LMFDB - Embedded newform 245.10.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,10,Mod(1,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, 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("245.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	245.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:	$126.183779860$
Analytic rank:	$0$
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			1.1
Root			$-1.41421$ of defining polynomial
Character	$\chi$	$=$	245.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-14.8284 q^{2} +239.735 q^{3} -292.118 q^{4} -625.000 q^{5} -3554.89 q^{6} +11923.8 q^{8} +37789.9 q^{9} +O(q^{10})$	\(q-14.8284 q^{2} +239.735 q^{3} -292.118 q^{4} -625.000 q^{5} -3554.89 q^{6} +11923.8 q^{8} +37789.9 q^{9} +9267.77 q^{10} -16523.6 q^{11} -70030.9 q^{12} -26311.4 q^{13} -149834. q^{15} -27246.9 q^{16} +144003. q^{17} -560365. q^{18} +159710. q^{19} +182574. q^{20} +245019. q^{22} +2.07393e6 q^{23} +2.85855e6 q^{24} +390625. q^{25} +390156. q^{26} +4.34086e6 q^{27} -4.94938e6 q^{29} +2.22181e6 q^{30} -4.22040e6 q^{31} -5.70096e6 q^{32} -3.96128e6 q^{33} -2.13533e6 q^{34} -1.10391e7 q^{36} -1.29081e7 q^{37} -2.36824e6 q^{38} -6.30776e6 q^{39} -7.45238e6 q^{40} +2.87518e7 q^{41} +3.54825e7 q^{43} +4.82683e6 q^{44} -2.36187e7 q^{45} -3.07532e7 q^{46} -5.95633e7 q^{47} -6.53205e6 q^{48} -5.79235e6 q^{50} +3.45225e7 q^{51} +7.68602e6 q^{52} +2.31161e6 q^{53} -6.43681e7 q^{54} +1.03272e7 q^{55} +3.82880e7 q^{57} +7.33915e7 q^{58} +1.68651e8 q^{59} +4.37693e7 q^{60} +6.70167e7 q^{61} +6.25819e7 q^{62} +9.84867e7 q^{64} +1.64446e7 q^{65} +5.87395e7 q^{66} -1.56259e8 q^{67} -4.20657e7 q^{68} +4.97195e8 q^{69} +6.95067e7 q^{71} +4.50599e8 q^{72} +7.83438e7 q^{73} +1.91407e8 q^{74} +9.36465e7 q^{75} -4.66540e7 q^{76} +9.35342e7 q^{78} -4.26957e8 q^{79} +1.70293e7 q^{80} +2.96838e8 q^{81} -4.26344e8 q^{82} +5.31242e8 q^{83} -9.00016e7 q^{85} -5.26149e8 q^{86} -1.18654e9 q^{87} -1.97024e8 q^{88} +1.14168e8 q^{89} +3.50228e8 q^{90} -6.05833e8 q^{92} -1.01178e9 q^{93} +8.83231e8 q^{94} -9.98185e7 q^{95} -1.36672e9 q^{96} +1.46573e9 q^{97} -6.24424e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 24 q^{2} + 174 q^{3} - 720 q^{4} - 1250 q^{5} - 2952 q^{6} + 20544 q^{8} + 22428 q^{9}+O(q^{10}) $ 2 * q - 24 * q^2 + 174 * q^3 - 720 * q^4 - 1250 * q^5 - 2952 * q^6 + 20544 * q^8 + 22428 * q^9	\( 2 q - 24 q^{2} + 174 q^{3} - 720 q^{4} - 1250 q^{5} - 2952 q^{6} + 20544 q^{8} + 22428 q^{9} + 15000 q^{10} + 18566 q^{11} - 41904 q^{12} + 51090 q^{13} - 108750 q^{15} + 112768 q^{16} + 373910 q^{17} - 419472 q^{18} + 143276 q^{19} + 450000 q^{20} - 76808 q^{22} - 498908 q^{23} + 2291904 q^{24} + 781250 q^{25} - 319736 q^{26} + 6644538 q^{27} - 11577554 q^{29} + 1845000 q^{30} + 3953760 q^{31} - 11398656 q^{32} - 6267894 q^{33} - 4243944 q^{34} - 4466016 q^{36} - 3205412 q^{37} - 2217520 q^{38} - 11395746 q^{39} - 12840000 q^{40} - 1058992 q^{41} + 15948180 q^{43} - 10187376 q^{44} - 14017500 q^{45} - 7156176 q^{46} - 65501290 q^{47} - 15735936 q^{48} - 9375000 q^{50} + 19409466 q^{51} - 25432656 q^{52} - 25114688 q^{53} - 85496472 q^{54} - 11603750 q^{55} + 39368244 q^{57} + 134182296 q^{58} + 116159208 q^{59} + 26190000 q^{60} + 44688544 q^{61} - 12388000 q^{62} + 79055872 q^{64} - 31931250 q^{65} + 79894824 q^{66} + 118092496 q^{67} - 140439024 q^{68} + 666320892 q^{69} - 294165824 q^{71} + 318176640 q^{72} + 57419332 q^{73} + 102418064 q^{74} + 67968750 q^{75} - 39622368 q^{76} + 140199000 q^{78} - 692852854 q^{79} - 70480000 q^{80} + 447773346 q^{81} - 152932128 q^{82} + 540679928 q^{83} - 233693750 q^{85} - 346989008 q^{86} - 750836190 q^{87} + 105455296 q^{88} + 779043704 q^{89} + 262170000 q^{90} + 495040608 q^{92} - 1549107360 q^{93} + 937691032 q^{94} - 89547500 q^{95} - 992180736 q^{96} + 2673039406 q^{97} - 1163466540 q^{99}+O(q^{100}) \) 2 * q - 24 * q^2 + 174 * q^3 - 720 * q^4 - 1250 * q^5 - 2952 * q^6 + 20544 * q^8 + 22428 * q^9 + 15000 * q^10 + 18566 * q^11 - 41904 * q^12 + 51090 * q^13 - 108750 * q^15 + 112768 * q^16 + 373910 * q^17 - 419472 * q^18 + 143276 * q^19 + 450000 * q^20 - 76808 * q^22 - 498908 * q^23 + 2291904 * q^24 + 781250 * q^25 - 319736 * q^26 + 6644538 * q^27 - 11577554 * q^29 + 1845000 * q^30 + 3953760 * q^31 - 11398656 * q^32 - 6267894 * q^33 - 4243944 * q^34 - 4466016 * q^36 - 3205412 * q^37 - 2217520 * q^38 - 11395746 * q^39 - 12840000 * q^40 - 1058992 * q^41 + 15948180 * q^43 - 10187376 * q^44 - 14017500 * q^45 - 7156176 * q^46 - 65501290 * q^47 - 15735936 * q^48 - 9375000 * q^50 + 19409466 * q^51 - 25432656 * q^52 - 25114688 * q^53 - 85496472 * q^54 - 11603750 * q^55 + 39368244 * q^57 + 134182296 * q^58 + 116159208 * q^59 + 26190000 * q^60 + 44688544 * q^61 - 12388000 * q^62 + 79055872 * q^64 - 31931250 * q^65 + 79894824 * q^66 + 118092496 * q^67 - 140439024 * q^68 + 666320892 * q^69 - 294165824 * q^71 + 318176640 * q^72 + 57419332 * q^73 + 102418064 * q^74 + 67968750 * q^75 - 39622368 * q^76 + 140199000 * q^78 - 692852854 * q^79 - 70480000 * q^80 + 447773346 * q^81 - 152932128 * q^82 + 540679928 * q^83 - 233693750 * q^85 - 346989008 * q^86 - 750836190 * q^87 + 105455296 * q^88 + 779043704 * q^89 + 262170000 * q^90 + 495040608 * q^92 - 1549107360 * q^93 + 937691032 * q^94 - 89547500 * q^95 - 992180736 * q^96 + 2673039406 * q^97 - 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	$-0.606262\pi$
$2$	−14.8284	−0.655330	−0.327665	+	0.944794i	$0.606262\pi$
$3$	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
$5$	−625.000	−0.447214
$5$	−625.000	−0.447214
$6$	−3554.89	−1.11981
$7$	0	0
$7$	0	0
$8$	11923.8	1.02922
$9$	37789.9	1.91993
$10$	9267.77	0.293073
$11$	−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	$0.540776\pi$
$14$	0	0
$15$	−149834.	−0.764189
$16$	−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	$-0.455105\pi$
$19$	159710.	0.281151	0.140576	+	0.990070i	$0.455105\pi$
$20$	182574.	0.255154
$21$	0	0
$22$	245019.	0.222996
$23$	2.07393e6	1.54533	0.772663	−	0.634817i	$-0.218925\pi$
$23$	2.07393e6	1.54533	0.772663	+	0.634817i	$0.218925\pi$
$24$	2.85855e6	1.75872
$25$	390625.	0.200000
$26$	390156.	0.167440
$27$	4.34086e6	1.57195
$28$	0	0
$29$	−4.94938e6	−1.29945	−0.649725	−	0.760169i	$-0.725116\pi$
$29$	−4.94938e6	−1.29945	−0.649725	+	0.760169i	$0.725116\pi$
$30$	2.22181e6	0.500796
$31$	−4.22040e6	−0.820779	−0.410389	−	0.911910i	$-0.634607\pi$
$31$	−4.22040e6	−0.820779	−0.410389	+	0.911910i	$0.634607\pi$
$32$	−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	$-0.691565\pi$
$37$	−1.29081e7	−1.13228	−0.566142	+	0.824308i	$0.691565\pi$
$38$	−2.36824e6	−0.184247
$39$	−6.30776e6	−0.436601
$40$	−7.45238e6	−0.460283
$41$	2.87518e7	1.58905	0.794525	−	0.607231i	$-0.207720\pi$
$41$	2.87518e7	1.58905	0.794525	+	0.607231i	$0.207720\pi$
$42$	0	0
$43$	3.54825e7	1.58273	0.791363	−	0.611347i	$-0.209372\pi$
$43$	3.54825e7	1.58273	0.791363	+	0.611347i	$0.209372\pi$
$44$	4.82683e6	0.194144
$45$	−2.36187e7	−0.858617
$46$	−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
$49$	0	0
$50$	−5.79235e6	−0.131066
$51$	3.45225e7	0.714555
$52$	7.68602e6	0.145776
$53$	2.31161e6	0.0402414	0.0201207	−	0.999798i	$-0.493595\pi$
$53$	2.31161e6	0.0402414	0.0201207	+	0.999798i	$0.493595\pi$
$54$	−6.43681e7	−1.03015
$55$	1.03272e7	0.152178
$56$	0	0
$57$	3.82880e7	0.480425
$58$	7.33915e7	0.851569
$59$	1.68651e8	1.81198	0.905992	−	0.423296i	$-0.139127\pi$
$59$	1.68651e8	1.81198	0.905992	+	0.423296i	$0.139127\pi$
$60$	4.37693e7	0.436002
$61$	6.70167e7	0.619725	0.309863	−	0.950781i	$-0.399717\pi$
$61$	6.70167e7	0.619725	0.309863	+	0.950781i	$0.399717\pi$
$62$	6.25819e7	0.537881
$63$	0	0
$64$	9.84867e7	0.733783
$65$	1.64446e7	0.114265
$66$	5.87395e7	0.381051
$67$	−1.56259e8	−0.947343	−0.473671	−	0.880702i	$-0.657072\pi$
$67$	−1.56259e8	−0.947343	−0.473671	+	0.880702i	$0.657072\pi$
$68$	−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
$75$	9.36465e7	0.341756
$76$	−4.66540e7	−0.160409
$77$	0	0
$78$	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	$0.711507\pi$
$80$	1.70293e7	0.0464828
$81$	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	$0.289421\pi$
$84$	0	0
$85$	−9.00016e7	−0.187010
$86$	−5.26149e8	−1.03721
$87$	−1.18654e9	−2.22047
$88$	−1.97024e8	−0.350225
$89$	1.14168e8	0.192881	0.0964404	−	0.995339i	$-0.469254\pi$
$89$	1.14168e8	0.192881	0.0964404	+	0.995339i	$0.469254\pi$
$90$	3.50228e8	0.562678
$91$	0	0
$92$	−6.05833e8	−0.881674
$93$	−1.01178e9	−1.40253
$94$	8.83231e8	1.16681
$95$	−9.98185e7	−0.125735
$96$	−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	$0.182247\pi$
$98$	0	0
$99$	−6.24424e8	−0.653313
$100$	−1.14108e8	−0.114108
$101$	−7.53733e8	−0.720728	−0.360364	−	0.932812i	$-0.617348\pi$
$101$	−7.53733e8	−0.720728	−0.360364	+	0.932812i	$0.617348\pi$
$102$	−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	$-0.370427\pi$
$107$	1.07364e9	0.791831	0.395915	+	0.918287i	$0.370427\pi$
$108$	−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	$0.379830\pi$
$110$	−1.53137e8	−0.0997268
$111$	−3.09453e9	−1.93482
$112$	0	0
$113$	2.85559e9	1.64757	0.823783	−	0.566906i	$-0.191860\pi$
$113$	2.85559e9	1.64757	0.823783	+	0.566906i	$0.191860\pi$
$114$	−5.67751e8	−0.314837
$115$	−1.29621e9	−0.691090
$116$	1.44580e9	0.741392
$117$	−9.94305e8	−0.490550
$118$	−2.50083e9	−1.18745
$119$	0	0
$120$	−1.78660e9	−0.786522
$121$	−2.08492e9	−0.884209
$122$	−9.93753e8	−0.406125
$123$	6.89281e9	2.71534
$124$	1.23285e9	0.468289
$125$	−2.44141e8	−0.0894427
$126$	0	0
$127$	−3.86082e9	−1.31693	−0.658465	−	0.752611i	$-0.728794\pi$
$127$	−3.86082e9	−1.31693	−0.658465	+	0.752611i	$0.728794\pi$
$128$	1.45849e9	0.480240
$129$	8.50639e9	2.70453
$130$	−2.43848e8	−0.0748814
$131$	−4.01900e8	−0.119233	−0.0596166	−	0.998221i	$-0.518988\pi$
$131$	−4.01900e8	−0.119233	−0.0596166	+	0.998221i	$0.518988\pi$
$132$	1.15716e9	0.331750
$133$	0	0
$134$	2.31707e9	0.620822
$135$	−2.71304e9	−0.702997
$136$	1.71706e9	0.430388
$137$	3.04172e9	0.737695	0.368847	−	0.929490i	$-0.379753\pi$
$137$	3.04172e9	0.737695	0.368847	+	0.929490i	$0.379753\pi$
$138$	−7.37262e9	−1.73048
$139$	−8.36421e8	−0.190046	−0.0950229	−	0.995475i	$-0.530292\pi$
$139$	−8.36421e8	−0.190046	−0.0950229	+	0.995475i	$0.530292\pi$
$140$	0	0
$141$	−1.42794e10	−3.04246
$142$	−1.03068e9	−0.212728
$143$	4.34758e8	0.0869431
$144$	−1.02966e9	−0.199555
$145$	3.09336e9	0.581132
$146$	−1.16172e9	−0.211598
$147$	0	0
$148$	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	$0.723177\pi$
$150$	−1.38863e9	−0.223963
$151$	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
$154$	0	0
$155$	2.63775e9	0.367063
$156$	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
$160$	3.56310e9	0.429821
$161$	0	0
$162$	−4.40163e9	−0.502107
$163$	4.25863e9	0.472526	0.236263	−	0.971689i	$-0.424077\pi$
$163$	4.25863e9	0.472526	0.236263	+	0.971689i	$0.424077\pi$
$164$	−8.39891e9	−0.906621
$165$	2.47580e9	0.260039
$166$	−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	$0.514629\pi$
$168$	0	0
$169$	−9.91221e9	−0.934717
$170$	1.33458e9	0.122553
$171$	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	$0.612053\pi$
$180$	6.89944e9	0.489877
$181$	7.85395e9	0.543919	0.271960	−	0.962309i	$-0.412328\pi$
$181$	7.85395e9	0.543919	0.271960	+	0.962309i	$0.412328\pi$
$182$	0	0
$183$	1.60663e10	1.05897
$184$	2.47292e10	1.59049
$185$	8.06758e9	0.506373
$186$	1.50031e10	0.919120
$187$	−2.37944e9	−0.142294
$188$	1.73995e10	1.01584
$189$	0	0
$190$	1.48015e9	0.0823976
$191$	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	$-0.515951\pi$
$193$	−1.93101e9	−0.100179	−0.0500894	+	0.998745i	$0.515951\pi$
$194$	−2.17344e10	−1.10164
$195$	3.94235e9	0.195254
$196$	0	0
$197$	3.24598e10	1.53549	0.767746	−	0.640755i	$-0.221378\pi$
$197$	3.24598e10	1.53549	0.767746	+	0.640755i	$0.221378\pi$
$198$	9.25923e9	0.428136
$199$	2.75463e10	1.24516	0.622578	−	0.782558i	$-0.286085\pi$
$199$	2.75463e10	1.24516	0.622578	+	0.782558i	$0.286085\pi$
$200$	4.65773e9	0.205845
$201$	−3.74606e10	−1.61880
$202$	1.11767e10	0.472315
$203$	0	0
$204$	−1.00846e10	−0.407684
$205$	−1.79699e10	−0.710645
$206$	−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
$215$	−2.21765e10	−0.707817
$216$	5.17595e10	1.61789
$217$	0	0
$218$	−1.61111e10	−0.483139
$219$	1.87818e10	0.551744
$220$	−3.01677e9	−0.0868240
$221$	−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	$0.268836\pi$
$224$	0	0
$225$	1.47617e10	0.383985
$226$	−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	$-0.488201\pi$
$229$	3.08456e9	0.0741198	0.0370599	+	0.999313i	$0.488201\pi$
$230$	1.92207e10	0.452892
$231$	0	0
$232$	−5.90154e10	−1.33743
$233$	−1.48643e10	−0.330402	−0.165201	−	0.986260i	$-0.552827\pi$
$233$	−1.48643e10	−0.330402	−0.165201	+	0.986260i	$0.552827\pi$
$234$	1.47440e10	0.321472
$235$	3.72271e10	0.796258
$236$	−4.92659e10	−1.03381
$237$	−1.02357e11	−2.10741
$238$	0	0
$239$	4.06416e10	0.805713	0.402857	−	0.915263i	$-0.368017\pi$
$239$	4.06416e10	0.805713	0.402857	+	0.915263i	$0.368017\pi$
$240$	4.08253e9	0.0794289
$241$	2.09799e10	0.400615	0.200308	−	0.979733i	$-0.435806\pi$
$241$	2.09799e10	0.400615	0.200308	+	0.979733i	$0.435806\pi$
$242$	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
$250$	3.62022e9	0.0586145
$251$	9.95566e10	1.58321	0.791605	−	0.611034i	$-0.209246\pi$
$251$	9.95566e10	1.58321	0.791605	+	0.611034i	$0.209246\pi$
$252$	0	0
$253$	−3.42688e10	−0.525844
$254$	5.72499e10	0.863024
$255$	−2.15765e10	−0.319559
$256$	−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
$259$	0	0
$260$	−4.80376e9	−0.0651931
$261$	−1.87037e11	−2.49485
$262$	5.95954e9	0.0781371
$263$	−3.27938e10	−0.422660	−0.211330	−	0.977415i	$-0.567779\pi$
$263$	−3.27938e10	−0.422660	−0.211330	+	0.977415i	$0.567779\pi$
$264$	−4.72335e10	−0.598456
$265$	−1.44475e9	−0.0179965
$266$	0	0
$267$	2.73700e10	0.329591
$268$	4.56459e10	0.540499
$269$	−7.47690e9	−0.0870636	−0.0435318	−	0.999052i	$-0.513861\pi$
$269$	−7.47690e9	−0.0870636	−0.0435318	+	0.999052i	$0.513861\pi$
$270$	4.02301e10	0.460695
$271$	−6.72735e9	−0.0757674	−0.0378837	−	0.999282i	$-0.512062\pi$
$271$	−6.72735e9	−0.0757674	−0.0378837	+	0.999282i	$0.512062\pi$
$272$	−3.92363e9	−0.0434638
$273$	0	0
$274$	−4.51039e10	−0.483434
$275$	−6.45452e9	−0.0680561
$276$	−1.45239e11	−1.50659
$277$	−1.52676e11	−1.55815	−0.779077	−	0.626928i	$-0.784312\pi$
$277$	−1.52676e11	−1.55815	−0.779077	+	0.626928i	$0.784312\pi$
$278$	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
$285$	−2.39300e10	−0.214853
$286$	−6.44678e9	−0.0569765
$287$	0	0
$288$	−2.15439e11	−1.84526
$289$	−9.78512e10	−0.825136
$290$	−4.58697e10	−0.380833
$291$	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	$0.580341\pi$
$294$	0	0
$295$	−1.05407e11	−0.810344
$296$	−1.53914e11	−1.16537
$297$	−7.17265e10	−0.534904
$298$	1.15101e11	0.845483
$299$	−5.45681e10	−0.394838
$300$	−2.73558e10	−0.194986
$301$	0	0
$302$	−1.24268e11	−0.859665
$303$	−1.80696e11	−1.23157
$304$	−4.35160e9	−0.0292225
$305$	−4.18855e10	−0.277150
$306$	−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	$0.371295\pi$
$308$	0	0
$309$	3.16793e11	1.97680
$310$	−3.91137e10	−0.240548
$311$	−2.77926e11	−1.68464	−0.842321	−	0.538975i	$-0.818812\pi$
$311$	−2.77926e11	−1.68464	−0.842321	+	0.538975i	$0.818812\pi$
$312$	−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	$-0.276775\pi$
$317$	2.32000e11	1.29039	0.645197	+	0.764016i	$0.276775\pi$
$318$	−8.21752e9	−0.0450628
$319$	8.17814e10	0.442177
$320$	−6.15542e10	−0.328158
$321$	2.57390e11	1.35306
$322$	0	0
$323$	2.29986e10	0.117568
$324$	−8.67115e10	−0.437144
$325$	−1.02779e10	−0.0511009
$326$	−6.31487e10	−0.309660
$327$	2.60473e11	1.25979
$328$	3.42831e11	1.63549
$329$	0	0
$330$	−3.67122e10	−0.170411
$331$	−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
$335$	9.76616e10	0.423665
$336$	0	0
$337$	3.35878e11	1.41856	0.709280	−	0.704927i	$-0.249020\pi$
$337$	3.35878e11	1.41856	0.709280	+	0.704927i	$0.249020\pi$
$338$	1.46982e11	0.612548
$339$	6.84585e11	2.81533
$340$	2.62911e10	0.106697
$341$	6.97361e10	0.279295
$342$	−8.94956e10	−0.353740
$343$	0	0
$344$	4.23086e11	1.62898
$345$	−3.10747e11	−1.18092
$346$	−7.05842e10	−0.264768
$347$	−3.63698e11	−1.34666	−0.673331	−	0.739341i	$-0.735137\pi$
$347$	−3.63698e11	−1.34666	−0.673331	+	0.739341i	$0.735137\pi$
$348$	3.46609e11	1.26687
$349$	−1.08740e11	−0.392350	−0.196175	−	0.980569i	$-0.562852\pi$
$349$	−1.08740e11	−0.392350	−0.196175	+	0.980569i	$0.562852\pi$
$350$	0	0
$351$	−1.14214e11	−0.401640
$352$	9.42002e10	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
$355$	−4.34417e10	−0.145171
$356$	−3.33505e10	−0.110047
$357$	0	0
$358$	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	$0.161712\pi$
$360$	−2.81625e11	−0.883709
$361$	−2.97181e11	−0.920954
$362$	−1.16462e11	−0.356447
$363$	−4.99828e11	−1.51092
$364$	0	0
$365$	−4.89649e10	−0.144400
$366$	−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
$370$	−1.19630e11	−0.331841
$371$	0	0
$372$	2.95558e11	0.800203
$373$	4.88064e11	1.30553	0.652765	−	0.757560i	$-0.273609\pi$
$373$	4.88064e11	1.30553	0.652765	+	0.757560i	$0.273609\pi$
$374$	3.52833e10	0.0932496
$375$	−5.85291e10	−0.152838
$376$	−7.10222e11	−1.83252
$377$	1.30225e11	0.332015
$378$	0	0
$379$	3.00162e11	0.747274	0.373637	−	0.927575i	$-0.378111\pi$
$379$	3.00162e11	0.747274	0.373637	+	0.927575i	$0.378111\pi$
$380$	2.91587e10	0.0717369
$381$	−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	$0.560314\pi$
$390$	−5.84589e10	−0.127956
$391$	2.98652e11	0.646204
$392$	0	0
$393$	−9.63495e10	−0.203743
$394$	−4.81327e11	−1.00625
$395$	2.66848e11	0.551540
$396$	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
$399$	0	0
$400$	−1.06433e10	−0.0207878
$401$	−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
$405$	−1.85523e11	−0.342650
$406$	0	0
$407$	2.13288e11	0.385294
$408$	4.11639e11	0.735437
$409$	−9.42996e10	−0.166631	−0.0833153	−	0.996523i	$-0.526551\pi$
$409$	−9.42996e10	−0.166631	−0.0833153	+	0.996523i	$0.526551\pi$
$410$	2.66465e11	0.465707
$411$	7.29207e11	1.26056
$412$	−3.86013e11	−0.660032
$413$	0	0
$414$	−1.16216e12	−1.94431
$415$	−3.32026e11	−0.549485
$416$	1.50000e11	0.245568
$417$	−2.00519e11	−0.324746
$418$	3.91318e10	0.0626955
$419$	−1.66874e11	−0.264500	−0.132250	−	0.991216i	$-0.542220\pi$
$419$	−1.66874e11	−0.264500	−0.132250	+	0.991216i	$0.542220\pi$
$420$	0	0
$421$	−5.52779e11	−0.857594	−0.428797	−	0.903401i	$-0.641062\pi$
$421$	−5.52779e11	−0.857594	−0.428797	+	0.903401i	$0.641062\pi$
$422$	−2.88339e11	−0.442585
$423$	−2.25089e12	−3.41840
$424$	2.75631e10	0.0414174
$425$	5.62510e10	0.0836334
$426$	−2.47089e11	−0.363505
$427$	0	0
$428$	−3.13630e11	−0.451773
$429$	1.04227e11	0.148567
$430$	3.28843e11	0.463853
$431$	−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	$0.561265\pi$
$434$	0	0
$435$	7.41587e11	0.993026
$436$	−3.17387e11	−0.420630
$437$	3.31227e11	0.434470
$438$	−2.78504e11	−0.361575
$439$	−8.87150e11	−1.14000	−0.570002	−	0.821643i	$-0.693058\pi$
$439$	−8.87150e11	−1.14000	−0.570002	+	0.821643i	$0.693058\pi$
$440$	1.23140e11	0.156625
$441$	0	0
$442$	5.61835e10	0.0700178
$443$	−5.87852e11	−0.725189	−0.362594	−	0.931947i	$-0.618109\pi$
$443$	−5.87852e11	−0.725189	−0.362594	+	0.931947i	$0.618109\pi$
$444$	9.03967e11	1.10390
$445$	−7.13549e10	−0.0862589
$446$	−7.27274e11	−0.870344
$447$	−1.86086e12	−2.20460
$448$	0	0
$449$	−5.19918e11	−0.603707	−0.301854	−	0.953354i	$-0.597605\pi$
$449$	−5.19918e11	−0.603707	−0.301854	+	0.953354i	$0.597605\pi$
$450$	−2.18892e11	−0.251637
$451$	−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	$-0.686367\pi$
$457$	−1.03055e12	−1.10521	−0.552607	+	0.833442i	$0.686367\pi$
$458$	−4.57392e10	−0.0485729
$459$	6.25095e11	0.657338
$460$	3.78646e11	0.394296
$461$	−9.37018e11	−0.966259	−0.483130	−	0.875549i	$-0.660500\pi$
$461$	−9.37018e11	−0.966259	−0.483130	+	0.875549i	$0.660500\pi$
$462$	0	0
$463$	1.08281e12	1.09506	0.547529	−	0.836787i	$-0.315569\pi$
$463$	1.08281e12	1.09506	0.547529	+	0.836787i	$0.315569\pi$
$464$	1.34855e11	0.135063
$465$	6.32361e11	0.627230
$466$	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
$469$	0	0
$470$	−5.52019e11	−0.521812
$471$	2.03703e12	1.90723
$472$	2.01096e12	1.86494
$473$	−5.86297e11	−0.538570
$474$	1.51779e12	1.38105
$475$	6.23865e10	0.0562302
$476$	0	0
$477$	8.73554e10	0.0772604
$478$	−6.02652e11	−0.528008
$479$	2.02244e11	0.175535	0.0877677	−	0.996141i	$-0.472027\pi$
$479$	2.02244e11	0.175535	0.0877677	+	0.996141i	$0.472027\pi$
$480$	8.54200e11	0.734470
$481$	3.39631e11	0.289304
$482$	−3.11099e11	−0.262535
$483$	0	0
$484$	6.09042e11	0.504479
$485$	−9.16079e11	−0.751788
$486$	2.11732e11	0.172156
$487$	8.35572e11	0.673137	0.336568	−	0.941659i	$-0.390734\pi$
$487$	8.35572e11	0.673137	0.336568	+	0.941659i	$0.390734\pi$
$488$	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
$495$	3.90265e11	0.292170
$496$	1.14993e11	0.0853108
$497$	0	0
$498$	−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	$0.538467\pi$
$500$	7.13178e10	0.0510309
$501$	−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	$0.459882\pi$
$504$	0	0
$505$	4.71083e11	0.322319
$506$	5.08152e11	0.344601
$507$	−2.37630e12	−1.59723
$508$	1.12781e12	0.751365
$509$	−4.09926e11	−0.270692	−0.135346	−	0.990798i	$-0.543215\pi$
$509$	−4.09926e11	−0.270692	−0.135346	+	0.990798i	$0.543215\pi$
$510$	3.19946e11	0.209417
$511$	0	0
$512$	3.21676e11	0.206873
$513$	6.93277e11	0.441955
$514$	−1.93928e12	−1.22548
$515$	−8.25894e11	−0.517359
$516$	−2.48487e12	−1.54305
$517$	9.84199e11	0.605865
$518$	0	0
$519$	1.14115e12	0.690384
$520$	1.96082e11	0.117604
$521$	1.09884e12	0.653377	0.326688	−	0.945132i	$-0.394067\pi$
$521$	1.09884e12	0.653377	0.326688	+	0.945132i	$0.394067\pi$
$522$	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
$530$	2.14234e10	0.0117936
$531$	6.37329e12	3.47887
$532$	0	0
$533$	−7.56500e11	−0.406010
$534$	−4.05855e11	−0.215991
$535$	−6.71026e11	−0.354118
$536$	−1.86320e12	−0.975028
$537$	−2.27074e12	−1.17837
$538$	1.10871e11	0.0570554
$539$	0	0
$540$	7.92526e11	0.401090
$541$	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
$545$	−6.79065e11	−0.329706
$546$	0	0
$547$	−1.50514e12	−0.718842	−0.359421	−	0.933176i	$-0.617026\pi$
$547$	−1.50514e12	−0.718842	−0.359421	+	0.933176i	$0.617026\pi$
$548$	−8.88540e11	−0.420886
$549$	2.53256e12	1.18983
$550$	9.57104e10	0.0445992
$551$	−7.90463e11	−0.365342
$552$	5.92845e12	2.71779
$553$	0	0
$554$	2.26394e12	1.02111
$555$	1.93408e12	0.865279
$556$	2.44333e11	0.108429
$557$	−2.17354e12	−0.956797	−0.478399	−	0.878143i	$-0.658783\pi$
$557$	−2.17354e12	−0.956797	−0.478399	+	0.878143i	$0.658783\pi$
$558$	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
$565$	−1.78474e12	−0.736814
$566$	−1.32281e12	−0.541781
$567$	0	0
$568$	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	$0.618042\pi$
$570$	3.54844e11	0.140799
$571$	−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
$574$	0	0
$575$	8.10131e11	0.309065
$576$	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
$580$	−9.03626e11	−0.331560
$581$	0	0
$582$	−5.21050e12	−1.88246
$583$	−3.81960e10	−0.0136933
$584$	9.34156e11	0.332324
$585$	6.21440e11	0.219381
$586$	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	$0.456391\pi$
$588$	0	0
$589$	−6.74039e11	−0.230763
$590$	1.56302e12	0.531043
$591$	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	$0.501316\pi$
$600$	1.11662e12	0.351743
$601$	−1.90372e11	−0.0595207	−0.0297603	−	0.999557i	$-0.509474\pi$
$601$	−1.90372e11	−0.0595207	−0.0297603	+	0.999557i	$0.509474\pi$
$602$	0	0
$603$	−5.90499e12	−1.81883
$604$	−2.44807e12	−0.748441
$605$	1.30307e12	0.395430
$606$	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
$609$	0	0
$610$	6.21096e11	0.181624
$611$	1.56719e12	0.454922
$612$	−1.58966e12	−0.458060
$613$	−2.48518e11	−0.0710863	−0.0355431	−	0.999368i	$-0.511316\pi$
$613$	−2.48518e11	−0.0710863	−0.0355431	+	0.999368i	$0.511316\pi$
$614$	−1.81591e12	−0.515628
$615$	−4.30801e12	−1.21434
$616$	0	0
$617$	3.52347e12	0.978786	0.489393	−	0.872063i	$-0.337218\pi$
$617$	3.52347e12	0.978786	0.489393	+	0.872063i	$0.337218\pi$
$618$	−4.69755e12	−1.29546
$619$	6.69712e12	1.83350	0.916748	−	0.399466i	$-0.130804\pi$
$619$	6.69712e12	1.83350	0.916748	+	0.399466i	$0.130804\pi$
$620$	−7.70534e11	−0.209425
$621$	9.00266e12	2.42917
$622$	4.12121e12	1.10400
$623$	0	0
$624$	1.71867e11	0.0453798
$625$	1.52588e11	0.0400000
$626$	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
$635$	2.41301e12	0.588949
$636$	−1.61884e11	−0.0392325
$637$	0	0
$638$	−1.21269e12	−0.289772
$639$	2.62665e12	0.623231
$640$	−9.11555e11	−0.214770
$641$	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	$0.811831\pi$
$644$	0	0
$645$	−5.31649e12	−1.20950
$646$	−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
$650$	1.52405e11	0.0334880
$651$	0	0
$652$	−1.24402e12	−0.269596
$653$	−1.54599e12	−0.332734	−0.166367	−	0.986064i	$-0.553204\pi$
$653$	−1.54599e12	−0.332734	−0.166367	+	0.986064i	$0.553204\pi$
$654$	−3.86240e12	−0.825578
$655$	2.51187e11	0.0533227
$656$	−7.83398e11	−0.165164
$657$	2.96061e12	0.619921
$658$	0	0
$659$	2.38624e12	0.492868	0.246434	−	0.969160i	$-0.420741\pi$
$659$	2.38624e12	0.492868	0.246434	+	0.969160i	$0.420741\pi$
$660$	−7.23225e11	−0.148363
$661$	2.35488e12	0.479802	0.239901	−	0.970797i	$-0.422885\pi$
$661$	2.35488e12	0.479802	0.239901	+	0.970797i	$0.422885\pi$
$662$	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
$670$	−1.44817e12	−0.277640
$671$	−1.10736e12	−0.210880
$672$	0	0
$673$	−6.32709e12	−1.18887	−0.594437	−	0.804142i	$-0.702625\pi$
$673$	−6.32709e12	−1.18887	−0.594437	+	0.804142i	$0.702625\pi$
$674$	−4.98055e12	−0.929625
$675$	1.69565e12	0.314390
$676$	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
$679$	0	0
$680$	−1.07316e12	−0.192475
$681$	1.64935e13	2.93868
$682$	−1.03408e12	−0.183030
$683$	−6.06916e12	−1.06717	−0.533587	−	0.845745i	$-0.679156\pi$
$683$	−6.06916e12	−1.06717	−0.533587	+	0.845745i	$0.679156\pi$
$684$	−1.76305e12	−0.307973
$685$	−1.90107e12	−0.329907
$686$	0	0
$687$	7.39478e11	0.126654
$688$	−9.66788e11	−0.164507
$689$	−6.08216e10	−0.0102818
$690$	4.60789e12	0.773893
$691$	1.36410e12	0.227611	0.113806	−	0.993503i	$-0.463696\pi$
$691$	1.36410e12	0.227611	0.113806	+	0.993503i	$0.463696\pi$
$692$	−1.39050e12	−0.230512
$693$	0	0
$694$	5.39307e12	0.882508
$695$	5.22763e11	0.0849911
$696$	−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
$705$	8.92464e12	1.36063
$706$	−4.98605e12	−0.755328
$707$	0	0
$708$	−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	$0.384800\pi$
$710$	6.44172e11	0.0951348
$711$	−1.61347e13	−2.36781
$712$	1.36132e12	0.198517
$713$	−8.75284e12	−1.26837
$714$	0	0
$715$	−2.71724e11	−0.0388822
$716$	2.76690e12	0.393446
$717$	9.74323e12	1.37679
$718$	−8.15481e12	−1.14513
$719$	2.64192e12	0.368671	0.184336	−	0.982863i	$-0.440987\pi$
$719$	2.64192e12	0.368671	0.184336	+	0.982863i	$0.440987\pi$
$720$	6.43537e11	0.0892436
$721$	0	0
$722$	4.40672e12	0.603529
$723$	5.02963e12	0.684563
$724$	−2.29428e12	−0.310329
$725$	−1.93335e12	−0.259890
$726$	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	$0.424304\pi$
$728$	0	0
$729$	−9.26577e12	−1.21509
$730$	7.26072e11	0.0946296
$731$	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	$0.806658\pi$
$740$	−2.35668e12	−0.288907
$741$	−1.00741e12	−0.122751
$742$	0	0
$743$	1.37811e13	1.65896	0.829479	−	0.558538i	$-0.188637\pi$
$743$	1.37811e13	1.65896	0.829479	+	0.558538i	$0.188637\pi$
$744$	−1.20642e13	−1.44352
$745$	4.85135e12	0.576979
$746$	−7.23722e12	−0.855553
$747$	2.00756e13	2.35899
$748$	6.95075e11	0.0811848
$749$	0	0
$750$	8.67894e11	0.100159
$751$	−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
$755$	−5.23776e12	−0.586657
$756$	0	0
$757$	1.31405e13	1.45439	0.727196	−	0.686430i	$-0.240823\pi$
$757$	1.31405e13	1.45439	0.727196	+	0.686430i	$0.240823\pi$
$758$	−4.45093e12	−0.489711
$759$	−8.21543e12	−0.898551
$760$	−1.19022e12	−0.129409
$761$	−4.85816e12	−0.525099	−0.262549	−	0.964919i	$-0.584563\pi$
$761$	−4.85816e12	−0.525099	−0.262549	+	0.964919i	$0.584563\pi$
$762$	1.37248e13	1.47472
$763$	0	0
$764$	−5.20584e12	−0.552804
$765$	−3.40115e12	−0.359045
$766$	1.14802e13	1.20481
$767$	−4.43743e12	−0.462970
$768$	−1.72735e13	−1.79165
$769$	1.57384e13	1.62290	0.811452	−	0.584420i	$-0.198678\pi$
$769$	1.57384e13	1.62290	0.811452	+	0.584420i	$0.198678\pi$
$770$	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
$775$	−1.64859e12	−0.164156
$776$	1.74770e13	1.73017
$777$	0	0
$778$	2.52271e12	0.246865
$779$	4.59194e12	0.446763
$780$	−1.15163e12	−0.111401
$781$	−1.14850e12	−0.110459
$782$	−4.42854e12	−0.423477
$783$	−2.14846e13	−2.04267
$784$	0	0
$785$	−5.31062e12	−0.499150
$786$	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
$790$	−3.95694e12	−0.361441
$791$	0	0
$792$	−7.44551e12	−0.672405
$793$	−1.76330e12	−0.158343
$794$	−8.11474e12	−0.724573
$795$	−3.46358e11	−0.0307520
$796$	−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	$0.651571\pi$
$798$	0	0
$799$	−8.57727e12	−0.744541
$800$	−2.22694e12	−0.192222
$801$	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	$0.592633\pi$
$810$	2.75102e12	0.224549
$811$	1.14380e13	0.928442	0.464221	−	0.885719i	$-0.346334\pi$
$811$	1.14380e13	0.928442	0.464221	+	0.885719i	$0.346334\pi$
$812$	0	0
$813$	−1.61278e12	−0.129470
$814$	−3.16273e12	−0.252495
$815$	−2.66164e12	−0.211320
$816$	−9.40631e11	−0.0742700
$817$	5.66689e12	0.444985
$818$	1.39831e12	0.109198
$819$	0	0
$820$	5.24932e12	0.405453
$821$	−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	$-0.273412\pi$
$823$	1.71948e13	1.30647	0.653234	+	0.757156i	$0.273412\pi$
$824$	1.57565e13	1.19066
$825$	−1.54737e12	−0.116293
$826$	0	0
$827$	3.04498e12	0.226365	0.113182	−	0.993574i	$-0.463896\pi$
$827$	3.04498e12	0.226365	0.113182	+	0.993574i	$0.463896\pi$
$828$	−2.28944e13	−1.69275
$829$	8.03416e12	0.590806	0.295403	−	0.955373i	$-0.404546\pi$
$829$	8.03416e12	0.590806	0.295403	+	0.955373i	$0.404546\pi$
$830$	4.92343e12	0.360094
$831$	−3.66017e13	−2.66254
$832$	−2.59132e12	−0.187485
$833$	0	0
$834$	2.97339e12	0.212816
$835$	5.77210e11	0.0410908
$836$	7.70891e11	0.0545839
$837$	−1.83202e13	−1.29022
$838$	2.47448e12	0.173335
$839$	−1.36209e13	−0.949020	−0.474510	−	0.880250i	$-0.657375\pi$
$839$	−1.36209e13	−0.949020	−0.474510	+	0.880250i	$0.657375\pi$
$840$	0	0
$841$	9.98921e12	0.688571
$842$	8.19684e12	0.562007
$843$	7.42689e12	0.506504
$844$	−5.68023e12	−0.385323
$845$	6.19513e12	0.418018
$846$	3.33772e13	2.24018
$847$	0	0
$848$	−6.29842e10	−0.00418264
$849$	2.13862e13	1.41270
$850$	−8.34114e11	−0.0548075
$851$	−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	$0.537576\pi$
$854$	0	0
$855$	−3.77213e12	−0.241401
$856$	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	$-0.677704\pi$
$859$	−1.69063e13	−1.05944	−0.529722	+	0.848171i	$0.677704\pi$
$860$	6.47816e12	0.403839
$861$	0	0
$862$	6.48608e12	0.400128
$863$	−1.56857e13	−0.962619	−0.481310	−	0.876551i	$-0.659839\pi$
$863$	−1.56857e13	−0.962619	−0.481310	+	0.876551i	$0.659839\pi$
$864$	−2.47471e13	−1.51082
$865$	−2.97504e12	−0.180684
$866$	4.14955e12	0.250709
$867$	−2.34584e13	−1.40998
$868$	0	0
$869$	7.05485e12	0.419661
$870$	−1.09966e13	−0.650760
$871$	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	$-0.262884\pi$
$877$	2.37521e13	1.35583	0.677914	+	0.735141i	$0.262884\pi$
$878$	1.31550e13	0.747079
$879$	−1.51055e13	−0.853462
$880$	−2.81385e11	−0.0158172
$881$	−1.13698e13	−0.635858	−0.317929	−	0.948115i	$-0.602987\pi$
$881$	−1.13698e13	−0.635858	−0.317929	+	0.948115i	$0.602987\pi$
$882$	0	0
$883$	−1.21711e12	−0.0673762	−0.0336881	−	0.999432i	$-0.510725\pi$
$883$	−1.21711e12	−0.0673762	−0.0336881	+	0.999432i	$0.510725\pi$
$884$	1.10681e12	0.0609588
$885$	−2.52697e13	−1.38470
$886$	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
$889$	0	0
$890$	1.05808e12	0.0565281
$891$	−4.90482e12	−0.260719
$892$	−1.43272e13	−0.757738
$893$	−9.51284e12	−0.500586
$894$	2.75937e13	1.44474
$895$	5.91992e12	0.308398
$896$	0	0
$897$	−1.30819e13	−0.674690
$898$	7.70957e12	0.395627
$899$	2.08884e13	1.06656
$900$	−4.31215e12	−0.219080
$901$	3.32877e11	0.0168276
$902$	7.04472e12	0.354352
$903$	0	0
$904$	3.40495e13	1.69571
$905$	−4.90872e12	−0.243248
$906$	−2.97915e13	−1.46898
$907$	−3.08586e13	−1.51406	−0.757030	−	0.653381i	$-0.773350\pi$
$907$	−3.08586e13	−1.51406	−0.757030	+	0.653381i	$0.773350\pi$
$908$	−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
$915$	−1.00414e13	−0.473587
$916$	−9.01056e11	−0.0422885
$917$	0	0
$918$	−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	$0.609772\pi$
$920$	−1.54557e13	−0.711287
$921$	2.93583e13	1.34450
$922$	1.38945e13	0.633219
$923$	−1.82882e12	−0.0829398
$924$	0	0
$925$	−5.04224e12	−0.226457
$926$	−1.60563e13	−0.717625
$927$	4.99367e13	2.22107
$928$	2.82162e13	1.24891
$929$	1.36244e13	0.600130	0.300065	−	0.953919i	$-0.402992\pi$
$929$	1.36244e13	0.600130	0.300065	+	0.953919i	$0.402992\pi$
$930$	−9.37693e12	−0.411043
$931$	0	0
$932$	4.34213e12	0.188508
$933$	−6.66287e13	−2.87868
$934$	2.26013e12	0.0971790
$935$	1.48715e12	0.0636358
$936$	−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	$0.427485\pi$
$938$	0	0
$939$	−2.93658e13	−1.23267
$940$	−1.08747e13	−0.454299
$941$	−1.54253e13	−0.641328	−0.320664	−	0.947193i	$-0.603906\pi$
$941$	−1.54253e13	−0.641328	−0.320664	+	0.947193i	$0.603906\pi$
$942$	−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	$-0.369524\pi$
$947$	1.97267e13	0.797039	0.398519	+	0.917160i	$0.369524\pi$
$948$	2.99002e13	1.20236
$949$	−2.06133e12	−0.0824993
$950$	−9.25094e11	−0.0368493
$951$	5.56186e13	2.20500
$952$	0	0
$953$	−1.39214e12	−0.0546721	−0.0273361	−	0.999626i	$-0.508702\pi$
$953$	−1.39214e12	−0.0546721	−0.0273361	+	0.999626i	$0.508702\pi$
$954$	−1.29534e12	−0.0506311
$955$	−1.11381e13	−0.433309
$956$	−1.18721e13	−0.459694
$957$	1.96059e13	0.755583
$958$	−2.99895e12	−0.115034
$959$	0	0
$960$	−1.47567e13	−0.560749
$961$	−8.62783e12	−0.326322
$962$	−5.03619e12	−0.189589
$963$	4.05728e13	1.52026
$964$	−6.12861e12	−0.228568
$965$	1.20688e12	0.0448013
$966$	0	0
$967$	5.29760e12	0.194832	0.0974160	−	0.995244i	$-0.468942\pi$
$967$	5.29760e12	0.194832	0.0974160	+	0.995244i	$0.468942\pi$
$968$	−2.48602e13	−0.910049
$969$	5.51357e12	0.200898
$970$	1.35840e13	0.492669
$971$	7.97890e12	0.288042	0.144021	−	0.989575i	$-0.453997\pi$
$971$	7.97890e12	0.288042	0.144021	+	0.989575i	$0.453997\pi$
$972$	4.17108e12	0.149882
$973$	0	0
$974$	−1.23902e13	−0.441127
$975$	−2.46397e12	−0.0873202
$976$	−1.82600e12	−0.0644135
$977$	−6.27831e12	−0.220454	−0.110227	−	0.993906i	$-0.535158\pi$
$977$	−6.27831e12	−0.220454	−0.110227	+	0.993906i	$0.535158\pi$
$978$	−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
$985$	−2.02874e13	−0.686692
$986$	1.05686e13	0.356098
$987$	0	0
$988$	1.22753e12	0.0409851
$989$	7.35883e13	2.44583
$990$	−5.78702e12	−0.191468
$991$	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
$994$	0	0
$995$	−1.72164e13	−0.556851
$996$	−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	245.10.a.c.1.1		2
7.6	odd	2		35.10.a.b.1.1	✓	2
21.20	even	2		315.10.a.b.1.2		2
35.13	even	4		175.10.b.c.99.4		4
35.27	even	4		175.10.b.c.99.1		4
35.34	odd	2		175.10.a.c.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.10.a.b.1.1	✓	2	7.6	odd	2
175.10.a.c.1.2		2	35.34	odd	2
175.10.b.c.99.1		4	35.27	even	4
175.10.b.c.99.4		4	35.13	even	4
245.10.a.c.1.1		2	1.1	even	1	trivial
315.10.a.b.1.2		2	21.20	even	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:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	245.a (trivial)

\(f(q)\)	\(=\)	\(q-14.8284 q^{2} +239.735 q^{3} -292.118 q^{4} -625.000 q^{5} -3554.89 q^{6} +11923.8 q^{8} +37789.9 q^{9} +O(q^{10})\)	\(q-14.8284 q^{2} +239.735 q^{3} -292.118 q^{4} -625.000 q^{5} -3554.89 q^{6} +11923.8 q^{8} +37789.9 q^{9} +9267.77 q^{10} -16523.6 q^{11} -70030.9 q^{12} -26311.4 q^{13} -149834. q^{15} -27246.9 q^{16} +144003. q^{17} -560365. q^{18} +159710. q^{19} +182574. q^{20} +245019. q^{22} +2.07393e6 q^{23} +2.85855e6 q^{24} +390625. q^{25} +390156. q^{26} +4.34086e6 q^{27} -4.94938e6 q^{29} +2.22181e6 q^{30} -4.22040e6 q^{31} -5.70096e6 q^{32} -3.96128e6 q^{33} -2.13533e6 q^{34} -1.10391e7 q^{36} -1.29081e7 q^{37} -2.36824e6 q^{38} -6.30776e6 q^{39} -7.45238e6 q^{40} +2.87518e7 q^{41} +3.54825e7 q^{43} +4.82683e6 q^{44} -2.36187e7 q^{45} -3.07532e7 q^{46} -5.95633e7 q^{47} -6.53205e6 q^{48} -5.79235e6 q^{50} +3.45225e7 q^{51} +7.68602e6 q^{52} +2.31161e6 q^{53} -6.43681e7 q^{54} +1.03272e7 q^{55} +3.82880e7 q^{57} +7.33915e7 q^{58} +1.68651e8 q^{59} +4.37693e7 q^{60} +6.70167e7 q^{61} +6.25819e7 q^{62} +9.84867e7 q^{64} +1.64446e7 q^{65} +5.87395e7 q^{66} -1.56259e8 q^{67} -4.20657e7 q^{68} +4.97195e8 q^{69} +6.95067e7 q^{71} +4.50599e8 q^{72} +7.83438e7 q^{73} +1.91407e8 q^{74} +9.36465e7 q^{75} -4.66540e7 q^{76} +9.35342e7 q^{78} -4.26957e8 q^{79} +1.70293e7 q^{80} +2.96838e8 q^{81} -4.26344e8 q^{82} +5.31242e8 q^{83} -9.00016e7 q^{85} -5.26149e8 q^{86} -1.18654e9 q^{87} -1.97024e8 q^{88} +1.14168e8 q^{89} +3.50228e8 q^{90} -6.05833e8 q^{92} -1.01178e9 q^{93} +8.83231e8 q^{94} -9.98185e7 q^{95} -1.36672e9 q^{96} +1.46573e9 q^{97} -6.24424e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 24 q^{2} + 174 q^{3} - 720 q^{4} - 1250 q^{5} - 2952 q^{6} + 20544 q^{8} + 22428 q^{9}+O(q^{10}) \) 2 * q - 24 * q^2 + 174 * q^3 - 720 * q^4 - 1250 * q^5 - 2952 * q^6 + 20544 * q^8 + 22428 * q^9	\( 2 q - 24 q^{2} + 174 q^{3} - 720 q^{4} - 1250 q^{5} - 2952 q^{6} + 20544 q^{8} + 22428 q^{9} + 15000 q^{10} + 18566 q^{11} - 41904 q^{12} + 51090 q^{13} - 108750 q^{15} + 112768 q^{16} + 373910 q^{17} - 419472 q^{18} + 143276 q^{19} + 450000 q^{20} - 76808 q^{22} - 498908 q^{23} + 2291904 q^{24} + 781250 q^{25} - 319736 q^{26} + 6644538 q^{27} - 11577554 q^{29} + 1845000 q^{30} + 3953760 q^{31} - 11398656 q^{32} - 6267894 q^{33} - 4243944 q^{34} - 4466016 q^{36} - 3205412 q^{37} - 2217520 q^{38} - 11395746 q^{39} - 12840000 q^{40} - 1058992 q^{41} + 15948180 q^{43} - 10187376 q^{44} - 14017500 q^{45} - 7156176 q^{46} - 65501290 q^{47} - 15735936 q^{48} - 9375000 q^{50} + 19409466 q^{51} - 25432656 q^{52} - 25114688 q^{53} - 85496472 q^{54} - 11603750 q^{55} + 39368244 q^{57} + 134182296 q^{58} + 116159208 q^{59} + 26190000 q^{60} + 44688544 q^{61} - 12388000 q^{62} + 79055872 q^{64} - 31931250 q^{65} + 79894824 q^{66} + 118092496 q^{67} - 140439024 q^{68} + 666320892 q^{69} - 294165824 q^{71} + 318176640 q^{72} + 57419332 q^{73} + 102418064 q^{74} + 67968750 q^{75} - 39622368 q^{76} + 140199000 q^{78} - 692852854 q^{79} - 70480000 q^{80} + 447773346 q^{81} - 152932128 q^{82} + 540679928 q^{83} - 233693750 q^{85} - 346989008 q^{86} - 750836190 q^{87} + 105455296 q^{88} + 779043704 q^{89} + 262170000 q^{90} + 495040608 q^{92} - 1549107360 q^{93} + 937691032 q^{94} - 89547500 q^{95} - 992180736 q^{96} + 2673039406 q^{97} - 1163466540 q^{99}+O(q^{100}) \) 2 * q - 24 * q^2 + 174 * q^3 - 720 * q^4 - 1250 * q^5 - 2952 * q^6 + 20544 * q^8 + 22428 * q^9 + 15000 * q^10 + 18566 * q^11 - 41904 * q^12 + 51090 * q^13 - 108750 * q^15 + 112768 * q^16 + 373910 * q^17 - 419472 * q^18 + 143276 * q^19 + 450000 * q^20 - 76808 * q^22 - 498908 * q^23 + 2291904 * q^24 + 781250 * q^25 - 319736 * q^26 + 6644538 * q^27 - 11577554 * q^29 + 1845000 * q^30 + 3953760 * q^31 - 11398656 * q^32 - 6267894 * q^33 - 4243944 * q^34 - 4466016 * q^36 - 3205412 * q^37 - 2217520 * q^38 - 11395746 * q^39 - 12840000 * q^40 - 1058992 * q^41 + 15948180 * q^43 - 10187376 * q^44 - 14017500 * q^45 - 7156176 * q^46 - 65501290 * q^47 - 15735936 * q^48 - 9375000 * q^50 + 19409466 * q^51 - 25432656 * q^52 - 25114688 * q^53 - 85496472 * q^54 - 11603750 * q^55 + 39368244 * q^57 + 134182296 * q^58 + 116159208 * q^59 + 26190000 * q^60 + 44688544 * q^61 - 12388000 * q^62 + 79055872 * q^64 - 31931250 * q^65 + 79894824 * q^66 + 118092496 * q^67 - 140439024 * q^68 + 666320892 * q^69 - 294165824 * q^71 + 318176640 * q^72 + 57419332 * q^73 + 102418064 * q^74 + 67968750 * q^75 - 39622368 * q^76 + 140199000 * q^78 - 692852854 * q^79 - 70480000 * q^80 + 447773346 * q^81 - 152932128 * q^82 + 540679928 * q^83 - 233693750 * q^85 - 346989008 * q^86 - 750836190 * q^87 + 105455296 * q^88 + 779043704 * q^89 + 262170000 * q^90 + 495040608 * q^92 - 1549107360 * q^93 + 937691032 * q^94 - 89547500 * q^95 - 992180736 * q^96 + 2673039406 * q^97 - 1163466540 * q^99

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