LMFDB - Embedded newform 50.26.b.b.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,26,Mod(49,50)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(50, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 26, names="a")

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

chi := DirichletCharacter("50.49");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 26 $
Character orbit:	$[\chi]$	$=$	50.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:	$197.998389976$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 10)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			49.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	50.49
Dual form			50.26.b.b.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-4096.00i q^{2} +162864. i q^{3} -1.67772e7 q^{4} +6.67091e8 q^{6} +1.76009e10i q^{7} +6.87195e10i q^{8} +8.20764e11 q^{9} -1.12404e13 q^{11} -2.73240e12i q^{12} +4.24221e12i q^{13} +7.20933e13 q^{14} +2.81475e14 q^{16} +1.13786e15i q^{17} -3.36185e15i q^{18} -2.98985e15 q^{19} -2.86655e15 q^{21} +4.60406e16i q^{22} -1.22305e17i q^{23} -1.11919e16 q^{24} +1.73761e16 q^{26} +2.71666e17i q^{27} -2.95294e17i q^{28} +2.12048e18 q^{29} +4.22586e18 q^{31} -1.15292e18i q^{32} -1.83065e18i q^{33} +4.66066e18 q^{34} -1.37701e19 q^{36} -2.41679e19i q^{37} +1.22464e19i q^{38} -6.90903e17 q^{39} -1.61564e20 q^{41} +1.17414e19i q^{42} -3.11612e20i q^{43} +1.88582e20 q^{44} -5.00963e20 q^{46} +1.22586e21i q^{47} +4.58421e19i q^{48} +1.03128e21 q^{49} -1.85316e20 q^{51} -7.11725e19i q^{52} -4.78915e20i q^{53} +1.11274e21 q^{54} -1.20952e21 q^{56} -4.86938e20i q^{57} -8.68547e21i q^{58} -1.21434e22 q^{59} -2.03328e22 q^{61} -1.73091e22i q^{62} +1.44462e22i q^{63} -4.72237e21 q^{64} -7.49835e21 q^{66} -6.15653e22i q^{67} -1.90901e22i q^{68} +1.99192e22 q^{69} +1.34077e23 q^{71} +5.64025e22i q^{72} +2.23779e23i q^{73} -9.89916e22 q^{74} +5.01613e22 q^{76} -1.97841e23i q^{77} +2.82994e21i q^{78} -3.82350e23 q^{79} +6.51179e23 q^{81} +6.61767e23i q^{82} -7.71818e23i q^{83} +4.80928e22 q^{84} -1.27636e24 q^{86} +3.45349e23i q^{87} -7.72433e23i q^{88} +8.40581e23 q^{89} -7.46667e22 q^{91} +2.05195e24i q^{92} +6.88241e23i q^{93} +5.02111e24 q^{94} +1.87769e23 q^{96} +6.19164e24i q^{97} -4.22411e24i q^{98} -9.22569e24 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 33554432 q^{4} + 1334181888 q^{6} + 1641527853894 q^{9} - 22480747671096 q^{11} + 144186519486464 q^{14} + 562949953421312 q^{16} - 59\!\cdots\!40 q^{19} - 57\!\cdots\!76 q^{21} - 22\!\cdots\!08 q^{24}+ \cdots - 18\!\cdots\!12 q^{99}+O(q^{100}) $ 2 * q - 33554432 * q^4 + 1334181888 * q^6 + 1641527853894 * q^9 - 22480747671096 * q^11 + 144186519486464 * q^14 + 562949953421312 * q^16 - 5979690773455240 * q^19 - 5733103835362176 * q^21 - 22383857718263808 * q^24 + 34752175596617728 * q^26 + 4240951159366415940 * q^29 + 8451726183377942704 * q^31 + 9321315931684061184 * q^34 - 27540267374796079104 * q^36 - 1381806232023327552 * q^39 - 323128641530597510796 * q^41 + 377164359519474548736 * q^44 - 1001926290180659576832 * q^46 + 2062554335894473893486 * q^49 - 370631542455515854656 * q^51 + 2225485482283998904320 * q^54 - 2419048381712615604224 * q^56 - 24286769256796795881720 * q^59 - 40665614069527393964996 * q^61 - 9444732965739290427392 * q^64 - 14996703185737232154624 * q^66 + 39838311358394272783488 * q^69 + 268153252990894462797504 * q^71 - 197983247997076156235776 * q^74 + 100322563719465627811840 * q^76 - 764699498524138082047360 * q^79 + 1302358724859014860662162 * q^81 + 96185521396299664982016 * q^84 - 2552727779050936041930752 * q^86 + 1681161365246136806433420 * q^89 - 149333335276208541495856 * q^91 + 10042222992826541561708544 * q^94 + 375538815852579051798528 * q^96 - 18451386739233377727423912 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$.

$n$	$27$
$\chi(n)$	$-1$

Coefficient data

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

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

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

$2$	− 4096.00i	− 0.707107i
$2$	− 4096.00i	− 0.707107i
$3$	162864.i	0.176933i	0.996079	+	0.0884666i	$0.0281967\pi$
$3$	162864.i	0.176933i	−0.996079	+	0.0884666i	$0.971803\pi$
$4$	−1.67772e7	−0.500000
$5$	0	0
$5$	0	0
$6$	6.67091e8	0.125111
$7$	1.76009e10i	0.480628i	0.970695	+	0.240314i	$0.0772504\pi$
$7$	1.76009e10i	0.480628i	−0.970695	+	0.240314i	$0.922750\pi$
$8$	6.87195e10i	0.353553i
$9$	8.20764e11	0.968695
$10$	0	0
$11$	−1.12404e13	−1.07987	−0.539936	−	0.841706i	$-0.681552\pi$
$11$	−1.12404e13	−1.07987	−0.539936	+	0.841706i	$0.681552\pi$
$12$	− 2.73240e12i	− 0.0884666i
$13$	4.24221e12i	0.0505010i	0.999681	+	0.0252505i	$0.00803834\pi$
$13$	4.24221e12i	0.0505010i	−0.999681	+	0.0252505i	$0.991962\pi$
$14$	7.20933e13	0.339855
$15$	0	0
$16$	2.81475e14	0.250000
$17$	1.13786e15i	0.473670i	0.971550	+	0.236835i	$0.0761101\pi$
$17$	1.13786e15i	0.473670i	−0.971550	+	0.236835i	$0.923890\pi$
$18$	− 3.36185e15i	− 0.684971i
$19$	−2.98985e15	−0.309905	−0.154953	−	0.987922i	$-0.549522\pi$
$19$	−2.98985e15	−0.309905	−0.154953	+	0.987922i	$0.549522\pi$
$20$	0	0
$21$	−2.86655e15	−0.0850391
$22$	4.60406e16i	0.763585i
$23$	− 1.22305e17i	− 1.16372i	−0.813290	−	0.581859i	$-0.802325\pi$
$23$	− 1.22305e17i	− 1.16372i	0.813290	−	0.581859i	$-0.197675\pi$
$24$	−1.11919e16	−0.0625553
$25$	0	0
$26$	1.73761e16	0.0357096
$27$	2.71666e17i	0.348328i
$28$	− 2.95294e17i	− 0.240314i
$29$	2.12048e18	1.11291	0.556453	−	0.830879i	$-0.312162\pi$
$29$	2.12048e18	1.11291	0.556453	+	0.830879i	$0.312162\pi$
$30$	0	0
$31$	4.22586e18	0.963594	0.481797	−	0.876283i	$-0.339984\pi$
$31$	4.22586e18	0.963594	0.481797	+	0.876283i	$0.339984\pi$
$32$	− 1.15292e18i	− 0.176777i
$33$	− 1.83065e18i	− 0.191065i
$34$	4.66066e18	0.334935
$35$	0	0
$36$	−1.37701e19	−0.484347
$37$	− 2.41679e19i	− 0.603555i	−0.953378	−	0.301778i	$-0.902420\pi$
$37$	− 2.41679e19i	− 0.603555i	0.953378	−	0.301778i	$-0.0975800\pi$
$38$	1.22464e19i	0.219136i
$39$	−6.90903e17	−0.00893531
$40$	0	0
$41$	−1.61564e20	−1.11827	−0.559136	−	0.829076i	$-0.688867\pi$
$41$	−1.61564e20	−1.11827	−0.559136	+	0.829076i	$0.688867\pi$
$42$	1.17414e19i	0.0601317i
$43$	− 3.11612e20i	− 1.18921i	−0.804018	−	0.594605i	$-0.797308\pi$
$43$	− 3.11612e20i	− 1.18921i	0.804018	−	0.594605i	$-0.202692\pi$
$44$	1.88582e20	0.539936
$45$	0	0
$46$	−5.00963e20	−0.822873
$47$	1.22586e21i	1.53892i	0.638694	+	0.769461i	$0.279475\pi$
$47$	1.22586e21i	1.53892i	−0.638694	+	0.769461i	$0.720525\pi$
$48$	4.58421e19i	0.0442333i
$49$	1.03128e21	0.768997
$50$	0	0
$51$	−1.85316e20	−0.0838079
$52$	− 7.11725e19i	− 0.0252505i
$53$	− 4.78915e20i	− 0.133909i	−0.997756	−	0.0669546i	$-0.978672\pi$
$53$	− 4.78915e20i	− 0.133909i	0.997756	−	0.0669546i	$-0.0213283\pi$
$54$	1.11274e21	0.246305
$55$	0	0
$56$	−1.20952e21	−0.169928
$57$	− 4.86938e20i	− 0.0548325i
$58$	− 8.68547e21i	− 0.786943i
$59$	−1.21434e22	−0.888566	−0.444283	−	0.895887i	$-0.646541\pi$
$59$	−1.21434e22	−0.888566	−0.444283	+	0.895887i	$0.646541\pi$
$60$	0	0
$61$	−2.03328e22	−0.980786	−0.490393	−	0.871501i	$-0.663147\pi$
$61$	−2.03328e22	−0.980786	−0.490393	+	0.871501i	$0.663147\pi$
$62$	− 1.73091e22i	− 0.681364i
$63$	1.44462e22i	0.465582i
$64$	−4.72237e21	−0.125000
$65$	0	0
$66$	−7.49835e21	−0.135104
$67$	− 6.15653e22i	− 0.919180i	−0.888131	−	0.459590i	$-0.847996\pi$
$67$	− 6.15653e22i	− 0.919180i	0.888131	−	0.459590i	$-0.152004\pi$
$68$	− 1.90901e22i	− 0.236835i
$69$	1.99192e22	0.205900
$70$	0	0
$71$	1.34077e23	0.969669	0.484835	−	0.874606i	$-0.338880\pi$
$71$	1.34077e23	0.969669	0.484835	+	0.874606i	$0.338880\pi$
$72$	5.64025e22i	0.342485i
$73$	2.23779e23i	1.14362i	0.820385	+	0.571811i	$0.193759\pi$
$73$	2.23779e23i	1.14362i	−0.820385	+	0.571811i	$0.806241\pi$
$74$	−9.89916e22	−0.426778
$75$	0	0
$76$	5.01613e22	0.154953
$77$	− 1.97841e23i	− 0.519017i
$78$	2.82994e21i	0.00631822i
$79$	−3.82350e23	−0.727985	−0.363992	−	0.931402i	$-0.618587\pi$
$79$	−3.82350e23	−0.727985	−0.363992	+	0.931402i	$0.618587\pi$
$80$	0	0
$81$	6.51179e23	0.907064
$82$	6.61767e23i	0.790737i
$83$	− 7.71818e23i	− 0.792572i	−0.918127	−	0.396286i	$-0.870299\pi$
$83$	− 7.71818e23i	− 0.792572i	0.918127	−	0.396286i	$-0.129701\pi$
$84$	4.80928e22	0.0425195
$85$	0	0
$86$	−1.27636e24	−0.840899
$87$	3.45349e23i	0.196910i
$88$	− 7.72433e23i	− 0.381792i
$89$	8.40581e23	0.360748	0.180374	−	0.983598i	$-0.442269\pi$
$89$	8.40581e23	0.360748	0.180374	+	0.983598i	$0.442269\pi$
$90$	0	0
$91$	−7.46667e22	−0.0242722
$92$	2.05195e24i	0.581859i
$93$	6.88241e23i	0.170492i
$94$	5.02111e24	1.08818
$95$	0	0
$96$	1.87769e23	0.0312777
$97$	6.19164e24i	0.906064i	0.891494	+	0.453032i	$0.149658\pi$
$97$	6.19164e24i	0.906064i	−0.891494	+	0.453032i	$0.850342\pi$
$98$	− 4.22411e24i	− 0.543763i
$99$	−9.22569e24	−1.04607
$100$	0	0
$101$	6.64342e24	0.586644	0.293322	−	0.956014i	$-0.405239\pi$
$101$	6.64342e24	0.586644	0.293322	+	0.956014i	$0.405239\pi$
$102$	7.59053e23i	0.0592612i
$103$	1.36741e25i	0.945004i	0.881330	+	0.472502i	$0.156649\pi$
$103$	1.36741e25i	0.945004i	−0.881330	+	0.472502i	$0.843351\pi$
$104$	−2.91522e23	−0.0178548
$105$	0	0
$106$	−1.96164e24	−0.0946881
$107$	− 1.97392e24i	− 0.0847290i	−0.999102	−	0.0423645i	$-0.986511\pi$
$107$	− 1.97392e24i	− 0.0847290i	0.999102	−	0.0423645i	$-0.0134891\pi$
$108$	− 4.55779e24i	− 0.174164i
$109$	−4.86252e25	−1.65588	−0.827942	−	0.560813i	$-0.810489\pi$
$109$	−4.86252e25	−1.65588	−0.827942	+	0.560813i	$0.810489\pi$
$110$	0	0
$111$	3.93608e24	0.106789
$112$	4.95421e24i	0.120157i
$113$	4.58410e25i	0.994886i	0.867497	+	0.497443i	$0.165728\pi$
$113$	4.58410e25i	0.994886i	−0.867497	+	0.497443i	$0.834272\pi$
$114$	−1.99450e24	−0.0387724
$115$	0	0
$116$	−3.55757e25	−0.556453
$117$	3.48185e24i	0.0489201i
$118$	4.97393e25i	0.628311i
$119$	−2.00273e25	−0.227659
$120$	0	0
$121$	1.79989e25	0.166123
$122$	8.32832e25i	0.693521i
$123$	− 2.63130e25i	− 0.197859i
$124$	−7.08982e25	−0.481797
$125$	0	0
$126$	5.91715e25	0.329216
$127$	1.31721e26i	0.663911i	0.943295	+	0.331955i	$0.107708\pi$
$127$	1.31721e26i	0.663911i	−0.943295	+	0.331955i	$0.892292\pi$
$128$	1.93428e25i	0.0883883i
$129$	5.07504e25	0.210411
$130$	0	0
$131$	−7.36281e25	−0.251856	−0.125928	−	0.992039i	$-0.540191\pi$
$131$	−7.36281e25	−0.251856	−0.125928	+	0.992039i	$0.540191\pi$
$132$	3.07132e25i	0.0955326i
$133$	− 5.26240e25i	− 0.148949i
$134$	−2.52171e26	−0.649959
$135$	0	0
$136$	−7.81929e25	−0.167468
$137$	9.58320e26i	1.87285i	0.350866	+	0.936426i	$0.385887\pi$
$137$	9.58320e26i	1.87285i	−0.350866	+	0.936426i	$0.614113\pi$
$138$	− 8.15889e25i	− 0.145594i
$139$	4.90566e26	0.799858	0.399929	−	0.916546i	$-0.369035\pi$
$139$	4.90566e26	0.799858	0.399929	+	0.916546i	$0.369035\pi$
$140$	0	0
$141$	−1.99648e26	−0.272286
$142$	− 5.49178e26i	− 0.685660i
$143$	− 4.76840e25i	− 0.0545346i
$144$	2.31025e26	0.242174
$145$	0	0
$146$	9.16597e26	0.808664
$147$	1.67958e26i	0.136061i
$148$	4.05470e26i	0.301778i
$149$	−9.09615e26	−0.622342	−0.311171	−	0.950354i	$-0.600721\pi$
$149$	−9.09615e26	−0.622342	−0.311171	+	0.950354i	$0.600721\pi$
$150$	0	0
$151$	8.24560e26	0.477541	0.238770	−	0.971076i	$-0.423256\pi$
$151$	8.24560e26	0.477541	0.238770	+	0.971076i	$0.423256\pi$
$152$	− 2.05461e26i	− 0.109568i
$153$	9.33911e26i	0.458841i
$154$	−8.10355e26	−0.367000
$155$	0	0
$156$	1.15914e25	0.00446765
$157$	− 9.72907e26i	− 0.346199i	−0.984904	−	0.173099i	$-0.944622\pi$
$157$	− 9.72907e26i	− 0.346199i	0.984904	−	0.173099i	$-0.0553782\pi$
$158$	1.56610e27i	0.514763i
$159$	7.79981e25	0.0236930
$160$	0	0
$161$	2.15269e27	0.559316
$162$	− 2.66723e27i	− 0.641391i
$163$	− 2.54973e27i	− 0.567740i	−0.958863	−	0.283870i	$-0.908382\pi$
$163$	− 2.54973e27i	− 0.567740i	0.958863	−	0.283870i	$-0.0916184\pi$
$164$	2.71060e27	0.559136
$165$	0	0
$166$	−3.16137e27	−0.560433
$167$	− 8.09067e27i	− 1.33054i	−0.746602	−	0.665271i	$-0.768316\pi$
$167$	− 8.09067e27i	− 1.33054i	0.746602	−	0.665271i	$-0.231684\pi$
$168$	− 1.96988e26i	− 0.0300659i
$169$	7.03841e27	0.997450
$170$	0	0
$171$	−2.45396e27	−0.300203
$172$	5.22799e27i	0.594605i
$173$	4.51555e27i	0.477677i	0.971059	+	0.238838i	$0.0767667\pi$
$173$	4.51555e27i	0.477677i	−0.971059	+	0.238838i	$0.923233\pi$
$174$	1.41455e27	0.139236
$175$	0	0
$176$	−3.16388e27	−0.269968
$177$	− 1.97772e27i	− 0.157217i
$178$	− 3.44302e27i	− 0.255088i
$179$	1.94694e28	1.34490	0.672450	−	0.740143i	$-0.265242\pi$
$179$	1.94694e28	1.34490	0.672450	+	0.740143i	$0.265242\pi$
$180$	0	0
$181$	−1.21952e28	−0.733176	−0.366588	−	0.930383i	$-0.619474\pi$
$181$	−1.21952e28	−0.733176	−0.366588	+	0.930383i	$0.619474\pi$
$182$	3.05835e26i	0.0171630i
$183$	− 3.31148e27i	− 0.173534i
$184$	8.40477e27	0.411437
$185$	0	0
$186$	2.81903e27	0.120556
$187$	− 1.27899e28i	− 0.511503i
$188$	− 2.05665e28i	− 0.769461i
$189$	−4.78156e27	−0.167416
$190$	0	0
$191$	6.11119e28	1.87590	0.937948	−	0.346775i	$-0.112723\pi$
$191$	6.11119e28	1.87590	0.937948	+	0.346775i	$0.112723\pi$
$192$	− 7.69103e26i	− 0.0221167i
$193$	6.48935e28i	1.74878i	0.485226	+	0.874389i	$0.338737\pi$
$193$	6.48935e28i	1.74878i	−0.485226	+	0.874389i	$0.661263\pi$
$194$	2.53610e28	0.640684
$195$	0	0
$196$	−1.73020e28	−0.384498
$197$	3.17525e28i	0.662140i	0.943606	+	0.331070i	$0.107410\pi$
$197$	3.17525e28i	0.662140i	−0.943606	+	0.331070i	$0.892590\pi$
$198$	3.77884e28i	0.739680i
$199$	7.39236e28	1.35869	0.679344	−	0.733820i	$-0.262265\pi$
$199$	7.39236e28	1.35869	0.679344	+	0.733820i	$0.262265\pi$
$200$	0	0
$201$	1.00268e28	0.162634
$202$	− 2.72115e28i	− 0.414820i
$203$	3.73223e28i	0.534894i
$204$	3.10908e27	0.0419040
$205$	0	0
$206$	5.60091e28	0.668218
$207$	− 1.00384e29i	− 1.12729i
$208$	1.19408e27i	0.0126253i
$209$	3.36070e28	0.334658
$210$	0	0
$211$	1.18016e28	0.104330	0.0521652	−	0.998638i	$-0.483388\pi$
$211$	1.18016e28	0.104330	0.0521652	+	0.998638i	$0.483388\pi$
$212$	8.03487e27i	0.0669546i
$213$	2.18363e28i	0.171567i
$214$	−8.08517e27	−0.0599124
$215$	0	0
$216$	−1.86687e28	−0.123152
$217$	7.43790e28i	0.463131i
$218$	1.99169e29i	1.17089i
$219$	−3.64455e28	−0.202345
$220$	0	0
$221$	−4.82702e27	−0.0239208
$222$	− 1.61222e28i	− 0.0755112i
$223$	1.55992e28i	0.0690704i	0.999403	+	0.0345352i	$0.0109951\pi$
$223$	1.55992e28i	0.0690704i	−0.999403	+	0.0345352i	$0.989005\pi$
$224$	2.02924e28	0.0849639
$225$	0	0
$226$	1.87765e29	0.703491
$227$	3.57748e29i	1.26839i	0.773171	+	0.634197i	$0.218669\pi$
$227$	3.57748e29i	1.26839i	−0.773171	+	0.634197i	$0.781331\pi$
$228$	8.16947e27i	0.0274163i
$229$	6.16468e29	1.95870	0.979348	−	0.202179i	$-0.0648024\pi$
$229$	6.16468e29	1.95870	0.979348	+	0.202179i	$0.0648024\pi$
$230$	0	0
$231$	3.22211e28	0.0918313
$232$	1.45718e29i	0.393472i
$233$	5.68344e29i	1.45433i	0.686464	+	0.727163i	$0.259162\pi$
$233$	5.68344e29i	1.45433i	−0.686464	+	0.727163i	$0.740838\pi$
$234$	1.42617e28	0.0345917
$235$	0	0
$236$	2.03732e29	0.444283
$237$	− 6.22710e28i	− 0.128805i
$238$	8.20317e28i	0.160979i
$239$	5.96388e29	1.11059	0.555296	−	0.831653i	$-0.312605\pi$
$239$	5.96388e29	1.11059	0.555296	+	0.831653i	$0.312605\pi$
$240$	0	0
$241$	−4.97938e29	−0.835530	−0.417765	−	0.908555i	$-0.637187\pi$
$241$	−4.97938e29	−0.835530	−0.417765	+	0.908555i	$0.637187\pi$
$242$	− 7.37237e28i	− 0.117467i
$243$	3.36233e29i	0.508817i
$244$	3.41128e29	0.490393
$245$	0	0
$246$	−1.07778e29	−0.139908
$247$	− 1.26835e28i	− 0.0156505i
$248$	2.90399e29i	0.340682i
$249$	1.25701e29	0.140232
$250$	0	0
$251$	1.75610e30	1.77267	0.886335	−	0.463044i	$-0.153243\pi$
$251$	1.75610e30	1.77267	0.886335	+	0.463044i	$0.153243\pi$
$252$	− 2.42367e29i	− 0.232791i
$253$	1.37476e30i	1.25667i
$254$	5.39531e29	0.469456
$255$	0	0
$256$	7.92282e28	0.0625000
$257$	− 1.22065e30i	− 0.917123i	−0.888663	−	0.458562i	$-0.848365\pi$
$257$	− 1.22065e30i	− 0.917123i	0.888663	−	0.458562i	$-0.151635\pi$
$258$	− 2.07874e29i	− 0.148783i
$259$	4.25376e29	0.290086
$260$	0	0
$261$	1.74041e30	1.07807
$262$	3.01581e29i	0.178089i
$263$	2.27827e30i	1.28280i	0.767207	+	0.641399i	$0.221646\pi$
$263$	2.27827e30i	1.28280i	−0.767207	+	0.641399i	$0.778354\pi$
$264$	1.25801e29	0.0675518
$265$	0	0
$266$	−2.15548e29	−0.105323
$267$	1.36900e29i	0.0638284i
$268$	1.03289e30i	0.459590i
$269$	3.12815e30	1.32857	0.664284	−	0.747480i	$-0.268736\pi$
$269$	3.12815e30	1.32857	0.664284	+	0.747480i	$0.268736\pi$
$270$	0	0
$271$	1.31818e30	0.510339	0.255170	−	0.966896i	$-0.417869\pi$
$271$	1.31818e30	0.510339	0.255170	+	0.966896i	$0.417869\pi$
$272$	3.20278e29i	0.118417i
$273$	− 1.21605e28i	− 0.00429456i
$274$	3.92528e30	1.32431
$275$	0	0
$276$	−3.34188e29	−0.102950
$277$	− 2.11862e30i	− 0.623815i	−0.950112	−	0.311908i	$-0.899032\pi$
$277$	− 2.11862e30i	− 0.623815i	0.950112	−	0.311908i	$-0.100968\pi$
$278$	− 2.00936e30i	− 0.565585i
$279$	3.46844e30	0.933429
$280$	0	0
$281$	−6.37141e30	−1.56822	−0.784109	−	0.620623i	$-0.786880\pi$
$281$	−6.37141e30	−1.56822	−0.784109	+	0.620623i	$0.786880\pi$
$282$	8.17758e29i	0.192536i
$283$	3.00725e30i	0.677391i	0.940896	+	0.338695i	$0.109986\pi$
$283$	3.00725e30i	0.677391i	−0.940896	+	0.338695i	$0.890014\pi$
$284$	−2.24943e30	−0.484835
$285$	0	0
$286$	−1.95314e29	−0.0385618
$287$	− 2.84368e30i	− 0.537473i
$288$	− 9.46276e29i	− 0.171243i
$289$	4.47591e30	0.775637
$290$	0	0
$291$	−1.00840e30	−0.160313
$292$	− 3.75438e30i	− 0.571811i
$293$	− 7.19334e30i	− 1.04975i	−0.851180	−	0.524875i	$-0.824112\pi$
$293$	− 7.19334e30i	− 1.04975i	0.851180	−	0.524875i	$-0.175888\pi$
$294$	6.87956e29	0.0962097
$295$	0	0
$296$	1.66080e30	0.213389
$297$	− 3.05362e30i	− 0.376149i
$298$	3.72578e30i	0.440063i
$299$	5.18845e29	0.0587690
$300$	0	0
$301$	5.48465e30	0.571568
$302$	− 3.37740e30i	− 0.337672i
$303$	1.08197e30i	0.103797i
$304$	−8.41567e29	−0.0774763
$305$	0	0
$306$	3.82530e30	0.324450
$307$	6.08638e30i	0.495597i	0.968812	+	0.247799i	$0.0797072\pi$
$307$	6.08638e30i	0.495597i	−0.968812	+	0.247799i	$0.920293\pi$
$308$	3.31921e30i	0.259508i
$309$	−2.22702e30	−0.167203
$310$	0	0
$311$	3.60168e30	0.249460	0.124730	−	0.992191i	$-0.460194\pi$
$311$	3.60168e30	0.249460	0.124730	+	0.992191i	$0.460194\pi$
$312$	− 4.74785e28i	− 0.00315911i
$313$	3.07166e30i	0.196367i	0.995168	+	0.0981835i	$0.0313032\pi$
$313$	3.07166e30i	0.196367i	−0.995168	+	0.0981835i	$0.968697\pi$
$314$	−3.98503e30	−0.244800
$315$	0	0
$316$	6.41476e30	0.363992
$317$	2.80660e31i	1.53088i	0.643510	+	0.765438i	$0.277478\pi$
$317$	2.80660e31i	1.53088i	−0.643510	+	0.765438i	$0.722522\pi$
$318$	− 3.19480e29i	− 0.0167535i
$319$	−2.38349e31	−1.20180
$320$	0	0
$321$	3.21480e29	0.0149914
$322$	− 8.81740e30i	− 0.395496i
$323$	− 3.40201e30i	− 0.146793i
$324$	−1.09250e31	−0.453532
$325$	0	0
$326$	−1.04437e31	−0.401453
$327$	− 7.91929e30i	− 0.292981i
$328$	− 1.11026e31i	− 0.395369i
$329$	−2.15762e31	−0.739649
$330$	0	0
$331$	−1.79893e31	−0.571694	−0.285847	−	0.958275i	$-0.592275\pi$
$331$	−1.79893e31	−0.571694	−0.285847	+	0.958275i	$0.592275\pi$
$332$	1.29490e31i	0.396286i
$333$	− 1.98361e31i	− 0.584661i
$334$	−3.31394e31	−0.940835
$335$	0	0
$336$	−8.06863e29	−0.0212598
$337$	3.37680e31i	0.857296i	0.903472	+	0.428648i	$0.141010\pi$
$337$	3.37680e31i	0.857296i	−0.903472	+	0.428648i	$0.858990\pi$
$338$	− 2.88293e31i	− 0.705303i
$339$	−7.46585e30	−0.176028
$340$	0	0
$341$	−4.75003e31	−1.04056
$342$	1.00514e31i	0.212276i
$343$	4.17554e31i	0.850230i
$344$	2.14138e31	0.420450
$345$	0	0
$346$	1.84957e31	0.337769
$347$	3.07070e30i	0.0540902i	0.999634	+	0.0270451i	$0.00860977\pi$
$347$	3.07070e30i	0.0540902i	−0.999634	+	0.0270451i	$0.991390\pi$
$348$	− 5.79400e30i	− 0.0984550i
$349$	−4.73553e31	−0.776338	−0.388169	−	0.921588i	$-0.626892\pi$
$349$	−4.73553e31	−0.776338	−0.388169	+	0.921588i	$0.626892\pi$
$350$	0	0
$351$	−1.15246e30	−0.0175909
$352$	1.29593e31i	0.190896i
$353$	− 1.13735e32i	− 1.61700i	−0.588496	−	0.808500i	$-0.700280\pi$
$353$	− 1.13735e32i	− 1.61700i	0.588496	−	0.808500i	$-0.299720\pi$
$354$	−8.10074e30	−0.111169
$355$	0	0
$356$	−1.41026e31	−0.180374
$357$	− 3.26172e30i	− 0.0402805i
$358$	− 7.97467e31i	− 0.950988i
$359$	−7.58317e31	−0.873313	−0.436656	−	0.899628i	$-0.643837\pi$
$359$	−7.58317e31	−0.873313	−0.436656	+	0.899628i	$0.643837\pi$
$360$	0	0
$361$	−8.41373e31	−0.903959
$362$	4.99517e31i	0.518434i
$363$	2.93138e30i	0.0293927i
$364$	1.25270e30	0.0121361
$365$	0	0
$366$	−1.35638e31	−0.122707
$367$	− 6.65888e31i	− 0.582205i	−0.956692	−	0.291102i	$-0.905978\pi$
$367$	− 6.65888e31i	− 0.582205i	0.956692	−	0.291102i	$-0.0940220\pi$
$368$	− 3.44259e31i	− 0.290930i
$369$	−1.32606e32	−1.08326
$370$	0	0
$371$	8.42934e30	0.0643605
$372$	− 1.15468e31i	− 0.0852459i
$373$	4.03892e31i	0.288340i	0.989553	+	0.144170i	$0.0460512\pi$
$373$	4.03892e31i	0.288340i	−0.989553	+	0.144170i	$0.953949\pi$
$374$	−5.23875e31	−0.361687
$375$	0	0
$376$	−8.42403e31	−0.544091
$377$	8.99550e30i	0.0562029i
$378$	1.95853e31i	0.118381i
$379$	−3.00036e32	−1.75462	−0.877309	−	0.479926i	$-0.840664\pi$
$379$	−3.00036e32	−1.75462	−0.877309	+	0.479926i	$0.840664\pi$
$380$	0	0
$381$	−2.14527e31	−0.117468
$382$	− 2.50314e32i	− 1.32646i
$383$	− 5.83515e31i	− 0.299273i	−0.988741	−	0.149636i	$-0.952190\pi$
$383$	− 5.83515e31i	− 0.299273i	0.988741	−	0.149636i	$-0.0478103\pi$
$384$	−3.15025e30	−0.0156388
$385$	0	0
$386$	2.65804e32	1.23657
$387$	− 2.55760e32i	− 1.15198i
$388$	− 1.03879e32i	− 0.453032i
$389$	4.65526e32	1.96595	0.982977	−	0.183726i	$-0.0588161\pi$
$389$	4.65526e32	1.96595	0.982977	+	0.183726i	$0.0588161\pi$
$390$	0	0
$391$	1.39166e32	0.551218
$392$	7.08688e31i	0.271881i
$393$	− 1.19914e31i	− 0.0445617i
$394$	1.30058e32	0.468204
$395$	0	0
$396$	1.54781e32	0.523033
$397$	3.57088e32i	1.16922i	0.811316	+	0.584608i	$0.198752\pi$
$397$	3.57088e32i	1.16922i	−0.811316	+	0.584608i	$0.801248\pi$
$398$	− 3.02791e32i	− 0.960737i
$399$	8.57055e30	0.0263540
$400$	0	0
$401$	−5.85410e32	−1.69105	−0.845523	−	0.533940i	$-0.820711\pi$
$401$	−5.85410e32	−1.69105	−0.845523	+	0.533940i	$0.820711\pi$
$402$	− 4.10696e31i	− 0.114999i
$403$	1.79270e31i	0.0486625i
$404$	−1.11458e32	−0.293322
$405$	0	0
$406$	1.52872e32	0.378227
$407$	2.71656e32i	0.651762i
$408$	− 1.27348e31i	− 0.0296306i
$409$	5.85778e32	1.32188	0.660939	−	0.750439i	$-0.270158\pi$
$409$	5.85778e32	1.32188	0.660939	+	0.750439i	$0.270158\pi$
$410$	0	0
$411$	−1.56076e32	−0.331370
$412$	− 2.29413e32i	− 0.472502i
$413$	− 2.13734e32i	− 0.427070i
$414$	−4.11172e32	−0.797113
$415$	0	0
$416$	4.89093e30	0.00892740
$417$	7.98956e31i	0.141521i
$418$	− 1.37654e32i	− 0.236639i
$419$	2.15945e32	0.360303	0.180152	−	0.983639i	$-0.442341\pi$
$419$	2.15945e32	0.360303	0.180152	+	0.983639i	$0.442341\pi$
$420$	0	0
$421$	−2.57301e32	−0.404497	−0.202249	−	0.979334i	$-0.564825\pi$
$421$	−2.57301e32	−0.404497	−0.202249	+	0.979334i	$0.564825\pi$
$422$	− 4.83394e31i	− 0.0737727i
$423$	1.00614e33i	1.49075i
$424$	3.29108e31	0.0473441
$425$	0	0
$426$	8.94413e31	0.121316
$427$	− 3.57876e32i	− 0.471394i
$428$	3.31169e31i	0.0423645i
$429$	7.76601e30	0.00964899
$430$	0	0
$431$	−4.87420e32	−0.571396	−0.285698	−	0.958320i	$-0.592225\pi$
$431$	−4.87420e32	−0.571396	−0.285698	+	0.958320i	$0.592225\pi$
$432$	7.64671e31i	0.0870819i
$433$	1.34127e33i	1.48394i	0.670433	+	0.741970i	$0.266108\pi$
$433$	1.34127e33i	1.48394i	−0.670433	+	0.741970i	$0.733892\pi$
$434$	3.04656e32	0.327483
$435$	0	0
$436$	8.15795e32	0.827942
$437$	3.65674e32i	0.360642i
$438$	1.49281e32i	0.143079i
$439$	−3.20033e32	−0.298118	−0.149059	−	0.988828i	$-0.547624\pi$
$439$	−3.20033e32	−0.298118	−0.149059	+	0.988828i	$0.547624\pi$
$440$	0	0
$441$	8.46435e32	0.744923
$442$	1.97715e31i	0.0169146i
$443$	1.50899e33i	1.25499i	0.778622	+	0.627494i	$0.215919\pi$
$443$	1.50899e33i	1.25499i	−0.778622	+	0.627494i	$0.784081\pi$
$444$	−6.60364e31	−0.0533945
$445$	0	0
$446$	6.38944e31	0.0488402
$447$	− 1.48144e32i	− 0.110113i
$448$	− 8.31179e31i	− 0.0600785i
$449$	7.32432e32	0.514859	0.257429	−	0.966297i	$-0.417125\pi$
$449$	7.32432e32	0.514859	0.257429	+	0.966297i	$0.417125\pi$
$450$	0	0
$451$	1.81604e33	1.20759
$452$	− 7.69084e32i	− 0.497443i
$453$	1.34291e32i	0.0844928i
$454$	1.46534e33	0.896890
$455$	0	0
$456$	3.34621e31	0.0193862
$457$	1.80848e33i	1.01944i	0.860341	+	0.509718i	$0.170250\pi$
$457$	1.80848e33i	1.01944i	−0.860341	+	0.509718i	$0.829750\pi$
$458$	− 2.52505e33i	− 1.38501i
$459$	−3.09116e32	−0.164992
$460$	0	0
$461$	−2.02348e33	−1.02291	−0.511454	−	0.859311i	$-0.670893\pi$
$461$	−2.02348e33	−1.02291	−0.511454	+	0.859311i	$0.670893\pi$
$462$	− 1.31978e32i	− 0.0649345i
$463$	4.00896e33i	1.91986i	0.280239	+	0.959930i	$0.409586\pi$
$463$	4.00896e33i	1.91986i	−0.280239	+	0.959930i	$0.590414\pi$
$464$	5.96861e32	0.278226
$465$	0	0
$466$	2.32794e33	1.02836
$467$	1.11951e33i	0.481466i	0.970591	+	0.240733i	$0.0773878\pi$
$467$	1.11951e33i	0.481466i	−0.970591	+	0.240733i	$0.922612\pi$
$468$	− 5.84158e31i	− 0.0244600i
$469$	1.08360e33	0.441784
$470$	0	0
$471$	1.58452e32	0.0612541
$472$	− 8.34487e32i	− 0.314155i
$473$	3.50264e33i	1.28420i
$474$	−2.55062e32	−0.0910786
$475$	0	0
$476$	3.36002e32	0.113830
$477$	− 3.93077e32i	− 0.129717i
$478$	− 2.44280e33i	− 0.785308i
$479$	5.66968e33	1.77568	0.887841	−	0.460151i	$-0.152205\pi$
$479$	5.66968e33	1.77568	0.887841	+	0.460151i	$0.152205\pi$
$480$	0	0
$481$	1.02525e32	0.0304802
$482$	2.03955e33i	0.590809i
$483$	3.50595e32i	0.0989616i
$484$	−3.01972e32	−0.0830615
$485$	0	0
$486$	1.37721e33	0.359788
$487$	− 1.76093e33i	− 0.448363i	−0.974547	−	0.224182i	$-0.928029\pi$
$487$	− 1.76093e33i	− 0.448363i	0.974547	−	0.224182i	$-0.0719709\pi$
$488$	− 1.39726e33i	− 0.346760i
$489$	4.15260e32	0.100452
$490$	0	0
$491$	−5.58354e33	−1.28348	−0.641742	−	0.766920i	$-0.721788\pi$
$491$	−5.58354e33	−1.28348	−0.641742	+	0.766920i	$0.721788\pi$
$492$	4.41459e32i	0.0989297i
$493$	2.41280e33i	0.527150i
$494$	−5.19518e31	−0.0110666
$495$	0	0
$496$	1.18947e33	0.240899
$497$	2.35987e33i	0.466050i
$498$	− 5.14873e32i	− 0.0991593i
$499$	4.37368e33	0.821468	0.410734	−	0.911755i	$-0.365273\pi$
$499$	4.37368e33	0.821468	0.410734	+	0.911755i	$0.365273\pi$
$500$	0	0
$501$	1.31768e33	0.235417
$502$	− 7.19299e33i	− 1.25347i
$503$	− 4.32379e33i	− 0.734962i	−0.930031	−	0.367481i	$-0.880220\pi$
$503$	− 4.32379e33i	− 0.734962i	0.930031	−	0.367481i	$-0.119780\pi$
$504$	−9.92734e32	−0.164608
$505$	0	0
$506$	5.63101e33	0.888597
$507$	1.14630e33i	0.176482i
$508$	− 2.20992e33i	− 0.331955i
$509$	−1.81736e33	−0.266360	−0.133180	−	0.991092i	$-0.542519\pi$
$509$	−1.81736e33	−0.266360	−0.133180	+	0.991092i	$0.542519\pi$
$510$	0	0
$511$	−3.93870e33	−0.549657
$512$	− 3.24519e32i	− 0.0441942i
$513$	− 8.12238e32i	− 0.107948i
$514$	−4.99979e33	−0.648504
$515$	0	0
$516$	−8.51451e32	−0.105205
$517$	− 1.37791e34i	− 1.66184i
$518$	− 1.74234e33i	− 0.205121i
$519$	−7.35420e32	−0.0845169
$520$	0	0
$521$	−7.48131e33	−0.819419	−0.409710	−	0.912216i	$-0.634370\pi$
$521$	−7.48131e33	−0.819419	−0.409710	+	0.912216i	$0.634370\pi$
$522$	− 7.12872e33i	− 0.762308i
$523$	1.34405e34i	1.40328i	0.712531	+	0.701641i	$0.247549\pi$
$523$	1.34405e34i	1.40328i	−0.712531	+	0.701641i	$0.752451\pi$
$524$	1.23527e33	0.125928
$525$	0	0
$526$	9.33180e33	0.907076
$527$	4.80842e33i	0.456426i
$528$	− 5.15283e32i	− 0.0477663i
$529$	−3.91286e33	−0.354240
$530$	0	0
$531$	−9.96685e33	−0.860749
$532$	8.82883e32i	0.0744746i
$533$	− 6.85390e32i	− 0.0564739i
$534$	5.60744e32	0.0451335
$535$	0	0
$536$	4.23073e33	0.324979
$537$	3.17087e33i	0.237958i
$538$	− 1.28129e34i	− 0.939440i
$539$	−1.15919e34	−0.830418
$540$	0	0
$541$	−9.16620e33	−0.626937	−0.313468	−	0.949599i	$-0.601491\pi$
$541$	−9.16620e33	−0.626937	−0.313468	+	0.949599i	$0.601491\pi$
$542$	− 5.39927e33i	− 0.360864i
$543$	− 1.98617e33i	− 0.129723i
$544$	1.31186e33	0.0837338
$545$	0	0
$546$	−4.98095e31	−0.00303671
$547$	2.47403e34i	1.47423i	0.675770	+	0.737113i	$0.263811\pi$
$547$	2.47403e34i	1.47423i	−0.675770	+	0.737113i	$0.736189\pi$
$548$	− 1.60779e34i	− 0.936426i
$549$	−1.66884e34	−0.950082
$550$	0	0
$551$	−6.33989e33	−0.344895
$552$	1.36883e33i	0.0727968i
$553$	− 6.72970e33i	− 0.349890i
$554$	−8.67787e33	−0.441104
$555$	0	0
$556$	−8.23034e33	−0.399929
$557$	2.03083e34i	0.964905i	0.875922	+	0.482452i	$0.160254\pi$
$557$	2.03083e34i	0.964905i	−0.875922	+	0.482452i	$0.839746\pi$
$558$	− 1.42067e34i	− 0.660034i
$559$	1.32192e33	0.0600564
$560$	0	0
$561$	2.08302e33	0.0905018
$562$	2.60973e34i	1.10890i
$563$	− 3.26297e34i	− 1.35599i	−0.735064	−	0.677997i	$-0.762848\pi$
$563$	− 3.26297e34i	− 1.35599i	0.735064	−	0.677997i	$-0.237152\pi$
$564$	3.34954e33	0.136143
$565$	0	0
$566$	1.23177e34	0.478988
$567$	1.14613e34i	0.435960i
$568$	9.21368e33i	0.342830i
$569$	−3.41443e34	−1.24284	−0.621419	−	0.783478i	$-0.713444\pi$
$569$	−3.41443e34	−1.24284	−0.621419	+	0.783478i	$0.713444\pi$
$570$	0	0
$571$	1.36450e33	0.0475359	0.0237679	−	0.999718i	$-0.492434\pi$
$571$	1.36450e33	0.0475359	0.0237679	+	0.999718i	$0.492434\pi$
$572$	8.00005e32i	0.0272673i
$573$	9.95293e33i	0.331908i
$574$	−1.16477e34	−0.380051
$575$	0	0
$576$	−3.87595e33	−0.121087
$577$	− 3.92987e34i	− 1.20138i	−0.799481	−	0.600691i	$-0.794892\pi$
$577$	− 3.92987e34i	− 1.20138i	0.799481	−	0.600691i	$-0.205108\pi$
$578$	− 1.83333e34i	− 0.548458i
$579$	−1.05688e34	−0.309417
$580$	0	0
$581$	1.35847e34	0.380933
$582$	4.13039e33i	0.113358i
$583$	5.38319e33i	0.144605i
$584$	−1.53780e34	−0.404332
$585$	0	0
$586$	−2.94639e34	−0.742285
$587$	− 3.72718e34i	− 0.919187i	−0.888129	−	0.459594i	$-0.847995\pi$
$587$	− 3.72718e34i	− 0.919187i	0.888129	−	0.459594i	$-0.152005\pi$
$588$	− 2.81787e33i	− 0.0680305i
$589$	−1.26347e34	−0.298623
$590$	0	0
$591$	−5.17134e33	−0.117155
$592$	− 6.80265e33i	− 0.150889i
$593$	7.75169e34i	1.68350i	0.539870	+	0.841749i	$0.318474\pi$
$593$	7.75169e34i	1.68350i	−0.539870	+	0.841749i	$0.681526\pi$
$594$	−1.25076e34	−0.265978
$595$	0	0
$596$	1.52608e34	0.311171
$597$	1.20395e34i	0.240397i
$598$	− 2.12519e33i	− 0.0415559i
$599$	−6.18820e34	−1.18503	−0.592515	−	0.805559i	$-0.701865\pi$
$599$	−6.18820e34	−1.18503	−0.592515	+	0.805559i	$0.701865\pi$
$600$	0	0
$601$	−2.95852e34	−0.543430	−0.271715	−	0.962378i	$-0.587591\pi$
$601$	−2.95852e34	−0.543430	−0.271715	+	0.962378i	$0.587591\pi$
$602$	− 2.24651e34i	− 0.404160i
$603$	− 5.05305e34i	− 0.890405i
$604$	−1.38338e34	−0.238770
$605$	0	0
$606$	4.43177e33	0.0733954
$607$	1.00617e35i	1.63234i	0.577810	+	0.816171i	$0.303907\pi$
$607$	1.00617e35i	1.63234i	−0.577810	+	0.816171i	$0.696093\pi$
$608$	3.44706e33i	0.0547840i
$609$	−6.07845e33	−0.0946405
$610$	0	0
$611$	−5.20034e33	−0.0777171
$612$	− 1.56684e34i	− 0.229421i
$613$	− 4.47446e34i	− 0.641926i	−0.947092	−	0.320963i	$-0.895993\pi$
$613$	− 4.47446e34i	− 0.641926i	0.947092	−	0.320963i	$-0.104007\pi$
$614$	2.49298e34	0.350440
$615$	0	0
$616$	1.35955e34	0.183500
$617$	− 2.58799e34i	− 0.342293i	−0.985246	−	0.171147i	$-0.945253\pi$
$617$	− 2.58799e34i	− 0.342293i	0.985246	−	0.171147i	$-0.0547472\pi$
$618$	9.12187e33i	0.118230i
$619$	1.37687e35	1.74889	0.874443	−	0.485129i	$-0.161227\pi$
$619$	1.37687e35	1.74889	0.874443	+	0.485129i	$0.161227\pi$
$620$	0	0
$621$	3.32262e34	0.405355
$622$	− 1.47525e34i	− 0.176395i
$623$	1.47950e34i	0.173386i
$624$	−1.94472e32	−0.00223383
$625$	0	0
$626$	1.25815e34	0.138852
$627$	5.47337e33i	0.0592121i
$628$	1.63227e34i	0.173099i
$629$	2.74996e34	0.285886
$630$	0	0
$631$	−2.83484e34	−0.283244	−0.141622	−	0.989921i	$-0.545232\pi$
$631$	−2.83484e34	−0.283244	−0.141622	+	0.989921i	$0.545232\pi$
$632$	− 2.62749e34i	− 0.257381i
$633$	1.92206e33i	0.0184595i
$634$	1.14958e35	1.08249
$635$	0	0
$636$	−1.30859e33	−0.0118465
$637$	4.37489e33i	0.0388351i
$638$	9.76279e34i	0.849798i
$639$	1.10045e35	0.939314
$640$	0	0
$641$	−1.36368e34	−0.111940	−0.0559701	−	0.998432i	$-0.517825\pi$
$641$	−1.36368e34	−0.111940	−0.0559701	+	0.998432i	$0.517825\pi$
$642$	− 1.31678e33i	− 0.0106005i
$643$	8.47939e32i	0.00669464i	0.999994	+	0.00334732i	$0.00106549\pi$
$643$	8.47939e32i	0.00669464i	−0.999994	+	0.00334732i	$0.998935\pi$
$644$	−3.61161e34	−0.279658
$645$	0	0
$646$	−1.39346e34	−0.103798
$647$	− 2.50478e35i	− 1.83007i	−0.403379	−	0.915033i	$-0.632164\pi$
$647$	− 2.50478e35i	− 1.83007i	0.403379	−	0.915033i	$-0.367836\pi$
$648$	4.47487e34i	0.320696i
$649$	1.36496e35	0.959537
$650$	0	0
$651$	−1.21137e34	−0.0819432
$652$	4.27774e34i	0.283870i
$653$	− 1.55775e35i	− 1.01410i	−0.861916	−	0.507051i	$-0.830735\pi$
$653$	− 1.55775e35i	− 1.01410i	0.861916	−	0.507051i	$-0.169265\pi$
$654$	−3.24374e34	−0.207169
$655$	0	0
$656$	−4.54763e34	−0.279568
$657$	1.83669e35i	1.10782i
$658$	8.83760e34i	0.523011i
$659$	1.85485e35	1.07706	0.538531	−	0.842605i	$-0.318979\pi$
$659$	1.85485e35	1.07706	0.538531	+	0.842605i	$0.318979\pi$
$660$	0	0
$661$	2.92623e35	1.63602	0.818012	−	0.575202i	$-0.195076\pi$
$661$	2.92623e35	1.63602	0.818012	+	0.575202i	$0.195076\pi$
$662$	7.36840e34i	0.404248i
$663$	− 7.86148e32i	− 0.00423239i
$664$	5.30389e34	0.280217
$665$	0	0
$666$	−8.12488e34	−0.413417
$667$	− 2.59346e35i	− 1.29511i
$668$	1.35739e35i	0.665271i
$669$	−2.54055e33	−0.0122209
$670$	0	0
$671$	2.28548e35	1.05912
$672$	3.30491e33i	0.0150329i
$673$	2.13829e35i	0.954724i	0.878707	+	0.477362i	$0.158407\pi$
$673$	2.13829e35i	0.954724i	−0.878707	+	0.477362i	$0.841593\pi$
$674$	1.38314e35	0.606200
$675$	0	0
$676$	−1.18085e35	−0.498725
$677$	− 1.59208e35i	− 0.660096i	−0.943964	−	0.330048i	$-0.892935\pi$
$677$	− 1.59208e35i	− 0.660096i	0.943964	−	0.330048i	$-0.107065\pi$
$678$	3.05801e34i	0.124471i
$679$	−1.08978e35	−0.435480
$680$	0	0
$681$	−5.82643e34	−0.224421
$682$	1.94561e35i	0.735786i
$683$	4.23003e35i	1.57067i	0.619071	+	0.785335i	$0.287509\pi$
$683$	4.23003e35i	1.57067i	−0.619071	+	0.785335i	$0.712491\pi$
$684$	4.11706e34	0.150102
$685$	0	0
$686$	1.71030e35	0.601203
$687$	1.00401e35i	0.346559i
$688$	− 8.77111e34i	− 0.297303i
$689$	2.03166e33	0.00676255
$690$	0	0
$691$	3.02759e35	0.971899	0.485950	−	0.873987i	$-0.338474\pi$
$691$	3.02759e35	0.971899	0.485950	+	0.873987i	$0.338474\pi$
$692$	− 7.57584e34i	− 0.238838i
$693$	− 1.62380e35i	− 0.502769i
$694$	1.25776e34	0.0382476
$695$	0	0
$696$	−2.37322e34	−0.0696182
$697$	− 1.83837e35i	− 0.529692i
$698$	1.93967e35i	0.548954i
$699$	−9.25627e34	−0.257319
$700$	0	0
$701$	2.66145e35	0.713909	0.356954	−	0.934122i	$-0.383815\pi$
$701$	2.66145e35	0.713909	0.356954	+	0.934122i	$0.383815\pi$
$702$	4.72049e33i	0.0124386i
$703$	7.22582e34i	0.187045i
$704$	5.30812e34	0.134984
$705$	0	0
$706$	−4.65859e35	−1.14339
$707$	1.16930e35i	0.281958i
$708$	3.31806e34i	0.0786084i
$709$	−2.81745e34	−0.0655810	−0.0327905	−	0.999462i	$-0.510439\pi$
$709$	−2.81745e34	−0.0655810	−0.0327905	+	0.999462i	$0.510439\pi$
$710$	0	0
$711$	−3.13819e35	−0.705195
$712$	5.77643e34i	0.127544i
$713$	− 5.16846e35i	− 1.12135i
$714$	−1.33600e34	−0.0284826
$715$	0	0
$716$	−3.26643e35	−0.672450
$717$	9.71301e34i	0.196501i
$718$	3.10606e35i	0.617526i
$719$	−2.87441e35	−0.561613	−0.280806	−	0.959764i	$-0.590602\pi$
$719$	−2.87441e35	−0.561613	−0.280806	+	0.959764i	$0.590602\pi$
$720$	0	0
$721$	−2.40676e35	−0.454195
$722$	3.44626e35i	0.639195i
$723$	− 8.10962e34i	− 0.147833i
$724$	2.04602e35	0.366588
$725$	0	0
$726$	1.20069e34	0.0207838
$727$	4.98046e35i	0.847402i	0.905802	+	0.423701i	$0.139269\pi$
$727$	4.98046e35i	0.847402i	−0.905802	+	0.423701i	$0.860731\pi$
$728$	− 5.13105e33i	− 0.00858152i
$729$	4.96977e35	0.817037
$730$	0	0
$731$	3.54570e35	0.563293
$732$	5.55575e34i	0.0867668i
$733$	− 8.47339e35i	− 1.30094i	−0.759531	−	0.650471i	$-0.774572\pi$
$733$	− 8.47339e35i	− 1.30094i	0.759531	−	0.650471i	$-0.225428\pi$
$734$	−2.72748e35	−0.411681
$735$	0	0
$736$	−1.41009e35	−0.205718
$737$	6.92016e35i	0.992597i
$738$	5.43155e35i	0.765983i
$739$	−7.12136e35	−0.987433	−0.493716	−	0.869623i	$-0.664362\pi$
$739$	−7.12136e35	−0.987433	−0.493716	+	0.869623i	$0.664362\pi$
$740$	0	0
$741$	2.06569e33	0.00276910
$742$	− 3.45266e34i	− 0.0455098i
$743$	− 6.18867e35i	− 0.802116i	−0.916053	−	0.401058i	$-0.868643\pi$
$743$	− 6.18867e35i	− 0.802116i	0.916053	−	0.401058i	$-0.131357\pi$
$744$	−4.72956e34	−0.0602780
$745$	0	0
$746$	1.65434e35	0.203887
$747$	− 6.33481e35i	− 0.767761i
$748$	2.14579e35i	0.255751i
$749$	3.47427e34	0.0407231
$750$	0	0
$751$	1.34082e36	1.52009	0.760046	−	0.649869i	$-0.225176\pi$
$751$	1.34082e36	1.52009	0.760046	+	0.649869i	$0.225176\pi$
$752$	3.45048e35i	0.384731i
$753$	2.86006e35i	0.313644i
$754$	3.68456e34	0.0397414
$755$	0	0
$756$	8.02213e34	0.0837080
$757$	− 8.81045e35i	− 0.904274i	−0.891949	−	0.452137i	$-0.850662\pi$
$757$	− 8.81045e35i	− 0.904274i	0.891949	−	0.452137i	$-0.149338\pi$
$758$	1.22895e36i	1.24070i
$759$	−2.23899e35	−0.222346
$760$	0	0
$761$	−9.08045e35	−0.872568	−0.436284	−	0.899809i	$-0.643706\pi$
$761$	−9.08045e35	−0.872568	−0.436284	+	0.899809i	$0.643706\pi$
$762$	8.78701e34i	0.0830623i
$763$	− 8.55847e35i	− 0.795865i
$764$	−1.02529e36	−0.937948
$765$	0	0
$766$	−2.39008e35	−0.211618
$767$	− 5.15148e34i	− 0.0448735i
$768$	1.29034e34i	0.0110583i
$769$	−1.57427e36	−1.32739	−0.663696	−	0.748003i	$-0.731013\pi$
$769$	−1.57427e36	−1.32739	−0.663696	+	0.748003i	$0.731013\pi$
$770$	0	0
$771$	1.98800e35	0.162270
$772$	− 1.08873e36i	− 0.874389i
$773$	− 1.97307e36i	− 1.55919i	−0.626284	−	0.779595i	$-0.715425\pi$
$773$	− 1.97307e36i	− 1.55919i	0.626284	−	0.779595i	$-0.284575\pi$
$774$	−1.04759e36	−0.814574
$775$	0	0
$776$	−4.25486e35	−0.320342
$777$	6.92785e34i	0.0513258i
$778$	− 1.90679e36i	− 1.39014i
$779$	4.83052e35	0.346558
$780$	0	0
$781$	−1.50707e36	−1.04712
$782$	− 5.70024e35i	− 0.389770i
$783$	5.76061e35i	0.387656i
$784$	2.90279e35	0.192249
$785$	0	0
$786$	−4.91166e34	−0.0315099
$787$	− 9.52553e35i	− 0.601458i	−0.953710	−	0.300729i	$-0.902770\pi$
$787$	− 9.52553e35i	− 0.601458i	0.953710	−	0.300729i	$-0.0972299\pi$
$788$	− 5.32719e35i	− 0.331070i
$789$	−3.71048e35	−0.226970
$790$	0	0
$791$	−8.06842e35	−0.478170
$792$	− 6.33985e35i	− 0.369840i
$793$	− 8.62560e34i	− 0.0495307i
$794$	1.46263e36	0.826760
$795$	0	0
$796$	−1.24023e36	−0.679344
$797$	− 3.70863e35i	− 0.199979i	−0.994989	−	0.0999894i	$-0.968119\pi$
$797$	− 3.70863e35i	− 0.199979i	0.994989	−	0.0999894i	$-0.0318809\pi$
$798$	− 3.51050e34i	− 0.0186351i
$799$	−1.39485e36	−0.728941
$800$	0	0
$801$	6.89918e35	0.349455
$802$	2.39784e36i	1.19575i
$803$	− 2.51536e36i	− 1.23497i
$804$	−1.68221e35	−0.0813168
$805$	0	0
$806$	7.34290e34	0.0344096
$807$	5.09463e35i	0.235068i
$808$	4.56532e35i	0.207410i
$809$	2.08152e36	0.931159	0.465580	−	0.885006i	$-0.345846\pi$
$809$	2.08152e36	0.931159	0.465580	+	0.885006i	$0.345846\pi$
$810$	0	0
$811$	−9.20046e34	−0.0399070	−0.0199535	−	0.999801i	$-0.506352\pi$
$811$	−9.20046e34	−0.0399070	−0.0199535	+	0.999801i	$0.506352\pi$
$812$	− 6.26164e35i	− 0.267447i
$813$	2.14684e35i	0.0902960i
$814$	1.11270e36	0.460865
$815$	0	0
$816$	−5.21618e34	−0.0209520
$817$	9.31673e35i	0.368543i
$818$	− 2.39935e36i	− 0.934709i
$819$	−6.12837e34	−0.0235124
$820$	0	0
$821$	9.64905e35	0.359083	0.179542	−	0.983750i	$-0.442539\pi$
$821$	9.64905e35	0.359083	0.179542	+	0.983750i	$0.442539\pi$
$822$	6.39286e35i	0.234314i
$823$	4.33977e35i	0.156664i	0.996927	+	0.0783319i	$0.0249594\pi$
$823$	4.33977e35i	0.156664i	−0.996927	+	0.0783319i	$0.975041\pi$
$824$	−9.39677e35	−0.334109
$825$	0	0
$826$	−8.75456e35	−0.301984
$827$	− 1.42223e36i	− 0.483227i	−0.970373	−	0.241614i	$-0.922323\pi$
$827$	− 1.42223e36i	− 0.483227i	0.970373	−	0.241614i	$-0.0776766\pi$
$828$	1.68416e36i	0.563644i
$829$	−4.07234e36	−1.34249	−0.671247	−	0.741234i	$-0.734241\pi$
$829$	−4.07234e36	−1.34249	−0.671247	+	0.741234i	$0.734241\pi$
$830$	0	0
$831$	3.45047e35	0.110374
$832$	− 2.00333e34i	− 0.00631263i
$833$	1.17344e36i	0.364251i
$834$	3.27252e35	0.100071
$835$	0	0
$836$	−5.63832e35	−0.167329
$837$	1.14802e36i	0.335646i
$838$	− 8.84511e35i	− 0.254773i
$839$	−1.54259e36	−0.437750	−0.218875	−	0.975753i	$-0.570239\pi$
$839$	−1.54259e36	−0.437750	−0.218875	+	0.975753i	$0.570239\pi$
$840$	0	0
$841$	8.66055e35	0.238559
$842$	1.05391e36i	0.286023i
$843$	− 1.03767e36i	− 0.277470i
$844$	−1.97998e35	−0.0521652
$845$	0	0
$846$	4.12115e36	1.05412
$847$	3.16798e35i	0.0798434i
$848$	− 1.34803e35i	− 0.0334773i
$849$	−4.89773e35	−0.119853
$850$	0	0
$851$	−2.95586e36	−0.702368
$852$	− 3.66352e35i	− 0.0857834i
$853$	7.94652e36i	1.83364i	0.399300	+	0.916820i	$0.369253\pi$
$853$	7.94652e36i	1.83364i	−0.399300	+	0.916820i	$0.630747\pi$
$854$	−1.46586e36	−0.333326
$855$	0	0
$856$	1.35647e35	0.0299562
$857$	7.37212e35i	0.160447i	0.996777	+	0.0802236i	$0.0255634\pi$
$857$	7.37212e35i	0.160447i	−0.996777	+	0.0802236i	$0.974437\pi$
$858$	− 3.18096e34i	− 0.00682286i
$859$	6.08537e36	1.28639	0.643195	−	0.765703i	$-0.277609\pi$
$859$	6.08537e36	1.28639	0.643195	+	0.765703i	$0.277609\pi$
$860$	0	0
$861$	4.63133e35	0.0950968
$862$	1.99647e36i	0.404038i
$863$	3.30325e36i	0.658880i	0.944177	+	0.329440i	$0.106860\pi$
$863$	3.30325e36i	0.658880i	−0.944177	+	0.329440i	$0.893140\pi$
$864$	3.13209e35	0.0615762
$865$	0	0
$866$	5.49382e36	1.04930
$867$	7.28965e35i	0.137236i
$868$	− 1.24787e36i	− 0.231565i
$869$	4.29775e36	0.786130
$870$	0	0
$871$	2.61173e35	0.0464195
$872$	− 3.34150e36i	− 0.585444i
$873$	5.08188e36i	0.877700i
$874$	1.49780e36	0.255013
$875$	0	0
$876$	6.11454e35	0.101172
$877$	2.53964e35i	0.0414264i	0.999785	+	0.0207132i	$0.00659369\pi$
$877$	2.53964e35i	0.0414264i	−0.999785	+	0.0207132i	$0.993406\pi$
$878$	1.31085e36i	0.210801i
$879$	1.17154e36	0.185736
$880$	0	0
$881$	7.01270e35	0.108065	0.0540327	−	0.998539i	$-0.482792\pi$
$881$	7.01270e35	0.108065	0.0540327	+	0.998539i	$0.482792\pi$
$882$	− 3.46700e36i	− 0.526740i
$883$	7.67538e36i	1.14972i	0.818253	+	0.574858i	$0.194943\pi$
$883$	7.67538e36i	1.14972i	−0.818253	+	0.574858i	$0.805057\pi$
$884$	8.09840e34	0.0119604
$885$	0	0
$886$	6.18082e36	0.887410
$887$	1.19088e37i	1.68586i	0.538024	+	0.842929i	$0.319171\pi$
$887$	1.19088e37i	1.68586i	−0.538024	+	0.842929i	$0.680829\pi$
$888$	2.70485e35i	0.0377556i
$889$	−2.31841e36	−0.319094
$890$	0	0
$891$	−7.31950e36	−0.979513
$892$	− 2.61712e35i	− 0.0345352i
$893$	− 3.66512e36i	− 0.476920i
$894$	−6.06796e35	−0.0778617
$895$	0	0
$896$	−3.40451e35	−0.0424819
$897$	8.45012e34i	0.0103982i
$898$	− 3.00004e36i	− 0.364060i
$899$	8.96084e36	1.07239
$900$	0	0
$901$	5.44937e35	0.0634288
$902$	− 7.43851e36i	− 0.853895i
$903$	8.93253e35i	0.101129i
$904$	−3.15017e36	−0.351745
$905$	0	0
$906$	5.50056e35	0.0597454
$907$	− 6.98769e36i	− 0.748587i	−0.927310	−	0.374294i	$-0.877885\pi$
$907$	− 6.98769e36i	− 0.748587i	0.927310	−	0.374294i	$-0.122115\pi$
$908$	− 6.00202e36i	− 0.634197i
$909$	5.45268e36	0.568279
$910$	0	0
$911$	−8.23719e36	−0.835217	−0.417608	−	0.908627i	$-0.637132\pi$
$911$	−8.23719e36	−0.835217	−0.417608	+	0.908627i	$0.637132\pi$
$912$	− 1.37061e35i	− 0.0137081i
$913$	8.67553e36i	0.855877i
$914$	7.40751e36	0.720850
$915$	0	0
$916$	−1.03426e37	−0.979348
$917$	− 1.29592e36i	− 0.121049i
$918$	1.26614e36i	0.116667i
$919$	8.31177e36	0.755526	0.377763	−	0.925902i	$-0.376693\pi$
$919$	8.31177e36	0.755526	0.377763	+	0.925902i	$0.376693\pi$
$920$	0	0
$921$	−9.91251e35	−0.0876877
$922$	8.28816e36i	0.723305i
$923$	5.68781e35i	0.0489693i
$924$	−5.40581e35	−0.0459157
$925$	0	0
$926$	1.64207e37	1.35755
$927$	1.12232e37i	0.915420i
$928$	− 2.44474e36i	− 0.196736i
$929$	1.48672e37	1.18041	0.590205	−	0.807253i	$-0.299047\pi$
$929$	1.48672e37	1.18041	0.590205	+	0.807253i	$0.299047\pi$
$930$	0	0
$931$	−3.08336e36	−0.238316
$932$	− 9.53522e36i	− 0.727163i
$933$	5.86585e35i	0.0441378i
$934$	4.58550e36	0.340448
$935$	0	0
$936$	−2.39271e35	−0.0172959
$937$	− 2.25559e37i	− 1.60885i	−0.594055	−	0.804424i	$-0.702474\pi$
$937$	− 2.25559e37i	− 1.60885i	0.594055	−	0.804424i	$-0.297526\pi$
$938$	− 4.43844e36i	− 0.312388i
$939$	−5.00263e35	−0.0347439
$940$	0	0
$941$	2.40580e37	1.62701	0.813504	−	0.581559i	$-0.197557\pi$
$941$	2.40580e37	1.62701	0.813504	+	0.581559i	$0.197557\pi$
$942$	− 6.49017e35i	− 0.0433132i
$943$	1.97602e37i	1.30135i
$944$	−3.41806e36	−0.222141
$945$	0	0
$946$	1.43468e37	0.908063
$947$	2.05868e35i	0.0128592i	0.999979	+	0.00642962i	$0.00204662\pi$
$947$	2.05868e35i	0.0128592i	−0.999979	+	0.00642962i	$0.997953\pi$
$948$	1.04473e36i	0.0644023i
$949$	−9.49316e35	−0.0577541
$950$	0	0
$951$	−4.57094e36	−0.270863
$952$	− 1.37626e36i	− 0.0804896i
$953$	7.96109e36i	0.459528i	0.973246	+	0.229764i	$0.0737954\pi$
$953$	7.96109e36i	0.459528i	−0.973246	+	0.229764i	$0.926205\pi$
$954$	−1.61004e36	−0.0917239
$955$	0	0
$956$	−1.00057e37	−0.555296
$957$	− 3.88185e36i	− 0.212638i
$958$	− 2.32230e37i	− 1.25560i
$959$	−1.68673e37	−0.900145
$960$	0	0
$961$	−1.37487e36	−0.0714859
$962$	− 4.19943e35i	− 0.0215527i
$963$	− 1.62012e36i	− 0.0820765i
$964$	8.35401e36	0.417765
$965$	0	0
$966$	1.43604e36	0.0699764
$967$	− 4.83856e36i	− 0.232748i	−0.993205	−	0.116374i	$-0.962873\pi$
$967$	− 4.83856e36i	− 0.232748i	0.993205	−	0.116374i	$-0.0371271\pi$
$968$	1.23688e36i	0.0587334i
$969$	5.54066e35	0.0259725
$970$	0	0
$971$	1.24060e37	0.566749	0.283375	−	0.959009i	$-0.408546\pi$
$971$	1.24060e37	0.566749	0.283375	+	0.959009i	$0.408546\pi$
$972$	− 5.64105e36i	− 0.254409i
$973$	8.63441e36i	0.384434i
$974$	−7.21277e36	−0.317041
$975$	0	0
$976$	−5.72318e36	−0.245197
$977$	− 5.52484e36i	− 0.233688i	−0.993150	−	0.116844i	$-0.962722\pi$
$977$	− 5.52484e36i	− 0.233688i	0.993150	−	0.116844i	$-0.0372778\pi$
$978$	− 1.70090e36i	− 0.0710303i
$979$	−9.44844e36	−0.389562
$980$	0	0
$981$	−3.99098e37	−1.60405
$982$	2.28702e37i	0.907561i
$983$	− 3.62327e37i	− 1.41965i	−0.704377	−	0.709826i	$-0.748774\pi$
$983$	− 3.62327e37i	− 1.41965i	0.704377	−	0.709826i	$-0.251226\pi$
$984$	1.80822e36	0.0699539
$985$	0	0
$986$	9.88281e36	0.372751
$987$	− 3.51398e36i	− 0.130869i
$988$	2.12795e35i	0.00782526i
$989$	−3.81119e37	−1.38391
$990$	0	0
$991$	−1.55999e37	−0.552334	−0.276167	−	0.961110i	$-0.589064\pi$
$991$	−1.55999e37	−0.552334	−0.276167	+	0.961110i	$0.589064\pi$
$992$	− 4.87209e36i	− 0.170341i
$993$	− 2.92980e36i	− 0.101152i
$994$	9.66602e36	0.329547
$995$	0	0
$996$	−2.10892e36	−0.0701162
$997$	5.89404e37i	1.93519i	0.252505	+	0.967596i	$0.418746\pi$
$997$	5.89404e37i	1.93519i	−0.252505	+	0.967596i	$0.581254\pi$
$998$	− 1.79146e37i	− 0.580865i
$999$	6.56558e36	0.210235

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.26.b.b.49.1		2
5.2	odd	4		10.26.a.a.1.1	✓	1
5.3	odd	4		50.26.a.a.1.1		1
5.4	even	2	inner	50.26.b.b.49.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.26.a.a.1.1	✓	1	5.2	odd	4
50.26.a.a.1.1		1	5.3	odd	4
50.26.b.b.49.1		2	1.1	even	1	trivial
50.26.b.b.49.2		2	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	50.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-4096.00i q^{2} +162864. i q^{3} -1.67772e7 q^{4} +6.67091e8 q^{6} +1.76009e10i q^{7} +6.87195e10i q^{8} +8.20764e11 q^{9} -1.12404e13 q^{11} -2.73240e12i q^{12} +4.24221e12i q^{13} +7.20933e13 q^{14} +2.81475e14 q^{16} +1.13786e15i q^{17} -3.36185e15i q^{18} -2.98985e15 q^{19} -2.86655e15 q^{21} +4.60406e16i q^{22} -1.22305e17i q^{23} -1.11919e16 q^{24} +1.73761e16 q^{26} +2.71666e17i q^{27} -2.95294e17i q^{28} +2.12048e18 q^{29} +4.22586e18 q^{31} -1.15292e18i q^{32} -1.83065e18i q^{33} +4.66066e18 q^{34} -1.37701e19 q^{36} -2.41679e19i q^{37} +1.22464e19i q^{38} -6.90903e17 q^{39} -1.61564e20 q^{41} +1.17414e19i q^{42} -3.11612e20i q^{43} +1.88582e20 q^{44} -5.00963e20 q^{46} +1.22586e21i q^{47} +4.58421e19i q^{48} +1.03128e21 q^{49} -1.85316e20 q^{51} -7.11725e19i q^{52} -4.78915e20i q^{53} +1.11274e21 q^{54} -1.20952e21 q^{56} -4.86938e20i q^{57} -8.68547e21i q^{58} -1.21434e22 q^{59} -2.03328e22 q^{61} -1.73091e22i q^{62} +1.44462e22i q^{63} -4.72237e21 q^{64} -7.49835e21 q^{66} -6.15653e22i q^{67} -1.90901e22i q^{68} +1.99192e22 q^{69} +1.34077e23 q^{71} +5.64025e22i q^{72} +2.23779e23i q^{73} -9.89916e22 q^{74} +5.01613e22 q^{76} -1.97841e23i q^{77} +2.82994e21i q^{78} -3.82350e23 q^{79} +6.51179e23 q^{81} +6.61767e23i q^{82} -7.71818e23i q^{83} +4.80928e22 q^{84} -1.27636e24 q^{86} +3.45349e23i q^{87} -7.72433e23i q^{88} +8.40581e23 q^{89} -7.46667e22 q^{91} +2.05195e24i q^{92} +6.88241e23i q^{93} +5.02111e24 q^{94} +1.87769e23 q^{96} +6.19164e24i q^{97} -4.22411e24i q^{98} -9.22569e24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 33554432 q^{4} + 1334181888 q^{6} + 1641527853894 q^{9} - 22480747671096 q^{11} + 144186519486464 q^{14} + 562949953421312 q^{16} - 59\!\cdots\!40 q^{19} - 57\!\cdots\!76 q^{21} - 22\!\cdots\!08 q^{24}+ \cdots - 18\!\cdots\!12 q^{99}+O(q^{100}) \) 2 * q - 33554432 * q^4 + 1334181888 * q^6 + 1641527853894 * q^9 - 22480747671096 * q^11 + 144186519486464 * q^14 + 562949953421312 * q^16 - 5979690773455240 * q^19 - 5733103835362176 * q^21 - 22383857718263808 * q^24 + 34752175596617728 * q^26 + 4240951159366415940 * q^29 + 8451726183377942704 * q^31 + 9321315931684061184 * q^34 - 27540267374796079104 * q^36 - 1381806232023327552 * q^39 - 323128641530597510796 * q^41 + 377164359519474548736 * q^44 - 1001926290180659576832 * q^46 + 2062554335894473893486 * q^49 - 370631542455515854656 * q^51 + 2225485482283998904320 * q^54 - 2419048381712615604224 * q^56 - 24286769256796795881720 * q^59 - 40665614069527393964996 * q^61 - 9444732965739290427392 * q^64 - 14996703185737232154624 * q^66 + 39838311358394272783488 * q^69 + 268153252990894462797504 * q^71 - 197983247997076156235776 * q^74 + 100322563719465627811840 * q^76 - 764699498524138082047360 * q^79 + 1302358724859014860662162 * q^81 + 96185521396299664982016 * q^84 - 2552727779050936041930752 * q^86 + 1681161365246136806433420 * q^89 - 149333335276208541495856 * q^91 + 10042222992826541561708544 * q^94 + 375538815852579051798528 * q^96 - 18451386739233377727423912 * q^99

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