$	14.4086			1.70998			0.854991	+	0.518643i	$0.173563\pi$
$72$		−	0.590025i		−	0.0695351i
$73$			4.15976i			0.486863i	0.969918	+	0.243432i	$0.0782732\pi$
$73$			4.15976i			0.486863i	−0.969918	+	0.243432i	$0.921727\pi$
$74$	−5.55241			−0.645454
$75$	−0.636449	−	7.73591i	−0.0734908	−	0.893266i
$76$	3.28832			0.377196
$77$			15.3299i			1.74700i
$78$			6.24190i			0.706755i
$79$	5.10482			0.574337			0.287168	−	0.957880i	$-0.407286\pi$
$79$	5.10482			0.574337			0.287168	+	0.957880i	$0.407286\pi$
$80$	−2.23418	+	0.0917505i	−0.249789	+	0.0102580i
$81$	−6.88180			−0.764644
$82$		−	10.4515i		−	1.15418i
$83$			2.73936i			0.300684i	0.988634	+	0.150342i	$0.0480375\pi$
$83$			2.73936i			0.300684i	−0.988634	+	0.150342i	$0.951963\pi$
$84$	−7.57319			−0.826303
$85$	−0.145886	−	3.55241i	−0.0158235	−	0.385313i
$86$	1.81114			0.195300
$87$		−	3.33129i		−	0.357152i
$88$		−	3.14243i		−	0.334985i
$89$	2.00690			0.212731			0.106366	−	0.994327i	$-0.466079\pi$
$89$	2.00690			0.212731			0.106366	+	0.994327i	$0.466079\pi$
$90$	−0.0541351	−	1.31822i	−0.00570634	−	0.138953i
$91$	−19.6147			−2.05618
$92$		−	6.16666i		−	0.642919i
$93$		−	1.55241i		−	0.160977i
$94$	6.26803			0.646498
$95$	7.34671	−	0.301705i	0.753757	−	0.0309543i
$96$	1.55241			0.158442
$97$			15.9010i			1.61451i	0.590206	+	0.807253i	$0.299046\pi$
$97$			15.9010i			1.61451i	−0.590206	+	0.807253i	$0.700954\pi$
$98$		−	16.7982i		−	1.69688i
$99$	1.85411			0.186346
$100$	−4.98316	+	0.409975i	−0.498316	+	0.0409975i
$101$	7.48724			0.745008			0.372504	−	0.928030i	$-0.378499\pi$
$101$	7.48724			0.745008			0.372504	+	0.928030i	$0.378499\pi$
$102$			2.46837i			0.244405i
$103$		−	3.39659i		−	0.334676i	−0.985900	−	0.167338i	$-0.946483\pi$
$103$		−	3.39659i		−	0.334676i	0.985900	−	0.167338i	$-0.0535171\pi$
$104$	4.02078			0.394270
$105$	−16.9199	+	0.694844i	−1.65121	+	0.0678098i
$106$	12.9575			1.25855
$107$		−	6.82847i		−	0.660133i	−0.943958	−	0.330067i	$-0.892929\pi$
$107$		−	6.82847i		−	0.660133i	0.943958	−	0.330067i	$-0.107071\pi$
$108$			5.57319i			0.536280i
$109$	7.13096			0.683022			0.341511	−	0.939878i	$-0.389061\pi$
$109$	7.13096			0.683022			0.341511	+	0.939878i	$0.389061\pi$
$110$	−0.288320	−	7.02078i	−0.0274902	−	0.669405i
$111$	8.61961			0.818137
$112$			4.87834i			0.460960i
$113$		−	7.24535i		−	0.681585i	−0.940139	−	0.340792i	$-0.889305\pi$
$113$		−	7.24535i		−	0.681585i	0.940139	−	0.340792i	$-0.110695\pi$
$114$	−5.10482			−0.478110
$115$	−0.565795	−	13.7775i	−0.0527606	−	1.28476i
$116$	−2.14589			−0.199240
$117$			2.37236i			0.219325i
$118$			14.6934i			1.35264i
$119$	−7.75669			−0.711055
$120$	3.46837	−	0.142434i	0.316617	−	0.0130024i
$121$	−1.12511			−0.102282
$122$		−	6.79085i		−	0.614815i
$123$			16.2251i			1.46296i
$124$	−1.00000			−0.0898027
$125$	−11.0957	+	1.37317i	−0.992429	+	0.122820i
$126$	−2.87834			−0.256423
$127$			6.15976i			0.546591i	0.961930	+	0.273295i	$0.0881136\pi$
$127$			6.15976i			0.546591i	−0.961930	+	0.273295i	$0.911886\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−2.81163			−0.247550
$130$	8.98316	−	0.368908i	0.787876	−	0.0323554i
$131$	11.3299			0.989896			0.494948	−	0.868923i	$-0.335187\pi$
$131$	11.3299			0.989896			0.494948	+	0.868923i	$0.335187\pi$
$132$			4.87834i			0.424605i
$133$		−	16.0416i		−	1.39098i
$134$	2.67801			0.231345
$135$	0.511343	+	12.4515i	0.0440094	+	1.07166i
$136$	1.59002			0.136344
$137$		−	1.95703i		−	0.167200i	−0.996499	−	0.0836000i	$-0.973358\pi$
$137$		−	1.95703i		−	0.167200i	0.996499	−	0.0836000i	$-0.0266418\pi$
$138$			9.57319i			0.814924i
$139$	9.41188			0.798305			0.399153	−	0.916884i	$-0.369304\pi$
$139$	9.41188			0.798305			0.399153	+	0.916884i	$0.369304\pi$
$140$	0.447591	+	10.8991i	0.0378283	+	0.921144i
$141$	−9.73055			−0.819460
$142$			14.4086i			1.20914i
$143$			12.6350i			1.05659i
$144$	0.590025			0.0491687
$145$	−4.79430	+	0.196886i	−0.398145	+	0.0163505i
$146$	−4.15976			−0.344264
$147$			26.0778i			2.15086i
$148$		−	5.55241i		−	0.456405i
$149$	−2.21654			−0.181586			−0.0907930	−	0.995870i	$-0.528940\pi$
$149$	−2.21654			−0.181586			−0.0907930	+	0.995870i	$0.528940\pi$
$150$	7.73591	−	0.636449i	0.631634	−	0.0519659i
$151$	−14.2512			−1.15975			−0.579873	−	0.814707i	$-0.696898\pi$
$151$	−14.2512			−1.15975			−0.579873	+	0.814707i	$0.696898\pi$
$152$			3.28832i			0.266718i
$153$			0.938154i			0.0758453i
$154$	−15.3299			−1.23532
$155$	−2.23418	+	0.0917505i	−0.179454	+	0.00736958i
$156$	−6.24190			−0.499752
$157$			2.89518i			0.231061i	0.993304	+	0.115530i	$0.0368567\pi$
$157$			2.89518i			0.231061i	−0.993304	+	0.115530i	$0.963143\pi$
$158$			5.10482i			0.406118i
$159$	−20.1154			−1.59525
$160$	−0.0917505	−	2.23418i	−0.00725351	−	0.176628i
$161$	−30.0831			−2.37088
$162$		−	6.88180i		−	0.540685i
$163$		−	17.0120i		−	1.33248i	−0.745737	−	0.666240i	$-0.767903\pi$
$163$		−	17.0120i		−	1.33248i	0.745737	−	0.666240i	$-0.232097\pi$
$164$	10.4515			0.816128
$165$	0.447591	+	10.8991i	0.0348449	+	0.848496i
$166$	−2.73936			−0.212616
$167$		−	1.22993i		−	0.0951745i	−0.998867	−	0.0475872i	$-0.984847\pi$
$167$		−	1.22993i		−	0.0951745i	0.998867	−	0.0475872i	$-0.0151532\pi$
$168$		−	7.57319i		−	0.584284i
$169$	−3.16666			−0.243590
$170$	3.55241	−	0.145886i	0.272457	−	0.0111889i
$171$	−1.94019			−0.148370
$172$			1.81114i			0.138098i
$173$		−	2.86151i		−	0.217556i	−0.994066	−	0.108778i	$-0.965306\pi$
$173$		−	2.86151i		−	0.217556i	0.994066	−	0.108778i	$-0.0346938\pi$
$174$	3.33129			0.252545
$175$	2.00000	+	24.3096i	0.151186	+	1.83763i
$176$	3.14243			0.236870
$177$		−	22.8102i		−	1.71452i
$178$			2.00690i			0.150424i
$179$	24.4386			1.82663			0.913315	−	0.407254i	$-0.133514\pi$
$179$	24.4386			1.82663			0.913315	+	0.407254i	$0.133514\pi$
$180$	1.31822	−	0.0541351i	0.0982547	−	0.00403499i
$181$	−21.3414			−1.58629			−0.793145	−	0.609032i	$-0.791558\pi$
$181$	−21.3414			−1.58629			−0.793145	+	0.609032i	$0.791558\pi$
$182$		−	19.6147i		−	1.45394i
$183$			10.5422i			0.779301i
$184$	6.16666			0.454613
$185$	−0.509436	−	12.4051i	−0.0374545	−	0.912042i
$186$	1.55241			0.113828
$187$			4.99655i			0.365384i
$188$			6.26803i			0.457143i
$189$	27.1879			1.97763
$190$	0.301705	+	7.34671i	0.0218880	+	0.532987i
$191$	−6.69484			−0.484422			−0.242211	−	0.970224i	$-0.577873\pi$
$191$	−6.69484			−0.484422			−0.242211	+	0.970224i	$0.577873\pi$
$192$			1.55241i			0.112036i
$193$			7.87348i			0.566745i	0.959010	+	0.283373i	$0.0914533\pi$
$193$			7.87348i			0.566745i	−0.959010	+	0.283373i	$0.908547\pi$
$194$	−15.9010			−1.14163
$195$	−13.9455	+	0.572697i	−0.998661	+	0.0410117i
$196$	16.7982			1.19987
$197$		−	1.34967i		−	0.0961603i	−0.998843	−	0.0480801i	$-0.984690\pi$
$197$		−	1.34967i		−	0.0961603i	0.998843	−	0.0480801i	$-0.0153103\pi$
$198$			1.85411i			0.131766i
$199$	9.91405			0.702789			0.351394	−	0.936228i	$-0.385708\pi$
$199$	9.91405			0.702789			0.351394	+	0.936228i	$0.385708\pi$
$200$	−0.409975	−	4.98316i	−0.0289896	−	0.352363i
$201$	−4.15736			−0.293238
$202$			7.48724i			0.526801i
$203$			10.4684i			0.734736i
$204$	−2.46837			−0.172820
$205$	23.3507	−	0.958933i	1.63088	−	0.0669748i
$206$	3.39659			0.236652
$207$			3.63849i			0.252892i
$208$			4.02078i			0.278791i
$209$	−10.3333			−0.714771
$210$	−0.694844	−	16.9199i	−0.0479488	−	1.16758i
$211$	18.7879			1.29341			0.646706	−	0.762739i	$-0.276146\pi$
$211$	18.7879			1.29341			0.646706	+	0.762739i	$0.276146\pi$
$212$			12.9575i			0.889926i
$213$		−	22.3680i		−	1.53263i
$214$	6.82847			0.466785
$215$	0.166173	+	4.04642i	0.0113329	+	0.275964i
$216$	−5.57319			−0.379207
$217$			4.87834i			0.331164i
$218$			7.13096i			0.482969i
$219$	6.45765			0.436368
$220$	7.02078	−	0.288320i	0.473341	−	0.0194385i
$221$	−6.39314			−0.430049
$222$			8.61961i			0.578511i
$223$		−	19.4811i		−	1.30455i	−0.757981	−	0.652276i	$-0.773814\pi$
$223$		−	19.4811i		−	1.30455i	0.757981	−	0.652276i	$-0.226186\pi$
$224$	−4.87834			−0.325948
$225$	2.94019	−	0.241896i	0.196013	−	0.0161264i
$226$	7.24535			0.481953
$227$		−	15.6330i		−	1.03760i	−0.854896	−	0.518799i	$-0.826379\pi$
$227$		−	15.6330i		−	1.03760i	0.854896	−	0.518799i	$-0.173621\pi$
$228$		−	5.10482i		−	0.338075i
$229$	7.97781			0.527188			0.263594	−	0.964634i	$-0.415092\pi$
$229$	7.97781			0.527188			0.263594	+	0.964634i	$0.415092\pi$
$230$	13.7775	−	0.565795i	0.908459	−	0.0373074i
$231$	23.7982			1.56581
$232$		−	2.14589i		−	0.140884i
$233$		−	0.668707i		−	0.0438084i	−0.999760	−	0.0219042i	$-0.993027\pi$
$233$		−	0.668707i		−	0.0438084i	0.999760	−	0.0219042i	$-0.00697289\pi$
$234$	−2.37236			−0.155086
$235$	0.575095	+	14.0039i	0.0375151	+	0.913517i
$236$	−14.6934			−0.956461
$237$		−	7.92477i		−	0.514769i
$238$		−	7.75669i		−	0.502792i
$239$	−2.37081			−0.153355			−0.0766776	−	0.997056i	$-0.524431\pi$
$239$	−2.37081			−0.153355			−0.0766776	+	0.997056i	$0.524431\pi$
$240$	0.142434	+	3.46837i	0.00919410	+	0.223882i
$241$	18.0793			1.16459			0.582295	−	0.812977i	$-0.302155\pi$
$241$	18.0793			1.16459			0.582295	+	0.812977i	$0.302155\pi$
$242$		−	1.12511i		−	0.0723246i
$243$		−	6.03620i		−	0.387222i
$244$	6.79085			0.434740
$245$	37.5304	−	1.54125i	2.39773	−	0.0984667i
$246$	−16.2251			−1.03447
$247$		−	13.2216i		−	0.841271i
$248$		−	1.00000i		−	0.0635001i
$249$	4.25261			0.269498
$250$	−1.37317	−	11.0957i	−0.0868468	−	0.701753i
$251$	−24.7902			−1.56474			−0.782372	−	0.622811i	$-0.785991\pi$
$251$	−24.7902			−1.56474			−0.782372	+	0.622811i	$0.785991\pi$
$252$		−	2.87834i		−	0.181319i
$253$			19.3783i			1.21831i
$254$	−6.15976			−0.386498
$255$	−5.51479	+	0.226474i	−0.345350	+	0.0141824i
$256$	1.00000			0.0625000
$257$		−	23.6638i		−	1.47611i	−0.674741	−	0.738055i	$-0.735745\pi$
$257$		−	23.6638i		−	1.47611i	0.674741	−	0.738055i	$-0.264255\pi$
$258$		−	2.81163i		−	0.175045i
$259$	−27.0866			−1.68308
$260$	0.368908	+	8.98316i	0.0228787	+	0.557112i
$261$	1.26613			0.0783712
$262$			11.3299i			0.699962i
$263$			14.0738i			0.867829i	0.900954	+	0.433914i	$0.142868\pi$
$263$			14.0738i			0.867829i	−0.900954	+	0.433914i	$0.857132\pi$
$264$	−4.87834			−0.300241
$265$	1.18886	+	28.9495i	0.0730310	+	1.77835i
$266$	16.0416			0.983571
$267$		−	3.11553i		−	0.190668i
$268$			2.67801i			0.163585i
$269$	−24.0562			−1.46673			−0.733367	−	0.679833i	$-0.762052\pi$
$269$	−24.0562			−1.46673			−0.733367	+	0.679833i	$0.762052\pi$
$270$	−12.4515	+	0.511343i	−0.757776	+	0.0311193i
$271$	17.3145			1.05178			0.525889	−	0.850553i	$-0.323733\pi$
$271$	17.3145			1.05178			0.525889	+	0.850553i	$0.323733\pi$
$272$			1.59002i			0.0964094i
$273$			30.4501i			1.84293i
$274$	1.95703			0.118228
$275$	15.6593	−	1.28832i	0.944289	−	0.0776886i
$276$	−9.57319			−0.576238
$277$		−	31.3592i		−	1.88419i	−0.335346	−	0.942095i	$-0.608853\pi$
$277$		−	31.3592i		−	1.88419i	0.335346	−	0.942095i	$-0.391147\pi$
$278$			9.41188i			0.564487i
$279$	0.590025			0.0353239
$280$	−10.8991	+	0.447591i	−0.651347	+	0.0267487i
$281$	1.39659			0.0833136			0.0416568	−	0.999132i	$-0.486736\pi$
$281$	1.39659			0.0833136			0.0416568	+	0.999132i	$0.486736\pi$
$282$		−	9.73055i		−	0.579446i
$283$		−	9.55395i		−	0.567924i	−0.958836	−	0.283962i	$-0.908351\pi$
$283$		−	9.55395i		−	0.567924i	0.958836	−	0.283962i	$-0.0916489\pi$
$284$	−14.4086			−0.854991
$285$	−0.468370	−	11.4051i	−0.0277438	−	0.675580i
$286$	−12.6350			−0.747125
$287$		−	50.9862i		−	3.00962i
$288$			0.590025i			0.0347675i
$289$	14.4718			0.851284
$290$	−0.196886	−	4.79430i	−0.0115615	−	0.281531i
$291$	24.6849			1.44706
$292$		−	4.15976i		−	0.243432i
$293$			2.41610i			0.141150i	0.997506	+	0.0705749i	$0.0224834\pi$
$293$			2.41610i			0.141150i	−0.997506	+	0.0705749i	$0.977517\pi$
$294$	−26.0778			−1.52089
$295$	−32.8278	+	1.34813i	−1.91131	+	0.0784911i
$296$	5.55241			0.322727
$297$		−	17.5134i		−	1.01623i
$298$		−	2.21654i		−	0.128401i
$299$	−24.7948			−1.43392
$300$	0.636449	+	7.73591i	0.0367454	+	0.446633i
$301$	8.83537			0.509262
$302$		−	14.2512i		−	0.820064i
$303$		−	11.6233i		−	0.667739i
$304$	−3.28832			−0.188598
$305$	15.1720	−	0.623064i	0.868747	−	0.0356766i
$306$	−0.938154			−0.0536307
$307$			28.4763i			1.62523i	0.582804	+	0.812613i	$0.301956\pi$
$307$			28.4763i			1.62523i	−0.582804	+	0.812613i	$0.698044\pi$
$308$		−	15.3299i		−	0.873501i
$309$	−5.27290			−0.299965
$310$	−0.0917505	−	2.23418i	−0.00521108	−	0.126893i
$311$	−14.3749			−0.815125			−0.407563	−	0.913177i	$-0.633621\pi$
$311$	−14.3749			−0.815125			−0.407563	+	0.913177i	$0.633621\pi$
$312$		−	6.24190i		−	0.353378i
$313$			0.869826i			0.0491655i	0.999698	+	0.0245827i	$0.00782572\pi$
$313$			0.869826i			0.0491655i	−0.999698	+	0.0245827i	$0.992174\pi$
$314$	−2.89518			−0.163385
$315$	−0.264090	−	6.43075i	−0.0148798	−	0.362332i
$316$	−5.10482			−0.287168
$317$			9.38587i			0.527163i	0.964637	+	0.263582i	$0.0849038\pi$
$317$			9.38587i			0.527163i	−0.964637	+	0.263582i	$0.915096\pi$
$318$		−	20.1154i		−	1.12801i
$319$	6.74330			0.377553
$320$	2.23418	−	0.0917505i	0.124895	−	0.00512901i
$321$	−10.6006			−0.591667
$322$		−	30.0831i		−	1.67647i
$323$		−	5.22851i		−	0.290922i
$324$	6.88180			0.382322
$325$	1.64842	+	20.0362i	0.0914379	+	1.11141i
$326$	17.0120			0.942206
$327$		−	11.0702i		−	0.612181i
$328$			10.4515i			0.577089i
$329$	30.5776			1.68580
$330$	−10.8991	+	0.447591i	−0.599977	+	0.0246390i
$331$	9.90948			0.544674			0.272337	−	0.962202i	$-0.412203\pi$
$331$	9.90948			0.544674			0.272337	+	0.962202i	$0.412203\pi$
$332$		−	2.73936i		−	0.150342i
$333$			3.27606i			0.179527i
$334$	1.22993			0.0672985
$335$	0.245709	+	5.98316i	0.0134245	+	0.326895i
$336$	7.57319			0.413151
$337$			27.0361i			1.47275i	0.676575	+	0.736374i	$0.263464\pi$
$337$			27.0361i			1.47275i	−0.676575	+	0.736374i	$0.736536\pi$
$338$		−	3.16666i		−	0.172244i
$339$	−11.2477			−0.610894
$340$	0.145886	+	3.55241i	0.00791176	+	0.192656i
$341$	3.14243			0.170172
$342$		−	1.94019i		−	0.104913i
$343$		−	47.7992i		−	2.58092i
$344$	−1.81114			−0.0976502
$345$	−21.3883	+	0.878345i	−1.15151	+	0.0472885i
$346$	2.86151			0.153836
$347$			17.4435i			0.936416i	0.883618	+	0.468208i	$0.155100\pi$
$347$			17.4435i			0.936416i	−0.883618	+	0.468208i	$0.844900\pi$
$348$			3.33129i			0.178576i
$349$	−7.47563			−0.400162			−0.200081	−	0.979779i	$-0.564120\pi$
$349$	−7.47563			−0.400162			−0.200081	+	0.979779i	$0.564120\pi$
$350$	−24.3096	+	2.00000i	−1.29940	+	0.106904i
$351$	22.4086			1.19608
$352$			3.14243i			0.167492i
$353$			13.0134i			0.692633i	0.938118	+	0.346316i	$0.112568\pi$
$353$			13.0134i			0.692633i	−0.938118	+	0.346316i	$0.887432\pi$
$354$	22.8102			1.21235
$355$	−32.1914	+	1.32199i	−1.70854	+	0.0701641i
$356$	−2.00690			−0.106366
$357$			12.0416i			0.637307i
$358$			24.4386i			1.29162i
$359$	−15.5969			−0.823174			−0.411587	−	0.911370i	$-0.635025\pi$
$359$	−15.5969			−0.823174			−0.411587	+	0.911370i	$0.635025\pi$
$360$	0.0541351	+	1.31822i	0.00285317	+	0.0694765i
$361$	−8.18695			−0.430892
$362$		−	21.3414i		−	1.12168i
$363$			1.74663i			0.0916741i
$364$	19.6147			1.02809
$365$	−0.381660	−	9.29368i	−0.0199770	−	0.486453i
$366$	−10.5422			−0.551049
$367$		−	17.9126i		−	0.935032i	−0.883985	−	0.467516i	$-0.845149\pi$
$367$		−	17.9126i		−	0.935032i	0.883985	−	0.467516i	$-0.154851\pi$
$368$			6.16666i			0.321460i
$369$	−6.16666			−0.321024
$370$	12.4051	−	0.509436i	0.644911	−	0.0264843i
$371$	63.2112			3.28176
$372$			1.55241i			0.0804887i
$373$			1.48724i			0.0770065i	0.999258	+	0.0385032i	$0.0122590\pi$
$373$			1.48724i			0.0770065i	−0.999258	+	0.0385032i	$0.987741\pi$
$374$	−4.99655			−0.258365
$375$	2.13172	+	17.2251i	0.110081	+	0.889498i
$376$	−6.26803			−0.323249
$377$			8.62813i			0.444371i
$378$			27.1879i			1.39840i
$379$	−1.17624			−0.0604192			−0.0302096	−	0.999544i	$-0.509617\pi$
$379$	−1.17624			−0.0604192			−0.0302096	+	0.999544i	$0.509617\pi$
$380$	−7.34671	+	0.301705i	−0.376878	+	0.0154771i
$381$	9.56247			0.489900
$382$		−	6.69484i		−	0.342538i
$383$			18.6612i			0.953541i	0.879028	+	0.476771i	$0.158193\pi$
$383$			18.6612i			0.953541i	−0.879028	+	0.476771i	$0.841807\pi$
$384$	−1.55241			−0.0792211
$385$	−1.40652	−	34.2498i	−0.0716831	−	1.74553i
$386$	−7.87348			−0.400750
$387$		−	1.06862i		−	0.0543209i
$388$		−	15.9010i		−	0.807253i
$389$	−5.55790			−0.281797			−0.140898	−	0.990024i	$-0.544999\pi$
$389$	−5.55790			−0.281797			−0.140898	+	0.990024i	$0.544999\pi$
$390$	−0.572697	−	13.9455i	−0.0289996	−	0.706160i
$391$	−9.80515			−0.495868
$392$			16.7982i			0.848440i
$393$		−	17.5886i		−	0.887228i
$394$	1.34967			0.0679956
$395$	−11.4051	+	0.468370i	−0.573853	+	0.0235662i
$396$	−1.85411			−0.0931728
$397$			31.6786i			1.58990i	0.606672	+	0.794952i	$0.292504\pi$
$397$			31.6786i			1.58990i	−0.606672	+	0.794952i	$0.707496\pi$
$398$			9.91405i			0.496947i
$399$	−24.9031			−1.24671
$400$	4.98316	−	0.409975i	0.249158	−	0.0204988i
$401$	−23.9179			−1.19440			−0.597201	−	0.802092i	$-0.703720\pi$
$401$	−23.9179			−1.19440			−0.597201	+	0.802092i	$0.703720\pi$
$402$		−	4.15736i		−	0.207350i
$403$			4.02078i			0.200289i
$404$	−7.48724			−0.372504
$405$	15.3752	−	0.631408i	0.764000	−	0.0313749i
$406$	−10.4684			−0.519536
$407$			17.4481i			0.864869i
$408$		−	2.46837i		−	0.122203i
$409$	23.3453			1.15435			0.577175	−	0.816620i	$-0.304155\pi$
$409$	23.3453			1.15435			0.577175	+	0.816620i	$0.304155\pi$
$410$	0.958933	+	23.3507i	0.0473583	+	1.15321i
$411$	−3.03811			−0.149859
$412$			3.39659i			0.167338i
$413$			71.6796i			3.52712i
$414$	−3.63849			−0.178822
$415$	−0.251338	−	6.12024i	−0.0123377	−	0.300431i
$416$	−4.02078			−0.197135
$417$		−	14.6111i		−	0.715508i
$418$		−	10.3333i		−	0.505420i
$419$	11.5657			0.565019			0.282510	−	0.959264i	$-0.408833\pi$
$419$	11.5657			0.565019			0.282510	+	0.959264i	$0.408833\pi$
$420$	16.9199	−	0.694844i	0.825607	−	0.0339049i
$421$	15.0979			0.735827			0.367914	−	0.929860i	$-0.380072\pi$
$421$	15.0979			0.735827			0.367914	+	0.929860i	$0.380072\pi$
$422$			18.7879i			0.914580i
$423$		−	3.69830i		−	0.179817i
$424$	−12.9575			−0.629273
$425$	0.651871	+	7.92335i	0.0316204	+	0.384339i
$426$	22.3680			1.08373
$427$		−	33.1281i		−	1.60318i
$428$			6.82847i			0.330067i
$429$	19.6147			0.947009
$430$	−4.04642	+	0.166173i	−0.195136	+	0.00801358i
$431$	−0.900669			−0.0433837			−0.0216918	−	0.999765i	$-0.506905\pi$
$431$	−0.900669			−0.0433837			−0.0216918	+	0.999765i	$0.506905\pi$
$432$		−	5.57319i		−	0.268140i
$433$		−	35.6464i		−	1.71306i	−0.516101	−	0.856528i	$-0.672617\pi$
$433$		−	35.6464i		−	1.71306i	0.516101	−	0.856528i	$-0.327383\pi$
$434$	−4.87834			−0.234168
$435$	0.305648	+	7.44272i	0.0146547	+	0.356851i
$436$	−7.13096			−0.341511
$437$		−	20.2780i		−	0.970027i
$438$			6.45765i			0.308559i
$439$	17.5387			0.837078			0.418539	−	0.908199i	$-0.362542\pi$
$439$	17.5387			0.837078			0.418539	+	0.908199i	$0.362542\pi$
$440$	0.288320	+	7.02078i	0.0137451	+	0.334703i
$441$	−9.91138			−0.471971
$442$		−	6.39314i		−	0.304091i
$443$		−	7.22161i		−	0.343109i	−0.985175	−	0.171554i	$-0.945121\pi$
$443$		−	7.22161i		−	0.343109i	0.985175	−	0.171554i	$-0.0548790\pi$
$444$	−8.61961			−0.409069
$445$	−4.48379	+	0.184134i	−0.212552	+	0.00872880i
$446$	19.4811			0.922458
$447$			3.44098i			0.162753i
$448$		−	4.87834i		−	0.230480i
$449$	34.6636			1.63587			0.817937	−	0.575307i	$-0.195117\pi$
$449$	34.6636			1.63587			0.817937	+	0.575307i	$0.195117\pi$
$450$	0.241896	+	2.94019i	0.0114031	+	0.138602i
$451$	−32.8433			−1.54653
$452$			7.24535i			0.340792i
$453$			22.1237i			1.03946i
$454$	15.6330			0.733693
$455$	43.8230	−	1.79966i	2.05445	−	0.0843695i
$456$	5.10482			0.239055
$457$		−	11.4474i		−	0.535489i	−0.963490	−	0.267745i	$-0.913722\pi$
$457$		−	11.4474i		−	0.535489i	0.963490	−	0.267745i	$-0.0862783\pi$
$458$			7.97781i			0.372778i
$459$	8.86151			0.413620
$460$	0.565795	+	13.7775i	0.0263803	+	0.642378i
$461$	21.4689			0.999905			0.499952	−	0.866053i	$-0.333351\pi$
$461$	21.4689			0.999905			0.499952	+	0.866053i	$0.333351\pi$
$462$			23.7982i			1.10719i
$463$		−	11.6722i		−	0.542451i	−0.962516	−	0.271226i	$-0.912571\pi$
$463$		−	11.6722i		−	0.542451i	0.962516	−	0.271226i	$-0.0874289\pi$
$464$	2.14589			0.0996202
$465$	0.142434	+	3.46837i	0.00660523	+	0.160842i
$466$	0.668707			0.0309773
$467$		−	18.9116i		−	0.875124i	−0.899188	−	0.437562i	$-0.855842\pi$
$467$		−	18.9116i		−	0.875124i	0.899188	−	0.437562i	$-0.144158\pi$
$468$		−	2.37236i		−	0.109662i
$469$	13.0642			0.603251
$470$	−14.0039	+	0.575095i	−0.645954	+	0.0265272i
$471$	4.49451			0.207096
$472$		−	14.6934i		−	0.676320i
$473$		−	5.69139i		−	0.261691i
$474$	7.92477			0.363997
$475$	−16.3862	+	1.34813i	−0.751852	+	0.0618564i
$476$	7.75669			0.355527
$477$		−	7.64526i		−	0.350052i
$478$		−	2.37081i		−	0.108439i
$479$	15.1303			0.691322			0.345661	−	0.938359i	$-0.387655\pi$
$479$	15.1303			0.691322			0.345661	+	0.938359i	$0.387655\pi$
$480$	−3.46837	+	0.142434i	−0.158309	+	0.00650121i
$481$	−22.3250			−1.01793
$482$			18.0793i			0.823490i
$483$			46.7013i			2.12498i
$484$	1.12511			0.0511412
$485$	−1.45893	−	35.5258i	−0.0662465	−	1.61315i
$486$	6.03620			0.273808
$487$			23.3952i			1.06014i	0.847955	+	0.530068i	$0.177834\pi$
$487$			23.3952i			1.06014i	−0.847955	+	0.530068i	$0.822166\pi$
$488$			6.79085i			0.307408i
$489$	−26.4095			−1.19428
$490$	1.54125	+	37.5304i	0.0696265	+	1.69545i
$491$	−32.0747			−1.44751			−0.723756	−	0.690056i	$-0.757586\pi$
$491$	−32.0747			−1.44751			−0.723756	+	0.690056i	$0.757586\pi$
$492$		−	16.2251i		−	0.731482i
$493$			3.41201i			0.153669i
$494$	13.2216			0.594868
$495$	−4.14243	+	0.170116i	−0.186189	+	0.00764614i
$496$	1.00000			0.0449013
$497$			70.2899i			3.15293i
$498$			4.25261i			0.190564i
$499$	9.69612			0.434058			0.217029	−	0.976165i	$-0.430363\pi$
$499$	9.69612			0.434058			0.217029	+	0.976165i	$0.430363\pi$
$500$	11.0957	−	1.37317i	0.496214	−	0.0614099i
$501$	−1.90935			−0.0853034
$502$		−	24.7902i		−	1.10644i
$503$		−	5.14638i		−	0.229466i	−0.993396	−	0.114733i	$-0.963399\pi$
$503$		−	5.14638i		−	0.229466i	0.993396	−	0.114733i	$-0.0366012\pi$
$504$	2.87834			0.128212
$505$	−16.7279	+	0.686958i	−0.744381	+	0.0305692i
$506$	−19.3783			−0.861472
$507$			4.91596i			0.218325i
$508$		−	6.15976i		−	0.273295i
$509$	−34.8894			−1.54645			−0.773223	−	0.634135i	$-0.781356\pi$
$509$	−34.8894			−1.54645			−0.773223	+	0.634135i	$0.781356\pi$
$510$	−0.226474	−	5.51479i	−0.0100284	−	0.244199i
$511$	−20.2928			−0.897699
$512$			1.00000i			0.0441942i
$513$			18.3264i			0.809132i
$514$	23.6638			1.04377
$515$	0.311639	+	7.58861i	0.0137324	+	0.334394i
$516$	2.81163			0.123775
$517$		−	19.6969i		−	0.866268i
$518$		−	27.0866i		−	1.19012i
$519$	−4.44223			−0.194992
$520$	−8.98316	+	0.368908i	−0.393938	+	0.0161777i
$521$	2.50522			0.109756			0.0548779	−	0.998493i	$-0.482523\pi$
$521$	2.50522			0.109756			0.0548779	+	0.998493i	$0.482523\pi$
$522$			1.26613i			0.0554168i
$523$			27.0029i			1.18075i	0.807128	+	0.590377i	$0.201021\pi$
$523$			27.0029i			1.18075i	−0.807128	+	0.590377i	$0.798979\pi$
$524$	−11.3299			−0.494948
$525$	37.7384	−	3.10482i	1.64704	−	0.135505i
$526$	−14.0738			−0.613648
$527$			1.59002i			0.0692626i
$528$		−	4.87834i		−	0.212303i
$529$	−15.0278			−0.653381
$530$	−28.9495	+	1.18886i	−1.25749	+	0.0516407i
$531$	8.66949			0.376224
$532$			16.0416i			0.695490i
$533$		−	42.0233i		−	1.82023i
$534$	3.11553			0.134822
$535$	0.626515	+	15.2561i	0.0270866	+	0.659577i
$536$	−2.67801			−0.115672
$537$		−	37.9388i		−	1.63718i
$538$		−	24.0562i		−	1.03714i
$539$	−52.7874			−2.27371
$540$	−0.511343	−	12.4515i	−0.0220047	−	0.535829i
$541$	31.3123			1.34622			0.673110	−	0.739543i	$-0.264958\pi$
$541$	31.3123			1.34622			0.673110	+	0.739543i	$0.264958\pi$
$542$			17.3145i			0.743720i
$543$			33.1305i			1.42177i
$544$	−1.59002			−0.0681718
$545$	−15.9319	+	0.654269i	−0.682446	+	0.0280258i
$546$	−30.4501			−1.30314
$547$			31.9663i			1.36678i	0.730053	+	0.683391i	$0.239495\pi$
$547$			31.9663i			1.36678i	−0.730053	+	0.683391i	$0.760505\pi$
$548$			1.95703i			0.0836000i
$549$	−4.00677			−0.171005
$550$	1.28832	+	15.6593i	0.0549341	+	0.667713i
$551$	−7.05636			−0.300611
$552$		−	9.57319i		−	0.407462i
$553$			24.9031i			1.05899i
$554$	31.3592			1.33232
$555$	−19.2578	+	0.790854i	−0.817448	+	0.0335699i
$556$	−9.41188			−0.399153
$557$			34.3359i			1.45486i	0.686184	+	0.727428i	$0.259285\pi$
$557$			34.3359i			1.45486i	−0.686184	+	0.727428i	$0.740715\pi$
$558$			0.590025i			0.0249777i
$559$	7.28220			0.308004
$560$	−0.447591	−	10.8991i	−0.0189142	−	0.460572i
$561$	7.75669			0.327488
$562$			1.39659i			0.0589116i
$563$		−	20.0907i		−	0.846720i	−0.905962	−	0.423360i	$-0.860851\pi$
$563$		−	20.0907i		−	0.846720i	0.905962	−	0.423360i	$-0.139149\pi$
$564$	9.73055			0.409730
$565$	0.664764	+	16.1874i	0.0279668	+	0.681011i
$566$	9.55395			0.401583
$567$		−	33.5718i		−	1.40988i
$568$		−	14.4086i		−	0.604570i
$569$	−33.8505			−1.41909			−0.709544	−	0.704661i	$-0.751099\pi$
$569$	−33.8505			−1.41909			−0.709544	+	0.704661i	$0.751099\pi$
$570$	11.4051	−	0.468370i	0.477707	−	0.0196178i
$571$	−37.0100			−1.54882			−0.774410	−	0.632684i	$-0.781953\pi$
$571$	−37.0100			−1.54882			−0.774410	+	0.632684i	$0.781953\pi$
$572$		−	12.6350i		−	0.528297i
$573$			10.3931i			0.434180i
$574$	50.9862			2.12812
$575$	2.52818	+	30.7295i	0.105432	+	1.28151i
$576$	−0.590025			−0.0245844
$577$		−	9.69139i		−	0.403458i	−0.979441	−	0.201729i	$-0.935344\pi$
$577$		−	9.69139i		−	0.403458i	0.979441	−	0.201729i	$-0.0646560\pi$
$578$			14.4718i			0.601948i
$579$	12.2229			0.507965
$580$	4.79430	−	0.196886i	0.199073	−	0.00817525i
$581$	−13.3636			−0.554414
$582$			24.6849i			1.02322i
$583$		−	40.7182i		−	1.68637i
$584$	4.15976			0.172132
$585$	−0.217665	−	5.30029i	−0.00899935	−	0.219140i
$586$	−2.41610			−0.0998080
$587$		−	26.6528i		−	1.10008i	−0.835139	−	0.550039i	$-0.814613\pi$
$587$		−	26.6528i		−	1.10008i	0.835139	−	0.550039i	$-0.185387\pi$
$588$		−	26.0778i		−	1.07543i
$589$	−3.28832			−0.135493
$590$	−1.34813	−	32.8278i	−0.0555016	−	1.35150i
$591$	−2.09525			−0.0861869
$592$			5.55241i			0.228203i
$593$			7.44808i			0.305856i	0.988237	+	0.152928i	$0.0488703\pi$
$593$			7.44808i			0.305856i	−0.988237	+	0.152928i	$0.951130\pi$
$594$	17.5134			0.718583
$595$	17.3299	−	0.711680i	0.710456	−	0.0291760i
$596$	2.21654			0.0907930
$597$		−	15.3907i		−	0.629898i
$598$		−	24.7948i		−	1.01393i
$599$	−29.6869			−1.21298			−0.606488	−	0.795093i	$-0.707422\pi$
$599$	−29.6869			−1.21298			−0.606488	+	0.795093i	$0.707422\pi$
$600$	−7.73591	+	0.636449i	−0.315817	+	0.0259829i
$601$	−11.0296			−0.449906			−0.224953	−	0.974370i	$-0.572223\pi$
$601$	−11.0296			−0.449906			−0.224953	+	0.974370i	$0.572223\pi$
$602$			8.83537i			0.360103i
$603$		−	1.58009i		−	0.0643463i
$604$	14.2512			0.579873
$605$	2.51370	−	0.103229i	0.102196	−	0.00419686i
$606$	11.6233			0.472163
$607$			17.0158i			0.690649i	0.938483	+	0.345325i	$0.112231\pi$
$607$			17.0158i			0.690649i	−0.938483	+	0.345325i	$0.887769\pi$
$608$		−	3.28832i		−	0.133359i
$609$	16.2512			0.658532
$610$	0.623064	+	15.1720i	0.0252271	+	0.614297i
$611$	25.2024			1.01958
$612$		−	0.938154i		−	0.0379226i
$613$		−	30.3280i		−	1.22494i	−0.790496	−	0.612468i	$-0.790177\pi$
$613$		−	30.3280i		−	1.22494i	0.790496	−	0.612468i	$-0.209823\pi$
$614$	−28.4763			−1.14921
$615$	−1.48866	−	36.2498i	−0.0600285	−	1.46173i
$616$	15.3299			0.617658
$617$			5.91688i			0.238205i	0.992882	+	0.119102i	$0.0380017\pi$
$617$			5.91688i			0.238205i	−0.992882	+	0.119102i	$0.961998\pi$
$618$		−	5.27290i		−	0.212107i
$619$	−37.1541			−1.49335			−0.746675	−	0.665189i	$-0.768351\pi$
$619$	−37.1541			−1.49335			−0.746675	+	0.665189i	$0.768351\pi$
$620$	2.23418	−	0.0917505i	0.0897270	−	0.00368479i
$621$	34.3680			1.37914
$622$		−	14.3749i		−	0.576380i
$623$			9.79036i			0.392243i
$624$	6.24190			0.249876
$625$	24.6638	−	4.08595i	0.986554	−	0.163438i
$626$	−0.869826			−0.0347652
$627$			16.0416i			0.640638i
$628$		−	2.89518i		−	0.115530i
$629$	−8.82847			−0.352014
$630$	6.43075	−	0.264090i	0.256207	−	0.0105216i
$631$	35.1234			1.39824			0.699121	−	0.715004i	$-0.253575\pi$
$631$	35.1234			1.39824			0.699121	+	0.715004i	$0.253575\pi$
$632$		−	5.10482i		−	0.203059i
$633$		−	29.1665i		−	1.15926i
$634$	−9.38587			−0.372761
$635$	−0.565161	−	13.7620i	−0.0224277	−	0.546130i
$636$	20.1154			0.797626
$637$		−	67.5420i		−	2.67611i
$638$			6.74330i			0.266970i
$639$	8.50141			0.336311
$640$	0.0917505	+	2.23418i	0.00362676	+	0.0883139i
$641$	0.0484607			0.00191408			0.000957041	−	1.00000i	$-0.499695\pi$
$641$	0.0484607			0.00191408			0.000957041		1.00000i	$0.499695\pi$
$642$		−	10.6006i		−	0.418372i
$643$			0.407015i			0.0160511i	0.999968	+	0.00802556i	$0.00255464\pi$
$643$			0.407015i			0.0160511i	−0.999968	+	0.00802556i	$0.997445\pi$
$644$	30.0831			1.18544
$645$	6.28171	−	0.257969i	0.247342	−	0.0101575i
$646$	5.22851			0.205713
$647$		−	17.7206i		−	0.696669i	−0.937370	−	0.348335i	$-0.886747\pi$
$647$		−	17.7206i		−	0.696669i	0.937370	−	0.348335i	$-0.113253\pi$
$648$			6.88180i			0.270342i
$649$	46.1731			1.81245
$650$	−20.0362	+	1.64842i	−0.785884	+	0.0646563i
$651$	7.57319			0.296817
$652$			17.0120i			0.666240i
$653$			13.0450i			0.510491i	0.966876	+	0.255245i	$0.0821562\pi$
$653$			13.0450i			0.510491i	−0.966876	+	0.255245i	$0.917844\pi$
$654$	11.0702			0.432878
$655$	−25.3130	+	1.03952i	−0.989062	+	0.0406175i
$656$	−10.4515			−0.408064
$657$			2.45436i			0.0957538i
$658$			30.5776i			1.19204i
$659$	−2.11208			−0.0822751			−0.0411375	−	0.999153i	$-0.513098\pi$
$659$	−2.11208			−0.0822751			−0.0411375	+	0.999153i	$0.513098\pi$
$660$	−0.447591	−	10.8991i	−0.0174224	−	0.424248i
$661$	−29.6831			−1.15454			−0.577269	−	0.816554i	$-0.695882\pi$
$661$	−29.6831			−1.15454			−0.577269	+	0.816554i	$0.695882\pi$
$662$			9.90948i			0.385143i
$663$			9.92477i			0.385446i
$664$	2.73936			0.106308
$665$	1.47182	+	35.8398i	0.0570748	+	1.38981i
$666$	−3.27606			−0.126945
$667$			13.2330i			0.512382i
$668$			1.22993i			0.0475872i
$669$	−30.2427			−1.16925
$670$	−5.98316	+	0.245709i	−0.231150	+	0.00949255i
$671$	−21.3398			−0.823814
$672$			7.57319i			0.292142i
$673$		−	28.8047i		−	1.11034i	−0.831737	−	0.555170i	$-0.812653\pi$
$673$		−	28.8047i		−	1.11034i	0.831737	−	0.555170i	$-0.187347\pi$
$674$	−27.0361			−1.04139
$675$	−2.28487	−	27.7721i	−0.0879446	−	1.06895i
$676$	3.16666			0.121795
$677$			39.1643i			1.50521i	0.658474	+	0.752604i	$0.271202\pi$
$677$			39.1643i			1.50521i	−0.658474	+	0.752604i	$0.728798\pi$
$678$		−	11.2477i		−	0.431967i
$679$	−77.5707			−2.97689
$680$	−3.55241	+	0.145886i	−0.136229	+	0.00559446i
$681$	−24.2688			−0.929983
$682$			3.14243i			0.120330i
$683$		−	48.2506i		−	1.84626i	−0.384492	−	0.923128i	$-0.625623\pi$
$683$		−	48.2506i		−	1.84626i	0.384492	−	0.923128i	$-0.374377\pi$
$684$	1.94019			0.0741850
$685$	0.179558	+	4.37236i	0.00686057	+	0.167059i
$686$	47.7992			1.82498
$687$		−	12.3848i		−	0.472510i
$688$		−	1.81114i		−	0.0690491i
$689$	52.0993			1.98483
$690$	−0.878345	−	21.3883i	−0.0334380	−	0.814238i
$691$	26.5014			1.00816			0.504081	−	0.863657i	$-0.331831\pi$
$691$	26.5014			1.00816			0.504081	+	0.863657i	$0.331831\pi$
$692$			2.86151i			0.108778i
$693$			9.04501i			0.343591i
$694$	−17.4435			−0.662146
$695$	−21.0279	+	0.863545i	−0.797633	+	0.0327561i
$696$	−3.33129			−0.126272
$697$		−	16.6182i		−	0.629459i
$698$		−	7.47563i		−	0.282957i
$699$	−1.03811			−0.0392648
$700$	−2.00000	−	24.3096i	−0.0755929	−	0.918816i
$701$	16.7873			0.634046			0.317023	−	0.948418i	$-0.397317\pi$
$701$	16.7873			0.634046			0.317023	+	0.948418i	$0.397317\pi$
$702$			22.4086i			0.845757i
$703$		−	18.2581i		−	0.688617i
$704$	−3.14243			−0.118435
$705$	21.7399	−	0.892783i	0.818770	−	0.0336242i
$706$	−13.0134			−0.489765
$707$			36.5253i			1.37368i
$708$			22.8102i			0.857260i
$709$	8.77950			0.329721			0.164861	−	0.986317i	$-0.447283\pi$
$709$	8.77950			0.329721			0.164861	+	0.986317i	$0.447283\pi$
$710$	−1.32199	−	32.1914i	−0.0496135	−	1.20812i
$711$	3.01197			0.112958
$712$		−	2.00690i		−	0.0752118i
$713$			6.16666i			0.230943i
$714$	−12.0416			−0.450644
$715$	−1.15927	−	28.2290i	−0.0433543	−	1.05570i
$716$	−24.4386			−0.913315
$717$			3.68048i			0.137450i
$718$		−	15.5969i		−	0.582072i
$719$	−31.4420			−1.17259			−0.586294	−	0.810099i	$-0.699414\pi$
$719$	−31.4420			−1.17259			−0.586294	+	0.810099i	$0.699414\pi$
$720$	−1.31822	+	0.0541351i	−0.0491273	+	0.00201750i
$721$	16.5697			0.617089
$722$		−	8.18695i		−	0.304687i
$723$		−	28.0665i		−	1.04380i
$724$	21.3414			0.793145
$725$	10.6933	−	0.879760i	0.397139	−	0.0326735i
$726$	−1.74663			−0.0648234
$727$			14.6881i			0.544751i	0.962191	+	0.272376i	$0.0878093\pi$
$727$			14.6881i			0.544751i	−0.962191	+	0.272376i	$0.912191\pi$
$728$			19.6147i			0.726971i
$729$	−30.0160			−1.11171
$730$	9.29368	−	0.381660i	0.343974	−	0.0141259i
$731$	2.87976			0.106512
$732$		−	10.5422i		−	0.389650i
$733$			7.31755i			0.270280i	0.990827	+	0.135140i	$0.0431484\pi$
$733$			7.31755i			0.270280i	−0.990827	+	0.135140i	$0.956852\pi$
$734$	17.9126			0.661168
$735$	−2.39265	−	58.2625i	−0.0882541	−	2.14905i
$736$	−6.16666			−0.227306
$737$		−	8.41546i		−	0.309988i
$738$		−	6.16666i		−	0.226998i
$739$	−26.3981			−0.971069			−0.485534	−	0.874218i	$-0.661375\pi$
$739$	−26.3981			−0.971069			−0.485534	+	0.874218i	$0.661375\pi$
$740$	0.509436	+	12.4051i	0.0187273	+	0.456021i
$741$	−20.5253			−0.754018
$742$			63.2112i			2.32056i
$743$			29.5497i			1.08407i	0.840355	+	0.542037i	$0.182347\pi$
$743$			29.5497i			1.08407i	−0.840355	+	0.542037i	$0.817653\pi$
$744$	−1.55241			−0.0569141
$745$	4.95216	−	0.203369i	0.181433	−	0.00745085i
$746$	−1.48724			−0.0544518
$747$			1.61629i			0.0591370i
$748$		−	4.99655i		−	0.182692i
$749$	33.3116			1.21718
$750$	−17.2251	+	2.13172i	−0.628970	+	0.0778394i
$751$	−12.8698			−0.469627			−0.234813	−	0.972040i	$-0.575448\pi$
$751$	−12.8698			−0.469627			−0.234813	+	0.972040i	$0.575448\pi$
$752$		−	6.26803i		−	0.228572i
$753$			38.4846i			1.40246i
$754$	−8.62813			−0.314218
$755$	31.8398	−	1.30755i	1.15877	−	0.0475868i
$756$	−27.1879			−0.988816
$757$			18.3645i			0.667468i	0.942667	+	0.333734i	$0.108309\pi$
$757$			18.3645i			0.667468i	−0.942667	+	0.333734i	$0.891691\pi$
$758$		−	1.17624i		−	0.0427228i
$759$	30.0831			1.09195
$760$	−0.301705	−	7.34671i	−0.0109440	−	0.266493i
$761$	−2.35221			−0.0852677			−0.0426338	−	0.999091i	$-0.513575\pi$
$761$	−2.35221			−0.0852677			−0.0426338	+	0.999091i	$0.513575\pi$
$762$			9.56247i			0.346412i
$763$			34.7873i			1.25938i
$764$	6.69484			0.242211
$765$	−0.0860761	−	2.09601i	−0.00311209	−	0.0757814i
$766$	−18.6612			−0.674256
$767$			59.0790i			2.13322i
$768$		−	1.55241i		−	0.0560178i
$769$	−35.4207			−1.27730			−0.638651	−	0.769496i	$-0.720507\pi$
$769$	−35.4207			−1.27730			−0.638651	+	0.769496i	$0.720507\pi$
$770$	34.2498	−	1.40652i	1.23428	−	0.0506876i
$771$	−36.7360			−1.32301
$772$		−	7.87348i		−	0.283373i
$773$		−	31.1426i		−	1.12012i	−0.828451	−	0.560061i	$-0.810778\pi$
$773$		−	31.1426i		−	1.12012i	0.828451	−	0.560061i	$-0.189222\pi$
$774$	1.06862			0.0384107
$775$	4.98316	−	0.409975i	0.179001	−	0.0147267i
$776$	15.9010			0.570814
$777$			42.0494i			1.50852i
$778$		−	5.55790i		−	0.199260i
$779$	34.3680			1.23136
$780$	13.9455	−	0.572697i	0.499331	−	0.0205058i
$781$	45.2780			1.62017
$782$		−	9.80515i		−	0.350631i
$783$		−	11.9594i		−	0.427395i
$784$	−16.7982			−0.599937
$785$	−0.265634	−	6.46837i	−0.00948089	−	0.230866i
$786$	17.5886			0.627365
$787$			4.34559i			0.154904i	0.996996	+	0.0774518i	$0.0246784\pi$
$787$			4.34559i			0.154904i	−0.996996	+	0.0774518i	$0.975322\pi$
$788$			1.34967i			0.0480801i
$789$	21.8483			0.777821
$790$	−0.468370	−	11.4051i	−0.0166638	−	0.405776i
$791$	35.3453			1.25673
$792$		−	1.85411i		−	0.0658831i
$793$		−	27.3045i		−	0.969612i
$794$	−31.6786			−1.12423
$795$	44.9415	−	1.84560i	1.59391	−	0.0654565i
$796$	−9.91405			−0.351394
$797$		−	22.3881i		−	0.793028i	−0.918029	−	0.396514i	$-0.870220\pi$
$797$		−	22.3881i		−	0.793028i	0.918029	−	0.396514i	$-0.129780\pi$
$798$		−	24.9031i		−	0.881559i
$799$	9.96633			0.352583
$800$	0.409975	+	4.98316i	0.0144948	+	0.176181i
$801$	1.18412			0.0418389
$802$		−	23.9179i		−	0.844569i
$803$			13.0718i			0.461293i
$804$	4.15736			0.146619
$805$	67.2112	−	2.76014i	2.36889	−	0.0972822i
$806$	−4.02078			−0.141626
$807$			37.3451i			1.31461i
$808$		−	7.48724i		−	0.263400i
$809$	7.61694			0.267797			0.133899	−	0.990995i	$-0.457250\pi$
$809$	7.61694			0.267797			0.133899	+	0.990995i	$0.457250\pi$
$810$	0.631408	+	15.3752i	0.0221854	+	0.540230i
$811$	47.6459			1.67308			0.836538	−	0.547910i	$-0.184576\pi$
$811$	47.6459			1.67308			0.836538	+	0.547910i	$0.184576\pi$
$812$		−	10.4684i		−	0.367368i
$813$		−	26.8791i		−	0.942692i
$814$	−17.4481			−0.611555
$815$	1.56086	+	38.0079i	0.0546744	+	1.33136i
$816$	2.46837			0.0864102
$817$			5.95561i			0.208360i
$818$			23.3453i			0.816249i
$819$	−11.5732			−0.404400
$820$	−23.3507	+	0.958933i	−0.815440	+	0.0334874i
$821$	−2.68787			−0.0938073			−0.0469036	−	0.998899i	$-0.514935\pi$
$821$	−2.68787			−0.0938073			−0.0469036	+	0.998899i	$0.514935\pi$
$822$		−	3.03811i		−	0.105966i
$823$		−	11.7660i		−	0.410137i	−0.978748	−	0.205068i	$-0.934258\pi$
$823$		−	11.7660i		−	0.410137i	0.978748	−	0.205068i	$-0.0657417\pi$
$824$	−3.39659			−0.118326
$825$	−2.00000	−	24.3096i	−0.0696311	−	0.846351i
$826$	−71.6796			−2.49405
$827$			1.99401i			0.0693385i	0.999399	+	0.0346692i	$0.0110378\pi$
$827$			1.99401i			0.0693385i	−0.999399	+	0.0346692i	$0.988962\pi$
$828$		−	3.63849i		−	0.126446i
$829$	−10.1197			−0.351473			−0.175737	−	0.984437i	$-0.556231\pi$
$829$	−10.1197			−0.351473			−0.175737	+	0.984437i	$0.556231\pi$
$830$	6.12024	−	0.251338i	0.212437	−	0.00872406i
$831$	−48.6823			−1.68877
$832$		−	4.02078i		−	0.139395i
$833$		−	26.7096i		−	0.925434i
$834$	14.6111			0.505941
$835$	0.112846	+	2.74788i	0.00390521	+	0.0950943i
$836$	10.3333			0.357386
$837$		−	5.57319i		−	0.192638i
$838$			11.5657i			0.399529i
$839$	35.9335			1.24056			0.620281	−	0.784380i	$-0.287019\pi$
$839$	35.9335			1.24056			0.620281	+	0.784380i	$0.287019\pi$
$840$	0.694844	+	16.9199i	0.0239744	+	0.583792i
$841$	−24.3952			−0.841213
$842$			15.0979i			0.520309i
$843$		−	2.16808i		−	0.0746726i
$844$	−18.7879			−0.646706
$845$	7.07491	−	0.290543i	0.243384	−	0.00999498i
$846$	3.69830			0.127150
$847$		−	5.48866i		−	0.188592i
$848$		−	12.9575i		−	0.444963i
$849$	−14.8316			−0.509021
$850$	−7.92335	+	0.651871i	−0.271769	+	0.0223590i
$851$	−34.2398			−1.17373
$852$			22.3680i			0.766315i
$853$		−	37.0560i		−	1.26877i	−0.773016	−	0.634386i	$-0.781253\pi$
$853$		−	37.0560i		−	1.26877i	0.773016	−	0.634386i	$-0.218747\pi$
$854$	33.1281			1.13362
$855$	4.33474	−	0.178013i	0.148245	−	0.00608793i
$856$	−6.82847			−0.233392
$857$		−	47.5222i		−	1.62333i	−0.584124	−	0.811665i	$-0.698562\pi$
$857$		−	47.5222i		−	1.62333i	0.584124	−	0.811665i	$-0.301438\pi$
$858$			19.6147i			0.669636i
$859$	−17.5271			−0.598015			−0.299008	−	0.954251i	$-0.596656\pi$
$859$	−17.5271			−0.598015			−0.299008	+	0.954251i	$0.596656\pi$
$860$	−0.166173	−	4.04642i	−0.00566646	−	0.137982i
$861$	−79.1514			−2.69747
$862$		−	0.900669i		−	0.0306769i
$863$		−	1.08637i		−	0.0369803i	−0.999829	−	0.0184902i	$-0.994114\pi$
$863$		−	1.08637i		−	0.0369803i	0.999829	−	0.0184902i	$-0.00588594\pi$
$864$	5.57319			0.189604
$865$	0.262545	+	6.39314i	0.00892679	+	0.217373i
$866$	35.6464			1.21131
$867$		−	22.4662i		−	0.762992i
$868$		−	4.87834i		−	0.165582i
$869$	16.0416			0.544173
$870$	−7.44272	+	0.305648i	−0.252332	+	0.0103624i
$871$	10.7677			0.364849
$872$		−	7.13096i		−	0.241485i
$873$			9.38200i			0.317533i
$874$	20.2780			0.685912
$875$	−6.69879	−	54.1286i	−0.226460	−	1.82988i
$876$	−6.45765			−0.218184
$877$		−	32.2096i		−	1.08764i	−0.839201	−	0.543821i	$-0.816977\pi$
$877$		−	32.2096i		−	1.08764i	0.839201	−	0.543821i	$-0.183023\pi$
$878$			17.5387i			0.591904i
$879$	3.75077			0.126510
$880$	−7.02078	+	0.288320i	−0.236670	+	0.00971926i
$881$	−53.6679			−1.80812			−0.904059	−	0.427408i	$-0.859427\pi$
$881$	−53.6679			−1.80812			−0.904059	+	0.427408i	$0.859427\pi$
$882$		−	9.91138i		−	0.333734i
$883$			56.8574i			1.91340i	0.291070	+	0.956702i	$0.405989\pi$
$883$			56.8574i			1.91340i	−0.291070	+	0.956702i	$0.594011\pi$
$884$	6.39314			0.215025
$885$	2.09285	+	50.9622i	0.0703503	+	1.71308i
$886$	7.22161			0.242615
$887$		−	0.847502i		−	0.0284563i	−0.999899	−	0.0142282i	$-0.995471\pi$
$887$		−	0.847502i		−	0.0284563i	0.999899	−	0.0142282i	$-0.00452912\pi$
$888$		−	8.61961i		−	0.289255i
$889$	−30.0494			−1.00783
$890$	−0.184134	−	4.48379i	−0.00617220	−	0.150297i
$891$	−21.6256			−0.724485
$892$			19.4811i			0.652276i
$893$			20.6113i			0.689731i
$894$	−3.44098			−0.115084
$895$	−54.6004	+	2.24226i	−1.82509	+	0.0749504i
$896$	4.87834			0.162974
$897$			38.4917i			1.28520i
$898$			34.6636i			1.15674i
$899$	2.14589			0.0715693
$900$	−2.94019	+	0.241896i	−0.0980064	+	0.00806318i
$901$	20.6028			0.686378
$902$		−	32.8433i		−	1.09356i
$903$		−	13.7161i		−	0.456444i
$904$	−7.24535			−0.240977
$905$	47.6805	−	1.95808i	1.58495	−	0.0650888i
$906$	−22.1237			−0.735010
$907$			46.2299i			1.53504i	0.641027	+	0.767519i	$0.278509\pi$
$907$			46.2299i			1.53504i	−0.641027	+	0.767519i	$0.721491\pi$
$908$			15.6330i			0.518799i
$909$	4.41766			0.146525
$910$	1.79966	+	43.8230i	0.0596582	+	1.45272i
$911$	32.1622			1.06558			0.532790	−	0.846248i	$-0.321144\pi$
$911$	32.1622			1.06558			0.532790	+	0.846248i	$0.321144\pi$
$912$			5.10482i			0.169037i
$913$			8.60826i			0.284892i
$914$	11.4474			0.378648
$915$	−0.967251	−	23.5532i	−0.0319763	−	0.778644i
$916$	−7.97781			−0.263594
$917$			55.2711i			1.82521i
$918$			8.86151i			0.292473i
$919$	19.8842			0.655919			0.327960	−	0.944692i	$-0.393639\pi$
$919$	19.8842			0.655919			0.327960	+	0.944692i	$0.393639\pi$
$920$	−13.7775	+	0.565795i	−0.454230	+	0.0186537i
$921$	44.2068			1.45666
$922$			21.4689i			0.707039i
$923$			57.9336i			1.90691i
$924$	−23.7982			−0.782905
$925$	2.27635	+	27.6686i	0.0748459	+	0.909737i
$926$	11.6722			0.383571
$927$		−	2.00407i		−	0.0658224i
$928$			2.14589i			0.0704421i
$929$	20.5858			0.675398			0.337699	−	0.941254i	$-0.390351\pi$
$929$	20.5858			0.675398			0.337699	+	0.941254i	$0.390351\pi$
$930$	−3.46837	+	0.142434i	−0.113732	+	0.00467061i
$931$	55.2380			1.81035
$932$			0.668707i			0.0219042i
$933$			22.3157i			0.730584i
$934$	18.9116			0.618806
$935$	−0.458436	−	11.1632i	−0.0149925	−	0.365076i
$936$	2.37236			0.0775430
$937$			54.8143i			1.79070i	0.445358	+	0.895352i	$0.353076\pi$
$937$			54.8143i			1.79070i	−0.445358	+	0.895352i	$0.646924\pi$
$938$			13.0642i			0.426563i
$939$	1.35033			0.0440662
$940$	−0.575095	−	14.0039i	−0.0187575	−	0.456758i
$941$	−13.9297			−0.454095			−0.227048	−	0.973884i	$-0.572907\pi$
$941$	−13.9297			−0.454095			−0.227048	+	0.973884i	$0.572907\pi$
$942$			4.49451i			0.146439i
$943$		−	64.4511i		−	2.09882i
$944$	14.6934			0.478230
$945$	−60.7429	+	2.49451i	−1.97597	+	0.0811463i
$946$	5.69139			0.185043
$947$		−	20.8829i		−	0.678604i	−0.940678	−	0.339302i	$-0.889809\pi$
$947$		−	20.8829i		−	0.678604i	0.940678	−	0.339302i	$-0.110191\pi$
$948$			7.92477i			0.257385i
$949$	−16.7255			−0.542932
$950$	−1.34813	−	16.3862i	−0.0437391	−	0.531640i
$951$	14.5707			0.472488
$952$			7.75669i			0.251396i
$953$			1.44338i			0.0467555i	0.999727	+	0.0233778i	$0.00744205\pi$
$953$			1.44338i			0.0467555i	−0.999727	+	0.0233778i	$0.992558\pi$
$954$	7.64526			0.247524
$955$	14.9575	−	0.614255i	0.484014	−	0.0198768i
$956$	2.37081			0.0766776
$957$		−	10.4684i		−	0.338394i
$958$			15.1303i			0.488839i
$959$	9.54705			0.308290
$960$	−0.142434	−	3.46837i	−0.00459705	−	0.111941i
$961$	1.00000			0.0322581
$962$		−	22.3250i		−	0.719787i
$963$		−	4.02897i		−	0.129832i
$964$	−18.0793			−0.582295
$965$	−0.722396	−	17.5908i	−0.0232547	−	0.566268i
$966$	−46.7013			−1.50259
$967$			61.0146i			1.96210i	0.193759	+	0.981049i	$0.437932\pi$
$967$			61.0146i			1.96210i	−0.193759	+	0.981049i	$0.562068\pi$
$968$			1.12511i			0.0361623i
$969$	−8.11679			−0.260749
$970$	35.5258	−	1.45893i	1.14067	−	0.0468433i
$971$	45.5251			1.46097			0.730485	−	0.682929i	$-0.239294\pi$
$971$	45.5251			1.46097			0.730485	+	0.682929i	$0.239294\pi$
$972$			6.03620i			0.193611i
$973$			45.9144i			1.47195i
$974$	−23.3952			−0.749630
$975$	31.1044	−	2.55902i	0.996138	−	0.0819543i
$976$	−6.79085			−0.217370
$977$			45.3422i			1.45063i	0.688419	+	0.725313i	$0.258305\pi$
$977$			45.3422i			1.45063i	−0.688419	+	0.725313i	$0.741695\pi$
$978$		−	26.4095i		−	0.844484i
$979$	6.30656			0.201559
$980$	−37.5304	+	1.54125i	−1.19886	+	0.0492333i
$981$	4.20744			0.134333
$982$		−	32.0747i		−	1.02355i
$983$			25.1342i			0.801658i	0.916153	+	0.400829i	$0.131278\pi$
$983$			25.1342i			0.801658i	−0.916153	+	0.400829i	$0.868722\pi$
$984$	16.2251			0.517236
$985$	0.123833	+	3.01542i	0.00394566	+	0.0960793i
$986$	−3.41201			−0.108661
$987$		−	47.4690i		−	1.51095i
$988$			13.2216i			0.420635i
$989$	11.1687			0.355144
$990$	−0.170116	−	4.14243i	−0.00540664	−	0.131655i
$991$	18.4529			0.586177			0.293089	−	0.956085i	$-0.405317\pi$
$991$	18.4529			0.586177			0.293089	+	0.956085i	$0.405317\pi$
$992$			1.00000i			0.0317500i
$993$		−	15.3836i		−	0.488183i
$994$	−70.2899			−2.22946
$995$	−22.1498	+	0.909619i	−0.702197	+	0.0288369i
$996$	−4.25261			−0.134749
$997$		−	15.6601i		−	0.495961i	−0.968765	−	0.247980i	$-0.920233\pi$
$997$		−	15.6601i		−	0.495961i	0.968765	−	0.247980i	$-0.0797669\pi$
$998$			9.69612i			0.306925i
$999$	30.9446			0.979045

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	310.2.b.b.249.6	yes	8
3.2	odd	2		2790.2.d.l.559.4		8
4.3	odd	2		2480.2.d.e.1489.6		8
5.2	odd	4		1550.2.a.n.1.2		4
5.3	odd	4		1550.2.a.q.1.3		4
5.4	even	2	inner	310.2.b.b.249.3	✓	8
15.14	odd	2		2790.2.d.l.559.8		8
20.19	odd	2		2480.2.d.e.1489.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
310.2.b.b.249.3	✓	8	5.4	even	2	inner
310.2.b.b.249.6	yes	8	1.1	even	1	trivial
1550.2.a.n.1.2		4	5.2	odd	4
1550.2.a.q.1.3		4	5.3	odd	4
2480.2.d.e.1489.3		8	20.19	odd	2
2480.2.d.e.1489.6		8	4.3	odd	2
2790.2.d.l.559.4		8	3.2	odd	2
2790.2.d.l.559.8		8	15.14	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)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.55241i q^{3} -1.00000 q^{4} +(-2.23418 + 0.0917505i) q^{5} +1.55241 q^{6} +4.87834i q^{7} -1.00000i q^{8} +0.590025 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -1.55241i q^{3} -1.00000 q^{4} +(-2.23418 + 0.0917505i) q^{5} +1.55241 q^{6} +4.87834i q^{7} -1.00000i q^{8} +0.590025 q^{9} +(-0.0917505 - 2.23418i) q^{10} +3.14243 q^{11} +1.55241i q^{12} +4.02078i q^{13} -4.87834 q^{14} +(0.142434 + 3.46837i) q^{15} +1.00000 q^{16} +1.59002i q^{17} +0.590025i q^{18} -3.28832 q^{19} +(2.23418 - 0.0917505i) q^{20} +7.57319 q^{21} +3.14243i q^{22} +6.16666i q^{23} -1.55241 q^{24} +(4.98316 - 0.409975i) q^{25} -4.02078 q^{26} -5.57319i q^{27} -4.87834i q^{28} +2.14589 q^{29} +(-3.46837 + 0.142434i) q^{30} +1.00000 q^{31} +1.00000i q^{32} -4.87834i q^{33} -1.59002 q^{34} +(-0.447591 - 10.8991i) q^{35} -0.590025 q^{36} +5.55241i q^{37} -3.28832i q^{38} +6.24190 q^{39} +(0.0917505 + 2.23418i) q^{40} -10.4515 q^{41} +7.57319i q^{42} -1.81114i q^{43} -3.14243 q^{44} +(-1.31822 + 0.0541351i) q^{45} -6.16666 q^{46} -6.26803i q^{47} -1.55241i q^{48} -16.7982 q^{49} +(0.409975 + 4.98316i) q^{50} +2.46837 q^{51} -4.02078i q^{52} -12.9575i q^{53} +5.57319 q^{54} +(-7.02078 + 0.288320i) q^{55} +4.87834 q^{56} +5.10482i q^{57} +2.14589i q^{58} +14.6934 q^{59} +(-0.142434 - 3.46837i) q^{60} -6.79085 q^{61} +1.00000i q^{62} +2.87834i q^{63} -1.00000 q^{64} +(-0.368908 - 8.98316i) q^{65} +4.87834 q^{66} -2.67801i q^{67} -1.59002i q^{68} +9.57319 q^{69} +(10.8991 - 0.447591i) q^{70} +14.4086 q^{71} -0.590025i q^{72} +4.15976i q^{73} -5.55241 q^{74} +(-0.636449 - 7.73591i) q^{75} +3.28832 q^{76} +15.3299i q^{77} +6.24190i q^{78} +5.10482 q^{79} +(-2.23418 + 0.0917505i) q^{80} -6.88180 q^{81} -10.4515i q^{82} +2.73936i q^{83} -7.57319 q^{84} +(-0.145886 - 3.55241i) q^{85} +1.81114 q^{86} -3.33129i q^{87} -3.14243i q^{88} +2.00690 q^{89} +(-0.0541351 - 1.31822i) q^{90} -19.6147 q^{91} -6.16666i q^{92} -1.55241i q^{93} +6.26803 q^{94} +(7.34671 - 0.301705i) q^{95} +1.55241 q^{96} +15.9010i q^{97} -16.7982i q^{98} +1.85411 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 2 q^{5} + 4 q^{6}+O(q^{10}) \) 8 * q - 8 * q^4 - 2 * q^5 + 4 * q^6	\( 8 q - 8 q^{4} - 2 q^{5} + 4 q^{6} + 2 q^{10} + 12 q^{11} - 12 q^{14} - 12 q^{15} + 8 q^{16} - 4 q^{19} + 2 q^{20} + 12 q^{21} - 4 q^{24} - 4 q^{25} + 8 q^{26} + 8 q^{29} + 4 q^{30} + 8 q^{31} - 8 q^{34} - 12 q^{35} + 8 q^{39} - 2 q^{40} - 8 q^{41} - 12 q^{44} - 18 q^{45} + 8 q^{50} - 12 q^{51} - 4 q^{54} - 16 q^{55} + 12 q^{56} + 12 q^{60} - 8 q^{64} + 12 q^{66} + 28 q^{69} + 20 q^{70} + 24 q^{71} - 36 q^{74} - 20 q^{75} + 4 q^{76} + 24 q^{79} - 2 q^{80} - 32 q^{81} - 12 q^{84} + 8 q^{85} + 8 q^{86} + 24 q^{89} + 6 q^{90} - 28 q^{91} - 20 q^{94} + 4 q^{96} + 24 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 - 2 * q^5 + 4 * q^6 + 2 * q^10 + 12 * q^11 - 12 * q^14 - 12 * q^15 + 8 * q^16 - 4 * q^19 + 2 * q^20 + 12 * q^21 - 4 * q^24 - 4 * q^25 + 8 * q^26 + 8 * q^29 + 4 * q^30 + 8 * q^31 - 8 * q^34 - 12 * q^35 + 8 * q^39 - 2 * q^40 - 8 * q^41 - 12 * q^44 - 18 * q^45 + 8 * q^50 - 12 * q^51 - 4 * q^54 - 16 * q^55 + 12 * q^56 + 12 * q^60 - 8 * q^64 + 12 * q^66 + 28 * q^69 + 20 * q^70 + 24 * q^71 - 36 * q^74 - 20 * q^75 + 4 * q^76 + 24 * q^79 - 2 * q^80 - 32 * q^81 - 12 * q^84 + 8 * q^85 + 8 * q^86 + 24 * q^89 + 6 * q^90 - 28 * q^91 - 20 * q^94 + 4 * q^96 + 24 * q^99

Introduction

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