LMFDB - Embedded newform 605.6.a.p.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,6,Mod(1,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("605.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	605.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:	$97.0322109869$
Analytic rank:	$1$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} - 523 x^{18} + 521 x^{17} + 115018 x^{16} - 115347 x^{15} - 13821739 x^{14} + \cdots - 32708279373824 $ x^20 - x^19 - 523x^18 + 521x^17 + 115018x^16 - 115347x^15 - 13821739x^14 + 14112735x^13 + 987264735x^12 - 1043264932x^11 - 42703408468x^10 + 48021607312x^9 + 1089062915552x^8 - 1362443421632x^7 - 15019635572992x^6 + 22119016261376x^5 + 88321308161536x^4 - 163614980036608x^3 - 51220983567360x^2 + 157475390795776x - 32708279373824
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 11^{8} $
Twist minimal:	no (minimal twist has level 55)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$5.27089$ of defining polynomial
Character	$\chi$	$=$	605.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.27089 q^{2} -17.5243 q^{3} -4.21770 q^{4} -25.0000 q^{5} -92.3688 q^{6} +132.134 q^{7} -190.900 q^{8} +64.1015 q^{9} +O(q^{10})$	\(q+5.27089 q^{2} -17.5243 q^{3} -4.21770 q^{4} -25.0000 q^{5} -92.3688 q^{6} +132.134 q^{7} -190.900 q^{8} +64.1015 q^{9} -131.772 q^{10} +73.9122 q^{12} -62.7834 q^{13} +696.466 q^{14} +438.108 q^{15} -871.245 q^{16} -112.520 q^{17} +337.872 q^{18} +1780.95 q^{19} +105.442 q^{20} -2315.56 q^{21} +2243.05 q^{23} +3345.38 q^{24} +625.000 q^{25} -330.925 q^{26} +3135.07 q^{27} -557.303 q^{28} +14.2602 q^{29} +2309.22 q^{30} +307.154 q^{31} +1516.55 q^{32} -593.083 q^{34} -3303.36 q^{35} -270.361 q^{36} -15533.9 q^{37} +9387.18 q^{38} +1100.24 q^{39} +4772.49 q^{40} +5632.94 q^{41} -12205.1 q^{42} +18430.8 q^{43} -1602.54 q^{45} +11822.9 q^{46} -774.851 q^{47} +15268.0 q^{48} +652.484 q^{49} +3294.31 q^{50} +1971.84 q^{51} +264.801 q^{52} -4743.45 q^{53} +16524.6 q^{54} -25224.4 q^{56} -31209.9 q^{57} +75.1641 q^{58} -25623.0 q^{59} -1847.81 q^{60} -3603.09 q^{61} +1618.97 q^{62} +8470.01 q^{63} +35873.4 q^{64} +1569.59 q^{65} -53750.0 q^{67} +474.577 q^{68} -39308.0 q^{69} -17411.6 q^{70} +32070.0 q^{71} -12237.0 q^{72} +60838.2 q^{73} -81877.6 q^{74} -10952.7 q^{75} -7511.49 q^{76} +5799.23 q^{78} +72475.6 q^{79} +21781.1 q^{80} -70516.7 q^{81} +29690.6 q^{82} -5733.58 q^{83} +9766.35 q^{84} +2813.01 q^{85} +97146.9 q^{86} -249.901 q^{87} -105591. q^{89} -8446.80 q^{90} -8295.85 q^{91} -9460.53 q^{92} -5382.66 q^{93} -4084.16 q^{94} -44523.7 q^{95} -26576.5 q^{96} -138277. q^{97} +3439.17 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + q^{2} + 407 q^{4} - 500 q^{5} - 264 q^{6} - 167 q^{7} - 57 q^{8} + 1598 q^{9}+O(q^{10}) $ 20 * q + q^2 + 407 * q^4 - 500 * q^5 - 264 * q^6 - 167 * q^7 - 57 * q^8 + 1598 * q^9	\( 20 q + q^{2} + 407 q^{4} - 500 q^{5} - 264 q^{6} - 167 q^{7} - 57 q^{8} + 1598 q^{9} - 25 q^{10} - 253 q^{12} - 769 q^{13} - 1045 q^{14} + 6963 q^{16} + 2989 q^{17} - 3775 q^{18} - 5828 q^{19} - 10175 q^{20} - 3310 q^{21} - 695 q^{23} - 16724 q^{24} + 12500 q^{25} - 7384 q^{26} + 5925 q^{27} + 3508 q^{28} - 11268 q^{29} + 6600 q^{30} - 11465 q^{31} + 9062 q^{32} + 1217 q^{34} + 4175 q^{35} + 112083 q^{36} - 3057 q^{37} - 13510 q^{38} - 13459 q^{39} + 1425 q^{40} + 839 q^{41} - 14772 q^{42} - 43671 q^{43} - 39950 q^{45} - 81471 q^{46} + 32245 q^{47} - 104315 q^{48} + 2959 q^{49} + 625 q^{50} - 69047 q^{51} - 42696 q^{52} + 27981 q^{53} - 61212 q^{54} - 28294 q^{56} - 79425 q^{57} + 37274 q^{58} - 56847 q^{59} + 6325 q^{60} - 85616 q^{61} - 38095 q^{62} - 100055 q^{63} - 18233 q^{64} + 19225 q^{65} - 31091 q^{67} + 83972 q^{68} - 48708 q^{69} + 26125 q^{70} - 106431 q^{71} - 350510 q^{72} - 117959 q^{73} - 154757 q^{74} - 451972 q^{76} + 348898 q^{78} - 215138 q^{79} - 174075 q^{80} + 75516 q^{81} - 127864 q^{82} - 66761 q^{83} - 521275 q^{84} - 74725 q^{85} - 32222 q^{86} + 5311 q^{87} + 270560 q^{89} + 94375 q^{90} - 269192 q^{91} - 461663 q^{92} + 9345 q^{93} - 479494 q^{94} + 145700 q^{95} - 1247523 q^{96} + 45338 q^{97} + 420757 q^{98}+O(q^{100}) \) 20 * q + q^2 + 407 * q^4 - 500 * q^5 - 264 * q^6 - 167 * q^7 - 57 * q^8 + 1598 * q^9 - 25 * q^10 - 253 * q^12 - 769 * q^13 - 1045 * q^14 + 6963 * q^16 + 2989 * q^17 - 3775 * q^18 - 5828 * q^19 - 10175 * q^20 - 3310 * q^21 - 695 * q^23 - 16724 * q^24 + 12500 * q^25 - 7384 * q^26 + 5925 * q^27 + 3508 * q^28 - 11268 * q^29 + 6600 * q^30 - 11465 * q^31 + 9062 * q^32 + 1217 * q^34 + 4175 * q^35 + 112083 * q^36 - 3057 * q^37 - 13510 * q^38 - 13459 * q^39 + 1425 * q^40 + 839 * q^41 - 14772 * q^42 - 43671 * q^43 - 39950 * q^45 - 81471 * q^46 + 32245 * q^47 - 104315 * q^48 + 2959 * q^49 + 625 * q^50 - 69047 * q^51 - 42696 * q^52 + 27981 * q^53 - 61212 * q^54 - 28294 * q^56 - 79425 * q^57 + 37274 * q^58 - 56847 * q^59 + 6325 * q^60 - 85616 * q^61 - 38095 * q^62 - 100055 * q^63 - 18233 * q^64 + 19225 * q^65 - 31091 * q^67 + 83972 * q^68 - 48708 * q^69 + 26125 * q^70 - 106431 * q^71 - 350510 * q^72 - 117959 * q^73 - 154757 * q^74 - 451972 * q^76 + 348898 * q^78 - 215138 * q^79 - 174075 * q^80 + 75516 * q^81 - 127864 * q^82 - 66761 * q^83 - 521275 * q^84 - 74725 * q^85 - 32222 * q^86 + 5311 * q^87 + 270560 * q^89 + 94375 * q^90 - 269192 * q^91 - 461663 * q^92 + 9345 * q^93 - 479494 * q^94 + 145700 * q^95 - 1247523 * q^96 + 45338 * q^97 + 420757 * q^98

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 $

$2$	5.27089	0.931771	0.465885	−	0.884845i	$-0.345736\pi$
$2$	5.27089	0.931771	0.465885	+	0.884845i	$0.345736\pi$
$3$	−17.5243	−1.12419	−0.562093	−	0.827074i	$-0.690004\pi$
$3$	−17.5243	−1.12419	−0.562093	+	0.827074i	$0.690004\pi$
$4$	−4.21770	−0.131803
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−92.3688	−1.04748
$7$	132.134	1.01923	0.509613	−	0.860404i	$-0.329789\pi$
$7$	132.134	1.01923	0.509613	+	0.860404i	$0.329789\pi$
$8$	−190.900	−1.05458
$9$	64.1015	0.263792
$10$	−131.772	−0.416701
$11$	0	0
$11$	0	0
$12$	73.9122	0.148171
$13$	−62.7834	−0.103035	−0.0515177	−	0.998672i	$-0.516406\pi$
$13$	−62.7834	−0.103035	−0.0515177	+	0.998672i	$0.516406\pi$
$14$	696.466	0.949685
$15$	438.108	0.502751
$16$	−871.245	−0.850825
$17$	−112.520	−0.0944298	−0.0472149	−	0.998885i	$-0.515035\pi$
$17$	−112.520	−0.0944298	−0.0472149	+	0.998885i	$0.515035\pi$
$18$	337.872	0.245794
$19$	1780.95	1.13179	0.565896	−	0.824476i	$-0.308530\pi$
$19$	1780.95	1.13179	0.565896	+	0.824476i	$0.308530\pi$
$20$	105.442	0.0589441
$21$	−2315.56	−1.14580
$22$	0	0
$23$	2243.05	0.884139	0.442069	−	0.896981i	$-0.354245\pi$
$23$	2243.05	0.884139	0.442069	+	0.896981i	$0.354245\pi$
$24$	3345.38	1.18554
$25$	625.000	0.200000
$26$	−330.925	−0.0960054
$27$	3135.07	0.827634
$28$	−557.303	−0.134337
$29$	14.2602	0.00314870	0.00157435	−	0.999999i	$-0.499499\pi$
$29$	14.2602	0.00314870	0.00157435	+	0.999999i	$0.499499\pi$
$30$	2309.22	0.468449
$31$	307.154	0.0574053	0.0287026	−	0.999588i	$-0.490862\pi$
$31$	307.154	0.0574053	0.0287026	+	0.999588i	$0.490862\pi$
$32$	1516.55	0.261807
$33$	0	0
$34$	−593.083	−0.0879870
$35$	−3303.36	−0.455812
$36$	−270.361	−0.0347686
$37$	−15533.9	−1.86542	−0.932710	−	0.360627i	$-0.882563\pi$
$37$	−15533.9	−1.86542	−0.932710	+	0.360627i	$0.882563\pi$
$38$	9387.18	1.05457
$39$	1100.24	0.115831
$40$	4772.49	0.471623
$41$	5632.94	0.523330	0.261665	−	0.965159i	$-0.415728\pi$
$41$	5632.94	0.523330	0.261665	+	0.965159i	$0.415728\pi$
$42$	−12205.1	−1.06762
$43$	18430.8	1.52010	0.760052	−	0.649862i	$-0.225173\pi$
$43$	18430.8	1.52010	0.760052	+	0.649862i	$0.225173\pi$
$44$	0	0
$45$	−1602.54	−0.117971
$46$	11822.9	0.823815
$47$	−774.851	−0.0511651	−0.0255825	−	0.999673i	$-0.508144\pi$
$47$	−774.851	−0.0511651	−0.0255825	+	0.999673i	$0.508144\pi$
$48$	15268.0	0.956485
$49$	652.484	0.0388221
$50$	3294.31	0.186354
$51$	1971.84	0.106157
$52$	264.801	0.0135804
$53$	−4743.45	−0.231955	−0.115978	−	0.993252i	$-0.537000\pi$
$53$	−4743.45	−0.231955	−0.115978	+	0.993252i	$0.537000\pi$
$54$	16524.6	0.771165
$55$	0	0
$56$	−25224.4	−1.07486
$57$	−31209.9	−1.27234
$58$	75.1641	0.00293387
$59$	−25623.0	−0.958297	−0.479149	−	0.877734i	$-0.659055\pi$
$59$	−25623.0	−0.958297	−0.479149	+	0.877734i	$0.659055\pi$
$60$	−1847.81	−0.0662641
$61$	−3603.09	−0.123980	−0.0619899	−	0.998077i	$-0.519745\pi$
$61$	−3603.09	−0.123980	−0.0619899	+	0.998077i	$0.519745\pi$
$62$	1618.97	0.0534886
$63$	8470.01	0.268864
$64$	35873.4	1.09477
$65$	1569.59	0.0460788
$66$	0	0
$67$	−53750.0	−1.46282	−0.731410	−	0.681938i	$-0.761138\pi$
$67$	−53750.0	−1.46282	−0.731410	+	0.681938i	$0.761138\pi$
$68$	474.577	0.0124461
$69$	−39308.0	−0.993935
$70$	−17411.6	−0.424712
$71$	32070.0	0.755010	0.377505	−	0.926008i	$-0.376782\pi$
$71$	32070.0	0.755010	0.377505	+	0.926008i	$0.376782\pi$
$72$	−12237.0	−0.278190
$73$	60838.2	1.33619	0.668096	−	0.744075i	$-0.267109\pi$
$73$	60838.2	1.33619	0.668096	+	0.744075i	$0.267109\pi$
$74$	−81877.6	−1.73814
$75$	−10952.7	−0.224837
$76$	−7511.49	−0.149174
$77$	0	0
$78$	5799.23	0.107928
$79$	72475.6	1.30654	0.653272	−	0.757123i	$-0.273396\pi$
$79$	72475.6	1.30654	0.653272	+	0.757123i	$0.273396\pi$
$80$	21781.1	0.380500
$81$	−70516.7	−1.19421
$82$	29690.6	0.487624
$83$	−5733.58	−0.0913547	−0.0456773	−	0.998956i	$-0.514545\pi$
$83$	−5733.58	−0.0913547	−0.0456773	+	0.998956i	$0.514545\pi$
$84$	9766.35	0.151020
$85$	2813.01	0.0422303
$86$	97146.9	1.41639
$87$	−249.901	−0.00353972
$88$	0	0
$89$	−105591.	−1.41304	−0.706518	−	0.707696i	$-0.749735\pi$
$89$	−105591.	−1.41304	−0.706518	+	0.707696i	$0.749735\pi$
$90$	−8446.80	−0.109922
$91$	−8295.85	−0.105016
$92$	−9460.53	−0.116532
$93$	−5382.66	−0.0645341
$94$	−4084.16	−0.0476741
$95$	−44523.7	−0.506153
$96$	−26576.5	−0.294320
$97$	−138277.	−1.49217	−0.746087	−	0.665848i	$-0.768070\pi$
$97$	−138277.	−1.49217	−0.746087	+	0.665848i	$0.768070\pi$
$98$	3439.17	0.0361733
$99$	0	0
$100$	−2636.06	−0.0263606
$101$	−159801.	−1.55875	−0.779377	−	0.626556i	$-0.784464\pi$
$101$	−159801.	−1.55875	−0.779377	+	0.626556i	$0.784464\pi$
$102$	10393.4	0.0989136
$103$	−173542.	−1.61180	−0.805901	−	0.592050i	$-0.798319\pi$
$103$	−173542.	−1.61180	−0.805901	+	0.592050i	$0.798319\pi$
$104$	11985.3	0.108659
$105$	57889.1	0.512417
$106$	−25002.2	−0.216129
$107$	178660.	1.50858	0.754288	−	0.656543i	$-0.227982\pi$
$107$	178660.	1.50858	0.754288	+	0.656543i	$0.227982\pi$
$108$	−13222.8	−0.109085
$109$	−128168.	−1.03327	−0.516635	−	0.856206i	$-0.672816\pi$
$109$	−128168.	−1.03327	−0.516635	+	0.856206i	$0.672816\pi$
$110$	0	0
$111$	272221.	2.09708
$112$	−115121.	−0.867183
$113$	−8299.66	−0.0611455	−0.0305727	−	0.999533i	$-0.509733\pi$
$113$	−8299.66	−0.0611455	−0.0305727	+	0.999533i	$0.509733\pi$
$114$	−164504.	−1.18553
$115$	−56076.4	−0.395399
$116$	−60.1453	−0.000415009 0
$117$	−4024.51	−0.0271799
$118$	−135056.	−0.892914
$119$	−14867.8	−0.0962453
$120$	−83634.6	−0.530192
$121$	0	0
$122$	−18991.5	−0.115521
$123$	−98713.4	−0.588320
$124$	−1295.48	−0.00756619
$125$	−15625.0	−0.0894427
$126$	44644.5	0.250520
$127$	−239126.	−1.31558	−0.657790	−	0.753202i	$-0.728508\pi$
$127$	−239126.	−1.31558	−0.657790	+	0.753202i	$0.728508\pi$
$128$	140555.	0.758267
$129$	−322987.	−1.70888
$130$	8273.12	0.0429349
$131$	−8032.16	−0.0408935	−0.0204467	−	0.999791i	$-0.506509\pi$
$131$	−8032.16	−0.0408935	−0.0204467	+	0.999791i	$0.506509\pi$
$132$	0	0
$133$	235324.	1.15355
$134$	−283310.	−1.36301
$135$	−78376.8	−0.370129
$136$	21480.1	0.0995839
$137$	−304931.	−1.38803	−0.694016	−	0.719960i	$-0.744160\pi$
$137$	−304931.	−1.38803	−0.694016	+	0.719960i	$0.744160\pi$
$138$	−207188.	−0.926120
$139$	257918.	1.13226	0.566128	−	0.824318i	$-0.308441\pi$
$139$	257918.	1.13226	0.566128	+	0.824318i	$0.308441\pi$
$140$	13932.6	0.0600774
$141$	13578.7	0.0575190
$142$	169037.	0.703496
$143$	0	0
$144$	−55848.1	−0.224441
$145$	−356.506	−0.00140814
$146$	320671.	1.24503
$147$	−11434.3	−0.0436433
$148$	65517.4	0.245868
$149$	−430165.	−1.58734	−0.793670	−	0.608349i	$-0.791832\pi$
$149$	−430165.	−1.58734	−0.793670	+	0.608349i	$0.791832\pi$
$150$	−57730.5	−0.209497
$151$	32349.4	0.115458	0.0577289	−	0.998332i	$-0.481614\pi$
$151$	32349.4	0.115458	0.0577289	+	0.998332i	$0.481614\pi$
$152$	−339982.	−1.19357
$153$	−7212.73	−0.0249099
$154$	0	0
$155$	−7678.85	−0.0256724
$156$	−4640.46	−0.0152669
$157$	−319793.	−1.03543	−0.517715	−	0.855553i	$-0.673217\pi$
$157$	−319793.	−1.03543	−0.517715	+	0.855553i	$0.673217\pi$
$158$	382011.	1.21740
$159$	83125.7	0.260761
$160$	−37913.7	−0.117084
$161$	296385.	0.901137
$162$	−371686.	−1.11273
$163$	−117724.	−0.347052	−0.173526	−	0.984829i	$-0.555516\pi$
$163$	−117724.	−0.347052	−0.173526	+	0.984829i	$0.555516\pi$
$164$	−23758.0	−0.0689765
$165$	0	0
$166$	−30221.1	−0.0851216
$167$	−316993.	−0.879547	−0.439773	−	0.898109i	$-0.644941\pi$
$167$	−316993.	−0.879547	−0.439773	+	0.898109i	$0.644941\pi$
$168$	442040.	1.20834
$169$	−367351.	−0.989384
$170$	14827.1	0.0393490
$171$	114161.	0.298558
$172$	−77735.6	−0.200354
$173$	−314235.	−0.798252	−0.399126	−	0.916896i	$-0.630686\pi$
$173$	−314235.	−0.798252	−0.399126	+	0.916896i	$0.630686\pi$
$174$	−1317.20	−0.00329821
$175$	82584.0	0.203845
$176$	0	0
$177$	449026.	1.07730
$178$	−556560.	−1.31662
$179$	617107.	1.43955	0.719777	−	0.694205i	$-0.244244\pi$
$179$	617107.	1.43955	0.719777	+	0.694205i	$0.244244\pi$
$180$	6759.02	0.0155490
$181$	−397452.	−0.901754	−0.450877	−	0.892586i	$-0.648889\pi$
$181$	−397452.	−0.901754	−0.450877	+	0.892586i	$0.648889\pi$
$182$	−43726.5	−0.0978512
$183$	63141.7	0.139376
$184$	−428198.	−0.932396
$185$	388348.	0.834241
$186$	−28371.4	−0.0601310
$187$	0	0
$188$	3268.09	0.00674371
$189$	414251.	0.843546
$190$	−234679.	−0.471619
$191$	270073.	0.535670	0.267835	−	0.963465i	$-0.413692\pi$
$191$	270073.	0.535670	0.267835	+	0.963465i	$0.413692\pi$
$192$	−628657.	−1.23072
$193$	12228.3	0.0236305	0.0118152	−	0.999930i	$-0.496239\pi$
$193$	12228.3	0.0236305	0.0118152	+	0.999930i	$0.496239\pi$
$194$	−728841.	−1.39036
$195$	−27505.9	−0.0518012
$196$	−2751.98	−0.00511688
$197$	538890.	0.989314	0.494657	−	0.869088i	$-0.335294\pi$
$197$	538890.	0.989314	0.494657	+	0.869088i	$0.335294\pi$
$198$	0	0
$199$	499957.	0.894952	0.447476	−	0.894296i	$-0.352323\pi$
$199$	499957.	0.894952	0.447476	+	0.894296i	$0.352323\pi$
$200$	−119312.	−0.210916
$201$	941931.	1.64448
$202$	−842296.	−1.45240
$203$	1884.27	0.00320924
$204$	−8316.64	−0.0139918
$205$	−140824.	−0.234040
$206$	−914721.	−1.50183
$207$	143783.	0.233229
$208$	54699.7	0.0876651
$209$	0	0
$210$	305127.	0.477455
$211$	−574610.	−0.888520	−0.444260	−	0.895898i	$-0.646533\pi$
$211$	−574610.	−0.888520	−0.444260	+	0.895898i	$0.646533\pi$
$212$	20006.4	0.0305724
$213$	−562004.	−0.848771
$214$	941696.	1.40565
$215$	−460771.	−0.679812
$216$	−598484.	−0.872807
$217$	40585.6	0.0585090
$218$	−675560.	−0.962771
$219$	−1.06615e6	−1.50213
$220$	0	0
$221$	7064.42	0.00972962
$222$	1.43485e6	1.95400
$223$	1.13138e6	1.52352	0.761759	−	0.647861i	$-0.224336\pi$
$223$	1.13138e6	1.52352	0.761759	+	0.647861i	$0.224336\pi$
$224$	200388.	0.266841
$225$	40063.4	0.0527584
$226$	−43746.6	−0.0569736
$227$	−301848.	−0.388797	−0.194399	−	0.980923i	$-0.562276\pi$
$227$	−301848.	−0.388797	−0.194399	+	0.980923i	$0.562276\pi$
$228$	131634.	0.167699
$229$	−216260.	−0.272513	−0.136257	−	0.990674i	$-0.543507\pi$
$229$	−216260.	−0.272513	−0.136257	+	0.990674i	$0.543507\pi$
$230$	−295573.	−0.368421
$231$	0	0
$232$	−2722.27	−0.00332056
$233$	811718.	0.979524	0.489762	−	0.871856i	$-0.337084\pi$
$233$	811718.	0.979524	0.489762	+	0.871856i	$0.337084\pi$
$234$	−21212.8	−0.0253255
$235$	19371.3	0.0228817
$236$	108070.	0.126307
$237$	−1.27009e6	−1.46880
$238$	−78366.6	−0.0896786
$239$	1.40157e6	1.58716	0.793581	−	0.608465i	$-0.208214\pi$
$239$	1.40157e6	1.58716	0.793581	+	0.608465i	$0.208214\pi$
$240$	−381699.	−0.427753
$241$	1.29593e6	1.43727	0.718635	−	0.695388i	$-0.244767\pi$
$241$	1.29593e6	1.43727	0.718635	+	0.695388i	$0.244767\pi$
$242$	0	0
$243$	473933.	0.514875
$244$	15196.7	0.0163409
$245$	−16312.1	−0.0173618
$246$	−520308.	−0.548179
$247$	−111814.	−0.116615
$248$	−58635.5	−0.0605385
$249$	100477.	0.102700
$250$	−82357.7	−0.0833401
$251$	64104.7	0.0642252	0.0321126	−	0.999484i	$-0.489776\pi$
$251$	64104.7	0.0642252	0.0321126	+	0.999484i	$0.489776\pi$
$252$	−35723.9	−0.0354371
$253$	0	0
$254$	−1.26041e6	−1.22582
$255$	−49296.1	−0.0474747
$256$	−407097.	−0.388238
$257$	−415498.	−0.392406	−0.196203	−	0.980563i	$-0.562861\pi$
$257$	−415498.	−0.392406	−0.196203	+	0.980563i	$0.562861\pi$
$258$	−1.70243e6	−1.59228
$259$	−2.05256e6	−1.90129
$260$	−6620.04	−0.00607333
$261$	914.102	0.000830603 0
$262$	−42336.6	−0.0381033
$263$	1.83618e6	1.63691	0.818456	−	0.574569i	$-0.194830\pi$
$263$	1.83618e6	1.63691	0.818456	+	0.574569i	$0.194830\pi$
$264$	0	0
$265$	118586.	0.103734
$266$	1.24037e6	1.07485
$267$	1.85041e6	1.58851
$268$	226701.	0.192804
$269$	1.61504e6	1.36082	0.680412	−	0.732830i	$-0.261801\pi$
$269$	1.61504e6	1.36082	0.680412	+	0.732830i	$0.261801\pi$
$270$	−413116.	−0.344876
$271$	889193.	0.735484	0.367742	−	0.929928i	$-0.380131\pi$
$271$	889193.	0.735484	0.367742	+	0.929928i	$0.380131\pi$
$272$	98032.8	0.0803432
$273$	145379.	0.118058
$274$	−1.60726e6	−1.29333
$275$	0	0
$276$	165789.	0.131004
$277$	−27491.5	−0.0215278	−0.0107639	−	0.999942i	$-0.503426\pi$
$277$	−27491.5	−0.0215278	−0.0107639	+	0.999942i	$0.503426\pi$
$278$	1.35946e6	1.05500
$279$	19689.0	0.0151431
$280$	630610.	0.480691
$281$	−675176.	−0.510095	−0.255048	−	0.966928i	$-0.582091\pi$
$281$	−675176.	−0.510095	−0.255048	+	0.966928i	$0.582091\pi$
$282$	71572.0	0.0535945
$283$	−499789.	−0.370955	−0.185477	−	0.982649i	$-0.559383\pi$
$283$	−499789.	−0.370955	−0.185477	+	0.982649i	$0.559383\pi$
$284$	−135261.	−0.0995126
$285$	780246.	0.569010
$286$	0	0
$287$	744305.	0.533392
$288$	97213.1	0.0690627
$289$	−1.40720e6	−0.991083
$290$	−1879.10	−0.00131207
$291$	2.42320e6	1.67748
$292$	−256597.	−0.176114
$293$	557553.	0.379417	0.189709	−	0.981840i	$-0.439246\pi$
$293$	557553.	0.379417	0.189709	+	0.981840i	$0.439246\pi$
$294$	−60269.1	−0.0406655
$295$	640576.	0.428564
$296$	2.96542e6	1.96724
$297$	0	0
$298$	−2.26736e6	−1.47904
$299$	−140827.	−0.0910976
$300$	46195.2	0.0296342
$301$	2.43534e6	1.54933
$302$	170510.	0.107580
$303$	2.80041e6	1.75233
$304$	−1.55164e6	−0.962957
$305$	90077.3	0.0554454
$306$	−38017.5	−0.0232103
$307$	−1.92461e6	−1.16546	−0.582728	−	0.812667i	$-0.698015\pi$
$307$	−1.92461e6	−1.16546	−0.582728	+	0.812667i	$0.698015\pi$
$308$	0	0
$309$	3.04121e6	1.81196
$310$	−40474.4	−0.0239208
$311$	−1.12454e6	−0.659287	−0.329643	−	0.944106i	$-0.606929\pi$
$311$	−1.12454e6	−0.659287	−0.329643	+	0.944106i	$0.606929\pi$
$312$	−210035.	−0.122153
$313$	−1.58153e6	−0.912467	−0.456234	−	0.889860i	$-0.650802\pi$
$313$	−1.58153e6	−0.912467	−0.456234	+	0.889860i	$0.650802\pi$
$314$	−1.68560e6	−0.964783
$315$	−211750.	−0.120240
$316$	−305680.	−0.172207
$317$	208890.	0.116753	0.0583767	−	0.998295i	$-0.481408\pi$
$317$	208890.	0.116753	0.0583767	+	0.998295i	$0.481408\pi$
$318$	438146.	0.242969
$319$	0	0
$320$	−896835.	−0.489596
$321$	−3.13089e6	−1.69592
$322$	1.56221e6	0.839653
$323$	−200393.	−0.106875
$324$	297418.	0.157400
$325$	−39239.6	−0.0206071
$326$	−620509.	−0.323373
$327$	2.24606e6	1.16159
$328$	−1.07533e6	−0.551894
$329$	−102384.	−0.0521488
$330$	0	0
$331$	−2.84522e6	−1.42740	−0.713700	−	0.700452i	$-0.752982\pi$
$331$	−2.84522e6	−1.42740	−0.713700	+	0.700452i	$0.752982\pi$
$332$	24182.5	0.0120408
$333$	−995748.	−0.492083
$334$	−1.67084e6	−0.819536
$335$	1.34375e6	0.654193
$336$	2.01742e6	0.974874
$337$	2.16209e6	1.03705	0.518524	−	0.855063i	$-0.326482\pi$
$337$	2.16209e6	1.03705	0.518524	+	0.855063i	$0.326482\pi$
$338$	−1.93627e6	−0.921879
$339$	145446.	0.0687388
$340$	−11864.4	−0.00556608
$341$	0	0
$342$	601732.	0.278188
$343$	−2.13457e6	−0.979658
$344$	−3.51844e6	−1.60307
$345$	982700.	0.444501
$346$	−1.65630e6	−0.743788
$347$	3.39795e6	1.51493	0.757467	−	0.652874i	$-0.226437\pi$
$347$	3.39795e6	1.51493	0.757467	+	0.652874i	$0.226437\pi$
$348$	1054.01	0.000466546 0
$349$	−340903.	−0.149819	−0.0749096	−	0.997190i	$-0.523867\pi$
$349$	−340903.	−0.149819	−0.0749096	+	0.997190i	$0.523867\pi$
$350$	435291.	0.189937
$351$	−196831.	−0.0852756
$352$	0	0
$353$	1.30706e6	0.558288	0.279144	−	0.960249i	$-0.409949\pi$
$353$	1.30706e6	0.558288	0.279144	+	0.960249i	$0.409949\pi$
$354$	2.36677e6	1.00380
$355$	−801749.	−0.337651
$356$	445352.	0.186242
$357$	260548.	0.108198
$358$	3.25271e6	1.34134
$359$	−3.18657e6	−1.30493	−0.652465	−	0.757819i	$-0.726265\pi$
$359$	−3.18657e6	−1.30493	−0.652465	+	0.757819i	$0.726265\pi$
$360$	305924.	0.124410
$361$	695670.	0.280954
$362$	−2.09493e6	−0.840228
$363$	0	0
$364$	34989.4	0.0138415
$365$	−1.52095e6	−0.597563
$366$	332813.	0.129867
$367$	−3.81814e6	−1.47975	−0.739873	−	0.672747i	$-0.765114\pi$
$367$	−3.81814e6	−1.47975	−0.739873	+	0.672747i	$0.765114\pi$
$368$	−1.95425e6	−0.752247
$369$	361080.	0.138050
$370$	2.04694e6	0.777322
$371$	−626772.	−0.236415
$372$	22702.4	0.00850580
$373$	194732.	0.0724713	0.0362357	−	0.999343i	$-0.488463\pi$
$373$	194732.	0.0724713	0.0362357	+	0.999343i	$0.488463\pi$
$374$	0	0
$375$	273817.	0.100550
$376$	147919.	0.0539577
$377$	−895.306	−0.000324428 0
$378$	2.18347e6	0.785992
$379$	−2.95891e6	−1.05812	−0.529059	−	0.848585i	$-0.677455\pi$
$379$	−2.95891e6	−1.05812	−0.529059	+	0.848585i	$0.677455\pi$
$380$	187787.	0.0667125
$381$	4.19051e6	1.47895
$382$	1.42352e6	0.499122
$383$	1.51551e6	0.527914	0.263957	−	0.964535i	$-0.414972\pi$
$383$	1.51551e6	0.527914	0.263957	+	0.964535i	$0.414972\pi$
$384$	−2.46313e6	−0.852432
$385$	0	0
$386$	64453.9	0.0220182
$387$	1.18144e6	0.400992
$388$	583209.	0.196673
$389$	708662.	0.237446	0.118723	−	0.992927i	$-0.462120\pi$
$389$	708662.	0.237446	0.118723	+	0.992927i	$0.462120\pi$
$390$	−144981.	−0.0482668
$391$	−252390.	−0.0834890
$392$	−124559.	−0.0409411
$393$	140758.	0.0459718
$394$	2.84043e6	0.921814
$395$	−1.81189e6	−0.584304
$396$	0	0
$397$	−3.26743e6	−1.04047	−0.520235	−	0.854023i	$-0.674156\pi$
$397$	−3.26743e6	−1.04047	−0.520235	+	0.854023i	$0.674156\pi$
$398$	2.63522e6	0.833890
$399$	−4.12389e6	−1.29681
$400$	−544528.	−0.170165
$401$	−3.90717e6	−1.21339	−0.606697	−	0.794933i	$-0.707506\pi$
$401$	−3.90717e6	−1.21339	−0.606697	+	0.794933i	$0.707506\pi$
$402$	4.96482e6	1.53228
$403$	−19284.2	−0.00591478
$404$	673994.	0.205448
$405$	1.76292e6	0.534065
$406$	9931.76	0.00299028
$407$	0	0
$408$	−376424.	−0.111951
$409$	−123225.	−0.0364243	−0.0182121	−	0.999834i	$-0.505797\pi$
$409$	−123225.	−0.0364243	−0.0182121	+	0.999834i	$0.505797\pi$
$410$	−742266.	−0.218072
$411$	5.34370e6	1.56040
$412$	731948.	0.212440
$413$	−3.38568e6	−0.976722
$414$	757866.	0.217316
$415$	143340.	0.0408550
$416$	−95214.2	−0.0269754
$417$	−4.51983e6	−1.27286
$418$	0	0
$419$	−1.81267e6	−0.504409	−0.252205	−	0.967674i	$-0.581156\pi$
$419$	−1.81267e6	−0.504409	−0.252205	+	0.967674i	$0.581156\pi$
$420$	−244159.	−0.0675381
$421$	−3.42765e6	−0.942521	−0.471260	−	0.881994i	$-0.656201\pi$
$421$	−3.42765e6	−0.942521	−0.471260	+	0.881994i	$0.656201\pi$
$422$	−3.02871e6	−0.827897
$423$	−49669.1	−0.0134969
$424$	905522.	0.244616
$425$	−70325.3	−0.0188860
$426$	−2.96226e6	−0.790860
$427$	−476092.	−0.126363
$428$	−753533.	−0.198835
$429$	0	0
$430$	−2.42867e6	−0.633429
$431$	−6.68872e6	−1.73440	−0.867201	−	0.497959i	$-0.834083\pi$
$431$	−6.68872e6	−1.73440	−0.867201	+	0.497959i	$0.834083\pi$
$432$	−2.73142e6	−0.704171
$433$	965895.	0.247577	0.123788	−	0.992309i	$-0.460496\pi$
$433$	965895.	0.247577	0.123788	+	0.992309i	$0.460496\pi$
$434$	213922.	0.0545169
$435$	6247.52	0.00158301
$436$	540574.	0.136188
$437$	3.99476e6	1.00066
$438$	−5.61955e6	−1.39964
$439$	−6.74701e6	−1.67090	−0.835449	−	0.549568i	$-0.814792\pi$
$439$	−6.74701e6	−1.67090	−0.835449	+	0.549568i	$0.814792\pi$
$440$	0	0
$441$	41825.2	0.0102410
$442$	37235.8	0.00906577
$443$	−8.17480e6	−1.97910	−0.989550	−	0.144193i	$-0.953941\pi$
$443$	−8.17480e6	−1.97910	−0.989550	+	0.144193i	$0.953941\pi$
$444$	−1.14815e6	−0.276401
$445$	2.63978e6	0.631929
$446$	5.96340e6	1.41957
$447$	7.53835e6	1.78446
$448$	4.74011e6	1.11582
$449$	−7.92360e6	−1.85484	−0.927421	−	0.374020i	$-0.877979\pi$
$449$	−7.92360e6	−1.85484	−0.927421	+	0.374020i	$0.877979\pi$
$450$	211170.	0.0491588
$451$	0	0
$452$	35005.5	0.00805916
$453$	−566901.	−0.129796
$454$	−1.59101e6	−0.362270
$455$	207396.	0.0469648
$456$	5.95795e6	1.34179
$457$	−3.51327e6	−0.786902	−0.393451	−	0.919346i	$-0.628719\pi$
$457$	−3.51327e6	−0.786902	−0.393451	+	0.919346i	$0.628719\pi$
$458$	−1.13988e6	−0.253920
$459$	−352760.	−0.0781533
$460$	236513.	0.0521148
$461$	8.02873e6	1.75952	0.879761	−	0.475416i	$-0.157702\pi$
$461$	8.02873e6	1.75952	0.879761	+	0.475416i	$0.157702\pi$
$462$	0	0
$463$	8.07125e6	1.74980	0.874899	−	0.484305i	$-0.160927\pi$
$463$	8.07125e6	1.74980	0.874899	+	0.484305i	$0.160927\pi$
$464$	−12424.2	−0.00267899
$465$	134566.	0.0288605
$466$	4.27848e6	0.912692
$467$	−6.30026e6	−1.33680	−0.668399	−	0.743803i	$-0.733020\pi$
$467$	−6.30026e6	−1.33680	−0.668399	+	0.743803i	$0.733020\pi$
$468$	16974.2	0.00358240
$469$	−7.10221e6	−1.49095
$470$	102104.	0.0213205
$471$	5.60416e6	1.16401
$472$	4.89142e6	1.01060
$473$	0	0
$474$	−6.69448e6	−1.36858
$475$	1.11309e6	0.226358
$476$	62707.9	0.0126854
$477$	−304062.	−0.0611880
$478$	7.38754e6	1.47887
$479$	1.70783e6	0.340100	0.170050	−	0.985435i	$-0.445607\pi$
$479$	1.70783e6	0.340100	0.170050	+	0.985435i	$0.445607\pi$
$480$	664412.	0.131624
$481$	975272.	0.192204
$482$	6.83070e6	1.33921
$483$	−5.19394e6	−1.01305
$484$	0	0
$485$	3.45692e6	0.667320
$486$	2.49805e6	0.479745
$487$	−572045.	−0.109297	−0.0546484	−	0.998506i	$-0.517404\pi$
$487$	−572045.	−0.109297	−0.0546484	+	0.998506i	$0.517404\pi$
$488$	687828.	0.130747
$489$	2.06303e6	0.390151
$490$	−85979.3	−0.0161772
$491$	−7.14161e6	−1.33688	−0.668440	−	0.743766i	$-0.733038\pi$
$491$	−7.14161e6	−1.33688	−0.668440	+	0.743766i	$0.733038\pi$
$492$	416343.	0.0775423
$493$	−1604.57	−0.000297331 0
$494$	−589359.	−0.108658
$495$	0	0
$496$	−267606.	−0.0488418
$497$	4.23754e6	0.769526
$498$	529604.	0.0956924
$499$	6.99557e6	1.25768	0.628842	−	0.777533i	$-0.283529\pi$
$499$	6.99557e6	1.25768	0.628842	+	0.777533i	$0.283529\pi$
$500$	65901.5	0.0117888
$501$	5.55509e6	0.988773
$502$	337889.	0.0598432
$503$	6.84118e6	1.20562	0.602811	−	0.797884i	$-0.294047\pi$
$503$	6.84118e6	1.20562	0.602811	+	0.797884i	$0.294047\pi$
$504$	−1.61692e6	−0.283539
$505$	3.99504e6	0.697096
$506$	0	0
$507$	6.43758e6	1.11225
$508$	1.00856e6	0.173397
$509$	2.00555e6	0.343115	0.171557	−	0.985174i	$-0.445120\pi$
$509$	2.00555e6	0.343115	0.171557	+	0.985174i	$0.445120\pi$
$510$	−259834.	−0.0442355
$511$	8.03881e6	1.36188
$512$	−6.64353e6	−1.12002
$513$	5.58340e6	0.936710
$514$	−2.19004e6	−0.365633
$515$	4.33855e6	0.720820
$516$	1.36226e6	0.225236
$517$	0	0
$518$	−1.08188e7	−1.77156
$519$	5.50676e6	0.897383
$520$	−299633.	−0.0485939
$521$	4.75777e6	0.767908	0.383954	−	0.923352i	$-0.374562\pi$
$521$	4.75777e6	0.767908	0.383954	+	0.923352i	$0.374562\pi$
$522$	4818.14	0.000773932 0
$523$	6.59206e6	1.05382	0.526911	−	0.849921i	$-0.323350\pi$
$523$	6.59206e6	1.05382	0.526911	+	0.849921i	$0.323350\pi$
$524$	33877.2	0.00538988
$525$	−1.44723e6	−0.229160
$526$	9.67829e6	1.52523
$527$	−34561.1	−0.00542077
$528$	0	0
$529$	−1.40505e6	−0.218299
$530$	625055.	0.0966560
$531$	−1.64247e6	−0.252791
$532$	−992526.	−0.152042
$533$	−353655.	−0.0539215
$534$	9.75333e6	1.48013
$535$	−4.46649e6	−0.674656
$536$	1.02608e7	1.54266
$537$	−1.08144e7	−1.61833
$538$	8.51269e6	1.26798
$539$	0	0
$540$	330570.	0.0487841
$541$	−2.62910e6	−0.386201	−0.193101	−	0.981179i	$-0.561854\pi$
$541$	−2.62910e6	−0.386201	−0.193101	+	0.981179i	$0.561854\pi$
$542$	4.68684e6	0.685302
$543$	6.96507e6	1.01374
$544$	−170643.	−0.0247224
$545$	3.20420e6	0.462092
$546$	766277.	0.110003
$547$	5.78421e6	0.826563	0.413281	−	0.910603i	$-0.364383\pi$
$547$	5.78421e6	0.826563	0.413281	+	0.910603i	$0.364383\pi$
$548$	1.28610e6	0.182947
$549$	−230964.	−0.0327049
$550$	0	0
$551$	25396.7	0.00356368
$552$	7.50388e6	1.04819
$553$	9.57652e6	1.33166
$554$	−144905.	−0.0200589
$555$	−6.80553e6	−0.937842
$556$	−1.08782e6	−0.149235
$557$	−1.93560e6	−0.264349	−0.132174	−	0.991226i	$-0.542196\pi$
$557$	−1.93560e6	−0.264349	−0.132174	+	0.991226i	$0.542196\pi$
$558$	103779.	0.0141099
$559$	−1.15715e6	−0.156625
$560$	2.87803e6	0.387816
$561$	0	0
$562$	−3.55878e6	−0.475292
$563$	−39310.1	−0.00522676	−0.00261338	−	0.999997i	$-0.500832\pi$
$563$	−39310.1	−0.00522676	−0.00261338	+	0.999997i	$0.500832\pi$
$564$	−57271.0	−0.00758118
$565$	207492.	0.0273451
$566$	−2.63434e6	−0.345645
$567$	−9.31767e6	−1.21717
$568$	−6.12214e6	−0.796219
$569$	−1.80420e6	−0.233617	−0.116809	−	0.993154i	$-0.537266\pi$
$569$	−1.80420e6	−0.233617	−0.116809	+	0.993154i	$0.537266\pi$
$570$	4.11259e6	0.530187
$571$	−7.07090e6	−0.907579	−0.453789	−	0.891109i	$-0.649928\pi$
$571$	−7.07090e6	−0.907579	−0.453789	+	0.891109i	$0.649928\pi$
$572$	0	0
$573$	−4.73284e6	−0.602192
$574$	3.92315e6	0.496999
$575$	1.40191e6	0.176828
$576$	2.29954e6	0.288792
$577$	−7.47730e6	−0.934986	−0.467493	−	0.883997i	$-0.654843\pi$
$577$	−7.47730e6	−0.934986	−0.467493	+	0.883997i	$0.654843\pi$
$578$	−7.41718e6	−0.923462
$579$	−214292.	−0.0265650
$580$	1503.63	0.000185597 0
$581$	−757603.	−0.0931111
$582$	1.27724e7	1.56303
$583$	0	0
$584$	−1.16140e7	−1.40912
$585$	100613.	0.0121552
$586$	2.93880e6	0.353530
$587$	−9.70416e6	−1.16242	−0.581209	−	0.813754i	$-0.697420\pi$
$587$	−9.70416e6	−1.16242	−0.581209	+	0.813754i	$0.697420\pi$
$588$	48226.5	0.00575232
$589$	547024.	0.0649708
$590$	3.37640e6	0.399323
$591$	−9.44367e6	−1.11217
$592$	1.35338e7	1.58715
$593$	−1.08322e7	−1.26497	−0.632485	−	0.774573i	$-0.717965\pi$
$593$	−1.08322e7	−1.26497	−0.632485	+	0.774573i	$0.717965\pi$
$594$	0	0
$595$	371695.	0.0430422
$596$	1.81431e6	0.209216
$597$	−8.76140e6	−1.00609
$598$	−742282.	−0.0848821
$599$	−94683.7	−0.0107822	−0.00539111	−	0.999985i	$-0.501716\pi$
$599$	−94683.7	−0.0107822	−0.00539111	+	0.999985i	$0.501716\pi$
$600$	2.09086e6	0.237109
$601$	−2.53178e6	−0.285917	−0.142958	−	0.989729i	$-0.545661\pi$
$601$	−2.53178e6	−0.285917	−0.142958	+	0.989729i	$0.545661\pi$
$602$	1.28364e7	1.44362
$603$	−3.44545e6	−0.385881
$604$	−136440.	−0.0152177
$605$	0	0
$606$	1.47607e7	1.63277
$607$	1.55888e7	1.71728	0.858641	−	0.512577i	$-0.171309\pi$
$607$	1.55888e7	1.71728	0.858641	+	0.512577i	$0.171309\pi$
$608$	2.70089e6	0.296311
$609$	−33020.5	−0.00360778
$610$	474788.	0.0516624
$611$	48647.8	0.00527181
$612$	30421.1	0.00328319
$613$	−1.74384e7	−1.87437	−0.937187	−	0.348826i	$-0.886580\pi$
$613$	−1.74384e7	−1.87437	−0.937187	+	0.348826i	$0.886580\pi$
$614$	−1.01444e7	−1.08594
$615$	2.46784e6	0.263105
$616$	0	0
$617$	6.56778e6	0.694553	0.347277	−	0.937763i	$-0.387106\pi$
$617$	6.56778e6	0.694553	0.347277	+	0.937763i	$0.387106\pi$
$618$	1.60299e7	1.68834
$619$	1.62625e7	1.70593	0.852966	−	0.521967i	$-0.174802\pi$
$619$	1.62625e7	1.70593	0.852966	+	0.521967i	$0.174802\pi$
$620$	32387.0	0.00338370
$621$	7.03214e6	0.731743
$622$	−5.92734e6	−0.614304
$623$	−1.39522e7	−1.44020
$624$	−958575.	−0.0985518
$625$	390625.	0.0400000
$626$	−8.33609e6	−0.850210
$627$	0	0
$628$	1.34879e6	0.136473
$629$	1.74788e6	0.176151
$630$	−1.11611e6	−0.112036
$631$	9.80660e6	0.980494	0.490247	−	0.871583i	$-0.336907\pi$
$631$	9.80660e6	0.980494	0.490247	+	0.871583i	$0.336907\pi$
$632$	−1.38356e7	−1.37786
$633$	1.00696e7	0.998861
$634$	1.10104e6	0.108787
$635$	5.97814e6	0.588345
$636$	−350599.	−0.0343691
$637$	−40965.2	−0.00400006
$638$	0	0
$639$	2.05573e6	0.199166
$640$	−3.51388e6	−0.339107
$641$	5.61080e6	0.539361	0.269680	−	0.962950i	$-0.413082\pi$
$641$	5.61080e6	0.539361	0.269680	+	0.962950i	$0.413082\pi$
$642$	−1.65026e7	−1.58021
$643$	9.62242e6	0.917819	0.458909	−	0.888483i	$-0.348240\pi$
$643$	9.62242e6	0.917819	0.458909	+	0.888483i	$0.348240\pi$
$644$	−1.25006e6	−0.118773
$645$	8.07469e6	0.764234
$646$	−1.05625e6	−0.0995830
$647$	−1.22696e7	−1.15231	−0.576156	−	0.817340i	$-0.695448\pi$
$647$	−1.22696e7	−1.15231	−0.576156	+	0.817340i	$0.695448\pi$
$648$	1.34616e7	1.25939
$649$	0	0
$650$	−206828.	−0.0192011
$651$	−711234.	−0.0657749
$652$	496523.	0.0457425
$653$	−785380.	−0.0720770	−0.0360385	−	0.999350i	$-0.511474\pi$
$653$	−785380.	−0.0720770	−0.0360385	+	0.999350i	$0.511474\pi$
$654$	1.18387e7	1.08233
$655$	200804.	0.0182881
$656$	−4.90767e6	−0.445262
$657$	3.89982e6	0.352477
$658$	−539657.	−0.0485907
$659$	4.79089e6	0.429737	0.214869	−	0.976643i	$-0.431068\pi$
$659$	4.79089e6	0.429737	0.214869	+	0.976643i	$0.431068\pi$
$660$	0	0
$661$	−1.10302e7	−0.981927	−0.490964	−	0.871180i	$-0.663355\pi$
$661$	−1.10302e7	−0.981927	−0.490964	+	0.871180i	$0.663355\pi$
$662$	−1.49968e7	−1.33001
$663$	−123799.	−0.0109379
$664$	1.09454e6	0.0963409
$665$	−5.88310e6	−0.515884
$666$	−5.24848e6	−0.458509
$667$	31986.5	0.00278389
$668$	1.33698e6	0.115927
$669$	−1.98267e7	−1.71272
$670$	7.08276e6	0.609558
$671$	0	0
$672$	−3.51167e6	−0.299978
$673$	−1.29135e7	−1.09902	−0.549510	−	0.835487i	$-0.685186\pi$
$673$	−1.29135e7	−1.09902	−0.549510	+	0.835487i	$0.685186\pi$
$674$	1.13961e7	0.966290
$675$	1.95942e6	0.165527
$676$	1.54938e6	0.130404
$677$	9.53287e6	0.799378	0.399689	−	0.916651i	$-0.369118\pi$
$677$	9.53287e6	0.799378	0.399689	+	0.916651i	$0.369118\pi$
$678$	766629.	0.0640488
$679$	−1.82711e7	−1.52086
$680$	−537003.	−0.0445353
$681$	5.28967e6	0.437080
$682$	0	0
$683$	1.90585e6	0.156328	0.0781642	−	0.996940i	$-0.475094\pi$
$683$	1.90585e6	0.156328	0.0781642	+	0.996940i	$0.475094\pi$
$684$	−481498.	−0.0393509
$685$	7.62326e6	0.620747
$686$	−1.12511e7	−0.912817
$687$	3.78981e6	0.306355
$688$	−1.60578e7	−1.29334
$689$	297810.	0.0238996
$690$	5.17971e6	0.414173
$691$	6.90919e6	0.550468	0.275234	−	0.961377i	$-0.411245\pi$
$691$	6.90919e6	0.550468	0.275234	+	0.961377i	$0.411245\pi$
$692$	1.32535e6	0.105212
$693$	0	0
$694$	1.79102e7	1.41157
$695$	−6.44795e6	−0.506360
$696$	47705.9	0.00373293
$697$	−633821.	−0.0494180
$698$	−1.79686e6	−0.139597
$699$	−1.42248e7	−1.10117
$700$	−348314.	−0.0268674
$701$	−1.03163e7	−0.792918	−0.396459	−	0.918052i	$-0.629761\pi$
$701$	−1.03163e7	−0.792918	−0.396459	+	0.918052i	$0.629761\pi$
$702$	−1.03747e6	−0.0794573
$703$	−2.76651e7	−2.11127
$704$	0	0
$705$	−339468.	−0.0257233
$706$	6.88937e6	0.520197
$707$	−2.11153e7	−1.58872
$708$	−1.89385e6	−0.141992
$709$	−1.18641e7	−0.886378	−0.443189	−	0.896428i	$-0.646153\pi$
$709$	−1.18641e7	−0.886378	−0.443189	+	0.896428i	$0.646153\pi$
$710$	−4.22593e6	−0.314613
$711$	4.64580e6	0.344656
$712$	2.01573e7	1.49016
$713$	688963.	0.0507542
$714$	1.37332e6	0.100815
$715$	0	0
$716$	−2.60277e6	−0.189738
$717$	−2.45616e7	−1.78426
$718$	−1.67961e7	−1.21590
$719$	2.66382e7	1.92169	0.960845	−	0.277086i	$-0.0893686\pi$
$719$	2.66382e7	1.92169	0.960845	+	0.277086i	$0.0893686\pi$
$720$	1.39620e6	0.100373
$721$	−2.29309e7	−1.64279
$722$	3.66680e6	0.261785
$723$	−2.27102e7	−1.61576
$724$	1.67633e6	0.118854
$725$	8912.64	0.000629740 0
$726$	0	0
$727$	1.72858e7	1.21298	0.606489	−	0.795092i	$-0.292578\pi$
$727$	1.72858e7	1.21298	0.606489	+	0.795092i	$0.292578\pi$
$728$	1.58367e6	0.110748
$729$	8.83019e6	0.615391
$730$	−8.01679e6	−0.556792
$731$	−2.07384e6	−0.143543
$732$	−266313.	−0.0183702
$733$	−7.99921e6	−0.549904	−0.274952	−	0.961458i	$-0.588662\pi$
$733$	−7.99921e6	−0.549904	−0.274952	+	0.961458i	$0.588662\pi$
$734$	−2.01250e7	−1.37878
$735$	285858.	0.0195179
$736$	3.40170e6	0.231474
$737$	0	0
$738$	1.90321e6	0.128631
$739$	−8.50248e6	−0.572710	−0.286355	−	0.958124i	$-0.592444\pi$
$739$	−8.50248e6	−0.572710	−0.286355	+	0.958124i	$0.592444\pi$
$740$	−1.63793e6	−0.109956
$741$	1.95946e6	0.131097
$742$	−3.30365e6	−0.220285
$743$	−1.73539e7	−1.15325	−0.576626	−	0.817008i	$-0.695631\pi$
$743$	−1.73539e7	−1.15325	−0.576626	+	0.817008i	$0.695631\pi$
$744$	1.02755e6	0.0680565
$745$	1.07541e7	0.709880
$746$	1.02641e6	0.0675267
$747$	−367531.	−0.0240986
$748$	0	0
$749$	2.36071e7	1.53758
$750$	1.44326e6	0.0936897
$751$	−1.00934e7	−0.653039	−0.326519	−	0.945190i	$-0.605876\pi$
$751$	−1.00934e7	−0.653039	−0.326519	+	0.945190i	$0.605876\pi$
$752$	675085.	0.0435325
$753$	−1.12339e6	−0.0722010
$754$	−4719.06	−0.000302292 0
$755$	−808734.	−0.0516343
$756$	−1.74718e6	−0.111182
$757$	2.24672e7	1.42498	0.712490	−	0.701682i	$-0.247567\pi$
$757$	2.24672e7	1.42498	0.712490	+	0.701682i	$0.247567\pi$
$758$	−1.55961e7	−0.985924
$759$	0	0
$760$	8.49955e6	0.533779
$761$	−2.83824e7	−1.77659	−0.888297	−	0.459270i	$-0.848111\pi$
$761$	−2.83824e7	−1.77659	−0.888297	+	0.459270i	$0.848111\pi$
$762$	2.20877e7	1.37805
$763$	−1.69354e7	−1.05314
$764$	−1.13909e6	−0.0706029
$765$	180318.	0.0111400
$766$	7.98811e6	0.491894
$767$	1.60870e6	0.0987386
$768$	7.13410e6	0.436452
$769$	−1.47650e7	−0.900360	−0.450180	−	0.892938i	$-0.648640\pi$
$769$	−1.47650e7	−0.900360	−0.450180	+	0.892938i	$0.648640\pi$
$770$	0	0
$771$	7.28131e6	0.441137
$772$	−51575.2	−0.00311457
$773$	2.15472e6	0.129700	0.0648502	−	0.997895i	$-0.479343\pi$
$773$	2.15472e6	0.129700	0.0648502	+	0.997895i	$0.479343\pi$
$774$	6.22726e6	0.373633
$775$	191971.	0.0114811
$776$	2.63970e7	1.57362
$777$	3.59698e7	2.13740
$778$	3.73528e6	0.221246
$779$	1.00320e7	0.592301
$780$	116012.	0.00682755
$781$	0	0
$782$	−1.33032e6	−0.0777927
$783$	44706.9	0.00260597
$784$	−568473.	−0.0330308
$785$	7.99484e6	0.463058
$786$	741920.	0.0428352
$787$	449565.	0.0258735	0.0129368	−	0.999916i	$-0.495882\pi$
$787$	449565.	0.0258735	0.0129368	+	0.999916i	$0.495882\pi$
$788$	−2.27287e6	−0.130395
$789$	−3.21778e7	−1.84019
$790$	−9.55028e6	−0.544438
$791$	−1.09667e6	−0.0623211
$792$	0	0
$793$	226214.	0.0127743
$794$	−1.72223e7	−0.969480
$795$	−2.07814e6	−0.116616
$796$	−2.10867e6	−0.117957
$797$	−2.52272e7	−1.40677	−0.703385	−	0.710809i	$-0.748329\pi$
$797$	−2.52272e7	−1.40677	−0.703385	+	0.710809i	$0.748329\pi$
$798$	−2.17366e7	−1.20833
$799$	87186.6	0.00483151
$800$	947843.	0.0523614
$801$	−6.76856e6	−0.372748
$802$	−2.05943e7	−1.13060
$803$	0	0
$804$	−3.97278e6	−0.216748
$805$	−7.40961e6	−0.403001
$806$	−101645.	−0.00551122
$807$	−2.83024e7	−1.52982
$808$	3.05060e7	1.64383
$809$	2.46384e7	1.32355	0.661775	−	0.749702i	$-0.269803\pi$
$809$	2.46384e7	1.32355	0.661775	+	0.749702i	$0.269803\pi$
$810$	9.29214e6	0.497626
$811$	−3.70795e7	−1.97962	−0.989810	−	0.142396i	$-0.954519\pi$
$811$	−3.70795e7	−1.97962	−0.989810	+	0.142396i	$0.954519\pi$
$812$	−7947.26	−0.000422988 0
$813$	−1.55825e7	−0.826820
$814$	0	0
$815$	2.94309e6	0.155207
$816$	−1.71796e6	−0.0903207
$817$	3.28243e7	1.72044
$818$	−649506.	−0.0339391
$819$	−531776.	−0.0277025
$820$	593951.	0.0308472
$821$	−1.00357e7	−0.519624	−0.259812	−	0.965659i	$-0.583661\pi$
$821$	−1.00357e7	−0.519624	−0.259812	+	0.965659i	$0.583661\pi$
$822$	2.81661e7	1.45394
$823$	7.25992e6	0.373622	0.186811	−	0.982396i	$-0.440185\pi$
$823$	7.25992e6	0.373622	0.186811	+	0.982396i	$0.440185\pi$
$824$	3.31291e7	1.69978
$825$	0	0
$826$	−1.78456e7	−0.910081
$827$	−1.54300e7	−0.784517	−0.392259	−	0.919855i	$-0.628306\pi$
$827$	−1.54300e7	−0.784517	−0.392259	+	0.919855i	$0.628306\pi$
$828$	−606434.	−0.0307403
$829$	−9.32873e6	−0.471451	−0.235725	−	0.971820i	$-0.575747\pi$
$829$	−9.32873e6	−0.471451	−0.235725	+	0.971820i	$0.575747\pi$
$830$	755527.	0.0380675
$831$	481770.	0.0242012
$832$	−2.25225e6	−0.112800
$833$	−73417.8	−0.00366597
$834$	−2.38236e7	−1.18602
$835$	7.92483e6	0.393345
$836$	0	0
$837$	962950.	0.0475105
$838$	−9.55437e6	−0.469994
$839$	−2.99913e7	−1.47093	−0.735463	−	0.677565i	$-0.763035\pi$
$839$	−2.99913e7	−1.47093	−0.735463	+	0.677565i	$0.763035\pi$
$840$	−1.10510e7	−0.540385
$841$	−2.05109e7	−0.999990
$842$	−1.80668e7	−0.878213
$843$	1.18320e7	0.573442
$844$	2.42353e6	0.117110
$845$	9.18378e6	0.442466
$846$	−261801.	−0.0125761
$847$	0	0
$848$	4.13270e6	0.197353
$849$	8.75847e6	0.417022
$850$	−370677.	−0.0175974
$851$	−3.48434e7	−1.64929
$852$	2.37036e6	0.111871
$853$	1.84835e7	0.869783	0.434891	−	0.900483i	$-0.356787\pi$
$853$	1.84835e7	0.869783	0.434891	+	0.900483i	$0.356787\pi$
$854$	−2.50943e6	−0.117742
$855$	−2.85403e6	−0.133519
$856$	−3.41061e7	−1.59092
$857$	3.39019e7	1.57678	0.788392	−	0.615173i	$-0.210914\pi$
$857$	3.39019e7	1.57678	0.788392	+	0.615173i	$0.210914\pi$
$858$	0	0
$859$	−2.36241e7	−1.09237	−0.546187	−	0.837663i	$-0.683921\pi$
$859$	−2.36241e7	−1.09237	−0.546187	+	0.837663i	$0.683921\pi$
$860$	1.94339e6	0.0896012
$861$	−1.30434e7	−0.599631
$862$	−3.52555e7	−1.61606
$863$	−1.86287e7	−0.851444	−0.425722	−	0.904854i	$-0.639980\pi$
$863$	−1.86287e7	−0.851444	−0.425722	+	0.904854i	$0.639980\pi$
$864$	4.75449e6	0.216681
$865$	7.85589e6	0.356989
$866$	5.09113e6	0.230685
$867$	2.46601e7	1.11416
$868$	−171178.	−0.00771166
$869$	0	0
$870$	32930.0	0.00147501
$871$	3.37461e6	0.150722
$872$	2.44672e7	1.08967
$873$	−8.86374e6	−0.393624
$874$	2.10559e7	0.932387
$875$	−2.06460e6	−0.0911624
$876$	4.49669e6	0.197985
$877$	−8.73201e6	−0.383367	−0.191684	−	0.981457i	$-0.561395\pi$
$877$	−8.73201e6	−0.383367	−0.191684	+	0.981457i	$0.561395\pi$
$878$	−3.55628e7	−1.55689
$879$	−9.77074e6	−0.426535
$880$	0	0
$881$	1.79872e6	0.0780772	0.0390386	−	0.999238i	$-0.487570\pi$
$881$	1.79872e6	0.0780772	0.0390386	+	0.999238i	$0.487570\pi$
$882$	220456.	0.00954224
$883$	−2.01826e7	−0.871115	−0.435558	−	0.900161i	$-0.643449\pi$
$883$	−2.01826e7	−0.871115	−0.435558	+	0.900161i	$0.643449\pi$
$884$	−29795.6	−0.00128239
$885$	−1.12256e7	−0.481785
$886$	−4.30885e7	−1.84407
$887$	4.27642e6	0.182503	0.0912517	−	0.995828i	$-0.470913\pi$
$887$	4.27642e6	0.182503	0.0912517	+	0.995828i	$0.470913\pi$
$888$	−5.19669e7	−2.21154
$889$	−3.15967e7	−1.34087
$890$	1.39140e7	0.588813
$891$	0	0
$892$	−4.77183e6	−0.200804
$893$	−1.37997e6	−0.0579082
$894$	3.97338e7	1.66271
$895$	−1.54277e7	−0.643789
$896$	1.85722e7	0.772846
$897$	2.46789e6	0.102411
$898$	−4.17644e7	−1.72829
$899$	4380.08	0.000180752 0
$900$	−168975.	−0.00695372
$901$	533735.	0.0219035
$902$	0	0
$903$	−4.26777e7	−1.74173
$904$	1.58440e6	0.0644829
$905$	9.93629e6	0.403277
$906$	−2.98807e6	−0.120940
$907$	2.30346e7	0.929743	0.464871	−	0.885378i	$-0.346101\pi$
$907$	2.30346e7	0.929743	0.464871	+	0.885378i	$0.346101\pi$
$908$	1.27310e6	0.0512447
$909$	−1.02435e7	−0.411187
$910$	1.09316e6	0.0437604
$911$	−1.32227e7	−0.527867	−0.263934	−	0.964541i	$-0.585020\pi$
$911$	−1.32227e7	−0.527867	−0.263934	+	0.964541i	$0.585020\pi$
$912$	2.71914e7	1.08254
$913$	0	0
$914$	−1.85181e7	−0.733213
$915$	−1.57854e6	−0.0623309
$916$	912119.	0.0359181
$917$	−1.06132e6	−0.0416797
$918$	−1.85936e6	−0.0728210
$919$	1.25949e7	0.491934	0.245967	−	0.969278i	$-0.420895\pi$
$919$	1.25949e7	0.491934	0.245967	+	0.969278i	$0.420895\pi$
$920$	1.07050e7	0.416980
$921$	3.37274e7	1.31019
$922$	4.23186e7	1.63947
$923$	−2.01346e6	−0.0777928
$924$	0	0
$925$	−9.70870e6	−0.373084
$926$	4.25427e7	1.63041
$927$	−1.11243e7	−0.425181
$928$	21626.3	0.000824353 0
$929$	−4.63165e7	−1.76074	−0.880372	−	0.474284i	$-0.842707\pi$
$929$	−4.63165e7	−1.76074	−0.880372	+	0.474284i	$0.842707\pi$
$930$	709285.	0.0268914
$931$	1.16204e6	0.0439386
$932$	−3.42358e6	−0.129104
$933$	1.97068e7	0.741161
$934$	−3.32080e7	−1.24559
$935$	0	0
$936$	768278.	0.0286635
$937$	7.83724e6	0.291618	0.145809	−	0.989313i	$-0.453421\pi$
$937$	7.83724e6	0.291618	0.145809	+	0.989313i	$0.453421\pi$
$938$	−3.74350e7	−1.38922
$939$	2.77153e7	1.02578
$940$	−81702.2	−0.00301588
$941$	−2.22549e7	−0.819315	−0.409657	−	0.912239i	$-0.634352\pi$
$941$	−2.22549e7	−0.819315	−0.409657	+	0.912239i	$0.634352\pi$
$942$	2.95389e7	1.08459
$943$	1.26350e7	0.462696
$944$	2.23239e7	0.815343
$945$	−1.03563e7	−0.377245
$946$	0	0
$947$	2.71283e7	0.982988	0.491494	−	0.870881i	$-0.336451\pi$
$947$	2.71283e7	0.982988	0.491494	+	0.870881i	$0.336451\pi$
$948$	5.35684e6	0.193592
$949$	−3.81963e6	−0.137675
$950$	5.86698e6	0.210914
$951$	−3.66065e6	−0.131252
$952$	2.83826e6	0.101499
$953$	6.41672e6	0.228866	0.114433	−	0.993431i	$-0.463495\pi$
$953$	6.41672e6	0.228866	0.114433	+	0.993431i	$0.463495\pi$
$954$	−1.60268e6	−0.0570132
$955$	−6.75182e6	−0.239559
$956$	−5.91141e6	−0.209193
$957$	0	0
$958$	9.00181e6	0.316896
$959$	−4.02918e7	−1.41472
$960$	1.57164e7	0.550396
$961$	−2.85348e7	−0.996705
$962$	5.14056e6	0.179090
$963$	1.14524e7	0.397951
$964$	−5.46583e6	−0.189436
$965$	−305707.	−0.0105679
$966$	−2.73767e7	−0.943926
$967$	−1.44957e7	−0.498508	−0.249254	−	0.968438i	$-0.580185\pi$
$967$	−1.44957e7	−0.498508	−0.249254	+	0.968438i	$0.580185\pi$
$968$	0	0
$969$	3.51175e6	0.120147
$970$	1.82210e7	0.621790
$971$	1.38138e6	0.0470182	0.0235091	−	0.999724i	$-0.492516\pi$
$971$	1.38138e6	0.0470182	0.0235091	+	0.999724i	$0.492516\pi$
$972$	−1.99891e6	−0.0678620
$973$	3.40798e7	1.15402
$974$	−3.01519e6	−0.101840
$975$	687648.	0.0231662
$976$	3.13917e6	0.105485
$977$	3.29561e7	1.10459	0.552293	−	0.833650i	$-0.313753\pi$
$977$	3.29561e7	1.10459	0.552293	+	0.833650i	$0.313753\pi$
$978$	1.08740e7	0.363531
$979$	0	0
$980$	68799.5	0.00228834
$981$	−8.21577e6	−0.272569
$982$	−3.76427e7	−1.24567
$983$	3.84777e7	1.27006	0.635032	−	0.772486i	$-0.280987\pi$
$983$	3.84777e7	1.27006	0.635032	+	0.772486i	$0.280987\pi$
$984$	1.88444e7	0.620431
$985$	−1.34722e7	−0.442435
$986$	−8457.50	−0.000277045 0
$987$	1.79422e6	0.0586249
$988$	471597.	0.0153702
$989$	4.13413e7	1.34398
$990$	0	0
$991$	−5.46161e7	−1.76659	−0.883297	−	0.468815i	$-0.844681\pi$
$991$	−5.46161e7	−1.76659	−0.883297	+	0.468815i	$0.844681\pi$
$992$	465814.	0.0150291
$993$	4.98605e7	1.60466
$994$	2.23356e7	0.717022
$995$	−1.24989e7	−0.400235
$996$	−423782.	−0.0135361
$997$	5.27251e7	1.67988	0.839942	−	0.542676i	$-0.182589\pi$
$997$	5.27251e7	1.67988	0.839942	+	0.542676i	$0.182589\pi$
$998$	3.68729e7	1.17187
$999$	−4.87000e7	−1.54388

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.6.a.p.1.14		20
11.3	even	5		55.6.g.b.31.7	yes	40
11.4	even	5		55.6.g.b.16.7	✓	40
11.10	odd	2		605.6.a.o.1.7		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.6.g.b.16.7	✓	40	11.4	even	5
55.6.g.b.31.7	yes	40	11.3	even	5
605.6.a.o.1.7		20	11.10	odd	2
605.6.a.p.1.14		20	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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	605.a (trivial)

\(f(q)\)	\(=\)	\(q+5.27089 q^{2} -17.5243 q^{3} -4.21770 q^{4} -25.0000 q^{5} -92.3688 q^{6} +132.134 q^{7} -190.900 q^{8} +64.1015 q^{9} +O(q^{10})\)	\(q+5.27089 q^{2} -17.5243 q^{3} -4.21770 q^{4} -25.0000 q^{5} -92.3688 q^{6} +132.134 q^{7} -190.900 q^{8} +64.1015 q^{9} -131.772 q^{10} +73.9122 q^{12} -62.7834 q^{13} +696.466 q^{14} +438.108 q^{15} -871.245 q^{16} -112.520 q^{17} +337.872 q^{18} +1780.95 q^{19} +105.442 q^{20} -2315.56 q^{21} +2243.05 q^{23} +3345.38 q^{24} +625.000 q^{25} -330.925 q^{26} +3135.07 q^{27} -557.303 q^{28} +14.2602 q^{29} +2309.22 q^{30} +307.154 q^{31} +1516.55 q^{32} -593.083 q^{34} -3303.36 q^{35} -270.361 q^{36} -15533.9 q^{37} +9387.18 q^{38} +1100.24 q^{39} +4772.49 q^{40} +5632.94 q^{41} -12205.1 q^{42} +18430.8 q^{43} -1602.54 q^{45} +11822.9 q^{46} -774.851 q^{47} +15268.0 q^{48} +652.484 q^{49} +3294.31 q^{50} +1971.84 q^{51} +264.801 q^{52} -4743.45 q^{53} +16524.6 q^{54} -25224.4 q^{56} -31209.9 q^{57} +75.1641 q^{58} -25623.0 q^{59} -1847.81 q^{60} -3603.09 q^{61} +1618.97 q^{62} +8470.01 q^{63} +35873.4 q^{64} +1569.59 q^{65} -53750.0 q^{67} +474.577 q^{68} -39308.0 q^{69} -17411.6 q^{70} +32070.0 q^{71} -12237.0 q^{72} +60838.2 q^{73} -81877.6 q^{74} -10952.7 q^{75} -7511.49 q^{76} +5799.23 q^{78} +72475.6 q^{79} +21781.1 q^{80} -70516.7 q^{81} +29690.6 q^{82} -5733.58 q^{83} +9766.35 q^{84} +2813.01 q^{85} +97146.9 q^{86} -249.901 q^{87} -105591. q^{89} -8446.80 q^{90} -8295.85 q^{91} -9460.53 q^{92} -5382.66 q^{93} -4084.16 q^{94} -44523.7 q^{95} -26576.5 q^{96} -138277. q^{97} +3439.17 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{2} + 407 q^{4} - 500 q^{5} - 264 q^{6} - 167 q^{7} - 57 q^{8} + 1598 q^{9}+O(q^{10}) \) 20 * q + q^2 + 407 * q^4 - 500 * q^5 - 264 * q^6 - 167 * q^7 - 57 * q^8 + 1598 * q^9	\( 20 q + q^{2} + 407 q^{4} - 500 q^{5} - 264 q^{6} - 167 q^{7} - 57 q^{8} + 1598 q^{9} - 25 q^{10} - 253 q^{12} - 769 q^{13} - 1045 q^{14} + 6963 q^{16} + 2989 q^{17} - 3775 q^{18} - 5828 q^{19} - 10175 q^{20} - 3310 q^{21} - 695 q^{23} - 16724 q^{24} + 12500 q^{25} - 7384 q^{26} + 5925 q^{27} + 3508 q^{28} - 11268 q^{29} + 6600 q^{30} - 11465 q^{31} + 9062 q^{32} + 1217 q^{34} + 4175 q^{35} + 112083 q^{36} - 3057 q^{37} - 13510 q^{38} - 13459 q^{39} + 1425 q^{40} + 839 q^{41} - 14772 q^{42} - 43671 q^{43} - 39950 q^{45} - 81471 q^{46} + 32245 q^{47} - 104315 q^{48} + 2959 q^{49} + 625 q^{50} - 69047 q^{51} - 42696 q^{52} + 27981 q^{53} - 61212 q^{54} - 28294 q^{56} - 79425 q^{57} + 37274 q^{58} - 56847 q^{59} + 6325 q^{60} - 85616 q^{61} - 38095 q^{62} - 100055 q^{63} - 18233 q^{64} + 19225 q^{65} - 31091 q^{67} + 83972 q^{68} - 48708 q^{69} + 26125 q^{70} - 106431 q^{71} - 350510 q^{72} - 117959 q^{73} - 154757 q^{74} - 451972 q^{76} + 348898 q^{78} - 215138 q^{79} - 174075 q^{80} + 75516 q^{81} - 127864 q^{82} - 66761 q^{83} - 521275 q^{84} - 74725 q^{85} - 32222 q^{86} + 5311 q^{87} + 270560 q^{89} + 94375 q^{90} - 269192 q^{91} - 461663 q^{92} + 9345 q^{93} - 479494 q^{94} + 145700 q^{95} - 1247523 q^{96} + 45338 q^{97} + 420757 q^{98}+O(q^{100}) \) 20 * q + q^2 + 407 * q^4 - 500 * q^5 - 264 * q^6 - 167 * q^7 - 57 * q^8 + 1598 * q^9 - 25 * q^10 - 253 * q^12 - 769 * q^13 - 1045 * q^14 + 6963 * q^16 + 2989 * q^17 - 3775 * q^18 - 5828 * q^19 - 10175 * q^20 - 3310 * q^21 - 695 * q^23 - 16724 * q^24 + 12500 * q^25 - 7384 * q^26 + 5925 * q^27 + 3508 * q^28 - 11268 * q^29 + 6600 * q^30 - 11465 * q^31 + 9062 * q^32 + 1217 * q^34 + 4175 * q^35 + 112083 * q^36 - 3057 * q^37 - 13510 * q^38 - 13459 * q^39 + 1425 * q^40 + 839 * q^41 - 14772 * q^42 - 43671 * q^43 - 39950 * q^45 - 81471 * q^46 + 32245 * q^47 - 104315 * q^48 + 2959 * q^49 + 625 * q^50 - 69047 * q^51 - 42696 * q^52 + 27981 * q^53 - 61212 * q^54 - 28294 * q^56 - 79425 * q^57 + 37274 * q^58 - 56847 * q^59 + 6325 * q^60 - 85616 * q^61 - 38095 * q^62 - 100055 * q^63 - 18233 * q^64 + 19225 * q^65 - 31091 * q^67 + 83972 * q^68 - 48708 * q^69 + 26125 * q^70 - 106431 * q^71 - 350510 * q^72 - 117959 * q^73 - 154757 * q^74 - 451972 * q^76 + 348898 * q^78 - 215138 * q^79 - 174075 * q^80 + 75516 * q^81 - 127864 * q^82 - 66761 * q^83 - 521275 * q^84 - 74725 * q^85 - 32222 * q^86 + 5311 * q^87 + 270560 * q^89 + 94375 * q^90 - 269192 * q^91 - 461663 * q^92 + 9345 * q^93 - 479494 * q^94 + 145700 * q^95 - 1247523 * q^96 + 45338 * q^97 + 420757 * q^98

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