LMFDB - Embedded newform 1815.2.c.h.364.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1815,2,Mod(364,1815)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1815, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1815.364");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1815 = 3 \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1815.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.4928479669$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 21x^{10} + 164x^{8} + 589x^{6} + 965x^{4} + 576x^{2} + 4 $ x^12 + 21x^10 + 164x^8 + 589x^6 + 965x^4 + 576*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			364.11
Root			$2.42911i$ of defining polynomial
Character	$\chi$	$=$	1815.364
Dual form			1815.2.c.h.364.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.42911i q^{2} -1.00000i q^{3} -3.90056 q^{4} +(2.04405 - 0.906565i) q^{5} +2.42911 q^{6} -1.34168i q^{7} -4.61665i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+2.42911i q^{2} -1.00000i q^{3} -3.90056 q^{4} +(2.04405 - 0.906565i) q^{5} +2.42911 q^{6} -1.34168i q^{7} -4.61665i q^{8} -1.00000 q^{9} +(2.20214 + 4.96521i) q^{10} +3.90056i q^{12} +4.12932i q^{13} +3.25908 q^{14} +(-0.906565 - 2.04405i) q^{15} +3.41322 q^{16} +5.87573i q^{17} -2.42911i q^{18} -3.51653 q^{19} +(-7.97293 + 3.53611i) q^{20} -1.34168 q^{21} -6.37088i q^{23} -4.61665 q^{24} +(3.35628 - 3.70613i) q^{25} -10.0305 q^{26} +1.00000i q^{27} +5.23330i q^{28} +6.39637 q^{29} +(4.96521 - 2.20214i) q^{30} +9.40429 q^{31} -0.942224i q^{32} -14.2728 q^{34} +(-1.21632 - 2.74246i) q^{35} +3.90056 q^{36} +7.01348i q^{37} -8.54203i q^{38} +4.12932 q^{39} +(-4.18529 - 9.43666i) q^{40} +8.63013 q^{41} -3.25908i q^{42} +5.31799i q^{43} +(-2.04405 + 0.906565i) q^{45} +15.4755 q^{46} +3.74642i q^{47} -3.41322i q^{48} +5.19989 q^{49} +(9.00258 + 8.15276i) q^{50} +5.87573 q^{51} -16.1066i q^{52} +6.41776i q^{53} -2.42911 q^{54} -6.19407 q^{56} +3.51653i q^{57} +15.5375i q^{58} -8.97551 q^{59} +(3.53611 + 7.97293i) q^{60} +6.52203 q^{61} +22.8440i q^{62} +1.34168i q^{63} +9.11521 q^{64} +(3.74349 + 8.44053i) q^{65} +8.83452i q^{67} -22.9186i q^{68} -6.37088 q^{69} +(6.66173 - 2.95457i) q^{70} -7.17440 q^{71} +4.61665i q^{72} -4.08569i q^{73} -17.0365 q^{74} +(-3.70613 - 3.35628i) q^{75} +13.7164 q^{76} +10.0305i q^{78} +9.97344 q^{79} +(6.97679 - 3.09431i) q^{80} +1.00000 q^{81} +20.9635i q^{82} +3.06020i q^{83} +5.23330 q^{84} +(5.32674 + 12.0103i) q^{85} -12.9180 q^{86} -6.39637i q^{87} +11.8382 q^{89} +(-2.20214 - 4.96521i) q^{90} +5.54022 q^{91} +24.8500i q^{92} -9.40429i q^{93} -9.10045 q^{94} +(-7.18796 + 3.18796i) q^{95} -0.942224 q^{96} -2.55370i q^{97} +12.6311i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 18 q^{4} - 2 q^{5} - 2 q^{6} - 12 q^{9}+O(q^{10}) $ 12 * q - 18 * q^4 - 2 * q^5 - 2 * q^6 - 12 * q^9	$ 12 q - 18 q^{4} - 2 q^{5} - 2 q^{6} - 12 q^{9} - 12 q^{10} + 20 q^{14} + 22 q^{16} - 4 q^{19} - 2 q^{20} + 8 q^{21} + 2 q^{25} + 24 q^{29} + 8 q^{30} + 36 q^{31} + 2 q^{34} - 24 q^{35} + 18 q^{36} + 4 q^{39} + 22 q^{40} + 12 q^{41} + 2 q^{45} + 22 q^{46} - 24 q^{49} + 58 q^{50} - 4 q^{51} + 2 q^{54} - 84 q^{56} + 36 q^{59} + 22 q^{60} - 8 q^{61} - 44 q^{64} + 14 q^{65} - 24 q^{69} - 16 q^{70} - 8 q^{74} - 12 q^{75} + 40 q^{76} + 4 q^{79} - 58 q^{80} + 12 q^{81} - 48 q^{84} + 2 q^{85} + 56 q^{86} + 32 q^{89} + 12 q^{90} + 48 q^{91} + 6 q^{94} - 62 q^{96}+O(q^{100}) $ 12 * q - 18 * q^4 - 2 * q^5 - 2 * q^6 - 12 * q^9 - 12 * q^10 + 20 * q^14 + 22 * q^16 - 4 * q^19 - 2 * q^20 + 8 * q^21 + 2 * q^25 + 24 * q^29 + 8 * q^30 + 36 * q^31 + 2 * q^34 - 24 * q^35 + 18 * q^36 + 4 * q^39 + 22 * q^40 + 12 * q^41 + 2 * q^45 + 22 * q^46 - 24 * q^49 + 58 * q^50 - 4 * q^51 + 2 * q^54 - 84 * q^56 + 36 * q^59 + 22 * q^60 - 8 * q^61 - 44 * q^64 + 14 * q^65 - 24 * q^69 - 16 * q^70 - 8 * q^74 - 12 * q^75 + 40 * q^76 + 4 * q^79 - 58 * q^80 + 12 * q^81 - 48 * q^84 + 2 * q^85 + 56 * q^86 + 32 * q^89 + 12 * q^90 + 48 * q^91 + 6 * q^94 - 62 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1815\mathbb{Z}\right)^\times$.

$n$	$727$	$1211$	$1696$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$			2.42911i			1.71764i	0.512280	+	0.858819i	$0.328801\pi$
$2$			2.42911i			1.71764i	−0.512280	+	0.858819i	$0.671199\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−3.90056			−1.95028
$5$	2.04405	−	0.906565i	0.914127	−	0.405428i
$5$	2.04405	−	0.906565i	0.914127	−	0.405428i
$6$	2.42911			0.991678
$7$		−	1.34168i		−	0.507108i	−0.967321	−	0.253554i	$-0.918400\pi$
$7$		−	1.34168i		−	0.507108i	0.967321	−	0.253554i	$-0.0815995\pi$
$8$		−	4.61665i		−	1.63223i
$9$	−1.00000			−0.333333
$10$	2.20214	+	4.96521i	0.696379	+	1.57014i
$11$		0			0
$11$		0			0
$12$			3.90056i			1.12599i
$13$			4.12932i			1.14527i	0.819812	+	0.572633i	$0.194078\pi$
$13$			4.12932i			1.14527i	−0.819812	+	0.572633i	$0.805922\pi$
$14$	3.25908			0.871027
$15$	−0.906565	−	2.04405i	−0.234074	−	0.527771i
$16$	3.41322			0.853305
$17$			5.87573i			1.42508i	0.701634	+	0.712538i	$0.252454\pi$
$17$			5.87573i			1.42508i	−0.701634	+	0.712538i	$0.747546\pi$
$18$		−	2.42911i		−	0.572546i
$19$	−3.51653			−0.806748			−0.403374	−	0.915035i	$-0.632163\pi$
$19$	−3.51653			−0.806748			−0.403374	+	0.915035i	$0.632163\pi$
$20$	−7.97293	+	3.53611i	−1.78280	+	0.790698i
$21$	−1.34168			−0.292779
$22$		0			0
$23$		−	6.37088i		−	1.32842i	−0.747546	−	0.664210i	$-0.768768\pi$
$23$		−	6.37088i		−	1.32842i	0.747546	−	0.664210i	$-0.231232\pi$
$24$	−4.61665			−0.942370
$25$	3.35628	−	3.70613i	0.671256	−	0.741226i
$26$	−10.0305			−1.96715
$27$			1.00000i			0.192450i
$28$			5.23330i			0.989001i
$29$	6.39637			1.18778			0.593888	−	0.804548i	$-0.297592\pi$
$29$	6.39637			1.18778			0.593888	+	0.804548i	$0.297592\pi$
$30$	4.96521	−	2.20214i	0.906520	−	0.402054i
$31$	9.40429			1.68906			0.844530	−	0.535509i	$-0.179880\pi$
$31$	9.40429			1.68906			0.844530	+	0.535509i	$0.179880\pi$
$32$		−	0.942224i		−	0.166563i
$33$		0			0
$34$	−14.2728			−2.44776
$35$	−1.21632	−	2.74246i	−0.205596	−	0.463561i
$36$	3.90056			0.650093
$37$			7.01348i			1.15301i	0.817094	+	0.576504i	$0.195584\pi$
$37$			7.01348i			1.15301i	−0.817094	+	0.576504i	$0.804416\pi$
$38$		−	8.54203i		−	1.38570i
$39$	4.12932			0.661220
$40$	−4.18529	−	9.43666i	−0.661753	−	1.49207i
$41$	8.63013			1.34780			0.673900	−	0.738823i	$-0.264618\pi$
$41$	8.63013			1.34780			0.673900	+	0.738823i	$0.264618\pi$
$42$		−	3.25908i		−	0.502888i
$43$			5.31799i			0.810985i	0.914098	+	0.405493i	$0.132900\pi$
$43$			5.31799i			0.810985i	−0.914098	+	0.405493i	$0.867100\pi$
$44$		0			0
$45$	−2.04405	+	0.906565i	−0.304709	+	0.135143i
$46$	15.4755			2.28174
$47$			3.74642i			0.546471i	0.961947	+	0.273236i	$0.0880939\pi$
$47$			3.74642i			0.546471i	−0.961947	+	0.273236i	$0.911906\pi$
$48$		−	3.41322i		−	0.492656i
$49$	5.19989			0.742842
$50$	9.00258	+	8.15276i	1.27316	+	1.15297i
$51$	5.87573			0.822767
$52$		−	16.1066i		−	2.23359i
$53$			6.41776i			0.881547i	0.897618	+	0.440774i	$0.145296\pi$
$53$			6.41776i			0.881547i	−0.897618	+	0.440774i	$0.854704\pi$
$54$	−2.42911			−0.330559
$55$		0			0
$56$	−6.19407			−0.827718
$57$			3.51653i			0.465776i
$58$			15.5375i			2.04017i
$59$	−8.97551			−1.16851			−0.584256	−	0.811570i	$-0.698614\pi$
$59$	−8.97551			−1.16851			−0.584256	+	0.811570i	$0.698614\pi$
$60$	3.53611	+	7.97293i	0.456510	+	1.02930i
$61$	6.52203			0.835061			0.417530	−	0.908663i	$-0.362896\pi$
$61$	6.52203			0.835061			0.417530	+	0.908663i	$0.362896\pi$
$62$			22.8440i			2.90119i
$63$			1.34168i			0.169036i
$64$	9.11521			1.13940
$65$	3.74349	+	8.44053i	0.464323	+	1.04692i
$66$		0			0
$67$			8.83452i			1.07931i	0.841887	+	0.539654i	$0.181445\pi$
$67$			8.83452i			1.07931i	−0.841887	+	0.539654i	$0.818555\pi$
$68$		−	22.9186i		−	2.77929i
$69$	−6.37088			−0.766964
$70$	6.66173	−	2.95457i	0.796229	−	0.353139i
$71$	−7.17440			−0.851444			−0.425722	−	0.904854i	$-0.639980\pi$
$71$	−7.17440			−0.851444			−0.425722	+	0.904854i	$0.639980\pi$
$72$			4.61665i			0.544077i
$73$		−	4.08569i		−	0.478194i	−0.970996	−	0.239097i	$-0.923149\pi$
$73$		−	4.08569i		−	0.478194i	0.970996	−	0.239097i	$-0.0768514\pi$
$74$	−17.0365			−1.98045
$75$	−3.70613	−	3.35628i	−0.427947	−	0.387550i
$76$	13.7164			1.57338
$77$		0			0
$78$			10.0305i			1.13574i
$79$	9.97344			1.12210			0.561050	−	0.827782i	$-0.310397\pi$
$79$	9.97344			1.12210			0.561050	+	0.827782i	$0.310397\pi$
$80$	6.97679	−	3.09431i	0.780029	−	0.345954i
$81$	1.00000			0.111111
$82$			20.9635i			2.31503i
$83$			3.06020i			0.335900i	0.985796	+	0.167950i	$0.0537147\pi$
$83$			3.06020i			0.335900i	−0.985796	+	0.167950i	$0.946285\pi$
$84$	5.23330			0.571000
$85$	5.32674	+	12.0103i	0.577766	+	1.30270i
$86$	−12.9180			−1.39298
$87$		−	6.39637i		−	0.685763i
$88$		0			0
$89$	11.8382			1.25485			0.627424	−	0.778677i	$-0.284109\pi$
$89$	11.8382			1.25485			0.627424	+	0.778677i	$0.284109\pi$
$90$	−2.20214	−	4.96521i	−0.232126	−	0.523379i
$91$	5.54022			0.580773
$92$			24.8500i			2.59079i
$93$		−	9.40429i		−	0.975179i
$94$	−9.10045			−0.938640
$95$	−7.18796	+	3.18796i	−0.737470	+	0.327078i
$96$	−0.942224			−0.0961654
$97$		−	2.55370i		−	0.259289i	−0.991561	−	0.129644i	$-0.958616\pi$
$97$		−	2.55370i		−	0.259289i	0.991561	−	0.129644i	$-0.0413836\pi$
$98$			12.6311i			1.27593i
$99$		0			0
$100$	−13.0914	+	14.4560i	−1.30914	+	1.44560i
$101$	15.7436			1.56654			0.783271	−	0.621680i	$-0.213550\pi$
$101$	15.7436			1.56654			0.783271	+	0.621680i	$0.213550\pi$
$102$			14.2728i			1.41322i
$103$		−	16.7498i		−	1.65041i	−0.564833	−	0.825205i	$-0.691060\pi$
$103$		−	16.7498i		−	1.65041i	0.564833	−	0.825205i	$-0.308940\pi$
$104$	19.0636			1.86934
$105$	−2.74246	+	1.21632i	−0.267637	+	0.118701i
$106$	−15.5894			−1.51418
$107$			4.51221i			0.436212i	0.975925	+	0.218106i	$0.0699879\pi$
$107$			4.51221i			0.436212i	−0.975925	+	0.218106i	$0.930012\pi$
$108$		−	3.90056i		−	0.375331i
$109$	−5.59672			−0.536068			−0.268034	−	0.963409i	$-0.586374\pi$
$109$	−5.59672			−0.536068			−0.268034	+	0.963409i	$0.586374\pi$
$110$		0			0
$111$	7.01348			0.665690
$112$		−	4.57945i		−	0.432718i
$113$		−	3.19237i		−	0.300313i	−0.988662	−	0.150157i	$-0.952022\pi$
$113$		−	3.19237i		−	0.300313i	0.988662	−	0.150157i	$-0.0479778\pi$
$114$	−8.54203			−0.800034
$115$	−5.77562	−	13.0224i	−0.538579	−	1.21434i
$116$	−24.9494			−2.31649
$117$		−	4.12932i		−	0.381755i
$118$		−	21.8025i		−	2.00708i
$119$	7.88336			0.722667
$120$	−9.43666	+	4.18529i	−0.861446	+	0.382063i
$121$		0			0
$122$			15.8427i			1.43433i
$123$		−	8.63013i		−	0.778152i
$124$	−36.6819			−3.29414
$125$	3.50055	−	10.6182i	0.313099	−	0.949720i
$126$	−3.25908			−0.290342
$127$		−	13.9500i		−	1.23786i	−0.785445	−	0.618932i	$-0.787566\pi$
$127$		−	13.9500i		−	1.23786i	0.785445	−	0.618932i	$-0.212434\pi$
$128$			20.2574i			1.79051i
$129$	5.31799			0.468223
$130$	−20.5029	+	9.09334i	−1.79823	+	0.797539i
$131$	−18.4618			−1.61301			−0.806507	−	0.591225i	$-0.798645\pi$
$131$	−18.4618			−1.61301			−0.806507	+	0.591225i	$0.798645\pi$
$132$		0			0
$133$			4.71806i			0.409108i
$134$	−21.4600			−1.85386
$135$	0.906565	+	2.04405i	0.0780247	+	0.175924i
$136$	27.1262			2.32605
$137$			7.56366i			0.646207i	0.946364	+	0.323103i	$0.104726\pi$
$137$			7.56366i			0.646207i	−0.946364	+	0.323103i	$0.895274\pi$
$138$		−	15.4755i		−	1.31737i
$139$	−0.572021			−0.0485182			−0.0242591	−	0.999706i	$-0.507723\pi$
$139$	−0.572021			−0.0485182			−0.0242591	+	0.999706i	$0.507723\pi$
$140$	4.74433	+	10.6971i	0.400969	+	0.904072i
$141$	3.74642			0.315505
$142$		−	17.4274i		−	1.46247i
$143$		0			0
$144$	−3.41322			−0.284435
$145$	13.0745	−	5.79873i	1.08578	−	0.481558i
$146$	9.92457			0.821364
$147$		−	5.19989i		−	0.428880i
$148$		−	27.3564i		−	2.24869i
$149$	−9.20494			−0.754098			−0.377049	−	0.926193i	$-0.623061\pi$
$149$	−9.20494			−0.754098			−0.377049	+	0.926193i	$0.623061\pi$
$150$	8.15276	−	9.00258i	0.665670	−	0.735057i
$151$	0.453311			0.0368899			0.0184450	−	0.999830i	$-0.494128\pi$
$151$	0.453311			0.0368899			0.0184450	+	0.999830i	$0.494128\pi$
$152$			16.2346i			1.31680i
$153$		−	5.87573i		−	0.475025i
$154$		0			0
$155$	19.2228	−	8.52560i	1.54401	−	0.684792i
$156$	−16.1066			−1.28956
$157$			3.14144i			0.250714i	0.992112	+	0.125357i	$0.0400077\pi$
$157$			3.14144i			0.250714i	−0.992112	+	0.125357i	$0.959992\pi$
$158$			24.2266i			1.92736i
$159$	6.41776			0.508962
$160$	−0.854188	−	1.92595i	−0.0675295	−	0.152260i
$161$	−8.54768			−0.673652
$162$			2.42911i			0.190849i
$163$			0.374743i			0.0293521i	0.999892	+	0.0146761i	$0.00467170\pi$
$163$			0.374743i			0.0293521i	−0.999892	+	0.0146761i	$0.995328\pi$
$164$	−33.6623			−2.62858
$165$		0			0
$166$	−7.43354			−0.576955
$167$			20.0873i			1.55440i	0.629252	+	0.777201i	$0.283361\pi$
$167$			20.0873i			1.55440i	−0.629252	+	0.777201i	$0.716639\pi$
$168$			6.19407i			0.477883i
$169$	−4.05125			−0.311635
$170$	−29.1743	+	12.9392i	−2.23756	+	0.992392i
$171$	3.51653			0.268916
$172$		−	20.7431i		−	1.58165i
$173$			2.71823i			0.206663i	0.994647	+	0.103331i	$0.0329502\pi$
$173$			2.71823i			0.206663i	−0.994647	+	0.103331i	$0.967050\pi$
$174$	15.5375			1.17789
$175$	−4.97244	−	4.50306i	−0.375881	−	0.340399i
$176$		0			0
$177$			8.97551i			0.674641i
$178$			28.7563i			2.15538i
$179$	−14.5157			−1.08496			−0.542478	−	0.840070i	$-0.682514\pi$
$179$	−14.5157			−1.08496			−0.542478	+	0.840070i	$0.682514\pi$
$180$	7.97293	−	3.53611i	0.594267	−	0.263566i
$181$	−20.5147			−1.52484			−0.762422	−	0.647080i	$-0.775990\pi$
$181$	−20.5147			−1.52484			−0.762422	+	0.647080i	$0.775990\pi$
$182$			13.4578i			0.997558i
$183$		−	6.52203i		−	0.482123i
$184$	−29.4121			−2.16829
$185$	6.35817	+	14.3359i	0.467462	+	1.05400i
$186$	22.8440			1.67500
$187$		0			0
$188$		−	14.6131i		−	1.06577i
$189$	1.34168			0.0975929
$190$	−7.74390	−	17.4603i	−0.561802	−	1.26671i
$191$	14.4836			1.04799			0.523997	−	0.851720i	$-0.324440\pi$
$191$	14.4836			1.04799			0.523997	+	0.851720i	$0.324440\pi$
$192$		−	9.11521i		−	0.657833i
$193$			11.8730i			0.854640i	0.904100	+	0.427320i	$0.140542\pi$
$193$			11.8730i			0.854640i	−0.904100	+	0.427320i	$0.859458\pi$
$194$	6.20321			0.445364
$195$	8.44053	−	3.74349i	0.604439	−	0.268077i
$196$	−20.2825			−1.44875
$197$			7.58073i			0.540104i	0.962846	+	0.270052i	$0.0870410\pi$
$197$			7.58073i			0.540104i	−0.962846	+	0.270052i	$0.912959\pi$
$198$		0			0
$199$	16.8804			1.19662			0.598310	−	0.801265i	$-0.295839\pi$
$199$	16.8804			1.19662			0.598310	+	0.801265i	$0.295839\pi$
$200$	−17.1099	−	15.4948i	−1.20985	−	1.09565i
$201$	8.83452			0.623139
$202$			38.2428i			2.69075i
$203$		−	8.58189i		−	0.602331i
$204$	−22.9186			−1.60463
$205$	17.6404	−	7.82377i	1.23206	−	0.546436i
$206$	40.6871			2.83481
$207$			6.37088i			0.442807i
$208$			14.0943i			0.977262i
$209$		0			0
$210$	−2.95457	−	6.66173i	−0.203885	−	0.459703i
$211$	−23.8041			−1.63874			−0.819370	−	0.573265i	$-0.805676\pi$
$211$	−23.8041			−1.63874			−0.819370	+	0.573265i	$0.805676\pi$
$212$		−	25.0328i		−	1.71926i
$213$			7.17440i			0.491582i
$214$	−10.9606			−0.749254
$215$	4.82110	+	10.8702i	0.328796	+	0.741344i
$216$	4.61665			0.314123
$217$		−	12.6175i		−	0.856535i
$218$		−	13.5950i		−	0.920771i
$219$	−4.08569			−0.276085
$220$		0			0
$221$	−24.2628			−1.63209
$222$			17.0365i			1.14341i
$223$		−	21.6870i		−	1.45227i	−0.687552	−	0.726135i	$-0.741315\pi$
$223$		−	21.6870i		−	1.45227i	0.687552	−	0.726135i	$-0.258685\pi$
$224$	−1.26416			−0.0844655
$225$	−3.35628	+	3.70613i	−0.223752	+	0.247075i
$226$	7.75461			0.515829
$227$		−	1.05996i		−	0.0703522i	−0.999381	−	0.0351761i	$-0.988801\pi$
$227$		−	1.05996i		−	0.0703522i	0.999381	−	0.0351761i	$-0.0111992\pi$
$228$		−	13.7164i		−	0.908392i
$229$	14.0678			0.929624			0.464812	−	0.885409i	$-0.346122\pi$
$229$	14.0678			0.929624			0.464812	+	0.885409i	$0.346122\pi$
$230$	31.6328	−	14.0296i	2.08580	−	0.925083i
$231$		0			0
$232$		−	29.5298i		−	1.93873i
$233$		−	0.300464i		−	0.0196841i	−0.999952	−	0.00984204i	$-0.996867\pi$
$233$		−	0.300464i		−	0.0196841i	0.999952	−	0.00984204i	$-0.00313287\pi$
$234$	10.0305			0.655717
$235$	3.39637	+	7.65787i	0.221555	+	0.499544i
$236$	35.0095			2.27892
$237$		−	9.97344i		−	0.647845i
$238$			19.1495i			1.24128i
$239$	−10.3905			−0.672107			−0.336054	−	0.941843i	$-0.609092\pi$
$239$	−10.3905			−0.672107			−0.336054	+	0.941843i	$0.609092\pi$
$240$	−3.09431	−	6.97679i	−0.199737	−	0.450350i
$241$	−5.73625			−0.369504			−0.184752	−	0.982785i	$-0.559148\pi$
$241$	−5.73625			−0.369504			−0.184752	+	0.982785i	$0.559148\pi$
$242$		0			0
$243$		−	1.00000i		−	0.0641500i
$244$	−25.4396			−1.62860
$245$	10.6288	−	4.71404i	0.679052	−	0.301169i
$246$	20.9635			1.33658
$247$		−	14.5209i		−	0.923941i
$248$		−	43.4163i		−	2.75694i
$249$	3.06020			0.193932
$250$	25.7927	+	8.50322i	1.63128	+	0.537791i
$251$	−2.09242			−0.132072			−0.0660361	−	0.997817i	$-0.521035\pi$
$251$	−2.09242			−0.132072			−0.0660361	+	0.997817i	$0.521035\pi$
$252$		−	5.23330i		−	0.329667i
$253$		0			0
$254$	33.8861			2.12620
$255$	12.0103	−	5.32674i	0.752114	−	0.333573i
$256$	−30.9768			−1.93605
$257$		−	23.2533i		−	1.45050i	−0.688486	−	0.725250i	$-0.741724\pi$
$257$		−	23.2533i		−	1.45050i	0.688486	−	0.725250i	$-0.258276\pi$
$258$			12.9180i			0.804237i
$259$	9.40985			0.584699
$260$	−14.6017	−	32.9227i	−0.905559	−	2.04178i
$261$	−6.39637			−0.395926
$262$		−	44.8456i		−	2.77057i
$263$			3.71929i			0.229341i	0.993404	+	0.114670i	$0.0365812\pi$
$263$			3.71929i			0.229341i	−0.993404	+	0.114670i	$0.963419\pi$
$264$		0			0
$265$	5.81812	+	13.1182i	0.357404	+	0.805846i
$266$	−11.4607			−0.702699
$267$		−	11.8382i		−	0.724487i
$268$		−	34.4595i		−	2.10495i
$269$	−12.0991			−0.737696			−0.368848	−	0.929490i	$-0.620248\pi$
$269$	−12.0991			−0.737696			−0.368848	+	0.929490i	$0.620248\pi$
$270$	−4.96521	+	2.20214i	−0.302173	+	0.134018i
$271$	−3.26311			−0.198220			−0.0991100	−	0.995076i	$-0.531600\pi$
$271$	−3.26311			−0.198220			−0.0991100	+	0.995076i	$0.531600\pi$
$272$			20.0552i			1.21602i
$273$		−	5.54022i		−	0.335310i
$274$	−18.3729			−1.10995
$275$		0			0
$276$	24.8500			1.49579
$277$		−	23.6465i		−	1.42078i	−0.703808	−	0.710390i	$-0.748518\pi$
$277$		−	23.6465i		−	1.42078i	0.703808	−	0.710390i	$-0.251482\pi$
$278$		−	1.38950i		−	0.0833367i
$279$	−9.40429			−0.563020
$280$	−12.6610	+	5.61533i	−0.756639	+	0.335580i
$281$	−30.2948			−1.80724			−0.903619	−	0.428336i	$-0.859100\pi$
$281$	−30.2948			−1.80724			−0.903619	+	0.428336i	$0.859100\pi$
$282$			9.10045i			0.541924i
$283$			12.6940i			0.754581i	0.926095	+	0.377291i	$0.123144\pi$
$283$			12.6940i			0.754581i	−0.926095	+	0.377291i	$0.876856\pi$
$284$	27.9841			1.66055
$285$	3.18796	+	7.18796i	0.188839	+	0.425778i
$286$		0			0
$287$		−	11.5789i		−	0.683479i
$288$			0.942224i			0.0555211i
$289$	−17.5243			−1.03084
$290$	14.0857	+	31.7594i	0.827142	+	1.86497i
$291$	−2.55370			−0.149701
$292$			15.9365i			0.932611i
$293$		−	2.10292i		−	0.122854i	−0.998112	−	0.0614271i	$-0.980435\pi$
$293$		−	2.10292i		−	0.122854i	0.998112	−	0.0614271i	$-0.0195652\pi$
$294$	12.6311			0.736660
$295$	−18.3464	+	8.13688i	−1.06817	+	0.473748i
$296$	32.3788			1.88198
$297$		0			0
$298$		−	22.3598i		−	1.29527i
$299$	26.3074			1.52139
$300$	14.4560	+	13.0914i	0.834615	+	0.755830i
$301$	7.13504			0.411257
$302$			1.10114i			0.0633635i
$303$		−	15.7436i		−	0.904444i
$304$	−12.0027			−0.688402
$305$	13.3314	−	5.91265i	0.763352	−	0.338557i
$306$	14.2728			0.815921
$307$			13.5435i			0.772967i	0.922296	+	0.386484i	$0.126310\pi$
$307$			13.5435i			0.772967i	−0.922296	+	0.386484i	$0.873690\pi$
$308$		0			0
$309$	−16.7498			−0.952865
$310$	20.7096	+	46.6943i	1.17623	+	2.65206i
$311$	7.20000			0.408274			0.204137	−	0.978942i	$-0.434561\pi$
$311$	7.20000			0.408274			0.204137	+	0.978942i	$0.434561\pi$
$312$		−	19.0636i		−	1.07926i
$313$			3.59811i			0.203377i	0.994816	+	0.101689i	$0.0324246\pi$
$313$			3.59811i			0.203377i	−0.994816	+	0.101689i	$0.967575\pi$
$314$	−7.63090			−0.430636
$315$	1.21632	+	2.74246i	0.0685319	+	0.154520i
$316$	−38.9020			−2.18841
$317$			24.7458i			1.38986i	0.719077	+	0.694931i	$0.244565\pi$
$317$			24.7458i			1.38986i	−0.719077	+	0.694931i	$0.755435\pi$
$318$			15.5894i			0.874211i
$319$		0			0
$320$	18.6319	−	8.26353i	1.04156	−	0.461945i
$321$	4.51221			0.251847
$322$		−	20.7632i		−	1.15709i
$323$		−	20.6622i		−	1.14968i
$324$	−3.90056			−0.216698
$325$	15.3038	+	13.8591i	0.848901	+	0.768767i
$326$	−0.910290			−0.0504163
$327$			5.59672i			0.309499i
$328$		−	39.8423i		−	2.19992i
$329$	5.02650			0.277120
$330$		0			0
$331$	13.3411			0.733292			0.366646	−	0.930361i	$-0.380506\pi$
$331$	13.3411			0.733292			0.366646	+	0.930361i	$0.380506\pi$
$332$		−	11.9365i		−	0.655098i
$333$		−	7.01348i		−	0.384336i
$334$	−48.7942			−2.66990
$335$	8.00907	+	18.0582i	0.437582	+	0.986625i
$336$	−4.57945			−0.249830
$337$		−	26.1890i		−	1.42661i	−0.700855	−	0.713304i	$-0.747198\pi$
$337$		−	26.1890i		−	1.42661i	0.700855	−	0.713304i	$-0.252802\pi$
$338$		−	9.84092i		−	0.535275i
$339$	−3.19237			−0.173386
$340$	−20.7772	−	46.8468i	−1.12680	−	2.54063i
$341$		0			0
$342$			8.54203i			0.461900i
$343$		−	16.3684i		−	0.883808i
$344$	24.5513			1.32372
$345$	−13.0224	+	5.77562i	−0.701102	+	0.310949i
$346$	−6.60286			−0.354972
$347$		−	2.23005i		−	0.119715i	−0.998207	−	0.0598577i	$-0.980935\pi$
$347$		−	2.23005i		−	0.119715i	0.998207	−	0.0598577i	$-0.0190647\pi$
$348$			24.9494i			1.33743i
$349$	−19.5128			−1.04449			−0.522247	−	0.852794i	$-0.674906\pi$
$349$	−19.5128			−1.04449			−0.522247	+	0.852794i	$0.674906\pi$
$350$	10.9384	−	12.0786i	0.584682	−	0.645628i
$351$	−4.12932			−0.220407
$352$		0			0
$353$			0.606483i			0.0322798i	0.999870	+	0.0161399i	$0.00513772\pi$
$353$			0.606483i			0.0322798i	−0.999870	+	0.0161399i	$0.994862\pi$
$354$	−21.8025			−1.15879
$355$	−14.6648	+	6.50406i	−0.778328	+	0.345200i
$356$	−46.1756			−2.44730
$357$		−	7.88336i		−	0.417232i
$358$		−	35.2603i		−	1.86356i
$359$	1.92548			0.101623			0.0508115	−	0.998708i	$-0.483819\pi$
$359$	1.92548			0.101623			0.0508115	+	0.998708i	$0.483819\pi$
$360$	4.18529	+	9.43666i	0.220584	+	0.497356i
$361$	−6.63401			−0.349158
$362$		−	49.8323i		−	2.61913i
$363$		0			0
$364$	−21.6100			−1.13267
$365$	−3.70394	−	8.35135i	−0.193873	−	0.437130i
$366$	15.8427			0.828112
$367$		−	21.6704i		−	1.13118i	−0.824685	−	0.565592i	$-0.808648\pi$
$367$		−	21.6704i		−	1.13118i	0.824685	−	0.565592i	$-0.191352\pi$
$368$		−	21.7452i		−	1.13355i
$369$	−8.63013			−0.449266
$370$	−34.8234	+	15.4447i	−1.81038	+	0.802930i
$371$	8.61059			0.447039
$372$			36.6819i			1.90187i
$373$			3.79920i			0.196715i	0.995151	+	0.0983576i	$0.0313589\pi$
$373$			3.79920i			0.196715i	−0.995151	+	0.0983576i	$0.968641\pi$
$374$		0			0
$375$	−10.6182	−	3.50055i	−0.548321	−	0.180768i
$376$	17.2959			0.891968
$377$			26.4126i			1.36032i
$378$			3.25908i			0.167629i
$379$	3.37217			0.173217			0.0866084	−	0.996242i	$-0.472397\pi$
$379$	3.37217			0.173217			0.0866084	+	0.996242i	$0.472397\pi$
$380$	28.0371	−	12.4348i	1.43827	−	0.637893i
$381$	−13.9500			−0.714681
$382$			35.1821i			1.80007i
$383$		−	12.1412i		−	0.620384i	−0.950674	−	0.310192i	$-0.899607\pi$
$383$		−	12.1412i		−	0.620384i	0.950674	−	0.310192i	$-0.100393\pi$
$384$	20.2574			1.03375
$385$		0			0
$386$	−28.8409			−1.46796
$387$		−	5.31799i		−	0.270328i
$388$			9.96085i			0.505685i
$389$	29.9203			1.51702			0.758509	−	0.651663i	$-0.225928\pi$
$389$	29.9203			1.51702			0.758509	+	0.651663i	$0.225928\pi$
$390$	9.09334	+	20.5029i	0.460459	+	1.03821i
$391$	37.4336			1.89310
$392$		−	24.0061i		−	1.21249i
$393$			18.4618i			0.931274i
$394$	−18.4144			−0.927703
$395$	20.3862	−	9.04158i	1.02574	−	0.454931i
$396$		0			0
$397$		−	26.3735i		−	1.32365i	−0.749658	−	0.661825i	$-0.769782\pi$
$397$		−	26.3735i		−	1.32365i	0.749658	−	0.661825i	$-0.230218\pi$
$398$			41.0043i			2.05536i
$399$	4.71806			0.236199
$400$	11.4557	−	12.6498i	0.572786	−	0.632492i
$401$	−3.39283			−0.169430			−0.0847148	−	0.996405i	$-0.526998\pi$
$401$	−3.39283			−0.169430			−0.0847148	+	0.996405i	$0.526998\pi$
$402$			21.4600i			1.07033i
$403$			38.8333i			1.93442i
$404$	−61.4086			−3.05519
$405$	2.04405	−	0.906565i	0.101570	−	0.0450476i
$406$	20.8463			1.03459
$407$		0			0
$408$		−	27.1262i		−	1.34295i
$409$	12.3786			0.612084			0.306042	−	0.952018i	$-0.400995\pi$
$409$	12.3786			0.612084			0.306042	+	0.952018i	$0.400995\pi$
$410$	19.0048	+	42.8504i	0.938579	+	2.11623i
$411$	7.56366			0.373088
$412$			65.3336i			3.21876i
$413$			12.0423i			0.592561i
$414$	−15.4755			−0.760581
$415$	2.77427	+	6.25519i	0.136183	+	0.307055i
$416$	3.89074			0.190759
$417$			0.572021i			0.0280120i
$418$		0			0
$419$	−5.92515			−0.289463			−0.144731	−	0.989471i	$-0.546232\pi$
$419$	−5.92515			−0.289463			−0.144731	+	0.989471i	$0.546232\pi$
$420$	10.6971	−	4.74433i	0.521966	−	0.231499i
$421$	25.2177			1.22904			0.614518	−	0.788903i	$-0.289350\pi$
$421$	25.2177			1.22904			0.614518	+	0.788903i	$0.289350\pi$
$422$		−	57.8226i		−	2.81476i
$423$		−	3.74642i		−	0.182157i
$424$	29.6286			1.43889
$425$	21.7762	+	19.7206i	1.05630	+	0.956590i
$426$	−17.4274			−0.844359
$427$		−	8.75049i		−	0.423466i
$428$		−	17.6001i		−	0.850735i
$429$		0			0
$430$	−26.4049	+	11.7110i	−1.27336	+	0.564753i
$431$	−7.51462			−0.361967			−0.180983	−	0.983486i	$-0.557928\pi$
$431$	−7.51462			−0.361967			−0.180983	+	0.983486i	$0.557928\pi$
$432$			3.41322i			0.164219i
$433$			15.0318i			0.722382i	0.932492	+	0.361191i	$0.117630\pi$
$433$			15.0318i			0.722382i	−0.932492	+	0.361191i	$0.882370\pi$
$434$	30.6494			1.47122
$435$	−5.79873	−	13.0745i	−0.278028	−	0.626875i
$436$	21.8303			1.04548
$437$			22.4034i			1.07170i
$438$		−	9.92457i		−	0.474215i
$439$	23.9302			1.14213			0.571063	−	0.820906i	$-0.306531\pi$
$439$	23.9302			1.14213			0.571063	+	0.820906i	$0.306531\pi$
$440$		0			0
$441$	−5.19989			−0.247614
$442$		−	58.9368i		−	2.80334i
$443$			38.2368i			1.81668i	0.418228	+	0.908342i	$0.362651\pi$
$443$			38.2368i			1.81668i	−0.418228	+	0.908342i	$0.637349\pi$
$444$	−27.3564			−1.29828
$445$	24.1979	−	10.7321i	1.14709	−	0.508751i
$446$	52.6800			2.49447
$447$			9.20494i			0.435379i
$448$		−	12.2297i		−	0.577799i
$449$	0.0371096			0.00175131			0.000875656	−	1.00000i	$-0.499721\pi$
$449$	0.0371096			0.00175131			0.000875656		1.00000i	$0.499721\pi$
$450$	−9.00258	−	8.15276i	−0.424386	−	0.384325i
$451$		0			0
$452$			12.4520i			0.585694i
$453$		−	0.453311i		−	0.0212984i
$454$	2.57476			0.120840
$455$	11.3245	−	5.02257i	0.530900	−	0.235462i
$456$	16.2346			0.760254
$457$		−	6.66208i		−	0.311639i	−0.987786	−	0.155819i	$-0.950198\pi$
$457$		−	6.66208i		−	0.311639i	0.987786	−	0.155819i	$-0.0498018\pi$
$458$			34.1721i			1.59676i
$459$	−5.87573			−0.274256
$460$	22.5281	+	50.7946i	1.05038	+	2.36831i
$461$	−41.4711			−1.93150			−0.965751	−	0.259469i	$-0.916452\pi$
$461$	−41.4711			−1.93150			−0.965751	+	0.259469i	$0.916452\pi$
$462$		0			0
$463$			9.90915i			0.460517i	0.973129	+	0.230259i	$0.0739572\pi$
$463$			9.90915i			0.460517i	−0.973129	+	0.230259i	$0.926043\pi$
$464$	21.8322			1.01354
$465$	−8.52560	−	19.2228i	−0.395365	−	0.891437i
$466$	0.729860			0.0338101
$467$		−	20.2241i		−	0.935862i	−0.883765	−	0.467931i	$-0.845000\pi$
$467$		−	20.2241i		−	0.935862i	0.883765	−	0.467931i	$-0.155000\pi$
$468$			16.1066i			0.744529i
$469$	11.8531			0.547325
$470$	−18.6018	+	8.25015i	−0.858036	+	0.380551i
$471$	3.14144			0.144750
$472$			41.4368i			1.90728i
$473$		0			0
$474$	24.2266			1.11276
$475$	−11.8025	+	13.0327i	−0.541534	+	0.597982i
$476$	−30.7495			−1.40940
$477$		−	6.41776i		−	0.293849i
$478$		−	25.2397i		−	1.15444i
$479$	14.6210			0.668050			0.334025	−	0.942564i	$-0.391593\pi$
$479$	14.6210			0.668050			0.334025	+	0.942564i	$0.391593\pi$
$480$	−1.92595	+	0.854188i	−0.0879074	+	0.0389882i
$481$	−28.9609			−1.32050
$482$		−	13.9340i		−	0.634675i
$483$			8.54768i			0.388933i
$484$		0			0
$485$	−2.31510	−	5.21989i	−0.105123	−	0.237023i
$486$	2.42911			0.110186
$487$			8.06456i			0.365440i	0.983165	+	0.182720i	$0.0584902\pi$
$487$			8.06456i			0.365440i	−0.983165	+	0.182720i	$0.941510\pi$
$488$		−	30.1100i		−	1.36301i
$489$	0.374743			0.0169464
$490$	11.4509	+	25.8186i	0.517299	+	1.16636i
$491$	9.09215			0.410323			0.205161	−	0.978728i	$-0.434228\pi$
$491$	9.09215			0.410323			0.205161	+	0.978728i	$0.434228\pi$
$492$			33.6623i			1.51761i
$493$			37.5834i			1.69267i
$494$	35.2727			1.58699
$495$		0			0
$496$	32.0989			1.44128
$497$			9.62575i			0.431774i
$498$			7.43354i			0.333105i
$499$	4.36117			0.195233			0.0976164	−	0.995224i	$-0.468878\pi$
$499$	4.36117			0.195233			0.0976164	+	0.995224i	$0.468878\pi$
$500$	−13.6541	+	41.4169i	−0.610630	+	1.85222i
$501$	20.0873			0.897434
$502$		−	5.08270i		−	0.226852i
$503$		−	10.3116i		−	0.459771i	−0.973218	−	0.229885i	$-0.926165\pi$
$503$		−	10.3116i		−	0.459771i	0.973218	−	0.229885i	$-0.0738351\pi$
$504$	6.19407			0.275906
$505$	32.1806	−	14.2726i	1.43202	−	0.635121i
$506$		0			0
$507$			4.05125i			0.179922i
$508$			54.4128i			2.41418i
$509$	−7.38429			−0.327303			−0.163652	−	0.986518i	$-0.552327\pi$
$509$	−7.38429			−0.327303			−0.163652	+	0.986518i	$0.552327\pi$
$510$	12.9392	+	29.1743i	0.572958	+	1.29186i
$511$	−5.48169			−0.242496
$512$		−	34.7313i		−	1.53492i
$513$		−	3.51653i		−	0.155259i
$514$	56.4847			2.49143
$515$	−15.1848	−	34.2375i	−0.669123	−	1.50868i
$516$	−20.7431			−0.913164
$517$		0			0
$518$			22.8575i			1.00430i
$519$	2.71823			0.119317
$520$	38.9670	−	17.2824i	1.70881	−	0.757883i
$521$	−43.3169			−1.89775			−0.948874	−	0.315655i	$-0.897776\pi$
$521$	−43.3169			−1.89775			−0.948874	+	0.315655i	$0.897776\pi$
$522$		−	15.5375i		−	0.680056i
$523$		−	17.9584i		−	0.785268i	−0.919695	−	0.392634i	$-0.871564\pi$
$523$		−	17.9584i		−	0.785268i	0.919695	−	0.392634i	$-0.128436\pi$
$524$	72.0112			3.14582
$525$	−4.50306	+	4.97244i	−0.196529	+	0.217015i
$526$	−9.03454			−0.393925
$527$			55.2571i			2.40704i
$528$		0			0
$529$	−17.5881			−0.764699
$530$	−31.8656	+	14.1328i	−1.38415	+	0.613891i
$531$	8.97551			0.389504
$532$		−	18.4031i		−	0.797874i
$533$			35.6365i			1.54359i
$534$	28.7563			1.24441
$535$	4.09062	+	9.22319i	0.176853	+	0.398753i
$536$	40.7859			1.76168
$537$			14.5157i			0.626400i
$538$		−	29.3900i		−	1.26709i
$539$		0			0
$540$	−3.53611	−	7.97293i	−0.152170	−	0.343100i
$541$	25.6681			1.10356			0.551780	−	0.833990i	$-0.313949\pi$
$541$	25.6681			1.10356			0.551780	+	0.833990i	$0.313949\pi$
$542$		−	7.92645i		−	0.340470i
$543$			20.5147i			0.880369i
$544$	5.53626			0.237365
$545$	−11.4400	+	5.07379i	−0.490034	+	0.217337i
$546$	13.4578			0.575940
$547$		−	6.31838i		−	0.270154i	−0.990835	−	0.135077i	$-0.956872\pi$
$547$		−	6.31838i		−	0.270154i	0.990835	−	0.135077i	$-0.0431282\pi$
$548$		−	29.5025i		−	1.26028i
$549$	−6.52203			−0.278354
$550$		0			0
$551$	−22.4930			−0.958236
$552$			29.4121i			1.25186i
$553$		−	13.3812i		−	0.569026i
$554$	57.4399			2.44039
$555$	14.3359	−	6.35817i	0.608525	−	0.269889i
$556$	2.23120			0.0946240
$557$		−	41.0505i		−	1.73936i	−0.493612	−	0.869682i	$-0.664324\pi$
$557$		−	41.0505i		−	1.73936i	0.493612	−	0.869682i	$-0.335676\pi$
$558$		−	22.8440i		−	0.967064i
$559$	−21.9597			−0.928794
$560$	−4.15157	−	9.36063i	−0.175436	−	0.395559i
$561$		0			0
$562$		−	73.5894i		−	3.10418i
$563$			8.99298i			0.379009i	0.981880	+	0.189505i	$0.0606882\pi$
$563$			8.99298i			0.379009i	−0.981880	+	0.189505i	$0.939312\pi$
$564$	−14.6131			−0.615323
$565$	−2.89409	−	6.52537i	−0.121755	−	0.274524i
$566$	−30.8351			−1.29610
$567$		−	1.34168i		−	0.0563453i
$568$			33.1217i			1.38975i
$569$	1.86723			0.0782785			0.0391393	−	0.999234i	$-0.487538\pi$
$569$	1.86723			0.0782785			0.0391393	+	0.999234i	$0.487538\pi$
$570$	−17.4603	+	7.74390i	−0.731333	+	0.324356i
$571$	−1.74298			−0.0729414			−0.0364707	−	0.999335i	$-0.511612\pi$
$571$	−1.74298			−0.0729414			−0.0364707	+	0.999335i	$0.511612\pi$
$572$		0			0
$573$		−	14.4836i		−	0.605060i
$574$	28.1263			1.17397
$575$	−23.6113	−	21.3824i	−0.984659	−	0.891710i
$576$	−9.11521			−0.379800
$577$			14.6183i			0.608566i	0.952582	+	0.304283i	$0.0984169\pi$
$577$			14.6183i			0.608566i	−0.952582	+	0.304283i	$0.901583\pi$
$578$		−	42.5683i		−	1.77061i
$579$	11.8730			0.493427
$580$	−50.9978	+	22.6183i	−2.11757	+	0.939172i
$581$	4.10581			0.170338
$582$		−	6.20321i		−	0.257131i
$583$		0			0
$584$	−18.8622			−0.780524
$585$	−3.74349	−	8.44053i	−0.154774	−	0.348973i
$586$	5.10823			0.211019
$587$		−	20.3498i		−	0.839924i	−0.907542	−	0.419962i	$-0.862043\pi$
$587$		−	20.3498i		−	0.839924i	0.907542	−	0.419962i	$-0.137957\pi$
$588$			20.2825i			0.836435i
$589$	−33.0705			−1.36264
$590$	−19.7654	−	44.5653i	−0.813727	−	1.83472i
$591$	7.58073			0.311829
$592$			23.9385i			0.983868i
$593$			22.6138i			0.928637i	0.885668	+	0.464318i	$0.153701\pi$
$593$			22.6138i			0.928637i	−0.885668	+	0.464318i	$0.846299\pi$
$594$		0			0
$595$	16.1140	−	7.14678i	0.660609	−	0.292989i
$596$	35.9044			1.47070
$597$		−	16.8804i		−	0.690868i
$598$			63.9034i			2.61320i
$599$	23.2627			0.950488			0.475244	−	0.879854i	$-0.342360\pi$
$599$	23.2627			0.950488			0.475244	+	0.879854i	$0.342360\pi$
$600$	−15.4948	+	17.1099i	−0.632571	+	0.698509i
$601$	−21.6032			−0.881214			−0.440607	−	0.897700i	$-0.645237\pi$
$601$	−21.6032			−0.881214			−0.440607	+	0.897700i	$0.645237\pi$
$602$			17.3318i			0.706390i
$603$		−	8.83452i		−	0.359769i
$604$	−1.76816			−0.0719456
$605$		0			0
$606$	38.2428			1.55351
$607$		−	17.3433i		−	0.703945i	−0.936010	−	0.351972i	$-0.885511\pi$
$607$		−	17.3433i		−	0.703945i	0.936010	−	0.351972i	$-0.114489\pi$
$608$			3.31336i			0.134375i
$609$	−8.58189			−0.347756
$610$	14.3625	+	32.3833i	0.581519	+	1.31116i
$611$	−15.4701			−0.625855
$612$			22.9186i			0.926431i
$613$		−	26.2287i		−	1.05937i	−0.848195	−	0.529684i	$-0.822311\pi$
$613$		−	26.2287i		−	1.05937i	0.848195	−	0.529684i	$-0.177689\pi$
$614$	−32.8986			−1.32768
$615$	−7.82377	−	17.6404i	−0.315485	−	0.711330i
$616$		0			0
$617$			24.3468i			0.980164i	0.871676	+	0.490082i	$0.163033\pi$
$617$			24.3468i			0.980164i	−0.871676	+	0.490082i	$0.836967\pi$
$618$		−	40.6871i		−	1.63668i
$619$	23.1100			0.928868			0.464434	−	0.885608i	$-0.346258\pi$
$619$	23.1100			0.928868			0.464434	+	0.885608i	$0.346258\pi$
$620$	−74.9797	+	33.2546i	−3.01126	+	1.33554i
$621$	6.37088			0.255655
$622$			17.4896i			0.701267i
$623$		−	15.8831i		−	0.636343i
$624$	14.0943			0.564222
$625$	−2.47078	−	24.8776i	−0.0988312	−	0.995104i
$626$	−8.74020			−0.349329
$627$		0			0
$628$		−	12.2534i		−	0.488963i
$629$	−41.2093			−1.64312
$630$	−6.66173	+	2.95457i	−0.265410	+	0.117713i
$631$	4.85469			0.193262			0.0966311	−	0.995320i	$-0.469193\pi$
$631$	4.85469			0.193262			0.0966311	+	0.995320i	$0.469193\pi$
$632$		−	46.0439i		−	1.83153i
$633$			23.8041i			0.946127i
$634$	−60.1101			−2.38728
$635$	−12.6466	−	28.5145i	−0.501865	−	1.13156i
$636$	−25.0328			−0.992616
$637$			21.4720i			0.850752i
$638$		0			0
$639$	7.17440			0.283815
$640$	18.3646	+	41.4070i	0.725925	+	1.63676i
$641$	21.8725			0.863911			0.431956	−	0.901895i	$-0.357824\pi$
$641$	21.8725			0.863911			0.431956	+	0.901895i	$0.357824\pi$
$642$			10.9606i			0.432582i
$643$		−	34.5523i		−	1.36261i	−0.732000	−	0.681305i	$-0.761413\pi$
$643$		−	34.5523i		−	1.36261i	0.732000	−	0.681305i	$-0.238587\pi$
$644$	33.3407			1.31381
$645$	10.8702	−	4.82110i	0.428015	−	0.189831i
$646$	50.1907			1.97473
$647$		−	19.5511i		−	0.768632i	−0.923202	−	0.384316i	$-0.874437\pi$
$647$		−	19.5511i		−	0.768632i	0.923202	−	0.384316i	$-0.125563\pi$
$648$		−	4.61665i		−	0.181359i
$649$		0			0
$650$	−33.6653	+	37.1745i	−1.32046	+	1.45810i
$651$	−12.6175			−0.494521
$652$		−	1.46170i		−	0.0572448i
$653$		−	34.6776i		−	1.35704i	−0.734582	−	0.678520i	$-0.762621\pi$
$653$		−	34.6776i		−	1.35704i	0.734582	−	0.678520i	$-0.237379\pi$
$654$	−13.5950			−0.531607
$655$	−37.7368	+	16.7368i	−1.47450	+	0.653961i
$656$	29.4565			1.15008
$657$			4.08569i			0.159398i
$658$			12.2099i			0.475991i
$659$	−33.0024			−1.28559			−0.642796	−	0.766037i	$-0.722226\pi$
$659$	−33.0024			−1.28559			−0.642796	+	0.766037i	$0.722226\pi$
$660$		0			0
$661$	19.8988			0.773974			0.386987	−	0.922085i	$-0.373516\pi$
$661$	19.8988			0.773974			0.386987	+	0.922085i	$0.373516\pi$
$662$			32.4069i			1.25953i
$663$			24.2628i			0.942288i
$664$	14.1279			0.548267
$665$	4.27723	+	9.64395i	0.165864	+	0.373976i
$666$	17.0365			0.660150
$667$		−	40.7505i		−	1.57787i
$668$		−	78.3516i		−	3.03152i
$669$	−21.6870			−0.838468
$670$	−43.8653	+	19.4549i	−1.69466	+	0.751607i
$671$		0			0
$672$			1.26416i			0.0487662i
$673$		−	11.9694i		−	0.461388i	−0.973026	−	0.230694i	$-0.925900\pi$
$673$		−	11.9694i		−	0.461388i	0.973026	−	0.230694i	$-0.0740996\pi$
$674$	63.6159			2.45039
$675$	3.70613	+	3.35628i	0.142649	+	0.129183i
$676$	15.8021			0.607774
$677$			14.3812i			0.552714i	0.961055	+	0.276357i	$0.0891273\pi$
$677$			14.3812i			0.552714i	−0.961055	+	0.276357i	$0.910873\pi$
$678$		−	7.75461i		−	0.297814i
$679$	−3.42625			−0.131487
$680$	55.4473	−	24.5917i	2.12631	−	0.943048i
$681$	−1.05996			−0.0406179
$682$		0			0
$683$		−	30.0922i		−	1.15144i	−0.817645	−	0.575722i	$-0.804721\pi$
$683$		−	30.0922i		−	1.15144i	0.817645	−	0.575722i	$-0.195279\pi$
$684$	−13.7164			−0.524461
$685$	6.85695	+	15.4605i	0.261990	+	0.590715i
$686$	39.7605			1.51806
$687$		−	14.0678i		−	0.536719i
$688$			18.1515i			0.692018i
$689$	−26.5010			−1.00961
$690$	−14.0296	−	31.6328i	−0.534097	−	1.20424i
$691$	36.0306			1.37067			0.685334	−	0.728229i	$-0.259656\pi$
$691$	36.0306			1.37067			0.685334	+	0.728229i	$0.259656\pi$
$692$		−	10.6026i		−	0.403050i
$693$		0			0
$694$	5.41703			0.205628
$695$	−1.16924	+	0.518575i	−0.0443518	+	0.0196707i
$696$	−29.5298			−1.11932
$697$			50.7083i			1.92071i
$698$		−	47.3986i		−	1.79406i
$699$	−0.300464			−0.0113646
$700$	19.3953	+	17.5644i	0.733073	+	0.663873i
$701$	−20.9413			−0.790942			−0.395471	−	0.918478i	$-0.629419\pi$
$701$	−20.9413			−0.790942			−0.395471	+	0.918478i	$0.629419\pi$
$702$		−	10.0305i		−	0.378579i
$703$		−	24.6631i		−	0.930187i
$704$		0			0
$705$	7.65787	−	3.39637i	0.288412	−	0.127915i
$706$	−1.47321			−0.0554451
$707$		−	21.1228i		−	0.794406i
$708$		−	35.0095i		−	1.31574i
$709$	11.1784			0.419815			0.209907	−	0.977721i	$-0.432684\pi$
$709$	11.1784			0.419815			0.209907	+	0.977721i	$0.432684\pi$
$710$	−15.7990	−	35.6224i	−0.592928	−	1.33689i
$711$	−9.97344			−0.374033
$712$		−	54.6529i		−	2.04820i
$713$		−	59.9136i		−	2.24378i
$714$	19.1495			0.716653
$715$		0			0
$716$	56.6194			2.11597
$717$			10.3905i			0.388041i
$718$			4.67719i			0.174551i
$719$	3.91415			0.145973			0.0729865	−	0.997333i	$-0.476747\pi$
$719$	3.91415			0.145973			0.0729865	+	0.997333i	$0.476747\pi$
$720$	−6.97679	+	3.09431i	−0.260010	+	0.115318i
$721$	−22.4729			−0.836936
$722$		−	16.1147i		−	0.599728i
$723$			5.73625i			0.213334i
$724$	80.0186			2.97387
$725$	21.4680	−	23.7058i	0.797302	−	0.880411i
$726$		0			0
$727$		−	15.7446i		−	0.583934i	−0.956428	−	0.291967i	$-0.905690\pi$
$727$		−	15.7446i		−	0.583934i	0.956428	−	0.291967i	$-0.0943098\pi$
$728$		−	25.5773i		−	0.947957i
$729$	−1.00000			−0.0370370
$730$	20.2863	−	8.99727i	0.750831	−	0.333004i
$731$	−31.2471			−1.15572
$732$			25.4396i			0.940273i
$733$		−	41.4651i		−	1.53155i	−0.643109	−	0.765775i	$-0.722356\pi$
$733$		−	41.4651i		−	1.53155i	0.643109	−	0.765775i	$-0.277644\pi$
$734$	52.6397			1.94297
$735$	−4.71404	−	10.6288i	−0.173880	−	0.392051i
$736$	−6.00280			−0.221266
$737$		0			0
$738$		−	20.9635i		−	0.771677i
$739$	−38.5029			−1.41635			−0.708177	−	0.706035i	$-0.750482\pi$
$739$	−38.5029			−1.41635			−0.708177	+	0.706035i	$0.750482\pi$
$740$	−24.8004	−	55.9179i	−0.911681	−	2.05558i
$741$	−14.5209			−0.533437
$742$			20.9160i			0.767851i
$743$			22.4806i			0.824733i	0.911018	+	0.412366i	$0.135298\pi$
$743$			22.4806i			0.824733i	−0.911018	+	0.412366i	$0.864702\pi$
$744$	−43.4163			−1.59172
$745$	−18.8154	+	8.34488i	−0.689342	+	0.305733i
$746$	−9.22866			−0.337885
$747$		−	3.06020i		−	0.111967i
$748$		0			0
$749$	6.05395			0.221207
$750$	8.50322	−	25.7927i	0.310494	−	0.941817i
$751$	27.3369			0.997537			0.498769	−	0.866735i	$-0.333786\pi$
$751$	27.3369			0.997537			0.498769	+	0.866735i	$0.333786\pi$
$752$			12.7874i			0.466307i
$753$			2.09242i			0.0762519i
$754$	−64.1591			−2.33654
$755$	0.926590	−	0.410956i	0.0337221	−	0.0149562i
$756$	−5.23330			−0.190333
$757$			36.6287i			1.33129i	0.746267	+	0.665647i	$0.231844\pi$
$757$			36.6287i			1.33129i	−0.746267	+	0.665647i	$0.768156\pi$
$758$			8.19136i			0.297524i
$759$		0			0
$760$	14.7177	+	33.1843i	0.533868	+	1.20372i
$761$	−53.6199			−1.94372			−0.971859	−	0.235562i	$-0.924307\pi$
$761$	−53.6199			−1.94372			−0.971859	+	0.235562i	$0.924307\pi$
$762$		−	33.8861i		−	1.22756i
$763$			7.50901i			0.271844i
$764$	−56.4940			−2.04388
$765$	−5.32674	−	12.0103i	−0.192589	−	0.434233i
$766$	29.4921			1.06559
$767$		−	37.0627i		−	1.33826i
$768$			30.9768i			1.11778i
$769$	51.8506			1.86978			0.934890	−	0.354939i	$-0.115498\pi$
$769$	51.8506			1.86978			0.934890	+	0.354939i	$0.115498\pi$
$770$		0			0
$771$	−23.2533			−0.837447
$772$		−	46.3114i		−	1.66679i
$773$		−	1.50494i		−	0.0541288i	−0.999634	−	0.0270644i	$-0.991384\pi$
$773$		−	1.50494i		−	0.0541288i	0.999634	−	0.0270644i	$-0.00861592\pi$
$774$	12.9180			0.464326
$775$	31.5634	−	34.8535i	1.13379	−	1.25197i
$776$	−11.7895			−0.423220
$777$		−	9.40985i		−	0.337576i
$778$			72.6795i			2.60569i
$779$	−30.3481			−1.08733
$780$	−32.9227	+	14.6017i	−1.17882	+	0.522825i
$781$		0			0
$782$			90.9302i			3.25166i
$783$			6.39637i			0.228588i
$784$	17.7484			0.633871
$785$	2.84792	+	6.42126i	0.101647	+	0.229185i
$786$	−44.8456			−1.59959
$787$		−	22.5259i		−	0.802962i	−0.915867	−	0.401481i	$-0.868496\pi$
$787$		−	22.5259i		−	0.802962i	0.915867	−	0.401481i	$-0.131504\pi$
$788$		−	29.5690i		−	1.05335i
$789$	3.71929			0.132410
$790$	21.9629	+	49.5203i	0.781407	+	1.76185i
$791$	−4.28315			−0.152291
$792$		0			0
$793$			26.9315i			0.956367i
$794$	64.0641			2.27355
$795$	13.1182	−	5.81812i	0.465255	−	0.206347i
$796$	−65.8429			−2.33374
$797$			44.3628i			1.57141i	0.618600	+	0.785706i	$0.287700\pi$
$797$			44.3628i			1.57141i	−0.618600	+	0.785706i	$0.712300\pi$
$798$			11.4607i			0.405703i
$799$	−22.0130			−0.778763
$800$	−3.49200	−	3.16237i	−0.123461	−	0.111807i
$801$	−11.8382			−0.418283
$802$		−	8.24153i		−	0.291019i
$803$		0			0
$804$	−34.4595			−1.21529
$805$	−17.4719	+	7.74903i	−0.615803	+	0.273118i
$806$	−94.3301			−3.32264
$807$			12.0991i			0.425909i
$808$		−	72.6825i		−	2.55696i
$809$	7.69469			0.270531			0.135265	−	0.990809i	$-0.456811\pi$
$809$	7.69469			0.270531			0.135265	+	0.990809i	$0.456811\pi$
$810$	2.20214	+	4.96521i	0.0773754	+	0.174460i
$811$	−25.7414			−0.903902			−0.451951	−	0.892043i	$-0.649272\pi$
$811$	−25.7414			−0.903902			−0.451951	+	0.892043i	$0.649272\pi$
$812$			33.4741i			1.17471i
$813$			3.26311i			0.114442i
$814$		0			0
$815$	0.339729	+	0.765993i	0.0119002	+	0.0268316i
$816$	20.0552			0.702072
$817$		−	18.7009i		−	0.654261i
$818$			30.0690i			1.05134i
$819$	−5.54022			−0.193591
$820$	−68.8074	+	30.5171i	−2.40286	+	1.06570i
$821$	18.3921			0.641887			0.320944	−	0.947098i	$-0.396000\pi$
$821$	18.3921			0.641887			0.320944	+	0.947098i	$0.396000\pi$
$822$			18.3729i			0.640829i
$823$		−	3.49286i		−	0.121753i	−0.998145	−	0.0608767i	$-0.980610\pi$
$823$		−	3.49286i		−	0.121753i	0.998145	−	0.0608767i	$-0.0193896\pi$
$824$	−77.3281			−2.69385
$825$		0			0
$826$	−29.2519			−1.01781
$827$		−	0.466783i		−	0.0162317i	−0.999967	−	0.00811583i	$-0.997417\pi$
$827$		−	0.466783i		−	0.0162317i	0.999967	−	0.00811583i	$-0.00258338\pi$
$828$		−	24.8500i		−	0.863596i
$829$	50.9521			1.76964			0.884820	−	0.465933i	$-0.154281\pi$
$829$	50.9521			1.76964			0.884820	+	0.465933i	$0.154281\pi$
$830$	−15.1945	+	6.73899i	−0.527410	+	0.233914i
$831$	−23.6465			−0.820288
$832$			37.6396i			1.30492i
$833$			30.5532i			1.05861i
$834$	−1.38950			−0.0481145
$835$	18.2104	+	41.0594i	0.630199	+	1.42092i
$836$		0			0
$837$			9.40429i			0.325060i
$838$		−	14.3928i		−	0.497192i
$839$	−35.8479			−1.23761			−0.618804	−	0.785545i	$-0.712383\pi$
$839$	−35.8479			−1.23761			−0.618804	+	0.785545i	$0.712383\pi$
$840$	5.61533	+	12.6610i	0.193747	+	0.436846i
$841$	11.9136			0.410813
$842$			61.2565i			2.11104i
$843$			30.2948i			1.04341i
$844$	92.8491			3.19600
$845$	−8.28096	+	3.67272i	−0.284874	+	0.126346i
$846$	9.10045			0.312880
$847$		0			0
$848$			21.9052i			0.752229i
$849$	12.6940			0.435658
$850$	−47.9034	+	52.8968i	−1.64307	+	1.81434i
$851$	44.6820			1.53168
$852$		−	27.9841i		−	0.958721i
$853$		−	39.0874i		−	1.33833i	−0.743114	−	0.669164i	$-0.766652\pi$
$853$		−	39.0874i		−	1.33833i	0.743114	−	0.669164i	$-0.233348\pi$
$854$	21.2559			0.727361
$855$	7.18796	−	3.18796i	0.245823	−	0.109026i
$856$	20.8313			0.712000
$857$		−	49.2657i		−	1.68289i	−0.540346	−	0.841443i	$-0.681707\pi$
$857$		−	49.2657i		−	1.68289i	0.540346	−	0.841443i	$-0.318293\pi$
$858$		0			0
$859$	−9.27352			−0.316408			−0.158204	−	0.987406i	$-0.550570\pi$
$859$	−9.27352			−0.316408			−0.158204	+	0.987406i	$0.550570\pi$
$860$	−18.8050	−	42.3999i	−0.641244	−	1.44583i
$861$	−11.5789			−0.394607
$862$		−	18.2538i		−	0.621727i
$863$		−	11.8883i		−	0.404683i	−0.979315	−	0.202341i	$-0.935145\pi$
$863$		−	11.8883i		−	0.404683i	0.979315	−	0.202341i	$-0.0648551\pi$
$864$	0.942224			0.0320551
$865$	2.46425	+	5.55619i	0.0837870	+	0.188916i
$866$	−36.5138			−1.24079
$867$			17.5243i			0.595155i
$868$			49.2154i			1.67048i
$869$		0			0
$870$	31.7594	−	14.0857i	1.07674	−	0.477551i
$871$	−36.4805			−1.23610
$872$			25.8381i			0.874988i
$873$			2.55370i			0.0864296i
$874$	−54.4202			−1.84079
$875$	−14.2462	−	4.69663i	−0.481611	−	0.158775i
$876$	15.9365			0.538443
$877$			29.9283i			1.01061i	0.862942	+	0.505303i	$0.168619\pi$
$877$			29.9283i			1.01061i	−0.862942	+	0.505303i	$0.831381\pi$
$878$			58.1290i			1.96176i
$879$	−2.10292			−0.0709299
$880$		0			0
$881$	−36.7852			−1.23932			−0.619662	−	0.784869i	$-0.712730\pi$
$881$	−36.7852			−1.23932			−0.619662	+	0.784869i	$0.712730\pi$
$882$		−	12.6311i		−	0.425311i
$883$		−	21.6154i		−	0.727418i	−0.931513	−	0.363709i	$-0.881510\pi$
$883$		−	21.6154i		−	0.727418i	0.931513	−	0.363709i	$-0.118490\pi$
$884$	94.6383			3.18303
$885$	8.13688	+	18.3464i	0.273518	+	0.616707i
$886$	−92.8812			−3.12040
$887$			41.0937i			1.37979i	0.723909	+	0.689895i	$0.242343\pi$
$887$			41.0937i			1.37979i	−0.723909	+	0.689895i	$0.757657\pi$
$888$		−	32.3788i		−	1.08656i
$889$	−18.7165			−0.627730
$890$	26.0695	+	58.7793i	0.873850	+	1.97029i
$891$		0			0
$892$			84.5914i			2.83233i
$893$		−	13.1744i		−	0.440864i
$894$	−22.3598			−0.747823
$895$	−29.6709	+	13.1595i	−0.991788	+	0.439872i
$896$	27.1789			0.907983
$897$		−	26.3074i		−	0.878377i
$898$			0.0901432i			0.00300812i
$899$	60.1533			2.00623
$900$	13.0914	−	14.4560i	0.436378	−	0.481865i
$901$	−37.7091			−1.25627
$902$		0			0
$903$		−	7.13504i		−	0.237439i
$904$	−14.7381			−0.490181
$905$	−41.9330	+	18.5979i	−1.39390	+	0.618215i
$906$	1.10114			0.0365829
$907$			53.1355i			1.76433i	0.470936	+	0.882167i	$0.343916\pi$
$907$			53.1355i			1.76433i	−0.470936	+	0.882167i	$0.656084\pi$
$908$			4.13444i			0.137206i
$909$	−15.7436			−0.522181
$910$	12.2004	+	27.5084i	0.404438	+	0.911894i
$911$	−9.05845			−0.300120			−0.150060	−	0.988677i	$-0.547947\pi$
$911$	−9.05845			−0.300120			−0.150060	+	0.988677i	$0.547947\pi$
$912$			12.0027i			0.397449i
$913$		0			0
$914$	16.1829			0.535283
$915$	−5.91265	−	13.3314i	−0.195466	−	0.440721i
$916$	−54.8721			−1.81302
$917$			24.7698i			0.817971i
$918$		−	14.2728i		−	0.471072i
$919$	56.6136			1.86751			0.933755	−	0.357913i	$-0.116511\pi$
$919$	56.6136			1.86751			0.933755	+	0.357913i	$0.116511\pi$
$920$	−60.1198	+	26.6640i	−1.98209	+	0.879086i
$921$	13.5435			0.446273
$922$		−	100.738i		−	3.31762i
$923$		−	29.6254i		−	0.975130i
$924$		0			0
$925$	25.9928	+	23.5392i	0.854639	+	0.773964i
$926$	−24.0704			−0.791001
$927$			16.7498i			0.550137i
$928$		−	6.02682i		−	0.197840i
$929$	9.36897			0.307386			0.153693	−	0.988119i	$-0.450883\pi$
$929$	9.36897			0.307386			0.153693	+	0.988119i	$0.450883\pi$
$930$	46.6943	−	20.7096i	1.53117	−	0.679094i
$931$	−18.2856			−0.599286
$932$			1.17198i			0.0383894i
$933$		−	7.20000i		−	0.235717i
$934$	49.1266			1.60747
$935$		0			0
$936$	−19.0636			−0.623114
$937$			16.6027i			0.542386i	0.962525	+	0.271193i	$0.0874182\pi$
$937$			16.6027i			0.542386i	−0.962525	+	0.271193i	$0.912582\pi$
$938$			28.7924i			0.940107i
$939$	3.59811			0.117420
$940$	−13.2477	−	29.8699i	−0.432094	−	0.974250i
$941$	−11.1200			−0.362501			−0.181251	−	0.983437i	$-0.558015\pi$
$941$	−11.1200			−0.362501			−0.181251	+	0.983437i	$0.558015\pi$
$942$			7.63090i			0.248628i
$943$		−	54.9815i		−	1.79044i
$944$	−30.6354			−0.997097
$945$	2.74246	−	1.21632i	0.0892123	−	0.0395669i
$946$		0			0
$947$		−	52.1722i		−	1.69537i	−0.530500	−	0.847685i	$-0.677996\pi$
$947$		−	52.1722i		−	1.69537i	0.530500	−	0.847685i	$-0.322004\pi$
$948$			38.9020i			1.26348i
$949$	16.8711			0.547659
$950$	−31.6578	−	28.6694i	−1.02712	−	0.930159i
$951$	24.7458			0.802437
$952$		−	36.3947i		−	1.17956i
$953$		−	0.0462258i		−	0.00149740i	−1.00000		0.000748700i	$-0.999762\pi$
$953$		−	0.0462258i		−	0.00149740i	1.00000		0.000748700i	$-0.000238318\pi$
$954$	15.5894			0.504726
$955$	29.6051	−	13.1303i	0.958000	−	0.424886i
$956$	40.5288			1.31080
$957$		0			0
$958$			35.5159i			1.14747i
$959$	10.1480			0.327696
$960$	−8.26353	−	18.6319i	−0.266704	−	0.601343i
$961$	57.4406			1.85292
$962$		−	70.3490i		−	2.26814i
$963$		−	4.51221i		−	0.145404i
$964$	22.3746			0.720636
$965$	10.7637	+	24.2691i	0.346495	+	0.781249i
$966$	−20.7632			−0.668046
$967$			48.1618i			1.54878i	0.632709	+	0.774390i	$0.281943\pi$
$967$			48.1618i			1.54878i	−0.632709	+	0.774390i	$0.718057\pi$
$968$		0			0
$969$	−20.6622			−0.663766
$970$	12.6797	−	5.62361i	0.407119	−	0.180563i
$971$	5.42160			0.173988			0.0869938	−	0.996209i	$-0.472274\pi$
$971$	5.42160			0.173988			0.0869938	+	0.996209i	$0.472274\pi$
$972$			3.90056i			0.125110i
$973$			0.767470i			0.0246040i
$974$	−19.5897			−0.627694
$975$	13.8591	−	15.3038i	0.443848	−	0.490113i
$976$	22.2611			0.712562
$977$			17.0776i			0.546360i	0.961963	+	0.273180i	$0.0880754\pi$
$977$			17.0776i			0.546360i	−0.961963	+	0.273180i	$0.911925\pi$
$978$			0.910290i			0.0291079i
$979$		0			0
$980$	−41.4584	+	18.3874i	−1.32434	+	0.587363i
$981$	5.59672			0.178689
$982$			22.0858i			0.704786i
$983$			4.68860i			0.149543i	0.997201	+	0.0747715i	$0.0238227\pi$
$983$			4.68860i			0.149543i	−0.997201	+	0.0747715i	$0.976177\pi$
$984$	−39.8423			−1.27013
$985$	6.87242	+	15.4954i	0.218974	+	0.493724i
$986$	−91.2940			−2.90739
$987$		−	5.02650i		−	0.159995i
$988$			56.6394i			1.80194i
$989$	33.8802			1.07733
$990$		0			0
$991$	−55.7657			−1.77145			−0.885727	−	0.464206i	$-0.846340\pi$
$991$	−55.7657			−1.77145			−0.885727	+	0.464206i	$0.846340\pi$
$992$		−	8.86095i		−	0.281335i
$993$		−	13.3411i		−	0.423366i
$994$	−23.3820			−0.741631
$995$	34.5044	−	15.3032i	1.09386	−	0.485143i
$996$	−11.9365			−0.378221
$997$			39.1950i			1.24132i	0.784081	+	0.620658i	$0.213135\pi$
$997$			39.1950i			1.24132i	−0.784081	+	0.620658i	$0.786865\pi$
$998$			10.5937i			0.335339i
$999$	−7.01348			−0.221897

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.2.c.h.364.11	yes	12
5.2	odd	4		9075.2.a.dr.1.1		6
5.3	odd	4		9075.2.a.dp.1.6		6
5.4	even	2	inner	1815.2.c.h.364.2	✓	12
11.10	odd	2		1815.2.c.i.364.2	yes	12
55.32	even	4		9075.2.a.do.1.6		6
55.43	even	4		9075.2.a.ds.1.1		6
55.54	odd	2		1815.2.c.i.364.11	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1815.2.c.h.364.2	✓	12	5.4	even	2	inner
1815.2.c.h.364.11	yes	12	1.1	even	1	trivial
1815.2.c.i.364.2	yes	12	11.10	odd	2
1815.2.c.i.364.11	yes	12	55.54	odd	2
9075.2.a.do.1.6		6	55.32	even	4
9075.2.a.dp.1.6		6	5.3	odd	4
9075.2.a.dr.1.1		6	5.2	odd	4
9075.2.a.ds.1.1		6	55.43	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1815.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.42911i q^{2} -1.00000i q^{3} -3.90056 q^{4} +(2.04405 - 0.906565i) q^{5} +2.42911 q^{6} -1.34168i q^{7} -4.61665i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+2.42911i q^{2} -1.00000i q^{3} -3.90056 q^{4} +(2.04405 - 0.906565i) q^{5} +2.42911 q^{6} -1.34168i q^{7} -4.61665i q^{8} -1.00000 q^{9} +(2.20214 + 4.96521i) q^{10} +3.90056i q^{12} +4.12932i q^{13} +3.25908 q^{14} +(-0.906565 - 2.04405i) q^{15} +3.41322 q^{16} +5.87573i q^{17} -2.42911i q^{18} -3.51653 q^{19} +(-7.97293 + 3.53611i) q^{20} -1.34168 q^{21} -6.37088i q^{23} -4.61665 q^{24} +(3.35628 - 3.70613i) q^{25} -10.0305 q^{26} +1.00000i q^{27} +5.23330i q^{28} +6.39637 q^{29} +(4.96521 - 2.20214i) q^{30} +9.40429 q^{31} -0.942224i q^{32} -14.2728 q^{34} +(-1.21632 - 2.74246i) q^{35} +3.90056 q^{36} +7.01348i q^{37} -8.54203i q^{38} +4.12932 q^{39} +(-4.18529 - 9.43666i) q^{40} +8.63013 q^{41} -3.25908i q^{42} +5.31799i q^{43} +(-2.04405 + 0.906565i) q^{45} +15.4755 q^{46} +3.74642i q^{47} -3.41322i q^{48} +5.19989 q^{49} +(9.00258 + 8.15276i) q^{50} +5.87573 q^{51} -16.1066i q^{52} +6.41776i q^{53} -2.42911 q^{54} -6.19407 q^{56} +3.51653i q^{57} +15.5375i q^{58} -8.97551 q^{59} +(3.53611 + 7.97293i) q^{60} +6.52203 q^{61} +22.8440i q^{62} +1.34168i q^{63} +9.11521 q^{64} +(3.74349 + 8.44053i) q^{65} +8.83452i q^{67} -22.9186i q^{68} -6.37088 q^{69} +(6.66173 - 2.95457i) q^{70} -7.17440 q^{71} +4.61665i q^{72} -4.08569i q^{73} -17.0365 q^{74} +(-3.70613 - 3.35628i) q^{75} +13.7164 q^{76} +10.0305i q^{78} +9.97344 q^{79} +(6.97679 - 3.09431i) q^{80} +1.00000 q^{81} +20.9635i q^{82} +3.06020i q^{83} +5.23330 q^{84} +(5.32674 + 12.0103i) q^{85} -12.9180 q^{86} -6.39637i q^{87} +11.8382 q^{89} +(-2.20214 - 4.96521i) q^{90} +5.54022 q^{91} +24.8500i q^{92} -9.40429i q^{93} -9.10045 q^{94} +(-7.18796 + 3.18796i) q^{95} -0.942224 q^{96} -2.55370i q^{97} +12.6311i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 18 q^{4} - 2 q^{5} - 2 q^{6} - 12 q^{9}+O(q^{10}) \) 12 * q - 18 * q^4 - 2 * q^5 - 2 * q^6 - 12 * q^9	\( 12 q - 18 q^{4} - 2 q^{5} - 2 q^{6} - 12 q^{9} - 12 q^{10} + 20 q^{14} + 22 q^{16} - 4 q^{19} - 2 q^{20} + 8 q^{21} + 2 q^{25} + 24 q^{29} + 8 q^{30} + 36 q^{31} + 2 q^{34} - 24 q^{35} + 18 q^{36} + 4 q^{39} + 22 q^{40} + 12 q^{41} + 2 q^{45} + 22 q^{46} - 24 q^{49} + 58 q^{50} - 4 q^{51} + 2 q^{54} - 84 q^{56} + 36 q^{59} + 22 q^{60} - 8 q^{61} - 44 q^{64} + 14 q^{65} - 24 q^{69} - 16 q^{70} - 8 q^{74} - 12 q^{75} + 40 q^{76} + 4 q^{79} - 58 q^{80} + 12 q^{81} - 48 q^{84} + 2 q^{85} + 56 q^{86} + 32 q^{89} + 12 q^{90} + 48 q^{91} + 6 q^{94} - 62 q^{96}+O(q^{100}) \) 12 * q - 18 * q^4 - 2 * q^5 - 2 * q^6 - 12 * q^9 - 12 * q^10 + 20 * q^14 + 22 * q^16 - 4 * q^19 - 2 * q^20 + 8 * q^21 + 2 * q^25 + 24 * q^29 + 8 * q^30 + 36 * q^31 + 2 * q^34 - 24 * q^35 + 18 * q^36 + 4 * q^39 + 22 * q^40 + 12 * q^41 + 2 * q^45 + 22 * q^46 - 24 * q^49 + 58 * q^50 - 4 * q^51 + 2 * q^54 - 84 * q^56 + 36 * q^59 + 22 * q^60 - 8 * q^61 - 44 * q^64 + 14 * q^65 - 24 * q^69 - 16 * q^70 - 8 * q^74 - 12 * q^75 + 40 * q^76 + 4 * q^79 - 58 * q^80 + 12 * q^81 - 48 * q^84 + 2 * q^85 + 56 * q^86 + 32 * q^89 + 12 * q^90 + 48 * q^91 + 6 * q^94 - 62 * q^96

Introduction

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