LMFDB - Embedded newform 75.9.c.h.26.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,9,Mod(26,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("75.26");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	75.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:	$30.5533957546$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 64 x^{10} + 385774 x^{8} - 323639784 x^{6} - 48708595080 x^{4} + 21531002169600 x^{2} + 82\!\cdots\!00 $ x^12 + 64x^10 + 385774x^8 - 323639784x^6 - 48708595080x^4 + 21531002169600*x^2 + 8291960024040000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{16}\cdot 3^{18}\cdot 5^{8} $
Twist minimal:	no (minimal twist has level 15)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			26.2
Root			$4.76228 + 15.2142i$ of defining polynomial
Character	$\chi$	$=$	75.26
Dual form			75.9.c.h.26.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-29.2008i q^{2} +(80.0515 + 12.3596i) q^{3} -596.686 q^{4} +(360.909 - 2337.57i) q^{6} -2074.09 q^{7} +9948.30i q^{8} +(6255.48 + 1978.80i) q^{9} +O(q^{10})$	\(q-29.2008i q^{2} +(80.0515 + 12.3596i) q^{3} -596.686 q^{4} +(360.909 - 2337.57i) q^{6} -2074.09 q^{7} +9948.30i q^{8} +(6255.48 + 1978.80i) q^{9} +11967.5i q^{11} +(-47765.6 - 7374.78i) q^{12} -27810.7 q^{13} +60565.0i q^{14} +137746. q^{16} +32481.8i q^{17} +(57782.6 - 182665. i) q^{18} +122980. q^{19} +(-166034. - 25634.8i) q^{21} +349460. q^{22} +266239. i q^{23} +(-122957. + 796376. i) q^{24} +812096. i q^{26} +(476304. + 235721. i) q^{27} +1.23758e6 q^{28} +793695. i q^{29} +876091. q^{31} -1.47554e6i q^{32} +(-147913. + 958016. i) q^{33} +948494. q^{34} +(-3.73256e6 - 1.18072e6i) q^{36} -1.82354e6 q^{37} -3.59111e6i q^{38} +(-2.22629e6 - 343729. i) q^{39} +149999. i q^{41} +(-748556. + 4.84832e6i) q^{42} +1.65525e6 q^{43} -7.14084e6i q^{44} +7.77439e6 q^{46} -3.35225e6i q^{47} +(1.10268e7 + 1.70249e6i) q^{48} -1.46297e6 q^{49} +(-401461. + 2.60022e6i) q^{51} +1.65943e7 q^{52} +2.01969e6i q^{53} +(6.88324e6 - 1.39084e7i) q^{54} -2.06336e7i q^{56} +(9.84472e6 + 1.51998e6i) q^{57} +2.31765e7 q^{58} +2.16608e6i q^{59} -1.66730e7 q^{61} -2.55825e7i q^{62} +(-1.29744e7 - 4.10421e6i) q^{63} -7.82388e6 q^{64} +(2.79748e7 + 4.31918e6i) q^{66} -2.51124e7 q^{67} -1.93814e7i q^{68} +(-3.29060e6 + 2.13128e7i) q^{69} +4.99704e7i q^{71} +(-1.96857e7 + 6.22314e7i) q^{72} -4.82271e6 q^{73} +5.32488e7i q^{74} -7.33803e7 q^{76} -2.48216e7i q^{77} +(-1.00371e7 + 6.50095e7i) q^{78} -2.56922e7 q^{79} +(3.52154e7 + 2.47567e7i) q^{81} +4.38010e6 q^{82} -4.83717e7i q^{83} +(9.90700e7 + 1.52959e7i) q^{84} -4.83345e7i q^{86} +(-9.80972e6 + 6.35364e7i) q^{87} -1.19056e8 q^{88} +3.21720e6i q^{89} +5.76819e7 q^{91} -1.58861e8i q^{92} +(7.01324e7 + 1.08281e7i) q^{93} -9.78883e7 q^{94} +(1.82370e7 - 1.18119e8i) q^{96} +5.09232e7 q^{97} +4.27198e7i q^{98} +(-2.36813e7 + 7.48625e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 1704 q^{4} - 3012 q^{6} + 22824 q^{9}+O(q^{10}) $ 12 * q - 1704 * q^4 - 3012 * q^6 + 22824 * q^9	$ 12 q - 1704 q^{4} - 3012 q^{6} + 22824 q^{9} + 413328 q^{16} - 276192 q^{19} - 604044 q^{21} - 1173336 q^{24} - 279216 q^{31} + 1225344 q^{34} - 10311840 q^{36} - 3780864 q^{39} + 37414536 q^{46} + 6222300 q^{49} + 3931248 q^{51} + 53281692 q^{54} - 91958256 q^{61} - 57497760 q^{64} + 111065040 q^{66} - 8138748 q^{69} - 232646880 q^{76} - 420402672 q^{79} + 98480772 q^{81} + 528357816 q^{84} - 100211328 q^{91} - 543022776 q^{94} + 333306864 q^{96} + 640360080 q^{99}+O(q^{100}) $ 12 * q - 1704 * q^4 - 3012 * q^6 + 22824 * q^9 + 413328 * q^16 - 276192 * q^19 - 604044 * q^21 - 1173336 * q^24 - 279216 * q^31 + 1225344 * q^34 - 10311840 * q^36 - 3780864 * q^39 + 37414536 * q^46 + 6222300 * q^49 + 3931248 * q^51 + 53281692 * q^54 - 91958256 * q^61 - 57497760 * q^64 + 111065040 * q^66 - 8138748 * q^69 - 232646880 * q^76 - 420402672 * q^79 + 98480772 * q^81 + 528357816 * q^84 - 100211328 * q^91 - 543022776 * q^94 + 333306864 * q^96 + 640360080 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	29.2008i		−	1.82505i	−0.409022	−	0.912525i	$-0.634130\pi$
$2$		−	29.2008i		−	1.82505i	0.409022	−	0.912525i	$-0.365870\pi$
$3$	80.0515	+	12.3596i	0.988290	+	0.152587i
$3$	80.0515	+	12.3596i	0.988290	+	0.152587i
$4$	−596.686			−2.33080
$5$		0			0
$5$		0			0
$6$	360.909	−	2337.57i	0.278479	−	1.80368i
$7$	−2074.09			−0.863843			−0.431921	−	0.901911i	$-0.642164\pi$
$7$	−2074.09			−0.863843			−0.431921	+	0.901911i	$0.642164\pi$
$8$			9948.30i			2.42878i
$9$	6255.48	+	1978.80i	0.953434	+	0.301601i
$10$		0			0
$11$			11967.5i			0.817396i	0.912670	+	0.408698i	$0.134017\pi$
$11$			11967.5i			0.817396i	−0.912670	+	0.408698i	$0.865983\pi$
$12$	−47765.6	−	7374.78i	−2.30351	−	0.355651i
$13$	−27810.7			−0.973731			−0.486866	−	0.873477i	$-0.661860\pi$
$13$	−27810.7			−0.973731			−0.486866	+	0.873477i	$0.661860\pi$
$14$			60565.0i			1.57656i
$15$		0			0
$16$	137746.			2.10184
$17$			32481.8i			0.388906i	0.980912	+	0.194453i	$0.0622931\pi$
$17$			32481.8i			0.388906i	−0.980912	+	0.194453i	$0.937707\pi$
$18$	57782.6	−	182665.i	0.550436	−	1.74006i
$19$	122980.			0.943669			0.471834	−	0.881687i	$-0.343592\pi$
$19$	122980.			0.943669			0.471834	+	0.881687i	$0.343592\pi$
$20$		0			0
$21$	−166034.	−	25634.8i	−0.853727	−	0.131811i
$22$	349460.			1.49179
$23$			266239.i			0.951394i	0.879609	+	0.475697i	$0.157804\pi$
$23$			266239.i			0.951394i	−0.879609	+	0.475697i	$0.842196\pi$
$24$	−122957.	+	796376.i	−0.370601	+	2.40034i
$25$		0			0
$26$			812096.i			1.77711i
$27$	476304.	+	235721.i	0.896249	+	0.443551i
$28$	1.23758e6			2.01345
$29$			793695.i			1.12218i	0.827756	+	0.561089i	$0.189617\pi$
$29$			793695.i			1.12218i	−0.827756	+	0.561089i	$0.810383\pi$
$30$		0			0
$31$	876091.			0.948642			0.474321	−	0.880352i	$-0.342694\pi$
$31$	876091.			0.948642			0.474321	+	0.880352i	$0.342694\pi$
$32$		−	1.47554e6i		−	1.40719i
$33$	−147913.	+	958016.i	−0.124724	+	0.807824i
$34$	948494.			0.709772
$35$		0			0
$36$	−3.73256e6	−	1.18072e6i	−2.22227	−	0.702972i
$37$	−1.82354e6			−0.972991			−0.486495	−	0.873683i	$-0.661725\pi$
$37$	−1.82354e6			−0.972991			−0.486495	+	0.873683i	$0.661725\pi$
$38$		−	3.59111e6i		−	1.72224i
$39$	−2.22629e6	−	343729.i	−0.962329	−	0.148579i
$40$		0			0
$41$			149999.i			0.0530828i	0.999648	+	0.0265414i	$0.00844938\pi$
$41$			149999.i			0.0530828i	−0.999648	+	0.0265414i	$0.991551\pi$
$42$	−748556.	+	4.84832e6i	−0.240562	+	1.55809i
$43$	1.65525e6			0.484160			0.242080	−	0.970256i	$-0.422170\pi$
$43$	1.65525e6			0.484160			0.242080	+	0.970256i	$0.422170\pi$
$44$		−	7.14084e6i		−	1.90519i
$45$		0			0
$46$	7.77439e6			1.73634
$47$		−	3.35225e6i		−	0.686981i	−0.939156	−	0.343491i	$-0.888391\pi$
$47$		−	3.35225e6i		−	0.686981i	0.939156	−	0.343491i	$-0.111609\pi$
$48$	1.10268e7	+	1.70249e6i	2.07723	+	0.320715i
$49$	−1.46297e6			−0.253776
$50$		0			0
$51$	−401461.	+	2.60022e6i	−0.0593420	+	0.384352i
$52$	1.65943e7			2.26958
$53$			2.01969e6i			0.255965i	0.991776	+	0.127982i	$0.0408501\pi$
$53$			2.01969e6i			0.255965i	−0.991776	+	0.127982i	$0.959150\pi$
$54$	6.88324e6	−	1.39084e7i	0.809502	−	1.63570i
$55$		0			0
$56$		−	2.06336e7i		−	2.09809i
$57$	9.84472e6	+	1.51998e6i	0.932618	+	0.143992i
$58$	2.31765e7			2.04803
$59$			2.16608e6i			0.178758i	0.995998	+	0.0893792i	$0.0284883\pi$
$59$			2.16608e6i			0.178758i	−0.995998	+	0.0893792i	$0.971512\pi$
$60$		0			0
$61$	−1.66730e7			−1.20419			−0.602094	−	0.798425i	$-0.705667\pi$
$61$	−1.66730e7			−1.20419			−0.602094	+	0.798425i	$0.705667\pi$
$62$		−	2.55825e7i		−	1.73132i
$63$	−1.29744e7	−	4.10421e6i	−0.823617	−	0.260536i
$64$	−7.82388e6			−0.466339
$65$		0			0
$66$	2.79748e7	+	4.31918e6i	1.47432	+	0.227628i
$67$	−2.51124e7			−1.24620			−0.623102	−	0.782140i	$-0.714128\pi$
$67$	−2.51124e7			−1.24620			−0.623102	+	0.782140i	$0.714128\pi$
$68$		−	1.93814e7i		−	0.906463i
$69$	−3.29060e6	+	2.13128e7i	−0.145171	+	0.940253i
$70$		0			0
$71$			4.99704e7i			1.96643i	0.182441	+	0.983217i	$0.441600\pi$
$71$			4.99704e7i			1.96643i	−0.182441	+	0.983217i	$0.558400\pi$
$72$	−1.96857e7	+	6.22314e7i	−0.732523	+	2.31569i
$73$	−4.82271e6			−0.169824			−0.0849122	−	0.996388i	$-0.527061\pi$
$73$	−4.82271e6			−0.169824			−0.0849122	+	0.996388i	$0.527061\pi$
$74$			5.32488e7i			1.77576i
$75$		0			0
$76$	−7.33803e7			−2.19951
$77$		−	2.48216e7i		−	0.706102i
$78$	−1.00371e7	+	6.50095e7i	−0.271164	+	1.75630i
$79$	−2.56922e7			−0.659618			−0.329809	−	0.944048i	$-0.606984\pi$
$79$	−2.56922e7			−0.659618			−0.329809	+	0.944048i	$0.606984\pi$
$80$		0			0
$81$	3.52154e7	+	2.47567e7i	0.818074	+	0.575113i
$82$	4.38010e6			0.0968787
$83$		−	4.83717e7i		−	1.01925i	−0.860398	−	0.509623i	$-0.829785\pi$
$83$		−	4.83717e7i		−	1.01925i	0.860398	−	0.509623i	$-0.170215\pi$
$84$	9.90700e7	+	1.52959e7i	1.98987	+	0.307226i
$85$		0			0
$86$		−	4.83345e7i		−	0.883615i
$87$	−9.80972e6	+	6.35364e7i	−0.171230	+	1.10904i
$88$	−1.19056e8			−1.98528
$89$			3.21720e6i			0.0512764i	0.999671	+	0.0256382i	$0.00816178\pi$
$89$			3.21720e6i			0.0512764i	−0.999671	+	0.0256382i	$0.991838\pi$
$90$		0			0
$91$	5.76819e7			0.841151
$92$		−	1.58861e8i		−	2.21751i
$93$	7.01324e7	+	1.08281e7i	0.937533	+	0.144751i
$94$	−9.78883e7			−1.25377
$95$		0			0
$96$	1.82370e7	−	1.18119e8i	0.214719	−	1.39071i
$97$	5.09232e7			0.575214			0.287607	−	0.957749i	$-0.407140\pi$
$97$	5.09232e7			0.575214			0.287607	+	0.957749i	$0.407140\pi$
$98$			4.27198e7i			0.463153i
$99$	−2.36813e7	+	7.48625e7i	−0.246527	+	0.779334i
$100$		0			0
$101$			1.75796e8i			1.68936i	0.535271	+	0.844680i	$0.320209\pi$
$101$			1.75796e8i			1.68936i	−0.535271	+	0.844680i	$0.679791\pi$
$102$	7.59284e7	+	1.17230e7i	0.701461	+	0.108302i
$103$	−4.78629e7			−0.425256			−0.212628	−	0.977133i	$-0.568202\pi$
$103$	−4.78629e7			−0.425256			−0.212628	+	0.977133i	$0.568202\pi$
$104$		−	2.76669e8i		−	2.36498i
$105$		0			0
$106$	5.89764e7			0.467149
$107$			1.00866e8i			0.769500i	0.923021	+	0.384750i	$0.125712\pi$
$107$			1.00866e8i			0.769500i	−0.923021	+	0.384750i	$0.874288\pi$
$108$	−2.84204e8	−	1.40651e8i	−2.08898	−	1.03383i
$109$	1.41159e8			1.00001			0.500004	−	0.866023i	$-0.333332\pi$
$109$	1.41159e8			1.00001			0.500004	+	0.866023i	$0.333332\pi$
$110$		0			0
$111$	−1.45977e8	−	2.25382e7i	−0.961597	−	0.148466i
$112$	−2.85698e8			−1.81566
$113$			2.03148e8i			1.24595i	0.782243	+	0.622974i	$0.214076\pi$
$113$			2.03148e8i			1.24595i	−0.782243	+	0.622974i	$0.785924\pi$
$114$	4.43845e7	−	2.87474e8i	0.262792	−	1.70207i
$115$		0			0
$116$		−	4.73586e8i		−	2.61558i
$117$	−1.73970e8	−	5.50320e7i	−0.928389	−	0.293678i
$118$	6.32512e7			0.326243
$119$		−	6.73701e7i		−	0.335953i
$120$		0			0
$121$	7.11379e7			0.331864
$122$			4.86864e8i			2.19770i
$123$	−1.85393e6	+	1.20077e7i	−0.00809976	+	0.0524612i
$124$	−5.22751e8			−2.21110
$125$		0			0
$126$	−1.19846e8	+	3.78863e8i	−0.475490	+	1.50314i
$127$	−1.01064e8			−0.388493			−0.194247	−	0.980953i	$-0.562226\pi$
$127$	−1.01064e8			−0.388493			−0.194247	+	0.980953i	$0.562226\pi$
$128$		−	1.49275e8i		−	0.556094i
$129$	1.32505e8	+	2.04581e7i	0.478490	+	0.0738765i
$130$		0			0
$131$			3.45932e8i			1.17464i	0.809354	+	0.587322i	$0.199818\pi$
$131$			3.45932e8i			1.17464i	−0.809354	+	0.587322i	$0.800182\pi$
$132$	8.82576e7	−	5.71635e8i	0.290708	−	1.88288i
$133$	−2.55071e8			−0.815181
$134$			7.33302e8i			2.27438i
$135$		0			0
$136$	−3.23139e8			−0.944568
$137$		−	5.03253e8i		−	1.42858i	−0.699850	−	0.714290i	$-0.746750\pi$
$137$		−	5.03253e8i		−	1.42858i	0.699850	−	0.714290i	$-0.253250\pi$
$138$	6.22352e8	+	9.60881e7i	1.71601	+	0.264943i
$139$	3.10576e7			0.0831973			0.0415987	−	0.999134i	$-0.486755\pi$
$139$	3.10576e7			0.0831973			0.0415987	+	0.999134i	$0.486755\pi$
$140$		0			0
$141$	4.14323e7	−	2.68353e8i	0.104825	−	0.678937i
$142$	1.45917e9			3.58884
$143$		−	3.32825e8i		−	0.795924i
$144$	8.61671e8	+	2.72573e8i	2.00397	+	0.633918i
$145$		0			0
$146$			1.40827e8i			0.309938i
$147$	−1.17113e8	−	1.80816e7i	−0.250804	−	0.0387229i
$148$	1.08808e9			2.26785
$149$			2.95589e8i			0.599712i	0.953984	+	0.299856i	$0.0969387\pi$
$149$			2.95589e8i			0.599712i	−0.953984	+	0.299856i	$0.903061\pi$
$150$		0			0
$151$	2.81094e8			0.540684			0.270342	−	0.962764i	$-0.412863\pi$
$151$	2.81094e8			0.540684			0.270342	+	0.962764i	$0.412863\pi$
$152$			1.22344e9i			2.29197i
$153$	−6.42751e7	+	2.03189e8i	−0.117294	+	0.370796i
$154$	−7.24811e8			−1.28867
$155$		0			0
$156$	1.32840e9	+	2.05098e8i	2.24300	+	0.346308i
$157$	−9.80391e8			−1.61362			−0.806809	−	0.590812i	$-0.798807\pi$
$157$	−9.80391e8			−1.61362			−0.806809	+	0.590812i	$0.798807\pi$
$158$			7.50232e8i			1.20384i
$159$	−2.49624e7	+	1.61679e8i	−0.0390570	+	0.252968i
$160$		0			0
$161$		−	5.52203e8i		−	0.821855i
$162$	7.22916e8	−	1.02832e9i	1.04961	−	1.49303i
$163$	1.47481e8			0.208922			0.104461	−	0.994529i	$-0.466688\pi$
$163$	1.47481e8			0.208922			0.104461	+	0.994529i	$0.466688\pi$
$164$		−	8.95025e7i		−	0.123726i
$165$		0			0
$166$	−1.41249e9			−1.86017
$167$			1.01192e9i			1.30101i	0.759500	+	0.650507i	$0.225444\pi$
$167$			1.01192e9i			1.30101i	−0.759500	+	0.650507i	$0.774556\pi$
$168$	2.55023e8	−	1.65175e9i	0.320141	−	2.07352i
$169$	−4.22934e7			−0.0518472
$170$		0			0
$171$	7.69298e8	+	2.43353e8i	0.899726	+	0.284611i
$172$	−9.87661e8			−1.12848
$173$		−	1.60800e8i		−	0.179516i	−0.995964	−	0.0897578i	$-0.971391\pi$
$173$		−	1.60800e8i		−	0.179516i	0.995964	−	0.0897578i	$-0.0286093\pi$
$174$	1.85531e9	+	2.86452e8i	2.02405	+	0.312503i
$175$		0			0
$176$			1.64848e9i			1.71804i
$177$	−2.67718e7	+	1.73398e8i	−0.0272762	+	0.176665i
$178$	9.39446e7			0.0935819
$179$		−	1.90240e9i		−	1.85306i	−0.376218	−	0.926531i	$-0.622776\pi$
$179$		−	1.90240e9i		−	1.85306i	0.376218	−	0.926531i	$-0.377224\pi$
$180$		0			0
$181$	−1.50229e9			−1.39971			−0.699857	−	0.714283i	$-0.746753\pi$
$181$	−1.50229e9			−1.39971			−0.699857	+	0.714283i	$0.746753\pi$
$182$		−	1.68436e9i		−	1.53514i
$183$	−1.33470e9	−	2.06071e8i	−1.19009	−	0.183744i
$184$	−2.64863e9			−2.31073
$185$		0			0
$186$	3.16189e8	−	2.04792e9i	0.264177	−	1.71104i
$187$	−3.88726e8			−0.317890
$188$			2.00024e9i			1.60122i
$189$	−9.87895e8	−	4.88906e8i	−0.774218	−	0.383158i
$190$		0			0
$191$		−	2.19783e9i		−	1.65143i	−0.564088	−	0.825714i	$-0.690772\pi$
$191$		−	2.19783e9i		−	1.65143i	0.564088	−	0.825714i	$-0.309228\pi$
$192$	−6.26313e8	−	9.66997e7i	−0.460878	−	0.0711574i
$193$	4.40358e8			0.317378			0.158689	−	0.987329i	$-0.449273\pi$
$193$	4.40358e8			0.317378			0.158689	+	0.987329i	$0.449273\pi$
$194$		−	1.48700e9i		−	1.04979i
$195$		0			0
$196$	8.72931e8			0.591501
$197$			3.14912e8i			0.209085i	0.994520	+	0.104543i	$0.0333379\pi$
$197$			3.14912e8i			0.209085i	−0.994520	+	0.104543i	$0.966662\pi$
$198$	2.18604e9	+	6.91513e8i	1.42232	+	0.449924i
$199$	9.45118e8			0.602662			0.301331	−	0.953520i	$-0.402569\pi$
$199$	9.45118e8			0.602662			0.301331	+	0.953520i	$0.402569\pi$
$200$		0			0
$201$	−2.01029e9	−	3.10379e8i	−1.23161	−	0.190155i
$202$	5.13337e9			3.08317
$203$		−	1.64619e9i		−	0.969385i
$204$	2.39546e8	−	1.55151e9i	0.138315	−	0.895849i
$205$		0			0
$206$			1.39763e9i			0.776112i
$207$	−5.26835e8	+	1.66545e9i	−0.286941	+	0.907092i
$208$	−3.83083e9			−2.04663
$209$			1.47176e9i			0.771351i
$210$		0			0
$211$	1.48716e9			0.750286			0.375143	−	0.926967i	$-0.377594\pi$
$211$	1.48716e9			0.750286			0.375143	+	0.926967i	$0.377594\pi$
$212$		−	1.20512e9i		−	0.596604i
$213$	−6.17612e8	+	4.00020e9i	−0.300053	+	1.94341i
$214$	2.94536e9			1.40438
$215$		0			0
$216$	−2.34502e9	+	4.73841e9i	−1.07729	+	2.17679i
$217$	−1.81709e9			−0.819477
$218$		−	4.12196e9i		−	1.82506i
$219$	−3.86065e8	−	5.96066e7i	−0.167836	−	0.0259130i
$220$		0			0
$221$		−	9.03343e8i		−	0.378690i
$222$	−6.58132e8	+	4.26265e9i	−0.270958	+	1.75496i
$223$	−1.30153e8			−0.0526301			−0.0263150	−	0.999654i	$-0.508377\pi$
$223$	−1.30153e8			−0.0526301			−0.0263150	+	0.999654i	$0.508377\pi$
$224$			3.06040e9i			1.21559i
$225$		0			0
$226$	5.93209e9			2.27391
$227$		−	3.06375e9i		−	1.15385i	−0.816797	−	0.576926i	$-0.804252\pi$
$227$		−	3.06375e9i		−	1.15385i	0.816797	−	0.576926i	$-0.195748\pi$
$228$	−5.87421e9	−	9.06949e8i	−2.17375	−	0.335617i
$229$	−4.48632e9			−1.63135			−0.815677	−	0.578508i	$-0.803635\pi$
$229$	−4.48632e9			−1.63135			−0.815677	+	0.578508i	$0.803635\pi$
$230$		0			0
$231$	3.06784e8	−	1.98701e9i	0.107742	−	0.697833i
$232$	−7.89591e9			−2.72553
$233$		−	2.04765e9i		−	0.694756i	−0.937725	−	0.347378i	$-0.887072\pi$
$233$		−	2.04765e9i		−	0.694756i	0.937725	−	0.347378i	$-0.112928\pi$
$234$	−1.60698e9	+	5.08005e9i	−0.535977	+	1.69436i
$235$		0			0
$236$		−	1.29247e9i		−	0.416651i
$237$	−2.05670e9	−	3.17544e8i	−0.651894	−	0.100649i
$238$	−1.96726e9			−0.613131
$239$			2.57439e9i			0.789011i	0.918893	+	0.394506i	$0.129084\pi$
$239$			2.57439e9i			0.789011i	−0.918893	+	0.394506i	$0.870916\pi$
$240$		0			0
$241$	−2.53228e8			−0.0750662			−0.0375331	−	0.999295i	$-0.511950\pi$
$241$	−2.53228e8			−0.0750662			−0.0375331	+	0.999295i	$0.511950\pi$
$242$		−	2.07728e9i		−	0.605667i
$243$	2.51306e9	+	2.41706e9i	0.720739	+	0.693206i
$244$	9.94854e9			2.80673
$245$		0			0
$246$	3.50633e8	+	5.41361e7i	0.0957443	+	0.0147825i
$247$	−3.42016e9			−0.918880
$248$			8.71561e9i			2.30405i
$249$	5.97853e8	−	3.87222e9i	0.155524	−	1.00731i
$250$		0			0
$251$		−	3.88618e8i		−	0.0979101i	−0.998801	−	0.0489551i	$-0.984411\pi$
$251$		−	3.88618e8i		−	0.0979101i	0.998801	−	0.0489551i	$-0.0155891\pi$
$252$	7.74165e9	+	2.44892e9i	1.91969	+	0.607258i
$253$	−3.18622e9			−0.777666
$254$			2.95116e9i			0.709019i
$255$		0			0
$256$	−6.36187e9			−1.48124
$257$		−	2.95713e9i		−	0.677857i	−0.940812	−	0.338928i	$-0.889936\pi$
$257$		−	2.95713e9i		−	0.677857i	0.940812	−	0.338928i	$-0.110064\pi$
$258$	5.97393e8	−	3.86925e9i	0.134828	−	0.873268i
$259$	3.78218e9			0.840511
$260$		0			0
$261$	−1.57057e9	+	4.96494e9i	−0.338450	+	1.06992i
$262$	1.01015e10			2.14378
$263$		−	2.13881e9i		−	0.447042i	−0.974699	−	0.223521i	$-0.928245\pi$
$263$		−	2.13881e9i		−	0.447042i	0.974699	−	0.223521i	$-0.0717551\pi$
$264$	−9.53063e9	−	1.47148e9i	−1.96203	−	0.302928i
$265$		0			0
$266$			7.44827e9i			1.48775i
$267$	−3.97631e7	+	2.57541e8i	−0.00782412	+	0.0506759i
$268$	1.49842e10			2.90466
$269$			2.43278e9i			0.464616i	0.972642	+	0.232308i	$0.0746277\pi$
$269$			2.43278e9i			0.464616i	−0.972642	+	0.232308i	$0.925372\pi$
$270$		0			0
$271$	3.00867e9			0.557825			0.278913	−	0.960317i	$-0.410026\pi$
$271$	3.00867e9			0.557825			0.278913	+	0.960317i	$0.410026\pi$
$272$			4.47425e9i			0.817419i
$273$	4.61752e9	+	7.12923e8i	0.831301	+	0.128349i
$274$	−1.46954e10			−2.60723
$275$		0			0
$276$	1.96345e9	−	1.27171e10i	0.338364	−	2.19155i
$277$	7.84116e9			1.33187			0.665934	−	0.746011i	$-0.268033\pi$
$277$	7.84116e9			1.33187			0.665934	+	0.746011i	$0.268033\pi$
$278$		−	9.06908e8i		−	0.151839i
$279$	5.48037e9	+	1.73361e9i	0.904468	+	0.286111i
$280$		0			0
$281$			1.64823e9i			0.264358i	0.991226	+	0.132179i	$0.0421973\pi$
$281$			1.64823e9i			0.264358i	−0.991226	+	0.132179i	$0.957803\pi$
$282$	−7.83611e9	−	1.20986e9i	−1.23909	−	0.191310i
$283$	−9.15379e9			−1.42710			−0.713551	−	0.700603i	$-0.752914\pi$
$283$	−9.15379e9			−1.42710			−0.713551	+	0.700603i	$0.752914\pi$
$284$		−	2.98166e10i		−	4.58337i
$285$		0			0
$286$	−9.71875e9			−1.45260
$287$		−	3.11112e8i		−	0.0458552i
$288$	2.91981e9	−	9.23022e9i	0.424408	−	1.34166i
$289$	5.92069e9			0.848752
$290$		0			0
$291$	4.07648e9	+	6.29389e8i	0.568478	+	0.0877702i
$292$	2.87765e9			0.395827
$293$		−	1.35840e10i		−	1.84313i	−0.388224	−	0.921565i	$-0.626911\pi$
$293$		−	1.35840e10i		−	1.84313i	0.388224	−	0.921565i	$-0.373089\pi$
$294$	−5.27998e8	+	3.41978e9i	−0.0706712	+	0.457729i
$295$		0			0
$296$		−	1.81411e10i		−	2.36318i
$297$	−2.82099e9	+	5.70016e9i	−0.362557	+	0.732591i
$298$	8.63142e9			1.09450
$299$		−	7.40431e9i		−	0.926402i
$300$		0			0
$301$	−3.43312e9			−0.418238
$302$		−	8.20816e9i		−	0.986775i
$303$	−2.17276e9	+	1.40727e10i	−0.257775	+	1.66958i
$304$	1.69400e10			1.98344
$305$		0			0
$306$	5.93329e9	+	1.87688e9i	0.676721	+	0.214068i
$307$	−1.01834e10			−1.14640			−0.573202	−	0.819414i	$-0.694299\pi$
$307$	−1.01834e10			−1.14640			−0.573202	+	0.819414i	$0.694299\pi$
$308$			1.48107e10i			1.64579i
$309$	−3.83150e9	−	5.91564e8i	−0.420276	−	0.0648886i
$310$		0			0
$311$			1.21888e10i			1.30292i	0.758682	+	0.651462i	$0.225844\pi$
$311$			1.21888e10i			1.30292i	−0.758682	+	0.651462i	$0.774156\pi$
$312$	3.41951e9	−	2.21478e10i	0.360866	−	2.33729i
$313$	9.39665e9			0.979029			0.489515	−	0.871995i	$-0.337174\pi$
$313$	9.39665e9			0.979029			0.489515	+	0.871995i	$0.337174\pi$
$314$			2.86282e10i			2.94493i
$315$		0			0
$316$	1.53302e10			1.53744
$317$			1.70423e10i			1.68768i	0.536593	+	0.843841i	$0.319711\pi$
$317$			1.70423e10i			1.68768i	−0.536593	+	0.843841i	$0.680289\pi$
$318$	4.72115e9	+	7.28923e8i	0.461678	+	0.0712809i
$319$	−9.49854e9			−0.917263
$320$		0			0
$321$	−1.24666e9	+	8.07446e9i	−0.117416	+	0.760489i
$322$	−1.61248e10			−1.49993
$323$			3.99461e9i			0.366998i
$324$	−2.10125e10	−	1.47720e10i	−1.90677	−	1.34048i
$325$		0			0
$326$		−	4.30656e9i		−	0.381294i
$327$	1.13000e10	+	1.74467e9i	0.988297	+	0.152588i
$328$	−1.49224e9			−0.128927
$329$			6.95286e9i			0.593444i
$330$		0			0
$331$	1.59236e10			1.32657			0.663284	−	0.748368i	$-0.269162\pi$
$331$	1.59236e10			1.32657			0.663284	+	0.748368i	$0.269162\pi$
$332$			2.88627e10i			2.37566i
$333$	−1.14071e10	−	3.60843e9i	−0.927683	−	0.293455i
$334$	2.95490e10			2.37442
$335$		0			0
$336$	−2.28706e10	−	3.53110e9i	−1.79440	−	0.277047i
$337$	1.48149e10			1.14863			0.574315	−	0.818634i	$-0.305268\pi$
$337$	1.48149e10			1.14863			0.574315	+	0.818634i	$0.305268\pi$
$338$			1.23500e9i			0.0946238i
$339$	−2.51083e9	+	1.62623e10i	−0.190116	+	1.23136i
$340$		0			0
$341$			1.04846e10i			0.775416i
$342$	7.10610e9	−	2.24641e10i	0.519430	−	1.64204i
$343$	1.49910e10			1.08307
$344$			1.64669e10i			1.17592i
$345$		0			0
$346$	−4.69549e9			−0.327625
$347$		−	1.98893e10i		−	1.37183i	−0.727681	−	0.685916i	$-0.759402\pi$
$347$		−	1.98893e10i		−	1.37183i	0.727681	−	0.685916i	$-0.240598\pi$
$348$	5.85332e9	−	3.79113e10i	0.399103	−	2.58495i
$349$	8.03757e9			0.541780			0.270890	−	0.962610i	$-0.412682\pi$
$349$	8.03757e9			0.541780			0.270890	+	0.962610i	$0.412682\pi$
$350$		0			0
$351$	−1.32464e10	−	6.55558e9i	−0.872706	−	0.431899i
$352$	1.76585e10			1.15023
$353$		−	1.08598e10i		−	0.699398i	−0.936862	−	0.349699i	$-0.886284\pi$
$353$		−	1.08598e10i		−	0.699398i	0.936862	−	0.349699i	$-0.113716\pi$
$354$	5.06335e9	+	7.81757e8i	0.322422	+	0.0497805i
$355$		0			0
$356$		−	1.91966e9i		−	0.119515i
$357$	8.32664e8	−	5.39307e9i	0.0512622	−	0.332019i
$358$	−5.55516e10			−3.38193
$359$		−	1.46792e9i		−	0.0883741i	−0.999023	−	0.0441870i	$-0.985930\pi$
$359$		−	1.46792e9i		−	0.0883741i	0.999023	−	0.0441870i	$-0.0140698\pi$
$360$		0			0
$361$	−1.85952e9			−0.109489
$362$			4.38680e10i			2.55455i
$363$	5.69469e9	+	8.79233e8i	0.327977	+	0.0506381i
$364$	−3.44180e10			−1.96056
$365$		0			0
$366$	−6.01743e9	+	3.89742e10i	−0.335341	+	2.17197i
$367$	9.23259e9			0.508931			0.254466	−	0.967082i	$-0.418100\pi$
$367$	9.23259e9			0.508931			0.254466	+	0.967082i	$0.418100\pi$
$368$			3.66735e10i			1.99968i
$369$	−2.96819e8	+	9.38318e8i	−0.0160098	+	0.0506110i
$370$		0			0
$371$		−	4.18900e9i		−	0.221113i
$372$	−4.18470e10	−	6.46097e9i	−2.18521	−	0.337385i
$373$	1.35736e10			0.701230			0.350615	−	0.936520i	$-0.385973\pi$
$373$	1.35736e10			0.701230			0.350615	+	0.936520i	$0.385973\pi$
$374$			1.13511e10i			0.580165i
$375$		0			0
$376$	3.33492e10			1.66853
$377$		−	2.20732e10i		−	1.09270i
$378$	−1.42764e10	+	2.88473e10i	−0.699283	+	1.41299i
$379$	1.72701e10			0.837024			0.418512	−	0.908211i	$-0.362552\pi$
$379$	1.72701e10			0.837024			0.418512	+	0.908211i	$0.362552\pi$
$380$		0			0
$381$	−8.09035e9	−	1.24911e9i	−0.383944	−	0.0592791i
$382$	−6.41782e10			−3.01394
$383$			1.59940e9i			0.0743294i	0.999309	+	0.0371647i	$0.0118326\pi$
$383$			1.59940e9i			0.0743294i	−0.999309	+	0.0371647i	$0.988167\pi$
$384$	1.84498e9	−	1.19497e10i	0.0848528	−	0.549582i
$385$		0			0
$386$		−	1.28588e10i		−	0.579231i
$387$	1.03544e10	+	3.27540e9i	0.461614	+	0.146023i
$388$	−3.03852e10			−1.34071
$389$		−	1.30946e10i		−	0.571864i	−0.958250	−	0.285932i	$-0.907697\pi$
$389$		−	1.30946e10i		−	0.571864i	0.958250	−	0.285932i	$-0.0923031\pi$
$390$		0			0
$391$	−8.64792e9			−0.370003
$392$		−	1.45540e10i		−	0.616366i
$393$	−4.27557e9	+	2.76924e10i	−0.179236	+	1.16089i
$394$	9.19567e9			0.381591
$395$		0			0
$396$	1.41303e10	−	4.46694e10i	0.574607	−	1.81647i
$397$	−6.76571e9			−0.272365			−0.136183	−	0.990684i	$-0.543483\pi$
$397$	−6.76571e9			−0.272365			−0.136183	+	0.990684i	$0.543483\pi$
$398$		−	2.75982e10i		−	1.09989i
$399$	−2.04188e10	−	3.15256e9i	−0.805636	−	0.124386i
$400$		0			0
$401$		−	1.74684e10i		−	0.675577i	−0.941222	−	0.337788i	$-0.890321\pi$
$401$		−	1.74684e10i		−	0.675577i	0.941222	−	0.337788i	$-0.109679\pi$
$402$	−9.06330e9	+	5.87020e10i	−0.347042	+	2.24775i
$403$	−2.43647e10			−0.923722
$404$		−	1.04895e11i		−	3.93757i
$405$		0			0
$406$	−4.80701e10			−1.76917
$407$		−	2.18232e10i		−	0.795319i
$408$	−2.58677e10	−	3.99385e9i	−0.933507	−	0.144129i
$409$	−3.04268e10			−1.08733			−0.543667	−	0.839301i	$-0.682964\pi$
$409$	−3.04268e10			−1.08733			−0.543667	+	0.839301i	$0.682964\pi$
$410$		0			0
$411$	6.21999e9	−	4.02862e10i	0.217983	−	1.41185i
$412$	2.85591e10			0.991188
$413$		−	4.49264e9i		−	0.154419i
$414$	4.86326e10	+	1.53840e10i	1.65549	+	0.523682i
$415$		0			0
$416$			4.10359e10i			1.37022i
$417$	2.48621e9	+	3.83859e8i	0.0822231	+	0.0126948i
$418$	4.29766e10			1.40775
$419$		−	6.79143e8i		−	0.0220346i	−0.999939	−	0.0110173i	$-0.996493\pi$
$419$		−	6.79143e8i		−	0.0220346i	0.999939	−	0.0110173i	$-0.00350698\pi$
$420$		0			0
$421$	2.29924e10			0.731905			0.365953	−	0.930633i	$-0.380743\pi$
$421$	2.29924e10			0.731905			0.365953	+	0.930633i	$0.380743\pi$
$422$		−	4.34262e10i		−	1.36931i
$423$	6.63344e9	−	2.09699e10i	0.207194	−	0.654992i
$424$	−2.00924e10			−0.621683
$425$		0			0
$426$	1.16809e11	+	1.80348e10i	3.54681	+	0.547611i
$427$	3.45812e10			1.04023
$428$		−	6.01852e10i		−	1.79355i
$429$	4.11357e9	−	2.66431e10i	0.121448	−	0.786604i
$430$		0			0
$431$			2.00633e10i			0.581426i	0.956810	+	0.290713i	$0.0938925\pi$
$431$			2.00633e10i			0.581426i	−0.956810	+	0.290713i	$0.906108\pi$
$432$	6.56091e10	+	3.24698e10i	1.88378	+	0.932275i
$433$	5.21365e10			1.48317			0.741583	−	0.670861i	$-0.234075\pi$
$433$	5.21365e10			1.48317			0.741583	+	0.670861i	$0.234075\pi$
$434$			5.30604e10i			1.49559i
$435$		0			0
$436$	−8.42277e10			−2.33082
$437$			3.27420e10i			0.897801i
$438$	−1.74056e9	+	1.12734e10i	−0.0472925	+	0.306308i
$439$	−2.32256e10			−0.625330			−0.312665	−	0.949864i	$-0.601222\pi$
$439$	−2.32256e10			−0.625330			−0.312665	+	0.949864i	$0.601222\pi$
$440$		0			0
$441$	−9.15156e9	−	2.89492e9i	−0.241958	−	0.0765389i
$442$	−2.63783e10			−0.691127
$443$		−	1.55300e10i		−	0.403234i	−0.979464	−	0.201617i	$-0.935380\pi$
$443$		−	1.55300e10i		−	0.403234i	0.979464	−	0.201617i	$-0.0646196\pi$
$444$	8.71025e10	+	1.34482e10i	2.24129	+	0.346045i
$445$		0			0
$446$			3.80056e9i			0.0960524i
$447$	−3.65335e9	+	2.36623e10i	−0.0915084	+	0.592689i
$448$	1.62274e10			0.402844
$449$			1.61490e10i			0.397338i	0.980067	+	0.198669i	$0.0636619\pi$
$449$			1.61490e10i			0.397338i	−0.980067	+	0.198669i	$0.936338\pi$
$450$		0			0
$451$	−1.79512e9			−0.0433897
$452$		−	1.21216e11i		−	2.90406i
$453$	2.25020e10	+	3.47420e9i	0.534353	+	0.0825015i
$454$	−8.94639e10			−2.10584
$455$		0			0
$456$	−1.51212e10	+	9.79382e10i	−0.349725	+	2.26513i
$457$	5.74255e10			1.31656			0.658279	−	0.752774i	$-0.271285\pi$
$457$	5.74255e10			1.31656			0.658279	+	0.752774i	$0.271285\pi$
$458$			1.31004e11i			2.97730i
$459$	−7.65665e9	+	1.54712e10i	−0.172499	+	0.348556i
$460$		0			0
$461$		−	8.72792e10i		−	1.93245i	−0.257709	−	0.966223i	$-0.582968\pi$
$461$		−	8.72792e10i		−	1.93245i	0.257709	−	0.966223i	$-0.417032\pi$
$462$	−5.80222e10	−	8.95835e9i	−1.27358	−	0.196635i
$463$	−6.70739e10			−1.45958			−0.729792	−	0.683669i	$-0.760383\pi$
$463$	−6.70739e10			−1.45958			−0.729792	+	0.683669i	$0.760383\pi$
$464$			1.09329e11i			2.35864i
$465$		0			0
$466$	−5.97931e10			−1.26796
$467$			6.93467e10i			1.45800i	0.684512	+	0.729001i	$0.260015\pi$
$467$			6.93467e10i			1.45800i	−0.684512	+	0.729001i	$0.739985\pi$
$468$	1.03805e11	+	3.28368e10i	2.16389	+	0.684506i
$469$	5.20853e10			1.07652
$470$		0			0
$471$	−7.84818e10	−	1.21172e10i	−1.59472	−	0.246217i
$472$	−2.15488e10			−0.434165
$473$			1.98091e10i			0.395750i
$474$	−9.27253e9	+	6.00572e10i	−0.183690	+	1.18974i
$475$		0			0
$476$			4.01988e10i			0.783042i
$477$	−3.99656e9	+	1.26341e10i	−0.0771992	+	0.244046i
$478$	7.51743e10			1.43998
$479$		−	6.78536e10i		−	1.28893i	−0.764632	−	0.644467i	$-0.777079\pi$
$479$		−	6.78536e10i		−	1.28893i	0.764632	−	0.644467i	$-0.222921\pi$
$480$		0			0
$481$	5.07140e10			0.947432
$482$			7.39447e9i			0.136999i
$483$	6.82499e9	−	4.42047e10i	0.125405	−	0.812231i
$484$	−4.24470e10			−0.773509
$485$		0			0
$486$	7.05801e10	−	7.33834e10i	1.26514	−	1.31538i
$487$	−5.60442e10			−0.996357			−0.498179	−	0.867074i	$-0.665998\pi$
$487$	−5.60442e10			−0.996357			−0.498179	+	0.867074i	$0.665998\pi$
$488$		−	1.65868e11i		−	2.92471i
$489$	1.18061e10	+	1.82280e9i	0.206476	+	0.0318789i
$490$		0			0
$491$			2.96652e10i			0.510412i	0.966887	+	0.255206i	$0.0821433\pi$
$491$			2.96652e10i			0.510412i	−0.966887	+	0.255206i	$0.917857\pi$
$492$	1.10621e9	−	7.16481e9i	0.0188789	−	0.122277i
$493$	−2.57806e10			−0.436421
$494$			9.98714e10i			1.67700i
$495$		0			0
$496$	1.20678e11			1.99390
$497$		−	1.03643e11i		−	1.69869i
$498$	−1.13072e11	−	1.74578e10i	−1.83839	−	0.283838i
$499$	7.38741e10			1.19149			0.595744	−	0.803174i	$-0.296857\pi$
$499$	7.38741e10			1.19149			0.595744	+	0.803174i	$0.296857\pi$
$500$		0			0
$501$	−1.25069e10	+	8.10061e10i	−0.198518	+	1.28578i
$502$	−1.13479e10			−0.178691
$503$			2.33952e10i			0.365472i	0.983162	+	0.182736i	$0.0584954\pi$
$503$			2.33952e10i			0.365472i	−0.983162	+	0.182736i	$0.941505\pi$
$504$	4.08299e10	−	1.29073e11i	0.632785	−	2.00039i
$505$		0			0
$506$			9.30400e10i			1.41928i
$507$	−3.38565e9	−	5.22728e8i	−0.0512401	−	0.00791122i
$508$	6.03037e10			0.905501
$509$			3.61802e10i			0.539014i	0.962998	+	0.269507i	$0.0868608\pi$
$509$			3.61802e10i			0.539014i	−0.962998	+	0.269507i	$0.913139\pi$
$510$		0			0
$511$	1.00027e10			0.146702
$512$			1.47557e11i			2.14724i
$513$	5.85757e10	+	2.89890e10i	0.845762	+	0.418565i
$514$	−8.63505e10			−1.23712
$515$		0			0
$516$	−7.90638e10	−	1.22071e10i	−1.11527	−	0.172192i
$517$	4.01180e10			0.561536
$518$		−	1.10443e11i		−	1.53397i
$519$	1.98742e9	−	1.28723e10i	0.0273918	−	0.177413i
$520$		0			0
$521$		−	1.09399e11i		−	1.48478i	−0.669966	−	0.742392i	$-0.733691\pi$
$521$		−	1.09399e11i		−	1.48478i	0.669966	−	0.742392i	$-0.266309\pi$
$522$	1.44980e11	+	4.58617e10i	1.95266	+	0.617687i
$523$	1.03949e10			0.138936			0.0694679	−	0.997584i	$-0.477870\pi$
$523$	1.03949e10			0.138936			0.0694679	+	0.997584i	$0.477870\pi$
$524$		−	2.06413e11i		−	2.73786i
$525$		0			0
$526$	−6.24548e10			−0.815874
$527$			2.84570e10i			0.368932i
$528$	−2.03745e10	+	1.31963e11i	−0.262151	+	1.69792i
$529$	7.42772e9			0.0948491
$530$		0			0
$531$	−4.28624e9	+	1.35499e10i	−0.0539137	+	0.170434i
$532$	1.52197e11			1.90003
$533$		−	4.17159e9i		−	0.0516884i
$534$	7.52041e9	+	1.16111e9i	0.0924861	+	0.0142794i
$535$		0			0
$536$		−	2.49826e11i		−	3.02676i
$537$	2.35128e10	−	1.52290e11i	0.282754	−	1.83136i
$538$	7.10392e10			0.847947
$539$		−	1.75080e10i		−	0.207435i
$540$		0			0
$541$	1.14995e11			1.34243			0.671215	−	0.741263i	$-0.265773\pi$
$541$	1.14995e11			1.34243			0.671215	+	0.741263i	$0.265773\pi$
$542$		−	8.78557e10i		−	1.01806i
$543$	−1.20260e11	−	1.85676e10i	−1.38332	−	0.213578i
$544$	4.79282e10			0.547263
$545$		0			0
$546$	2.08179e10	−	1.34835e11i	0.234243	−	1.51717i
$547$	−9.64858e10			−1.07774			−0.538870	−	0.842389i	$-0.681149\pi$
$547$	−9.64858e10			−1.07774			−0.538870	+	0.842389i	$0.681149\pi$
$548$			3.00284e11i			3.32974i
$549$	−1.04298e11	−	3.29926e10i	−1.14811	−	0.363184i
$550$		0			0
$551$			9.76085e10i			1.05896i
$552$	−2.12026e11	−	3.27359e10i	−2.28367	−	0.352588i
$553$	5.32878e10			0.569806
$554$		−	2.28968e11i		−	2.43072i
$555$		0			0
$556$	−1.85317e10			−0.193917
$557$			7.55411e10i			0.784806i	0.919793	+	0.392403i	$0.128356\pi$
$557$			7.55411e10i			0.784806i	−0.919793	+	0.392403i	$0.871644\pi$
$558$	5.06228e10	−	1.60031e11i	0.522167	−	1.65070i
$559$	−4.60336e10			−0.471441
$560$		0			0
$561$	−3.11181e10	−	4.80448e9i	−0.314168	−	0.0485060i
$562$	4.81296e10			0.482466
$563$			1.11903e11i			1.11381i	0.830578	+	0.556903i	$0.188010\pi$
$563$			1.11903e11i			1.11381i	−0.830578	+	0.556903i	$0.811990\pi$
$564$	−2.47221e10	+	1.60122e11i	−0.244326	+	1.58247i
$565$		0			0
$566$			2.67298e11i			2.60453i
$567$	−7.30398e10	−	5.13476e10i	−0.706687	−	0.496807i
$568$	−4.97120e11			−4.77604
$569$			1.49452e11i			1.42578i	0.701275	+	0.712891i	$0.252615\pi$
$569$			1.49452e11i			1.42578i	−0.701275	+	0.712891i	$0.747385\pi$
$570$		0			0
$571$	5.21898e10			0.490954			0.245477	−	0.969402i	$-0.421055\pi$
$571$	5.21898e10			0.490954			0.245477	+	0.969402i	$0.421055\pi$
$572$			1.98592e11i			1.85514i
$573$	2.71642e10	−	1.75939e11i	0.251987	−	1.63209i
$574$	−9.08470e9			−0.0836880
$575$		0			0
$576$	−4.89421e10	−	1.54819e10i	−0.444624	−	0.140648i
$577$	−2.00263e11			−1.80674			−0.903372	−	0.428859i	$-0.858916\pi$
$577$	−2.00263e11			−1.80674			−0.903372	+	0.428859i	$0.858916\pi$
$578$		−	1.72889e11i		−	1.54901i
$579$	3.52513e10	+	5.44264e9i	0.313662	+	0.0484278i
$580$		0			0
$581$			1.00327e11i			0.880468i
$582$	1.83787e10	−	1.19036e11i	0.160185	−	1.03750i
$583$	−2.41706e10			−0.209225
$584$		−	4.79778e10i		−	0.412467i
$585$		0			0
$586$	−3.96662e11			−3.36380
$587$			4.86434e10i			0.409705i	0.978793	+	0.204852i	$0.0656714\pi$
$587$			4.86434e10i			0.409705i	−0.978793	+	0.204852i	$0.934329\pi$
$588$	6.98794e10	+	1.07890e10i	0.584575	+	0.0902555i
$589$	1.07742e11			0.895204
$590$		0			0
$591$	−3.89217e9	+	2.52092e10i	−0.0319038	+	0.206637i
$592$	−2.51186e11			−2.04507
$593$			2.19946e11i			1.77868i	0.457247	+	0.889340i	$0.348835\pi$
$593$			2.19946e11i			1.77868i	−0.457247	+	0.889340i	$0.651165\pi$
$594$	1.66449e11	+	8.23752e10i	1.33701	+	0.661684i
$595$		0			0
$596$		−	1.76374e11i		−	1.39781i
$597$	7.56581e10	+	1.16812e10i	0.595605	+	0.0919585i
$598$	−2.16212e11			−1.69073
$599$			1.45254e11i			1.12829i	0.825675	+	0.564145i	$0.190794\pi$
$599$			1.45254e11i			1.12829i	−0.825675	+	0.564145i	$0.809206\pi$
$600$		0			0
$601$	−3.38288e10			−0.259292			−0.129646	−	0.991560i	$-0.541384\pi$
$601$	−3.38288e10			−0.259292			−0.129646	+	0.991560i	$0.541384\pi$
$602$			1.00250e11i			0.763304i
$603$	−1.57090e11	−	4.96925e10i	−1.18817	−	0.375856i
$604$	−1.67725e11			−1.26023
$605$		0			0
$606$	4.10934e11	+	6.34462e10i	3.04706	+	0.470452i
$607$	8.61846e10			0.634856			0.317428	−	0.948282i	$-0.397181\pi$
$607$	8.61846e10			0.634856			0.317428	+	0.948282i	$0.397181\pi$
$608$		−	1.81462e11i		−	1.32792i
$609$	2.03462e10	−	1.31780e11i	0.147916	−	0.958033i
$610$		0			0
$611$			9.32286e10i			0.668935i
$612$	3.83520e10	−	1.21240e11i	0.273390	−	0.864253i
$613$	1.61967e11			1.14706			0.573528	−	0.819186i	$-0.305574\pi$
$613$	1.61967e11			1.14706			0.573528	+	0.819186i	$0.305574\pi$
$614$			2.97362e11i			2.09224i
$615$		0			0
$616$	2.46933e11			1.71497
$617$			1.33433e11i			0.920711i	0.887735	+	0.460356i	$0.152278\pi$
$617$			1.33433e11i			0.920711i	−0.887735	+	0.460356i	$0.847722\pi$
$618$	−1.72741e10	+	1.11883e11i	−0.118425	+	0.767024i
$619$	−8.29100e10			−0.564735			−0.282367	−	0.959306i	$-0.591120\pi$
$619$	−8.29100e10			−0.564735			−0.282367	+	0.959306i	$0.591120\pi$
$620$		0			0
$621$	−6.27582e10	+	1.26811e11i	−0.421992	+	0.852686i
$622$	3.55922e11			2.37790
$623$		−	6.67274e9i		−	0.0442947i
$624$	−3.06664e11	−	4.73474e10i	−2.02267	−	0.312290i
$625$		0			0
$626$		−	2.74390e11i		−	1.78678i
$627$	−1.81903e10	+	1.17817e11i	−0.117698	+	0.762319i
$628$	5.84986e11			3.76103
$629$		−	5.92319e10i		−	0.378402i
$630$		0			0
$631$	−1.87684e11			−1.18389			−0.591944	−	0.805979i	$-0.701639\pi$
$631$	−1.87684e11			−1.18389			−0.591944	+	0.805979i	$0.701639\pi$
$632$		−	2.55593e11i		−	1.60207i
$633$	1.19049e11	+	1.83806e10i	0.741501	+	0.114484i
$634$	4.97648e11			3.08010
$635$		0			0
$636$	1.48947e10	−	9.64715e10i	0.0910342	−	0.589618i
$637$	4.06862e10			0.247109
$638$			2.77365e11i			1.67405i
$639$	−9.88815e10	+	3.12589e11i	−0.593078	+	1.87487i
$640$		0			0
$641$			2.47743e11i			1.46747i	0.679436	+	0.733735i	$0.262225\pi$
$641$			2.47743e11i			1.46747i	−0.679436	+	0.733735i	$0.737775\pi$
$642$	2.35780e11	+	3.64034e10i	1.38793	+	0.214290i
$643$	−1.96282e11			−1.14825			−0.574125	−	0.818767i	$-0.694658\pi$
$643$	−1.96282e11			−1.14825			−0.574125	+	0.818767i	$0.694658\pi$
$644$			3.29492e11i			1.91558i
$645$		0			0
$646$	1.16646e11			0.669790
$647$		−	5.06782e10i		−	0.289204i	−0.989490	−	0.144602i	$-0.953810\pi$
$647$		−	5.06782e10i		−	0.289204i	0.989490	−	0.144602i	$-0.0461901\pi$
$648$	−2.46287e11	+	3.50333e11i	−1.39682	+	1.98692i
$649$	−2.59225e10			−0.146116
$650$		0			0
$651$	−1.45461e11	−	2.24584e10i	−0.809881	−	0.125042i
$652$	−8.79997e10			−0.486957
$653$		−	2.96579e11i		−	1.63113i	−0.578668	−	0.815563i	$-0.696427\pi$
$653$		−	2.96579e11i		−	1.63113i	0.578668	−	0.815563i	$-0.303573\pi$
$654$	5.09456e10	−	3.29969e11i	0.278481	−	1.80369i
$655$		0			0
$656$			2.06619e10i			0.111572i
$657$	−3.01684e10	−	9.54320e9i	−0.161916	−	0.0512192i
$658$	2.03029e11			1.08306
$659$		−	2.16427e11i		−	1.14754i	−0.819015	−	0.573772i	$-0.805479\pi$
$659$		−	2.16427e11i		−	1.14754i	0.819015	−	0.573772i	$-0.194521\pi$
$660$		0			0
$661$	2.43348e11			1.27474			0.637370	−	0.770558i	$-0.280022\pi$
$661$	2.43348e11			1.27474			0.637370	+	0.770558i	$0.280022\pi$
$662$		−	4.64982e11i		−	2.42105i
$663$	1.11649e10	−	7.23139e10i	0.0577832	−	0.374255i
$664$	4.81216e11			2.47553
$665$		0			0
$666$	−1.05369e11	+	3.33097e11i	−0.535569	+	1.69307i
$667$	−2.11313e11			−1.06763
$668$		−	6.03801e11i		−	3.03241i
$669$	−1.04189e10	−	1.60863e9i	−0.0520138	−	0.00803067i
$670$		0			0
$671$		−	1.99534e11i		−	0.984298i
$672$	−3.78252e10	+	2.44990e11i	−0.185483	+	1.20135i
$673$	−1.94434e11			−0.947790			−0.473895	−	0.880581i	$-0.657152\pi$
$673$	−1.94434e11			−0.947790			−0.473895	+	0.880581i	$0.657152\pi$
$674$		−	4.32608e11i		−	2.09631i
$675$		0			0
$676$	2.52359e10			0.120846
$677$			2.37969e11i			1.13283i	0.824119	+	0.566417i	$0.191671\pi$
$677$			2.37969e11i			1.13283i	−0.824119	+	0.566417i	$0.808329\pi$
$678$	4.74873e11	+	7.33181e10i	2.24729	+	0.346970i
$679$	−1.05619e11			−0.496894
$680$		0			0
$681$	3.78666e10	−	2.45258e11i	0.176063	−	1.14034i
$682$	3.06159e11			1.41517
$683$			3.02984e11i			1.39231i	0.717891	+	0.696156i	$0.245108\pi$
$683$			3.02984e11i			1.39231i	−0.717891	+	0.696156i	$0.754892\pi$
$684$	−4.59029e11	−	1.45205e11i	−2.09709	−	0.663373i
$685$		0			0
$686$		−	4.37749e11i		−	1.97665i
$687$	−3.59136e11	−	5.54489e10i	−1.61225	−	0.248924i
$688$	2.28004e11			1.01763
$689$		−	5.61690e10i		−	0.249241i
$690$		0			0
$691$	3.45611e11			1.51592			0.757959	−	0.652303i	$-0.226197\pi$
$691$	3.45611e11			1.51592			0.757959	+	0.652303i	$0.226197\pi$
$692$			9.59472e10i			0.418416i
$693$	4.91171e10	−	1.55271e11i	0.212961	−	0.673222i
$694$	−5.80782e11			−2.50366
$695$		0			0
$696$	−6.32079e11	−	9.75900e10i	−2.69361	−	0.415880i
$697$	−4.87225e9			−0.0206442
$698$		−	2.34703e11i		−	0.988775i
$699$	2.53081e10	−	1.63918e11i	0.106011	−	0.686621i
$700$		0			0
$701$		−	1.76735e11i		−	0.731896i	−0.930635	−	0.365948i	$-0.880745\pi$
$701$		−	1.76735e11i		−	0.731896i	0.930635	−	0.365948i	$-0.119255\pi$
$702$	−1.91428e11	+	3.86804e11i	−0.788238	+	1.59273i
$703$	−2.24259e11			−0.918181
$704$		−	9.36322e10i		−	0.381184i
$705$		0			0
$706$	−3.17116e11			−1.27644
$707$		−	3.64615e11i		−	1.45934i
$708$	1.59744e10	−	1.03464e11i	0.0635756	−	0.411772i
$709$	−6.57734e10			−0.260295			−0.130147	−	0.991495i	$-0.541545\pi$
$709$	−6.57734e10			−0.260295			−0.130147	+	0.991495i	$0.541545\pi$
$710$		0			0
$711$	−1.60717e11	−	5.08397e10i	−0.628902	−	0.198941i
$712$	−3.20056e10			−0.124539
$713$			2.33250e11i			0.902532i
$714$	−1.57482e11	−	2.43145e10i	−0.605952	−	0.0935560i
$715$		0			0
$716$			1.13514e12i			4.31912i
$717$	−3.18184e10	+	2.06084e11i	−0.120393	+	0.779772i
$718$	−4.28645e10			−0.161287
$719$		−	7.88079e10i		−	0.294886i	−0.989071	−	0.147443i	$-0.952896\pi$
$719$		−	7.88079e10i		−	0.294886i	0.989071	−	0.147443i	$-0.0471043\pi$
$720$		0			0
$721$	9.92718e10			0.367354
$722$			5.42994e10i			0.199823i
$723$	−2.02713e10	−	3.12979e9i	−0.0741871	−	0.0114541i
$724$	8.96395e11			3.26246
$725$		0			0
$726$	2.56743e10	−	1.66290e11i	0.0924171	−	0.598575i
$727$	1.84656e11			0.661036			0.330518	−	0.943800i	$-0.392777\pi$
$727$	1.84656e11			0.661036			0.330518	+	0.943800i	$0.392777\pi$
$728$			5.73836e11i			2.04297i
$729$	1.71301e11	+	2.24550e11i	0.606525	+	0.795064i
$730$		0			0
$731$			5.37653e10i			0.188292i
$732$	7.96395e11	+	1.22960e11i	2.77386	+	0.428270i
$733$	5.18772e11			1.79705			0.898526	−	0.438921i	$-0.144639\pi$
$733$	5.18772e11			1.79705			0.898526	+	0.438921i	$0.144639\pi$
$734$		−	2.69599e11i		−	0.928825i
$735$		0			0
$736$	3.92847e11			1.33879
$737$		−	3.00533e11i		−	1.01864i
$738$	2.73996e10	+	8.66735e9i	0.0923675	+	0.0292187i
$739$	3.63264e11			1.21799			0.608997	−	0.793173i	$-0.291572\pi$
$739$	3.63264e11			1.21799			0.608997	+	0.793173i	$0.291572\pi$
$740$		0			0
$741$	−2.73789e11	−	4.22717e10i	−0.908120	−	0.140209i
$742$	−1.22322e11			−0.403543
$743$			1.03812e11i			0.340637i	0.985389	+	0.170318i	$0.0544796\pi$
$743$			1.03812e11i			0.340637i	−0.985389	+	0.170318i	$0.945520\pi$
$744$	−1.07721e11	+	6.97698e11i	−0.351568	+	2.27707i
$745$		0			0
$746$		−	3.96360e11i		−	1.27978i
$747$	9.57180e10	−	3.02588e11i	0.307405	−	0.971783i
$748$	2.31947e11			0.740940
$749$		−	2.09204e11i		−	0.664727i
$750$		0			0
$751$	8.69686e10			0.273403			0.136701	−	0.990612i	$-0.456350\pi$
$751$	8.69686e10			0.273403			0.136701	+	0.990612i	$0.456350\pi$
$752$		−	4.61761e11i		−	1.44393i
$753$	4.80314e9	−	3.11094e10i	0.0149398	−	0.0967636i
$754$	−6.44556e11			−1.99423
$755$		0			0
$756$	5.89463e11	+	2.91723e11i	1.80455	+	0.893067i
$757$	9.42170e10			0.286910			0.143455	−	0.989657i	$-0.454179\pi$
$757$	9.42170e10			0.286910			0.143455	+	0.989657i	$0.454179\pi$
$758$		−	5.04300e11i		−	1.52761i
$759$	−2.55061e11	−	3.93802e10i	−0.768560	−	0.118662i
$760$		0			0
$761$		−	3.69015e11i		−	1.10029i	−0.835071	−	0.550143i	$-0.814573\pi$
$761$		−	3.69015e11i		−	1.10029i	0.835071	−	0.550143i	$-0.185427\pi$
$762$	−3.64750e10	+	2.36245e11i	−0.108187	+	0.700716i
$763$	−2.92776e11			−0.863849
$764$			1.31141e12i			3.84916i
$765$		0			0
$766$	4.67036e10			0.135655
$767$		−	6.02403e10i		−	0.174063i
$768$	−5.09277e11	−	7.86299e10i	−1.46389	−	0.226018i
$769$	2.57584e11			0.736569			0.368284	−	0.929713i	$-0.379945\pi$
$769$	2.57584e11			0.736569			0.368284	+	0.929713i	$0.379945\pi$
$770$		0			0
$771$	3.65488e10	−	2.36723e11i	0.103432	−	0.669919i
$772$	−2.62756e11			−0.739746
$773$		−	4.50174e11i		−	1.26085i	−0.776251	−	0.630424i	$-0.782881\pi$
$773$		−	4.50174e11i		−	1.26085i	0.776251	−	0.630424i	$-0.217119\pi$
$774$	9.56444e10	−	3.02355e11i	0.266499	−	0.842469i
$775$		0			0
$776$			5.06600e11i			1.39707i
$777$	3.02769e11	+	4.67461e10i	0.830669	+	0.128251i
$778$	−3.82371e11			−1.04368
$779$			1.84469e10i			0.0500926i
$780$		0			0
$781$	−5.98020e11			−1.60736
$782$			2.52526e11i			0.675273i
$783$	−1.87091e11	+	3.78040e11i	−0.497743	+	1.00575i
$784$	−2.01518e11			−0.533397
$785$		0			0
$786$	8.08640e11	+	1.24850e11i	2.11868	+	0.327114i
$787$	−1.63448e11			−0.426070			−0.213035	−	0.977045i	$-0.568335\pi$
$787$	−1.63448e11			−0.426070			−0.213035	+	0.977045i	$0.568335\pi$
$788$		−	1.87903e11i		−	0.487337i
$789$	2.64347e10	−	1.71215e11i	0.0682129	−	0.441807i
$790$		0			0
$791$		−	4.21347e11i		−	1.07630i
$792$	−7.44754e11	−	2.35589e11i	−1.89283	−	0.598761i
$793$	4.63688e11			1.17256
$794$			1.97564e11i			0.497080i
$795$		0			0
$796$	−5.63939e11			−1.40469
$797$			9.45344e10i			0.234292i	0.993115	+	0.117146i	$0.0373745\pi$
$797$			9.45344e10i			0.234292i	−0.993115	+	0.117146i	$0.962626\pi$
$798$	−9.20574e10	+	5.96245e11i	−0.227011	+	1.47032i
$799$	1.08887e11			0.267171
$800$		0			0
$801$	−6.36619e9	+	2.01251e10i	−0.0154650	+	0.0488887i
$802$	−5.10090e11			−1.23296
$803$		−	5.77158e10i		−	0.138814i
$804$	1.19951e12	+	1.85198e11i	2.87065	+	0.443214i
$805$		0			0
$806$			7.11469e11i			1.68584i
$807$	−3.00681e10	+	1.94748e11i	−0.0708944	+	0.459175i
$808$	−1.74887e12			−4.10309
$809$			1.27394e11i			0.297409i	0.988882	+	0.148704i	$0.0475102\pi$
$809$			1.27394e11i			0.297409i	−0.988882	+	0.148704i	$0.952490\pi$
$810$		0			0
$811$	8.64282e10			0.199789			0.0998946	−	0.994998i	$-0.468149\pi$
$811$	8.64282e10			0.199789			0.0998946	+	0.994998i	$0.468149\pi$
$812$			9.82259e11i			2.25945i
$813$	2.40849e11	+	3.71859e10i	0.551293	+	0.0851170i
$814$	−6.37255e11			−1.45150
$815$		0			0
$816$	−5.52998e10	+	3.58171e11i	−0.124728	+	0.807847i
$817$	2.03562e11			0.456886
$818$			8.88486e11i			1.98444i
$819$	3.60828e11	+	1.14141e11i	0.801982	+	0.253692i
$820$		0			0
$821$			4.69914e11i			1.03430i	0.855895	+	0.517149i	$0.173007\pi$
$821$			4.69914e11i			1.03430i	−0.855895	+	0.517149i	$0.826993\pi$
$822$	−1.17639e12	−	1.81629e11i	−2.57670	−	0.397830i
$823$	−2.66887e11			−0.581739			−0.290869	−	0.956763i	$-0.593944\pi$
$823$	−2.66887e11			−0.581739			−0.290869	+	0.956763i	$0.593944\pi$
$824$		−	4.76154e11i		−	1.03285i
$825$		0			0
$826$	−1.31189e11			−0.281822
$827$			7.66086e11i			1.63778i	0.573951	+	0.818889i	$0.305410\pi$
$827$			7.66086e11i			1.63778i	−0.573951	+	0.818889i	$0.694590\pi$
$828$	3.14355e11	−	9.93753e11i	0.668804	−	2.11425i
$829$	−5.72793e11			−1.21277			−0.606386	−	0.795170i	$-0.707381\pi$
$829$	−5.72793e11			−1.21277			−0.606386	+	0.795170i	$0.707381\pi$
$830$		0			0
$831$	6.27696e11	+	9.69133e10i	1.31627	+	0.203226i
$832$	2.17588e11			0.454089
$833$		−	4.75198e10i		−	0.0986948i
$834$	1.12090e10	−	7.25993e10i	0.0231687	−	0.150061i
$835$		0			0
$836$		−	8.78179e11i		−	1.79787i
$837$	4.17285e11	+	2.06513e11i	0.850219	+	0.420771i
$838$	−1.98315e10			−0.0402142
$839$			1.37426e11i			0.277346i	0.990338	+	0.138673i	$0.0442836\pi$
$839$			1.37426e11i			0.277346i	−0.990338	+	0.138673i	$0.955716\pi$
$840$		0			0
$841$	−1.29705e11			−0.259282
$842$		−	6.71395e11i		−	1.33576i
$843$	−2.03714e10	+	1.31943e11i	−0.0403376	+	0.261262i
$844$	−8.87366e11			−1.74877
$845$		0			0
$846$	−6.12339e11	−	1.93702e11i	−1.19539	−	0.378139i
$847$	−1.47546e11			−0.286678
$848$			2.78205e11i			0.537998i
$849$	−7.32774e11	−	1.13137e11i	−1.41039	−	0.217758i
$850$		0			0
$851$		−	4.85498e11i		−	0.925698i
$852$	3.68520e11	−	2.38687e12i	0.699364	−	4.52970i
$853$	5.59514e11			1.05685			0.528426	−	0.848979i	$-0.322782\pi$
$853$	5.59514e11			1.05685			0.528426	+	0.848979i	$0.322782\pi$
$854$		−	1.00980e12i		−	1.89847i
$855$		0			0
$856$	−1.00344e12			−1.86895
$857$		−	4.92440e11i		−	0.912914i	−0.889745	−	0.456457i	$-0.849118\pi$
$857$		−	4.92440e11i		−	0.912914i	0.889745	−	0.456457i	$-0.150882\pi$
$858$	−7.78000e11	−	1.20120e11i	−1.43559	−	0.221648i
$859$	2.33490e11			0.428840			0.214420	−	0.976742i	$-0.431214\pi$
$859$	2.33490e11			0.428840			0.214420	+	0.976742i	$0.431214\pi$
$860$		0			0
$861$	3.84520e9	−	2.49049e10i	0.00699692	−	0.0453182i
$862$	5.85866e11			1.06113
$863$		−	1.43714e11i		−	0.259093i	−0.991573	−	0.129546i	$-0.958648\pi$
$863$		−	1.43714e11i		−	0.259093i	0.991573	−	0.129546i	$-0.0413521\pi$
$864$	3.47816e11	−	7.02806e11i	0.624159	−	1.26119i
$865$		0			0
$866$		−	1.52243e12i		−	2.70685i
$867$	4.73960e11	+	7.31771e10i	0.838813	+	0.129509i
$868$	1.08423e12			1.91004
$869$		−	3.07471e11i		−	0.539169i
$870$		0			0
$871$	6.98395e11			1.21347
$872$			1.40429e12i			2.42880i
$873$	3.18549e11	+	1.00767e11i	0.548428	+	0.173485i
$874$	9.56094e11			1.63853
$875$		0			0
$876$	2.30360e11	+	3.55664e10i	0.391192	+	0.0603982i
$877$	6.46204e11			1.09237			0.546187	−	0.837663i	$-0.316079\pi$
$877$	6.46204e11			1.09237			0.546187	+	0.837663i	$0.316079\pi$
$878$			6.78206e11i			1.14126i
$879$	1.67892e11	−	1.08742e12i	0.281238	−	1.82155i
$880$		0			0
$881$			8.24361e11i			1.36840i	0.729294	+	0.684201i	$0.239849\pi$
$881$			8.24361e11i			1.36840i	−0.729294	+	0.684201i	$0.760151\pi$
$882$	−8.45340e10	+	2.67233e11i	−0.139687	+	0.441586i
$883$	−7.15195e11			−1.17647			−0.588236	−	0.808689i	$-0.700178\pi$
$883$	−7.15195e11			−1.17647			−0.588236	+	0.808689i	$0.700178\pi$
$884$			5.39012e11i			0.882652i
$885$		0			0
$886$	−4.53489e11			−0.735922
$887$			6.02155e11i			0.972779i	0.873742	+	0.486389i	$0.161686\pi$
$887$			6.02155e11i			0.972779i	−0.873742	+	0.486389i	$0.838314\pi$
$888$	2.24216e11	−	1.45222e12i	0.360592	−	2.33551i
$889$	2.09616e11			0.335597
$890$		0			0
$891$	−2.96276e11	+	4.21440e11i	−0.470095	+	0.668690i
$892$	7.76603e10			0.122670
$893$		−	4.12259e11i		−	0.648283i
$894$	6.90958e11	+	1.06681e11i	1.08169	+	0.167007i
$895$		0			0
$896$			3.09610e11i			0.480378i
$897$	9.15140e10	−	5.92726e11i	0.141357	−	0.915554i
$898$	4.71563e11			0.725162
$899$			6.95349e11i			1.06454i
$900$		0			0
$901$	−6.56030e10			−0.0995462
$902$			5.24188e10i			0.0791883i
$903$	−2.74827e11	−	4.24319e10i	−0.413340	−	0.0638177i
$904$	−2.02098e12			−3.02614
$905$		0			0
$906$	1.01449e11	−	6.57076e11i	0.150569	−	0.975220i
$907$	−5.73238e11			−0.847044			−0.423522	−	0.905886i	$-0.639206\pi$
$907$	−5.73238e11			−0.847044			−0.423522	+	0.905886i	$0.639206\pi$
$908$			1.82810e12i			2.68940i
$909$	−3.47865e11	+	1.09969e12i	−0.509512	+	1.61069i
$910$		0			0
$911$			5.47261e11i			0.794550i	0.917700	+	0.397275i	$0.130044\pi$
$911$			5.47261e11i			0.794550i	−0.917700	+	0.397275i	$0.869956\pi$
$912$	1.35608e12	+	2.09372e11i	1.96022	+	0.302648i
$913$	5.78888e11			0.833127
$914$		−	1.67687e12i		−	2.40278i
$915$		0			0
$916$	2.67692e12			3.80236
$917$		−	7.17494e11i		−	1.01471i
$918$	4.51771e11	+	2.23580e11i	0.636133	+	0.314820i
$919$	−5.41675e11			−0.759410			−0.379705	−	0.925108i	$-0.623975\pi$
$919$	−5.41675e11			−0.759410			−0.379705	+	0.925108i	$0.623975\pi$
$920$		0			0
$921$	−8.15193e11	−	1.25862e11i	−1.13298	−	0.174927i
$922$	−2.54862e12			−3.52681
$923$		−	1.38971e12i		−	1.91478i
$924$	−1.83054e11	+	1.18562e12i	−0.251126	+	1.62651i
$925$		0			0
$926$			1.95861e12i			2.66381i
$927$	−2.99406e11	−	9.47112e10i	−0.405453	−	0.128257i
$928$	1.17113e12			1.57911
$929$		−	3.66914e10i		−	0.0492608i	−0.999697	−	0.0246304i	$-0.992159\pi$
$929$		−	3.66914e10i		−	0.0492608i	0.999697	−	0.0246304i	$-0.00784090\pi$
$930$		0			0
$931$	−1.79915e11			−0.239480
$932$			1.22181e12i			1.61934i
$933$	−1.50648e11	+	9.75730e11i	−0.198809	+	1.28767i
$934$	2.02498e12			2.66093
$935$		0			0
$936$	5.47474e11	−	1.73070e12i	0.713281	−	2.25486i
$937$	1.06583e12			1.38271			0.691355	−	0.722515i	$-0.257014\pi$
$937$	1.06583e12			1.38271			0.691355	+	0.722515i	$0.257014\pi$
$938$		−	1.52093e12i		−	1.96471i
$939$	7.52216e11	+	1.16138e11i	0.967565	+	0.149387i
$940$		0			0
$941$		−	3.16869e11i		−	0.404130i	−0.979372	−	0.202065i	$-0.935235\pi$
$941$		−	3.16869e11i		−	0.404130i	0.979372	−	0.202065i	$-0.0647652\pi$
$942$	−3.53832e11	+	2.29173e12i	−0.449359	+	2.91045i
$943$	−3.99357e10			−0.0505027
$944$			2.98370e11i			0.375722i
$945$		0			0
$946$	5.78443e11			0.722264
$947$		−	1.13510e12i		−	1.41135i	−0.708535	−	0.705676i	$-0.750644\pi$
$947$		−	1.13510e12i		−	1.41135i	0.708535	−	0.705676i	$-0.249356\pi$
$948$	1.22720e12	+	1.89474e11i	1.51944	+	0.234594i
$949$	1.34123e11			0.165363
$950$		0			0
$951$	−2.10635e11	+	1.36426e12i	−0.257519	+	1.66792i
$952$	6.70217e11			0.815958
$953$			6.52210e10i			0.0790707i	0.999218	+	0.0395354i	$0.0125878\pi$
$953$			6.52210e10i			0.0790707i	−0.999218	+	0.0395354i	$0.987412\pi$
$954$	3.68926e11	+	1.16703e11i	0.445395	+	0.140892i
$955$		0			0
$956$		−	1.53610e12i		−	1.83903i
$957$	−7.60372e11	−	1.17398e11i	−0.906522	−	0.139963i
$958$	−1.98138e12			−2.35237
$959$			1.04379e12i			1.23407i
$960$		0			0
$961$	−8.53562e10			−0.100079
$962$		−	1.48089e12i		−	1.72911i
$963$	−1.99593e11	+	6.30964e11i	−0.232082	+	0.733668i
$964$	1.51098e11			0.174965
$965$		0			0
$966$	−1.29081e12	−	1.99295e11i	−1.48236	−	0.228869i
$967$	1.04679e12			1.19716			0.598580	−	0.801063i	$-0.295732\pi$
$967$	1.04679e12			1.19716			0.598580	+	0.801063i	$0.295732\pi$
$968$			7.07701e11i			0.806025i
$969$	−4.93716e10	+	3.19774e11i	−0.0559992	+	0.362701i
$970$		0			0
$971$		−	1.75655e10i		−	0.0197598i	−0.999951	−	0.00987992i	$-0.996855\pi$
$971$		−	1.75655e10i		−	0.0197598i	0.999951	−	0.00987992i	$-0.00314493\pi$
$972$	−1.49951e12	−	1.44223e12i	−1.67990	−	1.61573i
$973$	−6.44162e10			−0.0718694
$974$			1.63654e12i			1.81840i
$975$		0			0
$976$	−2.29665e12			−2.53101
$977$			6.94557e10i			0.0762307i	0.999273	+	0.0381153i	$0.0121354\pi$
$977$			6.94557e10i			0.0762307i	−0.999273	+	0.0381153i	$0.987865\pi$
$978$	5.32271e10	−	3.44746e11i	0.0581805	−	0.376829i
$979$	−3.85018e10			−0.0419131
$980$		0			0
$981$	8.83019e11	+	2.79326e11i	0.953441	+	0.301603i
$982$	8.66246e11			0.931527
$983$		−	4.48002e11i		−	0.479806i	−0.970797	−	0.239903i	$-0.922884\pi$
$983$		−	4.48002e11i		−	0.479806i	0.970797	−	0.239903i	$-0.0771156\pi$
$984$	−1.19456e11	−	1.84434e10i	−0.127417	−	0.0196725i
$985$		0			0
$986$			7.52815e11i			0.796490i
$987$	−8.59343e10	+	5.56587e11i	−0.0905519	+	0.586495i
$988$	2.04076e12			2.14173
$989$			4.40691e11i			0.460627i
$990$		0			0
$991$	−1.56270e11			−0.162025			−0.0810123	−	0.996713i	$-0.525815\pi$
$991$	−1.56270e11			−0.162025			−0.0810123	+	0.996713i	$0.525815\pi$
$992$		−	1.29271e12i		−	1.33492i
$993$	1.27471e12	+	1.96809e11i	1.31103	+	0.202417i
$994$	−3.02645e12			−3.10019
$995$		0			0
$996$	−3.56730e11	+	2.31050e12i	−0.362495	+	2.34784i
$997$	−4.60730e11			−0.466300			−0.233150	−	0.972441i	$-0.574903\pi$
$997$	−4.60730e11			−0.466300			−0.233150	+	0.972441i	$0.574903\pi$
$998$		−	2.15718e12i		−	2.17452i
$999$	−8.68559e11	−	4.29847e11i	−0.872042	−	0.431571i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.9.c.h.26.2		12
3.2	odd	2	inner	75.9.c.h.26.12		12
5.2	odd	4		15.9.d.c.14.11	yes	12
5.3	odd	4		15.9.d.c.14.2	yes	12
5.4	even	2	inner	75.9.c.h.26.11		12
15.2	even	4		15.9.d.c.14.1	✓	12
15.8	even	4		15.9.d.c.14.12	yes	12
15.14	odd	2	inner	75.9.c.h.26.1		12
20.3	even	4		240.9.c.c.209.7		12
20.7	even	4		240.9.c.c.209.6		12
60.23	odd	4		240.9.c.c.209.5		12
60.47	odd	4		240.9.c.c.209.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.9.d.c.14.1	✓	12	15.2	even	4
15.9.d.c.14.2	yes	12	5.3	odd	4
15.9.d.c.14.11	yes	12	5.2	odd	4
15.9.d.c.14.12	yes	12	15.8	even	4
75.9.c.h.26.1		12	15.14	odd	2	inner
75.9.c.h.26.2		12	1.1	even	1	trivial
75.9.c.h.26.11		12	5.4	even	2	inner
75.9.c.h.26.12		12	3.2	odd	2	inner
240.9.c.c.209.5		12	60.23	odd	4
240.9.c.c.209.6		12	20.7	even	4
240.9.c.c.209.7		12	20.3	even	4
240.9.c.c.209.8		12	60.47	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	75.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-29.2008i q^{2} +(80.0515 + 12.3596i) q^{3} -596.686 q^{4} +(360.909 - 2337.57i) q^{6} -2074.09 q^{7} +9948.30i q^{8} +(6255.48 + 1978.80i) q^{9} +O(q^{10})\)	\(q-29.2008i q^{2} +(80.0515 + 12.3596i) q^{3} -596.686 q^{4} +(360.909 - 2337.57i) q^{6} -2074.09 q^{7} +9948.30i q^{8} +(6255.48 + 1978.80i) q^{9} +11967.5i q^{11} +(-47765.6 - 7374.78i) q^{12} -27810.7 q^{13} +60565.0i q^{14} +137746. q^{16} +32481.8i q^{17} +(57782.6 - 182665. i) q^{18} +122980. q^{19} +(-166034. - 25634.8i) q^{21} +349460. q^{22} +266239. i q^{23} +(-122957. + 796376. i) q^{24} +812096. i q^{26} +(476304. + 235721. i) q^{27} +1.23758e6 q^{28} +793695. i q^{29} +876091. q^{31} -1.47554e6i q^{32} +(-147913. + 958016. i) q^{33} +948494. q^{34} +(-3.73256e6 - 1.18072e6i) q^{36} -1.82354e6 q^{37} -3.59111e6i q^{38} +(-2.22629e6 - 343729. i) q^{39} +149999. i q^{41} +(-748556. + 4.84832e6i) q^{42} +1.65525e6 q^{43} -7.14084e6i q^{44} +7.77439e6 q^{46} -3.35225e6i q^{47} +(1.10268e7 + 1.70249e6i) q^{48} -1.46297e6 q^{49} +(-401461. + 2.60022e6i) q^{51} +1.65943e7 q^{52} +2.01969e6i q^{53} +(6.88324e6 - 1.39084e7i) q^{54} -2.06336e7i q^{56} +(9.84472e6 + 1.51998e6i) q^{57} +2.31765e7 q^{58} +2.16608e6i q^{59} -1.66730e7 q^{61} -2.55825e7i q^{62} +(-1.29744e7 - 4.10421e6i) q^{63} -7.82388e6 q^{64} +(2.79748e7 + 4.31918e6i) q^{66} -2.51124e7 q^{67} -1.93814e7i q^{68} +(-3.29060e6 + 2.13128e7i) q^{69} +4.99704e7i q^{71} +(-1.96857e7 + 6.22314e7i) q^{72} -4.82271e6 q^{73} +5.32488e7i q^{74} -7.33803e7 q^{76} -2.48216e7i q^{77} +(-1.00371e7 + 6.50095e7i) q^{78} -2.56922e7 q^{79} +(3.52154e7 + 2.47567e7i) q^{81} +4.38010e6 q^{82} -4.83717e7i q^{83} +(9.90700e7 + 1.52959e7i) q^{84} -4.83345e7i q^{86} +(-9.80972e6 + 6.35364e7i) q^{87} -1.19056e8 q^{88} +3.21720e6i q^{89} +5.76819e7 q^{91} -1.58861e8i q^{92} +(7.01324e7 + 1.08281e7i) q^{93} -9.78883e7 q^{94} +(1.82370e7 - 1.18119e8i) q^{96} +5.09232e7 q^{97} +4.27198e7i q^{98} +(-2.36813e7 + 7.48625e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 1704 q^{4} - 3012 q^{6} + 22824 q^{9}+O(q^{10}) \) 12 * q - 1704 * q^4 - 3012 * q^6 + 22824 * q^9	\( 12 q - 1704 q^{4} - 3012 q^{6} + 22824 q^{9} + 413328 q^{16} - 276192 q^{19} - 604044 q^{21} - 1173336 q^{24} - 279216 q^{31} + 1225344 q^{34} - 10311840 q^{36} - 3780864 q^{39} + 37414536 q^{46} + 6222300 q^{49} + 3931248 q^{51} + 53281692 q^{54} - 91958256 q^{61} - 57497760 q^{64} + 111065040 q^{66} - 8138748 q^{69} - 232646880 q^{76} - 420402672 q^{79} + 98480772 q^{81} + 528357816 q^{84} - 100211328 q^{91} - 543022776 q^{94} + 333306864 q^{96} + 640360080 q^{99}+O(q^{100}) \) 12 * q - 1704 * q^4 - 3012 * q^6 + 22824 * q^9 + 413328 * q^16 - 276192 * q^19 - 604044 * q^21 - 1173336 * q^24 - 279216 * q^31 + 1225344 * q^34 - 10311840 * q^36 - 3780864 * q^39 + 37414536 * q^46 + 6222300 * q^49 + 3931248 * q^51 + 53281692 * q^54 - 91958256 * q^61 - 57497760 * q^64 + 111065040 * q^66 - 8138748 * q^69 - 232646880 * q^76 - 420402672 * q^79 + 98480772 * q^81 + 528357816 * q^84 - 100211328 * q^91 - 543022776 * q^94 + 333306864 * q^96 + 640360080 * q^99

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