LMFDB - Embedded newform 175.10.b.e.99.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [175,10,Mod(99,175)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [8,0,0,-3458] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$90.1312713287$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1297x^{6} + 417140x^{4} + 37202308x^{2} + 69022864 $ x^8 + 1297x^6 + 417140x^4 + 37202308*x^2 + 69022864
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3}\cdot 3^{4}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.5
Root			$-29.3917i$ of defining polynomial
Character	$\chi$	$=$	175.99
Dual form			175.10.b.e.99.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+15.4436i q^{2} -137.736i q^{3} +273.496 q^{4} +2127.13 q^{6} -2401.00i q^{7} +12130.9i q^{8} +711.820 q^{9} -8060.89 q^{11} -37670.3i q^{12} +137129. i q^{13} +37080.0 q^{14} -47313.7 q^{16} -23676.1i q^{17} +10993.0i q^{18} -572389. q^{19} -330704. q^{21} -124489. i q^{22} +997700. i q^{23} +1.67086e6 q^{24} -2.11777e6 q^{26} -2.80910e6i q^{27} -656664. i q^{28} -1.97927e6 q^{29} -8.47740e6 q^{31} +5.48031e6i q^{32} +1.11027e6i q^{33} +365643. q^{34} +194680. q^{36} -4.33062e6i q^{37} -8.83972e6i q^{38} +1.88876e7 q^{39} -1.48554e7 q^{41} -5.10725e6i q^{42} -3.14842e7i q^{43} -2.20462e6 q^{44} -1.54081e7 q^{46} +2.31045e7i q^{47} +6.51680e6i q^{48} -5.76480e6 q^{49} -3.26104e6 q^{51} +3.75044e7i q^{52} +6.79444e6i q^{53} +4.33825e7 q^{54} +2.91262e7 q^{56} +7.88385e7i q^{57} -3.05671e7i q^{58} -8.85117e7 q^{59} +1.24823e8 q^{61} -1.30921e8i q^{62} -1.70908e6i q^{63} -1.08860e8 q^{64} -1.71466e7 q^{66} +9.58712e7i q^{67} -6.47531e6i q^{68} +1.37419e8 q^{69} -2.16795e8 q^{71} +8.63500e6i q^{72} +1.50701e8i q^{73} +6.68803e7 q^{74} -1.56546e8 q^{76} +1.93542e7i q^{77} +2.91693e8i q^{78} +3.89487e8 q^{79} -3.72903e8 q^{81} -2.29420e8i q^{82} +7.43467e8i q^{83} -9.04463e7 q^{84} +4.86228e8 q^{86} +2.72617e8i q^{87} -9.77855e7i q^{88} -2.64429e8 q^{89} +3.29248e8 q^{91} +2.72867e8i q^{92} +1.16764e9i q^{93} -3.56816e8 q^{94} +7.54835e8 q^{96} +1.39343e9i q^{97} -8.90291e7i q^{98} -5.73790e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 3458 q^{4} - 288 q^{6} - 10764 q^{9} + 164876 q^{11} - 91238 q^{14} + 128514 q^{16} - 601464 q^{19} + 86436 q^{21} + 15272640 q^{24} + 2611332 q^{26} + 2744044 q^{29} - 9181776 q^{31} + 14398956 q^{34}+ \cdots - 2444739048 q^{99}+O(q^{100}) $ 8 * q - 3458 * q^4 - 288 * q^6 - 10764 * q^9 + 164876 * q^11 - 91238 * q^14 + 128514 * q^16 - 601464 * q^19 + 86436 * q^21 + 15272640 * q^24 + 2611332 * q^26 + 2744044 * q^29 - 9181776 * q^31 + 14398956 * q^34 - 18288486 * q^36 + 93332484 * q^39 + 114574168 * q^41 - 175278696 * q^44 + 57784832 * q^46 - 46118408 * q^49 + 172685268 * q^51 - 375179040 * q^54 + 146436990 * q^56 - 145139360 * q^59 - 451362072 * q^61 - 282886786 * q^64 - 239347296 * q^66 - 696601224 * q^69 - 940937968 * q^71 - 1855619004 * q^74 - 1784530688 * q^76 + 1197611292 * q^79 - 1694311992 * q^81 + 198457056 * q^84 + 1413582312 * q^86 + 2760306024 * q^89 + 350363524 * q^91 - 4933488304 * q^94 - 1598643648 * q^96 - 2444739048 * q^99

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 $

$2$	15.4436i	0.682516i	0.939970	+	0.341258i	$0.110853\pi$
$2$	15.4436i	0.682516i	−0.939970	+	0.341258i	$0.889147\pi$
$3$	− 137.736i	− 0.981751i	−0.871230	−	0.490876i	$-0.836677\pi$
$3$	− 137.736i	− 0.981751i	0.871230	−	0.490876i	$-0.163323\pi$
$4$	273.496	0.534172
$5$	0	0
$5$	0	0
$6$	2127.13	0.670061
$7$	− 2401.00i	− 0.377964i
$7$	− 2401.00i	− 0.377964i
$8$	12130.9i	1.04710i
$9$	711.820	0.0361642
$10$	0	0
$11$	−8060.89	−0.166003	−0.0830015	−	0.996549i	$-0.526451\pi$
$11$	−8060.89	−0.166003	−0.0830015	+	0.996549i	$0.526451\pi$
$12$	− 37670.3i	− 0.524424i
$13$	137129.i	1.33164i	0.746114	+	0.665818i	$0.231917\pi$
$13$	137129.i	1.33164i	−0.746114	+	0.665818i	$0.768083\pi$
$14$	37080.0	0.257967
$15$	0	0
$16$	−47313.7	−0.180488
$17$	− 23676.1i	− 0.0687526i	−0.999409	−	0.0343763i	$-0.989056\pi$
$17$	− 23676.1i	− 0.0687526i	0.999409	−	0.0343763i	$-0.0109445\pi$
$18$	10993.0i	0.0246826i
$19$	−572389.	−1.00763	−0.503814	−	0.863812i	$-0.668070\pi$
$19$	−572389.	−1.00763	−0.503814	+	0.863812i	$0.668070\pi$
$20$	0	0
$21$	−330704.	−0.371067
$22$	− 124489.i	− 0.113300i
$23$	997700.i	0.743404i	0.928352	+	0.371702i	$0.121226\pi$
$23$	997700.i	0.743404i	−0.928352	+	0.371702i	$0.878774\pi$
$24$	1.67086e6	1.02799
$25$	0	0
$26$	−2.11777e6	−0.908862
$27$	− 2.80910e6i	− 1.01726i
$28$	− 656664.i	− 0.201898i
$29$	−1.97927e6	−0.519655	−0.259827	−	0.965655i	$-0.583666\pi$
$29$	−1.97927e6	−0.519655	−0.259827	+	0.965655i	$0.583666\pi$
$30$	0	0
$31$	−8.47740e6	−1.64867	−0.824337	−	0.566099i	$-0.808452\pi$
$31$	−8.47740e6	−1.64867	−0.824337	+	0.566099i	$0.808452\pi$
$32$	5.48031e6i	0.923911i
$33$	1.11027e6i	0.162974i
$34$	365643.	0.0469247
$35$	0	0
$36$	194680.	0.0193179
$37$	− 4.33062e6i	− 0.379877i	−0.981796	−	0.189938i	$-0.939171\pi$
$37$	− 4.33062e6i	− 0.379877i	0.981796	−	0.189938i	$-0.0608288\pi$
$38$	− 8.83972e6i	− 0.687721i
$39$	1.88876e7	1.30734
$40$	0	0
$41$	−1.48554e7	−0.821024	−0.410512	−	0.911855i	$-0.634650\pi$
$41$	−1.48554e7	−0.821024	−0.410512	+	0.911855i	$0.634650\pi$
$42$	− 5.10725e6i	− 0.253259i
$43$	− 3.14842e7i	− 1.40438i	−0.711991	−	0.702189i	$-0.752206\pi$
$43$	− 3.14842e7i	− 1.40438i	0.711991	−	0.702189i	$-0.247794\pi$
$44$	−2.20462e6	−0.0886742
$45$	0	0
$46$	−1.54081e7	−0.507385
$47$	2.31045e7i	0.690647i	0.938484	+	0.345324i	$0.112231\pi$
$47$	2.31045e7i	0.690647i	−0.938484	+	0.345324i	$0.887769\pi$
$48$	6.51680e6i	0.177194i
$49$	−5.76480e6	−0.142857
$50$	0	0
$51$	−3.26104e6	−0.0674980
$52$	3.75044e7i	0.711323i
$53$	6.79444e6i	0.118280i	0.998250	+	0.0591401i	$0.0188359\pi$
$53$	6.79444e6i	0.118280i	−0.998250	+	0.0591401i	$0.981164\pi$
$54$	4.33825e7	0.694293
$55$	0	0
$56$	2.91262e7	0.395765
$57$	7.88385e7i	0.989239i
$58$	− 3.05671e7i	− 0.354673i
$59$	−8.85117e7	−0.950969	−0.475485	−	0.879724i	$-0.657727\pi$
$59$	−8.85117e7	−0.950969	−0.475485	+	0.879724i	$0.657727\pi$
$60$	0	0
$61$	1.24823e8	1.15428	0.577138	−	0.816647i	$-0.304169\pi$
$61$	1.24823e8	1.15428	0.577138	+	0.816647i	$0.304169\pi$
$62$	− 1.30921e8i	− 1.12525i
$63$	− 1.70908e6i	− 0.0136688i
$64$	−1.08860e8	−0.811071
$65$	0	0
$66$	−1.71466e7	−0.111232
$67$	9.58712e7i	0.581235i	0.956839	+	0.290617i	$0.0938606\pi$
$67$	9.58712e7i	0.581235i	−0.956839	+	0.290617i	$0.906139\pi$
$68$	− 6.47531e6i	− 0.0367257i
$69$	1.37419e8	0.729838
$70$	0	0
$71$	−2.16795e8	−1.01248	−0.506241	−	0.862392i	$-0.668965\pi$
$71$	−2.16795e8	−1.01248	−0.506241	+	0.862392i	$0.668965\pi$
$72$	8.63500e6i	0.0378674i
$73$	1.50701e8i	0.621101i	0.950557	+	0.310551i	$0.100513\pi$
$73$	1.50701e8i	0.621101i	−0.950557	+	0.310551i	$0.899487\pi$
$74$	6.68803e7	0.259272
$75$	0	0
$76$	−1.56546e8	−0.538247
$77$	1.93542e7i	0.0627432i
$78$	2.91693e8i	0.892277i
$79$	3.89487e8	1.12505	0.562523	−	0.826781i	$-0.309831\pi$
$79$	3.89487e8	1.12505	0.562523	+	0.826781i	$0.309831\pi$
$80$	0	0
$81$	−3.72903e8	−0.962528
$82$	− 2.29420e8i	− 0.560362i
$83$	7.43467e8i	1.71953i	0.510688	+	0.859766i	$0.329391\pi$
$83$	7.43467e8i	1.71953i	−0.510688	+	0.859766i	$0.670609\pi$
$84$	−9.04463e7	−0.198214
$85$	0	0
$86$	4.86228e8	0.958510
$87$	2.72617e8i	0.510172i
$88$	− 9.77855e7i	− 0.173821i
$89$	−2.64429e8	−0.446739	−0.223369	−	0.974734i	$-0.571706\pi$
$89$	−2.64429e8	−0.446739	−0.223369	+	0.974734i	$0.571706\pi$
$90$	0	0
$91$	3.29248e8	0.503311
$92$	2.72867e8i	0.397106i
$93$	1.16764e9i	1.61859i
$94$	−3.56816e8	−0.471378
$95$	0	0
$96$	7.54835e8	0.907051
$97$	1.39343e9i	1.59813i	0.601248	+	0.799063i	$0.294671\pi$
$97$	1.39343e9i	1.59813i	−0.601248	+	0.799063i	$0.705329\pi$
$98$	− 8.90291e7i	− 0.0975022i
$99$	−5.73790e6	−0.00600337
$100$	0	0
$101$	−6.43863e8	−0.615669	−0.307834	−	0.951440i	$-0.599604\pi$
$101$	−6.43863e8	−0.615669	−0.307834	+	0.951440i	$0.599604\pi$
$102$	− 5.03621e7i	− 0.0460684i
$103$	9.64216e8i	0.844125i	0.906567	+	0.422063i	$0.138694\pi$
$103$	9.64216e8i	0.844125i	−0.906567	+	0.422063i	$0.861306\pi$
$104$	−1.66350e9	−1.39435
$105$	0	0
$106$	−1.04930e8	−0.0807281
$107$	− 1.97477e9i	− 1.45643i	−0.685348	−	0.728215i	$-0.740350\pi$
$107$	− 1.97477e9i	− 1.45643i	0.685348	−	0.728215i	$-0.259650\pi$
$108$	− 7.68278e8i	− 0.543390i
$109$	−1.03957e9	−0.705401	−0.352701	−	0.935736i	$-0.614737\pi$
$109$	−1.03957e9	−0.705401	−0.352701	+	0.935736i	$0.614737\pi$
$110$	0	0
$111$	−5.96482e8	−0.372944
$112$	1.13600e8i	0.0682179i
$113$	− 5.48265e8i	− 0.316328i	−0.987413	−	0.158164i	$-0.949443\pi$
$113$	− 5.48265e8i	− 0.316328i	0.987413	−	0.158164i	$-0.0505574\pi$
$114$	−1.21755e9	−0.675171
$115$	0	0
$116$	−5.41324e8	−0.277585
$117$	9.76115e7i	0.0481576i
$118$	− 1.36694e9i	− 0.649052i
$119$	−5.68462e7	−0.0259860
$120$	0	0
$121$	−2.29297e9	−0.972443
$122$	1.92771e9i	0.787811i
$123$	2.04612e9i	0.806042i
$124$	−2.31854e9	−0.880676
$125$	0	0
$126$	2.63943e7	0.00932916
$127$	− 5.40565e9i	− 1.84387i	−0.387341	−	0.921936i	$-0.626606\pi$
$127$	− 5.40565e9i	− 1.84387i	0.387341	−	0.921936i	$-0.373394\pi$
$128$	1.12473e9i	0.370342i
$129$	−4.33650e9	−1.37875
$130$	0	0
$131$	−1.81287e9	−0.537832	−0.268916	−	0.963164i	$-0.586665\pi$
$131$	−1.81287e9	−0.537832	−0.268916	+	0.963164i	$0.586665\pi$
$132$	3.03656e8i	0.0870560i
$133$	1.37431e9i	0.380847i
$134$	−1.48059e9	−0.396702
$135$	0	0
$136$	2.87211e8	0.0719906
$137$	− 7.50191e8i	− 0.181940i	−0.995854	−	0.0909702i	$-0.971003\pi$
$137$	− 7.50191e8i	− 0.181940i	0.995854	−	0.0909702i	$-0.0289968\pi$
$138$	2.12224e9i	0.498126i
$139$	−6.59090e9	−1.49754	−0.748769	−	0.662831i	$-0.769355\pi$
$139$	−6.59090e9	−1.49754	−0.748769	+	0.662831i	$0.769355\pi$
$140$	0	0
$141$	3.18232e9	0.678044
$142$	− 3.34809e9i	− 0.691035i
$143$	− 1.10538e9i	− 0.221055i
$144$	−3.36789e7	−0.00652719
$145$	0	0
$146$	−2.32736e9	−0.423911
$147$	7.94020e8i	0.140250i
$148$	− 1.18441e9i	− 0.202920i
$149$	3.29437e9	0.547564	0.273782	−	0.961792i	$-0.411725\pi$
$149$	3.29437e9	0.547564	0.273782	+	0.961792i	$0.411725\pi$
$150$	0	0
$151$	−1.04401e10	−1.63421	−0.817103	−	0.576492i	$-0.804421\pi$
$151$	−1.04401e10	−1.63421	−0.817103	+	0.576492i	$0.804421\pi$
$152$	− 6.94357e9i	− 1.05508i
$153$	− 1.68531e7i	− 0.00248638i
$154$	−2.98898e8	−0.0428232
$155$	0	0
$156$	5.16570e9	0.698342
$157$	− 4.88247e9i	− 0.641344i	−0.947190	−	0.320672i	$-0.896091\pi$
$157$	− 4.88247e9i	− 0.641344i	0.947190	−	0.320672i	$-0.103909\pi$
$158$	6.01506e9i	0.767862i
$159$	9.35838e8	0.116122
$160$	0	0
$161$	2.39548e9	0.280980
$162$	− 5.75895e9i	− 0.656940i
$163$	1.00685e10i	1.11717i	0.829448	+	0.558584i	$0.188655\pi$
$163$	1.00685e10i	1.11717i	−0.829448	+	0.558584i	$0.811345\pi$
$164$	−4.06289e9	−0.438568
$165$	0	0
$166$	−1.14818e10	−1.17361
$167$	1.11826e10i	1.11255i	0.831000	+	0.556273i	$0.187769\pi$
$167$	1.11826e10i	1.11255i	−0.831000	+	0.556273i	$0.812231\pi$
$168$	− 4.01172e9i	− 0.388543i
$169$	−8.19997e9	−0.773254
$170$	0	0
$171$	−4.07438e8	−0.0364400
$172$	− 8.61080e9i	− 0.750180i
$173$	1.55595e10i	1.32065i	0.750980	+	0.660325i	$0.229582\pi$
$173$	1.55595e10i	1.32065i	−0.750980	+	0.660325i	$0.770418\pi$
$174$	−4.21018e9	−0.348200
$175$	0	0
$176$	3.81391e8	0.0299615
$177$	1.21912e10i	0.933616i
$178$	− 4.08372e9i	− 0.304906i
$179$	1.14811e10	0.835884	0.417942	−	0.908474i	$-0.362752\pi$
$179$	1.14811e10	0.835884	0.417942	+	0.908474i	$0.362752\pi$
$180$	0	0
$181$	1.64859e10	1.14172	0.570860	−	0.821047i	$-0.306610\pi$
$181$	1.64859e10	1.14172	0.570860	+	0.821047i	$0.306610\pi$
$182$	5.08476e9i	0.343518i
$183$	− 1.71926e10i	− 1.13321i
$184$	−1.21030e10	−0.778416
$185$	0	0
$186$	−1.80326e10	−1.10471
$187$	1.90850e8i	0.0114131i
$188$	6.31900e9i	0.368925i
$189$	−6.74465e9	−0.384486
$190$	0	0
$191$	1.75186e10	0.952466	0.476233	−	0.879319i	$-0.342002\pi$
$191$	1.75186e10	0.952466	0.476233	+	0.879319i	$0.342002\pi$
$192$	1.49940e10i	0.796270i
$193$	2.51278e10i	1.30361i	0.758387	+	0.651805i	$0.225988\pi$
$193$	2.51278e10i	1.30361i	−0.758387	+	0.651805i	$0.774012\pi$
$194$	−2.15195e10	−1.09075
$195$	0	0
$196$	−1.57665e9	−0.0763103
$197$	3.28481e10i	1.55386i	0.629587	+	0.776930i	$0.283224\pi$
$197$	3.28481e10i	1.55386i	−0.629587	+	0.776930i	$0.716776\pi$
$198$	− 8.86137e7i	− 0.00409739i
$199$	3.56924e9	0.161338	0.0806691	−	0.996741i	$-0.474294\pi$
$199$	3.56924e9	0.161338	0.0806691	+	0.996741i	$0.474294\pi$
$200$	0	0
$201$	1.32049e10	0.570628
$202$	− 9.94354e9i	− 0.420204i
$203$	4.75224e9i	0.196411i
$204$	−8.91883e8	−0.0360556
$205$	0	0
$206$	−1.48909e10	−0.576129
$207$	7.10183e8i	0.0268846i
$208$	− 6.48810e9i	− 0.240344i
$209$	4.61396e9	0.167269
$210$	0	0
$211$	−8.88255e9	−0.308508	−0.154254	−	0.988031i	$-0.549297\pi$
$211$	−8.88255e9	−0.308508	−0.154254	+	0.988031i	$0.549297\pi$
$212$	1.85825e9i	0.0631820i
$213$	2.98605e10i	0.994006i
$214$	3.04975e10	0.994037
$215$	0	0
$216$	3.40768e10	1.06517
$217$	2.03542e10i	0.623140i
$218$	− 1.60547e10i	− 0.481447i
$219$	2.07569e10	0.609767
$220$	0	0
$221$	3.24668e9	0.0915534
$222$	− 9.21182e9i	− 0.254540i
$223$	− 1.85138e10i	− 0.501330i	−0.968074	−	0.250665i	$-0.919351\pi$
$223$	− 1.85138e10i	− 0.501330i	0.968074	−	0.250665i	$-0.0806493\pi$
$224$	1.31582e10	0.349206
$225$	0	0
$226$	8.46716e9	0.215899
$227$	6.91501e10i	1.72853i	0.503037	+	0.864265i	$0.332216\pi$
$227$	6.91501e10i	1.72853i	−0.503037	+	0.864265i	$0.667784\pi$
$228$	2.15620e10i	0.528424i
$229$	4.14990e10	0.997190	0.498595	−	0.866835i	$-0.333850\pi$
$229$	4.14990e10	0.997190	0.498595	+	0.866835i	$0.333850\pi$
$230$	0	0
$231$	2.66577e9	0.0615982
$232$	− 2.40103e10i	− 0.544129i
$233$	− 1.06684e10i	− 0.237136i	−0.992946	−	0.118568i	$-0.962170\pi$
$233$	− 1.06684e10i	− 0.237136i	0.992946	−	0.118568i	$-0.0378304\pi$
$234$	−1.50747e9	−0.0328683
$235$	0	0
$236$	−2.42076e10	−0.507982
$237$	− 5.36463e10i	− 1.10452i
$238$	− 8.77908e8i	− 0.0177359i
$239$	−6.89311e9	−0.136655	−0.0683274	−	0.997663i	$-0.521766\pi$
$239$	−6.89311e9	−0.136655	−0.0683274	+	0.997663i	$0.521766\pi$
$240$	0	0
$241$	−2.72593e10	−0.520520	−0.260260	−	0.965539i	$-0.583808\pi$
$241$	−2.72593e10	−0.520520	−0.260260	+	0.965539i	$0.583808\pi$
$242$	− 3.54116e10i	− 0.663708i
$243$	− 3.92936e9i	− 0.0722925i
$244$	3.41386e10	0.616582
$245$	0	0
$246$	−3.15993e10	−0.550136
$247$	− 7.84913e10i	− 1.34179i
$248$	− 1.02838e11i	− 1.72632i
$249$	1.02402e11	1.68815
$250$	0	0
$251$	1.11185e11	1.76812	0.884062	−	0.467370i	$-0.154798\pi$
$251$	1.11185e11	1.76812	0.884062	+	0.467370i	$0.154798\pi$
$252$	− 4.67427e8i	− 0.00730149i
$253$	− 8.04235e9i	− 0.123407i
$254$	8.34825e10	1.25847
$255$	0	0
$256$	−7.31062e10	−1.06384
$257$	− 3.84555e10i	− 0.549869i	−0.961463	−	0.274935i	$-0.911344\pi$
$257$	− 3.84555e10i	− 0.549869i	0.961463	−	0.274935i	$-0.0886562\pi$
$258$	− 6.69710e10i	− 0.941018i
$259$	−1.03978e10	−0.143580
$260$	0	0
$261$	−1.40889e9	−0.0187929
$262$	− 2.79972e10i	− 0.367079i
$263$	− 1.50225e11i	− 1.93616i	−0.250634	−	0.968082i	$-0.580639\pi$
$263$	− 1.50225e11i	− 1.93616i	0.250634	−	0.968082i	$-0.419361\pi$
$264$	−1.34686e10	−0.170649
$265$	0	0
$266$	−2.12242e10	−0.259934
$267$	3.64213e10i	0.438587i
$268$	2.62204e10i	0.310479i
$269$	−9.22583e10	−1.07429	−0.537143	−	0.843491i	$-0.680497\pi$
$269$	−9.22583e10	−1.07429	−0.537143	+	0.843491i	$0.680497\pi$
$270$	0	0
$271$	−1.10392e11	−1.24330	−0.621649	−	0.783296i	$-0.713537\pi$
$271$	−1.10392e11	−1.24330	−0.621649	+	0.783296i	$0.713537\pi$
$272$	1.12020e9i	0.0124090i
$273$	− 4.53492e10i	− 0.494126i
$274$	1.15856e10	0.124177
$275$	0	0
$276$	3.75836e10	0.389859
$277$	1.06151e11i	1.08334i	0.840590	+	0.541672i	$0.182208\pi$
$277$	1.06151e11i	1.08334i	−0.840590	+	0.541672i	$0.817792\pi$
$278$	− 1.01787e11i	− 1.02209i
$279$	−6.03438e9	−0.0596230
$280$	0	0
$281$	1.69943e11	1.62602	0.813008	−	0.582252i	$-0.197828\pi$
$281$	1.69943e11	1.62602	0.813008	+	0.582252i	$0.197828\pi$
$282$	4.91464e10i	0.462776i
$283$	6.63477e10i	0.614875i	0.951568	+	0.307438i	$0.0994716\pi$
$283$	6.63477e10i	0.614875i	−0.951568	+	0.307438i	$0.900528\pi$
$284$	−5.92927e10	−0.540840
$285$	0	0
$286$	1.70711e10	0.150874
$287$	3.56677e10i	0.310318i
$288$	3.90100e9i	0.0334125i
$289$	1.18027e11	0.995273
$290$	0	0
$291$	1.91925e11	1.56896
$292$	4.12161e10i	0.331775i
$293$	− 7.54377e9i	− 0.0597976i	−0.999553	−	0.0298988i	$-0.990481\pi$
$293$	− 7.54377e9i	− 0.0597976i	0.999553	−	0.0298988i	$-0.00951850\pi$
$294$	−1.22625e10	−0.0957230
$295$	0	0
$296$	5.25342e10	0.397768
$297$	2.26438e10i	0.168867i
$298$	5.08769e10i	0.373721i
$299$	−1.36814e11	−0.989943
$300$	0	0
$301$	−7.55935e10	−0.530805
$302$	− 1.61232e11i	− 1.11537i
$303$	8.86830e10i	0.604434i
$304$	2.70818e10	0.181864
$305$	0	0
$306$	2.60272e8	0.00169700
$307$	− 9.90848e10i	− 0.636626i	−0.947986	−	0.318313i	$-0.896884\pi$
$307$	− 9.90848e10i	− 0.636626i	0.947986	−	0.318313i	$-0.103116\pi$
$308$	5.29330e9i	0.0335157i
$309$	1.32807e11	0.828721
$310$	0	0
$311$	−2.78000e10	−0.168509	−0.0842545	−	0.996444i	$-0.526851\pi$
$311$	−2.78000e10	−0.168509	−0.0842545	+	0.996444i	$0.526851\pi$
$312$	2.29123e11i	1.36891i
$313$	− 7.09223e10i	− 0.417670i	−0.977951	−	0.208835i	$-0.933033\pi$
$313$	− 7.09223e10i	− 0.417670i	0.977951	−	0.208835i	$-0.0669672\pi$
$314$	7.54027e10	0.437727
$315$	0	0
$316$	1.06523e11	0.600969
$317$	− 3.11422e11i	− 1.73214i	−0.499926	−	0.866068i	$-0.666640\pi$
$317$	− 3.11422e11i	− 1.73214i	0.499926	−	0.866068i	$-0.333360\pi$
$318$	1.44527e10i	0.0792550i
$319$	1.59547e10	0.0862643
$320$	0	0
$321$	−2.71997e11	−1.42985
$322$	3.69947e10i	0.191773i
$323$	1.35519e10i	0.0692770i
$324$	−1.01988e11	−0.514156
$325$	0	0
$326$	−1.55493e11	−0.762485
$327$	1.43187e11i	0.692529i
$328$	− 1.80208e11i	− 0.859692i
$329$	5.54739e10	0.261040
$330$	0	0
$331$	2.94782e11	1.34982	0.674908	−	0.737902i	$-0.264183\pi$
$331$	2.94782e11	1.34982	0.674908	+	0.737902i	$0.264183\pi$
$332$	2.03336e11i	0.918527i
$333$	− 3.08263e9i	− 0.0137379i
$334$	−1.72699e11	−0.759330
$335$	0	0
$336$	1.56468e10	0.0669730
$337$	− 2.02609e11i	− 0.855705i	−0.903849	−	0.427852i	$-0.859270\pi$
$337$	− 2.02609e11i	− 0.855705i	0.903849	−	0.427852i	$-0.140730\pi$
$338$	− 1.26637e11i	− 0.527758i
$339$	−7.55158e10	−0.310555
$340$	0	0
$341$	6.83353e10	0.273685
$342$	− 6.29229e9i	− 0.0248709i
$343$	1.38413e10i	0.0539949i
$344$	3.81930e11	1.47052
$345$	0	0
$346$	−2.40294e11	−0.901365
$347$	− 1.52000e11i	− 0.562810i	−0.959589	−	0.281405i	$-0.909200\pi$
$347$	− 1.52000e11i	− 0.562810i	0.959589	−	0.281405i	$-0.0908004\pi$
$348$	7.45598e10i	0.272520i
$349$	2.82049e11	1.01768	0.508840	−	0.860861i	$-0.330075\pi$
$349$	2.82049e11	1.01768	0.508840	+	0.860861i	$0.330075\pi$
$350$	0	0
$351$	3.85210e11	1.35461
$352$	− 4.41762e10i	− 0.153372i
$353$	4.32937e11i	1.48402i	0.670391	+	0.742008i	$0.266126\pi$
$353$	4.32937e11i	1.48402i	−0.670391	+	0.742008i	$0.733874\pi$
$354$	−1.88276e11	−0.637207
$355$	0	0
$356$	−7.23203e10	−0.238636
$357$	7.82976e9i	0.0255118i
$358$	1.77310e11i	0.570504i
$359$	−1.35500e10	−0.0430542	−0.0215271	−	0.999768i	$-0.506853\pi$
$359$	−1.35500e10	−0.0430542	−0.0215271	+	0.999768i	$0.506853\pi$
$360$	0	0
$361$	4.94112e9	0.0153124
$362$	2.54601e11i	0.779242i
$363$	3.15824e11i	0.954697i
$364$	9.00480e10	0.268855
$365$	0	0
$366$	2.65515e11	0.773435
$367$	− 1.26149e11i	− 0.362984i	−0.983392	−	0.181492i	$-0.941907\pi$
$367$	− 1.26149e11i	− 0.362984i	0.983392	−	0.181492i	$-0.0580927\pi$
$368$	− 4.72049e10i	− 0.134175i
$369$	−1.05744e10	−0.0296917
$370$	0	0
$371$	1.63135e10	0.0447057
$372$	3.19346e11i	0.864605i
$373$	2.45212e11i	0.655923i	0.944691	+	0.327961i	$0.106362\pi$
$373$	2.45212e11i	0.655923i	−0.944691	+	0.327961i	$0.893638\pi$
$374$	−2.94741e9	−0.00778964
$375$	0	0
$376$	−2.80278e11	−0.723175
$377$	− 2.71417e11i	− 0.691991i
$378$	− 1.04161e11i	− 0.262418i
$379$	−3.62591e11	−0.902694	−0.451347	−	0.892348i	$-0.649056\pi$
$379$	−3.62591e11	−0.902694	−0.451347	+	0.892348i	$0.649056\pi$
$380$	0	0
$381$	−7.44552e11	−1.81022
$382$	2.70550e11i	0.650073i
$383$	− 7.23039e10i	− 0.171699i	−0.996308	−	0.0858494i	$-0.972640\pi$
$383$	− 7.23039e10i	− 0.171699i	0.996308	−	0.0858494i	$-0.0273604\pi$
$384$	1.54916e11	0.363584
$385$	0	0
$386$	−3.88064e11	−0.889734
$387$	− 2.24111e10i	− 0.0507882i
$388$	3.81097e11i	0.853674i
$389$	−3.00609e11	−0.665624	−0.332812	−	0.942993i	$-0.607998\pi$
$389$	−3.00609e11	−0.665624	−0.332812	+	0.942993i	$0.607998\pi$
$390$	0	0
$391$	2.36216e10	0.0511110
$392$	− 6.99320e10i	− 0.149585i
$393$	2.49698e11i	0.528017i
$394$	−5.07291e11	−1.06053
$395$	0	0
$396$	−1.56930e9	−0.00320683
$397$	− 2.86335e11i	− 0.578518i	−0.957251	−	0.289259i	$-0.906591\pi$
$397$	− 2.86335e11i	− 0.578518i	0.957251	−	0.289259i	$-0.0934089\pi$
$398$	5.51219e10i	0.110116i
$399$	1.89291e11	0.373897
$400$	0	0
$401$	8.19964e11	1.58360	0.791800	−	0.610781i	$-0.209144\pi$
$401$	8.19964e11	1.58360	0.791800	+	0.610781i	$0.209144\pi$
$402$	2.03931e11i	0.389462i
$403$	− 1.16250e12i	− 2.19543i
$404$	−1.76094e11	−0.328873
$405$	0	0
$406$	−7.33915e10	−0.134054
$407$	3.49087e10i	0.0630607i
$408$	− 3.95593e10i	− 0.0706769i
$409$	−9.67528e11	−1.70966	−0.854828	−	0.518911i	$-0.826337\pi$
$409$	−9.67528e11	−1.70966	−0.854828	+	0.518911i	$0.826337\pi$
$410$	0	0
$411$	−1.03328e11	−0.178620
$412$	2.63710e11i	0.450908i
$413$	2.12517e11i	0.359433i
$414$	−1.09678e10	−0.0183492
$415$	0	0
$416$	−7.51511e11	−1.23031
$417$	9.07803e11i	1.47021i
$418$	7.12560e10i	0.114164i
$419$	8.51357e10	0.134942	0.0674712	−	0.997721i	$-0.478507\pi$
$419$	8.51357e10	0.134942	0.0674712	+	0.997721i	$0.478507\pi$
$420$	0	0
$421$	5.61043e10	0.0870415	0.0435207	−	0.999053i	$-0.486143\pi$
$421$	5.61043e10	0.0870415	0.0435207	+	0.999053i	$0.486143\pi$
$422$	− 1.37178e11i	− 0.210562i
$423$	1.64463e10i	0.0249767i
$424$	−8.24224e10	−0.123851
$425$	0	0
$426$	−4.61153e11	−0.678425
$427$	− 2.99700e11i	− 0.436275i
$428$	− 5.40093e11i	− 0.777985i
$429$	−1.52251e11	−0.217022
$430$	0	0
$431$	−1.36440e11	−0.190456	−0.0952278	−	0.995456i	$-0.530358\pi$
$431$	−1.36440e11	−0.190456	−0.0952278	+	0.995456i	$0.530358\pi$
$432$	1.32909e11i	0.183602i
$433$	− 3.25710e11i	− 0.445282i	−0.974900	−	0.222641i	$-0.928532\pi$
$433$	− 3.25710e11i	− 0.445282i	0.974900	−	0.222641i	$-0.0714678\pi$
$434$	−3.14342e11	−0.425303
$435$	0	0
$436$	−2.84320e11	−0.376806
$437$	− 5.71072e11i	− 0.749074i
$438$	3.20560e11i	0.416175i
$439$	−1.44336e11	−0.185474	−0.0927372	−	0.995691i	$-0.529562\pi$
$439$	−1.44336e11	−0.185474	−0.0927372	+	0.995691i	$0.529562\pi$
$440$	0	0
$441$	−4.10350e9	−0.00516632
$442$	5.01404e10i	0.0624867i
$443$	9.59823e11i	1.18406i	0.805915	+	0.592031i	$0.201674\pi$
$443$	9.59823e11i	1.18406i	−0.805915	+	0.592031i	$0.798326\pi$
$444$	−1.63136e11	−0.199217
$445$	0	0
$446$	2.85919e11	0.342166
$447$	− 4.53754e11i	− 0.537572i
$448$	2.61373e11i	0.306556i
$449$	1.02004e12	1.18443	0.592215	−	0.805780i	$-0.298253\pi$
$449$	1.02004e12	1.18443	0.592215	+	0.805780i	$0.298253\pi$
$450$	0	0
$451$	1.19747e11	0.136292
$452$	− 1.49948e11i	− 0.168974i
$453$	1.43797e12i	1.60438i
$454$	−1.06792e12	−1.17975
$455$	0	0
$456$	−9.56379e11	−1.03583
$457$	− 6.45199e11i	− 0.691944i	−0.938245	−	0.345972i	$-0.887549\pi$
$457$	− 6.45199e11i	− 0.691944i	0.938245	−	0.345972i	$-0.112451\pi$
$458$	6.40892e11i	0.680598i
$459$	−6.65084e10	−0.0699390
$460$	0	0
$461$	1.04575e12	1.07838	0.539192	−	0.842183i	$-0.318730\pi$
$461$	1.04575e12	1.07838	0.539192	+	0.842183i	$0.318730\pi$
$462$	4.11690e10i	0.0420418i
$463$	− 6.01465e11i	− 0.608269i	−0.952629	−	0.304134i	$-0.901633\pi$
$463$	− 6.01465e11i	− 0.608269i	0.952629	−	0.304134i	$-0.0983672\pi$
$464$	9.36469e10	0.0937913
$465$	0	0
$466$	1.64758e11	0.161849
$467$	9.53000e11i	0.927186i	0.886048	+	0.463593i	$0.153440\pi$
$467$	9.53000e11i	0.927186i	−0.886048	+	0.463593i	$0.846560\pi$
$468$	2.66964e10i	0.0257244i
$469$	2.30187e11	0.219686
$470$	0	0
$471$	−6.72491e11	−0.629640
$472$	− 1.07372e12i	− 0.995757i
$473$	2.53790e11i	0.233131i
$474$	8.28490e11	0.753850
$475$	0	0
$476$	−1.55472e10	−0.0138810
$477$	4.83642e9i	0.00427751i
$478$	− 1.06454e11i	− 0.0932690i
$479$	−1.99157e12	−1.72857	−0.864283	−	0.503005i	$-0.832228\pi$
$479$	−1.99157e12	−1.72857	−0.864283	+	0.503005i	$0.832228\pi$
$480$	0	0
$481$	5.93856e11	0.505857
$482$	− 4.20981e11i	− 0.355263i
$483$	− 3.29943e11i	− 0.275853i
$484$	−6.27119e11	−0.519452
$485$	0	0
$486$	6.06833e10	0.0493408
$487$	− 2.40847e12i	− 1.94027i	−0.242570	−	0.970134i	$-0.577990\pi$
$487$	− 2.40847e12i	− 1.94027i	0.242570	−	0.970134i	$-0.422010\pi$
$488$	1.51421e12i	1.20864i
$489$	1.38679e12	1.09678
$490$	0	0
$491$	2.85374e11	0.221589	0.110794	−	0.993843i	$-0.464661\pi$
$491$	2.85374e11	0.221589	0.110794	+	0.993843i	$0.464661\pi$
$492$	5.59605e11i	0.430565i
$493$	4.68614e10i	0.0357276i
$494$	1.21219e12	0.915794
$495$	0	0
$496$	4.01097e11	0.297565
$497$	5.20526e11i	0.382682i
$498$	1.58145e12i	1.15219i
$499$	−2.11594e12	−1.52775	−0.763873	−	0.645367i	$-0.776704\pi$
$499$	−2.11594e12	−1.52775	−0.763873	+	0.645367i	$0.776704\pi$
$500$	0	0
$501$	1.54024e12	1.09224
$502$	1.71709e12i	1.20677i
$503$	− 7.41865e11i	− 0.516736i	−0.966047	−	0.258368i	$-0.916815\pi$
$503$	− 7.41865e11i	− 0.516736i	0.966047	−	0.258368i	$-0.0831847\pi$
$504$	2.07326e10	0.0143125
$505$	0	0
$506$	1.24203e11	0.0842274
$507$	1.12943e12i	0.759143i
$508$	− 1.47842e12i	− 0.984946i
$509$	−1.62377e12	−1.07225	−0.536124	−	0.844140i	$-0.680112\pi$
$509$	−1.62377e12	−1.07225	−0.536124	+	0.844140i	$0.680112\pi$
$510$	0	0
$511$	3.61832e11	0.234754
$512$	− 5.53160e11i	− 0.355742i
$513$	1.60790e12i	1.02501i
$514$	5.93890e11	0.375294
$515$	0	0
$516$	−1.18602e12	−0.736490
$517$	− 1.86243e11i	− 0.114649i
$518$	− 1.60580e11i	− 0.0979955i
$519$	2.14310e12	1.29655
$520$	0	0
$521$	1.48817e12	0.884877	0.442439	−	0.896799i	$-0.354113\pi$
$521$	1.48817e12	0.884877	0.442439	+	0.896799i	$0.354113\pi$
$522$	− 2.17583e10i	− 0.0128265i
$523$	− 2.41360e12i	− 1.41061i	−0.708903	−	0.705306i	$-0.750810\pi$
$523$	− 2.41360e12i	− 1.41061i	0.708903	−	0.705306i	$-0.249190\pi$
$524$	−4.95814e11	−0.287295
$525$	0	0
$526$	2.32001e12	1.32146
$527$	2.00711e11i	0.113351i
$528$	− 5.25312e10i	− 0.0294147i
$529$	8.05747e11	0.447351
$530$	0	0
$531$	−6.30044e10	−0.0343911
$532$	3.75867e11i	0.203438i
$533$	− 2.03711e12i	− 1.09331i
$534$	−5.62475e11	−0.299342
$535$	0	0
$536$	−1.16300e12	−0.608609
$537$	− 1.58136e12i	− 0.820630i
$538$	− 1.42480e12i	− 0.733218i
$539$	4.64694e10	0.0237147
$540$	0	0
$541$	−2.14334e12	−1.07573	−0.537864	−	0.843032i	$-0.680769\pi$
$541$	−2.14334e12	−1.07573	−0.537864	+	0.843032i	$0.680769\pi$
$542$	− 1.70484e12i	− 0.848570i
$543$	− 2.27070e12i	− 1.12089i
$544$	1.29752e11	0.0635213
$545$	0	0
$546$	7.00354e11	0.337249
$547$	1.02462e12i	0.489349i	0.969605	+	0.244675i	$0.0786811\pi$
$547$	1.02462e12i	0.489349i	−0.969605	+	0.244675i	$0.921319\pi$
$548$	− 2.05174e11i	− 0.0971875i
$549$	8.88514e10	0.0417435
$550$	0	0
$551$	1.13291e12	0.523618
$552$	1.66701e12i	0.764211i
$553$	− 9.35157e11i	− 0.425228i
$554$	−1.63935e12	−0.739399
$555$	0	0
$556$	−1.80259e12	−0.799944
$557$	− 3.18977e12i	− 1.40414i	−0.712108	−	0.702070i	$-0.752259\pi$
$557$	− 3.18977e12i	− 1.40414i	0.712108	−	0.702070i	$-0.247741\pi$
$558$	− 9.31924e10i	− 0.0406936i
$559$	4.31740e12	1.87012
$560$	0	0
$561$	2.62869e10	0.0112049
$562$	2.62453e12i	1.10978i
$563$	− 1.08826e12i	− 0.456503i	−0.973602	−	0.228252i	$-0.926699\pi$
$563$	− 1.08826e12i	− 0.456503i	0.973602	−	0.228252i	$-0.0733009\pi$
$564$	8.70353e11	0.362192
$565$	0	0
$566$	−1.02465e12	−0.419662
$567$	8.95340e11i	0.363801i
$568$	− 2.62992e12i	− 1.06017i
$569$	3.28834e12	1.31514	0.657569	−	0.753394i	$-0.271585\pi$
$569$	3.28834e12	1.31514	0.657569	+	0.753394i	$0.271585\pi$
$570$	0	0
$571$	−1.88806e12	−0.743283	−0.371641	−	0.928376i	$-0.621205\pi$
$571$	−1.88806e12	−0.743283	−0.371641	+	0.928376i	$0.621205\pi$
$572$	− 3.02319e11i	− 0.118082i
$573$	− 2.41294e12i	− 0.935084i
$574$	−5.50837e11	−0.211797
$575$	0	0
$576$	−7.74889e10	−0.0293318
$577$	1.12881e12i	0.423963i	0.977274	+	0.211982i	$0.0679917\pi$
$577$	1.12881e12i	0.423963i	−0.977274	+	0.211982i	$0.932008\pi$
$578$	1.82276e12i	0.679289i
$579$	3.46101e12	1.27982
$580$	0	0
$581$	1.78506e12	0.649922
$582$	2.96400e12i	1.07084i
$583$	− 5.47692e10i	− 0.0196349i
$584$	−1.82813e12	−0.650353
$585$	0	0
$586$	1.16503e11	0.0408128
$587$	6.31776e11i	0.219630i	0.993952	+	0.109815i	$0.0350258\pi$
$587$	6.31776e11i	0.219630i	−0.993952	+	0.109815i	$0.964974\pi$
$588$	2.17162e11i	0.0749178i
$589$	4.85237e12	1.66125
$590$	0	0
$591$	4.52436e12	1.52550
$592$	2.04898e11i	0.0685630i
$593$	4.97504e12i	1.65215i	0.563557	+	0.826077i	$0.309432\pi$
$593$	4.97504e12i	1.65215i	−0.563557	+	0.826077i	$0.690568\pi$
$594$	−3.49702e11	−0.115255
$595$	0	0
$596$	9.00999e11	0.292493
$597$	− 4.91613e11i	− 0.158394i
$598$	− 2.11290e12i	− 0.675652i
$599$	4.55686e12	1.44626	0.723128	−	0.690714i	$-0.242704\pi$
$599$	4.55686e12	1.44626	0.723128	+	0.690714i	$0.242704\pi$
$600$	0	0
$601$	−5.78188e12	−1.80773	−0.903866	−	0.427815i	$-0.859283\pi$
$601$	−5.78188e12	−1.80773	−0.903866	+	0.427815i	$0.859283\pi$
$602$	− 1.16743e12i	− 0.362283i
$603$	6.82431e10i	0.0210199i
$604$	−2.85532e12	−0.872948
$605$	0	0
$606$	−1.36958e12	−0.412536
$607$	− 7.37332e11i	− 0.220452i	−0.993907	−	0.110226i	$-0.964843\pi$
$607$	− 7.37332e11i	− 0.220452i	0.993907	−	0.110226i	$-0.0351575\pi$
$608$	− 3.13687e12i	− 0.930958i
$609$	6.54554e11	0.192827
$610$	0	0
$611$	−3.16831e12	−0.919691
$612$	− 4.60926e9i	− 0.00132816i
$613$	3.50587e12i	1.00282i	0.865210	+	0.501410i	$0.167185\pi$
$613$	3.50587e12i	1.00282i	−0.865210	+	0.501410i	$0.832815\pi$
$614$	1.53022e12	0.434507
$615$	0	0
$616$	−2.34783e11	−0.0656982
$617$	2.47222e12i	0.686759i	0.939197	+	0.343380i	$0.111572\pi$
$617$	2.47222e12i	0.686759i	−0.939197	+	0.343380i	$0.888428\pi$
$618$	2.05102e12i	0.565615i
$619$	1.57589e12	0.431436	0.215718	−	0.976456i	$-0.430791\pi$
$619$	1.57589e12	0.431436	0.215718	+	0.976456i	$0.430791\pi$
$620$	0	0
$621$	2.80264e12	0.756232
$622$	− 4.29331e11i	− 0.115010i
$623$	6.34894e11i	0.168851i
$624$	−8.93645e11	−0.235958
$625$	0	0
$626$	1.09529e12	0.285066
$627$	− 6.35508e11i	− 0.164217i
$628$	− 1.33534e12i	− 0.342588i
$629$	−1.02532e11	−0.0261175
$630$	0	0
$631$	4.95895e11	0.124525	0.0622627	−	0.998060i	$-0.480168\pi$
$631$	4.95895e11	0.124525	0.0622627	+	0.998060i	$0.480168\pi$
$632$	4.72481e12i	1.17803i
$633$	1.22345e12i	0.302878i
$634$	4.80946e12	1.18221
$635$	0	0
$636$	2.55948e11	0.0620291
$637$	− 7.90524e11i	− 0.190234i
$638$	2.46398e11i	0.0588767i
$639$	−1.54319e11	−0.0366156
$640$	0	0
$641$	1.72054e12	0.402535	0.201268	−	0.979536i	$-0.435494\pi$
$641$	1.72054e12	0.402535	0.201268	+	0.979536i	$0.435494\pi$
$642$	− 4.20060e12i	− 0.975897i
$643$	− 8.19457e12i	− 1.89050i	−0.326346	−	0.945250i	$-0.605818\pi$
$643$	− 8.19457e12i	− 1.89050i	0.326346	−	0.945250i	$-0.394182\pi$
$644$	6.55154e11	0.150092
$645$	0	0
$646$	−2.09290e11	−0.0472826
$647$	− 2.56336e12i	− 0.575097i	−0.957766	−	0.287549i	$-0.907160\pi$
$647$	− 2.56336e12i	− 0.575097i	0.957766	−	0.287549i	$-0.0928403\pi$
$648$	− 4.52364e12i	− 1.00786i
$649$	7.13483e11	0.157864
$650$	0	0
$651$	2.80351e12	0.611769
$652$	2.75368e12i	0.596760i
$653$	2.23256e12i	0.480499i	0.970711	+	0.240250i	$0.0772293\pi$
$653$	2.23256e12i	0.480499i	−0.970711	+	0.240250i	$0.922771\pi$
$654$	−2.21131e12	−0.472662
$655$	0	0
$656$	7.02863e11	0.148185
$657$	1.07272e11i	0.0224616i
$658$	8.56715e11i	0.178164i
$659$	−6.47077e12	−1.33651	−0.668254	−	0.743933i	$-0.732958\pi$
$659$	−6.47077e12	−1.33651	−0.668254	+	0.743933i	$0.732958\pi$
$660$	0	0
$661$	−2.35514e12	−0.479856	−0.239928	−	0.970791i	$-0.577124\pi$
$661$	−2.35514e12	−0.479856	−0.239928	+	0.970791i	$0.577124\pi$
$662$	4.55248e12i	0.921270i
$663$	− 4.47185e11i	− 0.0898827i
$664$	−9.01890e12	−1.80052
$665$	0	0
$666$	4.76067e10	0.00937636
$667$	− 1.97472e12i	− 0.386314i
$668$	3.05839e12i	0.594291i
$669$	−2.55002e12	−0.492182
$670$	0	0
$671$	−1.00618e12	−0.191613
$672$	− 1.81236e12i	− 0.342833i
$673$	1.00068e13i	1.88030i	0.340764	+	0.940149i	$0.389314\pi$
$673$	1.00068e13i	1.88030i	−0.340764	+	0.940149i	$0.610686\pi$
$674$	3.12900e12	0.584032
$675$	0	0
$676$	−2.24266e12	−0.413051
$677$	− 4.75925e12i	− 0.870742i	−0.900251	−	0.435371i	$-0.856617\pi$
$677$	− 4.75925e12i	− 0.870742i	0.900251	−	0.435371i	$-0.143383\pi$
$678$	− 1.16623e12i	− 0.211959i
$679$	3.34561e12	0.604035
$680$	0	0
$681$	9.52446e12	1.69699
$682$	1.05534e12i	0.186794i
$683$	− 5.44016e11i	− 0.0956575i	−0.998856	−	0.0478287i	$-0.984770\pi$
$683$	− 5.44016e11i	− 0.0956575i	0.998856	−	0.0478287i	$-0.0152302\pi$
$684$	−1.11433e11	−0.0194653
$685$	0	0
$686$	−2.13759e11	−0.0368524
$687$	− 5.71590e12i	− 0.978992i
$688$	1.48963e12i	0.253473i
$689$	−9.31717e11	−0.157506
$690$	0	0
$691$	8.57339e12	1.43054	0.715272	−	0.698846i	$-0.246303\pi$
$691$	8.57339e12	1.43054	0.715272	+	0.698846i	$0.246303\pi$
$692$	4.25546e12i	0.705455i
$693$	1.37767e10i	0.00226906i
$694$	2.34743e12	0.384127
$695$	0	0
$696$	−3.30708e12	−0.534199
$697$	3.51716e11i	0.0564476i
$698$	4.35585e12i	0.694582i
$699$	−1.46942e12	−0.232809
$700$	0	0
$701$	1.25396e13	1.96133	0.980666	−	0.195687i	$-0.0626935\pi$
$701$	1.25396e13	1.96133	0.980666	+	0.195687i	$0.0626935\pi$
$702$	5.94902e12i	0.924545i
$703$	2.47880e12i	0.382774i
$704$	8.77510e11	0.134640
$705$	0	0
$706$	−6.68609e12	−1.01286
$707$	1.54591e12i	0.232701i
$708$	3.33426e12i	0.498712i
$709$	−4.37869e12	−0.650782	−0.325391	−	0.945580i	$-0.605496\pi$
$709$	−4.37869e12	−0.650782	−0.325391	+	0.945580i	$0.605496\pi$
$710$	0	0
$711$	2.77244e11	0.0406864
$712$	− 3.20775e12i	− 0.467779i
$713$	− 8.45790e12i	− 1.22563i
$714$	−1.20919e11	−0.0174122
$715$	0	0
$716$	3.14004e12	0.446506
$717$	9.49429e11i	0.134161i
$718$	− 2.09261e11i	− 0.0293852i
$719$	−7.76448e12	−1.08351	−0.541754	−	0.840537i	$-0.682240\pi$
$719$	−7.76448e12	−1.08351	−0.541754	+	0.840537i	$0.682240\pi$
$720$	0	0
$721$	2.31508e12	0.319049
$722$	7.63086e10i	0.0104510i
$723$	3.75458e12i	0.511022i
$724$	4.50884e12	0.609875
$725$	0	0
$726$	−4.87745e12	−0.651596
$727$	7.08318e11i	0.0940423i	0.998894	+	0.0470211i	$0.0149728\pi$
$727$	7.08318e11i	0.0940423i	−0.998894	+	0.0470211i	$0.985027\pi$
$728$	3.99406e12i	0.527015i
$729$	−7.88106e12	−1.03350
$730$	0	0
$731$	−7.45421e11	−0.0965547
$732$	− 4.70211e12i	− 0.605331i
$733$	− 6.81304e12i	− 0.871712i	−0.900017	−	0.435856i	$-0.856446\pi$
$733$	− 6.81304e12i	− 0.871712i	0.900017	−	0.435856i	$-0.143554\pi$
$734$	1.94820e12	0.247743
$735$	0	0
$736$	−5.46771e12	−0.686839
$737$	− 7.72807e11i	− 0.0964866i
$738$	− 1.63306e11i	− 0.0202651i
$739$	−9.20369e12	−1.13517	−0.567586	−	0.823314i	$-0.692123\pi$
$739$	−9.20369e12	−1.13517	−0.567586	+	0.823314i	$0.692123\pi$
$740$	0	0
$741$	−1.08111e13	−1.31731
$742$	2.51938e11i	0.0305124i
$743$	8.72196e12i	1.04994i	0.851121	+	0.524970i	$0.175923\pi$
$743$	8.72196e12i	1.04994i	−0.851121	+	0.524970i	$0.824077\pi$
$744$	−1.41645e13	−1.69482
$745$	0	0
$746$	−3.78695e12	−0.447678
$747$	5.29215e11i	0.0621856i
$748$	5.21968e10i	0.00609658i
$749$	−4.74143e12	−0.550479
$750$	0	0
$751$	−1.63201e13	−1.87216	−0.936078	−	0.351793i	$-0.885572\pi$
$751$	−1.63201e13	−1.87216	−0.936078	+	0.351793i	$0.885572\pi$
$752$	− 1.09316e12i	− 0.124653i
$753$	− 1.53141e13i	− 1.73586i
$754$	4.19164e12	0.472295
$755$	0	0
$756$	−1.84464e12	−0.205382
$757$	− 3.23287e12i	− 0.357813i	−0.983866	−	0.178907i	$-0.942744\pi$
$757$	− 3.23287e12i	− 0.357813i	0.983866	−	0.178907i	$-0.0572560\pi$
$758$	− 5.59970e12i	− 0.616103i
$759$	−1.10772e12	−0.121155
$760$	0	0
$761$	−6.46766e11	−0.0699063	−0.0349531	−	0.999389i	$-0.511128\pi$
$761$	−6.46766e11	−0.0699063	−0.0349531	+	0.999389i	$0.511128\pi$
$762$	− 1.14985e13i	− 1.23551i
$763$	2.49602e12i	0.266617i
$764$	4.79127e12	0.508781
$765$	0	0
$766$	1.11663e12	0.117187
$767$	− 1.21376e13i	− 1.26634i
$768$	1.00694e13i	1.04442i
$769$	2.42101e12	0.249648	0.124824	−	0.992179i	$-0.460163\pi$
$769$	2.42101e12	0.249648	0.124824	+	0.992179i	$0.460163\pi$
$770$	0	0
$771$	−5.29670e12	−0.539835
$772$	6.87237e12i	0.696352i
$773$	4.43910e12i	0.447185i	0.974683	+	0.223592i	$0.0717784\pi$
$773$	4.43910e12i	0.447185i	−0.974683	+	0.223592i	$0.928222\pi$
$774$	3.46107e11	0.0346638
$775$	0	0
$776$	−1.69035e13	−1.67339
$777$	1.43215e12i	0.140960i
$778$	− 4.64248e12i	− 0.454299i
$779$	8.50304e12	0.827286
$780$	0	0
$781$	1.74756e12	0.168075
$782$	3.64802e11i	0.0348840i
$783$	5.55998e12i	0.528622i
$784$	2.72754e11	0.0257839
$785$	0	0
$786$	−3.85622e12	−0.360380
$787$	− 1.72989e13i	− 1.60744i	−0.595011	−	0.803718i	$-0.702852\pi$
$787$	− 1.72989e13i	− 1.60744i	0.595011	−	0.803718i	$-0.297148\pi$
$788$	8.98382e12i	0.830029i
$789$	−2.06914e13	−1.90083
$790$	0	0
$791$	−1.31638e12	−0.119561
$792$	− 6.96057e10i	− 0.00628611i
$793$	1.71169e13i	1.53708i
$794$	4.42203e12	0.394848
$795$	0	0
$796$	9.76175e11	0.0861825
$797$	− 1.37776e13i	− 1.20951i	−0.796410	−	0.604756i	$-0.793270\pi$
$797$	− 1.37776e13i	− 1.20951i	0.796410	−	0.604756i	$-0.206730\pi$
$798$	2.92333e12i	0.255191i
$799$	5.47024e11	0.0474838
$800$	0	0
$801$	−1.88226e11	−0.0161560
$802$	1.26632e13i	1.08083i
$803$	− 1.21478e12i	− 0.103105i
$804$	3.61149e12	0.304814
$805$	0	0
$806$	1.79531e13	1.49842
$807$	1.27073e13i	1.05468i
$808$	− 7.81061e12i	− 0.644665i
$809$	−1.38369e13	−1.13572	−0.567860	−	0.823125i	$-0.692228\pi$
$809$	−1.38369e13	−1.13572	−0.567860	+	0.823125i	$0.692228\pi$
$810$	0	0
$811$	−1.96078e13	−1.59161	−0.795804	−	0.605555i	$-0.792951\pi$
$811$	−1.96078e13	−1.59161	−0.795804	+	0.605555i	$0.792951\pi$
$812$	1.29972e12i	0.104917i
$813$	1.52049e13i	1.22061i
$814$	−5.39114e11	−0.0430399
$815$	0	0
$816$	1.54292e11	0.0121825
$817$	1.80212e13i	1.41509i
$818$	− 1.49421e13i	− 1.16687i
$819$	2.34365e11	0.0182019
$820$	0	0
$821$	2.41017e13	1.85142	0.925708	−	0.378239i	$-0.123470\pi$
$821$	2.41017e13	1.85142	0.925708	+	0.378239i	$0.123470\pi$
$822$	− 1.59576e12i	− 0.121911i
$823$	− 8.20762e12i	− 0.623617i	−0.950145	−	0.311809i	$-0.899065\pi$
$823$	− 8.20762e12i	− 0.623617i	0.950145	−	0.311809i	$-0.100935\pi$
$824$	−1.16968e13	−0.883881
$825$	0	0
$826$	−3.28201e12	−0.245318
$827$	2.84612e12i	0.211582i	0.994388	+	0.105791i	$0.0337374\pi$
$827$	2.84612e12i	0.211582i	−0.994388	+	0.105791i	$0.966263\pi$
$828$	1.94233e11i	0.0143610i
$829$	5.88562e12	0.432809	0.216405	−	0.976304i	$-0.430567\pi$
$829$	5.88562e12	0.432809	0.216405	+	0.976304i	$0.430567\pi$
$830$	0	0
$831$	1.46208e13	1.06357
$832$	− 1.49279e13i	− 1.08005i
$833$	1.36488e11i	0.00982180i
$834$	−1.40197e13	−1.00344
$835$	0	0
$836$	1.26190e12	0.0893505
$837$	2.38138e13i	1.67712i
$838$	1.31480e12i	0.0921003i
$839$	8.44799e12	0.588606	0.294303	−	0.955712i	$-0.404913\pi$
$839$	8.44799e12	0.588606	0.294303	+	0.955712i	$0.404913\pi$
$840$	0	0
$841$	−1.05896e13	−0.729959
$842$	8.66450e11i	0.0594072i
$843$	− 2.34073e13i	− 1.59634i
$844$	−2.42934e12	−0.164796
$845$	0	0
$846$	−2.53989e11	−0.0170470
$847$	5.50542e12i	0.367549i
$848$	− 3.21470e11i	− 0.0213481i
$849$	9.13847e12	0.603655
$850$	0	0
$851$	4.32066e12	0.282402
$852$	8.16674e12i	0.530970i
$853$	7.17311e12i	0.463913i	0.972726	+	0.231957i	$0.0745128\pi$
$853$	7.17311e12i	0.463913i	−0.972726	+	0.231957i	$0.925487\pi$
$854$	4.62843e12	0.297765
$855$	0	0
$856$	2.39557e13	1.52502
$857$	2.17636e13i	1.37821i	0.724660	+	0.689107i	$0.241997\pi$
$857$	2.17636e13i	1.37821i	−0.724660	+	0.689107i	$0.758003\pi$
$858$	− 2.35130e12i	− 0.148121i
$859$	9.02945e12	0.565838	0.282919	−	0.959144i	$-0.408697\pi$
$859$	9.02945e12	0.565838	0.282919	+	0.959144i	$0.408697\pi$
$860$	0	0
$861$	4.91273e12	0.304655
$862$	− 2.10712e12i	− 0.129989i
$863$	1.84428e13i	1.13182i	0.824467	+	0.565910i	$0.191475\pi$
$863$	1.84428e13i	1.13182i	−0.824467	+	0.565910i	$0.808525\pi$
$864$	1.53947e13	0.939854
$865$	0	0
$866$	5.03012e12	0.303912
$867$	− 1.62566e13i	− 0.977111i
$868$	5.56680e12i	0.332864i
$869$	−3.13961e12	−0.186761
$870$	0	0
$871$	−1.31468e13	−0.773993
$872$	− 1.26109e13i	− 0.738623i
$873$	9.91868e11i	0.0577950i
$874$	8.81940e12	0.511255
$875$	0	0
$876$	5.67693e12	0.325721
$877$	− 1.12140e13i	− 0.640120i	−0.947397	−	0.320060i	$-0.896297\pi$
$877$	− 1.12140e13i	− 0.640120i	0.947397	−	0.320060i	$-0.103703\pi$
$878$	− 2.22906e12i	− 0.126589i
$879$	−1.03905e12	−0.0587064
$880$	0	0
$881$	3.00664e13	1.68147	0.840735	−	0.541446i	$-0.182123\pi$
$881$	3.00664e13	1.68147	0.840735	+	0.541446i	$0.182123\pi$
$882$	− 6.33727e10i	− 0.00352609i
$883$	1.58968e13i	0.880007i	0.897996	+	0.440004i	$0.145023\pi$
$883$	1.58968e13i	0.880007i	−0.897996	+	0.440004i	$0.854977\pi$
$884$	8.87956e11	0.0489053
$885$	0	0
$886$	−1.48231e13	−0.808141
$887$	1.46131e13i	0.792658i	0.918109	+	0.396329i	$0.129716\pi$
$887$	1.46131e13i	0.792658i	−0.918109	+	0.396329i	$0.870284\pi$
$888$	− 7.23585e12i	− 0.390509i
$889$	−1.29790e13	−0.696918
$890$	0	0
$891$	3.00593e12	0.159782
$892$	− 5.06346e12i	− 0.267797i
$893$	− 1.32248e13i	− 0.695915i
$894$	7.00758e12	0.366901
$895$	0	0
$896$	2.70047e12	0.139976
$897$	1.88442e13i	0.971878i
$898$	1.57531e13i	0.808393i
$899$	1.67791e13	0.856742
$900$	0	0
$901$	1.60866e11	0.00813208
$902$	1.84933e12i	0.0930217i
$903$	1.04119e13i	0.521118i
$904$	6.65093e12	0.331226
$905$	0	0
$906$	−2.22074e13	−1.09502
$907$	1.41504e12i	0.0694281i	0.999397	+	0.0347141i	$0.0110521\pi$
$907$	1.41504e12i	0.0694281i	−0.999397	+	0.0347141i	$0.988948\pi$
$908$	1.89123e13i	0.923333i
$909$	−4.58315e11	−0.0222652
$910$	0	0
$911$	−1.61901e13	−0.778784	−0.389392	−	0.921072i	$-0.627315\pi$
$911$	−1.61901e13	−0.778784	−0.389392	+	0.921072i	$0.627315\pi$
$912$	− 3.73014e12i	− 0.178545i
$913$	− 5.99301e12i	− 0.285447i
$914$	9.96417e12	0.472262
$915$	0	0
$916$	1.13498e13	0.532671
$917$	4.35271e12i	0.203281i
$918$	− 1.02713e12i	− 0.0477345i
$919$	1.60413e13	0.741858	0.370929	−	0.928661i	$-0.379039\pi$
$919$	1.60413e13	0.741858	0.370929	+	0.928661i	$0.379039\pi$
$920$	0	0
$921$	−1.36475e13	−0.625008
$922$	1.61501e13i	0.736014i
$923$	− 2.97290e13i	− 1.34826i
$924$	7.29077e11	0.0329041
$925$	0	0
$926$	9.28876e12	0.415153
$927$	6.86349e11i	0.0305271i
$928$	− 1.08470e13i	− 0.480115i
$929$	3.98759e13	1.75647	0.878233	−	0.478233i	$-0.158723\pi$
$929$	3.98759e13	1.75647	0.878233	+	0.478233i	$0.158723\pi$
$930$	0	0
$931$	3.29971e12	0.143947
$932$	− 2.91777e12i	− 0.126672i
$933$	3.82906e12i	0.165434i
$934$	−1.47177e13	−0.632819
$935$	0	0
$936$	−1.18411e12	−0.0504256
$937$	− 5.95427e12i	− 0.252348i	−0.992008	−	0.126174i	$-0.959730\pi$
$937$	− 5.95427e12i	− 0.252348i	0.992008	−	0.126174i	$-0.0402698\pi$
$938$	3.55490e12i	0.149939i
$939$	−9.76855e12	−0.410048
$940$	0	0
$941$	9.86055e12	0.409966	0.204983	−	0.978766i	$-0.434286\pi$
$941$	9.86055e12	0.409966	0.204983	+	0.978766i	$0.434286\pi$
$942$	− 1.03857e13i	− 0.429739i
$943$	− 1.48212e13i	− 0.610353i
$944$	4.18782e12	0.171638
$945$	0	0
$946$	−3.91943e12	−0.159115
$947$	− 2.10061e13i	− 0.848732i	−0.905491	−	0.424366i	$-0.860497\pi$
$947$	− 2.10061e13i	− 0.848732i	0.905491	−	0.424366i	$-0.139503\pi$
$948$	− 1.46721e13i	− 0.590002i
$949$	−2.06655e13	−0.827080
$950$	0	0
$951$	−4.28939e13	−1.70053
$952$	− 6.89594e11i	− 0.0272099i
$953$	4.25218e13i	1.66991i	0.550318	+	0.834955i	$0.314506\pi$
$953$	4.25218e13i	1.66991i	−0.550318	+	0.834955i	$0.685494\pi$
$954$	−7.46916e10	−0.00291947
$955$	0	0
$956$	−1.88524e12	−0.0729972
$957$	− 2.19754e12i	− 0.0846901i
$958$	− 3.07570e13i	− 1.17977i
$959$	−1.80121e12	−0.0687670
$960$	0	0
$961$	4.54266e13	1.71813
$962$	9.17125e12i	0.345256i
$963$	− 1.40568e12i	− 0.0526707i
$964$	−7.45531e12	−0.278048
$965$	0	0
$966$	5.09550e12	0.188274
$967$	− 1.21906e13i	− 0.448338i	−0.974550	−	0.224169i	$-0.928033\pi$
$967$	− 1.21906e13i	− 0.448338i	0.974550	−	0.224169i	$-0.0719667\pi$
$968$	− 2.78157e13i	− 1.01824i
$969$	1.86658e12	0.0680128
$970$	0	0
$971$	5.38639e12	0.194452	0.0972258	−	0.995262i	$-0.469003\pi$
$971$	5.38639e12	0.194452	0.0972258	+	0.995262i	$0.469003\pi$
$972$	− 1.07466e12i	− 0.0386167i
$973$	1.58247e13i	0.566016i
$974$	3.71954e13	1.32426
$975$	0	0
$976$	−5.90583e12	−0.208332
$977$	− 1.89284e13i	− 0.664643i	−0.943166	−	0.332321i	$-0.892168\pi$
$977$	− 1.89284e13i	− 0.664643i	0.943166	−	0.332321i	$-0.107832\pi$
$978$	2.14169e13i	0.748570i
$979$	2.13153e12	0.0741600
$980$	0	0
$981$	−7.39990e11	−0.0255103
$982$	4.40719e12i	0.151238i
$983$	− 3.98513e13i	− 1.36129i	−0.732612	−	0.680647i	$-0.761699\pi$
$983$	− 3.98513e13i	− 1.36129i	0.732612	−	0.680647i	$-0.238301\pi$
$984$	−2.48212e13	−0.844004
$985$	0	0
$986$	−7.23708e11	−0.0243847
$987$	− 7.64075e12i	− 0.256277i
$988$	− 2.14671e13i	− 0.716748i
$989$	3.14118e13	1.04402
$990$	0	0
$991$	−3.44424e13	−1.13439	−0.567194	−	0.823584i	$-0.691971\pi$
$991$	−3.44424e13	−1.13439	−0.567194	+	0.823584i	$0.691971\pi$
$992$	− 4.64588e13i	− 1.52323i
$993$	− 4.06020e13i	− 1.32518i
$994$	−8.03877e12	−0.261187
$995$	0	0
$996$	2.80066e13	0.901765
$997$	4.12406e13i	1.32189i	0.750433	+	0.660947i	$0.229845\pi$
$997$	4.12406e13i	1.32189i	−0.750433	+	0.660947i	$0.770155\pi$
$998$	− 3.26777e13i	− 1.04271i
$999$	−1.21652e13	−0.386432

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.10.b.e.99.5		8
5.2	odd	4		175.10.a.e.1.2		4
5.3	odd	4		35.10.a.c.1.3	✓	4
5.4	even	2	inner	175.10.b.e.99.4		8
15.8	even	4		315.10.a.g.1.2		4
35.13	even	4		245.10.a.e.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.10.a.c.1.3	✓	4	5.3	odd	4
175.10.a.e.1.2		4	5.2	odd	4
175.10.b.e.99.4		8	5.4	even	2	inner
175.10.b.e.99.5		8	1.1	even	1	trivial
245.10.a.e.1.3		4	35.13	even	4
315.10.a.g.1.2		4	15.8	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+15.4436i q^{2} -137.736i q^{3} +273.496 q^{4} +2127.13 q^{6} -2401.00i q^{7} +12130.9i q^{8} +711.820 q^{9} -8060.89 q^{11} -37670.3i q^{12} +137129. i q^{13} +37080.0 q^{14} -47313.7 q^{16} -23676.1i q^{17} +10993.0i q^{18} -572389. q^{19} -330704. q^{21} -124489. i q^{22} +997700. i q^{23} +1.67086e6 q^{24} -2.11777e6 q^{26} -2.80910e6i q^{27} -656664. i q^{28} -1.97927e6 q^{29} -8.47740e6 q^{31} +5.48031e6i q^{32} +1.11027e6i q^{33} +365643. q^{34} +194680. q^{36} -4.33062e6i q^{37} -8.83972e6i q^{38} +1.88876e7 q^{39} -1.48554e7 q^{41} -5.10725e6i q^{42} -3.14842e7i q^{43} -2.20462e6 q^{44} -1.54081e7 q^{46} +2.31045e7i q^{47} +6.51680e6i q^{48} -5.76480e6 q^{49} -3.26104e6 q^{51} +3.75044e7i q^{52} +6.79444e6i q^{53} +4.33825e7 q^{54} +2.91262e7 q^{56} +7.88385e7i q^{57} -3.05671e7i q^{58} -8.85117e7 q^{59} +1.24823e8 q^{61} -1.30921e8i q^{62} -1.70908e6i q^{63} -1.08860e8 q^{64} -1.71466e7 q^{66} +9.58712e7i q^{67} -6.47531e6i q^{68} +1.37419e8 q^{69} -2.16795e8 q^{71} +8.63500e6i q^{72} +1.50701e8i q^{73} +6.68803e7 q^{74} -1.56546e8 q^{76} +1.93542e7i q^{77} +2.91693e8i q^{78} +3.89487e8 q^{79} -3.72903e8 q^{81} -2.29420e8i q^{82} +7.43467e8i q^{83} -9.04463e7 q^{84} +4.86228e8 q^{86} +2.72617e8i q^{87} -9.77855e7i q^{88} -2.64429e8 q^{89} +3.29248e8 q^{91} +2.72867e8i q^{92} +1.16764e9i q^{93} -3.56816e8 q^{94} +7.54835e8 q^{96} +1.39343e9i q^{97} -8.90291e7i q^{98} -5.73790e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 3458 q^{4} - 288 q^{6} - 10764 q^{9} + 164876 q^{11} - 91238 q^{14} + 128514 q^{16} - 601464 q^{19} + 86436 q^{21} + 15272640 q^{24} + 2611332 q^{26} + 2744044 q^{29} - 9181776 q^{31} + 14398956 q^{34}+ \cdots - 2444739048 q^{99}+O(q^{100}) \) 8 * q - 3458 * q^4 - 288 * q^6 - 10764 * q^9 + 164876 * q^11 - 91238 * q^14 + 128514 * q^16 - 601464 * q^19 + 86436 * q^21 + 15272640 * q^24 + 2611332 * q^26 + 2744044 * q^29 - 9181776 * q^31 + 14398956 * q^34 - 18288486 * q^36 + 93332484 * q^39 + 114574168 * q^41 - 175278696 * q^44 + 57784832 * q^46 - 46118408 * q^49 + 172685268 * q^51 - 375179040 * q^54 + 146436990 * q^56 - 145139360 * q^59 - 451362072 * q^61 - 282886786 * q^64 - 239347296 * q^66 - 696601224 * q^69 - 940937968 * q^71 - 1855619004 * q^74 - 1784530688 * q^76 + 1197611292 * q^79 - 1694311992 * q^81 + 198457056 * q^84 + 1413582312 * q^86 + 2760306024 * q^89 + 350363524 * q^91 - 4933488304 * q^94 - 1598643648 * q^96 - 2444739048 * q^99

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