LMFDB - Embedded newform 175.10.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,10,Mod(1,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("175.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	175.a (trivial)

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:	yes
Analytic conductor:	$90.1312713287$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 35)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.41421$ of defining polynomial
Character	$\chi$	$=$	175.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+14.8284 q^{2} +239.735 q^{3} -292.118 q^{4} +3554.89 q^{6} -2401.00 q^{7} -11923.8 q^{8} +37789.9 q^{9} +O(q^{10})$	\(q+14.8284 q^{2} +239.735 q^{3} -292.118 q^{4} +3554.89 q^{6} -2401.00 q^{7} -11923.8 q^{8} +37789.9 q^{9} -16523.6 q^{11} -70030.9 q^{12} -26311.4 q^{13} -35603.1 q^{14} -27246.9 q^{16} +144003. q^{17} +560365. q^{18} -159710. q^{19} -575604. q^{21} -245019. q^{22} -2.07393e6 q^{23} -2.85855e6 q^{24} -390156. q^{26} +4.34086e6 q^{27} +701375. q^{28} -4.94938e6 q^{29} +4.22040e6 q^{31} +5.70096e6 q^{32} -3.96128e6 q^{33} +2.13533e6 q^{34} -1.10391e7 q^{36} +1.29081e7 q^{37} -2.36824e6 q^{38} -6.30776e6 q^{39} -2.87518e7 q^{41} -8.53530e6 q^{42} -3.54825e7 q^{43} +4.82683e6 q^{44} -3.07532e7 q^{46} -5.95633e7 q^{47} -6.53205e6 q^{48} +5.76480e6 q^{49} +3.45225e7 q^{51} +7.68602e6 q^{52} -2.31161e6 q^{53} +6.43681e7 q^{54} +2.86290e7 q^{56} -3.82880e7 q^{57} -7.33915e7 q^{58} -1.68651e8 q^{59} -6.70167e7 q^{61} +6.25819e7 q^{62} -9.07336e7 q^{63} +9.84867e7 q^{64} -5.87395e7 q^{66} +1.56259e8 q^{67} -4.20657e7 q^{68} -4.97195e8 q^{69} +6.95067e7 q^{71} -4.50599e8 q^{72} +7.83438e7 q^{73} +1.91407e8 q^{74} +4.66540e7 q^{76} +3.96731e7 q^{77} -9.35342e7 q^{78} -4.26957e8 q^{79} +2.96838e8 q^{81} -4.26344e8 q^{82} +5.31242e8 q^{83} +1.68144e8 q^{84} -5.26149e8 q^{86} -1.18654e9 q^{87} +1.97024e8 q^{88} -1.14168e8 q^{89} +6.31736e7 q^{91} +6.05833e8 q^{92} +1.01178e9 q^{93} -8.83231e8 q^{94} +1.36672e9 q^{96} +1.46573e9 q^{97} +8.54829e7 q^{98} -6.24424e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 24 q^{2} + 174 q^{3} - 720 q^{4} + 2952 q^{6} - 4802 q^{7} - 20544 q^{8} + 22428 q^{9}+O(q^{10}) $ 2 * q + 24 * q^2 + 174 * q^3 - 720 * q^4 + 2952 * q^6 - 4802 * q^7 - 20544 * q^8 + 22428 * q^9	\( 2 q + 24 q^{2} + 174 q^{3} - 720 q^{4} + 2952 q^{6} - 4802 q^{7} - 20544 q^{8} + 22428 q^{9} + 18566 q^{11} - 41904 q^{12} + 51090 q^{13} - 57624 q^{14} + 112768 q^{16} + 373910 q^{17} + 419472 q^{18} - 143276 q^{19} - 417774 q^{21} + 76808 q^{22} + 498908 q^{23} - 2291904 q^{24} + 319736 q^{26} + 6644538 q^{27} + 1728720 q^{28} - 11577554 q^{29} - 3953760 q^{31} + 11398656 q^{32} - 6267894 q^{33} + 4243944 q^{34} - 4466016 q^{36} + 3205412 q^{37} - 2217520 q^{38} - 11395746 q^{39} + 1058992 q^{41} - 7087752 q^{42} - 15948180 q^{43} - 10187376 q^{44} - 7156176 q^{46} - 65501290 q^{47} - 15735936 q^{48} + 11529602 q^{49} + 19409466 q^{51} - 25432656 q^{52} + 25114688 q^{53} + 85496472 q^{54} + 49326144 q^{56} - 39368244 q^{57} - 134182296 q^{58} - 116159208 q^{59} - 44688544 q^{61} - 12388000 q^{62} - 53849628 q^{63} + 79055872 q^{64} - 79894824 q^{66} - 118092496 q^{67} - 140439024 q^{68} - 666320892 q^{69} - 294165824 q^{71} - 318176640 q^{72} + 57419332 q^{73} + 102418064 q^{74} + 39622368 q^{76} - 44576966 q^{77} - 140199000 q^{78} - 692852854 q^{79} + 447773346 q^{81} - 152932128 q^{82} + 540679928 q^{83} + 100611504 q^{84} - 346989008 q^{86} - 750836190 q^{87} - 105455296 q^{88} - 779043704 q^{89} - 122667090 q^{91} - 495040608 q^{92} + 1549107360 q^{93} - 937691032 q^{94} + 992180736 q^{96} + 2673039406 q^{97} + 138355224 q^{98} - 1163466540 q^{99}+O(q^{100}) \) 2 * q + 24 * q^2 + 174 * q^3 - 720 * q^4 + 2952 * q^6 - 4802 * q^7 - 20544 * q^8 + 22428 * q^9 + 18566 * q^11 - 41904 * q^12 + 51090 * q^13 - 57624 * q^14 + 112768 * q^16 + 373910 * q^17 + 419472 * q^18 - 143276 * q^19 - 417774 * q^21 + 76808 * q^22 + 498908 * q^23 - 2291904 * q^24 + 319736 * q^26 + 6644538 * q^27 + 1728720 * q^28 - 11577554 * q^29 - 3953760 * q^31 + 11398656 * q^32 - 6267894 * q^33 + 4243944 * q^34 - 4466016 * q^36 + 3205412 * q^37 - 2217520 * q^38 - 11395746 * q^39 + 1058992 * q^41 - 7087752 * q^42 - 15948180 * q^43 - 10187376 * q^44 - 7156176 * q^46 - 65501290 * q^47 - 15735936 * q^48 + 11529602 * q^49 + 19409466 * q^51 - 25432656 * q^52 + 25114688 * q^53 + 85496472 * q^54 + 49326144 * q^56 - 39368244 * q^57 - 134182296 * q^58 - 116159208 * q^59 - 44688544 * q^61 - 12388000 * q^62 - 53849628 * q^63 + 79055872 * q^64 - 79894824 * q^66 - 118092496 * q^67 - 140439024 * q^68 - 666320892 * q^69 - 294165824 * q^71 - 318176640 * q^72 + 57419332 * q^73 + 102418064 * q^74 + 39622368 * q^76 - 44576966 * q^77 - 140199000 * q^78 - 692852854 * q^79 + 447773346 * q^81 - 152932128 * q^82 + 540679928 * q^83 + 100611504 * q^84 - 346989008 * q^86 - 750836190 * q^87 - 105455296 * q^88 - 779043704 * q^89 - 122667090 * q^91 - 495040608 * q^92 + 1549107360 * q^93 - 937691032 * q^94 + 992180736 * q^96 + 2673039406 * q^97 + 138355224 * q^98 - 1163466540 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	14.8284	0.655330	0.327665	−	0.944794i	$-0.393738\pi$
$2$	14.8284	0.655330	0.327665	+	0.944794i	$0.393738\pi$
$3$	239.735	1.70878	0.854390	−	0.519633i	$-0.173931\pi$
$3$	239.735	1.70878	0.854390	+	0.519633i	$0.173931\pi$
$4$	−292.118	−0.570542
$5$	0	0
$5$	0	0
$6$	3554.89	1.11981
$7$	−2401.00	−0.377964
$7$	−2401.00	−0.377964
$8$	−11923.8	−1.02922
$9$	37789.9	1.91993
$10$	0	0
$11$	−16523.6	−0.340280	−0.170140	−	0.985420i	$-0.554422\pi$
$11$	−16523.6	−0.340280	−0.170140	+	0.985420i	$0.554422\pi$
$12$	−70030.9	−0.974931
$13$	−26311.4	−0.255505	−0.127752	−	0.991806i	$-0.540776\pi$
$13$	−26311.4	−0.255505	−0.127752	+	0.991806i	$0.540776\pi$
$14$	−35603.1	−0.247691
$15$	0	0
$16$	−27246.9	−0.103939
$17$	144003.	0.418167	0.209084	−	0.977898i	$-0.432952\pi$
$17$	144003.	0.418167	0.209084	+	0.977898i	$0.432952\pi$
$18$	560365.	1.25819
$19$	−159710.	−0.281151	−0.140576	−	0.990070i	$-0.544895\pi$
$19$	−159710.	−0.281151	−0.140576	+	0.990070i	$0.544895\pi$
$20$	0	0
$21$	−575604.	−0.645858
$22$	−245019.	−0.222996
$23$	−2.07393e6	−1.54533	−0.772663	−	0.634817i	$-0.781075\pi$
$23$	−2.07393e6	−1.54533	−0.772663	+	0.634817i	$0.781075\pi$
$24$	−2.85855e6	−1.75872
$25$	0	0
$26$	−390156.	−0.167440
$27$	4.34086e6	1.57195
$28$	701375.	0.215645
$29$	−4.94938e6	−1.29945	−0.649725	−	0.760169i	$-0.725116\pi$
$29$	−4.94938e6	−1.29945	−0.649725	+	0.760169i	$0.725116\pi$
$30$	0	0
$31$	4.22040e6	0.820779	0.410389	−	0.911910i	$-0.365393\pi$
$31$	4.22040e6	0.820779	0.410389	+	0.911910i	$0.365393\pi$
$32$	5.70096e6	0.961110
$33$	−3.96128e6	−0.581464
$34$	2.13533e6	0.274038
$35$	0	0
$36$	−1.10391e7	−1.09540
$37$	1.29081e7	1.13228	0.566142	−	0.824308i	$-0.308435\pi$
$37$	1.29081e7	1.13228	0.566142	+	0.824308i	$0.308435\pi$
$38$	−2.36824e6	−0.184247
$39$	−6.30776e6	−0.436601
$40$	0	0
$41$	−2.87518e7	−1.58905	−0.794525	−	0.607231i	$-0.792280\pi$
$41$	−2.87518e7	−1.58905	−0.794525	+	0.607231i	$0.792280\pi$
$42$	−8.53530e6	−0.423250
$43$	−3.54825e7	−1.58273	−0.791363	−	0.611347i	$-0.790628\pi$
$43$	−3.54825e7	−1.58273	−0.791363	+	0.611347i	$0.790628\pi$
$44$	4.82683e6	0.194144
$45$	0	0
$46$	−3.07532e7	−1.01270
$47$	−5.95633e7	−1.78049	−0.890243	−	0.455485i	$-0.849466\pi$
$47$	−5.95633e7	−1.78049	−0.890243	+	0.455485i	$0.849466\pi$
$48$	−6.53205e6	−0.177608
$49$	5.76480e6	0.142857
$50$	0	0
$51$	3.45225e7	0.714555
$52$	7.68602e6	0.145776
$53$	−2.31161e6	−0.0402414	−0.0201207	−	0.999798i	$-0.506405\pi$
$53$	−2.31161e6	−0.0402414	−0.0201207	+	0.999798i	$0.506405\pi$
$54$	6.43681e7	1.03015
$55$	0	0
$56$	2.86290e7	0.389010
$57$	−3.82880e7	−0.480425
$58$	−7.33915e7	−0.851569
$59$	−1.68651e8	−1.81198	−0.905992	−	0.423296i	$-0.860873\pi$
$59$	−1.68651e8	−1.81198	−0.905992	+	0.423296i	$0.860873\pi$
$60$	0	0
$61$	−6.70167e7	−0.619725	−0.309863	−	0.950781i	$-0.600283\pi$
$61$	−6.70167e7	−0.619725	−0.309863	+	0.950781i	$0.600283\pi$
$62$	6.25819e7	0.537881
$63$	−9.07336e7	−0.725664
$64$	9.84867e7	0.733783
$65$	0	0
$66$	−5.87395e7	−0.381051
$67$	1.56259e8	0.947343	0.473671	−	0.880702i	$-0.342928\pi$
$67$	1.56259e8	0.947343	0.473671	+	0.880702i	$0.342928\pi$
$68$	−4.20657e7	−0.238582
$69$	−4.97195e8	−2.64062
$70$	0	0
$71$	6.95067e7	0.324612	0.162306	−	0.986740i	$-0.448107\pi$
$71$	6.95067e7	0.324612	0.162306	+	0.986740i	$0.448107\pi$
$72$	−4.50599e8	−1.97603
$73$	7.83438e7	0.322888	0.161444	−	0.986882i	$-0.448385\pi$
$73$	7.83438e7	0.322888	0.161444	+	0.986882i	$0.448385\pi$
$74$	1.91407e8	0.742020
$75$	0	0
$76$	4.66540e7	0.160409
$77$	3.96731e7	0.128614
$78$	−9.35342e7	−0.286118
$79$	−4.26957e8	−1.23328	−0.616641	−	0.787245i	$-0.711507\pi$
$79$	−4.26957e8	−1.23328	−0.616641	+	0.787245i	$0.711507\pi$
$80$	0	0
$81$	2.96838e8	0.766190
$82$	−4.26344e8	−1.04135
$83$	5.31242e8	1.22869	0.614343	−	0.789039i	$-0.289421\pi$
$83$	5.31242e8	1.22869	0.614343	+	0.789039i	$0.289421\pi$
$84$	1.68144e8	0.368489
$85$	0	0
$86$	−5.26149e8	−1.03721
$87$	−1.18654e9	−2.22047
$88$	1.97024e8	0.350225
$89$	−1.14168e8	−0.192881	−0.0964404	−	0.995339i	$-0.530746\pi$
$89$	−1.14168e8	−0.192881	−0.0964404	+	0.995339i	$0.530746\pi$
$90$	0	0
$91$	6.31736e7	0.0965716
$92$	6.05833e8	0.881674
$93$	1.01178e9	1.40253
$94$	−8.83231e8	−1.16681
$95$	0	0
$96$	1.36672e9	1.64232
$97$	1.46573e9	1.68105	0.840524	−	0.541774i	$-0.182247\pi$
$97$	1.46573e9	1.68105	0.840524	+	0.541774i	$0.182247\pi$
$98$	8.54829e7	0.0936186
$99$	−6.24424e8	−0.653313
$100$	0	0
$101$	7.53733e8	0.720728	0.360364	−	0.932812i	$-0.382652\pi$
$101$	7.53733e8	0.720728	0.360364	+	0.932812i	$0.382652\pi$
$102$	5.11914e8	0.468270
$103$	1.32143e9	1.15685	0.578425	−	0.815736i	$-0.303668\pi$
$103$	1.32143e9	1.15685	0.578425	+	0.815736i	$0.303668\pi$
$104$	3.13732e8	0.262971
$105$	0	0
$106$	−3.42775e7	−0.0263714
$107$	−1.07364e9	−0.791831	−0.395915	−	0.918287i	$-0.629573\pi$
$107$	−1.07364e9	−0.791831	−0.395915	+	0.918287i	$0.629573\pi$
$108$	−1.26804e9	−0.896864
$109$	1.08650e9	0.737245	0.368623	−	0.929579i	$-0.379830\pi$
$109$	1.08650e9	0.737245	0.368623	+	0.929579i	$0.379830\pi$
$110$	0	0
$111$	3.09453e9	1.93482
$112$	6.54199e7	0.0392852
$113$	−2.85559e9	−1.64757	−0.823783	−	0.566906i	$-0.808140\pi$
$113$	−2.85559e9	−1.64757	−0.823783	+	0.566906i	$0.808140\pi$
$114$	−5.67751e8	−0.314837
$115$	0	0
$116$	1.44580e9	0.741392
$117$	−9.94305e8	−0.490550
$118$	−2.50083e9	−1.18745
$119$	−3.45750e8	−0.158052
$120$	0	0
$121$	−2.08492e9	−0.884209
$122$	−9.93753e8	−0.406125
$123$	−6.89281e9	−2.71534
$124$	−1.23285e9	−0.468289
$125$	0	0
$126$	−1.34544e9	−0.475549
$127$	3.86082e9	1.31693	0.658465	−	0.752611i	$-0.271206\pi$
$127$	3.86082e9	1.31693	0.658465	+	0.752611i	$0.271206\pi$
$128$	−1.45849e9	−0.480240
$129$	−8.50639e9	−2.70453
$130$	0	0
$131$	4.01900e8	0.119233	0.0596166	−	0.998221i	$-0.481012\pi$
$131$	4.01900e8	0.119233	0.0596166	+	0.998221i	$0.481012\pi$
$132$	1.15716e9	0.331750
$133$	3.83463e8	0.106265
$134$	2.31707e9	0.620822
$135$	0	0
$136$	−1.71706e9	−0.430388
$137$	−3.04172e9	−0.737695	−0.368847	−	0.929490i	$-0.620247\pi$
$137$	−3.04172e9	−0.737695	−0.368847	+	0.929490i	$0.620247\pi$
$138$	−7.37262e9	−1.73048
$139$	8.36421e8	0.190046	0.0950229	−	0.995475i	$-0.469708\pi$
$139$	8.36421e8	0.190046	0.0950229	+	0.995475i	$0.469708\pi$
$140$	0	0
$141$	−1.42794e10	−3.04246
$142$	1.03068e9	0.212728
$143$	4.34758e8	0.0869431
$144$	−1.02966e9	−0.199555
$145$	0	0
$146$	1.16172e9	0.211598
$147$	1.38202e9	0.244111
$148$	−3.77069e9	−0.646016
$149$	−7.76217e9	−1.29016	−0.645082	−	0.764114i	$-0.723177\pi$
$149$	−7.76217e9	−1.29016	−0.645082	+	0.764114i	$0.723177\pi$
$150$	0	0
$151$	8.38042e9	1.31181	0.655903	−	0.754846i	$-0.272288\pi$
$151$	8.38042e9	1.31181	0.655903	+	0.754846i	$0.272288\pi$
$152$	1.90435e9	0.289367
$153$	5.44184e9	0.802850
$154$	5.88290e8	0.0842845
$155$	0	0
$156$	1.84261e9	0.249099
$157$	8.49699e9	1.11613	0.558067	−	0.829796i	$-0.311543\pi$
$157$	8.49699e9	1.11613	0.558067	+	0.829796i	$0.311543\pi$
$158$	−6.33110e9	−0.808206
$159$	−5.54173e8	−0.0687636
$160$	0	0
$161$	4.97952e9	0.584078
$162$	4.40163e9	0.502107
$163$	−4.25863e9	−0.472526	−0.236263	−	0.971689i	$-0.575923\pi$
$163$	−4.25863e9	−0.472526	−0.236263	+	0.971689i	$0.575923\pi$
$164$	8.39891e9	0.906621
$165$	0	0
$166$	7.87749e9	0.805195
$167$	−9.23536e8	−0.0918818	−0.0459409	−	0.998944i	$-0.514629\pi$
$167$	−9.23536e8	−0.0918818	−0.0459409	+	0.998944i	$0.514629\pi$
$168$	6.86339e9	0.664732
$169$	−9.91221e9	−0.934717
$170$	0	0
$171$	−6.03541e9	−0.539789
$172$	1.03651e10	0.903012
$173$	4.76006e9	0.404022	0.202011	−	0.979383i	$-0.435252\pi$
$173$	4.76006e9	0.404022	0.202011	+	0.979383i	$0.435252\pi$
$174$	−1.75945e10	−1.45514
$175$	0	0
$176$	4.50217e8	0.0353683
$177$	−4.04315e10	−3.09628
$178$	−1.69293e9	−0.126401
$179$	−9.47187e9	−0.689599	−0.344800	−	0.938676i	$-0.612053\pi$
$179$	−9.47187e9	−0.689599	−0.344800	+	0.938676i	$0.612053\pi$
$180$	0	0
$181$	−7.85395e9	−0.543919	−0.271960	−	0.962309i	$-0.587672\pi$
$181$	−7.85395e9	−0.543919	−0.271960	+	0.962309i	$0.587672\pi$
$182$	9.36766e8	0.0632863
$183$	−1.60663e10	−1.05897
$184$	2.47292e10	1.59049
$185$	0	0
$186$	1.50031e10	0.919120
$187$	−2.37944e9	−0.142294
$188$	1.73995e10	1.01584
$189$	−1.04224e10	−0.594141
$190$	0	0
$191$	1.78210e10	0.968909	0.484454	−	0.874817i	$-0.339018\pi$
$191$	1.78210e10	0.968909	0.484454	+	0.874817i	$0.339018\pi$
$192$	2.36107e10	1.25387
$193$	1.93101e9	0.100179	0.0500894	−	0.998745i	$-0.484049\pi$
$193$	1.93101e9	0.100179	0.0500894	+	0.998745i	$0.484049\pi$
$194$	2.17344e10	1.10164
$195$	0	0
$196$	−1.68400e9	−0.0815061
$197$	−3.24598e10	−1.53549	−0.767746	−	0.640755i	$-0.778622\pi$
$197$	−3.24598e10	−1.53549	−0.767746	+	0.640755i	$0.778622\pi$
$198$	−9.25923e9	−0.428136
$199$	−2.75463e10	−1.24516	−0.622578	−	0.782558i	$-0.713915\pi$
$199$	−2.75463e10	−1.24516	−0.622578	+	0.782558i	$0.713915\pi$
$200$	0	0
$201$	3.74606e10	1.61880
$202$	1.11767e10	0.472315
$203$	1.18835e10	0.491146
$204$	−1.00846e10	−0.407684
$205$	0	0
$206$	1.95947e10	0.758118
$207$	−7.83738e10	−2.96691
$208$	7.16904e8	0.0265568
$209$	2.63897e9	0.0956702
$210$	0	0
$211$	1.94450e10	0.675362	0.337681	−	0.941261i	$-0.390357\pi$
$211$	1.94450e10	0.675362	0.337681	+	0.941261i	$0.390357\pi$
$212$	6.75261e8	0.0229594
$213$	1.66632e10	0.554690
$214$	−1.59204e10	−0.518911
$215$	0	0
$216$	−5.17595e10	−1.61789
$217$	−1.01332e10	−0.310225
$218$	1.61111e10	0.483139
$219$	1.87818e10	0.551744
$220$	0	0
$221$	−3.78891e9	−0.106844
$222$	4.58870e10	1.26795
$223$	4.90459e10	1.32810	0.664050	−	0.747688i	$-0.268836\pi$
$223$	4.90459e10	1.32810	0.664050	+	0.747688i	$0.268836\pi$
$224$	−1.36880e10	−0.363265
$225$	0	0
$226$	−4.23439e10	−1.07970
$227$	6.87990e10	1.71975	0.859876	−	0.510503i	$-0.170541\pi$
$227$	6.87990e10	1.71975	0.859876	+	0.510503i	$0.170541\pi$
$228$	1.11846e10	0.274103
$229$	−3.08456e9	−0.0741198	−0.0370599	−	0.999313i	$-0.511799\pi$
$229$	−3.08456e9	−0.0741198	−0.0370599	+	0.999313i	$0.511799\pi$
$230$	0	0
$231$	9.51103e9	0.219773
$232$	5.90154e10	1.33743
$233$	1.48643e10	0.330402	0.165201	−	0.986260i	$-0.447173\pi$
$233$	1.48643e10	0.330402	0.165201	+	0.986260i	$0.447173\pi$
$234$	−1.47440e10	−0.321472
$235$	0	0
$236$	4.92659e10	1.03381
$237$	−1.02357e11	−2.10741
$238$	−5.12693e9	−0.103576
$239$	4.06416e10	0.805713	0.402857	−	0.915263i	$-0.368017\pi$
$239$	4.06416e10	0.805713	0.402857	+	0.915263i	$0.368017\pi$
$240$	0	0
$241$	−2.09799e10	−0.400615	−0.200308	−	0.979733i	$-0.564194\pi$
$241$	−2.09799e10	−0.400615	−0.200308	+	0.979733i	$0.564194\pi$
$242$	−3.09161e10	−0.579449
$243$	−1.42788e10	−0.262701
$244$	1.95768e10	0.353580
$245$	0	0
$246$	−1.02210e11	−1.77944
$247$	4.20218e9	0.0718354
$248$	−5.03232e10	−0.844765
$249$	1.27357e11	2.09955
$250$	0	0
$251$	−9.95566e10	−1.58321	−0.791605	−	0.611034i	$-0.790754\pi$
$251$	−9.95566e10	−1.58321	−0.791605	+	0.611034i	$0.790754\pi$
$252$	2.65049e10	0.414022
$253$	3.42688e10	0.525844
$254$	5.72499e10	0.863024
$255$	0	0
$256$	−7.20522e10	−1.04850
$257$	1.30781e11	1.87002	0.935009	−	0.354624i	$-0.115391\pi$
$257$	1.30781e11	1.87002	0.935009	+	0.354624i	$0.115391\pi$
$258$	−1.26136e11	−1.77236
$259$	−3.09924e10	−0.427963
$260$	0	0
$261$	−1.87037e11	−2.49485
$262$	5.95954e9	0.0781371
$263$	3.27938e10	0.422660	0.211330	−	0.977415i	$-0.432221\pi$
$263$	3.27938e10	0.422660	0.211330	+	0.977415i	$0.432221\pi$
$264$	4.72335e10	0.598456
$265$	0	0
$266$	5.68615e9	0.0696387
$267$	−2.73700e10	−0.329591
$268$	−4.56459e10	−0.540499
$269$	7.47690e9	0.0870636	0.0435318	−	0.999052i	$-0.486139\pi$
$269$	7.47690e9	0.0870636	0.0435318	+	0.999052i	$0.486139\pi$
$270$	0	0
$271$	6.72735e9	0.0757674	0.0378837	−	0.999282i	$-0.487938\pi$
$271$	6.72735e9	0.0757674	0.0378837	+	0.999282i	$0.487938\pi$
$272$	−3.92363e9	−0.0434638
$273$	1.51449e10	0.165020
$274$	−4.51039e10	−0.483434
$275$	0	0
$276$	1.45239e11	1.50659
$277$	1.52676e11	1.55815	0.779077	−	0.626928i	$-0.215688\pi$
$277$	1.52676e11	1.55815	0.779077	+	0.626928i	$0.215688\pi$
$278$	1.24028e10	0.124543
$279$	1.59489e11	1.57583
$280$	0	0
$281$	3.09796e10	0.296413	0.148206	−	0.988956i	$-0.452650\pi$
$281$	3.09796e10	0.296413	0.148206	+	0.988956i	$0.452650\pi$
$282$	−2.11741e11	−1.99381
$283$	8.92078e10	0.826731	0.413365	−	0.910565i	$-0.364353\pi$
$283$	8.92078e10	0.826731	0.413365	+	0.910565i	$0.364353\pi$
$284$	−2.03041e10	−0.185205
$285$	0	0
$286$	6.44678e9	0.0569765
$287$	6.90331e10	0.600605
$288$	2.15439e11	1.84526
$289$	−9.78512e10	−0.825136
$290$	0	0
$291$	3.51386e11	2.87254
$292$	−2.28856e10	−0.184221
$293$	−6.30090e10	−0.499457	−0.249728	−	0.968316i	$-0.580341\pi$
$293$	−6.30090e10	−0.499457	−0.249728	+	0.968316i	$0.580341\pi$
$294$	2.04933e10	0.159973
$295$	0	0
$296$	−1.53914e11	−1.16537
$297$	−7.17265e10	−0.534904
$298$	−1.15101e11	−0.845483
$299$	5.45681e10	0.394838
$300$	0	0
$301$	8.51934e10	0.598214
$302$	1.24268e11	0.859665
$303$	1.80696e11	1.23157
$304$	4.35160e9	0.0292225
$305$	0	0
$306$	8.06939e10	0.526132
$307$	1.22461e11	0.786821	0.393411	−	0.919363i	$-0.371295\pi$
$307$	1.22461e11	0.786821	0.393411	+	0.919363i	$0.371295\pi$
$308$	−1.15892e10	−0.0733797
$309$	3.16793e11	1.97680
$310$	0	0
$311$	2.77926e11	1.68464	0.842321	−	0.538975i	$-0.181188\pi$
$311$	2.77926e11	1.68464	0.842321	+	0.538975i	$0.181188\pi$
$312$	7.52125e10	0.449360
$313$	−1.22493e11	−0.721374	−0.360687	−	0.932687i	$-0.617458\pi$
$313$	−1.22493e11	−0.721374	−0.360687	+	0.932687i	$0.617458\pi$
$314$	1.25997e11	0.731436
$315$	0	0
$316$	1.24722e11	0.703639
$317$	−2.32000e11	−1.29039	−0.645197	−	0.764016i	$-0.723225\pi$
$317$	−2.32000e11	−1.29039	−0.645197	+	0.764016i	$0.723225\pi$
$318$	−8.21752e9	−0.0450628
$319$	8.17814e10	0.442177
$320$	0	0
$321$	−2.57390e11	−1.35306
$322$	7.38384e10	0.382764
$323$	−2.29986e10	−0.117568
$324$	−8.67115e10	−0.437144
$325$	0	0
$326$	−6.31487e10	−0.309660
$327$	2.60473e11	1.25979
$328$	3.42831e11	1.63549
$329$	1.43012e11	0.672961
$330$	0	0
$331$	−3.74253e11	−1.71372	−0.856859	−	0.515551i	$-0.827587\pi$
$331$	−3.74253e11	−1.71372	−0.856859	+	0.515551i	$0.827587\pi$
$332$	−1.55185e11	−0.701018
$333$	4.87797e11	2.17390
$334$	−1.36946e10	−0.0602129
$335$	0	0
$336$	1.56834e10	0.0671297
$337$	−3.35878e11	−1.41856	−0.709280	−	0.704927i	$-0.750980\pi$
$337$	−3.35878e11	−1.41856	−0.709280	+	0.704927i	$0.750980\pi$
$338$	−1.46982e11	−0.612548
$339$	−6.84585e11	−2.81533
$340$	0	0
$341$	−6.97361e10	−0.279295
$342$	−8.94956e10	−0.353740
$343$	−1.38413e10	−0.0539949
$344$	4.23086e11	1.62898
$345$	0	0
$346$	7.05842e10	0.264768
$347$	3.63698e11	1.34666	0.673331	−	0.739341i	$-0.264863\pi$
$347$	3.63698e11	1.34666	0.673331	+	0.739341i	$0.264863\pi$
$348$	3.46609e11	1.26687
$349$	1.08740e11	0.392350	0.196175	−	0.980569i	$-0.437148\pi$
$349$	1.08740e11	0.392350	0.196175	+	0.980569i	$0.437148\pi$
$350$	0	0
$351$	−1.14214e11	−0.401640
$352$	−9.42002e10	−0.327047
$353$	3.36249e11	1.15259	0.576296	−	0.817241i	$-0.304498\pi$
$353$	3.36249e11	1.15259	0.576296	+	0.817241i	$0.304498\pi$
$354$	−5.99535e11	−2.02908
$355$	0	0
$356$	3.33505e10	0.110047
$357$	−8.28884e10	−0.270077
$358$	−1.40453e11	−0.451915
$359$	5.49944e11	1.74741	0.873703	−	0.486460i	$-0.161712\pi$
$359$	5.49944e11	1.74741	0.873703	+	0.486460i	$0.161712\pi$
$360$	0	0
$361$	−2.97181e11	−0.920954
$362$	−1.16462e11	−0.356447
$363$	−4.99828e11	−1.51092
$364$	−1.84541e10	−0.0550982
$365$	0	0
$366$	−2.38237e11	−0.693977
$367$	1.32204e11	0.380405	0.190203	−	0.981745i	$-0.439086\pi$
$367$	1.32204e11	0.380405	0.190203	+	0.981745i	$0.439086\pi$
$368$	5.65084e10	0.160619
$369$	−1.08653e12	−3.05086
$370$	0	0
$371$	5.55017e9	0.0152098
$372$	−2.95558e11	−0.800203
$373$	−4.88064e11	−1.30553	−0.652765	−	0.757560i	$-0.726391\pi$
$373$	−4.88064e11	−1.30553	−0.652765	+	0.757560i	$0.726391\pi$
$374$	−3.52833e10	−0.0932496
$375$	0	0
$376$	7.10222e11	1.83252
$377$	1.30225e11	0.332015
$378$	−1.54548e11	−0.389359
$379$	3.00162e11	0.747274	0.373637	−	0.927575i	$-0.378111\pi$
$379$	3.00162e11	0.747274	0.373637	+	0.927575i	$0.378111\pi$
$380$	0	0
$381$	9.25574e11	2.25034
$382$	2.64258e11	0.634955
$383$	−7.74202e11	−1.83848	−0.919241	−	0.393694i	$-0.871197\pi$
$383$	−7.74202e11	−1.83848	−0.919241	+	0.393694i	$0.871197\pi$
$384$	−3.49651e11	−0.820623
$385$	0	0
$386$	2.86338e10	0.0656501
$387$	−1.34088e12	−3.03872
$388$	−4.28165e11	−0.959109
$389$	−1.70127e11	−0.376703	−0.188352	−	0.982102i	$-0.560314\pi$
$389$	−1.70127e11	−0.376703	−0.188352	+	0.982102i	$0.560314\pi$
$390$	0	0
$391$	−2.98652e11	−0.646204
$392$	−6.87383e10	−0.147032
$393$	9.63495e10	0.203743
$394$	−4.81327e11	−1.00625
$395$	0	0
$396$	1.82405e11	0.372743
$397$	5.47242e11	1.10566	0.552831	−	0.833293i	$-0.313548\pi$
$397$	5.47242e11	1.10566	0.552831	+	0.833293i	$0.313548\pi$
$398$	−4.08468e11	−0.815988
$399$	9.19294e10	0.181584
$400$	0	0
$401$	−4.57174e11	−0.882941	−0.441471	−	0.897276i	$-0.645543\pi$
$401$	−4.57174e11	−0.882941	−0.441471	+	0.897276i	$0.645543\pi$
$402$	5.55483e11	1.06085
$403$	−1.11045e11	−0.209713
$404$	−2.20179e11	−0.411206
$405$	0	0
$406$	1.76213e11	0.321863
$407$	−2.13288e11	−0.385294
$408$	−4.11639e11	−0.735437
$409$	9.42996e10	0.166631	0.0833153	−	0.996523i	$-0.473449\pi$
$409$	9.42996e10	0.166631	0.0833153	+	0.996523i	$0.473449\pi$
$410$	0	0
$411$	−7.29207e11	−1.26056
$412$	−3.86013e11	−0.660032
$413$	4.04930e11	0.684865
$414$	−1.16216e12	−1.94431
$415$	0	0
$416$	−1.50000e11	−0.245568
$417$	2.00519e11	0.324746
$418$	3.91318e10	0.0626955
$419$	1.66874e11	0.264500	0.132250	−	0.991216i	$-0.457780\pi$
$419$	1.66874e11	0.264500	0.132250	+	0.991216i	$0.457780\pi$
$420$	0	0
$421$	−5.52779e11	−0.857594	−0.428797	−	0.903401i	$-0.641062\pi$
$421$	−5.52779e11	−0.857594	−0.428797	+	0.903401i	$0.641062\pi$
$422$	2.88339e11	0.442585
$423$	−2.25089e12	−3.41840
$424$	2.75631e10	0.0414174
$425$	0	0
$426$	2.47089e11	0.363505
$427$	1.60907e11	0.234234
$428$	3.13630e11	0.451773
$429$	1.04227e11	0.148567
$430$	0	0
$431$	−4.37408e11	−0.610575	−0.305288	−	0.952260i	$-0.598753\pi$
$431$	−4.37408e11	−0.610575	−0.305288	+	0.952260i	$0.598753\pi$
$432$	−1.18275e11	−0.163387
$433$	−2.79837e11	−0.382569	−0.191285	−	0.981535i	$-0.561265\pi$
$433$	−2.79837e11	−0.382569	−0.191285	+	0.981535i	$0.561265\pi$
$434$	−1.50259e11	−0.203300
$435$	0	0
$436$	−3.17387e11	−0.420630
$437$	3.31227e11	0.434470
$438$	2.78504e11	0.361575
$439$	8.87150e11	1.14000	0.570002	−	0.821643i	$-0.306942\pi$
$439$	8.87150e11	1.14000	0.570002	+	0.821643i	$0.306942\pi$
$440$	0	0
$441$	2.17851e11	0.274275
$442$	−5.61835e10	−0.0700178
$443$	5.87852e11	0.725189	0.362594	−	0.931947i	$-0.381891\pi$
$443$	5.87852e11	0.725189	0.362594	+	0.931947i	$0.381891\pi$
$444$	−9.03967e11	−1.10390
$445$	0	0
$446$	7.27274e11	0.870344
$447$	−1.86086e12	−2.20460
$448$	−2.36466e11	−0.277344
$449$	−5.19918e11	−0.603707	−0.301854	−	0.953354i	$-0.597605\pi$
$449$	−5.19918e11	−0.603707	−0.301854	+	0.953354i	$0.597605\pi$
$450$	0	0
$451$	4.75082e11	0.540723
$452$	8.34168e11	0.940006
$453$	2.00908e12	2.24159
$454$	1.02018e12	1.12701
$455$	0	0
$456$	4.56538e11	0.494465
$457$	1.03055e12	1.10521	0.552607	−	0.833442i	$-0.313633\pi$
$457$	1.03055e12	1.10521	0.552607	+	0.833442i	$0.313633\pi$
$458$	−4.57392e10	−0.0485729
$459$	6.25095e11	0.657338
$460$	0	0
$461$	9.37018e11	0.966259	0.483130	−	0.875549i	$-0.339500\pi$
$461$	9.37018e11	0.966259	0.483130	+	0.875549i	$0.339500\pi$
$462$	1.41034e11	0.144024
$463$	−1.08281e12	−1.09506	−0.547529	−	0.836787i	$-0.684431\pi$
$463$	−1.08281e12	−1.09506	−0.547529	+	0.836787i	$0.684431\pi$
$464$	1.34855e11	0.135063
$465$	0	0
$466$	2.20414e11	0.216522
$467$	−1.52419e11	−0.148290	−0.0741451	−	0.997247i	$-0.523623\pi$
$467$	−1.52419e11	−0.148290	−0.0741451	+	0.997247i	$0.523623\pi$
$468$	2.90454e11	0.279879
$469$	−3.75177e11	−0.358062
$470$	0	0
$471$	2.03703e12	1.90723
$472$	2.01096e12	1.86494
$473$	5.86297e11	0.538570
$474$	−1.51779e12	−1.38105
$475$	0	0
$476$	1.01000e11	0.0901756
$477$	−8.73554e10	−0.0772604
$478$	6.02652e11	0.528008
$479$	−2.02244e11	−0.175535	−0.0877677	−	0.996141i	$-0.527973\pi$
$479$	−2.02244e11	−0.175535	−0.0877677	+	0.996141i	$0.527973\pi$
$480$	0	0
$481$	−3.39631e11	−0.289304
$482$	−3.11099e11	−0.262535
$483$	1.19376e12	0.998060
$484$	6.09042e11	0.504479
$485$	0	0
$486$	−2.11732e11	−0.172156
$487$	−8.35572e11	−0.673137	−0.336568	−	0.941659i	$-0.609266\pi$
$487$	−8.35572e11	−0.673137	−0.336568	+	0.941659i	$0.609266\pi$
$488$	7.99094e11	0.637836
$489$	−1.02094e12	−0.807442
$490$	0	0
$491$	−1.06242e12	−0.824953	−0.412476	−	0.910968i	$-0.635336\pi$
$491$	−1.06242e12	−0.824953	−0.412476	+	0.910968i	$0.635336\pi$
$492$	2.01351e12	1.54921
$493$	−7.12723e11	−0.543387
$494$	6.23117e10	0.0470759
$495$	0	0
$496$	−1.14993e11	−0.0853108
$497$	−1.66886e11	−0.122692
$498$	1.88851e12	1.37590
$499$	−3.33938e11	−0.241109	−0.120554	−	0.992707i	$-0.538467\pi$
$499$	−3.33938e11	−0.241109	−0.120554	+	0.992707i	$0.538467\pi$
$500$	0	0
$501$	−2.21404e11	−0.157006
$502$	−1.47627e12	−1.03752
$503$	3.60934e11	0.251404	0.125702	−	0.992068i	$-0.459882\pi$
$503$	3.60934e11	0.251404	0.125702	+	0.992068i	$0.459882\pi$
$504$	1.08189e12	0.746870
$505$	0	0
$506$	5.08152e11	0.344601
$507$	−2.37630e12	−1.59723
$508$	−1.12781e12	−0.751365
$509$	4.09926e11	0.270692	0.135346	−	0.990798i	$-0.456785\pi$
$509$	4.09926e11	0.270692	0.135346	+	0.990798i	$0.456785\pi$
$510$	0	0
$511$	−1.88104e11	−0.122040
$512$	−3.21676e11	−0.206873
$513$	−6.93277e11	−0.441955
$514$	1.93928e12	1.22548
$515$	0	0
$516$	2.48487e12	1.54305
$517$	9.84199e11	0.605865
$518$	−4.59569e11	−0.280457
$519$	1.14115e12	0.690384
$520$	0	0
$521$	−1.09884e12	−0.653377	−0.326688	−	0.945132i	$-0.605933\pi$
$521$	−1.09884e12	−0.653377	−0.326688	+	0.945132i	$0.605933\pi$
$522$	−2.77346e12	−1.63495
$523$	−2.97552e12	−1.73902	−0.869511	−	0.493914i	$-0.835566\pi$
$523$	−2.97552e12	−1.73902	−0.869511	+	0.493914i	$0.835566\pi$
$524$	−1.17402e11	−0.0680276
$525$	0	0
$526$	4.86280e11	0.276982
$527$	6.07748e11	0.343223
$528$	1.07933e11	0.0604367
$529$	2.50005e12	1.38803
$530$	0	0
$531$	−6.37329e12	−3.47887
$532$	−1.12016e11	−0.0606288
$533$	7.56500e11	0.406010
$534$	−4.05855e11	−0.215991
$535$	0	0
$536$	−1.86320e12	−0.975028
$537$	−2.27074e12	−1.17837
$538$	1.10871e11	0.0570554
$539$	−9.52551e10	−0.0486115
$540$	0	0
$541$	2.97095e12	1.49110	0.745551	−	0.666449i	$-0.232187\pi$
$541$	2.97095e12	1.49110	0.745551	+	0.666449i	$0.232187\pi$
$542$	9.97561e10	0.0496527
$543$	−1.88287e12	−0.929438
$544$	8.20952e11	0.401904
$545$	0	0
$546$	2.24576e11	0.108142
$547$	1.50514e12	0.718842	0.359421	−	0.933176i	$-0.382974\pi$
$547$	1.50514e12	0.718842	0.359421	+	0.933176i	$0.382974\pi$
$548$	8.88540e11	0.420886
$549$	−2.53256e12	−1.18983
$550$	0	0
$551$	7.90463e11	0.365342
$552$	5.92845e12	2.71779
$553$	1.02512e12	0.466136
$554$	2.26394e12	1.02111
$555$	0	0
$556$	−2.44333e11	−0.108429
$557$	2.17354e12	0.956797	0.478399	−	0.878143i	$-0.341217\pi$
$557$	2.17354e12	0.956797	0.478399	+	0.878143i	$0.341217\pi$
$558$	2.36496e12	1.03269
$559$	9.33593e11	0.404394
$560$	0	0
$561$	−5.70434e11	−0.243149
$562$	4.59379e11	0.194248
$563$	−1.40104e12	−0.587710	−0.293855	−	0.955850i	$-0.594938\pi$
$563$	−1.40104e12	−0.587710	−0.293855	+	0.955850i	$0.594938\pi$
$564$	4.17127e12	1.73585
$565$	0	0
$566$	1.32281e12	0.541781
$567$	−7.12707e11	−0.289592
$568$	−8.28784e11	−0.334098
$569$	−1.81226e12	−0.724795	−0.362397	−	0.932024i	$-0.618042\pi$
$569$	−1.81226e12	−0.724795	−0.362397	+	0.932024i	$0.618042\pi$
$570$	0	0
$571$	−3.38885e12	−1.33410	−0.667052	−	0.745012i	$-0.732444\pi$
$571$	−3.38885e12	−1.33410	−0.667052	+	0.745012i	$0.732444\pi$
$572$	−1.27001e11	−0.0496048
$573$	4.27233e12	1.65565
$574$	1.02365e12	0.393594
$575$	0	0
$576$	3.72180e12	1.40881
$577$	−2.86129e12	−1.07466	−0.537329	−	0.843373i	$-0.680567\pi$
$577$	−2.86129e12	−1.07466	−0.537329	+	0.843373i	$0.680567\pi$
$578$	−1.45098e12	−0.540737
$579$	4.62930e11	0.171183
$580$	0	0
$581$	−1.27551e12	−0.464400
$582$	5.21050e12	1.88246
$583$	3.81960e10	0.0136933
$584$	−9.34156e11	−0.332324
$585$	0	0
$586$	−9.34324e11	−0.327309
$587$	7.85729e11	0.273150	0.136575	−	0.990630i	$-0.456391\pi$
$587$	7.85729e11	0.273150	0.136575	+	0.990630i	$0.456391\pi$
$588$	−4.03714e11	−0.139276
$589$	−6.74039e11	−0.230763
$590$	0	0
$591$	−7.78174e12	−2.62382
$592$	−3.51707e11	−0.117688
$593$	−8.24271e11	−0.273731	−0.136865	−	0.990590i	$-0.543703\pi$
$593$	−8.24271e11	−0.273731	−0.136865	+	0.990590i	$0.543703\pi$
$594$	−1.06359e12	−0.350538
$595$	0	0
$596$	2.26747e12	0.736093
$597$	−6.60380e12	−2.12770
$598$	8.09159e11	0.258749
$599$	−2.60594e10	−0.00827073	−0.00413537	−	0.999991i	$-0.501316\pi$
$599$	−2.60594e10	−0.00827073	−0.00413537	+	0.999991i	$0.501316\pi$
$600$	0	0
$601$	1.90372e11	0.0595207	0.0297603	−	0.999557i	$-0.490526\pi$
$601$	1.90372e11	0.0595207	0.0297603	+	0.999557i	$0.490526\pi$
$602$	1.26328e12	0.392028
$603$	5.90499e12	1.81883
$604$	−2.44807e12	−0.748441
$605$	0	0
$606$	2.67944e12	0.807082
$607$	−1.77675e12	−0.531222	−0.265611	−	0.964080i	$-0.585574\pi$
$607$	−1.77675e12	−0.531222	−0.265611	+	0.964080i	$0.585574\pi$
$608$	−9.10497e11	−0.270217
$609$	2.84888e12	0.839260
$610$	0	0
$611$	1.56719e12	0.454922
$612$	−1.58966e12	−0.458060
$613$	2.48518e11	0.0710863	0.0355431	−	0.999368i	$-0.488684\pi$
$613$	2.48518e11	0.0710863	0.0355431	+	0.999368i	$0.488684\pi$
$614$	1.81591e12	0.515628
$615$	0	0
$616$	−4.73054e11	−0.132372
$617$	−3.52347e12	−0.978786	−0.489393	−	0.872063i	$-0.662782\pi$
$617$	−3.52347e12	−0.978786	−0.489393	+	0.872063i	$0.662782\pi$
$618$	4.69755e12	1.29546
$619$	−6.69712e12	−1.83350	−0.916748	−	0.399466i	$-0.869196\pi$
$619$	−6.69712e12	−1.83350	−0.916748	+	0.399466i	$0.869196\pi$
$620$	0	0
$621$	−9.00266e12	−2.42917
$622$	4.12121e12	1.10400
$623$	2.74117e11	0.0729021
$624$	1.71867e11	0.0453798
$625$	0	0
$626$	−1.81637e12	−0.472738
$627$	6.32654e11	0.163479
$628$	−2.48212e12	−0.636802
$629$	1.85880e12	0.473484
$630$	0	0
$631$	6.29917e11	0.158180	0.0790900	−	0.996867i	$-0.474799\pi$
$631$	6.29917e11	0.158180	0.0790900	+	0.996867i	$0.474799\pi$
$632$	5.09095e12	1.26932
$633$	4.66165e12	1.15404
$634$	−3.44020e12	−0.845634
$635$	0	0
$636$	1.61884e11	0.0392325
$637$	−1.51680e11	−0.0365006
$638$	1.21269e12	0.289772
$639$	2.62665e12	0.623231
$640$	0	0
$641$	2.82049e12	0.659877	0.329938	−	0.944002i	$-0.392972\pi$
$641$	2.82049e12	0.659877	0.329938	+	0.944002i	$0.392972\pi$
$642$	−3.81668e12	−0.886704
$643$	−7.19804e12	−1.66060	−0.830300	−	0.557317i	$-0.811831\pi$
$643$	−7.19804e12	−1.66060	−0.830300	+	0.557317i	$0.811831\pi$
$644$	−1.45461e12	−0.333241
$645$	0	0
$646$	−3.41033e11	−0.0770459
$647$	−7.17803e12	−1.61041	−0.805204	−	0.592998i	$-0.797944\pi$
$647$	−7.17803e12	−1.61041	−0.805204	+	0.592998i	$0.797944\pi$
$648$	−3.53943e12	−0.788580
$649$	2.78671e12	0.616582
$650$	0	0
$651$	−2.42928e12	−0.530106
$652$	1.24402e12	0.269596
$653$	1.54599e12	0.332734	0.166367	−	0.986064i	$-0.446796\pi$
$653$	1.54599e12	0.332734	0.166367	+	0.986064i	$0.446796\pi$
$654$	3.86240e12	0.825578
$655$	0	0
$656$	7.83398e11	0.165164
$657$	2.96061e12	0.619921
$658$	2.12064e12	0.441011
$659$	2.38624e12	0.492868	0.246434	−	0.969160i	$-0.420741\pi$
$659$	2.38624e12	0.492868	0.246434	+	0.969160i	$0.420741\pi$
$660$	0	0
$661$	−2.35488e12	−0.479802	−0.239901	−	0.970797i	$-0.577115\pi$
$661$	−2.35488e12	−0.479802	−0.239901	+	0.970797i	$0.577115\pi$
$662$	−5.54958e12	−1.12305
$663$	−9.08333e11	−0.182572
$664$	−6.33443e12	−1.26459
$665$	0	0
$666$	7.23326e12	1.42462
$667$	1.02647e13	2.00807
$668$	2.69781e11	0.0524225
$669$	1.17580e13	2.26943
$670$	0	0
$671$	1.10736e12	0.210880
$672$	−3.28149e12	−0.620740
$673$	6.32709e12	1.18887	0.594437	−	0.804142i	$-0.297375\pi$
$673$	6.32709e12	1.18887	0.594437	+	0.804142i	$0.297375\pi$
$674$	−4.98055e12	−0.929625
$675$	0	0
$676$	2.89553e12	0.533296
$677$	−3.16670e12	−0.579372	−0.289686	−	0.957122i	$-0.593551\pi$
$677$	−3.16670e12	−0.579372	−0.289686	+	0.957122i	$0.593551\pi$
$678$	−1.01513e13	−1.84497
$679$	−3.51921e12	−0.635376
$680$	0	0
$681$	1.64935e13	2.93868
$682$	−1.03408e12	−0.183030
$683$	6.06916e12	1.06717	0.533587	−	0.845745i	$-0.320844\pi$
$683$	6.06916e12	1.06717	0.533587	+	0.845745i	$0.320844\pi$
$684$	1.76305e12	0.307973
$685$	0	0
$686$	−2.05245e11	−0.0353845
$687$	−7.39478e11	−0.126654
$688$	9.66788e11	0.164507
$689$	6.08216e10	0.0102818
$690$	0	0
$691$	−1.36410e12	−0.227611	−0.113806	−	0.993503i	$-0.536304\pi$
$691$	−1.36410e12	−0.227611	−0.113806	+	0.993503i	$0.536304\pi$
$692$	−1.39050e12	−0.230512
$693$	1.49924e12	0.246929
$694$	5.39307e12	0.882508
$695$	0	0
$696$	1.41481e13	2.28536
$697$	−4.14033e12	−0.664489
$698$	1.61244e12	0.257119
$699$	3.56349e12	0.564584
$700$	0	0
$701$	4.27032e12	0.667927	0.333964	−	0.942586i	$-0.391614\pi$
$701$	4.27032e12	0.667927	0.333964	+	0.942586i	$0.391614\pi$
$702$	−1.69361e12	−0.263207
$703$	−2.06155e12	−0.318343
$704$	−1.62735e12	−0.249692
$705$	0	0
$706$	4.98605e12	0.755328
$707$	−1.80971e12	−0.272410
$708$	1.18108e13	1.76656
$709$	4.76449e12	0.708122	0.354061	−	0.935222i	$-0.384800\pi$
$709$	4.76449e12	0.708122	0.354061	+	0.935222i	$0.384800\pi$
$710$	0	0
$711$	−1.61347e13	−2.36781
$712$	1.36132e12	0.198517
$713$	−8.75284e12	−1.26837
$714$	−1.22910e12	−0.176989
$715$	0	0
$716$	2.76690e12	0.393446
$717$	9.74323e12	1.37679
$718$	8.15481e12	1.14513
$719$	−2.64192e12	−0.368671	−0.184336	−	0.982863i	$-0.559013\pi$
$719$	−2.64192e12	−0.368671	−0.184336	+	0.982863i	$0.559013\pi$
$720$	0	0
$721$	−3.17276e12	−0.437248
$722$	−4.40672e12	−0.603529
$723$	−5.02963e12	−0.684563
$724$	2.29428e12	0.310329
$725$	0	0
$726$	−7.41167e12	−0.990150
$727$	3.54861e12	0.471144	0.235572	−	0.971857i	$-0.424304\pi$
$727$	3.54861e12	0.471144	0.235572	+	0.971857i	$0.424304\pi$
$728$	−7.53270e11	−0.0993938
$729$	−9.26577e12	−1.21509
$730$	0	0
$731$	−5.10956e12	−0.661844
$732$	4.69324e12	0.604189
$733$	1.34909e13	1.72613	0.863063	−	0.505095i	$-0.168543\pi$
$733$	1.34909e13	1.72613	0.863063	+	0.505095i	$0.168543\pi$
$734$	1.96037e12	0.249291
$735$	0	0
$736$	−1.18234e13	−1.48523
$737$	−2.58195e12	−0.322362
$738$	−1.61115e13	−1.99932
$739$	−1.33151e13	−1.64227	−0.821133	−	0.570736i	$-0.806658\pi$
$739$	−1.33151e13	−1.64227	−0.821133	+	0.570736i	$0.806658\pi$
$740$	0	0
$741$	1.00741e12	0.122751
$742$	8.23003e10	0.00996744
$743$	−1.37811e13	−1.65896	−0.829479	−	0.558538i	$-0.811363\pi$
$743$	−1.37811e13	−1.65896	−0.829479	+	0.558538i	$0.811363\pi$
$744$	−1.20642e13	−1.44352
$745$	0	0
$746$	−7.23722e12	−0.855553
$747$	2.00756e13	2.35899
$748$	6.95075e11	0.0811848
$749$	2.57781e12	0.299284
$750$	0	0
$751$	−1.31166e12	−0.150467	−0.0752334	−	0.997166i	$-0.523970\pi$
$751$	−1.31166e12	−0.150467	−0.0752334	+	0.997166i	$0.523970\pi$
$752$	1.62292e12	0.185062
$753$	−2.38672e13	−2.70535
$754$	1.93103e12	0.217580
$755$	0	0
$756$	3.04457e12	0.338983
$757$	−1.31405e13	−1.45439	−0.727196	−	0.686430i	$-0.759177\pi$
$757$	−1.31405e13	−1.45439	−0.727196	+	0.686430i	$0.759177\pi$
$758$	4.45093e12	0.489711
$759$	8.21543e12	0.898551
$760$	0	0
$761$	4.85816e12	0.525099	0.262549	−	0.964919i	$-0.415437\pi$
$761$	4.85816e12	0.525099	0.262549	+	0.964919i	$0.415437\pi$
$762$	1.37248e13	1.47472
$763$	−2.60869e12	−0.278652
$764$	−5.20584e12	−0.552804
$765$	0	0
$766$	−1.14802e13	−1.20481
$767$	4.43743e12	0.462970
$768$	−1.72735e13	−1.79165
$769$	−1.57384e13	−1.62290	−0.811452	−	0.584420i	$-0.801322\pi$
$769$	−1.57384e13	−1.62290	−0.811452	+	0.584420i	$0.801322\pi$
$770$	0	0
$771$	3.13528e13	3.19545
$772$	−5.64081e11	−0.0571562
$773$	−1.97088e12	−0.198542	−0.0992710	−	0.995060i	$-0.531651\pi$
$773$	−1.97088e12	−0.198542	−0.0992710	+	0.995060i	$0.531651\pi$
$774$	−1.98831e13	−1.99136
$775$	0	0
$776$	−1.74770e13	−1.73017
$777$	−7.42997e12	−0.731295
$778$	−2.52271e12	−0.246865
$779$	4.59194e12	0.446763
$780$	0	0
$781$	−1.14850e12	−0.110459
$782$	−4.42854e12	−0.423477
$783$	−2.14846e13	−2.04267
$784$	−1.57073e11	−0.0148484
$785$	0	0
$786$	1.42871e12	0.133519
$787$	1.29627e13	1.20451	0.602253	−	0.798306i	$-0.294270\pi$
$787$	1.29627e13	1.20451	0.602253	+	0.798306i	$0.294270\pi$
$788$	9.48207e12	0.876063
$789$	7.86182e12	0.722232
$790$	0	0
$791$	6.85627e12	0.622721
$792$	7.44551e12	0.672405
$793$	1.76330e12	0.158343
$794$	8.11474e12	0.724573
$795$	0	0
$796$	8.04675e12	0.710414
$797$	−1.04429e13	−0.916762	−0.458381	−	0.888756i	$-0.651571\pi$
$797$	−1.04429e13	−0.916762	−0.458381	+	0.888756i	$0.651571\pi$
$798$	1.36317e12	0.118997
$799$	−8.57727e12	−0.744541
$800$	0	0
$801$	−4.31439e12	−0.370317
$802$	−6.77917e12	−0.578618
$803$	−1.29452e12	−0.109872
$804$	−1.09429e13	−0.923594
$805$	0	0
$806$	−1.64662e12	−0.137431
$807$	1.79248e12	0.148772
$808$	−8.98737e12	−0.741791
$809$	−6.99142e12	−0.573848	−0.286924	−	0.957953i	$-0.592633\pi$
$809$	−6.99142e12	−0.573848	−0.286924	+	0.957953i	$0.592633\pi$
$810$	0	0
$811$	−1.14380e13	−0.928442	−0.464221	−	0.885719i	$-0.653666\pi$
$811$	−1.14380e13	−0.928442	−0.464221	+	0.885719i	$0.653666\pi$
$812$	−3.47137e12	−0.280220
$813$	1.61278e12	0.129470
$814$	−3.16273e12	−0.252495
$815$	0	0
$816$	−9.40631e11	−0.0742700
$817$	5.66689e12	0.444985
$818$	1.39831e12	0.109198
$819$	2.38733e12	0.185410
$820$	0	0
$821$	−4.42435e12	−0.339864	−0.169932	−	0.985456i	$-0.554355\pi$
$821$	−4.42435e12	−0.339864	−0.169932	+	0.985456i	$0.554355\pi$
$822$	−1.08130e13	−0.826081
$823$	−1.71948e13	−1.30647	−0.653234	−	0.757156i	$-0.726588\pi$
$823$	−1.71948e13	−1.30647	−0.653234	+	0.757156i	$0.726588\pi$
$824$	−1.57565e13	−1.19066
$825$	0	0
$826$	6.00448e12	0.448813
$827$	−3.04498e12	−0.226365	−0.113182	−	0.993574i	$-0.536104\pi$
$827$	−3.04498e12	−0.226365	−0.113182	+	0.993574i	$0.536104\pi$
$828$	2.28944e13	1.69275
$829$	−8.03416e12	−0.590806	−0.295403	−	0.955373i	$-0.595454\pi$
$829$	−8.03416e12	−0.590806	−0.295403	+	0.955373i	$0.595454\pi$
$830$	0	0
$831$	3.66017e13	2.66254
$832$	−2.59132e12	−0.187485
$833$	8.30146e11	0.0597382
$834$	2.97339e12	0.212816
$835$	0	0
$836$	−7.70891e11	−0.0545839
$837$	1.83202e13	1.29022
$838$	2.47448e12	0.173335
$839$	1.36209e13	0.949020	0.474510	−	0.880250i	$-0.342625\pi$
$839$	1.36209e13	0.949020	0.474510	+	0.880250i	$0.342625\pi$
$840$	0	0
$841$	9.98921e12	0.688571
$842$	−8.19684e12	−0.562007
$843$	7.42689e12	0.506504
$844$	−5.68023e12	−0.385323
$845$	0	0
$846$	−3.33772e13	−2.24018
$847$	5.00589e12	0.334200
$848$	6.29842e10	0.00418264
$849$	2.13862e13	1.41270
$850$	0	0
$851$	−2.67706e13	−1.74975
$852$	−4.86762e12	−0.316474
$853$	−3.64211e12	−0.235549	−0.117775	−	0.993040i	$-0.537576\pi$
$853$	−3.64211e12	−0.235549	−0.117775	+	0.993040i	$0.537576\pi$
$854$	2.38600e12	0.153501
$855$	0	0
$856$	1.28019e13	0.814971
$857$	−1.62518e13	−1.02917	−0.514587	−	0.857438i	$-0.672055\pi$
$857$	−1.62518e13	−1.02917	−0.514587	+	0.857438i	$0.672055\pi$
$858$	1.54552e12	0.0973602
$859$	1.69063e13	1.05944	0.529722	−	0.848171i	$-0.322296\pi$
$859$	1.69063e13	1.05944	0.529722	+	0.848171i	$0.322296\pi$
$860$	0	0
$861$	1.65496e13	1.02630
$862$	−6.48608e12	−0.400128
$863$	1.56857e13	0.962619	0.481310	−	0.876551i	$-0.340161\pi$
$863$	1.56857e13	0.962619	0.481310	+	0.876551i	$0.340161\pi$
$864$	2.47471e13	1.51082
$865$	0	0
$866$	−4.14955e12	−0.250709
$867$	−2.34584e13	−1.40998
$868$	2.96008e12	0.176997
$869$	7.05485e12	0.419661
$870$	0	0
$871$	−4.11138e12	−0.242050
$872$	−1.29553e13	−0.758790
$873$	5.53897e13	3.22749
$874$	4.91158e12	0.284721
$875$	0	0
$876$	−5.48649e12	−0.314794
$877$	−2.37521e13	−1.35583	−0.677914	−	0.735141i	$-0.737116\pi$
$877$	−2.37521e13	−1.35583	−0.677914	+	0.735141i	$0.737116\pi$
$878$	1.31550e13	0.747079
$879$	−1.51055e13	−0.853462
$880$	0	0
$881$	1.13698e13	0.635858	0.317929	−	0.948115i	$-0.397013\pi$
$881$	1.13698e13	0.635858	0.317929	+	0.948115i	$0.397013\pi$
$882$	3.23039e12	0.179741
$883$	1.21711e12	0.0673762	0.0336881	−	0.999432i	$-0.489275\pi$
$883$	1.21711e12	0.0673762	0.0336881	+	0.999432i	$0.489275\pi$
$884$	1.10681e12	0.0609588
$885$	0	0
$886$	8.71692e12	0.475238
$887$	−3.43743e13	−1.86457	−0.932283	−	0.361730i	$-0.882186\pi$
$887$	−3.43743e13	−1.86457	−0.932283	+	0.361730i	$0.882186\pi$
$888$	−3.68986e13	−1.99137
$889$	−9.26983e12	−0.497753
$890$	0	0
$891$	−4.90482e12	−0.260719
$892$	−1.43272e13	−0.757738
$893$	9.51284e12	0.500586
$894$	−2.75937e13	−1.44474
$895$	0	0
$896$	3.50183e12	0.181513
$897$	1.30819e13	0.674690
$898$	−7.70957e12	−0.395627
$899$	−2.08884e13	−1.06656
$900$	0	0
$901$	−3.32877e11	−0.0168276
$902$	7.04472e12	0.354352
$903$	2.04238e13	1.02222
$904$	3.40495e13	1.69571
$905$	0	0
$906$	2.97915e13	1.46898
$907$	3.08586e13	1.51406	0.757030	−	0.653381i	$-0.226650\pi$
$907$	3.08586e13	1.51406	0.757030	+	0.653381i	$0.226650\pi$
$908$	−2.00974e13	−0.981192
$909$	2.84835e13	1.38374
$910$	0	0
$911$	−3.36006e13	−1.61627	−0.808136	−	0.588996i	$-0.799523\pi$
$911$	−3.36006e13	−1.61627	−0.808136	+	0.588996i	$0.799523\pi$
$912$	1.04323e12	0.0499348
$913$	−8.77802e12	−0.418098
$914$	1.52814e13	0.724280
$915$	0	0
$916$	9.01056e11	0.0422885
$917$	−9.64961e11	−0.0450659
$918$	9.26917e12	0.430773
$919$	−1.46200e13	−0.676127	−0.338063	−	0.941123i	$-0.609772\pi$
$919$	−1.46200e13	−0.676127	−0.338063	+	0.941123i	$0.609772\pi$
$920$	0	0
$921$	2.93583e13	1.34450
$922$	1.38945e13	0.633219
$923$	−1.82882e12	−0.0829398
$924$	−2.77834e12	−0.125390
$925$	0	0
$926$	−1.60563e13	−0.717625
$927$	4.99367e13	2.22107
$928$	−2.82162e13	−1.24891
$929$	−1.36244e13	−0.600130	−0.300065	−	0.953919i	$-0.597008\pi$
$929$	−1.36244e13	−0.600130	−0.300065	+	0.953919i	$0.597008\pi$
$930$	0	0
$931$	−9.20694e11	−0.0401644
$932$	−4.34213e12	−0.188508
$933$	6.66287e13	2.87868
$934$	−2.26013e12	−0.0971790
$935$	0	0
$936$	1.18559e13	0.504885
$937$	1.06580e13	0.451697	0.225848	−	0.974162i	$-0.427485\pi$
$937$	1.06580e13	0.451697	0.225848	+	0.974162i	$0.427485\pi$
$938$	−5.56328e12	−0.234649
$939$	−2.93658e13	−1.23267
$940$	0	0
$941$	1.54253e13	0.641328	0.320664	−	0.947193i	$-0.396094\pi$
$941$	1.54253e13	0.641328	0.320664	+	0.947193i	$0.396094\pi$
$942$	3.02059e13	1.24986
$943$	5.96294e13	2.45560
$944$	4.59522e12	0.188335
$945$	0	0
$946$	8.69386e12	0.352941
$947$	−1.97267e13	−0.797039	−0.398519	−	0.917160i	$-0.630476\pi$
$947$	−1.97267e13	−0.797039	−0.398519	+	0.917160i	$0.630476\pi$
$948$	2.99002e13	1.20236
$949$	−2.06133e12	−0.0824993
$950$	0	0
$951$	−5.56186e13	−2.20500
$952$	4.12265e12	0.162671
$953$	1.39214e12	0.0546721	0.0273361	−	0.999626i	$-0.491298\pi$
$953$	1.39214e12	0.0546721	0.0273361	+	0.999626i	$0.491298\pi$
$954$	−1.29534e12	−0.0506311
$955$	0	0
$956$	−1.18721e13	−0.459694
$957$	1.96059e13	0.755583
$958$	−2.99895e12	−0.115034
$959$	7.30317e12	0.278822
$960$	0	0
$961$	−8.62783e12	−0.326322
$962$	−5.03619e12	−0.189589
$963$	−4.05728e13	−1.52026
$964$	6.12861e12	0.228568
$965$	0	0
$966$	1.77017e13	0.654059
$967$	−5.29760e12	−0.194832	−0.0974160	−	0.995244i	$-0.531058\pi$
$967$	−5.29760e12	−0.194832	−0.0974160	+	0.995244i	$0.531058\pi$
$968$	2.48602e13	0.910049
$969$	−5.51357e12	−0.200898
$970$	0	0
$971$	−7.97890e12	−0.288042	−0.144021	−	0.989575i	$-0.546003\pi$
$971$	−7.97890e12	−0.288042	−0.144021	+	0.989575i	$0.546003\pi$
$972$	4.17108e12	0.149882
$973$	−2.00825e12	−0.0718306
$974$	−1.23902e13	−0.441127
$975$	0	0
$976$	1.82600e12	0.0644135
$977$	6.27831e12	0.220454	0.110227	−	0.993906i	$-0.464842\pi$
$977$	6.27831e12	0.220454	0.110227	+	0.993906i	$0.464842\pi$
$978$	−1.51390e13	−0.529141
$979$	1.88646e12	0.0656335
$980$	0	0
$981$	4.10589e13	1.41546
$982$	−1.57540e13	−0.540616
$983$	−1.25053e12	−0.0427173	−0.0213586	−	0.999772i	$-0.506799\pi$
$983$	−1.25053e12	−0.0427173	−0.0213586	+	0.999772i	$0.506799\pi$
$984$	8.21886e13	2.79469
$985$	0	0
$986$	−1.05686e13	−0.356098
$987$	3.42849e13	1.14994
$988$	−1.22753e12	−0.0409851
$989$	7.35883e13	2.44583
$990$	0	0
$991$	1.89095e13	0.622801	0.311400	−	0.950279i	$-0.399202\pi$
$991$	1.89095e13	0.622801	0.311400	+	0.950279i	$0.399202\pi$
$992$	2.40603e13	0.788858
$993$	−8.97216e13	−2.92836
$994$	−2.47465e12	−0.0804036
$995$	0	0
$996$	−3.72034e13	−1.19788
$997$	7.17482e12	0.229976	0.114988	−	0.993367i	$-0.463317\pi$
$997$	7.17482e12	0.229976	0.114988	+	0.993367i	$0.463317\pi$
$998$	−4.95178e12	−0.158006
$999$	5.60324e13	1.77989

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.10.a.b.1.1	✓	2	5.4	even	2
175.10.a.c.1.2		2	1.1	even	1	trivial
175.10.b.c.99.1		4	5.3	odd	4
175.10.b.c.99.4		4	5.2	odd	4
245.10.a.c.1.1		2	35.34	odd	2
315.10.a.b.1.2		2	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	175.a (trivial)

\(f(q)\)	\(=\)	\(q+14.8284 q^{2} +239.735 q^{3} -292.118 q^{4} +3554.89 q^{6} -2401.00 q^{7} -11923.8 q^{8} +37789.9 q^{9} +O(q^{10})\)	\(q+14.8284 q^{2} +239.735 q^{3} -292.118 q^{4} +3554.89 q^{6} -2401.00 q^{7} -11923.8 q^{8} +37789.9 q^{9} -16523.6 q^{11} -70030.9 q^{12} -26311.4 q^{13} -35603.1 q^{14} -27246.9 q^{16} +144003. q^{17} +560365. q^{18} -159710. q^{19} -575604. q^{21} -245019. q^{22} -2.07393e6 q^{23} -2.85855e6 q^{24} -390156. q^{26} +4.34086e6 q^{27} +701375. q^{28} -4.94938e6 q^{29} +4.22040e6 q^{31} +5.70096e6 q^{32} -3.96128e6 q^{33} +2.13533e6 q^{34} -1.10391e7 q^{36} +1.29081e7 q^{37} -2.36824e6 q^{38} -6.30776e6 q^{39} -2.87518e7 q^{41} -8.53530e6 q^{42} -3.54825e7 q^{43} +4.82683e6 q^{44} -3.07532e7 q^{46} -5.95633e7 q^{47} -6.53205e6 q^{48} +5.76480e6 q^{49} +3.45225e7 q^{51} +7.68602e6 q^{52} -2.31161e6 q^{53} +6.43681e7 q^{54} +2.86290e7 q^{56} -3.82880e7 q^{57} -7.33915e7 q^{58} -1.68651e8 q^{59} -6.70167e7 q^{61} +6.25819e7 q^{62} -9.07336e7 q^{63} +9.84867e7 q^{64} -5.87395e7 q^{66} +1.56259e8 q^{67} -4.20657e7 q^{68} -4.97195e8 q^{69} +6.95067e7 q^{71} -4.50599e8 q^{72} +7.83438e7 q^{73} +1.91407e8 q^{74} +4.66540e7 q^{76} +3.96731e7 q^{77} -9.35342e7 q^{78} -4.26957e8 q^{79} +2.96838e8 q^{81} -4.26344e8 q^{82} +5.31242e8 q^{83} +1.68144e8 q^{84} -5.26149e8 q^{86} -1.18654e9 q^{87} +1.97024e8 q^{88} -1.14168e8 q^{89} +6.31736e7 q^{91} +6.05833e8 q^{92} +1.01178e9 q^{93} -8.83231e8 q^{94} +1.36672e9 q^{96} +1.46573e9 q^{97} +8.54829e7 q^{98} -6.24424e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 24 q^{2} + 174 q^{3} - 720 q^{4} + 2952 q^{6} - 4802 q^{7} - 20544 q^{8} + 22428 q^{9}+O(q^{10}) \) 2 * q + 24 * q^2 + 174 * q^3 - 720 * q^4 + 2952 * q^6 - 4802 * q^7 - 20544 * q^8 + 22428 * q^9	\( 2 q + 24 q^{2} + 174 q^{3} - 720 q^{4} + 2952 q^{6} - 4802 q^{7} - 20544 q^{8} + 22428 q^{9} + 18566 q^{11} - 41904 q^{12} + 51090 q^{13} - 57624 q^{14} + 112768 q^{16} + 373910 q^{17} + 419472 q^{18} - 143276 q^{19} - 417774 q^{21} + 76808 q^{22} + 498908 q^{23} - 2291904 q^{24} + 319736 q^{26} + 6644538 q^{27} + 1728720 q^{28} - 11577554 q^{29} - 3953760 q^{31} + 11398656 q^{32} - 6267894 q^{33} + 4243944 q^{34} - 4466016 q^{36} + 3205412 q^{37} - 2217520 q^{38} - 11395746 q^{39} + 1058992 q^{41} - 7087752 q^{42} - 15948180 q^{43} - 10187376 q^{44} - 7156176 q^{46} - 65501290 q^{47} - 15735936 q^{48} + 11529602 q^{49} + 19409466 q^{51} - 25432656 q^{52} + 25114688 q^{53} + 85496472 q^{54} + 49326144 q^{56} - 39368244 q^{57} - 134182296 q^{58} - 116159208 q^{59} - 44688544 q^{61} - 12388000 q^{62} - 53849628 q^{63} + 79055872 q^{64} - 79894824 q^{66} - 118092496 q^{67} - 140439024 q^{68} - 666320892 q^{69} - 294165824 q^{71} - 318176640 q^{72} + 57419332 q^{73} + 102418064 q^{74} + 39622368 q^{76} - 44576966 q^{77} - 140199000 q^{78} - 692852854 q^{79} + 447773346 q^{81} - 152932128 q^{82} + 540679928 q^{83} + 100611504 q^{84} - 346989008 q^{86} - 750836190 q^{87} - 105455296 q^{88} - 779043704 q^{89} - 122667090 q^{91} - 495040608 q^{92} + 1549107360 q^{93} - 937691032 q^{94} + 992180736 q^{96} + 2673039406 q^{97} + 138355224 q^{98} - 1163466540 q^{99}+O(q^{100}) \) 2 * q + 24 * q^2 + 174 * q^3 - 720 * q^4 + 2952 * q^6 - 4802 * q^7 - 20544 * q^8 + 22428 * q^9 + 18566 * q^11 - 41904 * q^12 + 51090 * q^13 - 57624 * q^14 + 112768 * q^16 + 373910 * q^17 + 419472 * q^18 - 143276 * q^19 - 417774 * q^21 + 76808 * q^22 + 498908 * q^23 - 2291904 * q^24 + 319736 * q^26 + 6644538 * q^27 + 1728720 * q^28 - 11577554 * q^29 - 3953760 * q^31 + 11398656 * q^32 - 6267894 * q^33 + 4243944 * q^34 - 4466016 * q^36 + 3205412 * q^37 - 2217520 * q^38 - 11395746 * q^39 + 1058992 * q^41 - 7087752 * q^42 - 15948180 * q^43 - 10187376 * q^44 - 7156176 * q^46 - 65501290 * q^47 - 15735936 * q^48 + 11529602 * q^49 + 19409466 * q^51 - 25432656 * q^52 + 25114688 * q^53 + 85496472 * q^54 + 49326144 * q^56 - 39368244 * q^57 - 134182296 * q^58 - 116159208 * q^59 - 44688544 * q^61 - 12388000 * q^62 - 53849628 * q^63 + 79055872 * q^64 - 79894824 * q^66 - 118092496 * q^67 - 140439024 * q^68 - 666320892 * q^69 - 294165824 * q^71 - 318176640 * q^72 + 57419332 * q^73 + 102418064 * q^74 + 39622368 * q^76 - 44576966 * q^77 - 140199000 * q^78 - 692852854 * q^79 + 447773346 * q^81 - 152932128 * q^82 + 540679928 * q^83 + 100611504 * q^84 - 346989008 * q^86 - 750836190 * q^87 - 105455296 * q^88 - 779043704 * q^89 - 122667090 * q^91 - 495040608 * q^92 + 1549107360 * q^93 - 937691032 * q^94 + 992180736 * q^96 + 2673039406 * q^97 + 138355224 * q^98 - 1163466540 * q^99

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