LMFDB - Embedded newform 177.12.a.a.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,12,Mod(1,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	177.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:	$135.996742959$
Analytic rank:	$1$
Dimension:	$26$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+10.8639 q^{2} -243.000 q^{3} -1929.97 q^{4} +8237.50 q^{5} -2639.94 q^{6} +85962.3 q^{7} -43216.5 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+10.8639 q^{2} -243.000 q^{3} -1929.97 q^{4} +8237.50 q^{5} -2639.94 q^{6} +85962.3 q^{7} -43216.5 q^{8} +59049.0 q^{9} +89491.8 q^{10} -483868. q^{11} +468984. q^{12} +396263. q^{13} +933890. q^{14} -2.00171e6 q^{15} +3.48309e6 q^{16} -1.10618e7 q^{17} +641505. q^{18} +2.99198e6 q^{19} -1.58982e7 q^{20} -2.08888e7 q^{21} -5.25672e6 q^{22} +1.83605e7 q^{23} +1.05016e7 q^{24} +1.90283e7 q^{25} +4.30498e6 q^{26} -1.43489e7 q^{27} -1.65905e8 q^{28} +2.21124e7 q^{29} -2.17465e7 q^{30} -2.01984e8 q^{31} +1.26347e8 q^{32} +1.17580e8 q^{33} -1.20175e8 q^{34} +7.08115e8 q^{35} -1.13963e8 q^{36} -8.11946e8 q^{37} +3.25047e7 q^{38} -9.62920e7 q^{39} -3.55996e8 q^{40} -1.31207e9 q^{41} -2.26935e8 q^{42} +1.05670e8 q^{43} +9.33854e8 q^{44} +4.86416e8 q^{45} +1.99467e8 q^{46} +2.23379e9 q^{47} -8.46390e8 q^{48} +5.41220e9 q^{49} +2.06722e8 q^{50} +2.68803e9 q^{51} -7.64778e8 q^{52} +3.80575e9 q^{53} -1.55886e8 q^{54} -3.98587e9 q^{55} -3.71499e9 q^{56} -7.27050e8 q^{57} +2.40228e8 q^{58} +7.14924e8 q^{59} +3.86326e9 q^{60} +7.57915e9 q^{61} -2.19434e9 q^{62} +5.07599e9 q^{63} -5.76073e9 q^{64} +3.26422e9 q^{65} +1.27738e9 q^{66} -9.14960e9 q^{67} +2.13491e10 q^{68} -4.46159e9 q^{69} +7.69292e9 q^{70} +1.16988e10 q^{71} -2.55189e9 q^{72} -9.76078e9 q^{73} -8.82094e9 q^{74} -4.62388e9 q^{75} -5.77444e9 q^{76} -4.15945e10 q^{77} -1.04611e9 q^{78} +8.26975e9 q^{79} +2.86919e10 q^{80} +3.48678e9 q^{81} -1.42543e10 q^{82} -1.53345e10 q^{83} +4.03150e10 q^{84} -9.11220e10 q^{85} +1.14799e9 q^{86} -5.37331e9 q^{87} +2.09111e10 q^{88} +1.16326e9 q^{89} +5.28440e9 q^{90} +3.40637e10 q^{91} -3.54352e10 q^{92} +4.90821e10 q^{93} +2.42677e10 q^{94} +2.46464e10 q^{95} -3.07024e10 q^{96} -8.72582e10 q^{97} +5.87978e10 q^{98} -2.85719e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9}+O(q^{10}) $ 26 * q - 78 * q^2 - 6318 * q^3 + 23070 * q^4 + 3808 * q^5 + 18954 * q^6 - 98819 * q^7 - 117645 * q^8 + 1535274 * q^9	\( 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9} - 859751 q^{10} + 579094 q^{11} - 5606010 q^{12} - 2018538 q^{13} + 4157413 q^{14} - 925344 q^{15} + 20190274 q^{16} - 13084493 q^{17} - 4605822 q^{18} + 9917231 q^{19} + 10165633 q^{20} + 24013017 q^{21} - 89820518 q^{22} - 63513223 q^{23} + 28587735 q^{24} + 218986852 q^{25} - 77999532 q^{26} - 373071582 q^{27} - 444601862 q^{28} + 81530981 q^{29} + 208919493 q^{30} - 408861231 q^{31} - 26253128 q^{32} - 140719842 q^{33} - 508910076 q^{34} - 75731421 q^{35} + 1362260430 q^{36} - 802381301 q^{37} + 732704675 q^{38} + 490504734 q^{39} - 646130800 q^{40} - 1354472849 q^{41} - 1010251359 q^{42} + 282952194 q^{43} + 1846047996 q^{44} + 224858592 q^{45} + 9629305849 q^{46} - 1196794197 q^{47} - 4906236582 q^{48} + 10889725683 q^{49} - 6236232091 q^{50} + 3179531799 q^{51} - 1968200812 q^{52} - 8276044236 q^{53} + 1119214746 q^{54} - 6672895076 q^{55} + 2579741342 q^{56} - 2409887133 q^{57} - 9401656060 q^{58} + 18588031774 q^{59} - 2470248819 q^{60} - 21181559029 q^{61} - 6117706514 q^{62} - 5835163131 q^{63} + 42975855037 q^{64} + 25680681860 q^{65} + 21826385874 q^{66} + 26234163394 q^{67} + 19707344091 q^{68} + 15433713189 q^{69} + 129203099090 q^{70} + 52088830406 q^{71} - 6946819605 q^{72} + 20943384867 q^{73} + 41969200146 q^{74} - 53213805036 q^{75} + 223987219368 q^{76} + 94604773153 q^{77} + 18953886276 q^{78} + 68965662774 q^{79} + 218947784293 q^{80} + 90656394426 q^{81} + 11938614923 q^{82} + 17947446393 q^{83} + 108038252466 q^{84} - 52849386709 q^{85} + 384986147852 q^{86} - 19812028383 q^{87} - 49061112607 q^{88} + 38570593981 q^{89} - 50767436799 q^{90} - 226268806999 q^{91} - 79559686310 q^{92} + 99353279133 q^{93} - 16709400108 q^{94} - 252795831501 q^{95} + 6379510104 q^{96} - 186894587836 q^{97} - 252443311612 q^{98} + 34194921606 q^{99}+O(q^{100}) \) 26 * q - 78 * q^2 - 6318 * q^3 + 23070 * q^4 + 3808 * q^5 + 18954 * q^6 - 98819 * q^7 - 117645 * q^8 + 1535274 * q^9 - 859751 * q^10 + 579094 * q^11 - 5606010 * q^12 - 2018538 * q^13 + 4157413 * q^14 - 925344 * q^15 + 20190274 * q^16 - 13084493 * q^17 - 4605822 * q^18 + 9917231 * q^19 + 10165633 * q^20 + 24013017 * q^21 - 89820518 * q^22 - 63513223 * q^23 + 28587735 * q^24 + 218986852 * q^25 - 77999532 * q^26 - 373071582 * q^27 - 444601862 * q^28 + 81530981 * q^29 + 208919493 * q^30 - 408861231 * q^31 - 26253128 * q^32 - 140719842 * q^33 - 508910076 * q^34 - 75731421 * q^35 + 1362260430 * q^36 - 802381301 * q^37 + 732704675 * q^38 + 490504734 * q^39 - 646130800 * q^40 - 1354472849 * q^41 - 1010251359 * q^42 + 282952194 * q^43 + 1846047996 * q^44 + 224858592 * q^45 + 9629305849 * q^46 - 1196794197 * q^47 - 4906236582 * q^48 + 10889725683 * q^49 - 6236232091 * q^50 + 3179531799 * q^51 - 1968200812 * q^52 - 8276044236 * q^53 + 1119214746 * q^54 - 6672895076 * q^55 + 2579741342 * q^56 - 2409887133 * q^57 - 9401656060 * q^58 + 18588031774 * q^59 - 2470248819 * q^60 - 21181559029 * q^61 - 6117706514 * q^62 - 5835163131 * q^63 + 42975855037 * q^64 + 25680681860 * q^65 + 21826385874 * q^66 + 26234163394 * q^67 + 19707344091 * q^68 + 15433713189 * q^69 + 129203099090 * q^70 + 52088830406 * q^71 - 6946819605 * q^72 + 20943384867 * q^73 + 41969200146 * q^74 - 53213805036 * q^75 + 223987219368 * q^76 + 94604773153 * q^77 + 18953886276 * q^78 + 68965662774 * q^79 + 218947784293 * q^80 + 90656394426 * q^81 + 11938614923 * q^82 + 17947446393 * q^83 + 108038252466 * q^84 - 52849386709 * q^85 + 384986147852 * q^86 - 19812028383 * q^87 - 49061112607 * q^88 + 38570593981 * q^89 - 50767436799 * q^90 - 226268806999 * q^91 - 79559686310 * q^92 + 99353279133 * q^93 - 16709400108 * q^94 - 252795831501 * q^95 + 6379510104 * q^96 - 186894587836 * q^97 - 252443311612 * q^98 + 34194921606 * 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 $

$2$	10.8639	0.240062	0.120031	−	0.992770i	$-0.461701\pi$
$2$	10.8639	0.240062	0.120031	+	0.992770i	$0.461701\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	−1929.97	−0.942370
$5$	8237.50	1.17886	0.589428	−	0.807821i	$-0.299353\pi$
$5$	8237.50	1.17886	0.589428	+	0.807821i	$0.299353\pi$
$6$	−2639.94	−0.138600
$7$	85962.3	1.93317	0.966583	−	0.256355i	$-0.0825216\pi$
$7$	85962.3	1.93317	0.966583	+	0.256355i	$0.0825216\pi$
$8$	−43216.5	−0.466288
$9$	59049.0	0.333333
$10$	89491.8	0.282998
$11$	−483868.	−0.905873	−0.452937	−	0.891543i	$-0.649624\pi$
$11$	−483868.	−0.905873	−0.452937	+	0.891543i	$0.649624\pi$
$12$	468984.	0.544078
$13$	396263.	0.296002	0.148001	−	0.988987i	$-0.452716\pi$
$13$	396263.	0.296002	0.148001	+	0.988987i	$0.452716\pi$
$14$	933890.	0.464079
$15$	−2.00171e6	−0.680612
$16$	3.48309e6	0.830432
$17$	−1.10618e7	−1.88955	−0.944775	−	0.327719i	$-0.893720\pi$
$17$	−1.10618e7	−1.88955	−0.944775	+	0.327719i	$0.893720\pi$
$18$	641505.	0.0800205
$19$	2.99198e6	0.277213	0.138606	−	0.990348i	$-0.455738\pi$
$19$	2.99198e6	0.277213	0.138606	+	0.990348i	$0.455738\pi$
$20$	−1.58982e7	−1.11092
$21$	−2.08888e7	−1.11611
$22$	−5.25672e6	−0.217465
$23$	1.83605e7	0.594813	0.297406	−	0.954751i	$-0.403878\pi$
$23$	1.83605e7	0.594813	0.297406	+	0.954751i	$0.403878\pi$
$24$	1.05016e7	0.269212
$25$	1.90283e7	0.389700
$26$	4.30498e6	0.0710588
$27$	−1.43489e7	−0.192450
$28$	−1.65905e8	−1.82176
$29$	2.21124e7	0.200192	0.100096	−	0.994978i	$-0.468085\pi$
$29$	2.21124e7	0.200192	0.100096	+	0.994978i	$0.468085\pi$
$30$	−2.17465e7	−0.163389
$31$	−2.01984e8	−1.26715	−0.633574	−	0.773682i	$-0.718413\pi$
$31$	−2.01984e8	−1.26715	−0.633574	+	0.773682i	$0.718413\pi$
$32$	1.26347e8	0.665643
$33$	1.17580e8	0.523006
$34$	−1.20175e8	−0.453608
$35$	7.08115e8	2.27892
$36$	−1.13963e8	−0.314123
$37$	−8.11946e8	−1.92494	−0.962471	−	0.271385i	$-0.912518\pi$
$37$	−8.11946e8	−1.92494	−0.962471	+	0.271385i	$0.912518\pi$
$38$	3.25047e7	0.0665482
$39$	−9.62920e7	−0.170897
$40$	−3.55996e8	−0.549687
$41$	−1.31207e9	−1.76867	−0.884335	−	0.466853i	$-0.845388\pi$
$41$	−1.31207e9	−1.76867	−0.884335	+	0.466853i	$0.845388\pi$
$42$	−2.26935e8	−0.267936
$43$	1.05670e8	0.109616	0.0548080	−	0.998497i	$-0.482545\pi$
$43$	1.05670e8	0.109616	0.0548080	+	0.998497i	$0.482545\pi$
$44$	9.33854e8	0.853668
$45$	4.86416e8	0.392952
$46$	1.99467e8	0.142792
$47$	2.23379e9	1.42070	0.710351	−	0.703847i	$-0.248536\pi$
$47$	2.23379e9	1.42070	0.710351	+	0.703847i	$0.248536\pi$
$48$	−8.46390e8	−0.479450
$49$	5.41220e9	2.73713
$50$	2.06722e8	0.0935519
$51$	2.68803e9	1.09093
$52$	−7.64778e8	−0.278944
$53$	3.80575e9	1.25004	0.625019	−	0.780610i	$-0.285091\pi$
$53$	3.80575e9	1.25004	0.625019	+	0.780610i	$0.285091\pi$
$54$	−1.55886e8	−0.0461999
$55$	−3.98587e9	−1.06789
$56$	−3.71499e9	−0.901413
$57$	−7.27050e8	−0.160049
$58$	2.40228e8	0.0480584
$59$	7.14924e8	0.130189
$59$	7.14924e8	0.130189
$60$	3.86326e9	0.641389
$61$	7.57915e9	1.14896	0.574482	−	0.818517i	$-0.305204\pi$
$61$	7.57915e9	1.14896	0.574482	+	0.818517i	$0.305204\pi$
$62$	−2.19434e9	−0.304193
$63$	5.07599e9	0.644388
$64$	−5.76073e9	−0.670637
$65$	3.26422e9	0.348944
$66$	1.27738e9	0.125554
$67$	−9.14960e9	−0.827925	−0.413962	−	0.910294i	$-0.635856\pi$
$67$	−9.14960e9	−0.827925	−0.413962	+	0.910294i	$0.635856\pi$
$68$	2.13491e10	1.78066
$69$	−4.46159e9	−0.343415
$70$	7.69292e9	0.547082
$71$	1.16988e10	0.769518	0.384759	−	0.923017i	$-0.374285\pi$
$71$	1.16988e10	0.769518	0.384759	+	0.923017i	$0.374285\pi$
$72$	−2.55189e9	−0.155429
$73$	−9.76078e9	−0.551073	−0.275536	−	0.961291i	$-0.588855\pi$
$73$	−9.76078e9	−0.551073	−0.275536	+	0.961291i	$0.588855\pi$
$74$	−8.82094e9	−0.462105
$75$	−4.62388e9	−0.224993
$76$	−5.77444e9	−0.261237
$77$	−4.15945e10	−1.75120
$78$	−1.04611e9	−0.0410258
$79$	8.26975e9	0.302373	0.151187	−	0.988505i	$-0.451691\pi$
$79$	8.26975e9	0.302373	0.151187	+	0.988505i	$0.451691\pi$
$80$	2.86919e10	0.978960
$81$	3.48678e9	0.111111
$82$	−1.42543e10	−0.424590
$83$	−1.53345e10	−0.427308	−0.213654	−	0.976909i	$-0.568537\pi$
$83$	−1.53345e10	−0.427308	−0.213654	+	0.976909i	$0.568537\pi$
$84$	4.03150e10	1.05179
$85$	−9.11220e10	−2.22751
$86$	1.14799e9	0.0263146
$87$	−5.37331e9	−0.115581
$88$	2.09111e10	0.422398
$89$	1.16326e9	0.0220816	0.0110408	−	0.999939i	$-0.496486\pi$
$89$	1.16326e9	0.0220816	0.0110408	+	0.999939i	$0.496486\pi$
$90$	5.28440e9	0.0943326
$91$	3.40637e10	0.572222
$92$	−3.54352e10	−0.560534
$93$	4.90821e10	0.731588
$94$	2.42677e10	0.341056
$95$	2.46464e10	0.326794
$96$	−3.07024e10	−0.384309
$97$	−8.72582e10	−1.03172	−0.515860	−	0.856673i	$-0.672527\pi$
$97$	−8.72582e10	−1.03172	−0.515860	+	0.856673i	$0.672527\pi$
$98$	5.87978e10	0.657079
$99$	−2.85719e10	−0.301958
$100$	−3.67241e10	−0.367241
$101$	−1.13741e11	−1.07683	−0.538417	−	0.842678i	$-0.680978\pi$
$101$	−1.13741e11	−1.07683	−0.538417	+	0.842678i	$0.680978\pi$
$102$	2.92026e10	0.261891
$103$	−1.22475e11	−1.04098	−0.520489	−	0.853869i	$-0.674250\pi$
$103$	−1.22475e11	−1.04098	−0.520489	+	0.853869i	$0.674250\pi$
$104$	−1.71251e10	−0.138023
$105$	−1.72072e11	−1.31574
$106$	4.13455e10	0.300086
$107$	−7.70211e10	−0.530883	−0.265441	−	0.964127i	$-0.585518\pi$
$107$	−7.70211e10	−0.530883	−0.265441	+	0.964127i	$0.585518\pi$
$108$	2.76930e10	0.181359
$109$	−2.18663e11	−1.36123	−0.680613	−	0.732643i	$-0.738287\pi$
$109$	−2.18663e11	−1.36123	−0.680613	+	0.732643i	$0.738287\pi$
$110$	−4.33022e10	−0.256360
$111$	1.97303e11	1.11137
$112$	2.99414e11	1.60536
$113$	−1.83692e11	−0.937907	−0.468953	−	0.883223i	$-0.655369\pi$
$113$	−1.83692e11	−0.937907	−0.468953	+	0.883223i	$0.655369\pi$
$114$	−7.89864e9	−0.0384216
$115$	1.51244e11	0.701198
$116$	−4.26764e10	−0.188655
$117$	2.33989e10	0.0986675
$118$	7.76690e9	0.0312534
$119$	−9.50902e11	−3.65281
$120$	8.65070e10	0.317362
$121$	−5.11831e10	−0.179394
$122$	8.23395e10	0.275822
$123$	3.18834e11	1.02114
$124$	3.89824e11	1.19412
$125$	−2.45476e11	−0.719456
$126$	5.51453e10	0.154693
$127$	2.26605e10	0.0608624	0.0304312	−	0.999537i	$-0.490312\pi$
$127$	2.26605e10	0.0608624	0.0304312	+	0.999537i	$0.490312\pi$
$128$	−3.21344e11	−0.826638
$129$	−2.56777e10	−0.0632868
$130$	3.54623e10	0.0837681
$131$	6.04141e11	1.36819	0.684095	−	0.729393i	$-0.260197\pi$
$131$	6.04141e11	1.36819	0.684095	+	0.729393i	$0.260197\pi$
$132$	−2.26926e11	−0.492866
$133$	2.57197e11	0.535898
$134$	−9.94008e10	−0.198753
$135$	−1.18199e11	−0.226871
$136$	4.78054e11	0.881076
$137$	6.09570e10	0.107910	0.0539548	−	0.998543i	$-0.482817\pi$
$137$	6.09570e10	0.107910	0.0539548	+	0.998543i	$0.482817\pi$
$138$	−4.84705e10	−0.0824408
$139$	−1.08597e12	−1.77515	−0.887575	−	0.460664i	$-0.847611\pi$
$139$	−1.08597e12	−1.77515	−0.887575	+	0.460664i	$0.847611\pi$
$140$	−1.36664e12	−2.14759
$141$	−5.42810e11	−0.820243
$142$	1.27095e11	0.184732
$143$	−1.91739e11	−0.268141
$144$	2.05673e11	0.276811
$145$	1.82151e11	0.235998
$146$	−1.06041e11	−0.132291
$147$	−1.31516e12	−1.58028
$148$	1.56704e12	1.81401
$149$	1.17467e12	1.31036	0.655179	−	0.755474i	$-0.272593\pi$
$149$	1.17467e12	1.31036	0.655179	+	0.755474i	$0.272593\pi$
$150$	−5.02336e10	−0.0540122
$151$	1.70016e12	1.76244	0.881222	−	0.472702i	$-0.156721\pi$
$151$	1.70016e12	1.76244	0.881222	+	0.472702i	$0.156721\pi$
$152$	−1.29303e11	−0.129261
$153$	−6.53191e11	−0.629850
$154$	−4.51880e11	−0.420396
$155$	−1.66384e12	−1.49378
$156$	1.85841e11	0.161048
$157$	−1.21187e12	−1.01393	−0.506965	−	0.861967i	$-0.669233\pi$
$157$	−1.21187e12	−1.01393	−0.506965	+	0.861967i	$0.669233\pi$
$158$	8.98422e10	0.0725882
$159$	−9.24798e11	−0.721710
$160$	1.04079e12	0.784697
$161$	1.57831e12	1.14987
$162$	3.78802e10	0.0266735
$163$	5.80190e11	0.394947	0.197473	−	0.980308i	$-0.436726\pi$
$163$	5.80190e11	0.394947	0.197473	+	0.980308i	$0.436726\pi$
$164$	2.53227e12	1.66674
$165$	9.68565e11	0.616549
$166$	−1.66594e11	−0.102580
$167$	−2.85780e12	−1.70252	−0.851258	−	0.524747i	$-0.824160\pi$
$167$	−2.85780e12	−1.70252	−0.851258	+	0.524747i	$0.824160\pi$
$168$	9.02743e11	0.520431
$169$	−1.63514e12	−0.912383
$170$	−9.89944e11	−0.534739
$171$	1.76673e11	0.0924043
$172$	−2.03940e11	−0.103299
$173$	−2.29060e11	−0.112381	−0.0561907	−	0.998420i	$-0.517895\pi$
$173$	−2.29060e11	−0.112381	−0.0561907	+	0.998420i	$0.517895\pi$
$174$	−5.83754e10	−0.0277465
$175$	1.63572e12	0.753354
$176$	−1.68536e12	−0.752267
$177$	−1.73727e11	−0.0751646
$178$	1.26376e10	0.00530096
$179$	1.96341e12	0.798581	0.399290	−	0.916824i	$-0.369257\pi$
$179$	1.96341e12	0.798581	0.399290	+	0.916824i	$0.369257\pi$
$180$	−9.38771e11	−0.370306
$181$	−3.39509e12	−1.29903	−0.649514	−	0.760349i	$-0.725028\pi$
$181$	−3.39509e12	−1.29903	−0.649514	+	0.760349i	$0.725028\pi$
$182$	3.70066e11	0.137368
$183$	−1.84173e12	−0.663355
$184$	−7.93475e11	−0.277354
$185$	−6.68841e12	−2.26923
$186$	5.33225e11	0.175626
$187$	5.35248e12	1.71169
$188$	−4.31115e12	−1.33883
$189$	−1.23347e12	−0.372038
$190$	2.67757e11	0.0784506
$191$	−1.17412e12	−0.334218	−0.167109	−	0.985938i	$-0.553443\pi$
$191$	−1.17412e12	−0.334218	−0.167109	+	0.985938i	$0.553443\pi$
$192$	1.39986e12	0.387193
$193$	1.88890e12	0.507744	0.253872	−	0.967238i	$-0.418296\pi$
$193$	1.88890e12	0.507744	0.253872	+	0.967238i	$0.418296\pi$
$194$	−9.47968e11	−0.247676
$195$	−7.93205e11	−0.201463
$196$	−1.04454e13	−2.57939
$197$	6.29932e12	1.51262	0.756310	−	0.654214i	$-0.227000\pi$
$197$	6.29932e12	1.51262	0.756310	+	0.654214i	$0.227000\pi$
$198$	−3.10404e11	−0.0724884
$199$	−9.06904e11	−0.206001	−0.103001	−	0.994681i	$-0.532844\pi$
$199$	−9.06904e11	−0.206001	−0.103001	+	0.994681i	$0.532844\pi$
$200$	−8.22337e11	−0.181712
$201$	2.22335e12	0.478003
$202$	−1.23567e12	−0.258507
$203$	1.90083e12	0.387004
$204$	−5.18783e12	−1.02806
$205$	−1.08082e13	−2.08501
$206$	−1.33056e12	−0.249899
$207$	1.08417e12	0.198271
$208$	1.38022e12	0.245810
$209$	−1.44772e12	−0.251120
$210$	−1.86938e12	−0.315858
$211$	3.90505e12	0.642796	0.321398	−	0.946944i	$-0.395847\pi$
$211$	3.90505e12	0.642796	0.321398	+	0.946944i	$0.395847\pi$
$212$	−7.34500e12	−1.17800
$213$	−2.84280e12	−0.444281
$214$	−8.36753e11	−0.127445
$215$	8.70454e11	0.129221
$216$	6.20110e11	0.0897373
$217$	−1.73630e13	−2.44961
$218$	−2.37555e12	−0.326778
$219$	2.37187e12	0.318162
$220$	7.69262e12	1.00635
$221$	−4.38340e12	−0.559312
$222$	2.14349e12	0.266796
$223$	−7.60771e12	−0.923798	−0.461899	−	0.886933i	$-0.652832\pi$
$223$	−7.60771e12	−0.923798	−0.461899	+	0.886933i	$0.652832\pi$
$224$	1.08611e13	1.28680
$225$	1.12360e12	0.129900
$226$	−1.99562e12	−0.225155
$227$	−1.20683e13	−1.32894	−0.664468	−	0.747317i	$-0.731342\pi$
$227$	−1.20683e13	−1.32894	−0.664468	+	0.747317i	$0.731342\pi$
$228$	1.40319e12	0.150825
$229$	7.78483e12	0.816872	0.408436	−	0.912787i	$-0.366074\pi$
$229$	7.78483e12	0.816872	0.408436	+	0.912787i	$0.366074\pi$
$230$	1.64311e12	0.168331
$231$	1.01075e13	1.01106
$232$	−9.55621e11	−0.0933473
$233$	1.58706e13	1.51403	0.757016	−	0.653396i	$-0.226656\pi$
$233$	1.58706e13	1.51403	0.757016	+	0.653396i	$0.226656\pi$
$234$	2.54205e11	0.0236863
$235$	1.84008e13	1.67480
$236$	−1.37979e12	−0.122686
$237$	−2.00955e12	−0.174575
$238$	−1.03305e13	−0.876900
$239$	1.46660e13	1.21653	0.608264	−	0.793735i	$-0.291866\pi$
$239$	1.46660e13	1.21653	0.608264	+	0.793735i	$0.291866\pi$
$240$	−6.97214e12	−0.565203
$241$	−1.66704e13	−1.32085	−0.660423	−	0.750894i	$-0.729623\pi$
$241$	−1.66704e13	−1.32085	−0.660423	+	0.750894i	$0.729623\pi$
$242$	−5.56051e11	−0.0430655
$243$	−8.47289e11	−0.0641500
$244$	−1.46276e13	−1.08275
$245$	4.45830e13	3.22668
$246$	3.46379e12	0.245137
$247$	1.18561e12	0.0820557
$248$	8.72903e12	0.590856
$249$	3.72629e12	0.246707
$250$	−2.66684e12	−0.172714
$251$	9.30603e12	0.589602	0.294801	−	0.955559i	$-0.404747\pi$
$251$	9.30603e12	0.589602	0.294801	+	0.955559i	$0.404747\pi$
$252$	−9.79653e12	−0.607253
$253$	−8.88404e12	−0.538825
$254$	2.46182e11	0.0146107
$255$	2.21426e13	1.28605
$256$	8.30691e12	0.472193
$257$	6.33866e12	0.352667	0.176334	−	0.984330i	$-0.443576\pi$
$257$	6.33866e12	0.352667	0.176334	+	0.984330i	$0.443576\pi$
$258$	−2.78962e11	−0.0151927
$259$	−6.97968e13	−3.72123
$260$	−6.29986e12	−0.328835
$261$	1.30572e12	0.0667307
$262$	6.56336e12	0.328450
$263$	−2.79755e13	−1.37095	−0.685474	−	0.728097i	$-0.740405\pi$
$263$	−2.79755e13	−1.37095	−0.685474	+	0.728097i	$0.740405\pi$
$264$	−5.08140e12	−0.243872
$265$	3.13499e13	1.47361
$266$	2.79418e12	0.128649
$267$	−2.82672e11	−0.0127488
$268$	1.76585e13	0.780212
$269$	−2.54120e13	−1.10002	−0.550011	−	0.835157i	$-0.685377\pi$
$269$	−2.54120e13	−1.10002	−0.550011	+	0.835157i	$0.685377\pi$
$270$	−1.28411e12	−0.0544630
$271$	−1.78642e13	−0.742426	−0.371213	−	0.928548i	$-0.621058\pi$
$271$	−1.78642e13	−0.742426	−0.371213	+	0.928548i	$0.621058\pi$
$272$	−3.85294e13	−1.56914
$273$	−8.27748e12	−0.330372
$274$	6.62234e11	0.0259050
$275$	−9.20719e12	−0.353019
$276$	8.61076e12	0.323624
$277$	−3.46602e13	−1.27700	−0.638501	−	0.769621i	$-0.720445\pi$
$277$	−3.46602e13	−1.27700	−0.638501	+	0.769621i	$0.720445\pi$
$278$	−1.17979e13	−0.426145
$279$	−1.19269e13	−0.422383
$280$	−3.06023e13	−1.06264
$281$	6.87979e12	0.234256	0.117128	−	0.993117i	$-0.462631\pi$
$281$	6.87979e12	0.234256	0.117128	+	0.993117i	$0.462631\pi$
$282$	−5.89706e12	−0.196909
$283$	−3.44800e13	−1.12913	−0.564563	−	0.825390i	$-0.690955\pi$
$283$	−3.44800e13	−1.12913	−0.564563	+	0.825390i	$0.690955\pi$
$284$	−2.25783e13	−0.725171
$285$	−5.98908e12	−0.188675
$286$	−2.08304e12	−0.0643703
$287$	−1.12789e14	−3.41913
$288$	7.46069e12	0.221881
$289$	8.80925e13	2.57040
$290$	1.97888e12	0.0566539
$291$	2.12037e13	0.595663
$292$	1.88381e13	0.519314
$293$	−5.73101e13	−1.55046	−0.775228	−	0.631681i	$-0.782365\pi$
$293$	−5.73101e13	−1.55046	−0.775228	+	0.631681i	$0.782365\pi$
$294$	−1.42879e13	−0.379365
$295$	5.88919e12	0.153474
$296$	3.50895e13	0.897578
$297$	6.94298e12	0.174335
$298$	1.27615e13	0.314566
$299$	7.27557e12	0.176066
$300$	8.92397e12	0.212027
$301$	9.08361e12	0.211906
$302$	1.84704e13	0.423095
$303$	2.76390e13	0.621711
$304$	1.04213e13	0.230207
$305$	6.24333e13	1.35446
$306$	−7.09623e12	−0.151203
$307$	1.85741e13	0.388728	0.194364	−	0.980929i	$-0.437736\pi$
$307$	1.85741e13	0.388728	0.194364	+	0.980929i	$0.437736\pi$
$308$	8.02762e13	1.65028
$309$	2.97613e13	0.601008
$310$	−1.80759e13	−0.358600
$311$	6.17250e12	0.120304	0.0601519	−	0.998189i	$-0.480841\pi$
$311$	6.17250e12	0.120304	0.0601519	+	0.998189i	$0.480841\pi$
$312$	4.16140e12	0.0796874
$313$	4.47637e13	0.842233	0.421117	−	0.907006i	$-0.361638\pi$
$313$	4.47637e13	0.842233	0.421117	+	0.907006i	$0.361638\pi$
$314$	−1.31657e13	−0.243406
$315$	4.18135e13	0.759641
$316$	−1.59604e13	−0.284948
$317$	−5.36595e13	−0.941500	−0.470750	−	0.882267i	$-0.656017\pi$
$317$	−5.36595e13	−0.941500	−0.470750	+	0.882267i	$0.656017\pi$
$318$	−1.00470e13	−0.173255
$319$	−1.06995e13	−0.181349
$320$	−4.74540e13	−0.790584
$321$	1.87161e13	0.306505
$322$	1.71466e13	0.276040
$323$	−3.30968e13	−0.523808
$324$	−6.72941e12	−0.104708
$325$	7.54022e12	0.115352
$326$	6.30315e12	0.0948115
$327$	5.31352e13	0.785905
$328$	5.67032e13	0.824710
$329$	1.92021e14	2.74645
$330$	1.05224e13	0.148010
$331$	−4.04640e13	−0.559777	−0.279888	−	0.960033i	$-0.590297\pi$
$331$	−4.04640e13	−0.559777	−0.279888	+	0.960033i	$0.590297\pi$
$332$	2.95953e13	0.402683
$333$	−4.79446e13	−0.641647
$334$	−3.10470e13	−0.408709
$335$	−7.53699e13	−0.976004
$336$	−7.27577e13	−0.926857
$337$	1.42628e14	1.78748	0.893741	−	0.448583i	$-0.148071\pi$
$337$	1.42628e14	1.78748	0.893741	+	0.448583i	$0.148071\pi$
$338$	−1.77640e13	−0.219028
$339$	4.46373e13	0.541501
$340$	1.75863e14	2.09914
$341$	9.77336e13	1.14788
$342$	1.91937e12	0.0221827
$343$	2.95270e14	3.35816
$344$	−4.56667e12	−0.0511127
$345$	−3.67524e13	−0.404837
$346$	−2.48849e12	−0.0269785
$347$	−7.80059e12	−0.0832368	−0.0416184	−	0.999134i	$-0.513251\pi$
$347$	−7.80059e12	−0.0832368	−0.0416184	+	0.999134i	$0.513251\pi$
$348$	1.03704e13	0.108920
$349$	7.69940e12	0.0796007	0.0398004	−	0.999208i	$-0.487328\pi$
$349$	7.69940e12	0.0796007	0.0398004	+	0.999208i	$0.487328\pi$
$350$	1.77703e13	0.180851
$351$	−5.68594e12	−0.0569657
$352$	−6.11355e13	−0.602989
$353$	7.78335e13	0.755797	0.377899	−	0.925847i	$-0.376647\pi$
$353$	7.78335e13	0.755797	0.377899	+	0.925847i	$0.376647\pi$
$354$	−1.88736e12	−0.0180441
$355$	9.63685e13	0.907150
$356$	−2.24506e12	−0.0208091
$357$	2.31069e14	2.10895
$358$	2.13304e13	0.191709
$359$	−2.86817e13	−0.253855	−0.126928	−	0.991912i	$-0.540512\pi$
$359$	−2.86817e13	−0.253855	−0.126928	+	0.991912i	$0.540512\pi$
$360$	−2.10212e13	−0.183229
$361$	−1.07538e14	−0.923153
$362$	−3.68840e13	−0.311847
$363$	1.24375e13	0.103573
$364$	−6.57421e13	−0.539245
$365$	−8.04044e13	−0.649635
$366$	−2.00085e13	−0.159246
$367$	−1.54421e14	−1.21072	−0.605361	−	0.795951i	$-0.706971\pi$
$367$	−1.54421e14	−1.21072	−0.605361	+	0.795951i	$0.706971\pi$
$368$	6.39510e13	0.493952
$369$	−7.74766e13	−0.589556
$370$	−7.26625e13	−0.544754
$371$	3.27151e14	2.41653
$372$	−9.47272e13	−0.689427
$373$	−1.03292e14	−0.740747	−0.370374	−	0.928883i	$-0.620770\pi$
$373$	−1.03292e14	−0.740747	−0.370374	+	0.928883i	$0.620770\pi$
$374$	5.81490e13	0.410912
$375$	5.96507e13	0.415378
$376$	−9.65364e13	−0.662457
$377$	8.76233e12	0.0592574
$378$	−1.34003e13	−0.0893120
$379$	5.20020e13	0.341589	0.170795	−	0.985307i	$-0.445367\pi$
$379$	5.20020e13	0.341589	0.170795	+	0.985307i	$0.445367\pi$
$380$	−4.75669e13	−0.307961
$381$	−5.50650e12	−0.0351389
$382$	−1.27556e13	−0.0802329
$383$	1.46641e14	0.909204	0.454602	−	0.890695i	$-0.349782\pi$
$383$	1.46641e14	0.909204	0.454602	+	0.890695i	$0.349782\pi$
$384$	7.80866e13	0.477259
$385$	−3.42634e14	−2.06441
$386$	2.05210e13	0.121890
$387$	6.23969e12	0.0365387
$388$	1.68406e14	0.972262
$389$	−7.06368e13	−0.402076	−0.201038	−	0.979583i	$-0.564432\pi$
$389$	−7.06368e13	−0.402076	−0.201038	+	0.979583i	$0.564432\pi$
$390$	−8.61734e12	−0.0483635
$391$	−2.03100e14	−1.12393
$392$	−2.33896e14	−1.27629
$393$	−1.46806e14	−0.789925
$394$	6.84355e13	0.363122
$395$	6.81221e13	0.356454
$396$	5.51431e13	0.284556
$397$	−2.55213e14	−1.29884	−0.649420	−	0.760430i	$-0.724988\pi$
$397$	−2.55213e14	−1.29884	−0.649420	+	0.760430i	$0.724988\pi$
$398$	−9.85256e12	−0.0494529
$399$	−6.24989e13	−0.309401
$400$	6.62772e13	0.323619
$401$	−2.40852e14	−1.16000	−0.579998	−	0.814618i	$-0.696947\pi$
$401$	−2.40852e14	−1.16000	−0.579998	+	0.814618i	$0.696947\pi$
$402$	2.41544e13	0.114750
$403$	−8.00388e13	−0.375079
$404$	2.19517e14	1.01478
$405$	2.87224e13	0.130984
$406$	2.06506e13	0.0929049
$407$	3.92875e14	1.74375
$408$	−1.16167e14	−0.508689
$409$	−6.22186e11	−0.00268808	−0.00134404	−	0.999999i	$-0.500428\pi$
$409$	−6.22186e11	−0.00268808	−0.00134404	+	0.999999i	$0.500428\pi$
$410$	−1.17420e14	−0.500530
$411$	−1.48126e13	−0.0623017
$412$	2.36373e14	0.980986
$413$	6.14566e13	0.251677
$414$	1.17783e13	0.0475972
$415$	−1.26318e14	−0.503735
$416$	5.00669e13	0.197032
$417$	2.63890e14	1.02488
$418$	−1.57280e13	−0.0602842
$419$	1.06449e12	0.00402686	0.00201343	−	0.999998i	$-0.499359\pi$
$419$	1.06449e12	0.00402686	0.00201343	+	0.999998i	$0.499359\pi$
$420$	3.32094e14	1.23991
$421$	−8.27486e13	−0.304936	−0.152468	−	0.988308i	$-0.548722\pi$
$421$	−8.27486e13	−0.304936	−0.152468	+	0.988308i	$0.548722\pi$
$422$	4.24243e13	0.154311
$423$	1.31903e14	0.473568
$424$	−1.64471e14	−0.582878
$425$	−2.10488e14	−0.736357
$426$	−3.08840e13	−0.106655
$427$	6.51522e14	2.22114
$428$	1.48649e14	0.500288
$429$	4.65926e13	0.154811
$430$	9.45657e12	0.0310211
$431$	−4.78272e13	−0.154900	−0.0774498	−	0.996996i	$-0.524678\pi$
$431$	−4.78272e13	−0.154900	−0.0774498	+	0.996996i	$0.524678\pi$
$432$	−4.99785e13	−0.159817
$433$	−5.79214e14	−1.82876	−0.914378	−	0.404862i	$-0.867319\pi$
$433$	−5.79214e14	−1.82876	−0.914378	+	0.404862i	$0.867319\pi$
$434$	−1.88631e14	−0.588056
$435$	−4.42627e13	−0.136253
$436$	4.22015e14	1.28278
$437$	5.49340e13	0.164890
$438$	2.57679e13	0.0763784
$439$	−4.41293e14	−1.29173	−0.645865	−	0.763452i	$-0.723503\pi$
$439$	−4.41293e14	−1.29173	−0.645865	+	0.763452i	$0.723503\pi$
$440$	1.72255e14	0.497946
$441$	3.19585e14	0.912376
$442$	−4.76210e13	−0.134269
$443$	7.49085e13	0.208598	0.104299	−	0.994546i	$-0.466740\pi$
$443$	7.49085e13	0.208598	0.104299	+	0.994546i	$0.466740\pi$
$444$	−3.80790e14	−1.04732
$445$	9.58235e12	0.0260311
$446$	−8.26497e13	−0.221768
$447$	−2.85444e14	−0.756535
$448$	−4.95206e14	−1.29645
$449$	−7.10060e13	−0.183628	−0.0918142	−	0.995776i	$-0.529267\pi$
$449$	−7.10060e13	−0.183628	−0.0918142	+	0.995776i	$0.529267\pi$
$450$	1.22068e13	0.0311840
$451$	6.34870e14	1.60219
$452$	3.54522e14	0.883856
$453$	−4.13138e14	−1.01755
$454$	−1.31109e14	−0.319027
$455$	2.80600e14	0.674567
$456$	3.14206e13	0.0746290
$457$	6.60526e14	1.55007	0.775034	−	0.631920i	$-0.217733\pi$
$457$	6.60526e14	1.55007	0.775034	+	0.631920i	$0.217733\pi$
$458$	8.45740e13	0.196100
$459$	1.58725e14	0.363644
$460$	−2.91898e14	−0.660788
$461$	−3.75432e14	−0.839800	−0.419900	−	0.907570i	$-0.637935\pi$
$461$	−3.75432e14	−0.839800	−0.419900	+	0.907570i	$0.637935\pi$
$462$	1.09807e14	0.242716
$463$	−4.33108e14	−0.946021	−0.473011	−	0.881057i	$-0.656833\pi$
$463$	−4.33108e14	−0.946021	−0.473011	+	0.881057i	$0.656833\pi$
$464$	7.70194e13	0.166246
$465$	4.04314e14	0.862437
$466$	1.72417e14	0.363461
$467$	−2.65554e14	−0.553235	−0.276618	−	0.960980i	$-0.589214\pi$
$467$	−2.65554e14	−0.553235	−0.276618	+	0.960980i	$0.589214\pi$
$468$	−4.51594e13	−0.0929813
$469$	−7.86521e14	−1.60052
$470$	1.99905e14	0.402056
$471$	2.94485e14	0.585393
$472$	−3.08965e13	−0.0607056
$473$	−5.11302e13	−0.0992982
$474$	−2.18316e13	−0.0419088
$475$	5.69322e13	0.108030
$476$	1.83522e15	3.44230
$477$	2.24726e14	0.416679
$478$	1.59330e14	0.292042
$479$	−6.60593e14	−1.19699	−0.598493	−	0.801128i	$-0.704233\pi$
$479$	−6.60593e14	−1.19699	−0.598493	+	0.801128i	$0.704233\pi$
$480$	−2.52911e14	−0.453045
$481$	−3.21744e14	−0.569788
$482$	−1.81106e14	−0.317084
$483$	−3.83529e14	−0.663879
$484$	9.87822e13	0.169055
$485$	−7.18789e14	−1.21625
$486$	−9.20490e12	−0.0154000
$487$	5.52491e14	0.913936	0.456968	−	0.889483i	$-0.348935\pi$
$487$	5.52491e14	0.913936	0.456968	+	0.889483i	$0.348935\pi$
$488$	−3.27544e14	−0.535749
$489$	−1.40986e14	−0.228023
$490$	4.84347e14	0.774602
$491$	−5.75971e14	−0.910862	−0.455431	−	0.890271i	$-0.650515\pi$
$491$	−5.75971e14	−0.910862	−0.455431	+	0.890271i	$0.650515\pi$
$492$	−6.15341e14	−0.962294
$493$	−2.44604e14	−0.378273
$494$	1.28804e13	0.0196984
$495$	−2.35361e14	−0.355964
$496$	−7.03527e14	−1.05228
$497$	1.00565e15	1.48761
$498$	4.04823e13	0.0592248
$499$	−4.91363e14	−0.710967	−0.355484	−	0.934683i	$-0.615684\pi$
$499$	−4.91363e14	−0.710967	−0.355484	+	0.934683i	$0.615684\pi$
$500$	4.73763e14	0.677994
$501$	6.94445e14	0.982948
$502$	1.01100e14	0.141541
$503$	−7.40782e13	−0.102581	−0.0512905	−	0.998684i	$-0.516333\pi$
$503$	−7.40782e13	−0.102581	−0.0512905	+	0.998684i	$0.516333\pi$
$504$	−2.19367e14	−0.300471
$505$	−9.36940e14	−1.26943
$506$	−9.65157e13	−0.129351
$507$	3.97338e14	0.526764
$508$	−4.37342e13	−0.0573549
$509$	5.93005e14	0.769327	0.384663	−	0.923057i	$-0.374318\pi$
$509$	5.93005e14	0.769327	0.384663	+	0.923057i	$0.374318\pi$
$510$	2.40556e14	0.308731
$511$	−8.39059e14	−1.06531
$512$	7.48358e14	0.939993
$513$	−4.29316e13	−0.0533496
$514$	6.88628e13	0.0846618
$515$	−1.00888e15	−1.22716
$516$	4.95574e13	0.0596396
$517$	−1.08086e15	−1.28698
$518$	−7.58268e14	−0.893325
$519$	5.56615e13	0.0648835
$520$	−1.41068e14	−0.162709
$521$	−8.94351e13	−0.102071	−0.0510353	−	0.998697i	$-0.516252\pi$
$521$	−8.94351e13	−0.102071	−0.0510353	+	0.998697i	$0.516252\pi$
$522$	1.41852e13	0.0160195
$523$	5.03702e14	0.562878	0.281439	−	0.959579i	$-0.409188\pi$
$523$	5.03702e14	0.562878	0.281439	+	0.959579i	$0.409188\pi$
$524$	−1.16598e15	−1.28934
$525$	−3.97479e14	−0.434949
$526$	−3.03924e14	−0.329112
$527$	2.23431e15	2.39434
$528$	4.09541e14	0.434321
$529$	−6.15704e14	−0.646198
$530$	3.40583e14	0.353758
$531$	4.22156e13	0.0433963
$532$	−4.96384e14	−0.505015
$533$	−5.19926e14	−0.523530
$534$	−3.07093e12	−0.00306051
$535$	−6.34461e14	−0.625834
$536$	3.95414e14	0.386052
$537$	−4.77108e14	−0.461061
$538$	−2.76075e14	−0.264073
$539$	−2.61879e15	−2.47949
$540$	2.28121e14	0.213796
$541$	1.23010e14	0.114118	0.0570591	−	0.998371i	$-0.481828\pi$
$541$	1.23010e14	0.114118	0.0570591	+	0.998371i	$0.481828\pi$
$542$	−1.94076e14	−0.178228
$543$	8.25006e14	0.749995
$544$	−1.39764e15	−1.25777
$545$	−1.80124e15	−1.60469
$546$	−8.99261e13	−0.0793097
$547$	−1.02482e15	−0.894779	−0.447389	−	0.894339i	$-0.647646\pi$
$547$	−1.02482e15	−0.894779	−0.447389	+	0.894339i	$0.647646\pi$
$548$	−1.17645e14	−0.101691
$549$	4.47541e14	0.382988
$550$	−1.00026e14	−0.0847462
$551$	6.61598e13	0.0554958
$552$	1.92814e14	0.160131
$553$	7.10887e14	0.584538
$554$	−3.76546e14	−0.306559
$555$	1.62528e15	1.31014
$556$	2.09589e15	1.67285
$557$	1.43675e15	1.13547	0.567736	−	0.823211i	$-0.307819\pi$
$557$	1.43675e15	1.13547	0.567736	+	0.823211i	$0.307819\pi$
$558$	−1.29574e14	−0.101398
$559$	4.18730e13	0.0324466
$560$	2.46643e15	1.89249
$561$	−1.30065e15	−0.988246
$562$	7.47417e13	0.0562358
$563$	−1.26652e15	−0.943658	−0.471829	−	0.881690i	$-0.656406\pi$
$563$	−1.26652e15	−0.943658	−0.471829	+	0.881690i	$0.656406\pi$
$564$	1.04761e15	0.772973
$565$	−1.51317e15	−1.10566
$566$	−3.74589e14	−0.271060
$567$	2.99732e14	0.214796
$568$	−5.05579e14	−0.358817
$569$	1.80928e14	0.127171	0.0635855	−	0.997976i	$-0.479746\pi$
$569$	1.80928e14	0.127171	0.0635855	+	0.997976i	$0.479746\pi$
$570$	−6.50650e13	−0.0452935
$571$	1.54365e15	1.06427	0.532133	−	0.846661i	$-0.321391\pi$
$571$	1.54365e15	1.06427	0.532133	+	0.846661i	$0.321391\pi$
$572$	3.70052e14	0.252688
$573$	2.85312e14	0.192961
$574$	−1.22533e15	−0.820802
$575$	3.49368e14	0.231798
$576$	−3.40165e14	−0.223546
$577$	2.99098e15	1.94691	0.973455	−	0.228877i	$-0.0735053\pi$
$577$	2.99098e15	1.94691	0.973455	+	0.228877i	$0.0735053\pi$
$578$	9.57032e14	0.617054
$579$	−4.59004e14	−0.293146
$580$	−3.51547e14	−0.222397
$581$	−1.31819e15	−0.826058
$582$	2.30356e14	0.142996
$583$	−1.84148e15	−1.13238
$584$	4.21827e14	0.256959
$585$	1.92749e14	0.116315
$586$	−6.22614e14	−0.372205
$587$	2.47994e15	1.46869	0.734346	−	0.678775i	$-0.237489\pi$
$587$	2.47994e15	1.46869	0.734346	+	0.678775i	$0.237489\pi$
$588$	2.53823e15	1.48921
$589$	−6.04331e14	−0.351270
$590$	6.39798e13	0.0368432
$591$	−1.53074e15	−0.873311
$592$	−2.82808e15	−1.59853
$593$	−5.82093e14	−0.325980	−0.162990	−	0.986628i	$-0.552114\pi$
$593$	−5.82093e14	−0.325980	−0.162990	+	0.986628i	$0.552114\pi$
$594$	7.54282e13	0.0418512
$595$	−7.83306e15	−4.30614
$596$	−2.26708e15	−1.23484
$597$	2.20378e14	0.118935
$598$	7.90414e13	0.0422667
$599$	−2.52906e15	−1.34002	−0.670010	−	0.742352i	$-0.733710\pi$
$599$	−2.52906e15	−1.34002	−0.670010	+	0.742352i	$0.733710\pi$
$600$	1.99828e14	0.104912
$601$	−2.26350e15	−1.17753	−0.588764	−	0.808305i	$-0.700385\pi$
$601$	−2.26350e15	−1.17753	−0.588764	+	0.808305i	$0.700385\pi$
$602$	9.86839e13	0.0508704
$603$	−5.40275e14	−0.275975
$604$	−3.28126e15	−1.66088
$605$	−4.21621e14	−0.211479
$606$	3.00269e14	0.149249
$607$	−1.26647e15	−0.623816	−0.311908	−	0.950112i	$-0.600968\pi$
$607$	−1.26647e15	−0.623816	−0.311908	+	0.950112i	$0.600968\pi$
$608$	3.78029e14	0.184525
$609$	−4.61903e14	−0.223437
$610$	6.78272e14	0.325154
$611$	8.85167e14	0.420532
$612$	1.26064e15	0.593552
$613$	−9.03727e14	−0.421701	−0.210850	−	0.977518i	$-0.567623\pi$
$613$	−9.03727e14	−0.421701	−0.210850	+	0.977518i	$0.567623\pi$
$614$	2.01788e14	0.0933188
$615$	2.62639e15	1.20378
$616$	1.79757e15	0.816566
$617$	−5.84125e14	−0.262989	−0.131494	−	0.991317i	$-0.541978\pi$
$617$	−5.84125e14	−0.262989	−0.131494	+	0.991317i	$0.541978\pi$
$618$	3.23325e14	0.144279
$619$	−1.25676e15	−0.555846	−0.277923	−	0.960603i	$-0.589646\pi$
$619$	−1.25676e15	−0.555846	−0.277923	+	0.960603i	$0.589646\pi$
$620$	3.21117e15	1.40770
$621$	−2.63452e14	−0.114472
$622$	6.70577e13	0.0288803
$623$	9.99965e13	0.0426875
$624$	−3.35393e14	−0.141919
$625$	−2.95123e15	−1.23783
$626$	4.86311e14	0.202188
$627$	3.51797e14	0.144984
$628$	2.33888e15	0.955498
$629$	8.98162e15	3.63727
$630$	4.54259e14	0.182361
$631$	4.09495e15	1.62962	0.814811	−	0.579727i	$-0.196841\pi$
$631$	4.09495e15	1.62962	0.814811	+	0.579727i	$0.196841\pi$
$632$	−3.57390e14	−0.140993
$633$	−9.48928e14	−0.371119
$634$	−5.82954e14	−0.226018
$635$	1.86666e14	0.0717479
$636$	1.78484e15	0.680118
$637$	2.14466e15	0.810197
$638$	−1.16239e14	−0.0435348
$639$	6.90800e14	0.256506
$640$	−2.64707e15	−0.974486
$641$	−1.76266e15	−0.643353	−0.321677	−	0.946850i	$-0.604246\pi$
$641$	−1.76266e15	−0.643353	−0.321677	+	0.946850i	$0.604246\pi$
$642$	2.03331e14	0.0735802
$643$	6.57445e14	0.235884	0.117942	−	0.993020i	$-0.462370\pi$
$643$	6.57445e14	0.235884	0.117942	+	0.993020i	$0.462370\pi$
$644$	−3.04609e15	−1.08360
$645$	−2.11520e14	−0.0746060
$646$	−3.59562e14	−0.125746
$647$	4.34672e15	1.50726	0.753630	−	0.657299i	$-0.228301\pi$
$647$	4.34672e15	1.50726	0.753630	+	0.657299i	$0.228301\pi$
$648$	−1.50687e14	−0.0518098
$649$	−3.45929e14	−0.117935
$650$	8.19165e13	0.0276916
$651$	4.21921e15	1.41428
$652$	−1.11975e15	−0.372186
$653$	2.44494e15	0.805833	0.402917	−	0.915237i	$-0.367996\pi$
$653$	2.44494e15	0.805833	0.402917	+	0.915237i	$0.367996\pi$
$654$	5.77258e14	0.188665
$655$	4.97662e15	1.61290
$656$	−4.57006e15	−1.46876
$657$	−5.76364e14	−0.183691
$658$	2.08611e15	0.659318
$659$	2.36423e15	0.741001	0.370501	−	0.928832i	$-0.379186\pi$
$659$	2.36423e15	0.741001	0.370501	+	0.928832i	$0.379186\pi$
$660$	−1.86931e15	−0.581017
$661$	1.16589e15	0.359377	0.179689	−	0.983724i	$-0.442491\pi$
$661$	1.16589e15	0.359377	0.179689	+	0.983724i	$0.442491\pi$
$662$	−4.39599e14	−0.134381
$663$	1.06517e15	0.322919
$664$	6.62705e14	0.199249
$665$	2.11866e15	0.631747
$666$	−5.20868e14	−0.154035
$667$	4.05994e14	0.119077
$668$	5.51548e15	1.60440
$669$	1.84867e15	0.533355
$670$	−8.18814e14	−0.234301
$671$	−3.66731e15	−1.04082
$672$	−2.63925e15	−0.742934
$673$	5.29220e15	1.47759	0.738794	−	0.673932i	$-0.235396\pi$
$673$	5.29220e15	1.47759	0.738794	+	0.673932i	$0.235396\pi$
$674$	1.54951e15	0.429106
$675$	−2.73035e14	−0.0749977
$676$	3.15577e15	0.859802
$677$	6.24406e15	1.68744	0.843722	−	0.536780i	$-0.180360\pi$
$677$	6.24406e15	1.68744	0.843722	+	0.536780i	$0.180360\pi$
$678$	4.84937e14	0.129994
$679$	−7.50092e15	−1.99448
$680$	3.93797e15	1.03866
$681$	2.93260e15	0.767262
$682$	1.06177e15	0.275561
$683$	−6.47234e15	−1.66628	−0.833139	−	0.553063i	$-0.813459\pi$
$683$	−6.47234e15	−1.66628	−0.833139	+	0.553063i	$0.813459\pi$
$684$	−3.40975e14	−0.0870791
$685$	5.02133e14	0.127210
$686$	3.20779e15	0.806165
$687$	−1.89171e15	−0.471621
$688$	3.68057e14	0.0910287
$689$	1.50808e15	0.370014
$690$	−3.99276e14	−0.0971858
$691$	−8.56379e14	−0.206793	−0.103397	−	0.994640i	$-0.532971\pi$
$691$	−8.56379e14	−0.206793	−0.103397	+	0.994640i	$0.532971\pi$
$692$	4.42079e14	0.105905
$693$	−2.45611e15	−0.583734
$694$	−8.47452e13	−0.0199819
$695$	−8.94565e15	−2.09264
$696$	2.32216e14	0.0538941
$697$	1.45139e16	3.34199
$698$	8.36459e13	0.0191091
$699$	−3.85655e15	−0.874127
$700$	−3.15689e15	−0.709939
$701$	5.92029e13	0.0132097	0.00660486	−	0.999978i	$-0.497898\pi$
$701$	5.92029e13	0.0132097	0.00660486	+	0.999978i	$0.497898\pi$
$702$	−6.17718e13	−0.0136753
$703$	−2.42932e15	−0.533619
$704$	2.78743e15	0.607512
$705$	−4.47140e15	−0.966948
$706$	8.45578e14	0.181438
$707$	−9.77743e15	−2.08170
$708$	3.35288e14	0.0708329
$709$	−3.72819e15	−0.781528	−0.390764	−	0.920491i	$-0.627789\pi$
$709$	−3.72819e15	−0.781528	−0.390764	+	0.920491i	$0.627789\pi$
$710$	1.04694e15	0.217772
$711$	4.88321e14	0.100791
$712$	−5.02720e13	−0.0102964
$713$	−3.70851e15	−0.753716
$714$	2.51032e15	0.506278
$715$	−1.57945e15	−0.316099
$716$	−3.78933e15	−0.752559
$717$	−3.56383e15	−0.702363
$718$	−3.11597e14	−0.0609409
$719$	4.38046e15	0.850180	0.425090	−	0.905151i	$-0.360242\pi$
$719$	4.38046e15	0.850180	0.425090	+	0.905151i	$0.360242\pi$
$720$	1.69423e15	0.326320
$721$	−1.05282e16	−2.01238
$722$	−1.16829e15	−0.221614
$723$	4.05090e15	0.762590
$724$	6.55243e15	1.22417
$725$	4.20762e14	0.0780148
$726$	1.35120e14	0.0248639
$727$	1.21393e15	0.221694	0.110847	−	0.993837i	$-0.464644\pi$
$727$	1.21393e15	0.221694	0.110847	+	0.993837i	$0.464644\pi$
$728$	−1.47211e15	−0.266820
$729$	2.05891e14	0.0370370
$730$	−8.73509e14	−0.155952
$731$	−1.16890e15	−0.207125
$732$	3.55450e15	0.625126
$733$	2.96462e15	0.517485	0.258742	−	0.965946i	$-0.416692\pi$
$733$	2.96462e15	0.517485	0.258742	+	0.965946i	$0.416692\pi$
$734$	−1.67763e15	−0.290648
$735$	−1.08337e16	−1.86292
$736$	2.31980e15	0.395933
$737$	4.42720e15	0.749995
$738$	−8.41701e14	−0.141530
$739$	−2.03703e15	−0.339980	−0.169990	−	0.985446i	$-0.554374\pi$
$739$	−2.03703e15	−0.339980	−0.169990	+	0.985446i	$0.554374\pi$
$740$	1.29085e16	2.13845
$741$	−2.88103e14	−0.0473749
$742$	3.55415e15	0.580116
$743$	6.69761e15	1.08513	0.542564	−	0.840014i	$-0.317454\pi$
$743$	6.69761e15	1.08513	0.542564	+	0.840014i	$0.317454\pi$
$744$	−2.12116e15	−0.341131
$745$	9.67631e15	1.54472
$746$	−1.12216e15	−0.177825
$747$	−9.05490e14	−0.142436
$748$	−1.03301e16	−1.61305
$749$	−6.62091e15	−1.02628
$750$	6.48042e14	0.0997163
$751$	7.35730e15	1.12383	0.561913	−	0.827197i	$-0.310066\pi$
$751$	7.35730e15	1.12383	0.561913	+	0.827197i	$0.310066\pi$
$752$	7.78047e15	1.17980
$753$	−2.26137e15	−0.340407
$754$	9.51935e13	0.0142254
$755$	1.40050e16	2.07767
$756$	2.38056e15	0.350597
$757$	1.95976e15	0.286534	0.143267	−	0.989684i	$-0.454239\pi$
$757$	1.95976e15	0.286534	0.143267	+	0.989684i	$0.454239\pi$
$758$	5.64947e14	0.0820025
$759$	2.15882e15	0.311091
$760$	−1.06513e15	−0.152380
$761$	6.64037e15	0.943141	0.471571	−	0.881828i	$-0.343687\pi$
$761$	6.64037e15	0.943141	0.471571	+	0.881828i	$0.343687\pi$
$762$	−5.98223e13	−0.00843550
$763$	−1.87968e16	−2.63148
$764$	2.26603e15	0.314957
$765$	−5.38066e15	−0.742502
$766$	1.59310e15	0.218265
$767$	2.83298e14	0.0385362
$768$	−2.01858e15	−0.272621
$769$	−1.22042e15	−0.163649	−0.0818245	−	0.996647i	$-0.526075\pi$
$769$	−1.22042e15	−0.163649	−0.0818245	+	0.996647i	$0.526075\pi$
$770$	−3.72236e15	−0.495587
$771$	−1.54029e15	−0.203612
$772$	−3.64554e15	−0.478483
$773$	4.40427e15	0.573967	0.286984	−	0.957936i	$-0.407347\pi$
$773$	4.40427e15	0.573967	0.286984	+	0.957936i	$0.407347\pi$
$774$	6.77876e13	0.00877153
$775$	−3.84341e15	−0.493807
$776$	3.77099e15	0.481079
$777$	1.69606e16	2.14845
$778$	−7.67395e14	−0.0965231
$779$	−3.92569e15	−0.490298
$780$	1.53087e15	0.189853
$781$	−5.66066e15	−0.697086
$782$	−2.20647e15	−0.269812
$783$	−3.17289e14	−0.0385270
$784$	1.88512e16	2.27300
$785$	−9.98279e15	−1.19528
$786$	−1.59490e15	−0.189631
$787$	6.50230e14	0.0767725	0.0383863	−	0.999263i	$-0.487778\pi$
$787$	6.50230e14	0.0767725	0.0383863	+	0.999263i	$0.487778\pi$
$788$	−1.21575e16	−1.42545
$789$	6.79804e15	0.791517
$790$	7.40075e14	0.0855710
$791$	−1.57906e16	−1.81313
$792$	1.23478e15	0.140799
$793$	3.00334e15	0.340096
$794$	−2.77262e15	−0.311802
$795$	−7.61802e15	−0.850791
$796$	1.75030e15	0.194129
$797$	6.73756e15	0.742133	0.371066	−	0.928606i	$-0.378992\pi$
$797$	6.73756e15	0.742133	0.371066	+	0.928606i	$0.378992\pi$
$798$	−6.78985e14	−0.0742753
$799$	−2.47098e16	−2.68449
$800$	2.40418e15	0.259401
$801$	6.86893e13	0.00736055
$802$	−2.61661e15	−0.278471
$803$	4.72293e15	0.499202
$804$	−4.29102e15	−0.450456
$805$	1.30013e16	1.35553
$806$	−8.69537e14	−0.0900420
$807$	6.17512e15	0.635098
$808$	4.91548e15	0.502116
$809$	3.23155e15	0.327864	0.163932	−	0.986472i	$-0.447582\pi$
$809$	3.23155e15	0.327864	0.163932	+	0.986472i	$0.447582\pi$
$810$	3.12039e14	0.0314442
$811$	1.00420e16	1.00509	0.502545	−	0.864551i	$-0.332397\pi$
$811$	1.00420e16	1.00509	0.502545	+	0.864551i	$0.332397\pi$
$812$	−3.66856e15	−0.364702
$813$	4.34101e15	0.428640
$814$	4.26817e15	0.418608
$815$	4.77932e15	0.465585
$816$	9.36263e15	0.905946
$817$	3.16161e14	0.0303870
$818$	−6.75939e12	−0.000645304 0
$819$	2.01143e15	0.190741
$820$	2.08596e16	1.96485
$821$	1.93004e16	1.80584	0.902921	−	0.429807i	$-0.141418\pi$
$821$	1.93004e16	1.80584	0.902921	+	0.429807i	$0.141418\pi$
$822$	−1.60923e14	−0.0149562
$823$	−1.83195e16	−1.69128	−0.845639	−	0.533756i	$-0.820780\pi$
$823$	−1.83195e16	−1.69128	−0.845639	+	0.533756i	$0.820780\pi$
$824$	5.29292e15	0.485396
$825$	2.23735e15	0.203815
$826$	6.67661e14	0.0604179
$827$	1.21826e16	1.09512	0.547558	−	0.836768i	$-0.315558\pi$
$827$	1.21826e16	1.09512	0.547558	+	0.836768i	$0.315558\pi$
$828$	−2.09241e15	−0.186845
$829$	1.91421e16	1.69801	0.849004	−	0.528386i	$-0.177203\pi$
$829$	1.91421e16	1.69801	0.849004	+	0.528386i	$0.177203\pi$
$830$	−1.37232e15	−0.120927
$831$	8.42242e15	0.737278
$832$	−2.28276e15	−0.198510
$833$	−5.98689e16	−5.17194
$834$	2.86688e15	0.246035
$835$	−2.35411e16	−2.00702
$836$	2.79407e15	0.236648
$837$	2.89825e15	0.243863
$838$	1.15646e13	0.000966693 0
$839$	4.48286e15	0.372276	0.186138	−	0.982524i	$-0.440403\pi$
$839$	4.48286e15	0.372276	0.186138	+	0.982524i	$0.440403\pi$
$840$	7.43635e15	0.613513
$841$	−1.17116e16	−0.959923
$842$	−8.98976e14	−0.0732034
$843$	−1.67179e15	−0.135248
$844$	−7.53665e15	−0.605752
$845$	−1.34694e16	−1.07557
$846$	1.43298e15	0.113685
$847$	−4.39982e15	−0.346798
$848$	1.32558e16	1.03807
$849$	8.37864e15	0.651901
$850$	−2.28673e15	−0.176771
$851$	−1.49077e16	−1.14498
$852$	5.48653e15	0.418678
$853$	−6.72216e15	−0.509670	−0.254835	−	0.966984i	$-0.582021\pi$
$853$	−6.72216e15	−0.509670	−0.254835	+	0.966984i	$0.582021\pi$
$854$	7.07809e15	0.533210
$855$	1.45535e15	0.108931
$856$	3.32858e15	0.247545
$857$	−7.04888e15	−0.520865	−0.260433	−	0.965492i	$-0.583865\pi$
$857$	−7.04888e15	−0.520865	−0.260433	+	0.965492i	$0.583865\pi$
$858$	5.06180e14	0.0371642
$859$	−2.45330e16	−1.78973	−0.894865	−	0.446337i	$-0.852728\pi$
$859$	−2.45330e16	−1.78973	−0.894865	+	0.446337i	$0.852728\pi$
$860$	−1.67995e15	−0.121774
$861$	2.74077e16	1.97404
$862$	−5.19593e14	−0.0371854
$863$	1.06121e16	0.754642	0.377321	−	0.926083i	$-0.376845\pi$
$863$	1.06121e16	0.754642	0.377321	+	0.926083i	$0.376845\pi$
$864$	−1.81295e15	−0.128103
$865$	−1.88688e15	−0.132482
$866$	−6.29255e15	−0.439014
$867$	−2.14065e16	−1.48402
$868$	3.35102e16	2.30844
$869$	−4.00147e15	−0.273912
$870$	−4.80867e14	−0.0327092
$871$	−3.62565e15	−0.245068
$872$	9.44987e15	0.634724
$873$	−5.15251e15	−0.343906
$874$	5.96800e14	0.0395837
$875$	−2.11017e16	−1.39083
$876$	−4.57765e15	−0.299826
$877$	−2.63364e16	−1.71419	−0.857095	−	0.515158i	$-0.827733\pi$
$877$	−2.63364e16	−1.71419	−0.857095	+	0.515158i	$0.827733\pi$
$878$	−4.79418e15	−0.310095
$879$	1.39264e16	0.895157
$880$	−1.38831e16	−0.886813
$881$	1.09544e16	0.695376	0.347688	−	0.937610i	$-0.386967\pi$
$881$	1.09544e16	0.695376	0.347688	+	0.937610i	$0.386967\pi$
$882$	3.47195e15	0.219026
$883$	1.44671e16	0.906977	0.453489	−	0.891262i	$-0.350179\pi$
$883$	1.44671e16	0.906977	0.453489	+	0.891262i	$0.350179\pi$
$884$	8.45985e15	0.527079
$885$	−1.43107e15	−0.0886082
$886$	8.13802e14	0.0500764
$887$	2.79787e15	0.171099	0.0855494	−	0.996334i	$-0.472735\pi$
$887$	2.79787e15	0.171099	0.0855494	+	0.996334i	$0.472735\pi$
$888$	−8.52674e15	−0.518217
$889$	1.94795e15	0.117657
$890$	1.04102e14	0.00624906
$891$	−1.68714e15	−0.100653
$892$	1.46827e16	0.870560
$893$	6.68343e15	0.393837
$894$	−3.10105e15	−0.181615
$895$	1.61736e16	0.941411
$896$	−2.76235e16	−1.59803
$897$	−1.76796e15	−0.101652
$898$	−7.71405e14	−0.0440821
$899$	−4.46635e15	−0.253673
$900$	−2.16852e15	−0.122414
$901$	−4.20986e16	−2.36201
$902$	6.89720e15	0.384624
$903$	−2.20732e15	−0.122344
$904$	7.93854e15	0.437335
$905$	−2.79670e16	−1.53137
$906$	−4.48831e15	−0.244274
$907$	−8.75436e14	−0.0473570	−0.0236785	−	0.999720i	$-0.507538\pi$
$907$	−8.75436e14	−0.0473570	−0.0236785	+	0.999720i	$0.507538\pi$
$908$	2.32915e16	1.25235
$909$	−6.71628e15	−0.358945
$910$	3.04842e15	0.161938
$911$	−2.34424e16	−1.23780	−0.618902	−	0.785468i	$-0.712422\pi$
$911$	−2.34424e16	−1.23780	−0.618902	+	0.785468i	$0.712422\pi$
$912$	−2.53238e15	−0.132910
$913$	7.41990e15	0.387087
$914$	7.17592e15	0.372112
$915$	−1.51713e16	−0.781999
$916$	−1.50245e16	−0.769796
$917$	5.19334e16	2.64494
$918$	1.72438e15	0.0872970
$919$	3.60450e16	1.81388	0.906942	−	0.421255i	$-0.138410\pi$
$919$	3.60450e16	1.81388	0.906942	+	0.421255i	$0.138410\pi$
$920$	−6.53625e15	−0.326961
$921$	−4.51350e15	−0.224433
$922$	−4.07867e15	−0.201604
$923$	4.63579e15	0.227779
$924$	−1.95071e16	−0.952791
$925$	−1.54500e16	−0.750149
$926$	−4.70526e15	−0.227103
$927$	−7.23200e15	−0.346992
$928$	2.79385e15	0.133257
$929$	9.70256e15	0.460045	0.230022	−	0.973185i	$-0.426120\pi$
$929$	9.70256e15	0.460045	0.230022	+	0.973185i	$0.426120\pi$
$930$	4.39244e15	0.207038
$931$	1.61932e16	0.758767
$932$	−3.06298e16	−1.42678
$933$	−1.49992e15	−0.0694574
$934$	−2.88496e15	−0.132811
$935$	4.40910e16	2.01784
$936$	−1.01122e15	−0.0460075
$937$	3.90978e16	1.76842	0.884209	−	0.467092i	$-0.154698\pi$
$937$	3.90978e16	1.76842	0.884209	+	0.467092i	$0.154698\pi$
$938$	−8.54473e15	−0.384222
$939$	−1.08776e16	−0.486264
$940$	−3.55131e16	−1.57828
$941$	1.82589e15	0.0806735	0.0403367	−	0.999186i	$-0.487157\pi$
$941$	1.82589e15	0.0806735	0.0403367	+	0.999186i	$0.487157\pi$
$942$	3.19926e15	0.140530
$943$	−2.40902e16	−1.05203
$944$	2.49014e15	0.108113
$945$	−1.01607e16	−0.438579
$946$	−5.55476e14	−0.0238377
$947$	−2.15121e16	−0.917819	−0.458910	−	0.888483i	$-0.651760\pi$
$947$	−2.15121e16	−0.917819	−0.458910	+	0.888483i	$0.651760\pi$
$948$	3.87838e15	0.164515
$949$	−3.86784e15	−0.163119
$950$	6.18509e14	0.0259338
$951$	1.30393e16	0.543575
$952$	4.10947e16	1.70326
$953$	7.52149e14	0.0309951	0.0154975	−	0.999880i	$-0.495067\pi$
$953$	7.52149e14	0.0309951	0.0154975	+	0.999880i	$0.495067\pi$
$954$	2.44141e15	0.100029
$955$	−9.67183e15	−0.393994
$956$	−2.83049e16	−1.14642
$957$	2.59998e15	0.104702
$958$	−7.17665e15	−0.287350
$959$	5.24001e15	0.208607
$960$	1.15313e16	0.456444
$961$	1.53890e16	0.605664
$962$	−3.49541e15	−0.136784
$963$	−4.54802e15	−0.176961
$964$	3.21734e16	1.24473
$965$	1.55599e16	0.598557
$966$	−4.16664e15	−0.159372
$967$	−2.01815e16	−0.767552	−0.383776	−	0.923426i	$-0.625376\pi$
$967$	−2.01815e16	−0.767552	−0.383776	+	0.923426i	$0.625376\pi$
$968$	2.21196e15	0.0836492
$969$	8.04252e15	0.302420
$970$	−7.80889e15	−0.291974
$971$	−9.72014e15	−0.361382	−0.180691	−	0.983540i	$-0.557833\pi$
$971$	−9.72014e15	−0.361382	−0.180691	+	0.983540i	$0.557833\pi$
$972$	1.63525e15	0.0604531
$973$	−9.33522e16	−3.43166
$974$	6.00223e15	0.219401
$975$	−1.83227e15	−0.0665985
$976$	2.63988e16	0.954137
$977$	−1.22870e15	−0.0441595	−0.0220797	−	0.999756i	$-0.507029\pi$
$977$	−1.22870e15	−0.0441595	−0.0220797	+	0.999756i	$0.507029\pi$
$978$	−1.53167e15	−0.0547394
$979$	−5.62864e14	−0.0200032
$980$	−8.60440e16	−3.04073
$981$	−1.29119e16	−0.453742
$982$	−6.25732e15	−0.218663
$983$	6.19993e15	0.215448	0.107724	−	0.994181i	$-0.465644\pi$
$983$	6.19993e15	0.215448	0.107724	+	0.994181i	$0.465644\pi$
$984$	−1.37789e16	−0.476147
$985$	5.18907e16	1.78316
$986$	−2.65736e15	−0.0908088
$987$	−4.66612e16	−1.58567
$988$	−2.28820e15	−0.0773269
$989$	1.94014e15	0.0652010
$990$	−2.55695e15	−0.0854534
$991$	−4.86156e16	−1.61574	−0.807868	−	0.589363i	$-0.799379\pi$
$991$	−4.86156e16	−1.61574	−0.807868	+	0.589363i	$0.799379\pi$
$992$	−2.55201e16	−0.843469
$993$	9.83275e15	0.323187
$994$	1.09254e16	0.357117
$995$	−7.47063e15	−0.242845
$996$	−7.19165e15	−0.232489
$997$	2.26942e16	0.729610	0.364805	−	0.931084i	$-0.381136\pi$
$997$	2.26942e16	0.729610	0.364805	+	0.931084i	$0.381136\pi$
$998$	−5.33814e15	−0.170676
$999$	1.16505e16	0.370455

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.a.1.15	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.a.1.15	✓	26	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q+10.8639 q^{2} -243.000 q^{3} -1929.97 q^{4} +8237.50 q^{5} -2639.94 q^{6} +85962.3 q^{7} -43216.5 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+10.8639 q^{2} -243.000 q^{3} -1929.97 q^{4} +8237.50 q^{5} -2639.94 q^{6} +85962.3 q^{7} -43216.5 q^{8} +59049.0 q^{9} +89491.8 q^{10} -483868. q^{11} +468984. q^{12} +396263. q^{13} +933890. q^{14} -2.00171e6 q^{15} +3.48309e6 q^{16} -1.10618e7 q^{17} +641505. q^{18} +2.99198e6 q^{19} -1.58982e7 q^{20} -2.08888e7 q^{21} -5.25672e6 q^{22} +1.83605e7 q^{23} +1.05016e7 q^{24} +1.90283e7 q^{25} +4.30498e6 q^{26} -1.43489e7 q^{27} -1.65905e8 q^{28} +2.21124e7 q^{29} -2.17465e7 q^{30} -2.01984e8 q^{31} +1.26347e8 q^{32} +1.17580e8 q^{33} -1.20175e8 q^{34} +7.08115e8 q^{35} -1.13963e8 q^{36} -8.11946e8 q^{37} +3.25047e7 q^{38} -9.62920e7 q^{39} -3.55996e8 q^{40} -1.31207e9 q^{41} -2.26935e8 q^{42} +1.05670e8 q^{43} +9.33854e8 q^{44} +4.86416e8 q^{45} +1.99467e8 q^{46} +2.23379e9 q^{47} -8.46390e8 q^{48} +5.41220e9 q^{49} +2.06722e8 q^{50} +2.68803e9 q^{51} -7.64778e8 q^{52} +3.80575e9 q^{53} -1.55886e8 q^{54} -3.98587e9 q^{55} -3.71499e9 q^{56} -7.27050e8 q^{57} +2.40228e8 q^{58} +7.14924e8 q^{59} +3.86326e9 q^{60} +7.57915e9 q^{61} -2.19434e9 q^{62} +5.07599e9 q^{63} -5.76073e9 q^{64} +3.26422e9 q^{65} +1.27738e9 q^{66} -9.14960e9 q^{67} +2.13491e10 q^{68} -4.46159e9 q^{69} +7.69292e9 q^{70} +1.16988e10 q^{71} -2.55189e9 q^{72} -9.76078e9 q^{73} -8.82094e9 q^{74} -4.62388e9 q^{75} -5.77444e9 q^{76} -4.15945e10 q^{77} -1.04611e9 q^{78} +8.26975e9 q^{79} +2.86919e10 q^{80} +3.48678e9 q^{81} -1.42543e10 q^{82} -1.53345e10 q^{83} +4.03150e10 q^{84} -9.11220e10 q^{85} +1.14799e9 q^{86} -5.37331e9 q^{87} +2.09111e10 q^{88} +1.16326e9 q^{89} +5.28440e9 q^{90} +3.40637e10 q^{91} -3.54352e10 q^{92} +4.90821e10 q^{93} +2.42677e10 q^{94} +2.46464e10 q^{95} -3.07024e10 q^{96} -8.72582e10 q^{97} +5.87978e10 q^{98} -2.85719e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9}+O(q^{10}) \) 26 * q - 78 * q^2 - 6318 * q^3 + 23070 * q^4 + 3808 * q^5 + 18954 * q^6 - 98819 * q^7 - 117645 * q^8 + 1535274 * q^9	\( 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9} - 859751 q^{10} + 579094 q^{11} - 5606010 q^{12} - 2018538 q^{13} + 4157413 q^{14} - 925344 q^{15} + 20190274 q^{16} - 13084493 q^{17} - 4605822 q^{18} + 9917231 q^{19} + 10165633 q^{20} + 24013017 q^{21} - 89820518 q^{22} - 63513223 q^{23} + 28587735 q^{24} + 218986852 q^{25} - 77999532 q^{26} - 373071582 q^{27} - 444601862 q^{28} + 81530981 q^{29} + 208919493 q^{30} - 408861231 q^{31} - 26253128 q^{32} - 140719842 q^{33} - 508910076 q^{34} - 75731421 q^{35} + 1362260430 q^{36} - 802381301 q^{37} + 732704675 q^{38} + 490504734 q^{39} - 646130800 q^{40} - 1354472849 q^{41} - 1010251359 q^{42} + 282952194 q^{43} + 1846047996 q^{44} + 224858592 q^{45} + 9629305849 q^{46} - 1196794197 q^{47} - 4906236582 q^{48} + 10889725683 q^{49} - 6236232091 q^{50} + 3179531799 q^{51} - 1968200812 q^{52} - 8276044236 q^{53} + 1119214746 q^{54} - 6672895076 q^{55} + 2579741342 q^{56} - 2409887133 q^{57} - 9401656060 q^{58} + 18588031774 q^{59} - 2470248819 q^{60} - 21181559029 q^{61} - 6117706514 q^{62} - 5835163131 q^{63} + 42975855037 q^{64} + 25680681860 q^{65} + 21826385874 q^{66} + 26234163394 q^{67} + 19707344091 q^{68} + 15433713189 q^{69} + 129203099090 q^{70} + 52088830406 q^{71} - 6946819605 q^{72} + 20943384867 q^{73} + 41969200146 q^{74} - 53213805036 q^{75} + 223987219368 q^{76} + 94604773153 q^{77} + 18953886276 q^{78} + 68965662774 q^{79} + 218947784293 q^{80} + 90656394426 q^{81} + 11938614923 q^{82} + 17947446393 q^{83} + 108038252466 q^{84} - 52849386709 q^{85} + 384986147852 q^{86} - 19812028383 q^{87} - 49061112607 q^{88} + 38570593981 q^{89} - 50767436799 q^{90} - 226268806999 q^{91} - 79559686310 q^{92} + 99353279133 q^{93} - 16709400108 q^{94} - 252795831501 q^{95} + 6379510104 q^{96} - 186894587836 q^{97} - 252443311612 q^{98} + 34194921606 q^{99}+O(q^{100}) \) 26 * q - 78 * q^2 - 6318 * q^3 + 23070 * q^4 + 3808 * q^5 + 18954 * q^6 - 98819 * q^7 - 117645 * q^8 + 1535274 * q^9 - 859751 * q^10 + 579094 * q^11 - 5606010 * q^12 - 2018538 * q^13 + 4157413 * q^14 - 925344 * q^15 + 20190274 * q^16 - 13084493 * q^17 - 4605822 * q^18 + 9917231 * q^19 + 10165633 * q^20 + 24013017 * q^21 - 89820518 * q^22 - 63513223 * q^23 + 28587735 * q^24 + 218986852 * q^25 - 77999532 * q^26 - 373071582 * q^27 - 444601862 * q^28 + 81530981 * q^29 + 208919493 * q^30 - 408861231 * q^31 - 26253128 * q^32 - 140719842 * q^33 - 508910076 * q^34 - 75731421 * q^35 + 1362260430 * q^36 - 802381301 * q^37 + 732704675 * q^38 + 490504734 * q^39 - 646130800 * q^40 - 1354472849 * q^41 - 1010251359 * q^42 + 282952194 * q^43 + 1846047996 * q^44 + 224858592 * q^45 + 9629305849 * q^46 - 1196794197 * q^47 - 4906236582 * q^48 + 10889725683 * q^49 - 6236232091 * q^50 + 3179531799 * q^51 - 1968200812 * q^52 - 8276044236 * q^53 + 1119214746 * q^54 - 6672895076 * q^55 + 2579741342 * q^56 - 2409887133 * q^57 - 9401656060 * q^58 + 18588031774 * q^59 - 2470248819 * q^60 - 21181559029 * q^61 - 6117706514 * q^62 - 5835163131 * q^63 + 42975855037 * q^64 + 25680681860 * q^65 + 21826385874 * q^66 + 26234163394 * q^67 + 19707344091 * q^68 + 15433713189 * q^69 + 129203099090 * q^70 + 52088830406 * q^71 - 6946819605 * q^72 + 20943384867 * q^73 + 41969200146 * q^74 - 53213805036 * q^75 + 223987219368 * q^76 + 94604773153 * q^77 + 18953886276 * q^78 + 68965662774 * q^79 + 218947784293 * q^80 + 90656394426 * q^81 + 11938614923 * q^82 + 17947446393 * q^83 + 108038252466 * q^84 - 52849386709 * q^85 + 384986147852 * q^86 - 19812028383 * q^87 - 49061112607 * q^88 + 38570593981 * q^89 - 50767436799 * q^90 - 226268806999 * q^91 - 79559686310 * q^92 + 99353279133 * q^93 - 16709400108 * q^94 - 252795831501 * q^95 + 6379510104 * q^96 - 186894587836 * q^97 - 252443311612 * q^98 + 34194921606 * q^99

Introduction

L-functions

Modular forms

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