LMFDB - Embedded newform 175.10.b.c.99.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,10,Mod(99,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("175.99");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	175.b (of order $2$, degree $1$, not 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:	$90.1312713287$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.4
Root			$-0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	175.99
Dual form			175.10.b.c.99.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+14.8284i q^{2} -239.735i q^{3} +292.118 q^{4} +3554.89 q^{6} -2401.00i q^{7} +11923.8i q^{8} -37789.9 q^{9} +O(q^{10})$	\(q+14.8284i q^{2} -239.735i q^{3} +292.118 q^{4} +3554.89 q^{6} -2401.00i q^{7} +11923.8i q^{8} -37789.9 q^{9} -16523.6 q^{11} -70030.9i q^{12} +26311.4i q^{13} +35603.1 q^{14} -27246.9 q^{16} +144003. i q^{17} -560365. i q^{18} +159710. q^{19} -575604. q^{21} -245019. i q^{22} +2.07393e6i q^{23} +2.85855e6 q^{24} -390156. q^{26} +4.34086e6i q^{27} -701375. i q^{28} +4.94938e6 q^{29} +4.22040e6 q^{31} +5.70096e6i q^{32} +3.96128e6i q^{33} -2.13533e6 q^{34} -1.10391e7 q^{36} +1.29081e7i q^{37} +2.36824e6i q^{38} +6.30776e6 q^{39} -2.87518e7 q^{41} -8.53530e6i q^{42} +3.54825e7i q^{43} -4.82683e6 q^{44} -3.07532e7 q^{46} -5.95633e7i q^{47} +6.53205e6i q^{48} -5.76480e6 q^{49} +3.45225e7 q^{51} +7.68602e6i q^{52} +2.31161e6i q^{53} -6.43681e7 q^{54} +2.86290e7 q^{56} -3.82880e7i q^{57} +7.33915e7i q^{58} +1.68651e8 q^{59} -6.70167e7 q^{61} +6.25819e7i q^{62} +9.07336e7i q^{63} -9.84867e7 q^{64} -5.87395e7 q^{66} +1.56259e8i q^{67} +4.20657e7i q^{68} +4.97195e8 q^{69} +6.95067e7 q^{71} -4.50599e8i q^{72} -7.83438e7i q^{73} -1.91407e8 q^{74} +4.66540e7 q^{76} +3.96731e7i q^{77} +9.35342e7i q^{78} +4.26957e8 q^{79} +2.96838e8 q^{81} -4.26344e8i q^{82} -5.31242e8i q^{83} -1.68144e8 q^{84} -5.26149e8 q^{86} -1.18654e9i q^{87} -1.97024e8i q^{88} +1.14168e8 q^{89} +6.31736e7 q^{91} +6.05833e8i q^{92} -1.01178e9i q^{93} +8.83231e8 q^{94} +1.36672e9 q^{96} +1.46573e9i q^{97} -8.54829e7i q^{98} +6.24424e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 1440 q^{4} + 5904 q^{6} - 44856 q^{9}+O(q^{10}) $ 4 * q + 1440 * q^4 + 5904 * q^6 - 44856 * q^9	$ 4 q + 1440 q^{4} + 5904 q^{6} - 44856 q^{9} + 37132 q^{11} + 115248 q^{14} + 225536 q^{16} + 286552 q^{19} - 835548 q^{21} + 4583808 q^{24} + 639472 q^{26} + 23155108 q^{29} - 7907520 q^{31} - 8487888 q^{34} - 8932032 q^{36} + 22791492 q^{39} + 2117984 q^{41} + 20374752 q^{44} - 14312352 q^{46} - 23059204 q^{49} + 38818932 q^{51} - 170992944 q^{54} + 98652288 q^{56} + 232318416 q^{59} - 89377088 q^{61} - 158111744 q^{64} - 159789648 q^{66} + 1332641784 q^{69} - 588331648 q^{71} - 204836128 q^{74} + 79244736 q^{76} + 1385705708 q^{79} + 895546692 q^{81} - 201223008 q^{84} - 693978016 q^{86} + 1558087408 q^{89} - 245334180 q^{91} + 1875382064 q^{94} + 1984361472 q^{96} + 2326933080 q^{99}+O(q^{100}) $ 4 * q + 1440 * q^4 + 5904 * q^6 - 44856 * q^9 + 37132 * q^11 + 115248 * q^14 + 225536 * q^16 + 286552 * q^19 - 835548 * q^21 + 4583808 * q^24 + 639472 * q^26 + 23155108 * q^29 - 7907520 * q^31 - 8487888 * q^34 - 8932032 * q^36 + 22791492 * q^39 + 2117984 * q^41 + 20374752 * q^44 - 14312352 * q^46 - 23059204 * q^49 + 38818932 * q^51 - 170992944 * q^54 + 98652288 * q^56 + 232318416 * q^59 - 89377088 * q^61 - 158111744 * q^64 - 159789648 * q^66 + 1332641784 * q^69 - 588331648 * q^71 - 204836128 * q^74 + 79244736 * q^76 + 1385705708 * q^79 + 895546692 * q^81 - 201223008 * q^84 - 693978016 * q^86 + 1558087408 * q^89 - 245334180 * q^91 + 1875382064 * q^94 + 1984361472 * q^96 + 2326933080 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$-1$

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 $

$2$	14.8284i	0.655330i	0.944794	+	0.327665i	$0.106262\pi$
$2$	14.8284i	0.655330i	−0.944794	+	0.327665i	$0.893738\pi$
$3$	− 239.735i	− 1.70878i	−0.519633	−	0.854390i	$-0.673931\pi$
$3$	− 239.735i	− 1.70878i	0.519633	−	0.854390i	$-0.326069\pi$
$4$	292.118	0.570542
$5$	0	0
$5$	0	0
$6$	3554.89	1.11981
$7$	− 2401.00i	− 0.377964i
$7$	− 2401.00i	− 0.377964i
$8$	11923.8i	1.02922i
$9$	−37789.9	−1.91993
$10$	0	0
$11$	−16523.6	−0.340280	−0.170140	−	0.985420i	$-0.554422\pi$
$11$	−16523.6	−0.340280	−0.170140	+	0.985420i	$0.554422\pi$
$12$	− 70030.9i	− 0.974931i
$13$	26311.4i	0.255505i	0.991806	+	0.127752i	$0.0407762\pi$
$13$	26311.4i	0.255505i	−0.991806	+	0.127752i	$0.959224\pi$
$14$	35603.1	0.247691
$15$	0	0
$16$	−27246.9	−0.103939
$17$	144003.i	0.418167i	0.977898	+	0.209084i	$0.0670481\pi$
$17$	144003.i	0.418167i	−0.977898	+	0.209084i	$0.932952\pi$
$18$	− 560365.i	− 1.25819i
$19$	159710.	0.281151	0.140576	−	0.990070i	$-0.455105\pi$
$19$	159710.	0.281151	0.140576	+	0.990070i	$0.455105\pi$
$20$	0	0
$21$	−575604.	−0.645858
$22$	− 245019.i	− 0.222996i
$23$	2.07393e6i	1.54533i	0.634817	+	0.772663i	$0.281075\pi$
$23$	2.07393e6i	1.54533i	−0.634817	+	0.772663i	$0.718925\pi$
$24$	2.85855e6	1.75872
$25$	0	0
$26$	−390156.	−0.167440
$27$	4.34086e6i	1.57195i
$28$	− 701375.i	− 0.215645i
$29$	4.94938e6	1.29945	0.649725	−	0.760169i	$-0.274884\pi$
$29$	4.94938e6	1.29945	0.649725	+	0.760169i	$0.274884\pi$
$30$	0	0
$31$	4.22040e6	0.820779	0.410389	−	0.911910i	$-0.365393\pi$
$31$	4.22040e6	0.820779	0.410389	+	0.911910i	$0.365393\pi$
$32$	5.70096e6i	0.961110i
$33$	3.96128e6i	0.581464i
$34$	−2.13533e6	−0.274038
$35$	0	0
$36$	−1.10391e7	−1.09540
$37$	1.29081e7i	1.13228i	0.824308	+	0.566142i	$0.191565\pi$
$37$	1.29081e7i	1.13228i	−0.824308	+	0.566142i	$0.808435\pi$
$38$	2.36824e6i	0.184247i
$39$	6.30776e6	0.436601
$40$	0	0
$41$	−2.87518e7	−1.58905	−0.794525	−	0.607231i	$-0.792280\pi$
$41$	−2.87518e7	−1.58905	−0.794525	+	0.607231i	$0.792280\pi$
$42$	− 8.53530e6i	− 0.423250i
$43$	3.54825e7i	1.58273i	0.611347	+	0.791363i	$0.290628\pi$
$43$	3.54825e7i	1.58273i	−0.611347	+	0.791363i	$0.709372\pi$
$44$	−4.82683e6	−0.194144
$45$	0	0
$46$	−3.07532e7	−1.01270
$47$	− 5.95633e7i	− 1.78049i	−0.455485	−	0.890243i	$-0.650534\pi$
$47$	− 5.95633e7i	− 1.78049i	0.455485	−	0.890243i	$-0.349466\pi$
$48$	6.53205e6i	0.177608i
$49$	−5.76480e6	−0.142857
$50$	0	0
$51$	3.45225e7	0.714555
$52$	7.68602e6i	0.145776i
$53$	2.31161e6i	0.0402414i	0.999798	+	0.0201207i	$0.00640504\pi$
$53$	2.31161e6i	0.0402414i	−0.999798	+	0.0201207i	$0.993595\pi$
$54$	−6.43681e7	−1.03015
$55$	0	0
$56$	2.86290e7	0.389010
$57$	− 3.82880e7i	− 0.480425i
$58$	7.33915e7i	0.851569i
$59$	1.68651e8	1.81198	0.905992	−	0.423296i	$-0.139127\pi$
$59$	1.68651e8	1.81198	0.905992	+	0.423296i	$0.139127\pi$
$60$	0	0
$61$	−6.70167e7	−0.619725	−0.309863	−	0.950781i	$-0.600283\pi$
$61$	−6.70167e7	−0.619725	−0.309863	+	0.950781i	$0.600283\pi$
$62$	6.25819e7i	0.537881i
$63$	9.07336e7i	0.725664i
$64$	−9.84867e7	−0.733783
$65$	0	0
$66$	−5.87395e7	−0.381051
$67$	1.56259e8i	0.947343i	0.880702	+	0.473671i	$0.157072\pi$
$67$	1.56259e8i	0.947343i	−0.880702	+	0.473671i	$0.842928\pi$
$68$	4.20657e7i	0.238582i
$69$	4.97195e8	2.64062
$70$	0	0
$71$	6.95067e7	0.324612	0.162306	−	0.986740i	$-0.448107\pi$
$71$	6.95067e7	0.324612	0.162306	+	0.986740i	$0.448107\pi$
$72$	− 4.50599e8i	− 1.97603i
$73$	− 7.83438e7i	− 0.322888i	−0.986882	−	0.161444i	$-0.948385\pi$
$73$	− 7.83438e7i	− 0.322888i	0.986882	−	0.161444i	$-0.0516151\pi$
$74$	−1.91407e8	−0.742020
$75$	0	0
$76$	4.66540e7	0.160409
$77$	3.96731e7i	0.128614i
$78$	9.35342e7i	0.286118i
$79$	4.26957e8	1.23328	0.616641	−	0.787245i	$-0.288493\pi$
$79$	4.26957e8	1.23328	0.616641	+	0.787245i	$0.288493\pi$
$80$	0	0
$81$	2.96838e8	0.766190
$82$	− 4.26344e8i	− 1.04135i
$83$	− 5.31242e8i	− 1.22869i	−0.789039	−	0.614343i	$-0.789421\pi$
$83$	− 5.31242e8i	− 1.22869i	0.789039	−	0.614343i	$-0.210579\pi$
$84$	−1.68144e8	−0.368489
$85$	0	0
$86$	−5.26149e8	−1.03721
$87$	− 1.18654e9i	− 2.22047i
$88$	− 1.97024e8i	− 0.350225i
$89$	1.14168e8	0.192881	0.0964404	−	0.995339i	$-0.469254\pi$
$89$	1.14168e8	0.192881	0.0964404	+	0.995339i	$0.469254\pi$
$90$	0	0
$91$	6.31736e7	0.0965716
$92$	6.05833e8i	0.881674i
$93$	− 1.01178e9i	− 1.40253i
$94$	8.83231e8	1.16681
$95$	0	0
$96$	1.36672e9	1.64232
$97$	1.46573e9i	1.68105i	0.541774	+	0.840524i	$0.317753\pi$
$97$	1.46573e9i	1.68105i	−0.541774	+	0.840524i	$0.682247\pi$
$98$	− 8.54829e7i	− 0.0936186i
$99$	6.24424e8	0.653313
$100$	0	0
$101$	7.53733e8	0.720728	0.360364	−	0.932812i	$-0.382652\pi$
$101$	7.53733e8	0.720728	0.360364	+	0.932812i	$0.382652\pi$
$102$	5.11914e8i	0.468270i
$103$	− 1.32143e9i	− 1.15685i	−0.815736	−	0.578425i	$-0.803668\pi$
$103$	− 1.32143e9i	− 1.15685i	0.815736	−	0.578425i	$-0.196332\pi$
$104$	−3.13732e8	−0.262971
$105$	0	0
$106$	−3.42775e7	−0.0263714
$107$	− 1.07364e9i	− 0.791831i	−0.918287	−	0.395915i	$-0.870427\pi$
$107$	− 1.07364e9i	− 0.791831i	0.918287	−	0.395915i	$-0.129573\pi$
$108$	1.26804e9i	0.896864i
$109$	−1.08650e9	−0.737245	−0.368623	−	0.929579i	$-0.620170\pi$
$109$	−1.08650e9	−0.737245	−0.368623	+	0.929579i	$0.620170\pi$
$110$	0	0
$111$	3.09453e9	1.93482
$112$	6.54199e7i	0.0392852i
$113$	2.85559e9i	1.64757i	0.566906	+	0.823783i	$0.308140\pi$
$113$	2.85559e9i	1.64757i	−0.566906	+	0.823783i	$0.691860\pi$
$114$	5.67751e8	0.314837
$115$	0	0
$116$	1.44580e9	0.741392
$117$	− 9.94305e8i	− 0.490550i
$118$	2.50083e9i	1.18745i
$119$	3.45750e8	0.158052
$120$	0	0
$121$	−2.08492e9	−0.884209
$122$	− 9.93753e8i	− 0.406125i
$123$	6.89281e9i	2.71534i
$124$	1.23285e9	0.468289
$125$	0	0
$126$	−1.34544e9	−0.475549
$127$	3.86082e9i	1.31693i	0.752611	+	0.658465i	$0.228794\pi$
$127$	3.86082e9i	1.31693i	−0.752611	+	0.658465i	$0.771206\pi$
$128$	1.45849e9i	0.480240i
$129$	8.50639e9	2.70453
$130$	0	0
$131$	4.01900e8	0.119233	0.0596166	−	0.998221i	$-0.481012\pi$
$131$	4.01900e8	0.119233	0.0596166	+	0.998221i	$0.481012\pi$
$132$	1.15716e9i	0.331750i
$133$	− 3.83463e8i	− 0.106265i
$134$	−2.31707e9	−0.620822
$135$	0	0
$136$	−1.71706e9	−0.430388
$137$	− 3.04172e9i	− 0.737695i	−0.929490	−	0.368847i	$-0.879753\pi$
$137$	− 3.04172e9i	− 0.737695i	0.929490	−	0.368847i	$-0.120247\pi$
$138$	7.37262e9i	1.73048i
$139$	−8.36421e8	−0.190046	−0.0950229	−	0.995475i	$-0.530292\pi$
$139$	−8.36421e8	−0.190046	−0.0950229	+	0.995475i	$0.530292\pi$
$140$	0	0
$141$	−1.42794e10	−3.04246
$142$	1.03068e9i	0.212728i
$143$	− 4.34758e8i	− 0.0869431i
$144$	1.02966e9	0.199555
$145$	0	0
$146$	1.16172e9	0.211598
$147$	1.38202e9i	0.244111i
$148$	3.77069e9i	0.646016i
$149$	7.76217e9	1.29016	0.645082	−	0.764114i	$-0.276823\pi$
$149$	7.76217e9	1.29016	0.645082	+	0.764114i	$0.276823\pi$
$150$	0	0
$151$	8.38042e9	1.31181	0.655903	−	0.754846i	$-0.272288\pi$
$151$	8.38042e9	1.31181	0.655903	+	0.754846i	$0.272288\pi$
$152$	1.90435e9i	0.289367i
$153$	− 5.44184e9i	− 0.802850i
$154$	−5.88290e8	−0.0842845
$155$	0	0
$156$	1.84261e9	0.249099
$157$	8.49699e9i	1.11613i	0.829796	+	0.558067i	$0.188457\pi$
$157$	8.49699e9i	1.11613i	−0.829796	+	0.558067i	$0.811543\pi$
$158$	6.33110e9i	0.808206i
$159$	5.54173e8	0.0687636
$160$	0	0
$161$	4.97952e9	0.584078
$162$	4.40163e9i	0.502107i
$163$	4.25863e9i	0.472526i	0.971689	+	0.236263i	$0.0759226\pi$
$163$	4.25863e9i	0.472526i	−0.971689	+	0.236263i	$0.924077\pi$
$164$	−8.39891e9	−0.906621
$165$	0	0
$166$	7.87749e9	0.805195
$167$	− 9.23536e8i	− 0.0918818i	−0.998944	−	0.0459409i	$-0.985371\pi$
$167$	− 9.23536e8i	− 0.0918818i	0.998944	−	0.0459409i	$-0.0146286\pi$
$168$	− 6.86339e9i	− 0.664732i
$169$	9.91221e9	0.934717
$170$	0	0
$171$	−6.03541e9	−0.539789
$172$	1.03651e10i	0.903012i
$173$	− 4.76006e9i	− 0.404022i	−0.979383	−	0.202011i	$-0.935252\pi$
$173$	− 4.76006e9i	− 0.404022i	0.979383	−	0.202011i	$-0.0647477\pi$
$174$	1.75945e10	1.45514
$175$	0	0
$176$	4.50217e8	0.0353683
$177$	− 4.04315e10i	− 3.09628i
$178$	1.69293e9i	0.126401i
$179$	9.47187e9	0.689599	0.344800	−	0.938676i	$-0.387947\pi$
$179$	9.47187e9	0.689599	0.344800	+	0.938676i	$0.387947\pi$
$180$	0	0
$181$	−7.85395e9	−0.543919	−0.271960	−	0.962309i	$-0.587672\pi$
$181$	−7.85395e9	−0.543919	−0.271960	+	0.962309i	$0.587672\pi$
$182$	9.36766e8i	0.0632863i
$183$	1.60663e10i	1.05897i
$184$	−2.47292e10	−1.59049
$185$	0	0
$186$	1.50031e10	0.919120
$187$	− 2.37944e9i	− 0.142294i
$188$	− 1.73995e10i	− 1.01584i
$189$	1.04224e10	0.594141
$190$	0	0
$191$	1.78210e10	0.968909	0.484454	−	0.874817i	$-0.339018\pi$
$191$	1.78210e10	0.968909	0.484454	+	0.874817i	$0.339018\pi$
$192$	2.36107e10i	1.25387i
$193$	− 1.93101e9i	− 0.100179i	−0.998745	−	0.0500894i	$-0.984049\pi$
$193$	− 1.93101e9i	− 0.100179i	0.998745	−	0.0500894i	$-0.0159506\pi$
$194$	−2.17344e10	−1.10164
$195$	0	0
$196$	−1.68400e9	−0.0815061
$197$	− 3.24598e10i	− 1.53549i	−0.640755	−	0.767746i	$-0.721378\pi$
$197$	− 3.24598e10i	− 1.53549i	0.640755	−	0.767746i	$-0.278622\pi$
$198$	9.25923e9i	0.428136i
$199$	2.75463e10	1.24516	0.622578	−	0.782558i	$-0.286085\pi$
$199$	2.75463e10	1.24516	0.622578	+	0.782558i	$0.286085\pi$
$200$	0	0
$201$	3.74606e10	1.61880
$202$	1.11767e10i	0.472315i
$203$	− 1.18835e10i	− 0.491146i
$204$	1.00846e10	0.407684
$205$	0	0
$206$	1.95947e10	0.758118
$207$	− 7.83738e10i	− 2.96691i
$208$	− 7.16904e8i	− 0.0265568i
$209$	−2.63897e9	−0.0956702
$210$	0	0
$211$	1.94450e10	0.675362	0.337681	−	0.941261i	$-0.390357\pi$
$211$	1.94450e10	0.675362	0.337681	+	0.941261i	$0.390357\pi$
$212$	6.75261e8i	0.0229594i
$213$	− 1.66632e10i	− 0.554690i
$214$	1.59204e10	0.518911
$215$	0	0
$216$	−5.17595e10	−1.61789
$217$	− 1.01332e10i	− 0.310225i
$218$	− 1.61111e10i	− 0.483139i
$219$	−1.87818e10	−0.551744
$220$	0	0
$221$	−3.78891e9	−0.106844
$222$	4.58870e10i	1.26795i
$223$	− 4.90459e10i	− 1.32810i	−0.747688	−	0.664050i	$-0.768836\pi$
$223$	− 4.90459e10i	− 1.32810i	0.747688	−	0.664050i	$-0.231164\pi$
$224$	1.36880e10	0.363265
$225$	0	0
$226$	−4.23439e10	−1.07970
$227$	6.87990e10i	1.71975i	0.510503	+	0.859876i	$0.329459\pi$
$227$	6.87990e10i	1.71975i	−0.510503	+	0.859876i	$0.670541\pi$
$228$	− 1.11846e10i	− 0.274103i
$229$	3.08456e9	0.0741198	0.0370599	−	0.999313i	$-0.488201\pi$
$229$	3.08456e9	0.0741198	0.0370599	+	0.999313i	$0.488201\pi$
$230$	0	0
$231$	9.51103e9	0.219773
$232$	5.90154e10i	1.33743i
$233$	− 1.48643e10i	− 0.330402i	−0.986260	−	0.165201i	$-0.947173\pi$
$233$	− 1.48643e10i	− 0.330402i	0.986260	−	0.165201i	$-0.0528273\pi$
$234$	1.47440e10	0.321472
$235$	0	0
$236$	4.92659e10	1.03381
$237$	− 1.02357e11i	− 2.10741i
$238$	5.12693e9i	0.103576i
$239$	−4.06416e10	−0.805713	−0.402857	−	0.915263i	$-0.631983\pi$
$239$	−4.06416e10	−0.805713	−0.402857	+	0.915263i	$0.631983\pi$
$240$	0	0
$241$	−2.09799e10	−0.400615	−0.200308	−	0.979733i	$-0.564194\pi$
$241$	−2.09799e10	−0.400615	−0.200308	+	0.979733i	$0.564194\pi$
$242$	− 3.09161e10i	− 0.579449i
$243$	1.42788e10i	0.262701i
$244$	−1.95768e10	−0.353580
$245$	0	0
$246$	−1.02210e11	−1.77944
$247$	4.20218e9i	0.0718354i
$248$	5.03232e10i	0.844765i
$249$	−1.27357e11	−2.09955
$250$	0	0
$251$	−9.95566e10	−1.58321	−0.791605	−	0.611034i	$-0.790754\pi$
$251$	−9.95566e10	−1.58321	−0.791605	+	0.611034i	$0.790754\pi$
$252$	2.65049e10i	0.414022i
$253$	− 3.42688e10i	− 0.525844i
$254$	−5.72499e10	−0.863024
$255$	0	0
$256$	−7.20522e10	−1.04850
$257$	1.30781e11i	1.87002i	0.354624	+	0.935009i	$0.384609\pi$
$257$	1.30781e11i	1.87002i	−0.354624	+	0.935009i	$0.615391\pi$
$258$	1.26136e11i	1.77236i
$259$	3.09924e10	0.427963
$260$	0	0
$261$	−1.87037e11	−2.49485
$262$	5.95954e9i	0.0781371i
$263$	− 3.27938e10i	− 0.422660i	−0.977415	−	0.211330i	$-0.932221\pi$
$263$	− 3.27938e10i	− 0.422660i	0.977415	−	0.211330i	$-0.0677794\pi$
$264$	−4.72335e10	−0.598456
$265$	0	0
$266$	5.68615e9	0.0696387
$267$	− 2.73700e10i	− 0.329591i
$268$	4.56459e10i	0.540499i
$269$	−7.47690e9	−0.0870636	−0.0435318	−	0.999052i	$-0.513861\pi$
$269$	−7.47690e9	−0.0870636	−0.0435318	+	0.999052i	$0.513861\pi$
$270$	0	0
$271$	6.72735e9	0.0757674	0.0378837	−	0.999282i	$-0.487938\pi$
$271$	6.72735e9	0.0757674	0.0378837	+	0.999282i	$0.487938\pi$
$272$	− 3.92363e9i	− 0.0434638i
$273$	− 1.51449e10i	− 0.165020i
$274$	4.51039e10	0.483434
$275$	0	0
$276$	1.45239e11	1.50659
$277$	1.52676e11i	1.55815i	0.626928	+	0.779077i	$0.284312\pi$
$277$	1.52676e11i	1.55815i	−0.626928	+	0.779077i	$0.715688\pi$
$278$	− 1.24028e10i	− 0.124543i
$279$	−1.59489e11	−1.57583
$280$	0	0
$281$	3.09796e10	0.296413	0.148206	−	0.988956i	$-0.452650\pi$
$281$	3.09796e10	0.296413	0.148206	+	0.988956i	$0.452650\pi$
$282$	− 2.11741e11i	− 1.99381i
$283$	− 8.92078e10i	− 0.826731i	−0.910565	−	0.413365i	$-0.864353\pi$
$283$	− 8.92078e10i	− 0.826731i	0.910565	−	0.413365i	$-0.135647\pi$
$284$	2.03041e10	0.185205
$285$	0	0
$286$	6.44678e9	0.0569765
$287$	6.90331e10i	0.600605i
$288$	− 2.15439e11i	− 1.84526i
$289$	9.78512e10	0.825136
$290$	0	0
$291$	3.51386e11	2.87254
$292$	− 2.28856e10i	− 0.184221i
$293$	6.30090e10i	0.499457i	0.968316	+	0.249728i	$0.0803414\pi$
$293$	6.30090e10i	0.499457i	−0.968316	+	0.249728i	$0.919659\pi$
$294$	−2.04933e10	−0.159973
$295$	0	0
$296$	−1.53914e11	−1.16537
$297$	− 7.17265e10i	− 0.534904i
$298$	1.15101e11i	0.845483i
$299$	−5.45681e10	−0.394838
$300$	0	0
$301$	8.51934e10	0.598214
$302$	1.24268e11i	0.859665i
$303$	− 1.80696e11i	− 1.23157i
$304$	−4.35160e9	−0.0292225
$305$	0	0
$306$	8.06939e10	0.526132
$307$	1.22461e11i	0.786821i	0.919363	+	0.393411i	$0.128705\pi$
$307$	1.22461e11i	0.786821i	−0.919363	+	0.393411i	$0.871295\pi$
$308$	1.15892e10i	0.0733797i
$309$	−3.16793e11	−1.97680
$310$	0	0
$311$	2.77926e11	1.68464	0.842321	−	0.538975i	$-0.181188\pi$
$311$	2.77926e11	1.68464	0.842321	+	0.538975i	$0.181188\pi$
$312$	7.52125e10i	0.449360i
$313$	1.22493e11i	0.721374i	0.932687	+	0.360687i	$0.117458\pi$
$313$	1.22493e11i	0.721374i	−0.932687	+	0.360687i	$0.882542\pi$
$314$	−1.25997e11	−0.731436
$315$	0	0
$316$	1.24722e11	0.703639
$317$	− 2.32000e11i	− 1.29039i	−0.764016	−	0.645197i	$-0.776775\pi$
$317$	− 2.32000e11i	− 1.29039i	0.764016	−	0.645197i	$-0.223225\pi$
$318$	8.21752e9i	0.0450628i
$319$	−8.17814e10	−0.442177
$320$	0	0
$321$	−2.57390e11	−1.35306
$322$	7.38384e10i	0.382764i
$323$	2.29986e10i	0.117568i
$324$	8.67115e10	0.437144
$325$	0	0
$326$	−6.31487e10	−0.309660
$327$	2.60473e11i	1.25979i
$328$	− 3.42831e11i	− 1.63549i
$329$	−1.43012e11	−0.672961
$330$	0	0
$331$	−3.74253e11	−1.71372	−0.856859	−	0.515551i	$-0.827587\pi$
$331$	−3.74253e11	−1.71372	−0.856859	+	0.515551i	$0.827587\pi$
$332$	− 1.55185e11i	− 0.701018i
$333$	− 4.87797e11i	− 2.17390i
$334$	1.36946e10	0.0602129
$335$	0	0
$336$	1.56834e10	0.0671297
$337$	− 3.35878e11i	− 1.41856i	−0.704927	−	0.709280i	$-0.749020\pi$
$337$	− 3.35878e11i	− 1.41856i	0.704927	−	0.709280i	$-0.250980\pi$
$338$	1.46982e11i	0.612548i
$339$	6.84585e11	2.81533
$340$	0	0
$341$	−6.97361e10	−0.279295
$342$	− 8.94956e10i	− 0.353740i
$343$	1.38413e10i	0.0539949i
$344$	−4.23086e11	−1.62898
$345$	0	0
$346$	7.05842e10	0.264768
$347$	3.63698e11i	1.34666i	0.739341	+	0.673331i	$0.235137\pi$
$347$	3.63698e11i	1.34666i	−0.739341	+	0.673331i	$0.764863\pi$
$348$	− 3.46609e11i	− 1.26687i
$349$	−1.08740e11	−0.392350	−0.196175	−	0.980569i	$-0.562852\pi$
$349$	−1.08740e11	−0.392350	−0.196175	+	0.980569i	$0.562852\pi$
$350$	0	0
$351$	−1.14214e11	−0.401640
$352$	− 9.42002e10i	− 0.327047i
$353$	− 3.36249e11i	− 1.15259i	−0.817241	−	0.576296i	$-0.804498\pi$
$353$	− 3.36249e11i	− 1.15259i	0.817241	−	0.576296i	$-0.195502\pi$
$354$	5.99535e11	2.02908
$355$	0	0
$356$	3.33505e10	0.110047
$357$	− 8.28884e10i	− 0.270077i
$358$	1.40453e11i	0.451915i
$359$	−5.49944e11	−1.74741	−0.873703	−	0.486460i	$-0.838288\pi$
$359$	−5.49944e11	−1.74741	−0.873703	+	0.486460i	$0.838288\pi$
$360$	0	0
$361$	−2.97181e11	−0.920954
$362$	− 1.16462e11i	− 0.356447i
$363$	4.99828e11i	1.51092i
$364$	1.84541e10	0.0550982
$365$	0	0
$366$	−2.38237e11	−0.693977
$367$	1.32204e11i	0.380405i	0.981745	+	0.190203i	$0.0609145\pi$
$367$	1.32204e11i	0.380405i	−0.981745	+	0.190203i	$0.939086\pi$
$368$	− 5.65084e10i	− 0.160619i
$369$	1.08653e12	3.05086
$370$	0	0
$371$	5.55017e9	0.0152098
$372$	− 2.95558e11i	− 0.800203i
$373$	4.88064e11i	1.30553i	0.757560	+	0.652765i	$0.226391\pi$
$373$	4.88064e11i	1.30553i	−0.757560	+	0.652765i	$0.773609\pi$
$374$	3.52833e10	0.0932496
$375$	0	0
$376$	7.10222e11	1.83252
$377$	1.30225e11i	0.332015i
$378$	1.54548e11i	0.389359i
$379$	−3.00162e11	−0.747274	−0.373637	−	0.927575i	$-0.621889\pi$
$379$	−3.00162e11	−0.747274	−0.373637	+	0.927575i	$0.621889\pi$
$380$	0	0
$381$	9.25574e11	2.25034
$382$	2.64258e11i	0.634955i
$383$	7.74202e11i	1.83848i	0.393694	+	0.919241i	$0.371197\pi$
$383$	7.74202e11i	1.83848i	−0.393694	+	0.919241i	$0.628803\pi$
$384$	3.49651e11	0.820623
$385$	0	0
$386$	2.86338e10	0.0656501
$387$	− 1.34088e12i	− 3.03872i
$388$	4.28165e11i	0.959109i
$389$	1.70127e11	0.376703	0.188352	−	0.982102i	$-0.439686\pi$
$389$	1.70127e11	0.376703	0.188352	+	0.982102i	$0.439686\pi$
$390$	0	0
$391$	−2.98652e11	−0.646204
$392$	− 6.87383e10i	− 0.147032i
$393$	− 9.63495e10i	− 0.203743i
$394$	4.81327e11	1.00625
$395$	0	0
$396$	1.82405e11	0.372743
$397$	5.47242e11i	1.10566i	0.833293	+	0.552831i	$0.186452\pi$
$397$	5.47242e11i	1.10566i	−0.833293	+	0.552831i	$0.813548\pi$
$398$	4.08468e11i	0.815988i
$399$	−9.19294e10	−0.181584
$400$	0	0
$401$	−4.57174e11	−0.882941	−0.441471	−	0.897276i	$-0.645543\pi$
$401$	−4.57174e11	−0.882941	−0.441471	+	0.897276i	$0.645543\pi$
$402$	5.55483e11i	1.06085i
$403$	1.11045e11i	0.209713i
$404$	2.20179e11	0.411206
$405$	0	0
$406$	1.76213e11	0.321863
$407$	− 2.13288e11i	− 0.385294i
$408$	4.11639e11i	0.735437i
$409$	−9.42996e10	−0.166631	−0.0833153	−	0.996523i	$-0.526551\pi$
$409$	−9.42996e10	−0.166631	−0.0833153	+	0.996523i	$0.526551\pi$
$410$	0	0
$411$	−7.29207e11	−1.26056
$412$	− 3.86013e11i	− 0.660032i
$413$	− 4.04930e11i	− 0.684865i
$414$	1.16216e12	1.94431
$415$	0	0
$416$	−1.50000e11	−0.245568
$417$	2.00519e11i	0.324746i
$418$	− 3.91318e10i	− 0.0626955i
$419$	−1.66874e11	−0.264500	−0.132250	−	0.991216i	$-0.542220\pi$
$419$	−1.66874e11	−0.264500	−0.132250	+	0.991216i	$0.542220\pi$
$420$	0	0
$421$	−5.52779e11	−0.857594	−0.428797	−	0.903401i	$-0.641062\pi$
$421$	−5.52779e11	−0.857594	−0.428797	+	0.903401i	$0.641062\pi$
$422$	2.88339e11i	0.442585i
$423$	2.25089e12i	3.41840i
$424$	−2.75631e10	−0.0414174
$425$	0	0
$426$	2.47089e11	0.363505
$427$	1.60907e11i	0.234234i
$428$	− 3.13630e11i	− 0.451773i
$429$	−1.04227e11	−0.148567
$430$	0	0
$431$	−4.37408e11	−0.610575	−0.305288	−	0.952260i	$-0.598753\pi$
$431$	−4.37408e11	−0.610575	−0.305288	+	0.952260i	$0.598753\pi$
$432$	− 1.18275e11i	− 0.163387i
$433$	2.79837e11i	0.382569i	0.981535	+	0.191285i	$0.0612653\pi$
$433$	2.79837e11i	0.382569i	−0.981535	+	0.191285i	$0.938735\pi$
$434$	1.50259e11	0.203300
$435$	0	0
$436$	−3.17387e11	−0.420630
$437$	3.31227e11i	0.434470i
$438$	− 2.78504e11i	− 0.361575i
$439$	−8.87150e11	−1.14000	−0.570002	−	0.821643i	$-0.693058\pi$
$439$	−8.87150e11	−1.14000	−0.570002	+	0.821643i	$0.693058\pi$
$440$	0	0
$441$	2.17851e11	0.274275
$442$	− 5.61835e10i	− 0.0700178i
$443$	− 5.87852e11i	− 0.725189i	−0.931947	−	0.362594i	$-0.881891\pi$
$443$	− 5.87852e11i	− 0.725189i	0.931947	−	0.362594i	$-0.118109\pi$
$444$	9.03967e11	1.10390
$445$	0	0
$446$	7.27274e11	0.870344
$447$	− 1.86086e12i	− 2.20460i
$448$	2.36466e11i	0.277344i
$449$	5.19918e11	0.603707	0.301854	−	0.953354i	$-0.402395\pi$
$449$	5.19918e11	0.603707	0.301854	+	0.953354i	$0.402395\pi$
$450$	0	0
$451$	4.75082e11	0.540723
$452$	8.34168e11i	0.940006i
$453$	− 2.00908e12i	− 2.24159i
$454$	−1.02018e12	−1.12701
$455$	0	0
$456$	4.56538e11	0.494465
$457$	1.03055e12i	1.10521i	0.833442	+	0.552607i	$0.186367\pi$
$457$	1.03055e12i	1.10521i	−0.833442	+	0.552607i	$0.813633\pi$
$458$	4.57392e10i	0.0485729i
$459$	−6.25095e11	−0.657338
$460$	0	0
$461$	9.37018e11	0.966259	0.483130	−	0.875549i	$-0.339500\pi$
$461$	9.37018e11	0.966259	0.483130	+	0.875549i	$0.339500\pi$
$462$	1.41034e11i	0.144024i
$463$	1.08281e12i	1.09506i	0.836787	+	0.547529i	$0.184431\pi$
$463$	1.08281e12i	1.09506i	−0.836787	+	0.547529i	$0.815569\pi$
$464$	−1.34855e11	−0.135063
$465$	0	0
$466$	2.20414e11	0.216522
$467$	− 1.52419e11i	− 0.148290i	−0.997247	−	0.0741451i	$-0.976377\pi$
$467$	− 1.52419e11i	− 0.148290i	0.997247	−	0.0741451i	$-0.0236228\pi$
$468$	− 2.90454e11i	− 0.279879i
$469$	3.75177e11	0.358062
$470$	0	0
$471$	2.03703e12	1.90723
$472$	2.01096e12i	1.86494i
$473$	− 5.86297e11i	− 0.538570i
$474$	1.51779e12	1.38105
$475$	0	0
$476$	1.01000e11	0.0901756
$477$	− 8.73554e10i	− 0.0772604i
$478$	− 6.02652e11i	− 0.528008i
$479$	2.02244e11	0.175535	0.0877677	−	0.996141i	$-0.472027\pi$
$479$	2.02244e11	0.175535	0.0877677	+	0.996141i	$0.472027\pi$
$480$	0	0
$481$	−3.39631e11	−0.289304
$482$	− 3.11099e11i	− 0.262535i
$483$	− 1.19376e12i	− 0.998060i
$484$	−6.09042e11	−0.504479
$485$	0	0
$486$	−2.11732e11	−0.172156
$487$	− 8.35572e11i	− 0.673137i	−0.941659	−	0.336568i	$-0.890734\pi$
$487$	− 8.35572e11i	− 0.673137i	0.941659	−	0.336568i	$-0.109266\pi$
$488$	− 7.99094e11i	− 0.637836i
$489$	1.02094e12	0.807442
$490$	0	0
$491$	−1.06242e12	−0.824953	−0.412476	−	0.910968i	$-0.635336\pi$
$491$	−1.06242e12	−0.824953	−0.412476	+	0.910968i	$0.635336\pi$
$492$	2.01351e12i	1.54921i
$493$	7.12723e11i	0.543387i
$494$	−6.23117e10	−0.0470759
$495$	0	0
$496$	−1.14993e11	−0.0853108
$497$	− 1.66886e11i	− 0.122692i
$498$	− 1.88851e12i	− 1.37590i
$499$	3.33938e11	0.241109	0.120554	−	0.992707i	$-0.461533\pi$
$499$	3.33938e11	0.241109	0.120554	+	0.992707i	$0.461533\pi$
$500$	0	0
$501$	−2.21404e11	−0.157006
$502$	− 1.47627e12i	− 1.03752i
$503$	− 3.60934e11i	− 0.251404i	−0.992068	−	0.125702i	$-0.959882\pi$
$503$	− 3.60934e11i	− 0.251404i	0.992068	−	0.125702i	$-0.0401183\pi$
$504$	−1.08189e12	−0.746870
$505$	0	0
$506$	5.08152e11	0.344601
$507$	− 2.37630e12i	− 1.59723i
$508$	1.12781e12i	0.751365i
$509$	−4.09926e11	−0.270692	−0.135346	−	0.990798i	$-0.543215\pi$
$509$	−4.09926e11	−0.270692	−0.135346	+	0.990798i	$0.543215\pi$
$510$	0	0
$511$	−1.88104e11	−0.122040
$512$	− 3.21676e11i	− 0.206873i
$513$	6.93277e11i	0.441955i
$514$	−1.93928e12	−1.22548
$515$	0	0
$516$	2.48487e12	1.54305
$517$	9.84199e11i	0.605865i
$518$	4.59569e11i	0.280457i
$519$	−1.14115e12	−0.690384
$520$	0	0
$521$	−1.09884e12	−0.653377	−0.326688	−	0.945132i	$-0.605933\pi$
$521$	−1.09884e12	−0.653377	−0.326688	+	0.945132i	$0.605933\pi$
$522$	− 2.77346e12i	− 1.63495i
$523$	2.97552e12i	1.73902i	0.493914	+	0.869511i	$0.335566\pi$
$523$	2.97552e12i	1.73902i	−0.493914	+	0.869511i	$0.664434\pi$
$524$	1.17402e11	0.0680276
$525$	0	0
$526$	4.86280e11	0.276982
$527$	6.07748e11i	0.343223i
$528$	− 1.07933e11i	− 0.0604367i
$529$	−2.50005e12	−1.38803
$530$	0	0
$531$	−6.37329e12	−3.47887
$532$	− 1.12016e11i	− 0.0606288i
$533$	− 7.56500e11i	− 0.406010i
$534$	4.05855e11	0.215991
$535$	0	0
$536$	−1.86320e12	−0.975028
$537$	− 2.27074e12i	− 1.17837i
$538$	− 1.10871e11i	− 0.0570554i
$539$	9.52551e10	0.0486115
$540$	0	0
$541$	2.97095e12	1.49110	0.745551	−	0.666449i	$-0.232187\pi$
$541$	2.97095e12	1.49110	0.745551	+	0.666449i	$0.232187\pi$
$542$	9.97561e10i	0.0496527i
$543$	1.88287e12i	0.929438i
$544$	−8.20952e11	−0.401904
$545$	0	0
$546$	2.24576e11	0.108142
$547$	1.50514e12i	0.718842i	0.933176	+	0.359421i	$0.117026\pi$
$547$	1.50514e12i	0.718842i	−0.933176	+	0.359421i	$0.882974\pi$
$548$	− 8.88540e11i	− 0.420886i
$549$	2.53256e12	1.18983
$550$	0	0
$551$	7.90463e11	0.365342
$552$	5.92845e12i	2.71779i
$553$	− 1.02512e12i	− 0.466136i
$554$	−2.26394e12	−1.02111
$555$	0	0
$556$	−2.44333e11	−0.108429
$557$	2.17354e12i	0.956797i	0.878143	+	0.478399i	$0.158783\pi$
$557$	2.17354e12i	0.956797i	−0.878143	+	0.478399i	$0.841217\pi$
$558$	− 2.36496e12i	− 1.03269i
$559$	−9.33593e11	−0.404394
$560$	0	0
$561$	−5.70434e11	−0.243149
$562$	4.59379e11i	0.194248i
$563$	1.40104e12i	0.587710i	0.955850	+	0.293855i	$0.0949383\pi$
$563$	1.40104e12i	0.587710i	−0.955850	+	0.293855i	$0.905062\pi$
$564$	−4.17127e12	−1.73585
$565$	0	0
$566$	1.32281e12	0.541781
$567$	− 7.12707e11i	− 0.289592i
$568$	8.28784e11i	0.334098i
$569$	1.81226e12	0.724795	0.362397	−	0.932024i	$-0.381958\pi$
$569$	1.81226e12	0.724795	0.362397	+	0.932024i	$0.381958\pi$
$570$	0	0
$571$	−3.38885e12	−1.33410	−0.667052	−	0.745012i	$-0.732444\pi$
$571$	−3.38885e12	−1.33410	−0.667052	+	0.745012i	$0.732444\pi$
$572$	− 1.27001e11i	− 0.0496048i
$573$	− 4.27233e12i	− 1.65565i
$574$	−1.02365e12	−0.393594
$575$	0	0
$576$	3.72180e12	1.40881
$577$	− 2.86129e12i	− 1.07466i	−0.843373	−	0.537329i	$-0.819433\pi$
$577$	− 2.86129e12i	− 1.07466i	0.843373	−	0.537329i	$-0.180567\pi$
$578$	1.45098e12i	0.540737i
$579$	−4.62930e11	−0.171183
$580$	0	0
$581$	−1.27551e12	−0.464400
$582$	5.21050e12i	1.88246i
$583$	− 3.81960e10i	− 0.0136933i
$584$	9.34156e11	0.332324
$585$	0	0
$586$	−9.34324e11	−0.327309
$587$	7.85729e11i	0.273150i	0.990630	+	0.136575i	$0.0436095\pi$
$587$	7.85729e11i	0.273150i	−0.990630	+	0.136575i	$0.956391\pi$
$588$	4.03714e11i	0.139276i
$589$	6.74039e11	0.230763
$590$	0	0
$591$	−7.78174e12	−2.62382
$592$	− 3.51707e11i	− 0.117688i
$593$	8.24271e11i	0.273731i	0.990590	+	0.136865i	$0.0437028\pi$
$593$	8.24271e11i	0.273731i	−0.990590	+	0.136865i	$0.956297\pi$
$594$	1.06359e12	0.350538
$595$	0	0
$596$	2.26747e12	0.736093
$597$	− 6.60380e12i	− 2.12770i
$598$	− 8.09159e11i	− 0.258749i
$599$	2.60594e10	0.00827073	0.00413537	−	0.999991i	$-0.498684\pi$
$599$	2.60594e10	0.00827073	0.00413537	+	0.999991i	$0.498684\pi$
$600$	0	0
$601$	1.90372e11	0.0595207	0.0297603	−	0.999557i	$-0.490526\pi$
$601$	1.90372e11	0.0595207	0.0297603	+	0.999557i	$0.490526\pi$
$602$	1.26328e12i	0.392028i
$603$	− 5.90499e12i	− 1.81883i
$604$	2.44807e12	0.748441
$605$	0	0
$606$	2.67944e12	0.807082
$607$	− 1.77675e12i	− 0.531222i	−0.964080	−	0.265611i	$-0.914426\pi$
$607$	− 1.77675e12i	− 0.531222i	0.964080	−	0.265611i	$-0.0855738\pi$
$608$	9.10497e11i	0.270217i
$609$	−2.84888e12	−0.839260
$610$	0	0
$611$	1.56719e12	0.454922
$612$	− 1.58966e12i	− 0.458060i
$613$	− 2.48518e11i	− 0.0710863i	−0.999368	−	0.0355431i	$-0.988684\pi$
$613$	− 2.48518e11i	− 0.0710863i	0.999368	−	0.0355431i	$-0.0113161\pi$
$614$	−1.81591e12	−0.515628
$615$	0	0
$616$	−4.73054e11	−0.132372
$617$	− 3.52347e12i	− 0.978786i	−0.872063	−	0.489393i	$-0.837218\pi$
$617$	− 3.52347e12i	− 0.978786i	0.872063	−	0.489393i	$-0.162782\pi$
$618$	− 4.69755e12i	− 1.29546i
$619$	6.69712e12	1.83350	0.916748	−	0.399466i	$-0.130804\pi$
$619$	6.69712e12	1.83350	0.916748	+	0.399466i	$0.130804\pi$
$620$	0	0
$621$	−9.00266e12	−2.42917
$622$	4.12121e12i	1.10400i
$623$	− 2.74117e11i	− 0.0729021i
$624$	−1.71867e11	−0.0453798
$625$	0	0
$626$	−1.81637e12	−0.472738
$627$	6.32654e11i	0.163479i
$628$	2.48212e12i	0.636802i
$629$	−1.85880e12	−0.473484
$630$	0	0
$631$	6.29917e11	0.158180	0.0790900	−	0.996867i	$-0.474799\pi$
$631$	6.29917e11	0.158180	0.0790900	+	0.996867i	$0.474799\pi$
$632$	5.09095e12i	1.26932i
$633$	− 4.66165e12i	− 1.15404i
$634$	3.44020e12	0.845634
$635$	0	0
$636$	1.61884e11	0.0392325
$637$	− 1.51680e11i	− 0.0365006i
$638$	− 1.21269e12i	− 0.289772i
$639$	−2.62665e12	−0.623231
$640$	0	0
$641$	2.82049e12	0.659877	0.329938	−	0.944002i	$-0.392972\pi$
$641$	2.82049e12	0.659877	0.329938	+	0.944002i	$0.392972\pi$
$642$	− 3.81668e12i	− 0.886704i
$643$	7.19804e12i	1.66060i	0.557317	+	0.830300i	$0.311831\pi$
$643$	7.19804e12i	1.66060i	−0.557317	+	0.830300i	$0.688169\pi$
$644$	1.45461e12	0.333241
$645$	0	0
$646$	−3.41033e11	−0.0770459
$647$	− 7.17803e12i	− 1.61041i	−0.592998	−	0.805204i	$-0.702056\pi$
$647$	− 7.17803e12i	− 1.61041i	0.592998	−	0.805204i	$-0.297944\pi$
$648$	3.53943e12i	0.788580i
$649$	−2.78671e12	−0.616582
$650$	0	0
$651$	−2.42928e12	−0.530106
$652$	1.24402e12i	0.269596i
$653$	− 1.54599e12i	− 0.332734i	−0.986064	−	0.166367i	$-0.946796\pi$
$653$	− 1.54599e12i	− 0.332734i	0.986064	−	0.166367i	$-0.0532037\pi$
$654$	−3.86240e12	−0.825578
$655$	0	0
$656$	7.83398e11	0.165164
$657$	2.96061e12i	0.619921i
$658$	− 2.12064e12i	− 0.441011i
$659$	−2.38624e12	−0.492868	−0.246434	−	0.969160i	$-0.579259\pi$
$659$	−2.38624e12	−0.492868	−0.246434	+	0.969160i	$0.579259\pi$
$660$	0	0
$661$	−2.35488e12	−0.479802	−0.239901	−	0.970797i	$-0.577115\pi$
$661$	−2.35488e12	−0.479802	−0.239901	+	0.970797i	$0.577115\pi$
$662$	− 5.54958e12i	− 1.12305i
$663$	9.08333e11i	0.182572i
$664$	6.33443e12	1.26459
$665$	0	0
$666$	7.23326e12	1.42462
$667$	1.02647e13i	2.00807i
$668$	− 2.69781e11i	− 0.0524225i
$669$	−1.17580e13	−2.26943
$670$	0	0
$671$	1.10736e12	0.210880
$672$	− 3.28149e12i	− 0.620740i
$673$	− 6.32709e12i	− 1.18887i	−0.804142	−	0.594437i	$-0.797375\pi$
$673$	− 6.32709e12i	− 1.18887i	0.804142	−	0.594437i	$-0.202625\pi$
$674$	4.98055e12	0.929625
$675$	0	0
$676$	2.89553e12	0.533296
$677$	− 3.16670e12i	− 0.579372i	−0.957122	−	0.289686i	$-0.906449\pi$
$677$	− 3.16670e12i	− 0.579372i	0.957122	−	0.289686i	$-0.0935510\pi$
$678$	1.01513e13i	1.84497i
$679$	3.51921e12	0.635376
$680$	0	0
$681$	1.64935e13	2.93868
$682$	− 1.03408e12i	− 0.183030i
$683$	− 6.06916e12i	− 1.06717i	−0.845745	−	0.533587i	$-0.820844\pi$
$683$	− 6.06916e12i	− 1.06717i	0.845745	−	0.533587i	$-0.179156\pi$
$684$	−1.76305e12	−0.307973
$685$	0	0
$686$	−2.05245e11	−0.0353845
$687$	− 7.39478e11i	− 0.126654i
$688$	− 9.66788e11i	− 0.164507i
$689$	−6.08216e10	−0.0102818
$690$	0	0
$691$	−1.36410e12	−0.227611	−0.113806	−	0.993503i	$-0.536304\pi$
$691$	−1.36410e12	−0.227611	−0.113806	+	0.993503i	$0.536304\pi$
$692$	− 1.39050e12i	− 0.230512i
$693$	− 1.49924e12i	− 0.246929i
$694$	−5.39307e12	−0.882508
$695$	0	0
$696$	1.41481e13	2.28536
$697$	− 4.14033e12i	− 0.664489i
$698$	− 1.61244e12i	− 0.257119i
$699$	−3.56349e12	−0.564584
$700$	0	0
$701$	4.27032e12	0.667927	0.333964	−	0.942586i	$-0.391614\pi$
$701$	4.27032e12	0.667927	0.333964	+	0.942586i	$0.391614\pi$
$702$	− 1.69361e12i	− 0.263207i
$703$	2.06155e12i	0.318343i
$704$	1.62735e12	0.249692
$705$	0	0
$706$	4.98605e12	0.755328
$707$	− 1.80971e12i	− 0.272410i
$708$	− 1.18108e13i	− 1.76656i
$709$	−4.76449e12	−0.708122	−0.354061	−	0.935222i	$-0.615200\pi$
$709$	−4.76449e12	−0.708122	−0.354061	+	0.935222i	$0.615200\pi$
$710$	0	0
$711$	−1.61347e13	−2.36781
$712$	1.36132e12i	0.198517i
$713$	8.75284e12i	1.26837i
$714$	1.22910e12	0.176989
$715$	0	0
$716$	2.76690e12	0.393446
$717$	9.74323e12i	1.37679i
$718$	− 8.15481e12i	− 1.14513i
$719$	2.64192e12	0.368671	0.184336	−	0.982863i	$-0.440987\pi$
$719$	2.64192e12	0.368671	0.184336	+	0.982863i	$0.440987\pi$
$720$	0	0
$721$	−3.17276e12	−0.437248
$722$	− 4.40672e12i	− 0.603529i
$723$	5.02963e12i	0.684563i
$724$	−2.29428e12	−0.310329
$725$	0	0
$726$	−7.41167e12	−0.990150
$727$	3.54861e12i	0.471144i	0.971857	+	0.235572i	$0.0756963\pi$
$727$	3.54861e12i	0.471144i	−0.971857	+	0.235572i	$0.924304\pi$
$728$	7.53270e11i	0.0993938i
$729$	9.26577e12	1.21509
$730$	0	0
$731$	−5.10956e12	−0.661844
$732$	4.69324e12i	0.604189i
$733$	− 1.34909e13i	− 1.72613i	−0.505095	−	0.863063i	$-0.668543\pi$
$733$	− 1.34909e13i	− 1.72613i	0.505095	−	0.863063i	$-0.331457\pi$
$734$	−1.96037e12	−0.249291
$735$	0	0
$736$	−1.18234e13	−1.48523
$737$	− 2.58195e12i	− 0.322362i
$738$	1.61115e13i	1.99932i
$739$	1.33151e13	1.64227	0.821133	−	0.570736i	$-0.193342\pi$
$739$	1.33151e13	1.64227	0.821133	+	0.570736i	$0.193342\pi$
$740$	0	0
$741$	1.00741e12	0.122751
$742$	8.23003e10i	0.00996744i
$743$	1.37811e13i	1.65896i	0.558538	+	0.829479i	$0.311363\pi$
$743$	1.37811e13i	1.65896i	−0.558538	+	0.829479i	$0.688637\pi$
$744$	1.20642e13	1.44352
$745$	0	0
$746$	−7.23722e12	−0.855553
$747$	2.00756e13i	2.35899i
$748$	− 6.95075e11i	− 0.0811848i
$749$	−2.57781e12	−0.299284
$750$	0	0
$751$	−1.31166e12	−0.150467	−0.0752334	−	0.997166i	$-0.523970\pi$
$751$	−1.31166e12	−0.150467	−0.0752334	+	0.997166i	$0.523970\pi$
$752$	1.62292e12i	0.185062i
$753$	2.38672e13i	2.70535i
$754$	−1.93103e12	−0.217580
$755$	0	0
$756$	3.04457e12	0.338983
$757$	− 1.31405e13i	− 1.45439i	−0.686430	−	0.727196i	$-0.740823\pi$
$757$	− 1.31405e13i	− 1.45439i	0.686430	−	0.727196i	$-0.259177\pi$
$758$	− 4.45093e12i	− 0.489711i
$759$	−8.21543e12	−0.898551
$760$	0	0
$761$	4.85816e12	0.525099	0.262549	−	0.964919i	$-0.415437\pi$
$761$	4.85816e12	0.525099	0.262549	+	0.964919i	$0.415437\pi$
$762$	1.37248e13i	1.47472i
$763$	2.60869e12i	0.278652i
$764$	5.20584e12	0.552804
$765$	0	0
$766$	−1.14802e13	−1.20481
$767$	4.43743e12i	0.462970i
$768$	1.72735e13i	1.79165i
$769$	1.57384e13	1.62290	0.811452	−	0.584420i	$-0.198678\pi$
$769$	1.57384e13	1.62290	0.811452	+	0.584420i	$0.198678\pi$
$770$	0	0
$771$	3.13528e13	3.19545
$772$	− 5.64081e11i	− 0.0571562i
$773$	1.97088e12i	0.198542i	0.995060	+	0.0992710i	$0.0316511\pi$
$773$	1.97088e12i	0.198542i	−0.995060	+	0.0992710i	$0.968349\pi$
$774$	1.98831e13	1.99136
$775$	0	0
$776$	−1.74770e13	−1.73017
$777$	− 7.42997e12i	− 0.731295i
$778$	2.52271e12i	0.246865i
$779$	−4.59194e12	−0.446763
$780$	0	0
$781$	−1.14850e12	−0.110459
$782$	− 4.42854e12i	− 0.423477i
$783$	2.14846e13i	2.04267i
$784$	1.57073e11	0.0148484
$785$	0	0
$786$	1.42871e12	0.133519
$787$	1.29627e13i	1.20451i	0.798306	+	0.602253i	$0.205730\pi$
$787$	1.29627e13i	1.20451i	−0.798306	+	0.602253i	$0.794270\pi$
$788$	− 9.48207e12i	− 0.876063i
$789$	−7.86182e12	−0.722232
$790$	0	0
$791$	6.85627e12	0.622721
$792$	7.44551e12i	0.672405i
$793$	− 1.76330e12i	− 0.158343i
$794$	−8.11474e12	−0.724573
$795$	0	0
$796$	8.04675e12	0.710414
$797$	− 1.04429e13i	− 0.916762i	−0.888756	−	0.458381i	$-0.848429\pi$
$797$	− 1.04429e13i	− 0.916762i	0.888756	−	0.458381i	$-0.151571\pi$
$798$	− 1.36317e12i	− 0.118997i
$799$	8.57727e12	0.744541
$800$	0	0
$801$	−4.31439e12	−0.370317
$802$	− 6.77917e12i	− 0.578618i
$803$	1.29452e12i	0.109872i
$804$	1.09429e13	0.923594
$805$	0	0
$806$	−1.64662e12	−0.137431
$807$	1.79248e12i	0.148772i
$808$	8.98737e12i	0.741791i
$809$	6.99142e12	0.573848	0.286924	−	0.957953i	$-0.407367\pi$
$809$	6.99142e12	0.573848	0.286924	+	0.957953i	$0.407367\pi$
$810$	0	0
$811$	−1.14380e13	−0.928442	−0.464221	−	0.885719i	$-0.653666\pi$
$811$	−1.14380e13	−0.928442	−0.464221	+	0.885719i	$0.653666\pi$
$812$	− 3.47137e12i	− 0.280220i
$813$	− 1.61278e12i	− 0.129470i
$814$	3.16273e12	0.252495
$815$	0	0
$816$	−9.40631e11	−0.0742700
$817$	5.66689e12i	0.444985i
$818$	− 1.39831e12i	− 0.109198i
$819$	−2.38733e12	−0.185410
$820$	0	0
$821$	−4.42435e12	−0.339864	−0.169932	−	0.985456i	$-0.554355\pi$
$821$	−4.42435e12	−0.339864	−0.169932	+	0.985456i	$0.554355\pi$
$822$	− 1.08130e13i	− 0.826081i
$823$	1.71948e13i	1.30647i	0.757156	+	0.653234i	$0.226588\pi$
$823$	1.71948e13i	1.30647i	−0.757156	+	0.653234i	$0.773412\pi$
$824$	1.57565e13	1.19066
$825$	0	0
$826$	6.00448e12	0.448813
$827$	− 3.04498e12i	− 0.226365i	−0.993574	−	0.113182i	$-0.963896\pi$
$827$	− 3.04498e12i	− 0.226365i	0.993574	−	0.113182i	$-0.0361045\pi$
$828$	− 2.28944e13i	− 1.69275i
$829$	8.03416e12	0.590806	0.295403	−	0.955373i	$-0.404546\pi$
$829$	8.03416e12	0.590806	0.295403	+	0.955373i	$0.404546\pi$
$830$	0	0
$831$	3.66017e13	2.66254
$832$	− 2.59132e12i	− 0.187485i
$833$	− 8.30146e11i	− 0.0597382i
$834$	−2.97339e12	−0.212816
$835$	0	0
$836$	−7.70891e11	−0.0545839
$837$	1.83202e13i	1.29022i
$838$	− 2.47448e12i	− 0.173335i
$839$	−1.36209e13	−0.949020	−0.474510	−	0.880250i	$-0.657375\pi$
$839$	−1.36209e13	−0.949020	−0.474510	+	0.880250i	$0.657375\pi$
$840$	0	0
$841$	9.98921e12	0.688571
$842$	− 8.19684e12i	− 0.562007i
$843$	− 7.42689e12i	− 0.506504i
$844$	5.68023e12	0.385323
$845$	0	0
$846$	−3.33772e13	−2.24018
$847$	5.00589e12i	0.334200i
$848$	− 6.29842e10i	− 0.00418264i
$849$	−2.13862e13	−1.41270
$850$	0	0
$851$	−2.67706e13	−1.74975
$852$	− 4.86762e12i	− 0.316474i
$853$	3.64211e12i	0.235549i	0.993040	+	0.117775i	$0.0375761\pi$
$853$	3.64211e12i	0.235549i	−0.993040	+	0.117775i	$0.962424\pi$
$854$	−2.38600e12	−0.153501
$855$	0	0
$856$	1.28019e13	0.814971
$857$	− 1.62518e13i	− 1.02917i	−0.857438	−	0.514587i	$-0.827945\pi$
$857$	− 1.62518e13i	− 1.02917i	0.857438	−	0.514587i	$-0.172055\pi$
$858$	− 1.54552e12i	− 0.0973602i
$859$	−1.69063e13	−1.05944	−0.529722	−	0.848171i	$-0.677704\pi$
$859$	−1.69063e13	−1.05944	−0.529722	+	0.848171i	$0.677704\pi$
$860$	0	0
$861$	1.65496e13	1.02630
$862$	− 6.48608e12i	− 0.400128i
$863$	− 1.56857e13i	− 0.962619i	−0.876551	−	0.481310i	$-0.840161\pi$
$863$	− 1.56857e13i	− 0.962619i	0.876551	−	0.481310i	$-0.159839\pi$
$864$	−2.47471e13	−1.51082
$865$	0	0
$866$	−4.14955e12	−0.250709
$867$	− 2.34584e13i	− 1.40998i
$868$	− 2.96008e12i	− 0.176997i
$869$	−7.05485e12	−0.419661
$870$	0	0
$871$	−4.11138e12	−0.242050
$872$	− 1.29553e13i	− 0.758790i
$873$	− 5.53897e13i	− 3.22749i
$874$	−4.91158e12	−0.284721
$875$	0	0
$876$	−5.48649e12	−0.314794
$877$	− 2.37521e13i	− 1.35583i	−0.735141	−	0.677914i	$-0.762884\pi$
$877$	− 2.37521e13i	− 1.35583i	0.735141	−	0.677914i	$-0.237116\pi$
$878$	− 1.31550e13i	− 0.747079i
$879$	1.51055e13	0.853462
$880$	0	0
$881$	1.13698e13	0.635858	0.317929	−	0.948115i	$-0.397013\pi$
$881$	1.13698e13	0.635858	0.317929	+	0.948115i	$0.397013\pi$
$882$	3.23039e12i	0.179741i
$883$	− 1.21711e12i	− 0.0673762i	−0.999432	−	0.0336881i	$-0.989275\pi$
$883$	− 1.21711e12i	− 0.0673762i	0.999432	−	0.0336881i	$-0.0107253\pi$
$884$	−1.10681e12	−0.0609588
$885$	0	0
$886$	8.71692e12	0.475238
$887$	− 3.43743e13i	− 1.86457i	−0.361730	−	0.932283i	$-0.617814\pi$
$887$	− 3.43743e13i	− 1.86457i	0.361730	−	0.932283i	$-0.382186\pi$
$888$	3.68986e13i	1.99137i
$889$	9.26983e12	0.497753
$890$	0	0
$891$	−4.90482e12	−0.260719
$892$	− 1.43272e13i	− 0.757738i
$893$	− 9.51284e12i	− 0.500586i
$894$	2.75937e13	1.44474
$895$	0	0
$896$	3.50183e12	0.181513
$897$	1.30819e13i	0.674690i
$898$	7.70957e12i	0.395627i
$899$	2.08884e13	1.06656
$900$	0	0
$901$	−3.32877e11	−0.0168276
$902$	7.04472e12i	0.354352i
$903$	− 2.04238e13i	− 1.02222i
$904$	−3.40495e13	−1.69571
$905$	0	0
$906$	2.97915e13	1.46898
$907$	3.08586e13i	1.51406i	0.653381	+	0.757030i	$0.273350\pi$
$907$	3.08586e13i	1.51406i	−0.653381	+	0.757030i	$0.726650\pi$
$908$	2.00974e13i	0.981192i
$909$	−2.84835e13	−1.38374
$910$	0	0
$911$	−3.36006e13	−1.61627	−0.808136	−	0.588996i	$-0.799523\pi$
$911$	−3.36006e13	−1.61627	−0.808136	+	0.588996i	$0.799523\pi$
$912$	1.04323e12i	0.0499348i
$913$	8.77802e12i	0.418098i
$914$	−1.52814e13	−0.724280
$915$	0	0
$916$	9.01056e11	0.0422885
$917$	− 9.64961e11i	− 0.0450659i
$918$	− 9.26917e12i	− 0.430773i
$919$	1.46200e13	0.676127	0.338063	−	0.941123i	$-0.390228\pi$
$919$	1.46200e13	0.676127	0.338063	+	0.941123i	$0.390228\pi$
$920$	0	0
$921$	2.93583e13	1.34450
$922$	1.38945e13i	0.633219i
$923$	1.82882e12i	0.0829398i
$924$	2.77834e12	0.125390
$925$	0	0
$926$	−1.60563e13	−0.717625
$927$	4.99367e13i	2.22107i
$928$	2.82162e13i	1.24891i
$929$	1.36244e13	0.600130	0.300065	−	0.953919i	$-0.402992\pi$
$929$	1.36244e13	0.600130	0.300065	+	0.953919i	$0.402992\pi$
$930$	0	0
$931$	−9.20694e11	−0.0401644
$932$	− 4.34213e12i	− 0.188508i
$933$	− 6.66287e13i	− 2.87868i
$934$	2.26013e12	0.0971790
$935$	0	0
$936$	1.18559e13	0.504885
$937$	1.06580e13i	0.451697i	0.974162	+	0.225848i	$0.0725154\pi$
$937$	1.06580e13i	0.451697i	−0.974162	+	0.225848i	$0.927485\pi$
$938$	5.56328e12i	0.234649i
$939$	2.93658e13	1.23267
$940$	0	0
$941$	1.54253e13	0.641328	0.320664	−	0.947193i	$-0.396094\pi$
$941$	1.54253e13	0.641328	0.320664	+	0.947193i	$0.396094\pi$
$942$	3.02059e13i	1.24986i
$943$	− 5.96294e13i	− 2.45560i
$944$	−4.59522e12	−0.188335
$945$	0	0
$946$	8.69386e12	0.352941
$947$	− 1.97267e13i	− 0.797039i	−0.917160	−	0.398519i	$-0.869524\pi$
$947$	− 1.97267e13i	− 0.797039i	0.917160	−	0.398519i	$-0.130476\pi$
$948$	− 2.99002e13i	− 1.20236i
$949$	2.06133e12	0.0824993
$950$	0	0
$951$	−5.56186e13	−2.20500
$952$	4.12265e12i	0.162671i
$953$	− 1.39214e12i	− 0.0546721i	−0.999626	−	0.0273361i	$-0.991298\pi$
$953$	− 1.39214e12i	− 0.0546721i	0.999626	−	0.0273361i	$-0.00870242\pi$
$954$	1.29534e12	0.0506311
$955$	0	0
$956$	−1.18721e13	−0.459694
$957$	1.96059e13i	0.755583i
$958$	2.99895e12i	0.115034i
$959$	−7.30317e12	−0.278822
$960$	0	0
$961$	−8.62783e12	−0.326322
$962$	− 5.03619e12i	− 0.189589i
$963$	4.05728e13i	1.52026i
$964$	−6.12861e12	−0.228568
$965$	0	0
$966$	1.77017e13	0.654059
$967$	− 5.29760e12i	− 0.194832i	−0.995244	−	0.0974160i	$-0.968942\pi$
$967$	− 5.29760e12i	− 0.194832i	0.995244	−	0.0974160i	$-0.0310577\pi$
$968$	− 2.48602e13i	− 0.910049i
$969$	5.51357e12	0.200898
$970$	0	0
$971$	−7.97890e12	−0.288042	−0.144021	−	0.989575i	$-0.546003\pi$
$971$	−7.97890e12	−0.288042	−0.144021	+	0.989575i	$0.546003\pi$
$972$	4.17108e12i	0.149882i
$973$	2.00825e12i	0.0718306i
$974$	1.23902e13	0.441127
$975$	0	0
$976$	1.82600e12	0.0644135
$977$	6.27831e12i	0.220454i	0.993906	+	0.110227i	$0.0351577\pi$
$977$	6.27831e12i	0.220454i	−0.993906	+	0.110227i	$0.964842\pi$
$978$	1.51390e13i	0.529141i
$979$	−1.88646e12	−0.0656335
$980$	0	0
$981$	4.10589e13	1.41546
$982$	− 1.57540e13i	− 0.540616i
$983$	1.25053e12i	0.0427173i	0.999772	+	0.0213586i	$0.00679918\pi$
$983$	1.25053e12i	0.0427173i	−0.999772	+	0.0213586i	$0.993201\pi$
$984$	−8.21886e13	−2.79469
$985$	0	0
$986$	−1.05686e13	−0.356098
$987$	3.42849e13i	1.14994i
$988$	1.22753e12i	0.0409851i
$989$	−7.35883e13	−2.44583
$990$	0	0
$991$	1.89095e13	0.622801	0.311400	−	0.950279i	$-0.399202\pi$
$991$	1.89095e13	0.622801	0.311400	+	0.950279i	$0.399202\pi$
$992$	2.40603e13i	0.788858i
$993$	8.97216e13i	2.92836i
$994$	2.47465e12	0.0804036
$995$	0	0
$996$	−3.72034e13	−1.19788
$997$	7.17482e12i	0.229976i	0.993367	+	0.114988i	$0.0366830\pi$
$997$	7.17482e12i	0.229976i	−0.993367	+	0.114988i	$0.963317\pi$
$998$	4.95178e12i	0.158006i
$999$	−5.60324e13	−1.77989

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.10.b.c.99.4		4
5.2	odd	4		35.10.a.b.1.1	✓	2
5.3	odd	4		175.10.a.c.1.2		2
5.4	even	2	inner	175.10.b.c.99.1		4
15.2	even	4		315.10.a.b.1.2		2
35.27	even	4		245.10.a.c.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.10.a.b.1.1	✓	2	5.2	odd	4
175.10.a.c.1.2		2	5.3	odd	4
175.10.b.c.99.1		4	5.4	even	2	inner
175.10.b.c.99.4		4	1.1	even	1	trivial
245.10.a.c.1.1		2	35.27	even	4
315.10.a.b.1.2		2	15.2	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	175.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+14.8284i q^{2} -239.735i q^{3} +292.118 q^{4} +3554.89 q^{6} -2401.00i q^{7} +11923.8i q^{8} -37789.9 q^{9} +O(q^{10})\)	\(q+14.8284i q^{2} -239.735i q^{3} +292.118 q^{4} +3554.89 q^{6} -2401.00i q^{7} +11923.8i q^{8} -37789.9 q^{9} -16523.6 q^{11} -70030.9i q^{12} +26311.4i q^{13} +35603.1 q^{14} -27246.9 q^{16} +144003. i q^{17} -560365. i q^{18} +159710. q^{19} -575604. q^{21} -245019. i q^{22} +2.07393e6i q^{23} +2.85855e6 q^{24} -390156. q^{26} +4.34086e6i q^{27} -701375. i q^{28} +4.94938e6 q^{29} +4.22040e6 q^{31} +5.70096e6i q^{32} +3.96128e6i q^{33} -2.13533e6 q^{34} -1.10391e7 q^{36} +1.29081e7i q^{37} +2.36824e6i q^{38} +6.30776e6 q^{39} -2.87518e7 q^{41} -8.53530e6i q^{42} +3.54825e7i q^{43} -4.82683e6 q^{44} -3.07532e7 q^{46} -5.95633e7i q^{47} +6.53205e6i q^{48} -5.76480e6 q^{49} +3.45225e7 q^{51} +7.68602e6i q^{52} +2.31161e6i q^{53} -6.43681e7 q^{54} +2.86290e7 q^{56} -3.82880e7i q^{57} +7.33915e7i q^{58} +1.68651e8 q^{59} -6.70167e7 q^{61} +6.25819e7i q^{62} +9.07336e7i q^{63} -9.84867e7 q^{64} -5.87395e7 q^{66} +1.56259e8i q^{67} +4.20657e7i q^{68} +4.97195e8 q^{69} +6.95067e7 q^{71} -4.50599e8i q^{72} -7.83438e7i q^{73} -1.91407e8 q^{74} +4.66540e7 q^{76} +3.96731e7i q^{77} +9.35342e7i q^{78} +4.26957e8 q^{79} +2.96838e8 q^{81} -4.26344e8i q^{82} -5.31242e8i q^{83} -1.68144e8 q^{84} -5.26149e8 q^{86} -1.18654e9i q^{87} -1.97024e8i q^{88} +1.14168e8 q^{89} +6.31736e7 q^{91} +6.05833e8i q^{92} -1.01178e9i q^{93} +8.83231e8 q^{94} +1.36672e9 q^{96} +1.46573e9i q^{97} -8.54829e7i q^{98} +6.24424e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 1440 q^{4} + 5904 q^{6} - 44856 q^{9}+O(q^{10}) \) 4 * q + 1440 * q^4 + 5904 * q^6 - 44856 * q^9	\( 4 q + 1440 q^{4} + 5904 q^{6} - 44856 q^{9} + 37132 q^{11} + 115248 q^{14} + 225536 q^{16} + 286552 q^{19} - 835548 q^{21} + 4583808 q^{24} + 639472 q^{26} + 23155108 q^{29} - 7907520 q^{31} - 8487888 q^{34} - 8932032 q^{36} + 22791492 q^{39} + 2117984 q^{41} + 20374752 q^{44} - 14312352 q^{46} - 23059204 q^{49} + 38818932 q^{51} - 170992944 q^{54} + 98652288 q^{56} + 232318416 q^{59} - 89377088 q^{61} - 158111744 q^{64} - 159789648 q^{66} + 1332641784 q^{69} - 588331648 q^{71} - 204836128 q^{74} + 79244736 q^{76} + 1385705708 q^{79} + 895546692 q^{81} - 201223008 q^{84} - 693978016 q^{86} + 1558087408 q^{89} - 245334180 q^{91} + 1875382064 q^{94} + 1984361472 q^{96} + 2326933080 q^{99}+O(q^{100}) \) 4 * q + 1440 * q^4 + 5904 * q^6 - 44856 * q^9 + 37132 * q^11 + 115248 * q^14 + 225536 * q^16 + 286552 * q^19 - 835548 * q^21 + 4583808 * q^24 + 639472 * q^26 + 23155108 * q^29 - 7907520 * q^31 - 8487888 * q^34 - 8932032 * q^36 + 22791492 * q^39 + 2117984 * q^41 + 20374752 * q^44 - 14312352 * q^46 - 23059204 * q^49 + 38818932 * q^51 - 170992944 * q^54 + 98652288 * q^56 + 232318416 * q^59 - 89377088 * q^61 - 158111744 * q^64 - 159789648 * q^66 + 1332641784 * q^69 - 588331648 * q^71 - 204836128 * q^74 + 79244736 * q^76 + 1385705708 * q^79 + 895546692 * q^81 - 201223008 * q^84 - 693978016 * q^86 + 1558087408 * q^89 - 245334180 * q^91 + 1875382064 * q^94 + 1984361472 * q^96 + 2326933080 * q^99

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