LMFDB - Embedded newform 95.11.c.a.56.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [95,11,Mod(56,95)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(95, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("95.56");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 95 = 5 \cdot 19 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	95.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:	$60.3589390040$
Analytic rank:	$0$
Dimension:	$68$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			56.11
Character	$\chi$	$=$	95.56
Dual form			95.11.c.a.56.58

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-49.4757i q^{2} +10.8416i q^{3} -1423.84 q^{4} -1397.54 q^{5} +536.394 q^{6} +13282.9 q^{7} +19782.5i q^{8} +58931.5 q^{9} +O(q^{10})$	\(q-49.4757i q^{2} +10.8416i q^{3} -1423.84 q^{4} -1397.54 q^{5} +536.394 q^{6} +13282.9 q^{7} +19782.5i q^{8} +58931.5 q^{9} +69144.4i q^{10} +134309. q^{11} -15436.7i q^{12} +74086.3i q^{13} -657182. i q^{14} -15151.5i q^{15} -479263. q^{16} -2.59783e6 q^{17} -2.91567e6i q^{18} +(-1.31333e6 + 2.09910e6i) q^{19} +1.98988e6 q^{20} +144008. i q^{21} -6.64503e6i q^{22} -9.76079e6 q^{23} -214473. q^{24} +1.95312e6 q^{25} +3.66547e6 q^{26} +1.27909e6i q^{27} -1.89128e7 q^{28} -2.07403e7i q^{29} -749633. q^{30} -2.24517e7i q^{31} +4.39691e7i q^{32} +1.45612e6i q^{33} +1.28529e8i q^{34} -1.85635e7 q^{35} -8.39091e7 q^{36} -4.45482e7i q^{37} +(1.03854e8 + 6.49779e7i) q^{38} -803211. q^{39} -2.76469e7i q^{40} +1.42384e8i q^{41} +7.12488e6 q^{42} -1.33561e8 q^{43} -1.91235e8 q^{44} -8.23592e7 q^{45} +4.82922e8i q^{46} +1.20804e8 q^{47} -5.19596e6i q^{48} -1.06039e8 q^{49} -9.66322e7i q^{50} -2.81645e7i q^{51} -1.05487e8i q^{52} +6.01545e8i q^{53} +6.32840e7 q^{54} -1.87703e8 q^{55} +2.62770e8i q^{56} +(-2.27575e7 - 1.42386e7i) q^{57} -1.02614e9 q^{58} -1.00758e9i q^{59} +2.15734e7i q^{60} -4.94958e8 q^{61} -1.11081e9 q^{62} +7.82783e8 q^{63} +1.68464e9 q^{64} -1.03539e8i q^{65} +7.20426e7 q^{66} +2.24514e9i q^{67} +3.69890e9 q^{68} -1.05822e8i q^{69} +9.18440e8i q^{70} -3.66685e8i q^{71} +1.16581e9i q^{72} -2.25465e9 q^{73} -2.20405e9 q^{74} +2.11749e7i q^{75} +(1.86998e9 - 2.98879e9i) q^{76} +1.78402e9 q^{77} +3.97394e7i q^{78} +2.70837e9i q^{79} +6.69790e8 q^{80} +3.46598e9 q^{81} +7.04455e9 q^{82} +2.01469e9 q^{83} -2.05044e8i q^{84} +3.63057e9 q^{85} +6.60804e9i q^{86} +2.24857e8 q^{87} +2.65697e9i q^{88} -4.24647e9i q^{89} +4.07478e9i q^{90} +9.84083e8i q^{91} +1.38978e10 q^{92} +2.43412e8 q^{93} -5.97684e9i q^{94} +(1.83544e9 - 2.93358e9i) q^{95} -4.76694e8 q^{96} +1.23690e10i q^{97} +5.24634e9i q^{98} +7.91503e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 35644 q^{4} - 2044 q^{6} + 76620 q^{7} - 1353552 q^{9}+O(q^{10}) $ 68 * q - 35644 * q^4 - 2044 * q^6 + 76620 * q^7 - 1353552 * q^9	$ 68 q - 35644 q^{4} - 2044 q^{6} + 76620 q^{7} - 1353552 q^{9} - 418144 q^{11} + 21763300 q^{16} - 10023236 q^{17} + 518264 q^{19} + 4962204 q^{23} + 2604244 q^{24} + 132812500 q^{25} + 32178588 q^{26} - 109025284 q^{28} + 39875000 q^{30} + 39875000 q^{35} + 420547696 q^{36} - 504912596 q^{38} + 51693988 q^{39} + 343589380 q^{42} + 72617360 q^{43} - 846875584 q^{44} + 148625000 q^{45} + 426767656 q^{47} + 3802641528 q^{49} + 594603476 q^{54} - 361360620 q^{57} - 1963881788 q^{58} + 7470512872 q^{61} - 2514646024 q^{62} - 6611740944 q^{63} - 13094608884 q^{64} + 9558616040 q^{66} + 17177918780 q^{68} - 2447766556 q^{73} - 1842337832 q^{74} - 5604056776 q^{76} - 320485400 q^{77} - 821875000 q^{80} + 5162401956 q^{81} - 17137563304 q^{82} - 14922506320 q^{83} - 4799500000 q^{85} + 5085654996 q^{87} - 27413957236 q^{92} - 11067885256 q^{93} + 1613500000 q^{95} - 67563054044 q^{96} + 76070139768 q^{99}+O(q^{100}) $ 68 * q - 35644 * q^4 - 2044 * q^6 + 76620 * q^7 - 1353552 * q^9 - 418144 * q^11 + 21763300 * q^16 - 10023236 * q^17 + 518264 * q^19 + 4962204 * q^23 + 2604244 * q^24 + 132812500 * q^25 + 32178588 * q^26 - 109025284 * q^28 + 39875000 * q^30 + 39875000 * q^35 + 420547696 * q^36 - 504912596 * q^38 + 51693988 * q^39 + 343589380 * q^42 + 72617360 * q^43 - 846875584 * q^44 + 148625000 * q^45 + 426767656 * q^47 + 3802641528 * q^49 + 594603476 * q^54 - 361360620 * q^57 - 1963881788 * q^58 + 7470512872 * q^61 - 2514646024 * q^62 - 6611740944 * q^63 - 13094608884 * q^64 + 9558616040 * q^66 + 17177918780 * q^68 - 2447766556 * q^73 - 1842337832 * q^74 - 5604056776 * q^76 - 320485400 * q^77 - 821875000 * q^80 + 5162401956 * q^81 - 17137563304 * q^82 - 14922506320 * q^83 - 4799500000 * q^85 + 5085654996 * q^87 - 27413957236 * q^92 - 11067885256 * q^93 + 1613500000 * q^95 - 67563054044 * q^96 + 76070139768 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/95\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	49.4757i		−	1.54611i	−0.634336	−	0.773057i	$-0.718726\pi$
$2$		−	49.4757i		−	1.54611i	0.634336	−	0.773057i	$-0.281274\pi$
$3$			10.8416i			0.0446155i	0.999751	+	0.0223077i	$0.00710136\pi$
$3$			10.8416i			0.0446155i	−0.999751	+	0.0223077i	$0.992899\pi$
$4$	−1423.84			−1.39047
$5$	−1397.54			−0.447214
$5$	−1397.54			−0.447214
$6$	536.394			0.0689807
$7$	13282.9			0.790322			0.395161	−	0.918612i	$-0.370689\pi$
$7$	13282.9			0.790322			0.395161	+	0.918612i	$0.370689\pi$
$8$			19782.5i			0.603714i
$9$	58931.5			0.998009
$10$			69144.4i			0.691444i
$11$	134309.			0.833954			0.416977	−	0.908917i	$-0.363090\pi$
$11$	134309.			0.833954			0.416977	+	0.908917i	$0.363090\pi$
$12$		−	15436.7i		−	0.0620366i
$13$			74086.3i			0.199536i	0.995011	+	0.0997679i	$0.0318100\pi$
$13$			74086.3i			0.199536i	−0.995011	+	0.0997679i	$0.968190\pi$
$14$		−	657182.i		−	1.22193i
$15$		−	15151.5i		−	0.0199526i
$16$	−479263.			−0.457061
$17$	−2.59783e6			−1.82964			−0.914820	−	0.403862i	$-0.867667\pi$
$17$	−2.59783e6			−1.82964			−0.914820	+	0.403862i	$0.867667\pi$
$18$		−	2.91567e6i		−	1.54304i
$19$	−1.31333e6	+	2.09910e6i	−0.530403	+	0.847745i
$19$	−1.31333e6	+	2.09910e6i	−0.530403	+	0.847745i
$20$	1.98988e6			0.621838
$21$			144008.i			0.0352606i
$22$		−	6.64503e6i		−	1.28939i
$23$	−9.76079e6			−1.51651			−0.758256	−	0.651957i	$-0.773948\pi$
$23$	−9.76079e6			−1.51651			−0.758256	+	0.651957i	$0.773948\pi$
$24$	−214473.			−0.0269350
$25$	1.95312e6			0.200000
$26$	3.66547e6			0.308505
$27$			1.27909e6i			0.0891421i
$28$	−1.89128e7			−1.09892
$29$		−	2.07403e7i		−	1.01117i	−0.862777	−	0.505585i	$-0.831277\pi$
$29$		−	2.07403e7i		−	1.01117i	0.862777	−	0.505585i	$-0.168723\pi$
$30$	−749633.			−0.0308491
$31$		−	2.24517e7i		−	0.784226i	−0.919917	−	0.392113i	$-0.871744\pi$
$31$		−	2.24517e7i		−	0.784226i	0.919917	−	0.392113i	$-0.128256\pi$
$32$			4.39691e7i			1.31038i
$33$			1.45612e6i			0.0372073i
$34$			1.28529e8i			2.82883i
$35$	−1.85635e7			−0.353443
$36$	−8.39091e7			−1.38770
$37$		−	4.45482e7i		−	0.642423i	−0.947007	−	0.321212i	$-0.895910\pi$
$37$		−	4.45482e7i		−	0.642423i	0.947007	−	0.321212i	$-0.104090\pi$
$38$	1.03854e8	+	6.49779e7i	1.31071	+	0.820064i
$39$	−803211.			−0.00890239
$40$		−	2.76469e7i		−	0.269989i
$41$			1.42384e8i			1.22897i	0.788927	+	0.614486i	$0.210637\pi$
$41$			1.42384e8i			1.22897i	−0.788927	+	0.614486i	$0.789363\pi$
$42$	7.12488e6			0.0545169
$43$	−1.33561e8			−0.908529			−0.454265	−	0.890867i	$-0.650098\pi$
$43$	−1.33561e8			−0.908529			−0.454265	+	0.890867i	$0.650098\pi$
$44$	−1.91235e8			−1.15959
$45$	−8.23592e7			−0.446323
$46$			4.82922e8i			2.34470i
$47$	1.20804e8			0.526733			0.263366	−	0.964696i	$-0.415167\pi$
$47$	1.20804e8			0.526733			0.263366	+	0.964696i	$0.415167\pi$
$48$		−	5.19596e6i		−	0.0203920i
$49$	−1.06039e8			−0.375391
$50$		−	9.66322e7i		−	0.309223i
$51$		−	2.81645e7i		−	0.0816302i
$52$		−	1.05487e8i		−	0.277449i
$53$			6.01545e8i			1.43843i	0.694787	+	0.719215i	$0.255499\pi$
$53$			6.01545e8i			1.43843i	−0.694787	+	0.719215i	$0.744501\pi$
$54$	6.32840e7			0.137824
$55$	−1.87703e8			−0.372956
$56$			2.62770e8i			0.477128i
$57$	−2.27575e7	−	1.42386e7i	−0.0378226	−	0.0236642i
$58$	−1.02614e9			−1.56339
$59$		−	1.00758e9i		−	1.40936i	−0.709526	−	0.704679i	$-0.751091\pi$
$59$		−	1.00758e9i		−	1.40936i	0.709526	−	0.704679i	$-0.248909\pi$
$60$			2.15734e7i			0.0277436i
$61$	−4.94958e8			−0.586029			−0.293014	−	0.956108i	$-0.594658\pi$
$61$	−4.94958e8			−0.586029			−0.293014	+	0.956108i	$0.594658\pi$
$62$	−1.11081e9			−1.21250
$63$	7.82783e8			0.788749
$64$	1.68464e9			1.56894
$65$		−	1.03539e8i		−	0.0892351i
$66$	7.20426e7			0.0575267
$67$			2.24514e9i			1.66291i	0.555593	+	0.831455i	$0.312491\pi$
$67$			2.24514e9i			1.66291i	−0.555593	+	0.831455i	$0.687509\pi$
$68$	3.69890e9			2.54406
$69$		−	1.05822e8i		−	0.0676599i
$70$			9.18440e8i			0.546463i
$71$		−	3.66685e8i		−	0.203236i	−0.994823	−	0.101618i	$-0.967598\pi$
$71$		−	3.66685e8i		−	0.203236i	0.994823	−	0.101618i	$-0.0324020\pi$
$72$			1.16581e9i			0.602512i
$73$	−2.25465e9			−1.08759			−0.543794	−	0.839218i	$-0.683013\pi$
$73$	−2.25465e9			−1.08759			−0.543794	+	0.839218i	$0.683013\pi$
$74$	−2.20405e9			−0.993260
$75$			2.11749e7i			0.00892310i
$76$	1.86998e9	−	2.98879e9i	0.737511	−	1.17877i
$77$	1.78402e9			0.659092
$78$			3.97394e7i			0.0137641i
$79$			2.70837e9i			0.880181i	0.897953	+	0.440091i	$0.145054\pi$
$79$			2.70837e9i			0.880181i	−0.897953	+	0.440091i	$0.854946\pi$
$80$	6.69790e8			0.204404
$81$	3.46598e9			0.994032
$82$	7.04455e9			1.90013
$83$	2.01469e9			0.511467			0.255733	−	0.966747i	$-0.417683\pi$
$83$	2.01469e9			0.511467			0.255733	+	0.966747i	$0.417683\pi$
$84$		−	2.05044e8i		−	0.0490288i
$85$	3.63057e9			0.818240
$86$			6.60804e9i			1.40469i
$87$	2.24857e8			0.0451139
$88$			2.65697e9i			0.503470i
$89$		−	4.24647e9i		−	0.760464i	−0.924891	−	0.380232i	$-0.875844\pi$
$89$		−	4.24647e9i		−	0.760464i	0.924891	−	0.380232i	$-0.124156\pi$
$90$			4.07478e9i			0.690067i
$91$			9.84083e8i			0.157698i
$92$	1.38978e10			2.10867
$93$	2.43412e8			0.0349886
$94$		−	5.97684e9i		−	0.814390i
$95$	1.83544e9	−	2.93358e9i	0.237204	−	0.379123i
$96$	−4.76694e8			−0.0584633
$97$			1.23690e10i			1.44037i	0.693780	+	0.720187i	$0.255944\pi$
$97$			1.23690e10i			1.44037i	−0.693780	+	0.720187i	$0.744056\pi$
$98$			5.24634e9i			0.580398i
$99$	7.91503e9			0.832294
$100$	−2.78094e9			−0.278094
$101$	−1.90689e10			−1.81434			−0.907168	−	0.420768i	$-0.861760\pi$
$101$	−1.90689e10			−1.81434			−0.907168	+	0.420768i	$0.861760\pi$
$102$	−1.39346e9			−0.126210
$103$		−	1.71155e9i		−	0.147640i	−0.997272	−	0.0738201i	$-0.976481\pi$
$103$		−	1.71155e9i		−	0.147640i	0.997272	−	0.0738201i	$-0.0235191\pi$
$104$	−1.46561e9			−0.120463
$105$		−	2.01257e8i		−	0.0157690i
$106$	2.97619e10			2.22398
$107$			2.57426e10i			1.83541i	0.397257	+	0.917707i	$0.369962\pi$
$107$			2.57426e10i			1.83541i	−0.397257	+	0.917707i	$0.630038\pi$
$108$		−	1.82123e9i		−	0.123950i
$109$		−	2.35425e10i		−	1.53010i	−0.643969	−	0.765051i	$-0.722714\pi$
$109$		−	2.35425e10i		−	1.53010i	0.643969	−	0.765051i	$-0.277286\pi$
$110$			9.28672e9i			0.576632i
$111$	4.82972e8			0.0286620
$112$	−6.36602e9			−0.361225
$113$		−	1.52148e10i		−	0.825801i	−0.910776	−	0.412901i	$-0.864516\pi$
$113$		−	1.52148e10i		−	0.825801i	0.910776	−	0.412901i	$-0.135484\pi$
$114$	−7.04462e8	+	1.12594e9i	−0.0365876	+	0.0584780i
$115$	1.36411e10			0.678205
$116$			2.95309e10i			1.40600i
$117$			4.36601e9i			0.199139i
$118$	−4.98509e10			−2.17903
$119$	−3.45068e10			−1.44600
$120$	2.99735e8			0.0120457
$121$	−7.89848e9			−0.304521
$122$			2.44884e10i			0.906068i
$123$	−1.54367e9			−0.0548312
$124$			3.19677e10i			1.09044i
$125$	−2.72958e9			−0.0894427
$126$		−	3.87287e10i		−	1.21950i
$127$			2.37187e10i			0.717914i	0.933354	+	0.358957i	$0.116868\pi$
$127$			2.37187e10i			0.717914i	−0.933354	+	0.358957i	$0.883132\pi$
$128$		−	3.83242e10i		−	1.11538i
$129$		−	1.44801e9i		−	0.0405345i
$130$	−5.12265e9			−0.137968
$131$	−5.03062e10			−1.30396			−0.651981	−	0.758235i	$-0.726062\pi$
$131$	−5.03062e10			−1.30396			−0.651981	+	0.758235i	$0.726062\pi$
$132$		−	2.07329e9i		−	0.0517356i
$133$	−1.74449e10	+	2.78822e10i	−0.419189	+	0.669992i
$134$	1.11080e11			2.57105
$135$		−	1.78759e9i		−	0.0398656i
$136$		−	5.13915e10i		−	1.10458i
$137$	−3.68495e10			−0.763534			−0.381767	−	0.924259i	$-0.624684\pi$
$137$	−3.68495e10			−0.763534			−0.381767	+	0.924259i	$0.624684\pi$
$138$	−5.23563e9			−0.104610
$139$	−2.96149e10			−0.570737			−0.285368	−	0.958418i	$-0.592116\pi$
$139$	−2.96149e10			−0.570737			−0.285368	+	0.958418i	$0.592116\pi$
$140$	2.64315e10			0.491452
$141$			1.30970e9i			0.0235004i
$142$	−1.81420e10			−0.314227
$143$			9.95046e9i			0.166404i
$144$	−2.82437e10			−0.456151
$145$			2.89854e10i			0.452209i
$146$			1.11550e11i			1.68154i
$147$		−	1.14963e9i		−	0.0167483i
$148$			6.34296e10i			0.893271i
$149$	4.96474e10			0.676029			0.338014	−	0.941141i	$-0.390245\pi$
$149$	4.96474e10			0.676029			0.338014	+	0.941141i	$0.390245\pi$
$150$	1.04764e9			0.0137961
$151$			3.89904e9i			0.0496676i	0.999692	+	0.0248338i	$0.00790565\pi$
$151$			3.89904e9i			0.0496676i	−0.999692	+	0.0248338i	$0.992094\pi$
$152$	−4.15255e10	−	2.59810e10i	−0.511796	−	0.320212i
$153$	−1.53094e11			−1.82600
$154$		−	8.82656e10i		−	1.01903i
$155$			3.13772e10i			0.350716i
$156$	1.14365e9			0.0123785
$157$	1.39711e11			1.46465			0.732323	−	0.680957i	$-0.238436\pi$
$157$	1.39711e11			1.46465			0.732323	+	0.680957i	$0.238436\pi$
$158$	1.33998e11			1.36086
$159$	−6.52169e9			−0.0641763
$160$		−	6.14487e10i		−	0.586021i
$161$	−1.29652e11			−1.19853
$162$		−	1.71482e11i		−	1.53689i
$163$	−5.13660e8			−0.00446414			−0.00223207	−	0.999998i	$-0.500710\pi$
$163$	−5.13660e8			−0.00446414			−0.00223207	+	0.999998i	$0.500710\pi$
$164$		−	2.02733e11i		−	1.70885i
$165$		−	2.03499e9i		−	0.0166396i
$166$		−	9.96780e10i		−	0.790786i
$167$		−	1.61863e11i		−	1.24614i	−0.782167	−	0.623068i	$-0.785886\pi$
$167$		−	1.61863e11i		−	1.24614i	0.782167	−	0.623068i	$-0.214114\pi$
$168$	−2.84883e9			−0.0212873
$169$	1.32370e11			0.960185
$170$		−	1.79625e11i		−	1.26509i
$171$	−7.73965e10	+	1.23703e11i	−0.529348	+	0.846058i
$172$	1.90171e11			1.26328
$173$			7.22000e9i			0.0465915i	0.999729	+	0.0232958i	$0.00741594\pi$
$173$			7.22000e9i			0.0465915i	−0.999729	+	0.0232958i	$0.992584\pi$
$174$		−	1.11249e10i		−	0.0697512i
$175$	2.59432e10			0.158064
$176$	−6.43694e10			−0.381167
$177$	1.09238e10			0.0628792
$178$	−2.10097e11			−1.17576
$179$		−	2.88768e11i		−	1.57139i	−0.618613	−	0.785696i	$-0.712305\pi$
$179$		−	2.88768e11i		−	1.57139i	0.618613	−	0.785696i	$-0.287695\pi$
$180$	1.17267e11			0.620600
$181$		−	1.82748e11i		−	0.940717i	−0.882475	−	0.470359i	$-0.844125\pi$
$181$		−	1.82748e11i		−	0.940717i	0.882475	−	0.470359i	$-0.155875\pi$
$182$	4.86882e10			0.243819
$183$		−	5.36612e9i		−	0.0261460i
$184$		−	1.93093e11i		−	0.915539i
$185$			6.22580e10i			0.287300i
$186$		−	1.20430e10i		−	0.0540964i
$187$	−3.48912e11			−1.52584
$188$	−1.72005e11			−0.732407
$189$			1.69901e10i			0.0704510i
$190$	−1.45141e11	−	9.08094e10i	−0.586168	−	0.366744i
$191$	2.46670e11			0.970398			0.485199	−	0.874404i	$-0.338747\pi$
$191$	2.46670e11			0.970398			0.485199	+	0.874404i	$0.338747\pi$
$192$			1.82641e10i			0.0699990i
$193$			4.61632e11i			1.72389i	0.507003	+	0.861944i	$0.330753\pi$
$193$			4.61632e11i			1.72389i	−0.507003	+	0.861944i	$0.669247\pi$
$194$	6.11964e11			2.22698
$195$	1.12252e9			0.00398127
$196$	1.50983e11			0.521971
$197$	−2.35177e11			−0.792616			−0.396308	−	0.918118i	$-0.629709\pi$
$197$	−2.35177e11			−0.792616			−0.396308	+	0.918118i	$0.629709\pi$
$198$		−	3.91602e11i		−	1.28682i
$199$	2.33015e10			0.0746653			0.0373327	−	0.999303i	$-0.488114\pi$
$199$	2.33015e10			0.0746653			0.0373327	+	0.999303i	$0.488114\pi$
$200$			3.86377e10i			0.120743i
$201$	−2.43408e10			−0.0741915
$202$			9.43445e11i			2.80517i
$203$		−	2.75492e11i		−	0.799150i
$204$			4.01018e10i			0.113505i
$205$		−	1.98988e11i		−	0.549613i
$206$	−8.46803e10			−0.228269
$207$	−5.75218e11			−1.51349
$208$		−	3.55068e10i		−	0.0912000i
$209$	−1.76392e11	+	2.81928e11i	−0.442332	+	0.706981i
$210$	−9.95733e9			−0.0243807
$211$			8.09546e11i			1.93566i	0.251605	+	0.967830i	$0.419042\pi$
$211$			8.09546e11i			1.93566i	−0.251605	+	0.967830i	$0.580958\pi$
$212$		−	8.56506e11i		−	2.00010i
$213$	3.97543e9			0.00906748
$214$	1.27363e12			2.83776
$215$	1.86658e11			0.406307
$216$	−2.53036e10			−0.0538163
$217$		−	2.98225e11i		−	0.619791i
$218$	−1.16478e12			−2.36571
$219$		−	2.44439e10i		−	0.0485233i
$220$	2.67259e11			0.518584
$221$		−	1.92463e11i		−	0.365079i
$222$		−	2.38954e10i		−	0.0443148i
$223$			1.02536e12i			1.85931i	0.368434	+	0.929654i	$0.379894\pi$
$223$			1.02536e12i			1.85931i	−0.368434	+	0.929654i	$0.620106\pi$
$224$			5.84039e11i			1.03562i
$225$	1.15101e11			0.199602
$226$	−7.52765e11			−1.27678
$227$		−	3.49060e10i		−	0.0579123i	−0.999581	−	0.0289561i	$-0.990782\pi$
$227$		−	3.49060e10i		−	0.0579123i	0.999581	−	0.0289561i	$-0.00921831\pi$
$228$	3.24032e10	+	2.02735e10i	0.0525912	+	0.0329044i
$229$	−7.50329e11			−1.19145			−0.595723	−	0.803190i	$-0.703135\pi$
$229$	−7.50329e11			−1.19145			−0.595723	+	0.803190i	$0.703135\pi$
$230$		−	6.74904e11i		−	1.04858i
$231$			1.93416e10i			0.0294057i
$232$	4.10294e11			0.610458
$233$	−1.03897e12			−1.51294			−0.756470	−	0.654029i	$-0.773078\pi$
$233$	−1.03897e12			−1.51294			−0.756470	+	0.654029i	$0.773078\pi$
$234$	2.16011e11			0.307891
$235$	−1.68828e11			−0.235562
$236$			1.43464e12i			1.95967i
$237$	−2.93629e10			−0.0392697
$238$			1.70725e12i			2.23569i
$239$	1.27618e12			1.63653			0.818264	−	0.574842i	$-0.194937\pi$
$239$	1.27618e12			1.63653			0.818264	+	0.574842i	$0.194937\pi$
$240$			7.26157e9i			0.00911957i
$241$			2.92171e11i			0.359379i	0.983723	+	0.179689i	$0.0575092\pi$
$241$			2.92171e11i			0.359379i	−0.983723	+	0.179689i	$0.942491\pi$
$242$			3.90783e11i			0.470824i
$243$			1.13106e11i			0.133491i
$244$	7.04742e11			0.814857
$245$	1.48194e11			0.167880
$246$			7.63739e10i			0.0847753i
$247$	−1.55515e11	−	9.72998e10i	−0.169156	−	0.105834i
$248$	4.44151e11			0.473448
$249$			2.18424e10i			0.0228193i
$250$			1.35048e11i			0.138289i
$251$	−6.16784e11			−0.619105			−0.309553	−	0.950882i	$-0.600179\pi$
$251$	−6.16784e11			−0.619105			−0.309553	+	0.950882i	$0.600179\pi$
$252$	−1.11456e12			−1.09673
$253$	−1.31096e12			−1.26470
$254$	1.17350e12			1.10998
$255$			3.93611e10i			0.0365062i
$256$	−1.71047e11			−0.155566
$257$		−	1.80164e12i		−	1.60695i	−0.595339	−	0.803475i	$-0.702982\pi$
$257$		−	1.80164e12i		−	1.60695i	0.595339	−	0.803475i	$-0.297018\pi$
$258$	−7.16415e10			−0.0626709
$259$		−	5.91731e11i		−	0.507721i
$260$			1.47423e11i			0.124079i
$261$		−	1.22225e12i		−	1.00916i
$262$			2.48893e12i			2.01608i
$263$	1.19043e12			0.946070			0.473035	−	0.881044i	$-0.343158\pi$
$263$	1.19043e12			0.946070			0.473035	+	0.881044i	$0.343158\pi$
$264$	−2.88057e10			−0.0224625
$265$		−	8.40685e11i		−	0.643286i
$266$	1.37949e12	+	8.63098e11i	1.03588	+	0.648115i
$267$	4.60384e10			0.0339285
$268$		−	3.19672e12i		−	2.31223i
$269$		−	7.84949e11i		−	0.557289i	−0.960394	−	0.278644i	$-0.910115\pi$
$269$		−	7.84949e11i		−	0.557289i	0.960394	−	0.278644i	$-0.0898850\pi$
$270$	−8.84420e10			−0.0616368
$271$	3.79151e11			0.259398			0.129699	−	0.991553i	$-0.458599\pi$
$271$	3.79151e11			0.259398			0.129699	+	0.991553i	$0.458599\pi$
$272$	1.24504e12			0.836256
$273$	−1.06690e10			−0.00703575
$274$			1.82315e12i			1.18051i
$275$	2.62323e11			0.166791
$276$			1.50674e11i			0.0940792i
$277$	7.77517e11			0.476773			0.238386	−	0.971170i	$-0.423382\pi$
$277$	7.77517e11			0.476773			0.238386	+	0.971170i	$0.423382\pi$
$278$			1.46522e12i			0.882425i
$279$		−	1.32311e12i		−	0.782664i
$280$		−	3.67232e11i		−	0.213378i
$281$			3.00924e11i			0.171761i	0.996305	+	0.0858806i	$0.0273704\pi$
$281$			3.00924e11i			0.171761i	−0.996305	+	0.0858806i	$0.972630\pi$
$282$	6.47983e10			0.0363344
$283$	−1.95608e12			−1.07759			−0.538797	−	0.842435i	$-0.681121\pi$
$283$	−1.95608e12			−1.07759			−0.538797	+	0.842435i	$0.681121\pi$
$284$			5.22101e11i			0.282594i
$285$	3.18046e10	+	1.98990e10i	0.0169148	+	0.0105830i
$286$	4.92306e11			0.257279
$287$			1.89128e12i			0.971284i
$288$			2.59116e12i			1.30777i
$289$	4.73271e12			2.34758
$290$	1.43407e12			0.699168
$291$	−1.34099e11			−0.0642630
$292$	3.21027e12			1.51226
$293$		−	1.69389e12i		−	0.784416i	−0.919877	−	0.392208i	$-0.871711\pi$
$293$		−	1.69389e12i		−	0.784416i	0.919877	−	0.392208i	$-0.128289\pi$
$294$	−5.68785e10			−0.0258947
$295$			1.40814e12i			0.630284i
$296$	8.81274e11			0.387840
$297$			1.71794e11i			0.0743404i
$298$		−	2.45634e12i		−	1.04522i
$299$		−	7.23141e11i		−	0.302599i
$300$		−	3.01498e10i		−	0.0124073i
$301$	−1.77409e12			−0.718031
$302$	1.92908e11			0.0767918
$303$		−	2.06736e11i		−	0.0809475i
$304$	6.29431e11	−	1.00602e12i	0.242426	−	0.387471i
$305$	6.91725e11			0.262080
$306$			7.57442e12i			2.82320i
$307$		−	4.06522e11i		−	0.149071i	−0.997218	−	0.0745353i	$-0.976253\pi$
$307$		−	4.06522e11i		−	0.149071i	0.997218	−	0.0745353i	$-0.0237473\pi$
$308$	−2.54016e12			−0.916449
$309$	1.85559e10			0.00658704
$310$	1.55241e12			0.542248
$311$	1.88277e12			0.647136			0.323568	−	0.946205i	$-0.395118\pi$
$311$	1.88277e12			0.647136			0.323568	+	0.946205i	$0.395118\pi$
$312$		−	1.58895e10i		−	0.00537449i
$313$	−2.43080e12			−0.809148			−0.404574	−	0.914505i	$-0.632580\pi$
$313$	−2.43080e12			−0.809148			−0.404574	+	0.914505i	$0.632580\pi$
$314$		−	6.91230e12i		−	2.26451i
$315$	−1.09397e12			−0.352739
$316$		−	3.85629e12i		−	1.22387i
$317$			2.13991e12i			0.668496i	0.942485	+	0.334248i	$0.108482\pi$
$317$			2.13991e12i			0.668496i	−0.942485	+	0.334248i	$0.891518\pi$
$318$			3.22665e11i			0.0992239i
$319$		−	2.78561e12i		−	0.843270i
$320$	−2.35435e12			−0.701652
$321$	−2.79090e11			−0.0818879
$322$			6.41462e12i			1.85307i
$323$	3.41181e12	−	5.45310e12i	0.970447	−	1.55107i
$324$	−4.93501e12			−1.38217
$325$			1.44700e11i			0.0399072i
$326$			2.54137e10i			0.00690207i
$327$	2.55238e11			0.0682663
$328$	−2.81671e12			−0.741948
$329$	1.60463e12			0.416289
$330$	−1.00683e11			−0.0257267
$331$			4.10457e11i			0.103307i	0.998665	+	0.0516533i	$0.0164491\pi$
$331$			4.10457e11i			0.103307i	−0.998665	+	0.0516533i	$0.983551\pi$
$332$	−2.86860e12			−0.711180
$333$		−	2.62529e12i		−	0.641144i
$334$	−8.00829e12			−1.92667
$335$		−	3.13767e12i		−	0.743676i
$336$		−	6.90176e10i		−	0.0161162i
$337$		−	4.20381e12i		−	0.967149i	−0.875303	−	0.483574i	$-0.839338\pi$
$337$		−	4.20381e12i		−	0.967149i	0.875303	−	0.483574i	$-0.160662\pi$
$338$		−	6.54908e12i		−	1.48456i
$339$	1.64953e11			0.0368435
$340$	−5.16936e12			−1.13774
$341$		−	3.01547e12i		−	0.654008i
$342$	6.12030e12	+	3.82925e12i	1.30810	+	0.818432i
$343$	−5.16061e12			−1.08700
$344$		−	2.64218e12i		−	0.548492i
$345$			1.47891e11i			0.0302584i
$346$	3.57215e11			0.0720359
$347$	3.62966e12			0.721470			0.360735	−	0.932668i	$-0.382526\pi$
$347$	3.62966e12			0.721470			0.360735	+	0.932668i	$0.382526\pi$
$348$	−3.20161e11			−0.0627295
$349$	−9.66951e12			−1.86757			−0.933786	−	0.357832i	$-0.883516\pi$
$349$	−9.66951e12			−1.86757			−0.933786	+	0.357832i	$0.883516\pi$
$350$		−	1.28356e12i		−	0.244386i
$351$	−9.47632e10			−0.0177871
$352$			5.90545e12i			1.09280i
$353$	8.70416e12			1.58801			0.794005	−	0.607911i	$-0.207992\pi$
$353$	8.70416e12			1.58801			0.794005	+	0.607911i	$0.207992\pi$
$354$		−	5.40462e11i		−	0.0972185i
$355$			5.12457e11i			0.0908900i
$356$			6.04631e12i			1.05740i
$357$		−	3.74107e11i		−	0.0645142i
$358$	−1.42870e13			−2.42955
$359$	−1.00622e13			−1.68742			−0.843708	−	0.536802i	$-0.819632\pi$
$359$	−1.00622e13			−1.68742			−0.843708	+	0.536802i	$0.819632\pi$
$360$		−	1.62927e12i		−	0.269452i
$361$	−2.68139e12	−	5.51363e12i	−0.437345	−	0.899294i
$362$	−9.04157e12			−1.45446
$363$		−	8.56319e10i		−	0.0135863i
$364$		−	1.40118e12i		−	0.219274i
$365$	3.15097e12			0.486385
$366$	−2.65492e11			−0.0404247
$367$	−5.16601e11			−0.0775934			−0.0387967	−	0.999247i	$-0.512352\pi$
$367$	−5.16601e11			−0.0775934			−0.0387967	+	0.999247i	$0.512352\pi$
$368$	4.67798e12			0.693138
$369$			8.39090e12i			1.22653i
$370$	3.08025e12			0.444199
$371$			7.99029e12i			1.13682i
$372$	−3.46580e11			−0.0486506
$373$		−	3.90441e12i		−	0.540768i	−0.962753	−	0.270384i	$-0.912849\pi$
$373$		−	3.90441e12i		−	0.540768i	0.962753	−	0.270384i	$-0.0871507\pi$
$374$			1.72626e13i			2.35912i
$375$		−	2.95929e10i		−	0.00399053i
$376$			2.38980e12i			0.317996i
$377$	1.53657e12			0.201765
$378$	8.40597e11			0.108925
$379$		−	8.77175e12i		−	1.12173i	−0.827906	−	0.560867i	$-0.810468\pi$
$379$		−	8.77175e12i		−	1.12173i	0.827906	−	0.560867i	$-0.189532\pi$
$380$	−2.61337e12	+	4.17696e12i	−0.329825	+	0.527160i
$381$	−2.57148e11			−0.0320301
$382$		−	1.22042e13i		−	1.50035i
$383$			4.94803e11i			0.0600397i	0.999549	+	0.0300198i	$0.00955705\pi$
$383$			4.94803e11i			0.0600397i	−0.999549	+	0.0300198i	$0.990443\pi$
$384$	4.15494e11			0.0497632
$385$	−2.49324e12			−0.294755
$386$	2.28395e13			2.66533
$387$	−7.87097e12			−0.906721
$388$		−	1.76115e13i		−	2.00280i
$389$	2.21992e12			0.249224			0.124612	−	0.992206i	$-0.460231\pi$
$389$	2.21992e12			0.249224			0.124612	+	0.992206i	$0.460231\pi$
$390$		−	5.55375e10i		−	0.00615550i
$391$	2.53568e13			2.77467
$392$		−	2.09771e12i		−	0.226629i
$393$		−	5.45398e11i		−	0.0581769i
$394$			1.16355e13i			1.22548i
$395$		−	3.78506e12i		−	0.393629i
$396$	−1.12698e13			−1.15728
$397$	−3.27453e12			−0.332044			−0.166022	−	0.986122i	$-0.553092\pi$
$397$	−3.27453e12			−0.332044			−0.166022	+	0.986122i	$0.553092\pi$
$398$		−	1.15286e12i		−	0.115441i
$399$	−3.02287e11	−	1.89130e11i	−0.0298920	−	0.0187023i
$400$	−9.36060e11			−0.0914121
$401$			3.40784e12i			0.328668i	0.986405	+	0.164334i	$0.0525476\pi$
$401$			3.40784e12i			0.328668i	−0.986405	+	0.164334i	$0.947452\pi$
$402$			1.20428e12i			0.114709i
$403$	1.66336e12			0.156481
$404$	2.71511e13			2.52278
$405$	−4.84385e12			−0.444545
$406$	−1.36301e13			−1.23558
$407$		−	5.98322e12i		−	0.535751i
$408$	5.57164e11			0.0492813
$409$			1.15881e13i			1.01250i	0.862386	+	0.506252i	$0.168969\pi$
$409$			1.15881e13i			1.01250i	−0.862386	+	0.506252i	$0.831031\pi$
$410$	−9.84506e12			−0.849765
$411$		−	3.99506e11i		−	0.0340654i
$412$			2.43698e12i			0.205289i
$413$		−	1.33837e13i		−	1.11385i
$414$			2.84593e13i			2.34003i
$415$	−2.81561e12			−0.228735
$416$	−3.25751e12			−0.261468
$417$		−	3.21072e11i		−	0.0254637i
$418$	1.39486e13	+	8.72713e12i	1.09307	+	0.683896i
$419$	−2.17493e12			−0.168413			−0.0842065	−	0.996448i	$-0.526836\pi$
$419$	−2.17493e12			−0.168413			−0.0842065	+	0.996448i	$0.526836\pi$
$420$			2.86558e11i			0.0219264i
$421$		−	5.36227e12i		−	0.405451i	−0.979236	−	0.202725i	$-0.935020\pi$
$421$		−	5.36227e12i		−	0.405451i	0.979236	−	0.202725i	$-0.0649799\pi$
$422$	4.00528e13			2.99275
$423$	7.11913e12			0.525684
$424$	−1.19001e13			−0.868400
$425$	−5.07388e12			−0.365928
$426$		−	1.96687e11i		−	0.0140194i
$427$	−6.57450e12			−0.463152
$428$		−	3.66535e13i		−	2.55209i
$429$	−1.07879e11			−0.00742418
$430$		−	9.23502e12i		−	0.628197i
$431$		−	1.79511e13i		−	1.20699i	−0.797367	−	0.603495i	$-0.793774\pi$
$431$		−	1.79511e13i		−	1.20699i	0.797367	−	0.603495i	$-0.206226\pi$
$432$		−	6.13021e11i		−	0.0407434i
$433$		−	2.20755e13i		−	1.45034i	−0.688568	−	0.725171i	$-0.741761\pi$
$433$		−	2.20755e13i		−	1.45034i	0.688568	−	0.725171i	$-0.258239\pi$
$434$	−1.47549e13			−0.958267
$435$	−3.14247e11			−0.0201755
$436$			3.35209e13i			2.12756i
$437$	1.28192e13	−	2.04889e13i	0.804363	−	1.28562i
$438$	−1.20938e12			−0.0750226
$439$		−	1.87732e13i		−	1.15137i	−0.817671	−	0.575685i	$-0.804735\pi$
$439$		−	1.87732e13i		−	1.15137i	0.817671	−	0.575685i	$-0.195265\pi$
$440$		−	3.71323e12i		−	0.225158i
$441$	−6.24902e12			−0.374644
$442$	−9.52225e12			−0.564454
$443$	1.41789e13			0.831045			0.415522	−	0.909583i	$-0.363599\pi$
$443$	1.41789e13			0.831045			0.415522	+	0.909583i	$0.363599\pi$
$444$	−6.87676e11			−0.0398537
$445$			5.93463e12i			0.340090i
$446$	5.07303e13			2.87470
$447$			5.38255e11i			0.0301613i
$448$	2.23769e13			1.23997
$449$			1.49386e13i			0.818610i	0.912398	+	0.409305i	$0.134229\pi$
$449$			1.49386e13i			0.818610i	−0.912398	+	0.409305i	$0.865771\pi$
$450$		−	5.69468e12i		−	0.308607i
$451$			1.91235e13i			1.02491i
$452$			2.16636e13i			1.14825i
$453$	−4.22717e10			−0.00221594
$454$	−1.72700e12			−0.0895390
$455$		−	1.37530e12i		−	0.0705245i
$456$	2.81674e11	−	4.50201e11i	0.0142864	−	0.0228340i
$457$	−2.07819e13			−1.04257			−0.521283	−	0.853384i	$-0.674547\pi$
$457$	−2.07819e13			−1.04257			−0.521283	+	0.853384i	$0.674547\pi$
$458$			3.71231e13i			1.84211i
$459$		−	3.32286e12i		−	0.163098i
$460$	−1.94228e13			−0.943025
$461$	1.48470e13			0.713072			0.356536	−	0.934282i	$-0.383958\pi$
$461$	1.48470e13			0.713072			0.356536	+	0.934282i	$0.383958\pi$
$462$	9.56937e11			0.0454646
$463$	−2.52780e13			−1.18806			−0.594029	−	0.804444i	$-0.702464\pi$
$463$	−2.52780e13			−1.18806			−0.594029	+	0.804444i	$0.702464\pi$
$464$			9.94004e12i			0.462166i
$465$	−3.40178e11			−0.0156474
$466$			5.14035e13i			2.33918i
$467$	2.67461e11			0.0120414			0.00602068	−	0.999982i	$-0.498084\pi$
$467$	2.67461e11			0.0120414			0.00602068	+	0.999982i	$0.498084\pi$
$468$		−	6.21651e12i		−	0.276897i
$469$			2.98220e13i			1.31423i
$470$			8.35289e12i			0.364206i
$471$			1.51469e12i			0.0653459i
$472$	1.99325e13			0.850849
$473$	−1.79385e13			−0.757672
$474$			1.45275e12i			0.0607155i
$475$	−2.56510e12	+	4.09981e12i	−0.106081	+	0.169549i
$476$	4.91322e13			2.01063
$477$			3.54499e13i			1.43557i
$478$		−	6.31400e13i		−	2.53026i
$479$	−3.26048e13			−1.29302			−0.646509	−	0.762907i	$-0.723772\pi$
$479$	−3.26048e13			−1.29302			−0.646509	+	0.762907i	$0.723772\pi$
$480$	6.66200e11			0.0261456
$481$	3.30041e12			0.128186
$482$	1.44554e13			0.555641
$483$		−	1.40563e12i		−	0.0534731i
$484$	1.12462e13			0.423427
$485$		−	1.72862e13i		−	0.644155i
$486$	5.59598e12			0.206393
$487$			1.57682e13i			0.575623i	0.957687	+	0.287811i	$0.0929276\pi$
$487$			1.57682e13i			0.575623i	−0.957687	+	0.287811i	$0.907072\pi$
$488$		−	9.79150e12i		−	0.353794i
$489$		−	5.56887e9i		−	0.000199170i
$490$		−	7.33198e12i		−	0.259562i
$491$	−2.72402e13			−0.954559			−0.477279	−	0.878752i	$-0.658377\pi$
$491$	−2.72402e13			−0.954559			−0.477279	+	0.878752i	$0.658377\pi$
$492$	2.19794e12			0.0762412
$493$			5.38796e13i			1.85008i
$494$	−4.81397e12	+	7.69419e12i	−0.163632	+	0.261534i
$495$	−1.10616e13			−0.372213
$496$			1.07603e13i			0.358439i
$497$		−	4.87065e12i		−	0.160622i
$498$	1.08067e12			0.0352813
$499$	−2.09664e13			−0.677673			−0.338836	−	0.940845i	$-0.610033\pi$
$499$	−2.09664e13			−0.677673			−0.338836	+	0.940845i	$0.610033\pi$
$500$	3.88649e12			0.124368
$501$	1.75485e12			0.0555970
$502$			3.05158e13i			0.957208i
$503$	−1.21062e13			−0.375982			−0.187991	−	0.982171i	$-0.560198\pi$
$503$	−1.21062e13			−0.375982			−0.187991	+	0.982171i	$0.560198\pi$
$504$			1.54854e13i			0.476178i
$505$	2.66495e13			0.811396
$506$			6.48608e13i			1.95537i
$507$			1.43509e12i			0.0428391i
$508$		−	3.37717e13i		−	0.998239i
$509$			2.65158e13i			0.776095i	0.921639	+	0.388048i	$0.126850\pi$
$509$			2.65158e13i			0.776095i	−0.921639	+	0.388048i	$0.873150\pi$
$510$	1.94742e12			0.0564427
$511$	−2.99484e13			−0.859545
$512$		−	3.07813e13i		−	0.874858i
$513$	−2.68494e12	−	1.67987e12i	−0.0755698	−	0.0472813i
$514$	−8.91373e13			−2.48453
$515$			2.39197e12i			0.0660267i
$516$			2.06175e12i			0.0563620i
$517$	1.62250e13			0.439271
$518$	−2.92763e13			−0.784995
$519$	−7.82761e10			−0.00207870
$520$	2.04825e12			0.0538725
$521$		−	1.23446e13i		−	0.321579i	−0.986989	−	0.160789i	$-0.948596\pi$
$521$		−	1.23446e13i		−	0.321579i	0.986989	−	0.160789i	$-0.0514040\pi$
$522$	−6.04719e13			−1.56027
$523$		−	3.44066e13i		−	0.879292i	−0.898171	−	0.439646i	$-0.855104\pi$
$523$		−	3.44066e13i		−	0.879292i	0.898171	−	0.439646i	$-0.144896\pi$
$524$	7.16281e13			1.81312
$525$			2.81265e11i			0.00705212i
$526$		−	5.88971e13i		−	1.46273i
$527$			5.83256e13i			1.43485i
$528$		−	6.97864e11i		−	0.0170060i
$529$	5.38466e13			1.29981
$530$	−4.15935e13			−0.994594
$531$		−	5.93784e13i		−	1.40655i
$532$	2.48388e13	−	3.96999e13i	0.582871	−	0.931604i
$533$	−1.05487e13			−0.245224
$534$		−	2.27778e12i		−	0.0524573i
$535$		−	3.59764e13i		−	0.820822i
$536$	−4.44144e13			−1.00392
$537$	3.13070e12			0.0701084
$538$	−3.88359e13			−0.861632
$539$	−1.42420e13			−0.313059
$540$			2.54524e12i			0.0554320i
$541$	−2.31607e13			−0.499764			−0.249882	−	0.968276i	$-0.580392\pi$
$541$	−2.31607e13			−0.499764			−0.249882	+	0.968276i	$0.580392\pi$
$542$		−	1.87588e13i		−	0.401058i
$543$	1.98127e12			0.0419706
$544$		−	1.14224e14i		−	2.39753i
$545$			3.29017e13i			0.684283i
$546$			5.27856e11i			0.0108781i
$547$			2.94964e13i			0.602327i	0.953573	+	0.301163i	$0.0973749\pi$
$547$			2.94964e13i			0.602327i	−0.953573	+	0.301163i	$0.902625\pi$
$548$	5.24679e13			1.06167
$549$	−2.91686e13			−0.584862
$550$		−	1.29786e13i		−	0.257878i
$551$	4.35359e13	+	2.72388e13i	0.857215	+	0.536328i
$552$	2.09343e12			0.0408472
$553$			3.59751e13i			0.695627i
$554$		−	3.84682e13i		−	0.737145i
$555$	−6.74973e11			−0.0128180
$556$	4.21669e13			0.793593
$557$	−2.93826e13			−0.548042			−0.274021	−	0.961724i	$-0.588354\pi$
$557$	−2.93826e13			−0.548042			−0.274021	+	0.961724i	$0.588354\pi$
$558$	−6.54619e13			−1.21009
$559$		−	9.89507e12i		−	0.181284i
$560$	8.89678e12			0.161545
$561$		−	3.78275e12i		−	0.0680759i
$562$	1.48884e13			0.265562
$563$		−	7.86776e13i		−	1.39094i	−0.718554	−	0.695471i	$-0.755196\pi$
$563$		−	7.86776e13i		−	1.39094i	0.718554	−	0.695471i	$-0.244804\pi$
$564$		−	1.86481e12i		−	0.0326767i
$565$			2.12634e13i			0.369309i
$566$			9.67786e13i			1.66608i
$567$	4.60384e13			0.785605
$568$	7.25394e12			0.122697
$569$		−	1.13813e14i		−	1.90823i	−0.299434	−	0.954117i	$-0.596798\pi$
$569$		−	1.13813e14i		−	1.90823i	0.299434	−	0.954117i	$-0.403202\pi$
$570$	9.84516e11	−	1.57356e12i	0.0163625	−	0.0261522i
$571$	2.06960e13			0.340962			0.170481	−	0.985361i	$-0.445468\pi$
$571$	2.06960e13			0.340962			0.170481	+	0.985361i	$0.445468\pi$
$572$		−	1.41679e13i		−	0.231380i
$573$			2.67429e12i			0.0432948i
$574$	9.35723e13			1.50172
$575$	−1.90640e13			−0.303302
$576$	9.92781e13			1.56582
$577$	−8.33152e13			−1.30270			−0.651351	−	0.758777i	$-0.725797\pi$
$577$	−8.33152e13			−1.30270			−0.651351	+	0.758777i	$0.725797\pi$
$578$		−	2.34154e14i		−	3.62963i
$579$	−5.00481e12			−0.0769121
$580$		−	4.12707e13i		−	0.628784i
$581$	2.67610e13			0.404223
$582$			6.63464e12i			0.0993579i
$583$			8.07930e13i			1.19958i
$584$		−	4.46026e13i		−	0.656592i
$585$		−	6.10169e12i		−	0.0890575i
$586$	−8.38062e13			−1.21280
$587$	4.46845e13			0.641161			0.320580	−	0.947221i	$-0.396122\pi$
$587$	4.46845e13			0.641161			0.320580	+	0.947221i	$0.396122\pi$
$588$			1.63689e12i			0.0232880i
$589$	4.71284e13	+	2.94865e13i	0.664824	+	0.415956i
$590$	6.96688e13			0.974492
$591$		−	2.54968e12i		−	0.0353629i
$592$			2.13503e13i			0.293626i
$593$	−8.78031e13			−1.19739			−0.598696	−	0.800976i	$-0.704314\pi$
$593$	−8.78031e13			−1.19739			−0.598696	+	0.800976i	$0.704314\pi$
$594$	8.49961e12			0.114939
$595$	4.82247e13			0.646673
$596$	−7.06901e13			−0.939999
$597$			2.52625e11i			0.00333123i
$598$	−3.57779e13			−0.467852
$599$		−	2.80621e13i		−	0.363903i	−0.983308	−	0.181951i	$-0.941759\pi$
$599$		−	2.80621e13i		−	0.363903i	0.983308	−	0.181951i	$-0.0582414\pi$
$600$	−4.18893e11			−0.00538700
$601$		−	7.53545e13i		−	0.961030i	−0.876987	−	0.480515i	$-0.840450\pi$
$601$		−	7.53545e13i		−	0.961030i	0.876987	−	0.480515i	$-0.159550\pi$
$602$			8.77743e13i			1.11016i
$603$			1.32309e14i			1.65960i
$604$		−	5.55162e12i		−	0.0690613i
$605$	1.10385e13			0.136186
$606$	−1.02284e13			−0.125154
$607$			5.00409e13i			0.607270i	0.952788	+	0.303635i	$0.0982003\pi$
$607$			5.00409e13i			0.607270i	−0.952788	+	0.303635i	$0.901800\pi$
$608$	−9.22957e13	−	5.77460e13i	−1.11087	−	0.695031i
$609$	2.98676e12			0.0356545
$610$		−	3.42235e13i		−	0.405206i
$611$			8.94988e12i			0.105102i
$612$	2.17981e14			2.53900
$613$	5.33238e13			0.616054			0.308027	−	0.951378i	$-0.400331\pi$
$613$	5.33238e13			0.616054			0.308027	+	0.951378i	$0.400331\pi$
$614$	−2.01129e13			−0.230480
$615$	2.15734e12			0.0245213
$616$			3.52924e13i			0.397903i
$617$	−2.75384e12			−0.0307973			−0.0153987	−	0.999881i	$-0.504902\pi$
$617$	−2.75384e12			−0.0307973			−0.0153987	+	0.999881i	$0.504902\pi$
$618$		−	9.18066e11i		−	0.0101843i
$619$	5.29572e13			0.582735			0.291368	−	0.956611i	$-0.405890\pi$
$619$	5.29572e13			0.582735			0.291368	+	0.956611i	$0.405890\pi$
$620$		−	4.46762e13i		−	0.487661i
$621$		−	1.24850e13i		−	0.135185i
$622$		−	9.31514e13i		−	1.00055i
$623$		−	5.64057e13i		−	0.601011i
$624$	3.84949e11			0.00406893
$625$	3.81470e12			0.0400000
$626$			1.20266e14i			1.25104i
$627$	−3.05655e12	−	1.91237e12i	−0.0315423	−	0.0197349i
$628$	−1.98927e14			−2.03655
$629$			1.15728e14i			1.17540i
$630$			5.41250e13i			0.545375i
$631$	7.70953e13			0.770692			0.385346	−	0.922772i	$-0.374082\pi$
$631$	7.70953e13			0.770692			0.385346	+	0.922772i	$0.374082\pi$
$632$	−5.35783e13			−0.531378
$633$	−8.77674e12			−0.0863604
$634$	1.05873e14			1.03357
$635$		−	3.31479e13i		−	0.321061i
$636$	9.28586e12			0.0892353
$637$		−	7.85602e12i		−	0.0749040i
$638$	−1.37820e14			−1.30379
$639$		−	2.16093e13i		−	0.202832i
$640$			5.35597e13i			0.498813i
$641$		−	2.90372e12i		−	0.0268327i	−0.999910	−	0.0134163i	$-0.995729\pi$
$641$		−	2.90372e12i		−	0.0268327i	0.999910	−	0.0134163i	$-0.00427068\pi$
$642$			1.38082e13i			0.126608i
$643$	−1.00563e14			−0.914919			−0.457459	−	0.889231i	$-0.651240\pi$
$643$	−1.00563e14			−0.914919			−0.457459	+	0.889231i	$0.651240\pi$
$644$	1.84604e14			1.66653
$645$			2.02366e12i			0.0181276i
$646$	−2.69796e14	−	1.68801e14i	−2.39813	−	1.50042i
$647$	3.83216e13			0.338004			0.169002	−	0.985616i	$-0.445946\pi$
$647$	3.83216e13			0.338004			0.169002	+	0.985616i	$0.445946\pi$
$648$			6.85657e13i			0.600111i
$649$		−	1.35328e14i		−	1.17534i
$650$	7.15912e12			0.0617011
$651$	3.23322e12			0.0276523
$652$	7.31371e11			0.00620726
$653$	1.41808e14			1.19436			0.597181	−	0.802106i	$-0.296287\pi$
$653$	1.41808e14			1.19436			0.597181	+	0.802106i	$0.296287\pi$
$654$		−	1.26281e13i		−	0.105547i
$655$	7.03051e13			0.583150
$656$		−	6.82394e13i		−	0.561715i
$657$	−1.32870e14			−1.08542
$658$		−	7.93900e13i		−	0.643630i
$659$			1.37868e13i			0.110927i	0.998461	+	0.0554633i	$0.0176636\pi$
$659$			1.37868e13i			0.110927i	−0.998461	+	0.0554633i	$0.982336\pi$
$660$			2.89751e12i			0.0231369i
$661$			2.29135e14i			1.81587i	0.419112	+	0.907935i	$0.362342\pi$
$661$			2.29135e14i			1.81587i	−0.419112	+	0.907935i	$0.637658\pi$
$662$	2.03076e13			0.159724
$663$	2.08660e12			0.0162882
$664$			3.98555e13i			0.308779i
$665$	2.43800e13	−	3.89666e13i	0.187467	−	0.299629i
$666$	−1.29888e14			−0.991283
$667$			2.02441e14i			1.53345i
$668$			2.30468e14i			1.73272i
$669$	−1.11165e13			−0.0829539
$670$	−1.55238e14			−1.14981
$671$	−6.64774e13			−0.488721
$672$	−6.33190e12			−0.0462048
$673$		−	2.07071e13i		−	0.149984i	−0.997184	−	0.0749919i	$-0.976107\pi$
$673$		−	2.07071e13i		−	0.149984i	0.997184	−	0.0749919i	$-0.0238931\pi$
$674$	−2.07986e14			−1.49532
$675$			2.49823e12i			0.0178284i
$676$	−1.88474e14			−1.33511
$677$		−	9.09759e13i		−	0.639710i	−0.947467	−	0.319855i	$-0.896366\pi$
$677$		−	9.09759e13i		−	0.639710i	0.947467	−	0.319855i	$-0.103634\pi$
$678$		−	8.16115e12i		−	0.0569643i
$679$			1.64296e14i			1.13836i
$680$			7.18218e13i			0.493983i
$681$	3.78435e11			0.00258378
$682$	−1.49192e14			−1.01117
$683$			2.64467e13i			0.177938i	0.996034	+	0.0889688i	$0.0283571\pi$
$683$			2.64467e13i			0.177938i	−0.996034	+	0.0889688i	$0.971643\pi$
$684$	1.10200e14	−	1.76134e14i	0.736043	−	1.17642i
$685$	5.14987e13			0.341463
$686$			2.55325e14i			1.68063i
$687$		−	8.13474e12i		−	0.0531570i
$688$	6.40110e13			0.415253
$689$	−4.45662e13			−0.287018
$690$	7.31701e12			0.0467830
$691$	1.07497e14			0.682351			0.341176	−	0.940000i	$-0.389175\pi$
$691$	1.07497e14			0.682351			0.341176	+	0.940000i	$0.389175\pi$
$692$		−	1.02802e13i		−	0.0647842i
$693$	1.05135e14			0.657780
$694$		−	1.79580e14i		−	1.11547i
$695$	4.13880e13			0.255241
$696$			4.44823e12i			0.0272359i
$697$		−	3.69889e14i		−	2.24858i
$698$			4.78406e14i			2.88748i
$699$		−	1.12640e13i		−	0.0675005i
$700$	−3.69391e13			−0.219784
$701$	2.67351e14			1.57940			0.789699	−	0.613495i	$-0.210237\pi$
$701$	2.67351e14			1.57940			0.789699	+	0.613495i	$0.210237\pi$
$702$			4.68847e12i			0.0275008i
$703$	9.35111e13	+	5.85065e13i	0.544611	+	0.340743i
$704$	2.26262e14			1.30842
$705$		−	1.83036e12i		−	0.0105097i
$706$		−	4.30644e14i		−	2.45525i
$707$	−2.53290e14			−1.43391
$708$	−1.55538e13			−0.0874317
$709$	2.66501e13			0.148754			0.0743768	−	0.997230i	$-0.476303\pi$
$709$	2.66501e13			0.148754			0.0743768	+	0.997230i	$0.476303\pi$
$710$	2.53542e13			0.140526
$711$			1.59608e14i			0.878429i
$712$	8.40059e13			0.459102
$713$			2.19146e14i			1.18929i
$714$	−1.85092e13			−0.0997463
$715$		−	1.39062e13i		−	0.0744180i
$716$			4.11161e14i			2.18497i
$717$			1.38358e13i			0.0730145i
$718$			4.97836e14i			2.60894i
$719$	5.46317e13			0.284315			0.142158	−	0.989844i	$-0.454596\pi$
$719$	5.46317e13			0.284315			0.142158	+	0.989844i	$0.454596\pi$
$720$	3.94717e13			0.203997
$721$		−	2.27345e13i		−	0.116683i
$722$	−2.72791e14	+	1.32664e14i	−1.39041	+	0.676185i
$723$	−3.16759e12			−0.0160338
$724$			2.60204e14i			1.30804i
$725$		−	4.05083e13i		−	0.202234i
$726$	−4.23670e12			−0.0210060
$727$	−1.85873e14			−0.915260			−0.457630	−	0.889143i	$-0.651302\pi$
$727$	−1.85873e14			−0.915260			−0.457630	+	0.889143i	$0.651302\pi$
$728$	−1.94676e13			−0.0952042
$729$	2.03436e14			0.988077
$730$		−	1.55896e14i		−	0.752006i
$731$	3.46970e14			1.66228
$732$			7.64051e12i			0.0363552i
$733$	−6.21325e13			−0.293629			−0.146815	−	0.989164i	$-0.546902\pi$
$733$	−6.21325e13			−0.293629			−0.146815	+	0.989164i	$0.546902\pi$
$734$			2.55592e13i			0.119968i
$735$			1.60665e12i			0.00749005i
$736$		−	4.29173e14i		−	1.98721i
$737$			3.01542e14i			1.38679i
$738$	4.15146e14			1.89635
$739$	3.95714e14			1.79539			0.897695	−	0.440617i	$-0.145240\pi$
$739$	3.95714e14			1.79539			0.897695	+	0.440617i	$0.145240\pi$
$740$		−	8.86455e13i		−	0.399483i
$741$	1.05488e12	−	1.68602e12i	0.00472186	−	0.00754696i
$742$	3.95325e14			1.75766
$743$		−	1.80911e14i		−	0.798952i	−0.916744	−	0.399476i	$-0.869192\pi$
$743$		−	1.80911e14i		−	0.798952i	0.916744	−	0.399476i	$-0.130808\pi$
$744$			4.81529e12i			0.0211231i
$745$	−6.93843e13			−0.302329
$746$	−1.93173e14			−0.836090
$747$	1.18728e14			0.510448
$748$	4.96796e14			2.12163
$749$			3.41938e14i			1.45057i
$750$	−1.46413e12			−0.00616982
$751$		−	2.24348e14i		−	0.939124i	−0.882899	−	0.469562i	$-0.844412\pi$
$751$		−	2.24348e14i		−	0.939124i	0.882899	−	0.469562i	$-0.155588\pi$
$752$	−5.78966e13			−0.240749
$753$		−	6.68690e12i		−	0.0276217i
$754$		−	7.60228e13i		−	0.311952i
$755$		−	5.44907e12i		−	0.0222120i
$756$		−	2.41912e13i		−	0.0979601i
$757$	−4.12283e13			−0.165850			−0.0829252	−	0.996556i	$-0.526426\pi$
$757$	−4.12283e13			−0.165850			−0.0829252	+	0.996556i	$0.526426\pi$
$758$	−4.33988e14			−1.73433
$759$		−	1.42129e13i		−	0.0564253i
$760$	5.80336e13	+	3.63095e13i	0.228882	+	0.143203i
$761$	1.23457e14			0.483719			0.241859	−	0.970311i	$-0.422243\pi$
$761$	1.23457e14			0.483719			0.241859	+	0.970311i	$0.422243\pi$
$762$			1.27226e13i			0.0495222i
$763$		−	3.12714e14i		−	1.20927i
$764$	−3.51219e14			−1.34931
$765$	2.13955e14			0.816611
$766$	2.44807e13			0.0928282
$767$	7.46482e13			0.281218
$768$		−	1.85441e12i		−	0.00694065i
$769$	−3.96515e13			−0.147444			−0.0737221	−	0.997279i	$-0.523488\pi$
$769$	−3.96515e13			−0.147444			−0.0737221	+	0.997279i	$0.523488\pi$
$770$			1.23355e14i			0.455725i
$771$	1.95326e13			0.0716948
$772$		−	6.57291e14i		−	2.39702i
$773$			2.29367e14i			0.831063i	0.909579	+	0.415532i	$0.136404\pi$
$773$			2.29367e14i			0.831063i	−0.909579	+	0.415532i	$0.863596\pi$
$774$			3.89422e14i			1.40189i
$775$		−	4.38510e13i		−	0.156845i
$776$	−2.44689e14			−0.869574
$777$	6.41528e12			0.0226522
$778$		−	1.09832e14i		−	0.385329i
$779$	−2.98879e14	−	1.86997e14i	−1.04186	−	0.651851i
$780$	−1.59829e12			−0.00553584
$781$		−	4.92491e13i		−	0.169490i
$782$		−	1.25455e15i		−	4.28996i
$783$	2.65287e13			0.0901379
$784$	5.08204e13			0.171577
$785$	−1.95252e14			−0.655010
$786$	−2.69839e13			−0.0899482
$787$		−	4.39104e14i		−	1.45443i	−0.686407	−	0.727217i	$-0.740813\pi$
$787$		−	4.39104e14i		−	1.45443i	0.686407	−	0.727217i	$-0.259187\pi$
$788$	3.34854e14			1.10211
$789$			1.29061e13i			0.0422094i
$790$	−1.87268e14			−0.608596
$791$		−	2.02098e14i		−	0.652649i
$792$			1.56579e14i			0.502467i
$793$		−	3.66696e13i		−	0.116934i
$794$			1.62010e14i			0.513379i
$795$	9.11434e12			0.0287005
$796$	−3.31777e13			−0.103820
$797$			5.02966e14i			1.56404i	0.623256	+	0.782018i	$0.285810\pi$
$797$			5.02966e14i			1.56404i	−0.623256	+	0.782018i	$0.714190\pi$
$798$	−9.35733e12	+	1.49559e13i	−0.0289160	+	0.0462165i
$799$	−3.13827e14			−0.963731
$800$			8.58772e13i			0.262076i
$801$		−	2.50251e14i		−	0.758950i
$802$	1.68605e14			0.508159
$803$	−3.02820e14			−0.906999
$804$	3.46574e13			0.103161
$805$	1.81194e14			0.536000
$806$		−	8.22960e13i		−	0.241938i
$807$	8.51007e12			0.0248637
$808$		−	3.77230e14i		−	1.09534i
$809$	−9.44587e13			−0.272583			−0.136292	−	0.990669i	$-0.543518\pi$
$809$	−9.44587e13			−0.272583			−0.136292	+	0.990669i	$0.543518\pi$
$810$			2.39653e14i			0.687317i
$811$		−	1.43483e14i		−	0.408976i	−0.978869	−	0.204488i	$-0.934447\pi$
$811$		−	1.43483e14i		−	0.408976i	0.978869	−	0.204488i	$-0.0655529\pi$
$812$			3.92257e14i			1.11120i
$813$			4.11059e12i			0.0115731i
$814$	−2.96024e14			−0.828333
$815$	7.17861e11			0.00199642
$816$			1.34982e13i			0.0373100i
$817$	1.75410e14	−	2.80359e14i	0.481887	−	0.770202i
$818$	5.73330e14			1.56545
$819$			5.79935e13i			0.157384i
$820$			2.83327e14i			0.764222i
$821$	5.72257e13			0.153418			0.0767088	−	0.997054i	$-0.475559\pi$
$821$	5.72257e13			0.153418			0.0767088	+	0.997054i	$0.475559\pi$
$822$	−1.97658e13			−0.0526691
$823$	−5.28593e14			−1.39998			−0.699990	−	0.714152i	$-0.746812\pi$
$823$	−5.28593e14			−1.39998			−0.699990	+	0.714152i	$0.746812\pi$
$824$	3.38588e13			0.0891324
$825$			2.84399e12i			0.00744145i
$826$	−6.62167e14			−1.72214
$827$			4.84912e14i			1.25353i	0.779208	+	0.626766i	$0.215622\pi$
$827$			4.84912e14i			1.25353i	−0.779208	+	0.626766i	$0.784378\pi$
$828$	8.19020e14			2.10447
$829$		−	7.83337e12i		−	0.0200067i	−0.999950	−	0.0100034i	$-0.996816\pi$
$829$		−	7.83337e12i		−	0.0200067i	0.999950	−	0.0100034i	$-0.00318422\pi$
$830$			1.39304e14i			0.353650i
$831$			8.42950e12i			0.0212714i
$832$			1.24808e14i			0.313060i
$833$	2.75470e14			0.686831
$834$	−1.58852e13			−0.0393698
$835$			2.26211e14i			0.557289i
$836$	2.51155e14	−	4.01422e14i	0.615050	−	0.983036i
$837$	2.87178e13			0.0699075
$838$			1.07606e14i			0.260386i
$839$		−	4.38603e14i		−	1.05502i	−0.849548	−	0.527512i	$-0.823125\pi$
$839$		−	4.38603e14i		−	1.05502i	0.849548	−	0.527512i	$-0.176875\pi$
$840$	3.98137e12			0.00951997
$841$	−9.45167e12			−0.0224662
$842$	−2.65302e14			−0.626874
$843$	−3.26248e12			−0.00766321
$844$		−	1.15267e15i		−	2.69148i
$845$	−1.84992e14			−0.429408
$846$		−	3.52224e14i		−	0.812769i
$847$	−1.04915e14			−0.240669
$848$		−	2.88298e14i		−	0.657450i
$849$		−	2.12070e13i		−	0.0480774i
$850$			2.51034e14i			0.565767i
$851$			4.34825e14i			0.974243i
$852$	−5.66039e12			−0.0126081
$853$	2.41203e14			0.534118			0.267059	−	0.963680i	$-0.413948\pi$
$853$	2.41203e14			0.534118			0.267059	+	0.963680i	$0.413948\pi$
$854$			3.25278e14i			0.716085i
$855$	1.08165e14	−	1.72880e14i	0.236731	−	0.378369i
$856$	−5.09254e14			−1.10807
$857$			8.37404e14i			1.81147i	0.423845	+	0.905735i	$0.360680\pi$
$857$			8.37404e14i			1.81147i	−0.423845	+	0.905735i	$0.639320\pi$
$858$			5.33736e12i			0.0114786i
$859$	−8.25194e14			−1.76437			−0.882186	−	0.470901i	$-0.843929\pi$
$859$	−8.25194e14			−1.76437			−0.882186	+	0.470901i	$0.843929\pi$
$860$	−2.65771e14			−0.564958
$861$	−2.05044e13			−0.0433343
$862$	−8.88141e14			−1.86615
$863$		−	3.60737e14i		−	0.753592i	−0.926296	−	0.376796i	$-0.877026\pi$
$863$		−	3.60737e14i		−	0.753592i	0.926296	−	0.376796i	$-0.122974\pi$
$864$	−5.62406e13			−0.116810
$865$		−	1.00903e13i		−	0.0208364i
$866$	−1.09220e15			−2.24240
$867$			5.13099e13i			0.104738i
$868$			4.24625e14i			0.861801i
$869$			3.63758e14i			0.734031i
$870$			1.55476e13i			0.0311937i
$871$	−1.66334e14			−0.331810
$872$	4.65730e14			0.923744
$873$			7.28922e14i			1.43751i
$874$	−1.01370e15	−	6.34236e14i	−1.98771	−	1.24364i
$875$	−3.62568e13			−0.0706885
$876$			3.48043e13i			0.0674703i
$877$			3.60812e14i			0.695477i	0.937592	+	0.347738i	$0.113050\pi$
$877$			3.60812e14i			0.695477i	−0.937592	+	0.347738i	$0.886950\pi$
$878$	−9.28816e14			−1.78015
$879$	1.83644e13			0.0349971
$880$	8.99589e13			0.170463
$881$	5.75162e14			1.08370			0.541852	−	0.840474i	$-0.317723\pi$
$881$	5.75162e14			1.08370			0.541852	+	0.840474i	$0.317723\pi$
$882$			3.09174e14i			0.579243i
$883$	4.68950e14			0.873621			0.436811	−	0.899553i	$-0.356108\pi$
$883$	4.68950e14			0.873621			0.436811	+	0.899553i	$0.356108\pi$
$884$			2.74037e14i			0.507631i
$885$	−1.52665e13			−0.0281204
$886$		−	7.01511e14i		−	1.28489i
$887$			6.90759e13i			0.125808i	0.998020	+	0.0629040i	$0.0200362\pi$
$887$			6.90759e13i			0.125808i	−0.998020	+	0.0629040i	$0.979964\pi$
$888$			9.55438e12i			0.0173037i
$889$			3.15054e14i			0.567383i
$890$	2.93620e14			0.525818
$891$	4.65512e14			0.828977
$892$		−	1.45995e15i		−	2.58531i
$893$	−1.58655e14	+	2.53579e14i	−0.279381	+	0.446535i
$894$	2.66305e13			0.0466329
$895$			4.03566e14i			0.702748i
$896$		−	5.09058e14i		−	0.881510i
$897$	7.83997e12			0.0135006
$898$	7.39095e14			1.26566
$899$	−4.65655e14			−0.792986
$900$	−1.63885e14			−0.277541
$901$		−	1.56271e15i		−	2.63181i
$902$	9.46147e14			1.58462
$903$		−	1.92339e13i		−	0.0320353i
$904$	3.00988e14			0.498548
$905$			2.55398e14i			0.420702i
$906$			2.09142e12i			0.00342610i
$907$			7.21181e14i			1.17492i	0.809254	+	0.587459i	$0.199872\pi$
$907$			7.21181e14i			1.17492i	−0.809254	+	0.587459i	$0.800128\pi$
$908$			4.97006e13i			0.0805254i
$909$	−1.12376e15			−1.81072
$910$	−6.80438e13			−0.109039
$911$		−	7.67499e14i		−	1.22317i	−0.791180	−	0.611583i	$-0.790533\pi$
$911$		−	7.67499e14i		−	1.22317i	0.791180	−	0.611583i	$-0.209467\pi$
$912$	1.09068e13	+	6.82401e12i	0.0172872	+	0.0108160i
$913$	2.70591e14			0.426540
$914$			1.02820e15i			1.61193i
$915$			7.49938e12i			0.0116928i
$916$	1.06835e15			1.65667
$917$	−6.68214e14			−1.03055
$918$	−1.64401e14			−0.252168
$919$	−9.61943e14			−1.46748			−0.733739	−	0.679431i	$-0.762226\pi$
$919$	−9.61943e14			−1.46748			−0.733739	+	0.679431i	$0.762226\pi$
$920$			2.69855e14i			0.409442i
$921$	4.40733e12			0.00665085
$922$		−	7.34565e14i		−	1.10249i
$923$	2.71663e13			0.0405529
$924$		−	2.75393e13i		−	0.0408878i
$925$		−	8.70081e13i		−	0.128485i
$926$			1.25065e15i			1.83687i
$927$		−	1.00864e14i		−	0.147346i
$928$	9.11932e14			1.32502
$929$	−3.10327e14			−0.448478			−0.224239	−	0.974534i	$-0.571990\pi$
$929$	−3.10327e14			−0.448478			−0.224239	+	0.974534i	$0.571990\pi$
$930$			1.68305e13i			0.0241926i
$931$	1.39264e14	−	2.22586e14i	0.199109	−	0.318236i
$932$	1.47932e15			2.10370
$933$			2.04122e13i			0.0288723i
$934$		−	1.32328e13i		−	0.0186173i
$935$	4.87619e14			0.682374
$936$	−8.63706e13			−0.120223
$937$	−1.18172e15			−1.63613			−0.818064	−	0.575127i	$-0.804953\pi$
$937$	−1.18172e15			−1.63613			−0.818064	+	0.575127i	$0.804953\pi$
$938$	1.47546e15			2.03196
$939$		−	2.63537e13i		−	0.0361005i
$940$	2.40385e14			0.327542
$941$			4.76478e14i			0.645795i	0.946434	+	0.322898i	$0.104657\pi$
$941$			4.76478e14i			0.645795i	−0.946434	+	0.322898i	$0.895343\pi$
$942$	7.49401e13			0.101032
$943$		−	1.38978e15i		−	1.86375i
$944$			4.82898e14i			0.644162i
$945$		−	2.37444e13i		−	0.0315066i
$946$			8.87521e14i			1.17145i
$947$	−5.41334e14			−0.710748			−0.355374	−	0.934724i	$-0.615646\pi$
$947$	−5.41334e14			−0.710748			−0.355374	+	0.934724i	$0.615646\pi$
$948$	4.18082e13			0.0546034
$949$		−	1.67039e14i		−	0.217013i
$950$	2.02841e14	+	1.26910e14i	0.262142	+	0.164013i
$951$	−2.32000e13			−0.0298253
$952$		−	6.82630e14i		−	0.872973i
$953$		−	1.36480e15i		−	1.73622i	−0.496368	−	0.868112i	$-0.665333\pi$
$953$		−	1.36480e15i		−	1.73622i	0.496368	−	0.868112i	$-0.334667\pi$
$954$	1.75391e15			2.21955
$955$	−3.44732e14			−0.433975
$956$	−1.81708e15			−2.27555
$957$	3.02003e13			0.0376229
$958$			1.61315e15i			1.99915i
$959$	−4.89469e14			−0.603438
$960$		−	2.55249e13i		−	0.0313045i
$961$	3.15549e14			0.384990
$962$		−	1.63290e14i		−	0.198191i
$963$			1.51705e15i			1.83176i
$964$		−	4.16006e14i		−	0.499706i
$965$		−	6.45150e14i		−	0.770946i
$966$	−6.95445e13			−0.0826756
$967$	8.50215e14			1.00553			0.502767	−	0.864422i	$-0.332315\pi$
$967$	8.50215e14			1.00553			0.502767	+	0.864422i	$0.332315\pi$
$968$		−	1.56252e14i		−	0.183843i
$969$	5.91201e13	+	3.69893e13i	0.0692017	+	0.0432970i
$970$	−8.55245e14			−0.995937
$971$		−	2.33581e14i		−	0.270608i	−0.990804	−	0.135304i	$-0.956799\pi$
$971$		−	2.33581e14i		−	0.270608i	0.990804	−	0.135304i	$-0.0432011\pi$
$972$		−	1.61045e14i		−	0.185616i
$973$	−3.93373e14			−0.451066
$974$	7.80143e14			0.889979
$975$	−1.56877e12			−0.00178048
$976$	2.37215e14			0.267851
$977$		−	4.15303e14i		−	0.466544i	−0.972412	−	0.233272i	$-0.925057\pi$
$977$		−	4.15303e14i		−	0.466544i	0.972412	−	0.233272i	$-0.0749432\pi$
$978$	−2.75524e11			−0.000307939
$979$		−	5.70340e14i		−	0.634192i
$980$	−2.11005e14			−0.233433
$981$		−	1.38740e15i		−	1.52706i
$982$			1.34773e15i			1.47586i
$983$		−	1.41619e15i		−	1.54296i	−0.636256	−	0.771478i	$-0.719518\pi$
$983$		−	1.41619e15i		−	1.54296i	0.636256	−	0.771478i	$-0.280482\pi$
$984$		−	3.05376e13i		−	0.0331024i
$985$	3.28669e14			0.354469
$986$	2.66573e15			2.86043
$987$			1.73967e13i			0.0185729i
$988$	2.21428e14	+	1.38540e14i	0.235206	+	0.147160i
$989$	1.30367e15			1.37780
$990$			5.47280e14i			0.575484i
$991$			1.17461e13i			0.0122892i	0.999981	+	0.00614461i	$0.00195590\pi$
$991$			1.17461e13i			0.0122892i	−0.999981	+	0.00614461i	$0.998044\pi$
$992$	9.87182e14			1.02763
$993$	−4.44999e12			−0.00460907
$994$	−2.40979e14			−0.248340
$995$	−3.25649e13			−0.0333914
$996$		−	3.11001e13i		−	0.0317296i
$997$	−1.12357e15			−1.14057			−0.570287	−	0.821446i	$-0.693168\pi$
$997$	−1.12357e15			−1.14057			−0.570287	+	0.821446i	$0.693168\pi$
$998$			1.03732e15i			1.04776i
$999$	5.69812e13			0.0572670

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	95.11.c.a.56.11	✓	68
19.18	odd	2	inner	95.11.c.a.56.58	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.11.c.a.56.11	✓	68	1.1	even	1	trivial
95.11.c.a.56.58	yes	68	19.18	odd	2	inner

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:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	95.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-49.4757i q^{2} +10.8416i q^{3} -1423.84 q^{4} -1397.54 q^{5} +536.394 q^{6} +13282.9 q^{7} +19782.5i q^{8} +58931.5 q^{9} +O(q^{10})\)	\(q-49.4757i q^{2} +10.8416i q^{3} -1423.84 q^{4} -1397.54 q^{5} +536.394 q^{6} +13282.9 q^{7} +19782.5i q^{8} +58931.5 q^{9} +69144.4i q^{10} +134309. q^{11} -15436.7i q^{12} +74086.3i q^{13} -657182. i q^{14} -15151.5i q^{15} -479263. q^{16} -2.59783e6 q^{17} -2.91567e6i q^{18} +(-1.31333e6 + 2.09910e6i) q^{19} +1.98988e6 q^{20} +144008. i q^{21} -6.64503e6i q^{22} -9.76079e6 q^{23} -214473. q^{24} +1.95312e6 q^{25} +3.66547e6 q^{26} +1.27909e6i q^{27} -1.89128e7 q^{28} -2.07403e7i q^{29} -749633. q^{30} -2.24517e7i q^{31} +4.39691e7i q^{32} +1.45612e6i q^{33} +1.28529e8i q^{34} -1.85635e7 q^{35} -8.39091e7 q^{36} -4.45482e7i q^{37} +(1.03854e8 + 6.49779e7i) q^{38} -803211. q^{39} -2.76469e7i q^{40} +1.42384e8i q^{41} +7.12488e6 q^{42} -1.33561e8 q^{43} -1.91235e8 q^{44} -8.23592e7 q^{45} +4.82922e8i q^{46} +1.20804e8 q^{47} -5.19596e6i q^{48} -1.06039e8 q^{49} -9.66322e7i q^{50} -2.81645e7i q^{51} -1.05487e8i q^{52} +6.01545e8i q^{53} +6.32840e7 q^{54} -1.87703e8 q^{55} +2.62770e8i q^{56} +(-2.27575e7 - 1.42386e7i) q^{57} -1.02614e9 q^{58} -1.00758e9i q^{59} +2.15734e7i q^{60} -4.94958e8 q^{61} -1.11081e9 q^{62} +7.82783e8 q^{63} +1.68464e9 q^{64} -1.03539e8i q^{65} +7.20426e7 q^{66} +2.24514e9i q^{67} +3.69890e9 q^{68} -1.05822e8i q^{69} +9.18440e8i q^{70} -3.66685e8i q^{71} +1.16581e9i q^{72} -2.25465e9 q^{73} -2.20405e9 q^{74} +2.11749e7i q^{75} +(1.86998e9 - 2.98879e9i) q^{76} +1.78402e9 q^{77} +3.97394e7i q^{78} +2.70837e9i q^{79} +6.69790e8 q^{80} +3.46598e9 q^{81} +7.04455e9 q^{82} +2.01469e9 q^{83} -2.05044e8i q^{84} +3.63057e9 q^{85} +6.60804e9i q^{86} +2.24857e8 q^{87} +2.65697e9i q^{88} -4.24647e9i q^{89} +4.07478e9i q^{90} +9.84083e8i q^{91} +1.38978e10 q^{92} +2.43412e8 q^{93} -5.97684e9i q^{94} +(1.83544e9 - 2.93358e9i) q^{95} -4.76694e8 q^{96} +1.23690e10i q^{97} +5.24634e9i q^{98} +7.91503e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 35644 q^{4} - 2044 q^{6} + 76620 q^{7} - 1353552 q^{9}+O(q^{10}) \) 68 * q - 35644 * q^4 - 2044 * q^6 + 76620 * q^7 - 1353552 * q^9	\( 68 q - 35644 q^{4} - 2044 q^{6} + 76620 q^{7} - 1353552 q^{9} - 418144 q^{11} + 21763300 q^{16} - 10023236 q^{17} + 518264 q^{19} + 4962204 q^{23} + 2604244 q^{24} + 132812500 q^{25} + 32178588 q^{26} - 109025284 q^{28} + 39875000 q^{30} + 39875000 q^{35} + 420547696 q^{36} - 504912596 q^{38} + 51693988 q^{39} + 343589380 q^{42} + 72617360 q^{43} - 846875584 q^{44} + 148625000 q^{45} + 426767656 q^{47} + 3802641528 q^{49} + 594603476 q^{54} - 361360620 q^{57} - 1963881788 q^{58} + 7470512872 q^{61} - 2514646024 q^{62} - 6611740944 q^{63} - 13094608884 q^{64} + 9558616040 q^{66} + 17177918780 q^{68} - 2447766556 q^{73} - 1842337832 q^{74} - 5604056776 q^{76} - 320485400 q^{77} - 821875000 q^{80} + 5162401956 q^{81} - 17137563304 q^{82} - 14922506320 q^{83} - 4799500000 q^{85} + 5085654996 q^{87} - 27413957236 q^{92} - 11067885256 q^{93} + 1613500000 q^{95} - 67563054044 q^{96} + 76070139768 q^{99}+O(q^{100}) \) 68 * q - 35644 * q^4 - 2044 * q^6 + 76620 * q^7 - 1353552 * q^9 - 418144 * q^11 + 21763300 * q^16 - 10023236 * q^17 + 518264 * q^19 + 4962204 * q^23 + 2604244 * q^24 + 132812500 * q^25 + 32178588 * q^26 - 109025284 * q^28 + 39875000 * q^30 + 39875000 * q^35 + 420547696 * q^36 - 504912596 * q^38 + 51693988 * q^39 + 343589380 * q^42 + 72617360 * q^43 - 846875584 * q^44 + 148625000 * q^45 + 426767656 * q^47 + 3802641528 * q^49 + 594603476 * q^54 - 361360620 * q^57 - 1963881788 * q^58 + 7470512872 * q^61 - 2514646024 * q^62 - 6611740944 * q^63 - 13094608884 * q^64 + 9558616040 * q^66 + 17177918780 * q^68 - 2447766556 * q^73 - 1842337832 * q^74 - 5604056776 * q^76 - 320485400 * q^77 - 821875000 * q^80 + 5162401956 * q^81 - 17137563304 * q^82 - 14922506320 * q^83 - 4799500000 * q^85 + 5085654996 * q^87 - 27413957236 * q^92 - 11067885256 * q^93 + 1613500000 * q^95 - 67563054044 * q^96 + 76070139768 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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