LMFDB - Embedded newform 7.7.b.b.6.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7,7,Mod(6,7)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("7.6");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 7 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	7.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:	$1.61037858534$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-510}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 510 $ x^2 + 510
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			6.1
Root			$-22.5832i$ of defining polynomial
Character	$\chi$	$=$	7.6
Dual form			7.7.b.b.6.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.00000 q^{2} -45.1664i q^{3} +45.1664i q^{5} +361.331i q^{6} +(133.000 - 316.165i) q^{7} +512.000 q^{8} -1311.00 q^{9} +O(q^{10})$	\(q-8.00000 q^{2} -45.1664i q^{3} +45.1664i q^{5} +361.331i q^{6} +(133.000 - 316.165i) q^{7} +512.000 q^{8} -1311.00 q^{9} -361.331i q^{10} +874.000 q^{11} -2213.15i q^{13} +(-1064.00 + 2529.32i) q^{14} +2040.00 q^{15} -4096.00 q^{16} +5961.96i q^{17} +10488.0 q^{18} -3116.48i q^{19} +(-14280.0 - 6007.13i) q^{21} -6992.00 q^{22} +4738.00 q^{23} -23125.2i q^{24} +13585.0 q^{25} +17705.2i q^{26} +26286.8i q^{27} +11146.0 q^{29} -16320.0 q^{30} +27461.1i q^{31} -39475.4i q^{33} -47695.7i q^{34} +(14280.0 + 6007.13i) q^{35} +3002.00 q^{37} +24931.8i q^{38} -99960.0 q^{39} +23125.2i q^{40} -57541.9i q^{41} +(114240. + 48057.0i) q^{42} +31418.0 q^{43} -59213.1i q^{45} -37904.0 q^{46} +72446.8i q^{47} +185001. i q^{48} +(-82271.0 - 84099.8i) q^{49} -108680. q^{50} +269280. q^{51} -76406.0 q^{53} -210295. i q^{54} +39475.4i q^{55} +(68096.0 - 161876. i) q^{56} -140760. q^{57} -89168.0 q^{58} -113232. i q^{59} +275108. i q^{61} -219689. i q^{62} +(-174363. + 414492. i) q^{63} +262144. q^{64} +99960.0 q^{65} +315803. i q^{66} +495242. q^{67} -213998. i q^{69} +(-114240. - 48057.0i) q^{70} -184406. q^{71} -671232. q^{72} +60974.6i q^{73} -24016.0 q^{74} -613585. i q^{75} +(116242. - 276328. i) q^{77} +799680. q^{78} -534934. q^{79} -185001. i q^{80} +231561. q^{81} +460336. i q^{82} +714848. i q^{83} -269280. q^{85} -251344. q^{86} -503424. i q^{87} +447488. q^{88} +629529. i q^{89} +473705. i q^{90} +(-699720. - 294349. i) q^{91} +1.24032e6 q^{93} -579575. i q^{94} +140760. q^{95} -814440. i q^{97} +(658168. + 672798. i) q^{98} -1.14581e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 16 q^{2} + 266 q^{7} + 1024 q^{8} - 2622 q^{9}+O(q^{10}) $ 2 * q - 16 * q^2 + 266 * q^7 + 1024 * q^8 - 2622 * q^9	$ 2 q - 16 q^{2} + 266 q^{7} + 1024 q^{8} - 2622 q^{9} + 1748 q^{11} - 2128 q^{14} + 4080 q^{15} - 8192 q^{16} + 20976 q^{18} - 28560 q^{21} - 13984 q^{22} + 9476 q^{23} + 27170 q^{25} + 22292 q^{29} - 32640 q^{30} + 28560 q^{35} + 6004 q^{37} - 199920 q^{39} + 228480 q^{42} + 62836 q^{43} - 75808 q^{46} - 164542 q^{49} - 217360 q^{50} + 538560 q^{51} - 152812 q^{53} + 136192 q^{56} - 281520 q^{57} - 178336 q^{58} - 348726 q^{63} + 524288 q^{64} + 199920 q^{65} + 990484 q^{67} - 228480 q^{70} - 368812 q^{71} - 1342464 q^{72} - 48032 q^{74} + 232484 q^{77} + 1599360 q^{78} - 1069868 q^{79} + 463122 q^{81} - 538560 q^{85} - 502688 q^{86} + 894976 q^{88} - 1399440 q^{91} + 2480640 q^{93} + 281520 q^{95} + 1316336 q^{98} - 2291628 q^{99}+O(q^{100}) $ 2 * q - 16 * q^2 + 266 * q^7 + 1024 * q^8 - 2622 * q^9 + 1748 * q^11 - 2128 * q^14 + 4080 * q^15 - 8192 * q^16 + 20976 * q^18 - 28560 * q^21 - 13984 * q^22 + 9476 * q^23 + 27170 * q^25 + 22292 * q^29 - 32640 * q^30 + 28560 * q^35 + 6004 * q^37 - 199920 * q^39 + 228480 * q^42 + 62836 * q^43 - 75808 * q^46 - 164542 * q^49 - 217360 * q^50 + 538560 * q^51 - 152812 * q^53 + 136192 * q^56 - 281520 * q^57 - 178336 * q^58 - 348726 * q^63 + 524288 * q^64 + 199920 * q^65 + 990484 * q^67 - 228480 * q^70 - 368812 * q^71 - 1342464 * q^72 - 48032 * q^74 + 232484 * q^77 + 1599360 * q^78 - 1069868 * q^79 + 463122 * q^81 - 538560 * q^85 - 502688 * q^86 + 894976 * q^88 - 1399440 * q^91 + 2480640 * q^93 + 281520 * q^95 + 1316336 * q^98 - 2291628 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/7\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$	−8.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$2$	−8.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$3$		−	45.1664i		−	1.67283i	−0.548098	−	0.836414i	$-0.684648\pi$
$3$		−	45.1664i		−	1.67283i	0.548098	−	0.836414i	$-0.315352\pi$
$4$		0			0
$5$			45.1664i			0.361331i	0.983545	+	0.180665i	$0.0578251\pi$
$5$			45.1664i			0.361331i	−0.983545	+	0.180665i	$0.942175\pi$
$6$			361.331i			1.67283i
$7$	133.000	−	316.165i	0.387755	−	0.921762i
$7$	133.000	−	316.165i	0.387755	−	0.921762i
$8$	512.000			1.00000
$9$	−1311.00			−1.79835
$10$		−	361.331i		−	0.361331i
$11$	874.000			0.656649			0.328325	−	0.944565i	$-0.393516\pi$
$11$	874.000			0.656649			0.328325	+	0.944565i	$0.393516\pi$
$12$		0			0
$13$		−	2213.15i		−	1.00735i	−0.863893	−	0.503676i	$-0.831981\pi$
$13$		−	2213.15i		−	1.00735i	0.863893	−	0.503676i	$-0.168019\pi$
$14$	−1064.00	+	2529.32i	−0.387755	+	0.921762i
$15$	2040.00			0.604444
$16$	−4096.00			−1.00000
$17$			5961.96i			1.21351i	0.794890	+	0.606753i	$0.207528\pi$
$17$			5961.96i			1.21351i	−0.794890	+	0.606753i	$0.792472\pi$
$18$	10488.0			1.79835
$19$		−	3116.48i		−	0.454363i	−0.973852	−	0.227182i	$-0.927049\pi$
$19$		−	3116.48i		−	0.454363i	0.973852	−	0.227182i	$-0.0729511\pi$
$20$		0			0
$21$	−14280.0	−	6007.13i	−1.54195	−	0.648648i
$22$	−6992.00			−0.656649
$23$	4738.00			0.389414			0.194707	−	0.980861i	$-0.437624\pi$
$23$	4738.00			0.389414			0.194707	+	0.980861i	$0.437624\pi$
$24$		−	23125.2i		−	1.67283i
$25$	13585.0			0.869440
$26$			17705.2i			1.00735i
$27$			26286.8i			1.33551i
$28$		0			0
$29$	11146.0			0.457009			0.228505	−	0.973543i	$-0.426616\pi$
$29$	11146.0			0.457009			0.228505	+	0.973543i	$0.426616\pi$
$30$	−16320.0			−0.604444
$31$			27461.1i			0.921793i	0.887454	+	0.460897i	$0.152472\pi$
$31$			27461.1i			0.921793i	−0.887454	+	0.460897i	$0.847528\pi$
$32$		0			0
$33$		−	39475.4i		−	1.09846i
$34$		−	47695.7i		−	1.21351i
$35$	14280.0	+	6007.13i	0.333061	+	0.140108i
$36$		0			0
$37$	3002.00			0.0592660			0.0296330	−	0.999561i	$-0.490566\pi$
$37$	3002.00			0.0592660			0.0296330	+	0.999561i	$0.490566\pi$
$38$			24931.8i			0.454363i
$39$	−99960.0			−1.68513
$40$			23125.2i			0.361331i
$41$		−	57541.9i		−	0.834897i	−0.908701	−	0.417449i	$-0.862924\pi$
$41$		−	57541.9i		−	0.834897i	0.908701	−	0.417449i	$-0.137076\pi$
$42$	114240.	+	48057.0i	1.54195	+	0.648648i
$43$	31418.0			0.395160			0.197580	−	0.980287i	$-0.436692\pi$
$43$	31418.0			0.395160			0.197580	+	0.980287i	$0.436692\pi$
$44$		0			0
$45$		−	59213.1i		−	0.649801i
$46$	−37904.0			−0.389414
$47$			72446.8i			0.697792i	0.937161	+	0.348896i	$0.113443\pi$
$47$			72446.8i			0.697792i	−0.937161	+	0.348896i	$0.886557\pi$
$48$			185001.i			1.67283i
$49$	−82271.0	−	84099.8i	−0.699292	−	0.714836i
$50$	−108680.			−0.869440
$51$	269280.			2.02999
$52$		0			0
$53$	−76406.0			−0.513216			−0.256608	−	0.966516i	$-0.582605\pi$
$53$	−76406.0			−0.513216			−0.256608	+	0.966516i	$0.582605\pi$
$54$		−	210295.i		−	1.33551i
$55$			39475.4i			0.237268i
$56$	68096.0	−	161876.i	0.387755	−	0.921762i
$57$	−140760.			−0.760072
$58$	−89168.0			−0.457009
$59$		−	113232.i		−	0.551332i	−0.961253	−	0.275666i	$-0.911102\pi$
$59$		−	113232.i		−	0.551332i	0.961253	−	0.275666i	$-0.0888984\pi$
$60$		0			0
$61$			275108.i			1.21203i	0.795452	+	0.606016i	$0.207233\pi$
$61$			275108.i			1.21203i	−0.795452	+	0.606016i	$0.792767\pi$
$62$		−	219689.i		−	0.921793i
$63$	−174363.	+	414492.i	−0.697321	+	1.65766i
$64$	262144.			1.00000
$65$	99960.0			0.363987
$66$			315803.i			1.09846i
$67$	495242.			1.64662			0.823309	−	0.567593i	$-0.192125\pi$
$67$	495242.			1.64662			0.823309	+	0.567593i	$0.192125\pi$
$68$		0			0
$69$		−	213998.i		−	0.651423i
$70$	−114240.	−	48057.0i	−0.333061	−	0.140108i
$71$	−184406.			−0.515229			−0.257614	−	0.966248i	$-0.582936\pi$
$71$	−184406.			−0.515229			−0.257614	+	0.966248i	$0.582936\pi$
$72$	−671232.			−1.79835
$73$			60974.6i			0.156740i	0.996924	+	0.0783701i	$0.0249716\pi$
$73$			60974.6i			0.156740i	−0.996924	+	0.0783701i	$0.975028\pi$
$74$	−24016.0			−0.0592660
$75$		−	613585.i		−	1.45442i
$76$		0			0
$77$	116242.	−	276328.i	0.254619	−	0.605275i
$78$	799680.			1.68513
$79$	−534934.			−1.08497			−0.542486	−	0.840065i	$-0.682517\pi$
$79$	−534934.			−1.08497			−0.542486	+	0.840065i	$0.682517\pi$
$80$		−	185001.i		−	0.361331i
$81$	231561.			0.435723
$82$			460336.i			0.834897i
$83$			714848.i			1.25020i	0.780545	+	0.625100i	$0.214942\pi$
$83$			714848.i			1.25020i	−0.780545	+	0.625100i	$0.785058\pi$
$84$		0			0
$85$	−269280.			−0.438478
$86$	−251344.			−0.395160
$87$		−	503424.i		−	0.764498i
$88$	447488.			0.656649
$89$			629529.i			0.892988i	0.894787	+	0.446494i	$0.147328\pi$
$89$			629529.i			0.892988i	−0.894787	+	0.446494i	$0.852672\pi$
$90$			473705.i			0.649801i
$91$	−699720.	−	294349.i	−0.928539	−	0.390606i
$92$		0			0
$93$	1.24032e6			1.54200
$94$		−	579575.i		−	0.697792i
$95$	140760.			0.164176
$96$		0			0
$97$		−	814440.i		−	0.892368i	−0.894941	−	0.446184i	$-0.852783\pi$
$97$		−	814440.i		−	0.892368i	0.894941	−	0.446184i	$-0.147217\pi$
$98$	658168.	+	672798.i	0.699292	+	0.714836i
$99$	−1.14581e6			−1.18089
$100$		0			0
$101$			1.95195e6i			1.89455i	0.320425	+	0.947274i	$0.396174\pi$
$101$			1.95195e6i			1.89455i	−0.320425	+	0.947274i	$0.603826\pi$
$102$	−2.15424e6			−2.02999
$103$		−	1.69744e6i		−	1.55340i	−0.629871	−	0.776700i	$-0.716892\pi$
$103$		−	1.69744e6i		−	1.55340i	0.629871	−	0.776700i	$-0.283108\pi$
$104$		−	1.13313e6i		−	1.00735i
$105$	271320.	−	644976.i	0.234376	−	0.557154i
$106$	611248.			0.513216
$107$	1.61603e6			1.31916			0.659579	−	0.751635i	$-0.270734\pi$
$107$	1.61603e6			1.31916			0.659579	+	0.751635i	$0.270734\pi$
$108$		0			0
$109$	199226.			0.153839			0.0769195	−	0.997037i	$-0.475492\pi$
$109$	199226.			0.153839			0.0769195	+	0.997037i	$0.475492\pi$
$110$		−	315803.i		−	0.237268i
$111$		−	135589.i		−	0.0991418i
$112$	−544768.	+	1.29501e6i	−0.387755	+	0.921762i
$113$	−1.80762e6			−1.25277			−0.626386	−	0.779513i	$-0.715467\pi$
$113$	−1.80762e6			−1.25277			−0.626386	+	0.779513i	$0.715467\pi$
$114$	1.12608e6			0.760072
$115$			213998.i			0.140707i
$116$		0			0
$117$			2.90144e6i			1.81157i
$118$			905856.i			0.551332i
$119$	1.88496e6	+	792941.i	1.11857	+	0.470543i
$120$	1.04448e6			0.604444
$121$	−1.00768e6			−0.568812
$122$		−	2.20087e6i		−	1.21203i
$123$	−2.59896e6			−1.39664
$124$		0			0
$125$			1.31931e6i			0.675486i
$126$	1.39490e6	−	3.31593e6i	0.697321	−	1.65766i
$127$	3.32472e6			1.62310			0.811548	−	0.584286i	$-0.198625\pi$
$127$	3.32472e6			1.62310			0.811548	+	0.584286i	$0.198625\pi$
$128$	−2.09715e6			−1.00000
$129$		−	1.41904e6i		−	0.661035i
$130$	−799680.			−0.363987
$131$		−	3.13567e6i		−	1.39482i	−0.716674	−	0.697408i	$-0.754336\pi$
$131$		−	3.13567e6i		−	1.39482i	0.716674	−	0.697408i	$-0.245664\pi$
$132$		0			0
$133$	−985320.	−	414492.i	−0.418815	−	0.176182i
$134$	−3.96194e6			−1.64662
$135$	−1.18728e6			−0.482561
$136$			3.05252e6i			1.21351i
$137$	2.12927e6			0.828072			0.414036	−	0.910260i	$-0.364119\pi$
$137$	2.12927e6			0.828072			0.414036	+	0.910260i	$0.364119\pi$
$138$			1.71199e6i			0.651423i
$139$			1.68421e6i			0.627121i	0.949568	+	0.313561i	$0.101522\pi$
$139$			1.68421e6i			0.627121i	−0.949568	+	0.313561i	$0.898478\pi$
$140$		0			0
$141$	3.27216e6			1.16729
$142$	1.47525e6			0.515229
$143$		−	1.93429e6i		−	0.661477i
$144$	5.36986e6			1.79835
$145$			503424.i			0.165132i
$146$		−	487797.i		−	0.156740i
$147$	−3.79848e6	+	3.71588e6i	−1.19580	+	1.16980i
$148$		0			0
$149$	−2.59573e6			−0.784696			−0.392348	−	0.919817i	$-0.628337\pi$
$149$	−2.59573e6			−0.784696			−0.392348	+	0.919817i	$0.628337\pi$
$150$			4.90868e6i			1.45442i
$151$	−1.68557e6			−0.489570			−0.244785	−	0.969577i	$-0.578717\pi$
$151$	−1.68557e6			−0.489570			−0.244785	+	0.969577i	$0.578717\pi$
$152$		−	1.59564e6i		−	0.454363i
$153$		−	7.81613e6i		−	2.18231i
$154$	−929936.	+	2.21062e6i	−0.254619	+	0.605275i
$155$	−1.24032e6			−0.333072
$156$		0			0
$157$		−	3.67641e6i		−	0.950002i	−0.879985	−	0.475001i	$-0.842448\pi$
$157$		−	3.67641e6i		−	0.950002i	0.879985	−	0.475001i	$-0.157552\pi$
$158$	4.27947e6			1.08497
$159$			3.45098e6i			0.858521i
$160$		0			0
$161$	630154.	−	1.49799e6i	0.150997	−	0.358947i
$162$	−1.85249e6			−0.435723
$163$	1.88191e6			0.434547			0.217274	−	0.976111i	$-0.430284\pi$
$163$	1.88191e6			0.434547			0.217274	+	0.976111i	$0.430284\pi$
$164$		0			0
$165$	1.78296e6			0.396908
$166$		−	5.71878e6i		−	1.25020i
$167$			3.15595e6i			0.677612i	0.940856	+	0.338806i	$0.110023\pi$
$167$			3.15595e6i			0.677612i	−0.940856	+	0.338806i	$0.889977\pi$
$168$	−7.31136e6	−	3.07565e6i	−1.54195	−	0.648648i
$169$	−71231.0			−0.0147574
$170$	2.15424e6			0.438478
$171$			4.08570e6i			0.817106i
$172$		0			0
$173$			2.29477e6i			0.443201i	0.975138	+	0.221600i	$0.0711280\pi$
$173$			2.29477e6i			0.443201i	−0.975138	+	0.221600i	$0.928872\pi$
$174$			4.02739e6i			0.764498i
$175$	1.80680e6	−	4.29509e6i	0.337130	−	0.801417i
$176$	−3.57990e6			−0.656649
$177$	−5.11428e6			−0.922284
$178$		−	5.03623e6i		−	0.892988i
$179$	3.51846e6			0.613470			0.306735	−	0.951795i	$-0.400763\pi$
$179$	3.51846e6			0.613470			0.306735	+	0.951795i	$0.400763\pi$
$180$		0			0
$181$			7.48267e6i			1.26189i	0.775829	+	0.630944i	$0.217332\pi$
$181$			7.48267e6i			1.26189i	−0.775829	+	0.630944i	$0.782668\pi$
$182$	5.59776e6	+	2.35479e6i	0.928539	+	0.390606i
$183$	1.24256e7			2.02752
$184$	2.42586e6			0.389414
$185$			135589.i			0.0214146i
$186$	−9.92256e6			−1.54200
$187$			5.21075e6i			0.796848i
$188$		0			0
$189$	8.31096e6	+	3.49615e6i	1.23102	+	0.517850i
$190$	−1.12608e6			−0.164176
$191$	−7.20028e6			−1.03335			−0.516677	−	0.856180i	$-0.672831\pi$
$191$	−7.20028e6			−1.03335			−0.516677	+	0.856180i	$0.672831\pi$
$192$		−	1.18401e7i		−	1.67283i
$193$	−1.30889e7			−1.82067			−0.910335	−	0.413872i	$-0.864176\pi$
$193$	−1.30889e7			−1.82067			−0.910335	+	0.413872i	$0.864176\pi$
$194$			6.51552e6i			0.892368i
$195$		−	4.51483e6i		−	0.608888i
$196$		0			0
$197$	−9.17476e6			−1.20004			−0.600020	−	0.799985i	$-0.704841\pi$
$197$	−9.17476e6			−1.20004			−0.600020	+	0.799985i	$0.704841\pi$
$198$	9.16651e6			1.18089
$199$			6.78769e6i			0.861317i	0.902515	+	0.430658i	$0.141719\pi$
$199$			6.78769e6i			0.861317i	−0.902515	+	0.430658i	$0.858281\pi$
$200$	6.95552e6			0.869440
$201$		−	2.23683e7i		−	2.75451i
$202$		−	1.56156e7i		−	1.89455i
$203$	1.48242e6	−	3.52397e6i	0.177208	−	0.421254i
$204$		0			0
$205$	2.59896e6			0.301674
$206$			1.35795e7i			1.55340i
$207$	−6.21152e6			−0.700304
$208$			9.06507e6i			1.00735i
$209$		−	2.72380e6i		−	0.298357i
$210$	−2.17056e6	+	5.15980e6i	−0.234376	+	0.557154i
$211$	8.40084e6			0.894284			0.447142	−	0.894463i	$-0.352442\pi$
$211$	8.40084e6			0.894284			0.447142	+	0.894463i	$0.352442\pi$
$212$		0			0
$213$			8.32895e6i			0.861889i
$214$	−1.29282e7			−1.31916
$215$			1.41904e6i			0.142784i
$216$			1.34589e7i			1.33551i
$217$	8.68224e6	+	3.65233e6i	0.849675	+	0.357430i
$218$	−1.59381e6			−0.153839
$219$	2.75400e6			0.262199
$220$		0			0
$221$	1.31947e7			1.22243
$222$			1.08472e6i			0.0991418i
$223$		−	4.90434e6i		−	0.442248i	−0.975246	−	0.221124i	$-0.929027\pi$
$223$		−	4.90434e6i		−	0.442248i	0.975246	−	0.221124i	$-0.0709726\pi$
$224$		0			0
$225$	−1.78099e7			−1.56356
$226$	1.44610e7			1.25277
$227$		−	1.32183e7i		−	1.13005i	−0.825075	−	0.565023i	$-0.808867\pi$
$227$		−	1.32183e7i		−	1.13005i	0.825075	−	0.565023i	$-0.191133\pi$
$228$		0			0
$229$			338974.i			0.0282266i	0.999900	+	0.0141133i	$0.00449256\pi$
$229$			338974.i			0.0282266i	−0.999900	+	0.0141133i	$0.995507\pi$
$230$		−	1.71199e6i		−	0.140707i
$231$	−1.24807e7	−	5.25023e6i	−1.01252	−	0.425934i
$232$	5.70675e6			0.457009
$233$	4.84146e6			0.382744			0.191372	−	0.981518i	$-0.438706\pi$
$233$	4.84146e6			0.382744			0.191372	+	0.981518i	$0.438706\pi$
$234$		−	2.32115e7i		−	1.81157i
$235$	−3.27216e6			−0.252134
$236$		0			0
$237$			2.41610e7i			1.81497i
$238$	−1.50797e7	−	6.34352e6i	−1.11857	−	0.470543i
$239$	−1.37297e7			−1.00570			−0.502850	−	0.864374i	$-0.667715\pi$
$239$	−1.37297e7			−1.00570			−0.502850	+	0.864374i	$0.667715\pi$
$240$	−8.35584e6			−0.604444
$241$		−	3.66913e6i		−	0.262127i	−0.991374	−	0.131064i	$-0.958161\pi$
$241$		−	3.66913e6i		−	0.262127i	0.991374	−	0.131064i	$-0.0418392\pi$
$242$	8.06148e6			0.568812
$243$			8.70433e6i			0.606619i
$244$		0			0
$245$	3.79848e6	−	3.71588e6i	0.258292	−	0.252676i
$246$	2.07917e7			1.39664
$247$	−6.89724e6			−0.457704
$248$			1.40601e7i			0.921793i
$249$	3.22871e7			2.09137
$250$		−	1.05545e7i		−	0.675486i
$251$		−	1.57289e7i		−	0.994664i	−0.867560	−	0.497332i	$-0.834313\pi$
$251$		−	1.57289e7i		−	0.994664i	0.867560	−	0.497332i	$-0.165687\pi$
$252$		0			0
$253$	4.14101e6			0.255708
$254$	−2.65978e7			−1.62310
$255$			1.21624e7i			0.733498i
$256$		0			0
$257$			7.54531e6i			0.444506i	0.974989	+	0.222253i	$0.0713411\pi$
$257$			7.54531e6i			0.444506i	−0.974989	+	0.222253i	$0.928659\pi$
$258$			1.13523e7i			0.661035i
$259$	399266.	−	949126.i	0.0229807	−	0.0546292i
$260$		0			0
$261$	−1.46124e7			−0.821864
$262$			2.50854e7i			1.39482i
$263$	−1.32059e7			−0.725942			−0.362971	−	0.931800i	$-0.618238\pi$
$263$	−1.32059e7			−0.725942			−0.362971	+	0.931800i	$0.618238\pi$
$264$		−	2.02114e7i		−	1.09846i
$265$		−	3.45098e6i		−	0.185441i
$266$	7.88256e6	+	3.31593e6i	0.418815	+	0.176182i
$267$	2.84335e7			1.49382
$268$		0			0
$269$		−	1.59600e7i		−	0.819930i	−0.912101	−	0.409965i	$-0.865541\pi$
$269$		−	1.59600e7i		−	0.819930i	0.912101	−	0.409965i	$-0.134459\pi$
$270$	9.49824e6			0.482561
$271$			2.48446e7i			1.24831i	0.781299	+	0.624157i	$0.214557\pi$
$271$			2.48446e7i			1.24831i	−0.781299	+	0.624157i	$0.785443\pi$
$272$		−	2.44202e7i		−	1.21351i
$273$	−1.32947e7	+	3.16038e7i	−0.653416	+	1.55329i
$274$	−1.70341e7			−0.828072
$275$	1.18733e7			0.570917
$276$		0			0
$277$	1.60013e7			0.752863			0.376432	−	0.926444i	$-0.377151\pi$
$277$	1.60013e7			0.752863			0.376432	+	0.926444i	$0.377151\pi$
$278$		−	1.34737e7i		−	0.627121i
$279$		−	3.60016e7i		−	1.65771i
$280$	7.31136e6	+	3.07565e6i	0.333061	+	0.140108i
$281$	−603566.			−0.0272023			−0.0136012	−	0.999908i	$-0.504330\pi$
$281$	−603566.			−0.0272023			−0.0136012	+	0.999908i	$0.504330\pi$
$282$	−2.61773e7			−1.16729
$283$		−	2.22195e7i		−	0.980334i	−0.871629	−	0.490167i	$-0.836936\pi$
$283$		−	2.22195e7i		−	0.980334i	0.871629	−	0.490167i	$-0.163064\pi$
$284$		0			0
$285$		−	6.35762e6i		−	0.274637i
$286$			1.54744e7i			0.661477i
$287$	−1.81927e7	−	7.65308e6i	−0.769577	−	0.323736i
$288$		0			0
$289$	−1.14074e7			−0.472599
$290$		−	4.02739e6i		−	0.165132i
$291$	−3.67853e7			−1.49278
$292$		0			0
$293$			4.28134e7i			1.70207i	0.525110	+	0.851034i	$0.324024\pi$
$293$			4.28134e7i			1.70207i	−0.525110	+	0.851034i	$0.675976\pi$
$294$	3.03878e7	−	2.97271e7i	1.19580	−	1.16980i
$295$	5.11428e6			0.199213
$296$	1.53702e6			0.0592660
$297$			2.29747e7i			0.876961i
$298$	2.07659e7			0.784696
$299$		−	1.04859e7i		−	0.392277i
$300$		0			0
$301$	4.17859e6	−	9.93326e6i	0.153225	−	0.364244i
$302$	1.34845e7			0.489570
$303$	8.81627e7			3.16925
$304$			1.27651e7i			0.454363i
$305$	−1.24256e7			−0.437945
$306$			6.25290e7i			2.18231i
$307$			4.02152e7i			1.38987i	0.719072	+	0.694936i	$0.244567\pi$
$307$			4.02152e7i			1.38987i	−0.719072	+	0.694936i	$0.755433\pi$
$308$		0			0
$309$	−7.66673e7			−2.59857
$310$	9.92256e6			0.333072
$311$		−	1.47381e7i		−	0.489958i	−0.969528	−	0.244979i	$-0.921219\pi$
$311$		−	1.47381e7i		−	0.489958i	0.969528	−	0.244979i	$-0.0787811\pi$
$312$	−5.11795e7			−1.68513
$313$		−	4.19490e7i		−	1.36801i	−0.729479	−	0.684004i	$-0.760237\pi$
$313$		−	4.19490e7i		−	1.36801i	0.729479	−	0.684004i	$-0.239763\pi$
$314$			2.94112e7i			0.950002i
$315$	−1.87211e7	−	7.87534e6i	−0.598962	−	0.251964i
$316$		0			0
$317$	4.30922e7			1.35276			0.676380	−	0.736553i	$-0.263548\pi$
$317$	4.30922e7			1.35276			0.676380	+	0.736553i	$0.263548\pi$
$318$		−	2.76078e7i		−	0.858521i
$319$	9.74160e6			0.300095
$320$			1.18401e7i			0.361331i
$321$		−	7.29900e7i		−	2.20673i
$322$	−5.04123e6	+	1.19839e7i	−0.150997	+	0.358947i
$323$	1.85803e7			0.551373
$324$		0			0
$325$		−	3.00657e7i		−	0.875832i
$326$	−1.50553e7			−0.434547
$327$		−	8.99831e6i		−	0.257346i
$328$		−	2.94615e7i		−	0.834897i
$329$	2.29051e7	+	9.63543e6i	0.643198	+	0.270572i
$330$	−1.42637e7			−0.396908
$331$	−5.32204e7			−1.46755			−0.733777	−	0.679390i	$-0.762244\pi$
$331$	−5.32204e7			−1.46755			−0.733777	+	0.679390i	$0.762244\pi$
$332$		0			0
$333$	−3.93562e6			−0.106581
$334$		−	2.52476e7i		−	0.677612i
$335$			2.23683e7i			0.594974i
$336$	5.84909e7	+	2.46052e7i	1.54195	+	0.648648i
$337$	2.34579e6			0.0612913			0.0306456	−	0.999530i	$-0.490244\pi$
$337$	2.34579e6			0.0612913			0.0306456	+	0.999530i	$0.490244\pi$
$338$	569848.			0.0147574
$339$			8.16437e7i			2.09567i
$340$		0			0
$341$			2.40010e7i			0.605295i
$342$		−	3.26856e7i		−	0.817106i
$343$	−3.75314e7	+	1.48259e7i	−0.930063	+	0.367400i
$344$	1.60860e7			0.395160
$345$	9.66552e6			0.235379
$346$		−	1.83581e7i		−	0.443201i
$347$	−4.80596e7			−1.15025			−0.575124	−	0.818066i	$-0.695046\pi$
$347$	−4.80596e7			−1.15025			−0.575124	+	0.818066i	$0.695046\pi$
$348$		0			0
$349$		−	1.00499e7i		−	0.236421i	−0.992989	−	0.118211i	$-0.962284\pi$
$349$		−	1.00499e7i		−	0.236421i	0.992989	−	0.118211i	$-0.0377158\pi$
$350$	−1.44544e7	+	3.43608e7i	−0.337130	+	0.801417i
$351$	5.81767e7			1.34533
$352$		0			0
$353$			7.65216e7i			1.73964i	0.493368	+	0.869821i	$0.335766\pi$
$353$			7.65216e7i			1.73964i	−0.493368	+	0.869821i	$0.664234\pi$
$354$	4.09142e7			0.922284
$355$		−	8.32895e6i		−	0.186168i
$356$		0			0
$357$	3.58142e7	−	8.51368e7i	0.787138	−	1.87117i
$358$	−2.81477e7			−0.613470
$359$	8.39735e6			0.181493			0.0907463	−	0.995874i	$-0.471075\pi$
$359$	8.39735e6			0.181493			0.0907463	+	0.995874i	$0.471075\pi$
$360$		−	3.03171e7i		−	0.649801i
$361$	3.73334e7			0.793554
$362$		−	5.98613e7i		−	1.26189i
$363$			4.55135e7i			0.951525i
$364$		0			0
$365$	−2.75400e6			−0.0566351
$366$	−9.94051e7			−2.02752
$367$			3.82776e6i			0.0774366i	0.999250	+	0.0387183i	$0.0123275\pi$
$367$			3.82776e6i			0.0774366i	−0.999250	+	0.0387183i	$0.987672\pi$
$368$	−1.94068e7			−0.389414
$369$			7.54375e7i			1.50144i
$370$		−	1.08472e6i		−	0.0214146i
$371$	−1.01620e7	+	2.41569e7i	−0.199002	+	0.473063i
$372$		0			0
$373$	−4.93836e7			−0.951604			−0.475802	−	0.879552i	$-0.657842\pi$
$373$	−4.93836e7			−0.951604			−0.475802	+	0.879552i	$0.657842\pi$
$374$		−	4.16860e7i		−	0.796848i
$375$	5.95884e7			1.12997
$376$			3.70928e7i			0.697792i
$377$		−	2.46678e7i		−	0.460369i
$378$	−6.64877e7	−	2.79692e7i	−1.23102	−	0.517850i
$379$	3.74561e7			0.688026			0.344013	−	0.938965i	$-0.388214\pi$
$379$	3.74561e7			0.688026			0.344013	+	0.938965i	$0.388214\pi$
$380$		0			0
$381$		−	1.50166e8i		−	2.71516i
$382$	5.76022e7			1.03335
$383$		−	5.01003e7i		−	0.891752i	−0.895095	−	0.445876i	$-0.852892\pi$
$383$		−	5.01003e7i		−	0.891752i	0.895095	−	0.445876i	$-0.147108\pi$
$384$			9.47207e7i			1.67283i
$385$	1.24807e7	+	5.25023e6i	0.218704	+	0.0920017i
$386$	1.04711e8			1.82067
$387$	−4.11890e7			−0.710638
$388$		0			0
$389$	224986.			0.00382214			0.00191107	−	0.999998i	$-0.499392\pi$
$389$	224986.			0.00382214			0.00191107	+	0.999998i	$0.499392\pi$
$390$			3.61186e7i			0.608888i
$391$			2.82478e7i			0.472557i
$392$	−4.21228e7	−	4.30591e7i	−0.699292	−	0.714836i
$393$	−1.41627e8			−2.33329
$394$	7.33981e7			1.20004
$395$		−	2.41610e7i		−	0.392034i
$396$		0			0
$397$		−	871937.i		−	0.0139352i	−0.999976	−	0.00696760i	$-0.997782\pi$
$397$		−	871937.i		−	0.0139352i	0.999976	−	0.00696760i	$-0.00221787\pi$
$398$		−	5.43015e7i		−	0.861317i
$399$	−1.87211e7	+	4.45033e7i	−0.294722	+	0.700606i
$400$	−5.56442e7			−0.869440
$401$	1.44909e7			0.224730			0.112365	−	0.993667i	$-0.464157\pi$
$401$	1.44909e7			0.224730			0.112365	+	0.993667i	$0.464157\pi$
$402$			1.78946e8i			2.75451i
$403$	6.07757e7			0.928570
$404$		0			0
$405$			1.04588e7i			0.157440i
$406$	−1.18593e7	+	2.81918e7i	−0.177208	+	0.421254i
$407$	2.62375e6			0.0389170
$408$	1.37871e8			2.02999
$409$			1.04303e8i			1.52450i	0.647284	+	0.762249i	$0.275905\pi$
$409$			1.04303e8i			1.52450i	−0.647284	+	0.762249i	$0.724095\pi$
$410$	−2.07917e7			−0.301674
$411$		−	9.61712e7i		−	1.38522i
$412$		0			0
$413$	−3.58000e7	−	1.50599e7i	−0.508197	−	0.213782i
$414$	4.96921e7			0.700304
$415$	−3.22871e7			−0.451736
$416$		0			0
$417$	7.60696e7			1.04907
$418$			2.17904e7i			0.298357i
$419$		−	8.22075e7i		−	1.11756i	−0.829317	−	0.558778i	$-0.811270\pi$
$419$		−	8.22075e7i		−	1.11756i	0.829317	−	0.558778i	$-0.188730\pi$
$420$		0			0
$421$	−1.33780e7			−0.179285			−0.0896427	−	0.995974i	$-0.528573\pi$
$421$	−1.33780e7			−0.179285			−0.0896427	+	0.995974i	$0.528573\pi$
$422$	−6.72067e7			−0.894284
$423$		−	9.49778e7i		−	1.25488i
$424$	−3.91199e7			−0.513216
$425$			8.09932e7i			1.05507i
$426$		−	6.66316e7i		−	0.861889i
$427$	8.69795e7	+	3.65894e7i	1.11721	+	0.469972i
$428$		0			0
$429$	−8.73650e7			−1.10654
$430$		−	1.13523e7i		−	0.142784i
$431$	−1.34244e8			−1.67673			−0.838367	−	0.545106i	$-0.816490\pi$
$431$	−1.34244e8			−1.67673			−0.838367	+	0.545106i	$0.816490\pi$
$432$		−	1.07671e8i		−	1.33551i
$433$		−	1.03230e8i		−	1.27158i	−0.771863	−	0.635789i	$-0.780675\pi$
$433$		−	1.03230e8i		−	1.27158i	0.771863	−	0.635789i	$-0.219325\pi$
$434$	−6.94579e7	−	2.92187e7i	−0.849675	−	0.357430i
$435$	2.27378e7			0.276237
$436$		0			0
$437$		−	1.47659e7i		−	0.176935i
$438$	−2.20320e7			−0.262199
$439$			2.65816e7i			0.314186i	0.987584	+	0.157093i	$0.0502123\pi$
$439$			2.65816e7i			0.314186i	−0.987584	+	0.157093i	$0.949788\pi$
$440$			2.02114e7i			0.237268i
$441$	1.07857e8	+	1.10255e8i	1.25757	+	1.28553i
$442$	−1.05558e8			−1.22243
$443$	1.31972e8			1.51799			0.758996	−	0.651096i	$-0.225690\pi$
$443$	1.31972e8			1.51799			0.758996	+	0.651096i	$0.225690\pi$
$444$		0			0
$445$	−2.84335e7			−0.322664
$446$			3.92348e7i			0.442248i
$447$			1.17240e8i			1.31266i
$448$	3.48652e7	−	8.28806e7i	0.387755	−	0.921762i
$449$	1.47766e8			1.63244			0.816218	−	0.577743i	$-0.196067\pi$
$449$	1.47766e8			1.63244			0.816218	+	0.577743i	$0.196067\pi$
$450$	1.42479e8			1.56356
$451$		−	5.02917e7i		−	0.548234i
$452$		0			0
$453$			7.61309e7i			0.818967i
$454$			1.05746e8i			1.13005i
$455$	1.32947e7	−	3.16038e7i	0.141138	−	0.335510i
$456$	−7.20691e7			−0.760072
$457$	−8.22868e7			−0.862147			−0.431074	−	0.902317i	$-0.641865\pi$
$457$	−8.22868e7			−0.862147			−0.431074	+	0.902317i	$0.641865\pi$
$458$		−	2.71179e6i		−	0.0282266i
$459$	−1.56721e8			−1.62065
$460$		0			0
$461$			1.31884e8i			1.34614i	0.739580	+	0.673068i	$0.235024\pi$
$461$			1.31884e8i			1.34614i	−0.739580	+	0.673068i	$0.764976\pi$
$462$	9.98458e7	+	4.20018e7i	1.01252	+	0.425934i
$463$	1.39927e6			0.0140981			0.00704904	−	0.999975i	$-0.497756\pi$
$463$	1.39927e6			0.0140981			0.00704904	+	0.999975i	$0.497756\pi$
$464$	−4.56540e7			−0.457009
$465$			5.60207e7i			0.557173i
$466$	−3.87317e7			−0.382744
$467$			1.81321e7i			0.178032i	0.996030	+	0.0890158i	$0.0283722\pi$
$467$			1.81321e7i			0.178032i	−0.996030	+	0.0890158i	$0.971628\pi$
$468$		0			0
$469$	6.58672e7	−	1.56578e8i	0.638485	−	1.51779i
$470$	2.61773e7			0.252134
$471$	−1.66050e8			−1.58919
$472$		−	5.79748e7i		−	0.551332i
$473$	2.74593e7			0.259482
$474$		−	1.93288e8i		−	1.81497i
$475$		−	4.23374e7i		−	0.395042i
$476$		0			0
$477$	1.00168e8			0.922943
$478$	1.09838e8			1.00570
$479$			2.89375e7i			0.263303i	0.991296	+	0.131651i	$0.0420279\pi$
$479$			2.89375e7i			0.263303i	−0.991296	+	0.131651i	$0.957972\pi$
$480$		0			0
$481$		−	6.64388e6i		−	0.0597017i
$482$			2.93531e7i			0.262127i
$483$	−6.76586e7	−	2.84618e7i	−0.600457	−	0.252592i
$484$		0			0
$485$	3.67853e7			0.322440
$486$		−	6.96346e7i		−	0.606619i
$487$	−9.47515e7			−0.820350			−0.410175	−	0.912007i	$-0.634532\pi$
$487$	−9.47515e7			−0.820350			−0.410175	+	0.912007i	$0.634532\pi$
$488$			1.40855e8i			1.21203i
$489$		−	8.49992e7i		−	0.726923i
$490$	−3.03878e7	+	2.97271e7i	−0.258292	+	0.252676i
$491$	−2.58834e7			−0.218663			−0.109332	−	0.994005i	$-0.534871\pi$
$491$	−2.58834e7			−0.218663			−0.109332	+	0.994005i	$0.534871\pi$
$492$		0			0
$493$			6.64520e7i			0.554584i
$494$	5.51779e7			0.457704
$495$		−	5.17522e7i		−	0.426691i
$496$		−	1.12481e8i		−	0.921793i
$497$	−2.45260e7	+	5.83026e7i	−0.199783	+	0.474918i
$498$	−2.58297e8			−2.09137
$499$	1.56023e8			1.25571			0.627853	−	0.778332i	$-0.283934\pi$
$499$	1.56023e8			1.25571			0.627853	+	0.778332i	$0.283934\pi$
$500$		0			0
$501$	1.42543e8			1.13353
$502$			1.25831e8i			0.994664i
$503$		−	1.11476e8i		−	0.875950i	−0.898987	−	0.437975i	$-0.855696\pi$
$503$		−	1.11476e8i		−	0.875950i	0.898987	−	0.437975i	$-0.144304\pi$
$504$	−8.92739e7	+	2.12220e8i	−0.697321	+	1.65766i
$505$	−8.81627e7			−0.684559
$506$	−3.31281e7			−0.255708
$507$			3.21724e6i			0.0246865i
$508$		0			0
$509$		−	7.45421e7i		−	0.565260i	−0.959229	−	0.282630i	$-0.908793\pi$
$509$		−	7.45421e7i		−	0.565260i	0.959229	−	0.282630i	$-0.0912068\pi$
$510$		−	9.72992e7i		−	0.733498i
$511$	1.92780e7	+	8.10962e6i	0.144477	+	0.0607768i
$512$	1.34218e8			1.00000
$513$	8.19223e7			0.606806
$514$		−	6.03625e7i		−	0.444506i
$515$	7.66673e7			0.561291
$516$		0			0
$517$			6.33185e7i			0.458204i
$518$	−3.19413e6	+	7.59301e6i	−0.0229807	+	0.0546292i
$519$	1.03646e8			0.741398
$520$	5.11795e7			0.363987
$521$			1.96232e8i			1.38758i	0.720179	+	0.693789i	$0.244060\pi$
$521$			1.96232e8i			1.38758i	−0.720179	+	0.693789i	$0.755940\pi$
$522$	1.16899e8			0.821864
$523$		−	4.62080e7i		−	0.323007i	−0.986872	−	0.161504i	$-0.948366\pi$
$523$		−	4.62080e7i		−	0.323007i	0.986872	−	0.161504i	$-0.0516344\pi$
$524$		0			0
$525$	−1.93994e8	−	8.16068e7i	−1.34063	−	0.563960i
$526$	1.05648e8			0.725942
$527$	−1.63722e8			−1.11860
$528$			1.61691e8i			1.09846i
$529$	−1.25587e8			−0.848357
$530$			2.76078e7i			0.185441i
$531$			1.48447e8i			0.991490i
$532$		0			0
$533$	−1.27349e8			−0.841035
$534$	−2.27468e8			−1.49382
$535$			7.29900e7i			0.476653i
$536$	2.53564e8			1.64662
$537$		−	1.58916e8i		−	1.02623i
$538$			1.27680e8i			0.819930i
$539$	−7.19049e7	−	7.35032e7i	−0.459189	−	0.469397i
$540$		0			0
$541$	−7.52906e7			−0.475498			−0.237749	−	0.971327i	$-0.576410\pi$
$541$	−7.52906e7			−0.475498			−0.237749	+	0.971327i	$0.576410\pi$
$542$		−	1.98757e8i		−	1.24831i
$543$	3.37965e8			2.11092
$544$		0			0
$545$			8.99831e6i			0.0555868i
$546$	1.06357e8	−	2.52830e8i	0.653416	−	1.55329i
$547$	7.26760e7			0.444047			0.222023	−	0.975041i	$-0.428734\pi$
$547$	7.26760e7			0.444047			0.222023	+	0.975041i	$0.428734\pi$
$548$		0			0
$549$		−	3.60667e8i		−	2.17966i
$550$	−9.49863e7			−0.570917
$551$		−	3.47363e7i		−	0.207648i
$552$		−	1.09567e8i		−	0.651423i
$553$	−7.11462e7	+	1.69127e8i	−0.420704	+	1.00009i
$554$	−1.28010e8			−0.752863
$555$	6.12408e6			0.0358230
$556$		0			0
$557$	−3.10741e8			−1.79818			−0.899090	−	0.437765i	$-0.855770\pi$
$557$	−3.10741e8			−1.79818			−0.899090	+	0.437765i	$0.855770\pi$
$558$			2.88013e8i			1.65771i
$559$		−	6.95328e7i		−	0.398065i
$560$	−5.84909e7	−	2.46052e7i	−0.333061	−	0.140108i
$561$	2.35351e8			1.33299
$562$	4.82853e6			0.0272023
$563$		−	5.66378e7i		−	0.317381i	−0.987328	−	0.158690i	$-0.949273\pi$
$563$		−	5.66378e7i		−	0.317381i	0.987328	−	0.158690i	$-0.0507272\pi$
$564$		0			0
$565$		−	8.16437e7i		−	0.452665i
$566$			1.77756e8i			0.980334i
$567$	3.07976e7	−	7.32114e7i	0.168954	−	0.401633i
$568$	−9.44159e7			−0.515229
$569$	5.17304e7			0.280808			0.140404	−	0.990094i	$-0.455160\pi$
$569$	5.17304e7			0.280808			0.140404	+	0.990094i	$0.455160\pi$
$570$			5.08609e7i			0.274637i
$571$	8.68765e7			0.466653			0.233326	−	0.972398i	$-0.425039\pi$
$571$	8.68765e7			0.466653			0.233326	+	0.972398i	$0.425039\pi$
$572$		0			0
$573$			3.25210e8i			1.72862i
$574$	1.45542e8	+	6.12246e7i	0.769577	+	0.323736i
$575$	6.43657e7			0.338572
$576$	−3.43671e8			−1.79835
$577$		−	5.89865e7i		−	0.307062i	−0.988144	−	0.153531i	$-0.950936\pi$
$577$		−	5.89865e7i		−	0.307062i	0.988144	−	0.153531i	$-0.0490644\pi$
$578$	9.12591e7			0.472599
$579$			5.91178e8i			3.04567i
$580$		0			0
$581$	2.26010e8	+	9.50748e7i	1.15239	+	0.484771i
$582$	2.94282e8			1.49278
$583$	−6.67788e7			−0.337003
$584$			3.12190e7i			0.156740i
$585$	−1.31048e8			−0.654578
$586$		−	3.42507e8i		−	1.70207i
$587$		−	3.10848e8i		−	1.53686i	−0.639934	−	0.768430i	$-0.721038\pi$
$587$		−	3.10848e8i		−	1.53686i	0.639934	−	0.768430i	$-0.278962\pi$
$588$		0			0
$589$	8.55821e7			0.418829
$590$	−4.09142e7			−0.199213
$591$			4.14390e8i			2.00746i
$592$	−1.22962e7			−0.0592660
$593$		−	3.46714e8i		−	1.66268i	−0.555766	−	0.831339i	$-0.687575\pi$
$593$		−	3.46714e8i		−	1.66268i	0.555766	−	0.831339i	$-0.312425\pi$
$594$		−	1.83797e8i		−	0.876961i
$595$	−3.58142e7	+	8.51368e7i	−0.170022	+	0.404172i
$596$		0			0
$597$	3.06575e8			1.44083
$598$			8.38873e7i			0.392277i
$599$	9.47771e7			0.440984			0.220492	−	0.975389i	$-0.429234\pi$
$599$	9.47771e7			0.440984			0.220492	+	0.975389i	$0.429234\pi$
$600$		−	3.14156e8i		−	1.45442i
$601$		−	2.04951e8i		−	0.944119i	−0.881567	−	0.472060i	$-0.843511\pi$
$601$		−	2.04951e8i		−	0.944119i	0.881567	−	0.472060i	$-0.156489\pi$
$602$	−3.34288e7	+	7.94661e7i	−0.153225	+	0.364244i
$603$	−6.49262e8			−2.96120
$604$		0			0
$605$		−	4.55135e7i		−	0.205529i
$606$	−7.05301e8			−3.16925
$607$			3.28634e8i			1.46942i	0.678379	+	0.734712i	$0.262683\pi$
$607$			3.28634e8i			1.46942i	−0.678379	+	0.734712i	$0.737317\pi$
$608$		0			0
$609$	−1.59165e8	−	6.69554e7i	−0.704686	−	0.296438i
$610$	9.94051e7			0.437945
$611$	1.60336e8			0.702922
$612$		0			0
$613$	2.67967e8			1.16332			0.581660	−	0.813432i	$-0.302403\pi$
$613$	2.67967e8			1.16332			0.581660	+	0.813432i	$0.302403\pi$
$614$		−	3.21721e8i		−	1.38987i
$615$		−	1.17386e8i		−	0.504649i
$616$	5.95159e7	−	1.41480e8i	0.254619	−	0.605275i
$617$	−3.88909e8			−1.65574			−0.827870	−	0.560921i	$-0.810447\pi$
$617$	−3.88909e8			−1.65574			−0.827870	+	0.560921i	$0.810447\pi$
$618$	6.13338e8			2.59857
$619$		−	6.30894e7i		−	0.266002i	−0.991116	−	0.133001i	$-0.957539\pi$
$619$		−	6.30894e7i		−	0.266002i	0.991116	−	0.133001i	$-0.0424613\pi$
$620$		0			0
$621$			1.24547e8i			0.520066i
$622$			1.17904e8i			0.489958i
$623$	1.99035e8	+	8.37273e7i	0.823123	+	0.346261i
$624$	4.09436e8			1.68513
$625$	1.52677e8			0.625366
$626$			3.35592e8i			1.36801i
$627$	−1.23024e8			−0.499101
$628$		0			0
$629$			1.78978e7i			0.0719197i
$630$	1.49769e8	+	6.30027e7i	0.598962	+	0.251964i
$631$	−1.30827e8			−0.520725			−0.260363	−	0.965511i	$-0.583842\pi$
$631$	−1.30827e8			−0.520725			−0.260363	+	0.965511i	$0.583842\pi$
$632$	−2.73886e8			−1.08497
$633$		−	3.79435e8i		−	1.49598i
$634$	−3.44738e8			−1.35276
$635$			1.50166e8i			0.586475i
$636$		0			0
$637$	−1.86126e8	+	1.82078e8i	−0.720091	+	0.704433i
$638$	−7.79328e7			−0.300095
$639$	2.41756e8			0.926563
$640$		−	9.47207e7i		−	0.361331i
$641$	−7.17536e7			−0.272439			−0.136220	−	0.990679i	$-0.543495\pi$
$641$	−7.17536e7			−0.272439			−0.136220	+	0.990679i	$0.543495\pi$
$642$			5.83920e8i			2.20673i
$643$			2.56068e8i			0.963214i	0.876387	+	0.481607i	$0.159947\pi$
$643$			2.56068e8i			0.963214i	−0.876387	+	0.481607i	$0.840053\pi$
$644$		0			0
$645$	6.40927e7			0.238852
$646$	−1.48643e8			−0.551373
$647$		−	4.93122e8i		−	1.82071i	−0.413827	−	0.910356i	$-0.635808\pi$
$647$		−	4.93122e8i		−	1.82071i	0.413827	−	0.910356i	$-0.364192\pi$
$648$	1.18559e8			0.435723
$649$		−	9.89648e7i		−	0.362032i
$650$			2.40525e8i			0.875832i
$651$	1.64963e8	−	3.92145e8i	0.597919	−	1.42136i
$652$		0			0
$653$	1.55036e8			0.556793			0.278397	−	0.960466i	$-0.410197\pi$
$653$	1.55036e8			0.556793			0.278397	+	0.960466i	$0.410197\pi$
$654$			7.19865e7i			0.257346i
$655$	1.41627e8			0.503990
$656$			2.35692e8i			0.834897i
$657$		−	7.99377e7i		−	0.281874i
$658$	−1.83241e8	−	7.70834e7i	−0.643198	−	0.270572i
$659$	−3.01683e8			−1.05413			−0.527065	−	0.849825i	$-0.676707\pi$
$659$	−3.01683e8			−1.05413			−0.527065	+	0.849825i	$0.676707\pi$
$660$		0			0
$661$			1.80227e8i			0.624044i	0.950075	+	0.312022i	$0.101006\pi$
$661$			1.80227e8i			0.624044i	−0.950075	+	0.312022i	$0.898994\pi$
$662$	4.25763e8			1.46755
$663$		−	5.95957e8i		−	2.04491i
$664$			3.66002e8i			1.25020i
$665$	1.87211e7	−	4.45033e7i	0.0636599	−	0.151331i
$666$	3.14850e7			0.106581
$667$	5.28097e7			0.177966
$668$		0			0
$669$	−2.21511e8			−0.739806
$670$		−	1.78946e8i		−	0.594974i
$671$			2.40445e8i			0.795880i
$672$		0			0
$673$	4.06265e8			1.33280			0.666399	−	0.745595i	$-0.267835\pi$
$673$	4.06265e8			1.33280			0.666399	+	0.745595i	$0.267835\pi$
$674$	−1.87663e7			−0.0612913
$675$			3.57106e8i			1.16114i
$676$		0			0
$677$			1.77837e7i			0.0573133i	0.999589	+	0.0286566i	$0.00912294\pi$
$677$			1.77837e7i			0.0573133i	−0.999589	+	0.0286566i	$0.990877\pi$
$678$		−	6.53150e8i		−	2.09567i
$679$	−2.57497e8	−	1.08320e8i	−0.822551	−	0.346020i
$680$	−1.37871e8			−0.438478
$681$	−5.97020e8			−1.89037
$682$		−	1.92008e8i		−	0.605295i
$683$	−2.66054e8			−0.835042			−0.417521	−	0.908667i	$-0.637101\pi$
$683$	−2.66054e8			−0.835042			−0.417521	+	0.908667i	$0.637101\pi$
$684$		0			0
$685$			9.61712e7i			0.299208i
$686$	3.00251e8	−	1.18607e8i	0.930063	−	0.367400i
$687$	1.53102e7			0.0472183
$688$	−1.28688e8			−0.395160
$689$			1.69098e8i			0.516989i
$690$	−7.73242e7			−0.235379
$691$		−	2.44451e8i		−	0.740898i	−0.928853	−	0.370449i	$-0.879204\pi$
$691$		−	2.44451e8i		−	0.740898i	0.928853	−	0.370449i	$-0.120796\pi$
$692$		0			0
$693$	−1.52393e8	+	3.62266e8i	−0.457895	+	1.08850i
$694$	3.84476e8			1.15025
$695$	−7.60696e7			−0.226598
$696$		−	2.57753e8i		−	0.764498i
$697$	3.43063e8			1.01315
$698$			8.03994e7i			0.236421i
$699$		−	2.18671e8i		−	0.640265i
$700$		0			0
$701$	2.31727e8			0.672702			0.336351	−	0.941737i	$-0.390807\pi$
$701$	2.31727e8			0.672702			0.336351	+	0.941737i	$0.390807\pi$
$702$	−4.65414e8			−1.34533
$703$		−	9.35567e6i		−	0.0269283i
$704$	2.29114e8			0.656649
$705$			1.47792e8i			0.421776i
$706$		−	6.12173e8i		−	1.73964i
$707$	6.17139e8	+	2.59610e8i	1.74632	+	0.734621i
$708$		0			0
$709$	−3.09705e8			−0.868979			−0.434489	−	0.900677i	$-0.643071\pi$
$709$	−3.09705e8			−0.868979			−0.434489	+	0.900677i	$0.643071\pi$
$710$			6.66316e7i			0.186168i
$711$	7.01298e8			1.95117
$712$			3.22319e8i			0.892988i
$713$			1.30111e8i			0.358959i
$714$	−2.86514e8	+	6.81094e8i	−0.787138	+	1.87117i
$715$	8.73650e7			0.239012
$716$		0			0
$717$			6.20122e8i			1.68236i
$718$	−6.71788e7			−0.181493
$719$			3.85416e8i			1.03692i	0.855103	+	0.518458i	$0.173494\pi$
$719$			3.85416e8i			1.03692i	−0.855103	+	0.518458i	$0.826506\pi$
$720$			2.42537e8i			0.649801i
$721$	−5.36671e8	−	2.25760e8i	−1.43187	−	0.602339i
$722$	−2.98668e8			−0.793554
$723$	−1.65721e8			−0.438494
$724$		0			0
$725$	1.51418e8			0.397342
$726$		−	3.64108e8i		−	0.951525i
$727$		−	3.13918e8i		−	0.816983i	−0.912762	−	0.408491i	$-0.866055\pi$
$727$		−	3.13918e8i		−	0.816983i	0.912762	−	0.408491i	$-0.133945\pi$
$728$	−3.58257e8	−	1.50707e8i	−0.928539	−	0.390606i
$729$	5.61951e8			1.45049
$730$	2.20320e7			0.0566351
$731$			1.87313e8i			0.479530i
$732$		0			0
$733$			7.18118e7i			0.182341i	0.995835	+	0.0911704i	$0.0290608\pi$
$733$			7.18118e7i			0.182341i	−0.995835	+	0.0911704i	$0.970939\pi$
$734$		−	3.06221e7i		−	0.0774366i
$735$	−1.67833e8	−	1.71564e8i	−0.422683	−	0.432079i
$736$		0			0
$737$	4.32842e8			1.08125
$738$		−	6.03500e8i		−	1.50144i
$739$	2.77815e7			0.0688370			0.0344185	−	0.999408i	$-0.489042\pi$
$739$	2.77815e7			0.0688370			0.0344185	+	0.999408i	$0.489042\pi$
$740$		0			0
$741$			3.11523e8i			0.765660i
$742$	8.12960e7	−	1.93255e8i	0.199002	−	0.473063i
$743$	−7.03366e8			−1.71481			−0.857403	−	0.514646i	$-0.827923\pi$
$743$	−7.03366e8			−1.71481			−0.857403	+	0.514646i	$0.827923\pi$
$744$	6.35044e8			1.54200
$745$		−	1.17240e8i		−	0.283535i
$746$	3.95069e8			0.951604
$747$		−	9.37166e8i		−	2.24830i
$748$		0			0
$749$	2.14931e8	−	5.10930e8i	0.511510	−	1.21595i
$750$	−4.76707e8			−1.12997
$751$	−3.00617e8			−0.709731			−0.354866	−	0.934917i	$-0.615473\pi$
$751$	−3.00617e8			−0.709731			−0.354866	+	0.934917i	$0.615473\pi$
$752$		−	2.96742e8i		−	0.697792i
$753$	−7.10416e8			−1.66390
$754$			1.97342e8i			0.460369i
$755$		−	7.61309e7i		−	0.176897i
$756$		0			0
$757$	1.17057e8			0.269841			0.134921	−	0.990856i	$-0.456922\pi$
$757$	1.17057e8			0.269841			0.134921	+	0.990856i	$0.456922\pi$
$758$	−2.99649e8			−0.688026
$759$		−	1.87034e8i		−	0.427756i
$760$	7.20691e7			0.164176
$761$			2.63542e8i			0.597992i	0.954254	+	0.298996i	$0.0966518\pi$
$761$			2.63542e8i			0.597992i	−0.954254	+	0.298996i	$0.903348\pi$
$762$			1.20132e9i			2.71516i
$763$	2.64971e7	−	6.29882e7i	0.0596519	−	0.141803i
$764$		0			0
$765$	3.53026e8			0.788538
$766$			4.00803e8i			0.891752i
$767$	−2.50600e8			−0.555385
$768$		0			0
$769$			1.25689e8i			0.276388i	0.990405	+	0.138194i	$0.0441298\pi$
$769$			1.25689e8i			0.276388i	−0.990405	+	0.138194i	$0.955870\pi$
$770$	−9.98458e7	−	4.20018e7i	−0.218704	−	0.0920017i
$771$	3.40794e8			0.743582
$772$		0			0
$773$			1.58329e8i			0.342786i	0.985203	+	0.171393i	$0.0548268\pi$
$773$			1.58329e8i			0.342786i	−0.985203	+	0.171393i	$0.945173\pi$
$774$	3.29512e8			0.710638
$775$			3.73060e8i			0.801444i
$776$		−	4.16993e8i		−	0.892368i
$777$	−4.28686e7	−	1.80334e7i	−0.0913852	−	0.0384427i
$778$	−1.79989e6			−0.00382214
$779$	−1.79328e8			−0.379347
$780$		0			0
$781$	−1.61171e8			−0.338324
$782$		−	2.25982e8i		−	0.472557i
$783$			2.92993e8i			0.610340i
$784$	3.36982e8	+	3.44473e8i	0.699292	+	0.714836i
$785$	1.66050e8			0.343265
$786$	1.13302e9			2.33329
$787$		−	5.15726e8i		−	1.05802i	−0.848615	−	0.529012i	$-0.822563\pi$
$787$		−	5.15726e8i		−	1.05802i	0.848615	−	0.529012i	$-0.177437\pi$
$788$		0			0
$789$			5.96464e8i			1.21438i
$790$			1.93288e8i			0.392034i
$791$	−2.40414e8	+	5.71506e8i	−0.485769	+	1.15476i
$792$	−5.86657e8			−1.18089
$793$	6.08856e8			1.22094
$794$			6.97549e6i			0.0139352i
$795$	−1.55868e8			−0.310210
$796$		0			0
$797$		−	9.29429e8i		−	1.83587i	−0.396735	−	0.917933i	$-0.629857\pi$
$797$		−	9.29429e8i		−	1.83587i	0.396735	−	0.917933i	$-0.370143\pi$
$798$	1.49769e8	−	3.56027e8i	0.294722	−	0.700606i
$799$	−4.31925e8			−0.846775
$800$		0			0
$801$		−	8.25312e8i		−	1.60591i
$802$	−1.15927e8			−0.224730
$803$			5.32918e7i			0.102923i
$804$		0			0
$805$	6.76586e7	+	2.84618e7i	0.129699	+	0.0545600i
$806$	−4.86205e8			−0.928570
$807$	−7.20856e8			−1.37160
$808$			9.99401e8i			1.89455i
$809$	−6.89731e8			−1.30267			−0.651335	−	0.758791i	$-0.725791\pi$
$809$	−6.89731e8			−1.30267			−0.651335	+	0.758791i	$0.725791\pi$
$810$		−	8.36701e7i		−	0.157440i
$811$			2.85961e7i			0.0536099i	0.999641	+	0.0268049i	$0.00853330\pi$
$811$			2.85961e7i			0.0536099i	−0.999641	+	0.0268049i	$0.991467\pi$
$812$		0			0
$813$	1.12214e9			2.08821
$814$	−2.09900e7			−0.0389170
$815$			8.49992e7i			0.157015i
$816$	−1.10297e9			−2.02999
$817$		−	9.79135e7i		−	0.179546i
$818$		−	8.34424e8i		−	1.52450i
$819$	9.17333e8	+	3.85892e8i	1.66984	+	0.702447i
$820$		0			0
$821$	−2.51151e8			−0.453844			−0.226922	−	0.973913i	$-0.572866\pi$
$821$	−2.51151e8			−0.453844			−0.226922	+	0.973913i	$0.572866\pi$
$822$			7.69370e8i			1.38522i
$823$	2.40085e8			0.430691			0.215346	−	0.976538i	$-0.430912\pi$
$823$	2.40085e8			0.430691			0.215346	+	0.976538i	$0.430912\pi$
$824$		−	8.69090e8i		−	1.55340i
$825$		−	5.36273e8i		−	0.955046i
$826$	2.86400e8	+	1.20479e8i	0.508197	+	0.213782i
$827$	9.14380e8			1.61663			0.808314	−	0.588751i	$-0.200380\pi$
$827$	9.14380e8			1.61663			0.808314	+	0.588751i	$0.200380\pi$
$828$		0			0
$829$			5.22917e8i			0.917845i	0.888476	+	0.458922i	$0.151764\pi$
$829$			5.22917e8i			0.917845i	−0.888476	+	0.458922i	$0.848236\pi$
$830$	2.58297e8			0.451736
$831$		−	7.22721e8i		−	1.25941i
$832$		−	5.80164e8i		−	1.00735i
$833$	5.01399e8	−	4.90496e8i	0.867459	−	0.848596i
$834$	−6.08556e8			−1.04907
$835$	−1.42543e8			−0.244842
$836$		0			0
$837$	−7.21866e8			−1.23106
$838$			6.57660e8i			1.11756i
$839$			9.46684e8i			1.60295i	0.598030	+	0.801474i	$0.295950\pi$
$839$			9.46684e8i			1.60295i	−0.598030	+	0.801474i	$0.704050\pi$
$840$	1.38916e8	−	3.30228e8i	0.234376	−	0.557154i
$841$	−4.70590e8			−0.791142
$842$	1.07024e8			0.179285
$843$			2.72609e7i			0.0455048i
$844$		0			0
$845$		−	3.21724e6i		−	0.00533229i
$846$			7.59822e8i			1.25488i
$847$	−1.34022e8	+	3.18594e8i	−0.220560	+	0.524309i
$848$	3.12959e8			0.513216
$849$	−1.00357e9			−1.63993
$850$		−	6.47946e8i		−	1.05507i
$851$	1.42235e7			0.0230790
$852$		0			0
$853$		−	2.30334e8i		−	0.371117i	−0.982633	−	0.185558i	$-0.940591\pi$
$853$		−	2.30334e8i		−	0.371117i	0.982633	−	0.185558i	$-0.0594094\pi$
$854$	−6.95836e8	−	2.92715e8i	−1.11721	−	0.469972i
$855$	−1.84536e8			−0.295246
$856$	8.27405e8			1.31916
$857$		−	4.34496e7i		−	0.0690308i	−0.999404	−	0.0345154i	$-0.989011\pi$
$857$		−	4.34496e7i		−	0.0690308i	0.999404	−	0.0345154i	$-0.0109888\pi$
$858$	6.98920e8			1.10654
$859$		−	1.61129e8i		−	0.254211i	−0.991889	−	0.127105i	$-0.959431\pi$
$859$		−	1.61129e8i		−	0.254211i	0.991889	−	0.127105i	$-0.0405686\pi$
$860$		0			0
$861$	−3.45662e8	+	8.21699e8i	−0.541554	+	1.28737i
$862$	1.07396e9			1.67673
$863$	2.56357e8			0.398853			0.199426	−	0.979913i	$-0.436092\pi$
$863$	2.56357e8			0.398853			0.199426	+	0.979913i	$0.436092\pi$
$864$		0			0
$865$	−1.03646e8			−0.160142
$866$			8.25842e8i			1.27158i
$867$			5.15230e8i			0.790577i
$868$		0			0
$869$	−4.67532e8			−0.712447
$870$	−1.81903e8			−0.276237
$871$		−	1.09605e9i		−	1.65872i
$872$	1.02004e8			0.153839
$873$			1.06773e9i			1.60479i
$874$			1.18127e8i			0.176935i
$875$	4.17119e8	+	1.75468e8i	0.622638	+	0.261923i
$876$		0			0
$877$	2.47675e8			0.367184			0.183592	−	0.983003i	$-0.441228\pi$
$877$	2.47675e8			0.367184			0.183592	+	0.983003i	$0.441228\pi$
$878$		−	2.12653e8i		−	0.314186i
$879$	1.93373e9			2.84727
$880$		−	1.61691e8i		−	0.237268i
$881$			1.05612e9i			1.54450i	0.635320	+	0.772249i	$0.280868\pi$
$881$			1.05612e9i			1.54450i	−0.635320	+	0.772249i	$0.719132\pi$
$882$	−8.62858e8	−	8.82038e8i	−1.25757	−	1.28553i
$883$	−5.38572e8			−0.782278			−0.391139	−	0.920332i	$-0.627919\pi$
$883$	−5.38572e8			−0.782278			−0.391139	+	0.920332i	$0.627919\pi$
$884$		0			0
$885$		−	2.30993e8i		−	0.333250i
$886$	−1.05577e9			−1.51799
$887$			1.13395e8i			0.162489i	0.996694	+	0.0812445i	$0.0258895\pi$
$887$			1.13395e8i			0.162489i	−0.996694	+	0.0812445i	$0.974111\pi$
$888$		−	6.94218e7i		−	0.0991418i
$889$	4.42188e8	−	1.05116e9i	0.629364	−	1.49611i
$890$	2.27468e8			0.322664
$891$	2.02384e8			0.286117
$892$		0			0
$893$	2.25779e8			0.317051
$894$		−	9.37919e8i		−	1.31266i
$895$			1.58916e8i			0.221666i
$896$	−2.78921e8	+	6.63045e8i	−0.387755	+	0.921762i
$897$	−4.73610e8			−0.656212
$898$	−1.18213e9			−1.63244
$899$			3.06082e8i			0.421268i
$900$		0			0
$901$		−	4.55529e8i		−	0.622791i
$902$			4.02333e8i			0.548234i
$903$	−4.48649e8	−	1.88732e8i	−0.609317	−	0.256320i
$904$	−9.25502e8			−1.25277
$905$	−3.37965e8			−0.455959
$906$		−	6.09047e8i		−	0.818967i
$907$	−4.58651e8			−0.614696			−0.307348	−	0.951597i	$-0.599442\pi$
$907$	−4.58651e8			−0.614696			−0.307348	+	0.951597i	$0.599442\pi$
$908$		0			0
$909$		−	2.55901e9i		−	3.40707i
$910$	−1.06357e8	+	2.52830e8i	−0.141138	+	0.335510i
$911$	6.00692e8			0.794505			0.397253	−	0.917709i	$-0.369964\pi$
$911$	6.00692e8			0.794505			0.397253	+	0.917709i	$0.369964\pi$
$912$	5.76553e8			0.760072
$913$			6.24777e8i			0.820943i
$914$	6.58294e8			0.862147
$915$			5.61221e8i			0.732606i
$916$		0			0
$917$	−9.91389e8	−	4.17045e8i	−1.28569	−	0.540847i
$918$	1.25377e9			1.62065
$919$	7.19637e8			0.927187			0.463593	−	0.886048i	$-0.346560\pi$
$919$	7.19637e8			0.927187			0.463593	+	0.886048i	$0.346560\pi$
$920$			1.09567e8i			0.140707i
$921$	1.81637e9			2.32502
$922$		−	1.05507e9i		−	1.34614i
$923$			4.08118e8i			0.519016i
$924$		0			0
$925$	4.07822e7			0.0515282
$926$	−1.11942e7			−0.0140981
$927$			2.22535e9i			2.79356i
$928$		0			0
$929$		−	4.63919e8i		−	0.578622i	−0.957235	−	0.289311i	$-0.906574\pi$
$929$		−	4.63919e8i		−	0.578622i	0.957235	−	0.289311i	$-0.0934262\pi$
$930$		−	4.48166e8i		−	0.557173i
$931$	−2.62095e8	+	2.56396e8i	−0.324795	+	0.317733i
$932$		0			0
$933$	−6.65664e8			−0.819616
$934$		−	1.45057e8i		−	0.178032i
$935$	−2.35351e8			−0.287926
$936$			1.48554e9i			1.81157i
$937$			1.26911e9i			1.54269i	0.636417	+	0.771345i	$0.280416\pi$
$937$			1.26911e9i			1.54269i	−0.636417	+	0.771345i	$0.719584\pi$
$938$	−5.26937e8	+	1.25262e9i	−0.638485	+	1.51779i
$939$	−1.89468e9			−2.28844
$940$		0			0
$941$		−	1.06092e8i		−	0.127325i	−0.997971	−	0.0636626i	$-0.979722\pi$
$941$		−	1.06092e8i		−	0.127325i	0.997971	−	0.0636626i	$-0.0202782\pi$
$942$	1.32840e9			1.58919
$943$		−	2.72634e8i		−	0.325121i
$944$			4.63799e8i			0.551332i
$945$	−1.57908e8	+	3.75376e8i	−0.187115	+	0.444806i
$946$	−2.19675e8			−0.259482
$947$	3.60651e8			0.424655			0.212328	−	0.977199i	$-0.431896\pi$
$947$	3.60651e8			0.424655			0.212328	+	0.977199i	$0.431896\pi$
$948$		0			0
$949$	1.34946e8			0.157892
$950$			3.38699e8i			0.395042i
$951$		−	1.94632e9i		−	2.26294i
$952$	9.65100e8	+	4.05986e8i	1.11857	+	0.470543i
$953$	1.35809e9			1.56910			0.784551	−	0.620064i	$-0.212893\pi$
$953$	1.35809e9			1.56910			0.784551	+	0.620064i	$0.212893\pi$
$954$	−8.01346e8			−0.922943
$955$		−	3.25210e8i		−	0.373383i
$956$		0			0
$957$		−	4.39993e8i		−	0.502007i
$958$		−	2.31500e8i		−	0.263303i
$959$	2.83192e8	−	6.73198e8i	0.321089	−	0.763286i
$960$	5.34774e8			0.604444
$961$	1.33389e8			0.150297
$962$			5.31510e7i			0.0597017i
$963$	−2.11861e9			−2.37231
$964$		0			0
$965$		−	5.91178e8i		−	0.657864i
$966$	5.41269e8	+	2.27694e8i	0.600457	+	0.252592i
$967$	4.83872e8			0.535119			0.267560	−	0.963541i	$-0.413783\pi$
$967$	4.83872e8			0.535119			0.267560	+	0.963541i	$0.413783\pi$
$968$	−5.15935e8			−0.568812
$969$		−	8.39205e8i		−	0.922353i
$970$	−2.94282e8			−0.322440
$971$		−	3.07992e8i		−	0.336420i	−0.985751	−	0.168210i	$-0.946201\pi$
$971$		−	3.07992e8i		−	0.336420i	0.985751	−	0.168210i	$-0.0537987\pi$
$972$		0			0
$973$	5.32487e8	+	2.24000e8i	0.578057	+	0.243169i
$974$	7.58012e8			0.820350
$975$	−1.35796e9			−1.46512
$976$		−	1.12684e9i		−	1.21203i
$977$	−2.33410e8			−0.250285			−0.125143	−	0.992139i	$-0.539939\pi$
$977$	−2.33410e8			−0.250285			−0.125143	+	0.992139i	$0.539939\pi$
$978$			6.79994e8i			0.726923i
$979$			5.50208e8i			0.586380i
$980$		0			0
$981$	−2.61185e8			−0.276657
$982$	2.07067e8			0.218663
$983$		−	6.02617e8i		−	0.634426i	−0.948354	−	0.317213i	$-0.897253\pi$
$983$		−	6.02617e8i		−	0.634426i	0.948354	−	0.317213i	$-0.102747\pi$
$984$	−1.33067e9			−1.39664
$985$		−	4.14390e8i		−	0.433612i
$986$		−	5.31616e8i		−	0.554584i
$987$	4.35197e8	−	1.03454e9i	0.452621	−	1.07596i
$988$		0			0
$989$	1.48858e8			0.153881
$990$			4.14018e8i			0.426691i
$991$	1.12772e9			1.15873			0.579364	−	0.815069i	$-0.303301\pi$
$991$	1.12772e9			1.15873			0.579364	+	0.815069i	$0.303301\pi$
$992$		0			0
$993$			2.40377e9i			2.45497i
$994$	1.96208e8	−	4.66421e8i	0.199783	−	0.474918i
$995$	−3.06575e8			−0.311220
$996$		0			0
$997$			1.17224e9i			1.18286i	0.806357	+	0.591429i	$0.201436\pi$
$997$			1.17224e9i			1.18286i	−0.806357	+	0.591429i	$0.798564\pi$
$998$	−1.24819e9			−1.25571
$999$			7.89130e7i			0.0791503i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.7.b.b.6.1	✓	2
3.2	odd	2		63.7.d.d.55.1		2
4.3	odd	2		112.7.c.b.97.2		2
5.2	odd	4		175.7.c.c.174.1		4
5.3	odd	4		175.7.c.c.174.4		4
5.4	even	2		175.7.d.e.76.2		2
7.2	even	3		49.7.d.d.31.2		4
7.3	odd	6		49.7.d.d.19.2		4
7.4	even	3		49.7.d.d.19.1		4
7.5	odd	6		49.7.d.d.31.1		4
7.6	odd	2	inner	7.7.b.b.6.2	yes	2
8.3	odd	2		448.7.c.c.321.1		2
8.5	even	2		448.7.c.d.321.2		2
21.20	even	2		63.7.d.d.55.2		2
28.27	even	2		112.7.c.b.97.1		2
35.13	even	4		175.7.c.c.174.3		4
35.27	even	4		175.7.c.c.174.2		4
35.34	odd	2		175.7.d.e.76.1		2
56.13	odd	2		448.7.c.d.321.1		2
56.27	even	2		448.7.c.c.321.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.7.b.b.6.1	✓	2	1.1	even	1	trivial
7.7.b.b.6.2	yes	2	7.6	odd	2	inner
49.7.d.d.19.1		4	7.4	even	3
49.7.d.d.19.2		4	7.3	odd	6
49.7.d.d.31.1		4	7.5	odd	6
49.7.d.d.31.2		4	7.2	even	3
63.7.d.d.55.1		2	3.2	odd	2
63.7.d.d.55.2		2	21.20	even	2
112.7.c.b.97.1		2	28.27	even	2
112.7.c.b.97.2		2	4.3	odd	2
175.7.c.c.174.1		4	5.2	odd	4
175.7.c.c.174.2		4	35.27	even	4
175.7.c.c.174.3		4	35.13	even	4
175.7.c.c.174.4		4	5.3	odd	4
175.7.d.e.76.1		2	35.34	odd	2
175.7.d.e.76.2		2	5.4	even	2
448.7.c.c.321.1		2	8.3	odd	2
448.7.c.c.321.2		2	56.27	even	2
448.7.c.d.321.1		2	56.13	odd	2
448.7.c.d.321.2		2	8.5	even	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:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	7.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-8.00000 q^{2} -45.1664i q^{3} +45.1664i q^{5} +361.331i q^{6} +(133.000 - 316.165i) q^{7} +512.000 q^{8} -1311.00 q^{9} +O(q^{10})\)	\(q-8.00000 q^{2} -45.1664i q^{3} +45.1664i q^{5} +361.331i q^{6} +(133.000 - 316.165i) q^{7} +512.000 q^{8} -1311.00 q^{9} -361.331i q^{10} +874.000 q^{11} -2213.15i q^{13} +(-1064.00 + 2529.32i) q^{14} +2040.00 q^{15} -4096.00 q^{16} +5961.96i q^{17} +10488.0 q^{18} -3116.48i q^{19} +(-14280.0 - 6007.13i) q^{21} -6992.00 q^{22} +4738.00 q^{23} -23125.2i q^{24} +13585.0 q^{25} +17705.2i q^{26} +26286.8i q^{27} +11146.0 q^{29} -16320.0 q^{30} +27461.1i q^{31} -39475.4i q^{33} -47695.7i q^{34} +(14280.0 + 6007.13i) q^{35} +3002.00 q^{37} +24931.8i q^{38} -99960.0 q^{39} +23125.2i q^{40} -57541.9i q^{41} +(114240. + 48057.0i) q^{42} +31418.0 q^{43} -59213.1i q^{45} -37904.0 q^{46} +72446.8i q^{47} +185001. i q^{48} +(-82271.0 - 84099.8i) q^{49} -108680. q^{50} +269280. q^{51} -76406.0 q^{53} -210295. i q^{54} +39475.4i q^{55} +(68096.0 - 161876. i) q^{56} -140760. q^{57} -89168.0 q^{58} -113232. i q^{59} +275108. i q^{61} -219689. i q^{62} +(-174363. + 414492. i) q^{63} +262144. q^{64} +99960.0 q^{65} +315803. i q^{66} +495242. q^{67} -213998. i q^{69} +(-114240. - 48057.0i) q^{70} -184406. q^{71} -671232. q^{72} +60974.6i q^{73} -24016.0 q^{74} -613585. i q^{75} +(116242. - 276328. i) q^{77} +799680. q^{78} -534934. q^{79} -185001. i q^{80} +231561. q^{81} +460336. i q^{82} +714848. i q^{83} -269280. q^{85} -251344. q^{86} -503424. i q^{87} +447488. q^{88} +629529. i q^{89} +473705. i q^{90} +(-699720. - 294349. i) q^{91} +1.24032e6 q^{93} -579575. i q^{94} +140760. q^{95} -814440. i q^{97} +(658168. + 672798. i) q^{98} -1.14581e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 16 q^{2} + 266 q^{7} + 1024 q^{8} - 2622 q^{9}+O(q^{10}) \) 2 * q - 16 * q^2 + 266 * q^7 + 1024 * q^8 - 2622 * q^9	\( 2 q - 16 q^{2} + 266 q^{7} + 1024 q^{8} - 2622 q^{9} + 1748 q^{11} - 2128 q^{14} + 4080 q^{15} - 8192 q^{16} + 20976 q^{18} - 28560 q^{21} - 13984 q^{22} + 9476 q^{23} + 27170 q^{25} + 22292 q^{29} - 32640 q^{30} + 28560 q^{35} + 6004 q^{37} - 199920 q^{39} + 228480 q^{42} + 62836 q^{43} - 75808 q^{46} - 164542 q^{49} - 217360 q^{50} + 538560 q^{51} - 152812 q^{53} + 136192 q^{56} - 281520 q^{57} - 178336 q^{58} - 348726 q^{63} + 524288 q^{64} + 199920 q^{65} + 990484 q^{67} - 228480 q^{70} - 368812 q^{71} - 1342464 q^{72} - 48032 q^{74} + 232484 q^{77} + 1599360 q^{78} - 1069868 q^{79} + 463122 q^{81} - 538560 q^{85} - 502688 q^{86} + 894976 q^{88} - 1399440 q^{91} + 2480640 q^{93} + 281520 q^{95} + 1316336 q^{98} - 2291628 q^{99}+O(q^{100}) \) 2 * q - 16 * q^2 + 266 * q^7 + 1024 * q^8 - 2622 * q^9 + 1748 * q^11 - 2128 * q^14 + 4080 * q^15 - 8192 * q^16 + 20976 * q^18 - 28560 * q^21 - 13984 * q^22 + 9476 * q^23 + 27170 * q^25 + 22292 * q^29 - 32640 * q^30 + 28560 * q^35 + 6004 * q^37 - 199920 * q^39 + 228480 * q^42 + 62836 * q^43 - 75808 * q^46 - 164542 * q^49 - 217360 * q^50 + 538560 * q^51 - 152812 * q^53 + 136192 * q^56 - 281520 * q^57 - 178336 * q^58 - 348726 * q^63 + 524288 * q^64 + 199920 * q^65 + 990484 * q^67 - 228480 * q^70 - 368812 * q^71 - 1342464 * q^72 - 48032 * q^74 + 232484 * q^77 + 1599360 * q^78 - 1069868 * q^79 + 463122 * q^81 - 538560 * q^85 - 502688 * q^86 + 894976 * q^88 - 1399440 * q^91 + 2480640 * q^93 + 281520 * q^95 + 1316336 * q^98 - 2291628 * q^99

Introduction

L-functions

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